Subgroups — C₆₇×#61107 #30740358

Order 17152.

2624 conjugacy classes of subgroups.

The subgroup lattice has 1408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3586	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3585	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3584	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#577×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3291	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3290	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3289	C₂	1	4	yes	maximal, complemented
8	C₆₇×#3288	C₂	1	4	yes	maximal, complemented
9	C₆₇×#3154	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3069	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3068	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3067	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#471×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3022	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3021	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3020	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3019	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2957	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2955	C₂	1	1	yes	maximal, characteristic, complemented
20	#585×C₆₇	C₂²	1	1	yes	characteristic
21	#585×C₆₇	C₂²	1	1	yes	characteristic, complemented
22	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic, complemented
23	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic, complemented
24	#578×C₆₇	—	2	2	no	—
25	#578×C₆₇	—	2	1	no	—
26	#578×C₆₇	C₂²	1	2	yes	complemented
27	#578×C₆₇	C₂²	1	4	yes	complemented
28	#577×C₆₇	—	2	2	no	—
29	#577×C₆₇	—	2	2	no	—
30	#577×C₆₇	—	2	2	no	—
31	#577×C₆₇	—	2	2	no	—
32	#577×C₆₇	—	2	1	no	—
33	#577×C₆₇	—	2	1	no	—
34	#577×C₆₇	C₂²	1	4	yes	complemented
35	#577×C₆₇	C₂²	1	4	yes	complemented
36	#577×C₆₇	C₂²	1	4	yes	complemented
37	#577×C₆₇	C₂²	1	4	yes	complemented
38	#577×C₆₇	C₂²	1	2	yes	complemented
39	#577×C₆₇	C₂²	1	2	yes	complemented
40	#576×C₆₇	—	2	2	no	—
41	#576×C₆₇	—	2	1	no	—
42	#576×C₆₇	C₂²	1	4	yes	complemented
43	#576×C₆₇	C₂²	1	2	yes	complemented
44	#575×C₆₇	—	2	2	no	—
45	#575×C₆₇	—	2	2	no	—
46	#575×C₆₇	—	2	2	no	—
47	#575×C₆₇	C₂²	1	1	yes	characteristic
48	#575×C₆₇	C₂²	1	1	yes	characteristic
49	#575×C₆₇	C₂²	1	1	yes	characteristic, complemented
50	#575×C₆₇	C₂²	1	1	yes	characteristic, complemented
51	#575×C₆₇	C₂²	1	1	yes	characteristic, complemented
52	C₂×#137×C₆₇	—	2	2	no	—
53	C₂×#137×C₆₇	—	2	1	no	—
54	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic, complemented
55	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic, complemented
56	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic, complemented
57	C₂×AGL(1,ℤ/8)×C₆₇	—	2	2	no	—
58	C₂×AGL(1,ℤ/8)×C₆₇	—	2	1	no	—
59	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
60	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic, complemented
62	C₂×#135×C₆₇	—	2	2	no	—
63	C₂×#135×C₆₇	—	2	1	no	—
64	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
65	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic, complemented
66	C₂²×SD₁₆×C₆₇	—	2	1	no	—
67	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	#568×C₆₇	C₂²	1	1	yes	characteristic, complemented
69	#568×C₆₇	C₂²	1	1	yes	characteristic, complemented
70	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
71	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
72	#536×C₆₇	C₂²	1	1	yes	characteristic, complemented
73	#535×C₆₇	C₂²	1	1	yes	characteristic, complemented
74	#497×C₆₇	C₂²	1	2	yes	complemented
75	#496×C₆₇	C₂²	1	2	yes	complemented
76	#495×C₆₇	C₂²	1	2	yes	complemented
77	#492×C₆₇	C₂²	1	2	yes	complemented
78	#473×C₆₇	C₂²	1	2	yes	complemented
79	#473×C₆₇	C₂²	1	4	yes	complemented
80	#472×C₆₇	C₂²	1	4	yes	complemented
81	#472×C₆₇	C₂²	1	2	yes	complemented
82	#471×C₆₇	C₂²	1	4	yes	complemented
83	#471×C₆₇	C₂²	1	4	yes	complemented
84	#471×C₆₇	C₂²	1	4	yes	complemented
85	#471×C₆₇	C₂²	1	4	yes	complemented
86	#471×C₆₇	C₂²	1	2	yes	complemented
87	#471×C₆₇	C₂²	1	2	yes	complemented
88	#456×C₆₇	C₂²	1	4	yes	complemented
89	#456×C₆₇	C₂²	1	4	yes	complemented
90	#455×C₆₇	C₂²	1	4	yes	complemented
91	#455×C₆₇	C₂²	1	4	yes	complemented
92	#454×C₆₇	C₂²	1	4	yes	complemented
93	#454×C₆₇	C₂²	1	4	yes	complemented
94	#453×C₆₇	C₂²	1	4	yes	complemented
95	#453×C₆₇	C₂²	1	4	yes	complemented
96	#444×C₆₇	C₂²	1	4	yes	complemented
97	#444×C₆₇	C₂²	1	4	yes	complemented
98	#443×C₆₇	C₂²	1	4	yes	complemented
99	#443×C₆₇	C₂²	1	4	yes	complemented
100	#430×C₆₇	C₂²	1	1	yes	characteristic, complemented
101	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic, complemented
102	#421×C₆₇	C₂²	1	1	yes	characteristic, complemented
103	#421×C₆₇	C₂²	1	1	yes	characteristic, complemented
104	#421×C₆₇	C₂²	1	1	yes	characteristic, complemented
105	#421×C₆₇	C₂²	1	1	yes	characteristic, complemented
106	#413×C₆₇	C₂²	1	1	yes	characteristic, complemented
107	#413×C₆₇	C₂²	1	1	yes	characteristic, complemented
108	C₂×#101×C₆₇	C₂²	1	1	yes	characteristic, complemented
109	C₂×#100×C₆₇	C₂²	1	1	yes	characteristic, complemented
110	#405×C₆₇	C₂²	1	1	yes	characteristic, complemented
111	2₋¹⁺⁴×C₆₇	—	2	2	no	—
112	2₋¹⁺⁴×C₆₇	—	2	2	no	—
113	2₋¹⁺⁴×C₆₇	—	2	1	no	—
114	2₋¹⁺⁴×C₆₇	—	2	1	no	—
115	2₋¹⁺⁴×C₆₇	—	2	1	no	—
116	2₋¹⁺⁴×C₆₇	—	2	1	no	—
117	2₋¹⁺⁴×C₆₇	—	4	1	no	—
118	2₋¹⁺⁴×C₆₇	C₂³	1	4	yes	—
119	2₋¹⁺⁴×C₆₇	C₂³	1	2	yes	—
120	2₋¹⁺⁴×C₆₇	C₂³	1	2	yes	complemented
121	H(5,𝔽₂)×C₆₇	—	2	2	no	—
122	H(5,𝔽₂)×C₆₇	—	2	2	no	—
123	H(5,𝔽₂)×C₆₇	—	2	1	no	—
124	H(5,𝔽₂)×C₆₇	—	2	1	no	—
125	H(5,𝔽₂)×C₆₇	—	2	1	no	—
126	H(5,𝔽₂)×C₆₇	—	2	1	no	—
127	H(5,𝔽₂)×C₆₇	—	4	1	no	—
128	H(5,𝔽₂)×C₆₇	—	4	1	no	—
129	H(5,𝔽₂)×C₆₇	—	4	1	no	—
130	H(5,𝔽₂)×C₆₇	C₂³	1	4	yes	—
131	H(5,𝔽₂)×C₆₇	C₂³	1	2	yes	—
132	H(5,𝔽₂)×C₆₇	C₂³	1	2	yes	complemented
133	C₂×#41×C₆₇	—	2	2	no	—
134	C₂×#41×C₆₇	—	2	2	no	—
135	C₂×#41×C₆₇	—	2	2	no	—
136	C₂×#41×C₆₇	—	2	2	no	—
137	C₂×#41×C₆₇	—	2	1	no	—
138	C₂×#41×C₆₇	—	2	1	no	—
139	C₂×#41×C₆₇	—	2	1	no	—
140	C₂×#41×C₆₇	—	2	1	no	—
141	C₂×#41×C₆₇	—	4	1	no	—
142	C₂×#41×C₆₇	—	4	1	no	—
143	C₂×#41×C₆₇	—	4	1	no	—
144	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
145	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
148	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
150	C₂²×Q₈×C₆₇	—	2	1	no	—
151	C₂²×Q₈×C₆₇	—	2	1	no	—
152	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
153	C₂²×D₄×C₆₇	—	2	1	no	—
154	C₂²×D₄×C₆₇	—	2	1	no	—
155	C₂²×D₄×C₆₇	—	4	1	no	—
156	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
157	#137×C₆₇	—	2	2	no	—
158	#137×C₆₇	—	2	2	no	—
159	#137×C₆₇	—	2	1	no	—
160	#137×C₆₇	—	2	1	no	—
161	#137×C₆₇	—	2	1	no	—
162	#137×C₆₇	—	2	1	no	—
163	#137×C₆₇	—	2	4	no	—
164	#137×C₆₇	—	2	4	no	—
165	#137×C₆₇	—	2	4	no	—
166	#137×C₆₇	—	2	4	no	—
167	#137×C₆₇	—	2	2	no	—
168	#137×C₆₇	—	2	2	no	—
169	#137×C₆₇	—	2	4	no	—
170	#137×C₆₇	—	2	2	no	—
171	#137×C₆₇	—	2	2	no	—
172	#137×C₆₇	—	2	4	no	—
173	#137×C₆₇	—	2	2	no	—
174	#137×C₆₇	—	2	2	no	—
175	#137×C₆₇	D₄	1	2	yes	complemented
176	#137×C₆₇	D₄	1	2	yes	complemented
177	#137×C₆₇	C₂³	1	2	yes	—
178	#137×C₆₇	C₂³	1	2	yes	—
179	#137×C₆₇	C₂³	1	4	yes	—
180	#137×C₆₇	C₂³	1	2	yes	—
181	#137×C₆₇	C₂³	1	4	yes	complemented
182	#137×C₆₇	C₂³	1	2	yes	complemented
183	AGL(1,ℤ/8)×C₆₇	—	2	2	no	—
184	AGL(1,ℤ/8)×C₆₇	—	2	2	no	—
185	AGL(1,ℤ/8)×C₆₇	—	2	1	no	—
186	AGL(1,ℤ/8)×C₆₇	—	2	1	no	—
187	AGL(1,ℤ/8)×C₆₇	—	2	1	no	—
188	AGL(1,ℤ/8)×C₆₇	—	2	1	no	—
189	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
190	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
191	AGL(1,ℤ/8)×C₆₇	—	2	2	no	—
192	AGL(1,ℤ/8)×C₆₇	—	2	2	no	—
193	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
194	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
195	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
196	AGL(1,ℤ/8)×C₆₇	—	2	2	no	—
197	AGL(1,ℤ/8)×C₆₇	—	2	2	no	—
198	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
199	AGL(1,ℤ/8)×C₆₇	—	2	2	no	—
200	AGL(1,ℤ/8)×C₆₇	—	2	2	no	—
201	AGL(1,ℤ/8)×C₆₇	D₄	1	2	yes	complemented
202	AGL(1,ℤ/8)×C₆₇	D₄	1	2	yes	complemented
203	AGL(1,ℤ/8)×C₆₇	C₂³	1	2	yes	—
204	AGL(1,ℤ/8)×C₆₇	C₂³	1	2	yes	—
205	AGL(1,ℤ/8)×C₆₇	C₂³	1	4	yes	—
206	AGL(1,ℤ/8)×C₆₇	C₂³	1	4	yes	—
207	AGL(1,ℤ/8)×C₆₇	C₂³	1	2	yes	—
208	AGL(1,ℤ/8)×C₆₇	C₂³	1	2	yes	complemented
209	#135×C₆₇	—	2	2	no	—
210	#135×C₆₇	—	2	2	no	—
211	#135×C₆₇	—	2	2	no	—
212	#135×C₆₇	—	2	2	no	—
213	#135×C₆₇	—	2	2	no	—
214	#135×C₆₇	—	2	4	no	—
215	#135×C₆₇	—	2	4	no	—
216	#135×C₆₇	—	2	4	no	—
217	#135×C₆₇	—	2	2	no	—
218	#135×C₆₇	—	2	2	no	—
219	#135×C₆₇	—	2	4	no	—
220	#135×C₆₇	—	2	4	no	—
221	#135×C₆₇	—	2	2	no	—
222	#135×C₆₇	—	2	4	no	—
223	#135×C₆₇	—	2	1	no	—
224	#135×C₆₇	—	2	1	no	—
225	#135×C₆₇	—	2	1	no	—
226	#135×C₆₇	—	2	1	no	—
227	#135×C₆₇	D₄	1	2	yes	complemented
228	#135×C₆₇	D₄	1	2	yes	complemented
229	#135×C₆₇	C₂³	1	2	yes	—
230	#135×C₆₇	C₂³	1	2	yes	—
231	#135×C₆₇	C₂³	1	4	yes	—
232	C₂×Q₁₆×C₆₇	—	2	1	no	—
233	C₂×Q₁₆×C₆₇	—	2	1	no	—
234	C₂×Q₁₆×C₆₇	—	2	2	no	—
235	C₂×Q₁₆×C₆₇	—	2	4	no	—
236	C₂×Q₁₆×C₆₇	D₄	1	1	yes	characteristic, complemented
237	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	complemented
238	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic, complemented
239	C₂×SD₁₆×C₆₇	—	2	1	no	—
240	C₂×SD₁₆×C₆₇	—	2	1	no	—
241	C₂×SD₁₆×C₆₇	—	2	1	no	—
242	C₂×SD₁₆×C₆₇	—	2	1	no	—
243	C₂×SD₁₆×C₆₇	—	2	4	no	—
244	C₂×SD₁₆×C₆₇	—	2	4	no	—
245	C₂×SD₁₆×C₆₇	—	2	2	no	—
246	C₂×SD₁₆×C₆₇	—	2	2	no	—
247	C₂×SD₁₆×C₆₇	—	2	4	no	—
248	C₂×SD₁₆×C₆₇	—	2	4	no	—
249	C₂×SD₁₆×C₆₇	—	2	1	no	—
250	C₂×SD₁₆×C₆₇	—	2	1	no	—
251	C₂×SD₁₆×C₆₇	—	2	1	no	—
252	C₂×SD₁₆×C₆₇	—	2	1	no	—
253	C₂×SD₁₆×C₆₇	D₄	1	1	yes	characteristic, complemented
254	C₂×SD₁₆×C₆₇	D₄	1	1	yes	characteristic, complemented
255	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
256	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
257	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
258	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic, complemented
259	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	complemented
260	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic, complemented
261	C₂×D₈×C₆₇	—	2	1	no	—
262	C₂×D₈×C₆₇	—	2	1	no	—
263	C₂×D₈×C₆₇	—	2	2	no	—
264	C₂×D₈×C₆₇	—	2	4	no	—
265	C₂×D₈×C₆₇	D₄	1	1	yes	characteristic, complemented
266	C₂×D₈×C₆₇	C₂³	1	2	yes	—
267	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
268	#131×C₆₇	—	2	2	no	—
269	#131×C₆₇	—	2	2	no	—
270	#131×C₆₇	—	2	1	no	—
271	#131×C₆₇	—	2	1	no	—
272	#131×C₆₇	—	2	1	no	—
273	#131×C₆₇	—	2	1	no	—
274	#131×C₆₇	C₂³	1	2	yes	—
275	#131×C₆₇	C₂³	1	4	yes	—
276	#131×C₆₇	C₂³	1	2	yes	—
277	#131×C₆₇	C₂³	1	2	yes	complemented
278	#131×C₆₇	C₂³	1	2	yes	complemented
279	#131×C₆₇	C₂³	1	4	yes	complemented
280	C₂×M₁₆×C₆₇	—	2	2	no	—
281	C₂×M₁₆×C₆₇	—	2	2	no	—
282	C₂×M₁₆×C₆₇	—	2	1	no	—
283	C₂×M₁₆×C₆₇	—	2	1	no	—
284	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
285	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
286	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
287	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
288	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
289	C₂²×C₈×C₆₇	—	2	1	no	—
290	C₂²×C₈×C₆₇	—	2	1	no	—
291	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
292	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	complemented
293	#127×C₆₇	C₂³	1	2	yes	—
294	#124×C₆₇	C₂³	1	2	yes	—
295	#124×C₆₇	C₂³	1	2	yes	complemented
296	#123×C₆₇	—	4	1	no	—
297	C₂²⋊Q₈×C₆₇	—	4	1	no	—
298	#121×C₆₇	—	4	1	no	—
299	#120×C₆₇	—	4	1	no	—
300	#117×C₆₇	C₂³	1	1	yes	characteristic
301	#108×C₆₇	C₂³	1	2	yes	complemented
302	#108×C₆₇	C₂³	1	2	yes	complemented
303	#108×C₆₇	C₂³	1	4	yes	complemented
304	#104×C₆₇	C₂³	1	4	yes	—
305	#104×C₆₇	C₂³	1	4	yes	—
306	#104×C₆₇	C₂³	1	4	yes	complemented
307	#104×C₆₇	C₂³	1	4	yes	complemented
308	#101×C₆₇	C₂³	1	2	yes	complemented
309	#101×C₆₇	C₂³	1	4	yes	complemented
310	#101×C₆₇	C₂³	1	2	yes	complemented
311	#100×C₆₇	C₂³	1	4	yes	—
312	#100×C₆₇	C₂³	1	2	yes	complemented
313	#100×C₆₇	C₂³	1	2	yes	complemented
314	#97×C₆₇	C₂³	1	2	yes	complemented
315	C₄×C₈×C₆₇	C₂³	1	2	yes	complemented
316	C₂⁴×C₆₇	—	2	1	no	—
317	C₂⁴×C₆₇	—	4	1	no	—
318	#41×C₆₇	—	2	1	no	—
319	#41×C₆₇	—	2	1	no	—
320	#41×C₆₇	—	2	1	no	—
321	#41×C₆₇	—	2	1	no	—
322	#41×C₆₇	—	2	1	no	—
323	#41×C₆₇	—	2	1	no	—
324	#41×C₆₇	—	2	1	no	—
325	#41×C₆₇	—	2	1	no	—
326	#41×C₆₇	—	2	2	no	—
327	#41×C₆₇	—	2	4	no	—
328	#41×C₆₇	—	2	2	no	—
329	#41×C₆₇	—	2	2	no	—
330	#41×C₆₇	—	2	4	no	—
331	#41×C₆₇	—	2	2	no	—
332	#41×C₆₇	—	2	2	no	—
333	#41×C₆₇	—	2	4	no	—
334	#41×C₆₇	—	2	2	no	—
335	#41×C₆₇	—	2	2	no	—
336	#41×C₆₇	—	2	4	no	—
337	#41×C₆₇	—	2	2	no	—
338	#41×C₆₇	—	2	1	no	—
339	#41×C₆₇	—	2	1	no	—
340	#41×C₆₇	—	2	1	no	—
341	#41×C₆₇	—	2	1	no	—
342	#41×C₆₇	—	2	1	no	—
343	#41×C₆₇	—	2	1	no	—
344	#41×C₆₇	—	2	1	no	—
345	#41×C₆₇	—	2	1	no	—
346	#41×C₆₇	—	4	2	no	—
347	#41×C₆₇	—	4	2	no	—
348	#41×C₆₇	—	4	2	no	—
349	#41×C₆₇	—	4	2	no	—
350	#41×C₆₇	—	4	4	no	—
351	#41×C₆₇	—	4	2	no	—
352	#41×C₆₇	—	4	2	no	—
353	#41×C₆₇	—	4	2	no	—
354	#41×C₆₇	—	4	2	no	—
355	#41×C₆₇	—	4	2	no	—
356	#41×C₆₇	—	4	2	no	—
357	#41×C₆₇	—	4	2	no	—
358	#41×C₆₇	—	4	2	no	—
359	#41×C₆₇	—	4	4	no	—
360	#41×C₆₇	—	4	1	no	—
361	#41×C₆₇	—	4	1	no	—
362	#41×C₆₇	—	4	1	no	—
363	#41×C₆₇	—	4	1	no	—
364	#41×C₆₇	C₂×D₄	1	2	yes	—
365	#41×C₆₇	C₂×D₄	1	2	yes	—
366	#41×C₆₇	C₂×D₄	1	2	yes	—
367	#41×C₆₇	C₂×D₄	1	2	yes	—
368	#41×C₆₇	C₂⁴	1	2	yes	—
369	#41×C₆₇	C₂⁴	1	2	yes	—
370	#41×C₆₇	C₂⁴	1	2	yes	—
371	#41×C₆₇	C₂⁴	1	2	yes	—
372	C₂×Q₈×C₆₇	—	2	1	no	—
373	C₂×Q₈×C₆₇	—	2	4	no	—
374	C₂×Q₈×C₆₇	—	2	2	no	—
375	C₂×Q₈×C₆₇	—	2	4	no	—
376	C₂×Q₈×C₆₇	—	2	2	no	—
377	C₂×Q₈×C₆₇	—	2	2	no	—
378	C₂×Q₈×C₆₇	—	2	2	no	—
379	C₂×Q₈×C₆₇	—	2	1	no	—
380	C₂×Q₈×C₆₇	—	2	1	no	—
381	C₂×Q₈×C₆₇	—	2	1	no	—
382	C₂×Q₈×C₆₇	—	2	1	no	—
383	C₂×Q₈×C₆₇	—	4	1	no	—
384	C₂×Q₈×C₆₇	—	4	2	no	—
385	C₂×Q₈×C₆₇	—	4	2	no	—
386	C₂×Q₈×C₆₇	—	4	1	no	—
387	C₂×Q₈×C₆₇	—	4	1	no	—
388	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
389	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
390	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
391	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
392	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
393	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
394	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
395	C₂×D₄×C₆₇	—	2	1	no	—
396	C₂×D₄×C₆₇	—	2	1	no	—
397	C₂×D₄×C₆₇	—	2	1	no	—
398	C₂×D₄×C₆₇	—	2	1	no	—
399	C₂×D₄×C₆₇	—	2	2	no	—
400	C₂×D₄×C₆₇	—	2	4	no	—
401	C₂×D₄×C₆₇	—	2	2	no	—
402	C₂×D₄×C₆₇	—	2	2	no	—
403	C₂×D₄×C₆₇	—	2	4	no	—
404	C₂×D₄×C₆₇	—	2	2	no	—
405	C₂×D₄×C₆₇	—	2	1	no	—
406	C₂×D₄×C₆₇	—	2	1	no	—
407	C₂×D₄×C₆₇	—	2	1	no	—
408	C₂×D₄×C₆₇	—	2	1	no	—
409	C₂×D₄×C₆₇	—	2	1	no	—
410	C₂×D₄×C₆₇	—	2	1	no	—
411	C₂×D₄×C₆₇	—	2	1	no	—
412	C₂×D₄×C₆₇	—	4	2	no	—
413	C₂×D₄×C₆₇	—	4	2	no	—
414	C₂×D₄×C₆₇	—	4	1	no	—
415	C₂×D₄×C₆₇	—	4	1	no	—
416	C₂×D₄×C₆₇	—	4	2	no	—
417	C₂×D₄×C₆₇	—	4	4	no	—
418	C₂×D₄×C₆₇	—	4	2	no	—
419	C₂×D₄×C₆₇	—	4	2	no	—
420	C₂×D₄×C₆₇	—	4	4	no	—
421	C₂×D₄×C₆₇	—	4	1	no	—
422	C₂×D₄×C₆₇	—	4	1	no	—
423	C₂×D₄×C₆₇	—	4	2	no	—
424	C₂×D₄×C₆₇	—	4	2	no	—
425	C₂×D₄×C₆₇	—	4	2	no	—
426	C₂×D₄×C₆₇	—	4	2	no	—
427	C₂×D₄×C₆₇	—	4	1	no	—
428	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
429	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
430	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
431	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
432	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
433	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
434	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
435	C₂²×C₄×C₆₇	—	2	1	no	—
436	C₂²×C₄×C₆₇	—	2	1	no	—
437	C₂²×C₄×C₆₇	—	2	1	no	—
438	C₂²×C₄×C₆₇	—	2	1	no	—
439	C₂²×C₄×C₆₇	—	2	1	no	—
440	C₂²×C₄×C₆₇	—	2	1	no	—
441	C₂²×C₄×C₆₇	—	2	1	no	—
442	C₂²×C₄×C₆₇	—	4	1	no	—
443	C₂²×C₄×C₆₇	—	4	2	no	—
444	C₂²×C₄×C₆₇	—	4	2	no	—
445	C₂²×C₄×C₆₇	—	4	1	no	—
446	C₂²×C₄×C₆₇	—	4	1	no	—
447	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
448	Q₁₆×C₆₇	—	2	2	no	—
449	Q₁₆×C₆₇	—	2	4	no	—
450	Q₁₆×C₆₇	—	2	4	no	—
451	Q₁₆×C₆₇	—	2	2	no	—
452	Q₁₆×C₆₇	—	2	2	no	—
453	Q₁₆×C₆₇	—	2	2	no	—
454	Q₁₆×C₆₇	—	2	1	no	—
455	Q₁₆×C₆₇	—	2	4	no	—
456	Q₁₆×C₆₇	—	2	1	no	—
457	Q₁₆×C₆₇	C₂×D₄	1	2	yes	—
458	Q₁₆×C₆₇	C₂×D₄	1	4	yes	—
459	Q₁₆×C₆₇	C₂×D₄	1	2	yes	—
460	SD₁₆×C₆₇	—	2	4	no	—
461	SD₁₆×C₆₇	—	2	4	no	—
462	SD₁₆×C₆₇	—	2	2	no	—
463	SD₁₆×C₆₇	—	2	2	no	—
464	SD₁₆×C₆₇	—	2	2	no	—
465	SD₁₆×C₆₇	—	2	2	no	—
466	SD₁₆×C₆₇	—	2	4	no	—
467	SD₁₆×C₆₇	—	2	2	no	—
468	SD₁₆×C₆₇	—	2	4	no	—
469	SD₁₆×C₆₇	—	2	2	no	—
470	SD₁₆×C₆₇	—	2	2	no	—
471	SD₁₆×C₆₇	—	2	2	no	—
472	SD₁₆×C₆₇	—	2	2	no	—
473	SD₁₆×C₆₇	—	2	2	no	—
474	SD₁₆×C₆₇	—	2	2	no	—
475	SD₁₆×C₆₇	—	2	2	no	—
476	SD₁₆×C₆₇	—	2	1	no	—
477	SD₁₆×C₆₇	—	2	1	no	—
478	SD₁₆×C₆₇	—	2	4	no	—
479	SD₁₆×C₆₇	—	2	4	no	—
480	SD₁₆×C₆₇	—	2	1	no	—
481	SD₁₆×C₆₇	—	2	1	no	—
482	SD₁₆×C₆₇	C₂×D₄	1	2	yes	—
483	SD₁₆×C₆₇	C₂×D₄	1	2	yes	—
484	SD₁₆×C₆₇	C₂×D₄	1	2	yes	—
485	SD₁₆×C₆₇	C₂×D₄	1	4	yes	—
486	SD₁₆×C₆₇	C₂×D₄	1	4	yes	—
487	SD₁₆×C₆₇	C₂×D₄	1	2	yes	—
488	D₈×C₆₇	—	2	2	no	—
489	D₈×C₆₇	—	2	4	no	—
490	D₈×C₆₇	—	2	2	no	—
491	D₈×C₆₇	—	2	4	no	—
492	D₈×C₆₇	—	2	2	no	—
493	D₈×C₆₇	—	2	2	no	—
494	D₈×C₆₇	—	2	1	no	—
495	D₈×C₆₇	—	2	4	no	—
496	D₈×C₆₇	—	2	1	no	—
497	D₈×C₆₇	C₂×D₄	1	2	yes	—
498	D₈×C₆₇	C₂×D₄	1	4	yes	—
499	D₈×C₆₇	C₂×D₄	1	2	yes	—
500	M₁₆×C₆₇	—	2	1	no	—
501	M₁₆×C₆₇	—	2	1	no	—
502	M₁₆×C₆₇	—	2	1	no	—
503	M₁₆×C₆₇	—	2	1	no	—
504	M₁₆×C₆₇	—	2	4	no	—
505	M₁₆×C₆₇	—	2	2	no	—
506	M₁₆×C₆₇	—	2	2	no	—
507	M₁₆×C₆₇	—	2	2	no	—
508	M₁₆×C₆₇	—	2	2	no	—
509	M₁₆×C₆₇	—	2	4	no	—
510	M₁₆×C₆₇	C₂×D₄	1	2	yes	—
511	M₁₆×C₆₇	C₂×D₄	1	2	yes	—
512	M₁₆×C₆₇	C₂⁴	1	2	yes	—
513	M₁₆×C₆₇	C₂⁴	1	2	yes	—
514	M₁₆×C₆₇	C₂⁴	1	2	yes	—
515	M₁₆×C₆₇	C₂⁴	1	2	yes	—
516	C₂×C₈×C₆₇	—	2	1	no	—
517	C₂×C₈×C₆₇	—	2	1	no	—
518	C₂×C₈×C₆₇	—	2	1	no	—
519	C₂×C₈×C₆₇	—	2	1	no	—
520	C₂×C₈×C₆₇	—	2	2	no	—
521	C₂×C₈×C₆₇	—	2	2	no	—
522	C₂×C₈×C₆₇	—	2	2	no	—
523	C₂×C₈×C₆₇	—	2	2	no	—
524	C₂×C₈×C₆₇	—	2	4	no	—
525	C₂×C₈×C₆₇	—	2	4	no	—
526	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
527	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
528	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
529	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
530	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
531	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
532	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
533	C₄⋊C₄×C₆₇	—	2	1	no	—
534	C₄⋊C₄×C₆₇	—	4	2	no	—
535	C₂²⋊C₄×C₆₇	—	2	1	no	—
536	C₂²⋊C₄×C₆₇	—	4	2	no	—
537	C₂²⋊C₄×C₆₇	—	4	2	no	—
538	C₄²×C₆₇	C₂⁴	1	2	yes	—
539	C₂³×C₆₇	—	2	1	no	—
540	C₂³×C₆₇	—	2	1	no	—
541	C₂³×C₆₇	—	2	1	no	—
542	C₂³×C₆₇	—	2	1	no	—
543	C₂³×C₆₇	—	2	1	no	—
544	C₂³×C₆₇	—	2	2	no	—
545	C₂³×C₆₇	—	2	1	no	—
546	C₂³×C₆₇	—	4	2	no	—
547	C₂³×C₆₇	—	4	2	no	—
548	C₂³×C₆₇	—	4	4	no	—
549	C₂³×C₆₇	—	4	1	no	—
550	C₂³×C₆₇	—	4	1	no	—
551	C₂³×C₆₇	—	16	1	no	—
552	C₂³×C₆₇	—	16	2	no	—
553	C₂³×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
554	Q₈×C₆₇	—	2	1	no	—
555	Q₈×C₆₇	—	2	1	no	—
556	Q₈×C₆₇	—	2	1	no	—
557	Q₈×C₆₇	—	2	1	no	—
558	Q₈×C₆₇	—	2	2	no	—
559	Q₈×C₆₇	—	2	1	no	—
560	Q₈×C₆₇	—	2	2	no	—
561	Q₈×C₆₇	—	2	1	no	—
562	Q₈×C₆₇	—	2	1	no	—
563	Q₈×C₆₇	—	2	1	no	—
564	Q₈×C₆₇	—	4	4	no	—
565	Q₈×C₆₇	—	4	2	no	—
566	Q₈×C₆₇	—	4	2	no	—
567	Q₈×C₆₇	—	4	1	no	—
568	Q₈×C₆₇	—	4	1	no	—
569	Q₈×C₆₇	C₂²×D₄	1	2	yes	—
570	Q₈×C₆₇	C₂²×D₄	1	2	yes	—
571	Q₈×C₆₇	C₂²×D₄	1	2	yes	—
572	Q₈×C₆₇	C₂²×D₄	1	2	yes	—
573	D₄×C₆₇	—	2	2	no	—
574	D₄×C₆₇	—	2	2	no	—
575	D₄×C₆₇	—	2	2	no	—
576	D₄×C₆₇	—	2	2	no	—
577	D₄×C₆₇	—	2	2	no	—
578	D₄×C₆₇	—	2	2	no	—
579	D₄×C₆₇	—	2	2	no	—
580	D₄×C₆₇	—	2	2	no	—
581	D₄×C₆₇	—	2	1	no	—
582	D₄×C₆₇	—	2	1	no	—
583	D₄×C₆₇	—	2	1	no	—
584	D₄×C₆₇	—	2	1	no	—
585	D₄×C₆₇	—	2	1	no	—
586	D₄×C₆₇	—	2	2	no	—
587	D₄×C₆₇	—	2	1	no	—
588	D₄×C₆₇	—	2	1	no	—
589	D₄×C₆₇	—	2	2	no	—
590	D₄×C₆₇	—	2	1	no	—
591	D₄×C₆₇	—	4	4	no	—
592	D₄×C₆₇	—	4	4	no	—
593	D₄×C₆₇	—	4	2	no	—
594	D₄×C₆₇	—	4	2	no	—
595	D₄×C₆₇	—	4	2	no	—
596	D₄×C₆₇	—	4	2	no	—
597	D₄×C₆₇	—	4	2	no	—
598	D₄×C₆₇	—	4	2	no	—
599	D₄×C₆₇	—	4	4	no	—
600	D₄×C₆₇	—	4	1	no	—
601	D₄×C₆₇	—	4	1	no	—
602	D₄×C₆₇	—	4	1	no	—
603	D₄×C₆₇	—	4	1	no	—
604	D₄×C₆₇	—	4	1	no	—
605	D₄×C₆₇	—	4	1	no	—
606	D₄×C₆₇	—	16	2	no	—
607	D₄×C₆₇	C₂²×D₄	1	2	yes	—
608	D₄×C₆₇	C₂²×D₄	1	2	yes	—
609	D₄×C₆₇	C₂²×D₄	1	2	yes	—
610	D₄×C₆₇	C₂²×D₄	1	2	yes	—
611	C₂×C₄×C₆₇	—	2	1	no	—
612	C₂×C₄×C₆₇	—	2	1	no	—
613	C₂×C₄×C₆₇	—	2	1	no	—
614	C₂×C₄×C₆₇	—	2	1	no	—
615	C₂×C₄×C₆₇	—	2	2	no	—
616	C₂×C₄×C₆₇	—	2	2	no	—
617	C₂×C₄×C₆₇	—	2	2	no	—
618	C₂×C₄×C₆₇	—	2	2	no	—
619	C₂×C₄×C₆₇	—	2	2	no	—
620	C₂×C₄×C₆₇	—	2	2	no	—
621	C₂×C₄×C₆₇	—	2	2	no	—
622	C₂×C₄×C₆₇	—	2	2	no	—
623	C₂×C₄×C₆₇	—	2	2	no	—
624	C₂×C₄×C₆₇	—	2	1	no	—
625	C₂×C₄×C₆₇	—	2	2	no	—
626	C₂×C₄×C₆₇	—	2	1	no	—
627	C₂×C₄×C₆₇	—	4	4	no	—
628	C₂×C₄×C₆₇	—	4	2	no	—
629	C₂×C₄×C₆₇	—	4	2	no	—
630	C₂×C₄×C₆₇	—	4	2	no	—
631	C₂×C₄×C₆₇	—	4	2	no	—
632	C₂×C₄×C₆₇	—	4	2	no	—
633	C₂×C₄×C₆₇	—	4	2	no	—
634	C₂×C₄×C₆₇	—	4	4	no	—
635	C₂×C₄×C₆₇	—	4	4	no	—
636	C₂×C₄×C₆₇	—	4	1	no	—
637	C₂×C₄×C₆₇	—	4	1	no	—
638	C₂×C₄×C₆₇	—	4	1	no	—
639	C₂×C₄×C₆₇	—	4	1	no	—
640	C₂×C₄×C₆₇	—	4	1	no	—
641	C₂×C₄×C₆₇	—	4	1	no	—
642	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
643	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
644	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
645	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
646	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
647	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
648	C₈×C₆₇	—	2	2	no	—
649	C₈×C₆₇	—	2	2	no	—
650	C₈×C₆₇	—	2	2	no	—
651	C₈×C₆₇	—	2	2	no	—
652	C₈×C₆₇	C₂²×D₄	1	1	yes	characteristic
653	C₈×C₆₇	C₂²×D₄	1	1	yes	characteristic
654	C₈×C₆₇	C₂²×D₄	1	1	yes	characteristic
655	C₈×C₆₇	C₂²×D₄	1	4	yes	—
656	C₈×C₆₇	C₂²×D₄	1	1	yes	characteristic
657	C₂²×C₆₇	—	2	2	no	—
658	C₂²×C₆₇	—	2	2	no	—
659	C₂²×C₆₇	—	2	2	no	—
660	C₂²×C₆₇	—	2	2	no	—
661	C₂²×C₆₇	—	4	1	no	—
662	C₂²×C₆₇	—	4	2	no	—
663	C₂²×C₆₇	—	4	1	no	—
664	C₂²×C₆₇	—	4	1	no	—
665	C₂²×C₆₇	—	4	2	no	—
666	C₂²×C₆₇	—	8	1	no	—
667	C₂²×C₆₇	—	8	1	no	—
668	C₂²×C₆₇	—	8	1	no	—
669	C₂²×C₆₇	—	8	1	no	—
670	C₂²×C₆₇	—	8	2	no	—
671	C₂²×C₆₇	—	8	1	no	—
672	C₂²×C₆₇	—	8	2	no	—
673	C₂²×C₆₇	—	16	1	no	—
674	C₂²×C₆₇	—	16	2	no	—
675	C₂²×C₆₇	—	16	2	no	—
676	C₂²×C₆₇	—	16	4	no	—
677	C₂²×C₆₇	D₄²	1	1	yes	characteristic
678	C₂²×C₆₇	D₄²	1	1	yes	characteristic
679	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
680	C₄×C₆₇	—	2	2	no	—
681	C₄×C₆₇	—	2	2	no	—
682	C₄×C₆₇	—	2	2	no	—
683	C₄×C₆₇	—	2	2	no	—
684	C₄×C₆₇	—	4	2	no	—
685	C₄×C₆₇	—	4	1	no	—
686	C₄×C₆₇	—	4	1	no	—
687	C₄×C₆₇	—	4	2	no	—
688	C₄×C₆₇	D₄²	1	1	yes	characteristic
689	C₄×C₆₇	D₄²	1	1	yes	characteristic
690	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
691	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
692	#61107	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
693	C₂×C₆₇	—	2	1	no	—
694	C₂×C₆₇	—	2	1	no	—
695	C₂×C₆₇	—	2	1	no	—
696	C₂×C₆₇	—	4	2	no	—
697	C₂×C₆₇	—	4	2	no	—
698	C₂×C₆₇	—	4	2	no	—
699	C₂×C₆₇	—	4	2	no	—
700	C₂×C₆₇	—	8	2	no	—
701	C₂×C₆₇	—	8	1	no	—
702	C₂×C₆₇	—	8	1	no	—
703	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
704	#3586	C₂×C₆₇	1	1	yes	characteristic, complemented
705	#3585	C₂×C₆₇	1	1	yes	characteristic, complemented
706	#3584	C₂×C₆₇	1	1	yes	characteristic, complemented
707	C₂×#577	C₂×C₆₇	1	1	yes	characteristic, complemented
708	#3291	C₂×C₆₇	1	4	yes	complemented
709	#3290	C₂×C₆₇	1	4	yes	complemented
710	#3289	C₂×C₆₇	1	4	yes	complemented
711	#3288	C₂×C₆₇	1	4	yes	complemented
712	#3154	C₂×C₆₇	1	1	yes	characteristic, complemented
713	#3069	C₂×C₆₇	1	1	yes	characteristic, complemented
714	#3068	C₂×C₆₇	1	1	yes	characteristic, complemented
715	#3067	C₂×C₆₇	1	1	yes	characteristic, complemented
716	C₂×#471	C₂×C₆₇	1	1	yes	characteristic, complemented
717	#3022	C₂×C₆₇	1	1	yes	characteristic, complemented
718	#3021	C₂×C₆₇	1	1	yes	characteristic, complemented
719	#3020	C₂×C₆₇	1	1	yes	characteristic, complemented
720	#3019	C₂×C₆₇	1	1	yes	characteristic, complemented
721	#2957	C₂×C₆₇	1	1	yes	characteristic, complemented
722	#2955	C₂×C₆₇	1	1	yes	characteristic, complemented
723	C₆₇	#61107	1	1	yes	characteristic, direct product factor, Sylow
724	#585	C₂²×C₆₇	1	1	yes	characteristic
725	#585	C₂²×C₆₇	1	1	yes	characteristic, complemented
726	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic, complemented
727	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic, complemented
728	#578	—	2	2	no	—
729	#578	—	2	1	no	—
730	#578	C₂²×C₆₇	1	2	yes	complemented
731	#578	C₂²×C₆₇	1	4	yes	complemented
732	#577	—	2	2	no	—
733	#577	—	2	2	no	—
734	#577	—	2	2	no	—
735	#577	—	2	2	no	—
736	#577	—	2	1	no	—
737	#577	—	2	1	no	—
738	#577	C₂²×C₆₇	1	4	yes	complemented
739	#577	C₂²×C₆₇	1	4	yes	complemented
740	#577	C₂²×C₆₇	1	4	yes	complemented
741	#577	C₂²×C₆₇	1	2	yes	complemented
742	#577	C₂²×C₆₇	1	4	yes	complemented
743	#577	C₂²×C₆₇	1	2	yes	complemented
744	#576	—	2	2	no	—
745	#576	—	2	1	no	—
746	#576	C₂²×C₆₇	1	4	yes	complemented
747	#576	C₂²×C₆₇	1	2	yes	complemented
748	#575	—	2	2	no	—
749	#575	—	2	2	no	—
750	#575	—	2	2	no	—
751	#575	C₂²×C₆₇	1	1	yes	characteristic
752	#575	C₂²×C₆₇	1	1	yes	characteristic
753	#575	C₂²×C₆₇	1	1	yes	characteristic, complemented
754	#575	C₂²×C₆₇	1	1	yes	characteristic, complemented
755	#575	C₂²×C₆₇	1	1	yes	characteristic, complemented
756	C₂×#137	—	2	2	no	—
757	C₂×#137	—	2	1	no	—
758	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic, complemented
759	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic, complemented
760	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic, complemented
761	C₂×AGL(1,ℤ/8)	—	2	2	no	—
762	C₂×AGL(1,ℤ/8)	—	2	1	no	—
763	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
764	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic, complemented
765	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic, complemented
766	C₂×#135	—	2	2	no	—
767	C₂×#135	—	2	1	no	—
768	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
769	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic, complemented
770	C₂²×SD₁₆	—	2	1	no	—
771	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
772	#568	C₂²×C₆₇	1	1	yes	characteristic, complemented
773	#568	C₂²×C₆₇	1	1	yes	characteristic, complemented
774	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
775	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
776	#536	C₂²×C₆₇	1	1	yes	characteristic, complemented
777	#535	C₂²×C₆₇	1	1	yes	characteristic, complemented
778	#497	C₂²×C₆₇	1	2	yes	complemented
779	#496	C₂²×C₆₇	1	2	yes	complemented
780	#495	C₂²×C₆₇	1	2	yes	complemented
781	#492	C₂²×C₆₇	1	2	yes	complemented
782	#473	C₂²×C₆₇	1	2	yes	complemented
783	#473	C₂²×C₆₇	1	4	yes	complemented
784	#472	C₂²×C₆₇	1	4	yes	complemented
785	#472	C₂²×C₆₇	1	2	yes	complemented
786	#471	C₂²×C₆₇	1	4	yes	complemented
787	#471	C₂²×C₆₇	1	4	yes	complemented
788	#471	C₂²×C₆₇	1	4	yes	complemented
789	#471	C₂²×C₆₇	1	4	yes	complemented
790	#471	C₂²×C₆₇	1	2	yes	complemented
791	#471	C₂²×C₆₇	1	2	yes	complemented
792	#456	C₂²×C₆₇	1	4	yes	complemented
793	#456	C₂²×C₆₇	1	4	yes	complemented
794	#455	C₂²×C₆₇	1	4	yes	complemented
795	#455	C₂²×C₆₇	1	4	yes	complemented
796	#454	C₂²×C₆₇	1	4	yes	complemented
797	#454	C₂²×C₆₇	1	4	yes	complemented
798	#453	C₂²×C₆₇	1	4	yes	complemented
799	#453	C₂²×C₆₇	1	4	yes	complemented
800	#444	C₂²×C₆₇	1	4	yes	complemented
801	#444	C₂²×C₆₇	1	4	yes	complemented
802	#443	C₂²×C₆₇	1	4	yes	complemented
803	#443	C₂²×C₆₇	1	4	yes	complemented
804	#430	C₂²×C₆₇	1	1	yes	characteristic, complemented
805	C₂×#108	C₂²×C₆₇	1	1	yes	characteristic, complemented
806	#421	C₂²×C₆₇	1	1	yes	characteristic, complemented
807	#421	C₂²×C₆₇	1	1	yes	characteristic, complemented
808	#421	C₂²×C₆₇	1	1	yes	characteristic, complemented
809	#421	C₂²×C₆₇	1	1	yes	characteristic, complemented
810	#413	C₂²×C₆₇	1	1	yes	characteristic, complemented
811	#413	C₂²×C₆₇	1	1	yes	characteristic, complemented
812	C₂×#101	C₂²×C₆₇	1	1	yes	characteristic, complemented
813	C₂×#100	C₂²×C₆₇	1	1	yes	characteristic, complemented
814	#405	C₂²×C₆₇	1	1	yes	characteristic, complemented
815	2₋¹⁺⁴	—	2	2	no	—
816	2₋¹⁺⁴	—	2	2	no	—
817	2₋¹⁺⁴	—	2	1	no	—
818	2₋¹⁺⁴	—	2	1	no	—
819	2₋¹⁺⁴	—	2	1	no	—
820	2₋¹⁺⁴	—	2	1	no	—
821	2₋¹⁺⁴	—	4	1	no	—
822	2₋¹⁺⁴	C₂³×C₆₇	1	4	yes	—
823	2₋¹⁺⁴	C₂³×C₆₇	1	2	yes	—
824	2₋¹⁺⁴	C₂³×C₆₇	1	2	yes	complemented
825	H(5,𝔽₂)	—	2	2	no	—
826	H(5,𝔽₂)	—	2	2	no	—
827	H(5,𝔽₂)	—	2	1	no	—
828	H(5,𝔽₂)	—	2	1	no	—
829	H(5,𝔽₂)	—	2	1	no	—
830	H(5,𝔽₂)	—	2	1	no	—
831	H(5,𝔽₂)	—	4	1	no	—
832	H(5,𝔽₂)	—	4	1	no	—
833	H(5,𝔽₂)	—	4	1	no	—
834	H(5,𝔽₂)	C₂³×C₆₇	1	2	yes	—
835	H(5,𝔽₂)	C₂³×C₆₇	1	4	yes	—
836	H(5,𝔽₂)	C₂³×C₆₇	1	2	yes	complemented
837	C₂×#41	—	2	2	no	—
838	C₂×#41	—	2	2	no	—
839	C₂×#41	—	2	2	no	—
840	C₂×#41	—	2	2	no	—
841	C₂×#41	—	2	1	no	—
842	C₂×#41	—	2	1	no	—
843	C₂×#41	—	2	1	no	—
844	C₂×#41	—	2	1	no	—
845	C₂×#41	—	4	1	no	—
846	C₂×#41	—	4	1	no	—
847	C₂×#41	—	4	1	no	—
848	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
849	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
850	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
851	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
852	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
853	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
854	C₂²×Q₈	—	2	1	no	—
855	C₂²×Q₈	—	2	1	no	—
856	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
857	C₂²×D₄	—	2	1	no	—
858	C₂²×D₄	—	2	1	no	—
859	C₂²×D₄	—	4	1	no	—
860	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
861	#137	—	2	2	no	—
862	#137	—	2	2	no	—
863	#137	—	2	1	no	—
864	#137	—	2	1	no	—
865	#137	—	2	1	no	—
866	#137	—	2	1	no	—
867	#137	—	2	4	no	—
868	#137	—	2	4	no	—
869	#137	—	2	4	no	—
870	#137	—	2	4	no	—
871	#137	—	2	2	no	—
872	#137	—	2	2	no	—
873	#137	—	2	4	no	—
874	#137	—	2	2	no	—
875	#137	—	2	2	no	—
876	#137	—	2	4	no	—
877	#137	—	2	2	no	—
878	#137	—	2	2	no	—
879	#137	D₄×C₆₇	1	2	yes	complemented
880	#137	D₄×C₆₇	1	2	yes	complemented
881	#137	C₂³×C₆₇	1	4	yes	—
882	#137	C₂³×C₆₇	1	2	yes	—
883	#137	C₂³×C₆₇	1	2	yes	—
884	#137	C₂³×C₆₇	1	2	yes	—
885	#137	C₂³×C₆₇	1	4	yes	complemented
886	#137	C₂³×C₆₇	1	2	yes	complemented
887	AGL(1,ℤ/8)	—	2	2	no	—
888	AGL(1,ℤ/8)	—	2	2	no	—
889	AGL(1,ℤ/8)	—	2	1	no	—
890	AGL(1,ℤ/8)	—	2	1	no	—
891	AGL(1,ℤ/8)	—	2	1	no	—
892	AGL(1,ℤ/8)	—	2	1	no	—
893	AGL(1,ℤ/8)	—	2	4	no	—
894	AGL(1,ℤ/8)	—	2	4	no	—
895	AGL(1,ℤ/8)	—	2	2	no	—
896	AGL(1,ℤ/8)	—	2	2	no	—
897	AGL(1,ℤ/8)	—	2	4	no	—
898	AGL(1,ℤ/8)	—	2	4	no	—
899	AGL(1,ℤ/8)	—	2	4	no	—
900	AGL(1,ℤ/8)	—	2	2	no	—
901	AGL(1,ℤ/8)	—	2	2	no	—
902	AGL(1,ℤ/8)	—	2	4	no	—
903	AGL(1,ℤ/8)	—	2	2	no	—
904	AGL(1,ℤ/8)	—	2	2	no	—
905	AGL(1,ℤ/8)	D₄×C₆₇	1	2	yes	complemented
906	AGL(1,ℤ/8)	D₄×C₆₇	1	2	yes	complemented
907	AGL(1,ℤ/8)	C₂³×C₆₇	1	4	yes	—
908	AGL(1,ℤ/8)	C₂³×C₆₇	1	4	yes	—
909	AGL(1,ℤ/8)	C₂³×C₆₇	1	2	yes	—
910	AGL(1,ℤ/8)	C₂³×C₆₇	1	2	yes	—
911	AGL(1,ℤ/8)	C₂³×C₆₇	1	2	yes	—
912	AGL(1,ℤ/8)	C₂³×C₆₇	1	2	yes	complemented
913	#135	—	2	2	no	—
914	#135	—	2	2	no	—
915	#135	—	2	2	no	—
916	#135	—	2	2	no	—
917	#135	—	2	2	no	—
918	#135	—	2	4	no	—
919	#135	—	2	4	no	—
920	#135	—	2	4	no	—
921	#135	—	2	2	no	—
922	#135	—	2	2	no	—
923	#135	—	2	4	no	—
924	#135	—	2	4	no	—
925	#135	—	2	2	no	—
926	#135	—	2	4	no	—
927	#135	—	2	1	no	—
928	#135	—	2	1	no	—
929	#135	—	2	1	no	—
930	#135	—	2	1	no	—
931	#135	D₄×C₆₇	1	2	yes	complemented
932	#135	D₄×C₆₇	1	2	yes	complemented
933	#135	C₂³×C₆₇	1	2	yes	—
934	#135	C₂³×C₆₇	1	2	yes	—
935	#135	C₂³×C₆₇	1	4	yes	—
936	C₂×Q₁₆	—	2	1	no	—
937	C₂×Q₁₆	—	2	1	no	—
938	C₂×Q₁₆	—	2	2	no	—
939	C₂×Q₁₆	—	2	4	no	—
940	C₂×Q₁₆	D₄×C₆₇	1	1	yes	characteristic, complemented
941	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic, complemented
942	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	complemented
943	C₂×SD₁₆	—	2	1	no	—
944	C₂×SD₁₆	—	2	1	no	—
945	C₂×SD₁₆	—	2	1	no	—
946	C₂×SD₁₆	—	2	1	no	—
947	C₂×SD₁₆	—	2	4	no	—
948	C₂×SD₁₆	—	2	4	no	—
949	C₂×SD₁₆	—	2	2	no	—
950	C₂×SD₁₆	—	2	2	no	—
951	C₂×SD₁₆	—	2	4	no	—
952	C₂×SD₁₆	—	2	4	no	—
953	C₂×SD₁₆	—	2	1	no	—
954	C₂×SD₁₆	—	2	1	no	—
955	C₂×SD₁₆	—	2	1	no	—
956	C₂×SD₁₆	—	2	1	no	—
957	C₂×SD₁₆	D₄×C₆₇	1	1	yes	characteristic, complemented
958	C₂×SD₁₆	D₄×C₆₇	1	1	yes	characteristic, complemented
959	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
960	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
961	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
962	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic, complemented
963	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic, complemented
964	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	complemented
965	C₂×D₈	—	2	1	no	—
966	C₂×D₈	—	2	1	no	—
967	C₂×D₈	—	2	2	no	—
968	C₂×D₈	—	2	4	no	—
969	C₂×D₈	D₄×C₆₇	1	1	yes	characteristic, complemented
970	C₂×D₈	C₂³×C₆₇	1	2	yes	—
971	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
972	#131	—	2	2	no	—
973	#131	—	2	2	no	—
974	#131	—	2	1	no	—
975	#131	—	2	1	no	—
976	#131	—	2	1	no	—
977	#131	—	2	1	no	—
978	#131	C₂³×C₆₇	1	2	yes	—
979	#131	C₂³×C₆₇	1	2	yes	—
980	#131	C₂³×C₆₇	1	4	yes	—
981	#131	C₂³×C₆₇	1	2	yes	complemented
982	#131	C₂³×C₆₇	1	2	yes	complemented
983	#131	C₂³×C₆₇	1	4	yes	complemented
984	C₂×M₁₆	—	2	2	no	—
985	C₂×M₁₆	—	2	2	no	—
986	C₂×M₁₆	—	2	1	no	—
987	C₂×M₁₆	—	2	1	no	—
988	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
989	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
990	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
991	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
992	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
993	C₂²×C₈	—	2	1	no	—
994	C₂²×C₈	—	2	1	no	—
995	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
996	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	complemented
997	#127	C₂³×C₆₇	1	2	yes	—
998	#124	C₂³×C₆₇	1	2	yes	—
999	#124	C₂³×C₆₇	1	2	yes	complemented
1000	#123	—	4	1	no	—
1001	C₂²⋊Q₈	—	4	1	no	—
1002	#121	—	4	1	no	—
1003	#120	—	4	1	no	—
1004	#117	C₂³×C₆₇	1	1	yes	characteristic
1005	#108	C₂³×C₆₇	1	2	yes	complemented
1006	#108	C₂³×C₆₇	1	2	yes	complemented
1007	#108	C₂³×C₆₇	1	4	yes	complemented
1008	#104	C₂³×C₆₇	1	4	yes	—
1009	#104	C₂³×C₆₇	1	4	yes	—
1010	#104	C₂³×C₆₇	1	4	yes	complemented
1011	#104	C₂³×C₆₇	1	4	yes	complemented
1012	#101	C₂³×C₆₇	1	4	yes	complemented
1013	#101	C₂³×C₆₇	1	2	yes	complemented
1014	#101	C₂³×C₆₇	1	2	yes	complemented
1015	#100	C₂³×C₆₇	1	4	yes	—
1016	#100	C₂³×C₆₇	1	2	yes	complemented
1017	#100	C₂³×C₆₇	1	2	yes	complemented
1018	#97	C₂³×C₆₇	1	2	yes	complemented
1019	C₄×C₈	C₂³×C₆₇	1	2	yes	complemented
1020	C₂⁴	—	2	1	no	—
1021	C₂⁴	—	4	1	no	—
1022	#41	—	2	1	no	—
1023	#41	—	2	1	no	—
1024	#41	—	2	1	no	—
1025	#41	—	2	1	no	—
1026	#41	—	2	1	no	—
1027	#41	—	2	1	no	—
1028	#41	—	2	1	no	—
1029	#41	—	2	1	no	—
1030	#41	—	2	2	no	—
1031	#41	—	2	4	no	—
1032	#41	—	2	2	no	—
1033	#41	—	2	2	no	—
1034	#41	—	2	4	no	—
1035	#41	—	2	2	no	—
1036	#41	—	2	2	no	—
1037	#41	—	2	4	no	—
1038	#41	—	2	2	no	—
1039	#41	—	2	2	no	—
1040	#41	—	2	4	no	—
1041	#41	—	2	2	no	—
1042	#41	—	2	1	no	—
1043	#41	—	2	1	no	—
1044	#41	—	2	1	no	—
1045	#41	—	2	1	no	—
1046	#41	—	2	1	no	—
1047	#41	—	2	1	no	—
1048	#41	—	2	1	no	—
1049	#41	—	2	1	no	—
1050	#41	—	4	2	no	—
1051	#41	—	4	2	no	—
1052	#41	—	4	2	no	—
1053	#41	—	4	2	no	—
1054	#41	—	4	4	no	—
1055	#41	—	4	2	no	—
1056	#41	—	4	2	no	—
1057	#41	—	4	2	no	—
1058	#41	—	4	2	no	—
1059	#41	—	4	2	no	—
1060	#41	—	4	2	no	—
1061	#41	—	4	2	no	—
1062	#41	—	4	2	no	—
1063	#41	—	4	4	no	—
1064	#41	—	4	1	no	—
1065	#41	—	4	1	no	—
1066	#41	—	4	1	no	—
1067	#41	—	4	1	no	—
1068	#41	C₂×D₄×C₆₇	1	2	yes	—
1069	#41	C₂×D₄×C₆₇	1	2	yes	—
1070	#41	C₂×D₄×C₆₇	1	2	yes	—
1071	#41	C₂×D₄×C₆₇	1	2	yes	—
1072	#41	C₂⁴×C₆₇	1	2	yes	—
1073	#41	C₂⁴×C₆₇	1	2	yes	—
1074	#41	C₂⁴×C₆₇	1	2	yes	—
1075	#41	C₂⁴×C₆₇	1	2	yes	—
1076	C₂×Q₈	—	2	1	no	—
1077	C₂×Q₈	—	2	4	no	—
1078	C₂×Q₈	—	2	2	no	—
1079	C₂×Q₈	—	2	4	no	—
1080	C₂×Q₈	—	2	2	no	—
1081	C₂×Q₈	—	2	2	no	—
1082	C₂×Q₈	—	2	2	no	—
1083	C₂×Q₈	—	2	1	no	—
1084	C₂×Q₈	—	2	1	no	—
1085	C₂×Q₈	—	2	1	no	—
1086	C₂×Q₈	—	2	1	no	—
1087	C₂×Q₈	—	4	1	no	—
1088	C₂×Q₈	—	4	2	no	—
1089	C₂×Q₈	—	4	2	no	—
1090	C₂×Q₈	—	4	1	no	—
1091	C₂×Q₈	—	4	1	no	—
1092	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
1093	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
1094	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
1095	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
1096	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1097	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
1098	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1099	C₂×D₄	—	2	1	no	—
1100	C₂×D₄	—	2	1	no	—
1101	C₂×D₄	—	2	1	no	—
1102	C₂×D₄	—	2	1	no	—
1103	C₂×D₄	—	2	2	no	—
1104	C₂×D₄	—	2	4	no	—
1105	C₂×D₄	—	2	2	no	—
1106	C₂×D₄	—	2	2	no	—
1107	C₂×D₄	—	2	4	no	—
1108	C₂×D₄	—	2	2	no	—
1109	C₂×D₄	—	2	1	no	—
1110	C₂×D₄	—	2	1	no	—
1111	C₂×D₄	—	2	1	no	—
1112	C₂×D₄	—	2	1	no	—
1113	C₂×D₄	—	2	1	no	—
1114	C₂×D₄	—	2	1	no	—
1115	C₂×D₄	—	2	1	no	—
1116	C₂×D₄	—	4	2	no	—
1117	C₂×D₄	—	4	2	no	—
1118	C₂×D₄	—	4	1	no	—
1119	C₂×D₄	—	4	1	no	—
1120	C₂×D₄	—	4	2	no	—
1121	C₂×D₄	—	4	4	no	—
1122	C₂×D₄	—	4	2	no	—
1123	C₂×D₄	—	4	2	no	—
1124	C₂×D₄	—	4	4	no	—
1125	C₂×D₄	—	4	1	no	—
1126	C₂×D₄	—	4	1	no	—
1127	C₂×D₄	—	4	2	no	—
1128	C₂×D₄	—	4	2	no	—
1129	C₂×D₄	—	4	2	no	—
1130	C₂×D₄	—	4	2	no	—
1131	C₂×D₄	—	4	1	no	—
1132	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1133	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1134	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1135	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1136	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1137	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1138	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1139	C₂²×C₄	—	2	1	no	—
1140	C₂²×C₄	—	2	1	no	—
1141	C₂²×C₄	—	2	1	no	—
1142	C₂²×C₄	—	2	1	no	—
1143	C₂²×C₄	—	2	1	no	—
1144	C₂²×C₄	—	2	1	no	—
1145	C₂²×C₄	—	2	1	no	—
1146	C₂²×C₄	—	4	1	no	—
1147	C₂²×C₄	—	4	2	no	—
1148	C₂²×C₄	—	4	2	no	—
1149	C₂²×C₄	—	4	1	no	—
1150	C₂²×C₄	—	4	1	no	—
1151	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1152	Q₁₆	—	2	2	no	—
1153	Q₁₆	—	2	4	no	—
1154	Q₁₆	—	2	4	no	—
1155	Q₁₆	—	2	2	no	—
1156	Q₁₆	—	2	2	no	—
1157	Q₁₆	—	2	2	no	—
1158	Q₁₆	—	2	1	no	—
1159	Q₁₆	—	2	4	no	—
1160	Q₁₆	—	2	1	no	—
1161	Q₁₆	C₂×D₄×C₆₇	1	2	yes	—
1162	Q₁₆	C₂×D₄×C₆₇	1	4	yes	—
1163	Q₁₆	C₂×D₄×C₆₇	1	2	yes	—
1164	SD₁₆	—	2	4	no	—
1165	SD₁₆	—	2	4	no	—
1166	SD₁₆	—	2	2	no	—
1167	SD₁₆	—	2	2	no	—
1168	SD₁₆	—	2	2	no	—
1169	SD₁₆	—	2	2	no	—
1170	SD₁₆	—	2	4	no	—
1171	SD₁₆	—	2	2	no	—
1172	SD₁₆	—	2	4	no	—
1173	SD₁₆	—	2	2	no	—
1174	SD₁₆	—	2	2	no	—
1175	SD₁₆	—	2	2	no	—
1176	SD₁₆	—	2	2	no	—
1177	SD₁₆	—	2	2	no	—
1178	SD₁₆	—	2	2	no	—
1179	SD₁₆	—	2	2	no	—
1180	SD₁₆	—	2	1	no	—
1181	SD₁₆	—	2	1	no	—
1182	SD₁₆	—	2	4	no	—
1183	SD₁₆	—	2	4	no	—
1184	SD₁₆	—	2	1	no	—
1185	SD₁₆	—	2	1	no	—
1186	SD₁₆	C₂×D₄×C₆₇	1	2	yes	—
1187	SD₁₆	C₂×D₄×C₆₇	1	2	yes	—
1188	SD₁₆	C₂×D₄×C₆₇	1	2	yes	—
1189	SD₁₆	C₂×D₄×C₆₇	1	4	yes	—
1190	SD₁₆	C₂×D₄×C₆₇	1	4	yes	—
1191	SD₁₆	C₂×D₄×C₆₇	1	2	yes	—
1192	D₈	—	2	2	no	—
1193	D₈	—	2	4	no	—
1194	D₈	—	2	2	no	—
1195	D₈	—	2	4	no	—
1196	D₈	—	2	2	no	—
1197	D₈	—	2	2	no	—
1198	D₈	—	2	1	no	—
1199	D₈	—	2	4	no	—
1200	D₈	—	2	1	no	—
1201	D₈	C₂×D₄×C₆₇	1	2	yes	—
1202	D₈	C₂×D₄×C₆₇	1	4	yes	—
1203	D₈	C₂×D₄×C₆₇	1	2	yes	—
1204	M₁₆	—	2	1	no	—
1205	M₁₆	—	2	1	no	—
1206	M₁₆	—	2	1	no	—
1207	M₁₆	—	2	1	no	—
1208	M₁₆	—	2	4	no	—
1209	M₁₆	—	2	2	no	—
1210	M₁₆	—	2	2	no	—
1211	M₁₆	—	2	2	no	—
1212	M₁₆	—	2	2	no	—
1213	M₁₆	—	2	4	no	—
1214	M₁₆	C₂×D₄×C₆₇	1	2	yes	—
1215	M₁₆	C₂×D₄×C₆₇	1	2	yes	—
1216	M₁₆	C₂⁴×C₆₇	1	2	yes	—
1217	M₁₆	C₂⁴×C₆₇	1	2	yes	—
1218	M₁₆	C₂⁴×C₆₇	1	2	yes	—
1219	M₁₆	C₂⁴×C₆₇	1	2	yes	—
1220	C₂×C₈	—	2	1	no	—
1221	C₂×C₈	—	2	1	no	—
1222	C₂×C₈	—	2	1	no	—
1223	C₂×C₈	—	2	1	no	—
1224	C₂×C₈	—	2	2	no	—
1225	C₂×C₈	—	2	2	no	—
1226	C₂×C₈	—	2	2	no	—
1227	C₂×C₈	—	2	2	no	—
1228	C₂×C₈	—	2	4	no	—
1229	C₂×C₈	—	2	4	no	—
1230	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
1231	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
1232	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
1233	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
1234	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1235	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1236	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1237	C₄⋊C₄	—	2	1	no	—
1238	C₄⋊C₄	—	4	2	no	—
1239	C₂²⋊C₄	—	2	1	no	—
1240	C₂²⋊C₄	—	4	2	no	—
1241	C₂²⋊C₄	—	4	2	no	—
1242	C₄²	C₂⁴×C₆₇	1	2	yes	—
1243	C₂³	—	2	1	no	—
1244	C₂³	—	2	1	no	—
1245	C₂³	—	2	1	no	—
1246	C₂³	—	2	1	no	—
1247	C₂³	—	2	1	no	—
1248	C₂³	—	2	2	no	—
1249	C₂³	—	2	1	no	—
1250	C₂³	—	4	2	no	—
1251	C₂³	—	4	2	no	—
1252	C₂³	—	4	4	no	—
1253	C₂³	—	4	1	no	—
1254	C₂³	—	4	1	no	—
1255	C₂³	—	16	1	no	—
1256	C₂³	—	16	2	no	—
1257	C₂³	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1258	Q₈	—	2	1	no	—
1259	Q₈	—	2	1	no	—
1260	Q₈	—	2	1	no	—
1261	Q₈	—	2	1	no	—
1262	Q₈	—	2	2	no	—
1263	Q₈	—	2	1	no	—
1264	Q₈	—	2	2	no	—
1265	Q₈	—	2	1	no	—
1266	Q₈	—	2	1	no	—
1267	Q₈	—	2	1	no	—
1268	Q₈	—	4	4	no	—
1269	Q₈	—	4	2	no	—
1270	Q₈	—	4	2	no	—
1271	Q₈	—	4	1	no	—
1272	Q₈	—	4	1	no	—
1273	Q₈	C₂²×D₄×C₆₇	1	2	yes	—
1274	Q₈	C₂²×D₄×C₆₇	1	2	yes	—
1275	Q₈	C₂²×D₄×C₆₇	1	2	yes	—
1276	Q₈	C₂²×D₄×C₆₇	1	2	yes	—
1277	D₄	—	2	2	no	—
1278	D₄	—	2	2	no	—
1279	D₄	—	2	2	no	—
1280	D₄	—	2	2	no	—
1281	D₄	—	2	2	no	—
1282	D₄	—	2	2	no	—
1283	D₄	—	2	2	no	—
1284	D₄	—	2	2	no	—
1285	D₄	—	2	1	no	—
1286	D₄	—	2	1	no	—
1287	D₄	—	2	1	no	—
1288	D₄	—	2	1	no	—
1289	D₄	—	2	1	no	—
1290	D₄	—	2	2	no	—
1291	D₄	—	2	1	no	—
1292	D₄	—	2	1	no	—
1293	D₄	—	2	2	no	—
1294	D₄	—	2	1	no	—
1295	D₄	—	4	4	no	—
1296	D₄	—	4	4	no	—
1297	D₄	—	4	2	no	—
1298	D₄	—	4	2	no	—
1299	D₄	—	4	2	no	—
1300	D₄	—	4	2	no	—
1301	D₄	—	4	2	no	—
1302	D₄	—	4	2	no	—
1303	D₄	—	4	4	no	—
1304	D₄	—	4	1	no	—
1305	D₄	—	4	1	no	—
1306	D₄	—	4	1	no	—
1307	D₄	—	4	1	no	—
1308	D₄	—	4	1	no	—
1309	D₄	—	4	1	no	—
1310	D₄	—	16	2	no	—
1311	D₄	C₂²×D₄×C₆₇	1	2	yes	—
1312	D₄	C₂²×D₄×C₆₇	1	2	yes	—
1313	D₄	C₂²×D₄×C₆₇	1	2	yes	—
1314	D₄	C₂²×D₄×C₆₇	1	2	yes	—
1315	C₂×C₄	—	2	1	no	—
1316	C₂×C₄	—	2	1	no	—
1317	C₂×C₄	—	2	1	no	—
1318	C₂×C₄	—	2	1	no	—
1319	C₂×C₄	—	2	2	no	—
1320	C₂×C₄	—	2	2	no	—
1321	C₂×C₄	—	2	2	no	—
1322	C₂×C₄	—	2	2	no	—
1323	C₂×C₄	—	2	2	no	—
1324	C₂×C₄	—	2	2	no	—
1325	C₂×C₄	—	2	2	no	—
1326	C₂×C₄	—	2	2	no	—
1327	C₂×C₄	—	2	2	no	—
1328	C₂×C₄	—	2	1	no	—
1329	C₂×C₄	—	2	2	no	—
1330	C₂×C₄	—	2	1	no	—
1331	C₂×C₄	—	4	4	no	—
1332	C₂×C₄	—	4	2	no	—
1333	C₂×C₄	—	4	2	no	—
1334	C₂×C₄	—	4	2	no	—
1335	C₂×C₄	—	4	2	no	—
1336	C₂×C₄	—	4	2	no	—
1337	C₂×C₄	—	4	2	no	—
1338	C₂×C₄	—	4	4	no	—
1339	C₂×C₄	—	4	4	no	—
1340	C₂×C₄	—	4	1	no	—
1341	C₂×C₄	—	4	1	no	—
1342	C₂×C₄	—	4	1	no	—
1343	C₂×C₄	—	4	1	no	—
1344	C₂×C₄	—	4	1	no	—
1345	C₂×C₄	—	4	1	no	—
1346	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1347	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1348	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1349	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1350	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1351	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1352	C₈	—	2	2	no	—
1353	C₈	—	2	2	no	—
1354	C₈	—	2	2	no	—
1355	C₈	—	2	2	no	—
1356	C₈	C₂²×D₄×C₆₇	1	1	yes	characteristic
1357	C₈	C₂²×D₄×C₆₇	1	1	yes	characteristic
1358	C₈	C₂²×D₄×C₆₇	1	1	yes	characteristic
1359	C₈	C₂²×D₄×C₆₇	1	4	yes	—
1360	C₈	C₂²×D₄×C₆₇	1	1	yes	characteristic
1361	C₂²	—	2	2	no	—
1362	C₂²	—	2	2	no	—
1363	C₂²	—	2	2	no	—
1364	C₂²	—	2	2	no	—
1365	C₂²	—	4	1	no	—
1366	C₂²	—	4	2	no	—
1367	C₂²	—	4	1	no	—
1368	C₂²	—	4	1	no	—
1369	C₂²	—	4	2	no	—
1370	C₂²	—	8	1	no	—
1371	C₂²	—	8	1	no	—
1372	C₂²	—	8	1	no	—
1373	C₂²	—	8	1	no	—
1374	C₂²	—	8	2	no	—
1375	C₂²	—	8	1	no	—
1376	C₂²	—	8	2	no	—
1377	C₂²	—	16	1	no	—
1378	C₂²	—	16	4	no	—
1379	C₂²	—	16	2	no	—
1380	C₂²	—	16	2	no	—
1381	C₂²	D₄²×C₆₇	1	1	yes	characteristic
1382	C₂²	D₄²×C₆₇	1	1	yes	characteristic
1383	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1384	C₄	—	2	2	no	—
1385	C₄	—	2	2	no	—
1386	C₄	—	2	2	no	—
1387	C₄	—	2	2	no	—
1388	C₄	—	4	2	no	—
1389	C₄	—	4	1	no	—
1390	C₄	—	4	1	no	—
1391	C₄	—	4	2	no	—
1392	C₄	D₄²×C₆₇	1	1	yes	characteristic
1393	C₄	D₄²×C₆₇	1	1	yes	characteristic
1394	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
1395	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
1396	C₂	—	2	1	no	—
1397	C₂	—	2	1	no	—
1398	C₂	—	2	1	no	—
1399	C₂	—	4	2	no	—
1400	C₂	—	4	2	no	—
1401	C₂	—	4	2	no	—
1402	C₂	—	4	2	no	—
1403	C₂	—	8	2	no	—
1404	C₂	—	8	1	no	—
1405	C₂	—	8	1	no	—
1406	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₆₇	C₂×D₄²
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₆₇ ◁ C₂²×C₄×C₆₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₆₇×#3586	C₂	semidirect
2. C₆₇×#3585	C₂	semidirect
3. C₆₇×#3584	C₂	semidirect
4. C₂×#577×C₆₇	C₂	semidirect
5. C₆₇×#3291	C₂	semidirect
6. C₆₇×#3290	C₂	semidirect
7. C₆₇×#3289	C₂	semidirect
8. C₆₇×#3288	C₂	semidirect
9. C₆₇×#3154	C₂	semidirect
10. C₆₇×#3069	C₂	semidirect
11. C₆₇×#3068	C₂	semidirect
12. C₆₇×#3067	C₂	semidirect
13. C₂×#471×C₆₇	C₂	semidirect
14. C₆₇×#3022	C₂	semidirect
15. C₆₇×#3021	C₂	semidirect
16. C₆₇×#3020	C₂	semidirect
17. C₆₇×#3019	C₂	semidirect
18. C₆₇×#2957	C₂	semidirect
19. C₆₇×#2955	C₂	semidirect
21. #585×C₆₇	C₂²	semidirect
22. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
23. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
26. #578×C₆₇	C₂²	semidirect
27. #578×C₆₇	C₂²	semidirect
34. #577×C₆₇	C₂²	semidirect
35. #577×C₆₇	C₂²	semidirect
36. #577×C₆₇	C₂²	semidirect
37. #577×C₆₇	C₂²	semidirect
38. #577×C₆₇	C₂²	semidirect
39. #577×C₆₇	C₂²	semidirect
42. #576×C₆₇	C₂²	semidirect
43. #576×C₆₇	C₂²	semidirect
49. #575×C₆₇	C₂²	semidirect
50. #575×C₆₇	C₂²	semidirect
51. #575×C₆₇	C₂²	semidirect
54. C₂×#137×C₆₇	C₂²	semidirect
55. C₂×#137×C₆₇	C₂²	semidirect
56. C₂×#137×C₆₇	C₂²	semidirect
60. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
61. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
65. C₂×#135×C₆₇	C₂²	semidirect
67. C₂²×SD₁₆×C₆₇	C₂²	semidirect
68. #568×C₆₇	C₂²	semidirect
69. #568×C₆₇	C₂²	semidirect
70. C₂×#131×C₆₇	C₂²	semidirect
71. C₂×#131×C₆₇	C₂²	semidirect
72. #536×C₆₇	C₂²	semidirect
73. #535×C₆₇	C₂²	semidirect
74. #497×C₆₇	C₂²	semidirect
75. #496×C₆₇	C₂²	semidirect
76. #495×C₆₇	C₂²	semidirect
77. #492×C₆₇	C₂²	semidirect
78. #473×C₆₇	C₂²	semidirect
79. #473×C₆₇	C₂²	semidirect
80. #472×C₆₇	C₂²	semidirect
81. #472×C₆₇	C₂²	semidirect
82. #471×C₆₇	C₂²	semidirect
83. #471×C₆₇	C₂²	semidirect
84. #471×C₆₇	C₂²	semidirect
85. #471×C₆₇	C₂²	semidirect
86. #471×C₆₇	C₂²	semidirect
87. #471×C₆₇	C₂²	semidirect
88. #456×C₆₇	C₂²	semidirect
89. #456×C₆₇	C₂²	semidirect
90. #455×C₆₇	C₂²	semidirect
91. #455×C₆₇	C₂²	semidirect
92. #454×C₆₇	C₂²	semidirect
93. #454×C₆₇	C₂²	semidirect
94. #453×C₆₇	C₂²	semidirect
95. #453×C₆₇	C₂²	semidirect
96. #444×C₆₇	C₂²	semidirect
97. #444×C₆₇	C₂²	semidirect
98. #443×C₆₇	C₂²	semidirect
99. #443×C₆₇	C₂²	semidirect
100. #430×C₆₇	C₂²	semidirect
101. C₂×#108×C₆₇	C₂²	semidirect
102. #421×C₆₇	C₂²	semidirect
103. #421×C₆₇	C₂²	semidirect
104. #421×C₆₇	C₂²	semidirect
105. #421×C₆₇	C₂²	semidirect
106. #413×C₆₇	C₂²	semidirect
107. #413×C₆₇	C₂²	semidirect
108. C₂×#101×C₆₇	C₂²	semidirect
109. C₂×#100×C₆₇	C₂²	semidirect
110. #405×C₆₇	C₂²	semidirect
120. 2₋¹⁺⁴×C₆₇	C₂³	semidirect
132. H(5,𝔽₂)×C₆₇	C₂³	semidirect
175. #137×C₆₇	D₄	semidirect
176. #137×C₆₇	D₄	semidirect
181. #137×C₆₇	C₂³	semidirect
182. #137×C₆₇	C₂³	semidirect
201. AGL(1,ℤ/8)×C₆₇	D₄	semidirect
202. AGL(1,ℤ/8)×C₆₇	D₄	semidirect
208. AGL(1,ℤ/8)×C₆₇	C₂³	semidirect
227. #135×C₆₇	D₄	semidirect
228. #135×C₆₇	D₄	semidirect
236. C₂×Q₁₆×C₆₇	D₄	semidirect
237. C₂×Q₁₆×C₆₇	C₂³	semidirect
238. C₂×Q₁₆×C₆₇	C₂³	semidirect
253. C₂×SD₁₆×C₆₇	D₄	semidirect
254. C₂×SD₁₆×C₆₇	D₄	semidirect
258. C₂×SD₁₆×C₆₇	C₂³	semidirect
259. C₂×SD₁₆×C₆₇	C₂³	semidirect
260. C₂×SD₁₆×C₆₇	C₂³	semidirect
265. C₂×D₈×C₆₇	D₄	semidirect
267. C₂×D₈×C₆₇	C₂³	semidirect
277. #131×C₆₇	C₂³	semidirect
278. #131×C₆₇	C₂³	semidirect
279. #131×C₆₇	C₂³	semidirect
292. C₄⋊Q₈×C₆₇	C₂³	semidirect
295. #124×C₆₇	C₂³	semidirect
301. #108×C₆₇	C₂³	semidirect
302. #108×C₆₇	C₂³	semidirect
303. #108×C₆₇	C₂³	semidirect
306. #104×C₆₇	C₂³	semidirect
307. #104×C₆₇	C₂³	semidirect
308. #101×C₆₇	C₂³	semidirect
309. #101×C₆₇	C₂³	semidirect
310. #101×C₆₇	C₂³	semidirect
312. #100×C₆₇	C₂³	semidirect
313. #100×C₆₇	C₂³	semidirect
314. #97×C₆₇	C₂³	semidirect
315. C₄×C₈×C₆₇	C₂³	semidirect
692. #61107	C₆₇	direct (N × H)
704. #3586	C₂×C₆₇	semidirect
705. #3585	C₂×C₆₇	semidirect
706. #3584	C₂×C₆₇	semidirect
707. C₂×#577	C₂×C₆₇	semidirect
708. #3291	C₂×C₆₇	semidirect
709. #3290	C₂×C₆₇	semidirect
710. #3289	C₂×C₆₇	semidirect
711. #3288	C₂×C₆₇	semidirect
712. #3154	C₂×C₆₇	semidirect
713. #3069	C₂×C₆₇	semidirect
714. #3068	C₂×C₆₇	semidirect
715. #3067	C₂×C₆₇	semidirect
716. C₂×#471	C₂×C₆₇	semidirect
717. #3022	C₂×C₆₇	semidirect
718. #3021	C₂×C₆₇	semidirect
719. #3020	C₂×C₆₇	semidirect
720. #3019	C₂×C₆₇	semidirect
721. #2957	C₂×C₆₇	semidirect
722. #2955	C₂×C₆₇	semidirect
723. C₆₇	#61107	direct (N × H)
725. #585	C₂²×C₆₇	semidirect
726. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
727. C₂×H(5,𝔽₂)	C₂²×C₆₇	semidirect
730. #578	C₂²×C₆₇	semidirect
731. #578	C₂²×C₆₇	semidirect
738. #577	C₂²×C₆₇	semidirect
739. #577	C₂²×C₆₇	semidirect
740. #577	C₂²×C₆₇	semidirect
741. #577	C₂²×C₆₇	semidirect
742. #577	C₂²×C₆₇	semidirect
743. #577	C₂²×C₆₇	semidirect
746. #576	C₂²×C₆₇	semidirect
747. #576	C₂²×C₆₇	semidirect
753. #575	C₂²×C₆₇	semidirect
754. #575	C₂²×C₆₇	semidirect
755. #575	C₂²×C₆₇	semidirect
758. C₂×#137	C₂²×C₆₇	semidirect
759. C₂×#137	C₂²×C₆₇	semidirect
760. C₂×#137	C₂²×C₆₇	semidirect
764. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
765. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
769. C₂×#135	C₂²×C₆₇	semidirect
771. C₂²×SD₁₆	C₂²×C₆₇	semidirect
772. #568	C₂²×C₆₇	semidirect
773. #568	C₂²×C₆₇	semidirect
774. C₂×#131	C₂²×C₆₇	semidirect
775. C₂×#131	C₂²×C₆₇	semidirect
776. #536	C₂²×C₆₇	semidirect
777. #535	C₂²×C₆₇	semidirect
778. #497	C₂²×C₆₇	semidirect
779. #496	C₂²×C₆₇	semidirect
780. #495	C₂²×C₆₇	semidirect
781. #492	C₂²×C₆₇	semidirect
782. #473	C₂²×C₆₇	semidirect
783. #473	C₂²×C₆₇	semidirect
784. #472	C₂²×C₆₇	semidirect
785. #472	C₂²×C₆₇	semidirect
786. #471	C₂²×C₆₇	semidirect
787. #471	C₂²×C₆₇	semidirect
788. #471	C₂²×C₆₇	semidirect
789. #471	C₂²×C₆₇	semidirect
790. #471	C₂²×C₆₇	semidirect
791. #471	C₂²×C₆₇	semidirect
792. #456	C₂²×C₆₇	semidirect
793. #456	C₂²×C₆₇	semidirect
794. #455	C₂²×C₆₇	semidirect
795. #455	C₂²×C₆₇	semidirect
796. #454	C₂²×C₆₇	semidirect
797. #454	C₂²×C₆₇	semidirect
798. #453	C₂²×C₆₇	semidirect
799. #453	C₂²×C₆₇	semidirect
800. #444	C₂²×C₆₇	semidirect
801. #444	C₂²×C₆₇	semidirect
802. #443	C₂²×C₆₇	semidirect
803. #443	C₂²×C₆₇	semidirect
804. #430	C₂²×C₆₇	semidirect
805. C₂×#108	C₂²×C₆₇	semidirect
806. #421	C₂²×C₆₇	semidirect
807. #421	C₂²×C₆₇	semidirect
808. #421	C₂²×C₆₇	semidirect
809. #421	C₂²×C₆₇	semidirect
810. #413	C₂²×C₆₇	semidirect
811. #413	C₂²×C₆₇	semidirect
812. C₂×#101	C₂²×C₆₇	semidirect
813. C₂×#100	C₂²×C₆₇	semidirect
814. #405	C₂²×C₆₇	semidirect
824. 2₋¹⁺⁴	C₂³×C₆₇	semidirect
836. H(5,𝔽₂)	C₂³×C₆₇	semidirect
879. #137	D₄×C₆₇	semidirect
880. #137	D₄×C₆₇	semidirect
885. #137	C₂³×C₆₇	semidirect
886. #137	C₂³×C₆₇	semidirect
905. AGL(1,ℤ/8)	D₄×C₆₇	semidirect
906. AGL(1,ℤ/8)	D₄×C₆₇	semidirect
912. AGL(1,ℤ/8)	C₂³×C₆₇	semidirect
931. #135	D₄×C₆₇	semidirect
932. #135	D₄×C₆₇	semidirect
940. C₂×Q₁₆	D₄×C₆₇	semidirect
941. C₂×Q₁₆	C₂³×C₆₇	semidirect
942. C₂×Q₁₆	C₂³×C₆₇	semidirect
957. C₂×SD₁₆	D₄×C₆₇	semidirect
958. C₂×SD₁₆	D₄×C₆₇	semidirect
962. C₂×SD₁₆	C₂³×C₆₇	semidirect
963. C₂×SD₁₆	C₂³×C₆₇	semidirect
964. C₂×SD₁₆	C₂³×C₆₇	semidirect
969. C₂×D₈	D₄×C₆₇	semidirect
971. C₂×D₈	C₂³×C₆₇	semidirect
981. #131	C₂³×C₆₇	semidirect
982. #131	C₂³×C₆₇	semidirect
983. #131	C₂³×C₆₇	semidirect
996. C₄⋊Q₈	C₂³×C₆₇	semidirect
999. #124	C₂³×C₆₇	semidirect
1005. #108	C₂³×C₆₇	semidirect
1006. #108	C₂³×C₆₇	semidirect
1007. #108	C₂³×C₆₇	semidirect
1010. #104	C₂³×C₆₇	semidirect
1011. #104	C₂³×C₆₇	semidirect
1012. #101	C₂³×C₆₇	semidirect
1013. #101	C₂³×C₆₇	semidirect
1014. #101	C₂³×C₆₇	semidirect
1016. #100	C₂³×C₆₇	semidirect
1017. #100	C₂³×C₆₇	semidirect
1018. #97	C₂³×C₆₇	semidirect
1019. C₄×C₈	C₂³×C₆₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₆₇×#3586	2
C₆₇×#3585	2
C₆₇×#3584	2
C₂×#577×C₆₇	2
C₆₇×#3291	2
C₆₇×#3290	2
C₆₇×#3289	2
C₆₇×#3288	2
C₆₇×#3154	2
C₆₇×#3069	2
C₆₇×#3068	2
C₆₇×#3067	2
C₂×#471×C₆₇	2
C₆₇×#3022	2
C₆₇×#3021	2
C₆₇×#3020	2
C₆₇×#3019	2
C₆₇×#2957	2
C₆₇×#2955	2
#61107	67

Subgroups — C67×#61107 #30740358

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61107 #30740358