Subgroups — C₆₇×#61106 #30740357

Order 17152.

2656 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3585	C₂	1	2	yes	maximal, complemented
2	C₆₇×#3584	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#576×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3292	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3290	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3288	C₂	1	8	yes	maximal, complemented
7	C₆₇×#3155	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3068	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3067	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#472×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3021	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3019	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2957	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2955	C₂	1	1	yes	maximal, characteristic, complemented
15	#585×C₆₇	C₂²	1	2	yes	complemented
16	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	2	yes	complemented
17	#578×C₆₇	—	2	1	no	—
18	#578×C₆₇	C₂²	1	2	yes	complemented
19	#577×C₆₇	—	2	4	no	—
20	#577×C₆₇	—	2	2	no	—
21	#577×C₆₇	C₂²	1	8	yes	complemented
22	#577×C₆₇	C₂²	1	4	yes	complemented
23	#576×C₆₇	—	2	4	no	—
24	#576×C₆₇	—	2	2	no	—
25	#576×C₆₇	—	2	2	no	—
26	#576×C₆₇	—	2	1	no	—
27	#576×C₆₇	C₂²	1	4	yes	complemented
28	#576×C₆₇	C₂²	1	4	yes	complemented
29	#576×C₆₇	C₂²	1	8	yes	complemented
30	#576×C₆₇	C₂²	1	2	yes	complemented
31	#575×C₆₇	—	2	4	no	—
32	#575×C₆₇	—	2	2	no	—
33	#575×C₆₇	C₂²	1	1	yes	characteristic
34	#575×C₆₇	C₂²	1	2	yes	complemented
35	#575×C₆₇	C₂²	1	2	yes	complemented
36	C₂×AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
37	C₂×AGL(1,ℤ/8)×C₆₇	—	2	2	no	—
38	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
39	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
40	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
41	C₂×#135×C₆₇	—	2	2	no	—
42	C₂×#135×C₆₇	—	2	1	no	—
43	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	C₂²×D₈×C₆₇	—	2	1	no	—
46	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
47	#568×C₆₇	C₂²	1	2	yes	complemented
48	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
50	#535×C₆₇	C₂²	1	2	yes	complemented
51	#496×C₆₇	C₂²	1	4	yes	complemented
52	#495×C₆₇	C₂²	1	2	yes	complemented
53	#493×C₆₇	C₂²	1	2	yes	complemented
54	#473×C₆₇	C₂²	1	2	yes	complemented
55	#472×C₆₇	C₂²	1	2	yes	complemented
56	#472×C₆₇	C₂²	1	4	yes	complemented
57	#472×C₆₇	C₂²	1	4	yes	complemented
58	#472×C₆₇	C₂²	1	8	yes	complemented
59	#471×C₆₇	C₂²	1	4	yes	complemented
60	#471×C₆₇	C₂²	1	8	yes	complemented
61	#455×C₆₇	C₂²	1	8	yes	complemented
62	#454×C₆₇	C₂²	1	8	yes	complemented
63	#453×C₆₇	C₂²	1	8	yes	complemented
64	#453×C₆₇	C₂²	1	8	yes	complemented
65	#444×C₆₇	C₂²	1	4	yes	complemented
66	#444×C₆₇	C₂²	1	4	yes	complemented
67	#443×C₆₇	C₂²	1	4	yes	complemented
68	#443×C₆₇	C₂²	1	4	yes	complemented
69	#430×C₆₇	C₂²	1	1	yes	characteristic, complemented
70	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic, complemented
71	#421×C₆₇	C₂²	1	1	yes	characteristic, complemented
72	#421×C₆₇	C₂²	1	2	yes	complemented
73	#421×C₆₇	C₂²	1	1	yes	characteristic, complemented
74	#413×C₆₇	C₂²	1	2	yes	complemented
75	C₂×#100×C₆₇	C₂²	1	2	yes	complemented
76	#405×C₆₇	C₂²	1	1	yes	characteristic, complemented
77	2₋¹⁺⁴×C₆₇	—	2	2	no	—
78	2₋¹⁺⁴×C₆₇	—	2	2	no	—
79	2₋¹⁺⁴×C₆₇	C₂³	1	4	yes	complemented
80	H(5,𝔽₂)×C₆₇	—	2	4	no	—
81	H(5,𝔽₂)×C₆₇	—	2	4	no	—
82	H(5,𝔽₂)×C₆₇	—	2	2	no	—
83	H(5,𝔽₂)×C₆₇	—	2	2	no	—
84	H(5,𝔽₂)×C₆₇	—	4	2	no	—
85	H(5,𝔽₂)×C₆₇	—	4	2	no	—
86	H(5,𝔽₂)×C₆₇	C₂³	1	8	yes	—
87	H(5,𝔽₂)×C₆₇	C₂³	1	4	yes	complemented
88	C₂×#41×C₆₇	—	2	4	no	—
89	C₂×#41×C₆₇	—	2	4	no	—
90	C₂×#41×C₆₇	—	2	2	no	—
91	C₂×#41×C₆₇	—	2	2	no	—
92	C₂×#41×C₆₇	—	4	2	no	—
93	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
94	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
95	C₂×#41×C₆₇	C₂³	1	2	yes	—
96	C₂×#41×C₆₇	C₂³	1	2	yes	—
97	C₂²×D₄×C₆₇	—	2	2	no	—
98	C₂²×D₄×C₆₇	—	2	2	no	—
99	C₂²×D₄×C₆₇	—	4	2	no	—
100	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
101	#137×C₆₇	—	2	2	no	—
102	#137×C₆₇	—	2	2	no	—
103	#137×C₆₇	—	2	8	no	—
104	#137×C₆₇	—	2	4	no	—
105	#137×C₆₇	—	2	4	no	—
106	#137×C₆₇	D₄	1	2	yes	complemented
107	#137×C₆₇	D₄	1	2	yes	complemented
108	#137×C₆₇	C₂³	1	4	yes	—
109	#137×C₆₇	C₂³	1	4	yes	complemented
110	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
111	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
112	AGL(1,ℤ/8)×C₆₇	—	2	2	no	—
113	AGL(1,ℤ/8)×C₆₇	—	2	2	no	—
114	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
115	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
116	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
117	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
118	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
119	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
120	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
121	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
122	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
123	AGL(1,ℤ/8)×C₆₇	D₄	1	2	yes	complemented
124	AGL(1,ℤ/8)×C₆₇	D₄	1	2	yes	complemented
125	AGL(1,ℤ/8)×C₆₇	C₂³	1	4	yes	—
126	AGL(1,ℤ/8)×C₆₇	C₂³	1	8	yes	—
127	AGL(1,ℤ/8)×C₆₇	C₂³	1	4	yes	complemented
128	AGL(1,ℤ/8)×C₆₇	C₂³	1	8	yes	complemented
129	#135×C₆₇	—	2	4	no	—
130	#135×C₆₇	—	2	4	no	—
131	#135×C₆₇	—	2	4	no	—
132	#135×C₆₇	—	2	4	no	—
133	#135×C₆₇	—	2	2	no	—
134	#135×C₆₇	—	2	8	no	—
135	#135×C₆₇	—	2	4	no	—
136	#135×C₆₇	—	2	8	no	—
137	#135×C₆₇	—	2	2	no	—
138	#135×C₆₇	—	2	1	no	—
139	#135×C₆₇	—	2	1	no	—
140	#135×C₆₇	—	2	1	no	—
141	#135×C₆₇	—	2	1	no	—
142	#135×C₆₇	D₄	1	2	yes	complemented
143	#135×C₆₇	D₄	1	2	yes	complemented
144	#135×C₆₇	C₂³	1	2	yes	—
145	#135×C₆₇	C₂³	1	2	yes	—
146	#135×C₆₇	C₂³	1	4	yes	—
147	C₂×Q₁₆×C₆₇	—	2	2	no	—
148	C₂×Q₁₆×C₆₇	D₄	1	1	yes	characteristic, complemented
149	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic, complemented
150	C₂×SD₁₆×C₆₇	—	2	2	no	—
151	C₂×SD₁₆×C₆₇	—	2	2	no	—
152	C₂×SD₁₆×C₆₇	—	2	4	no	—
153	C₂×SD₁₆×C₆₇	—	2	8	no	—
154	C₂×SD₁₆×C₆₇	D₄	1	2	yes	complemented
155	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	complemented
156	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	complemented
157	C₂×D₈×C₆₇	—	2	2	no	—
158	C₂×D₈×C₆₇	—	2	2	no	—
159	C₂×D₈×C₆₇	—	2	4	no	—
160	C₂×D₈×C₆₇	—	2	4	no	—
161	C₂×D₈×C₆₇	—	2	2	no	—
162	C₂×D₈×C₆₇	—	2	8	no	—
163	C₂×D₈×C₆₇	—	2	1	no	—
164	C₂×D₈×C₆₇	—	2	1	no	—
165	C₂×D₈×C₆₇	—	2	1	no	—
166	C₂×D₈×C₆₇	—	2	1	no	—
167	C₂×D₈×C₆₇	D₄	1	1	yes	characteristic, complemented
168	C₂×D₈×C₆₇	C₂³	1	2	yes	—
169	C₂×D₈×C₆₇	C₂³	1	2	yes	—
170	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
171	C₂×D₈×C₆₇	C₂³	1	4	yes	complemented
172	#131×C₆₇	—	2	4	no	—
173	#131×C₆₇	—	2	1	no	—
174	#131×C₆₇	—	2	1	no	—
175	#131×C₆₇	—	2	1	no	—
176	#131×C₆₇	—	2	1	no	—
177	#131×C₆₇	C₂³	1	2	yes	—
178	#131×C₆₇	C₂³	1	2	yes	—
179	#131×C₆₇	C₂³	1	8	yes	complemented
180	#131×C₆₇	C₂³	1	2	yes	complemented
181	#131×C₆₇	C₂³	1	2	yes	complemented
182	C₂×M₁₆×C₆₇	—	2	4	no	—
183	C₂×M₁₆×C₆₇	—	2	1	no	—
184	C₂×M₁₆×C₆₇	—	2	1	no	—
185	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
186	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
187	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
188	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
189	C₂²×C₈×C₆₇	—	2	1	no	—
190	C₂²×C₈×C₆₇	—	2	1	no	—
191	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
192	#127×C₆₇	C₂³	1	4	yes	complemented
193	#124×C₆₇	C₂³	1	4	yes	complemented
194	#121×C₆₇	—	4	2	no	—
195	#120×C₆₇	—	4	2	no	—
196	#117×C₆₇	C₂³	1	1	yes	characteristic
197	#108×C₆₇	C₂³	1	2	yes	complemented
198	#108×C₆₇	C₂³	1	4	yes	complemented
199	#108×C₆₇	C₂³	1	2	yes	complemented
200	#104×C₆₇	C₂³	1	4	yes	—
201	#104×C₆₇	C₂³	1	4	yes	complemented
202	#104×C₆₇	C₂³	1	8	yes	complemented
203	#101×C₆₇	C₂³	1	4	yes	complemented
204	#100×C₆₇	C₂³	1	4	yes	complemented
205	#100×C₆₇	C₂³	1	8	yes	complemented
206	#97×C₆₇	C₂³	1	2	yes	complemented
207	C₄×C₈×C₆₇	C₂³	1	2	yes	complemented
208	C₂⁴×C₆₇	—	2	2	no	—
209	C₂⁴×C₆₇	—	4	2	no	—
210	#41×C₆₇	—	2	1	no	—
211	#41×C₆₇	—	2	2	no	—
212	#41×C₆₇	—	2	1	no	—
213	#41×C₆₇	—	2	1	no	—
214	#41×C₆₇	—	2	2	no	—
215	#41×C₆₇	—	2	1	no	—
216	#41×C₆₇	—	2	8	no	—
217	#41×C₆₇	—	2	4	no	—
218	#41×C₆₇	—	2	8	no	—
219	#41×C₆₇	—	2	4	no	—
220	#41×C₆₇	—	2	4	no	—
221	#41×C₆₇	—	2	4	no	—
222	#41×C₆₇	—	2	2	no	—
223	#41×C₆₇	—	2	2	no	—
224	#41×C₆₇	—	2	2	no	—
225	#41×C₆₇	—	2	2	no	—
226	#41×C₆₇	—	4	4	no	—
227	#41×C₆₇	—	4	4	no	—
228	#41×C₆₇	—	4	4	no	—
229	#41×C₆₇	—	4	4	no	—
230	#41×C₆₇	—	4	4	no	—
231	#41×C₆₇	—	4	4	no	—
232	#41×C₆₇	—	4	2	no	—
233	#41×C₆₇	—	4	2	no	—
234	#41×C₆₇	C₂×D₄	1	2	yes	—
235	#41×C₆₇	C₂×D₄	1	4	yes	—
236	#41×C₆₇	C₂×D₄	1	2	yes	—
237	#41×C₆₇	C₂⁴	1	2	yes	—
238	#41×C₆₇	C₂⁴	1	4	yes	—
239	#41×C₆₇	C₂⁴	1	2	yes	—
240	C₂×Q₈×C₆₇	—	2	4	no	—
241	C₂×Q₈×C₆₇	—	2	4	no	—
242	C₂×Q₈×C₆₇	—	4	2	no	—
243	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
244	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
245	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
246	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
247	C₂×D₄×C₆₇	—	2	1	no	—
248	C₂×D₄×C₆₇	—	2	2	no	—
249	C₂×D₄×C₆₇	—	2	1	no	—
250	C₂×D₄×C₆₇	—	2	8	no	—
251	C₂×D₄×C₆₇	—	2	4	no	—
252	C₂×D₄×C₆₇	—	2	8	no	—
253	C₂×D₄×C₆₇	—	2	4	no	—
254	C₂×D₄×C₆₇	—	2	2	no	—
255	C₂×D₄×C₆₇	—	2	2	no	—
256	C₂×D₄×C₆₇	—	2	2	no	—
257	C₂×D₄×C₆₇	—	2	2	no	—
258	C₂×D₄×C₆₇	—	2	2	no	—
259	C₂×D₄×C₆₇	—	2	2	no	—
260	C₂×D₄×C₆₇	—	4	4	no	—
261	C₂×D₄×C₆₇	—	4	4	no	—
262	C₂×D₄×C₆₇	—	4	2	no	—
263	C₂×D₄×C₆₇	—	4	2	no	—
264	C₂×D₄×C₆₇	—	4	4	no	—
265	C₂×D₄×C₆₇	—	4	8	no	—
266	C₂×D₄×C₆₇	—	4	4	no	—
267	C₂×D₄×C₆₇	—	4	8	no	—
268	C₂×D₄×C₆₇	—	4	2	no	—
269	C₂×D₄×C₆₇	—	4	4	no	—
270	C₂×D₄×C₆₇	—	4	4	no	—
271	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
272	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
273	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
274	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
275	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₆₇	—	2	1	no	—
277	C₂²×C₄×C₆₇	—	2	1	no	—
278	C₂²×C₄×C₆₇	—	2	2	no	—
279	C₂²×C₄×C₆₇	—	2	2	no	—
280	C₂²×C₄×C₆₇	—	4	2	no	—
281	C₂²×C₄×C₆₇	—	4	4	no	—
282	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
283	Q₁₆×C₆₇	—	2	4	no	—
284	Q₁₆×C₆₇	—	2	4	no	—
285	Q₁₆×C₆₇	—	2	1	no	—
286	Q₁₆×C₆₇	—	2	1	no	—
287	Q₁₆×C₆₇	C₂×D₄	1	2	yes	—
288	Q₁₆×C₆₇	C₂×D₄	1	2	yes	—
289	Q₁₆×C₆₇	C₂×D₄	1	4	yes	—
290	SD₁₆×C₆₇	—	2	8	no	—
291	SD₁₆×C₆₇	—	2	8	no	—
292	SD₁₆×C₆₇	—	2	4	no	—
293	SD₁₆×C₆₇	—	2	4	no	—
294	SD₁₆×C₆₇	—	2	4	no	—
295	SD₁₆×C₆₇	—	2	4	no	—
296	SD₁₆×C₆₇	—	2	2	no	—
297	SD₁₆×C₆₇	—	2	8	no	—
298	SD₁₆×C₆₇	—	2	2	no	—
299	SD₁₆×C₆₇	C₂×D₄	1	4	yes	—
300	SD₁₆×C₆₇	C₂×D₄	1	4	yes	—
301	SD₁₆×C₆₇	C₂×D₄	1	4	yes	—
302	SD₁₆×C₆₇	C₂×D₄	1	4	yes	—
303	D₈×C₆₇	—	2	8	no	—
304	D₈×C₆₇	—	2	4	no	—
305	D₈×C₆₇	—	2	8	no	—
306	D₈×C₆₇	—	2	4	no	—
307	D₈×C₆₇	—	2	2	no	—
308	D₈×C₆₇	—	2	2	no	—
309	D₈×C₆₇	—	2	2	no	—
310	D₈×C₆₇	—	2	2	no	—
311	D₈×C₆₇	—	2	1	no	—
312	D₈×C₆₇	—	2	8	no	—
313	D₈×C₆₇	—	2	1	no	—
314	D₈×C₆₇	C₂×D₄	1	2	yes	—
315	D₈×C₆₇	C₂×D₄	1	2	yes	—
316	D₈×C₆₇	C₂×D₄	1	4	yes	—
317	M₁₆×C₆₇	—	2	2	no	—
318	M₁₆×C₆₇	—	2	1	no	—
319	M₁₆×C₆₇	—	2	1	no	—
320	M₁₆×C₆₇	—	2	2	no	—
321	M₁₆×C₆₇	—	2	2	no	—
322	M₁₆×C₆₇	—	2	8	no	—
323	M₁₆×C₆₇	—	2	2	no	—
324	M₁₆×C₆₇	—	2	2	no	—
325	M₁₆×C₆₇	C₂×D₄	1	2	yes	—
326	M₁₆×C₆₇	C₂×D₄	1	2	yes	—
327	M₁₆×C₆₇	C₂⁴	1	2	yes	—
328	M₁₆×C₆₇	C₂⁴	1	4	yes	—
329	M₁₆×C₆₇	C₂⁴	1	2	yes	—
330	C₂×C₈×C₆₇	—	2	1	no	—
331	C₂×C₈×C₆₇	—	2	1	no	—
332	C₂×C₈×C₆₇	—	2	2	no	—
333	C₂×C₈×C₆₇	—	2	2	no	—
334	C₂×C₈×C₆₇	—	2	2	no	—
335	C₂×C₈×C₆₇	—	2	2	no	—
336	C₂×C₈×C₆₇	—	2	2	no	—
337	C₂×C₈×C₆₇	—	2	8	no	—
338	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
339	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
340	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
341	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
342	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
343	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
344	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
345	C₄⋊C₄×C₆₇	—	2	1	no	—
346	C₂²⋊C₄×C₆₇	—	2	1	no	—
347	C₂²⋊C₄×C₆₇	—	4	4	no	—
348	C₄²×C₆₇	C₂⁴	1	2	yes	—
349	C₂³×C₆₇	—	2	1	no	—
350	C₂³×C₆₇	—	2	1	no	—
351	C₂³×C₆₇	—	2	2	no	—
352	C₂³×C₆₇	—	2	4	no	—
353	C₂³×C₆₇	—	2	2	no	—
354	C₂³×C₆₇	—	4	4	no	—
355	C₂³×C₆₇	—	4	8	no	—
356	C₂³×C₆₇	—	4	2	no	—
357	C₂³×C₆₇	—	4	2	no	—
358	C₂³×C₆₇	—	16	2	no	—
359	C₂³×C₆₇	—	16	4	no	—
360	C₂³×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
361	Q₈×C₆₇	—	2	1	no	—
362	Q₈×C₆₇	—	2	2	no	—
363	Q₈×C₆₇	—	2	1	no	—
364	Q₈×C₆₇	—	2	2	no	—
365	Q₈×C₆₇	—	2	2	no	—
366	Q₈×C₆₇	—	4	4	no	—
367	Q₈×C₆₇	C₂²×D₄	1	2	yes	—
368	Q₈×C₆₇	C₂²×D₄	1	4	yes	—
369	Q₈×C₆₇	C₂²×D₄	1	2	yes	—
370	D₄×C₆₇	—	2	2	no	—
371	D₄×C₆₇	—	2	4	no	—
372	D₄×C₆₇	—	2	2	no	—
373	D₄×C₆₇	—	2	2	no	—
374	D₄×C₆₇	—	2	4	no	—
375	D₄×C₆₇	—	2	2	no	—
376	D₄×C₆₇	—	2	1	no	—
377	D₄×C₆₇	—	2	2	no	—
378	D₄×C₆₇	—	2	1	no	—
379	D₄×C₆₇	—	2	4	no	—
380	D₄×C₆₇	—	2	2	no	—
381	D₄×C₆₇	—	2	4	no	—
382	D₄×C₆₇	—	2	2	no	—
383	D₄×C₆₇	—	4	8	no	—
384	D₄×C₆₇	—	4	8	no	—
385	D₄×C₆₇	—	4	4	no	—
386	D₄×C₆₇	—	4	4	no	—
387	D₄×C₆₇	—	4	4	no	—
388	D₄×C₆₇	—	4	2	no	—
389	D₄×C₆₇	—	4	2	no	—
390	D₄×C₆₇	—	4	2	no	—
391	D₄×C₆₇	—	4	2	no	—
392	D₄×C₆₇	—	16	4	no	—
393	D₄×C₆₇	C₂²×D₄	1	2	yes	—
394	D₄×C₆₇	C₂²×D₄	1	4	yes	—
395	D₄×C₆₇	C₂²×D₄	1	2	yes	—
396	C₂×C₄×C₆₇	—	2	1	no	—
397	C₂×C₄×C₆₇	—	2	2	no	—
398	C₂×C₄×C₆₇	—	2	1	no	—
399	C₂×C₄×C₆₇	—	2	2	no	—
400	C₂×C₄×C₆₇	—	2	4	no	—
401	C₂×C₄×C₆₇	—	2	2	no	—
402	C₂×C₄×C₆₇	—	2	2	no	—
403	C₂×C₄×C₆₇	—	2	4	no	—
404	C₂×C₄×C₆₇	—	2	2	no	—
405	C₂×C₄×C₆₇	—	2	2	no	—
406	C₂×C₄×C₆₇	—	2	2	no	—
407	C₂×C₄×C₆₇	—	4	8	no	—
408	C₂×C₄×C₆₇	—	4	4	no	—
409	C₂×C₄×C₆₇	—	4	4	no	—
410	C₂×C₄×C₆₇	—	4	4	no	—
411	C₂×C₄×C₆₇	—	4	2	no	—
412	C₂×C₄×C₆₇	—	4	2	no	—
413	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
418	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
419	C₈×C₆₇	—	2	2	no	—
420	C₈×C₆₇	—	2	4	no	—
421	C₈×C₆₇	—	2	2	no	—
422	C₈×C₆₇	C₂²×D₄	1	1	yes	characteristic
423	C₈×C₆₇	C₂²×D₄	1	1	yes	characteristic
424	C₈×C₆₇	C₂²×D₄	1	1	yes	characteristic
425	C₈×C₆₇	C₂²×D₄	1	4	yes	—
426	C₈×C₆₇	C₂²×D₄	1	1	yes	characteristic
427	C₂²×C₆₇	—	2	2	no	—
428	C₂²×C₆₇	—	2	4	no	—
429	C₂²×C₆₇	—	2	2	no	—
430	C₂²×C₆₇	—	4	1	no	—
431	C₂²×C₆₇	—	4	2	no	—
432	C₂²×C₆₇	—	4	2	no	—
433	C₂²×C₆₇	—	4	4	no	—
434	C₂²×C₆₇	—	8	1	no	—
435	C₂²×C₆₇	—	8	2	no	—
436	C₂²×C₆₇	—	8	2	no	—
437	C₂²×C₆₇	—	8	4	no	—
438	C₂²×C₆₇	—	8	4	no	—
439	C₂²×C₆₇	—	16	2	no	—
440	C₂²×C₆₇	—	16	4	no	—
441	C₂²×C₆₇	—	16	8	no	—
442	C₂²×C₆₇	D₄²	1	1	yes	characteristic
443	C₂²×C₆₇	D₄²	1	1	yes	characteristic
444	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
445	C₄×C₆₇	—	2	2	no	—
446	C₄×C₆₇	—	2	4	no	—
447	C₄×C₆₇	—	2	2	no	—
448	C₄×C₆₇	—	4	2	no	—
449	C₄×C₆₇	—	4	2	no	—
450	C₄×C₆₇	D₄²	1	1	yes	characteristic
451	C₄×C₆₇	D₄²	1	1	yes	characteristic
452	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
453	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
454	#61106	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
455	C₂×C₆₇	—	2	1	no	—
456	C₂×C₆₇	—	2	1	no	—
457	C₂×C₆₇	—	2	1	no	—
458	C₂×C₆₇	—	4	2	no	—
459	C₂×C₆₇	—	4	2	no	—
460	C₂×C₆₇	—	4	4	no	—
461	C₂×C₆₇	—	8	4	no	—
462	C₂×C₆₇	—	8	2	no	—
463	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
464	#3585	C₂×C₆₇	1	2	yes	complemented
465	#3584	C₂×C₆₇	1	1	yes	characteristic, complemented
466	C₂×#576	C₂×C₆₇	1	1	yes	characteristic, complemented
467	#3292	C₂×C₆₇	1	4	yes	complemented
468	#3290	C₂×C₆₇	1	4	yes	complemented
469	#3288	C₂×C₆₇	1	8	yes	complemented
470	#3155	C₂×C₆₇	1	1	yes	characteristic, complemented
471	#3068	C₂×C₆₇	1	2	yes	complemented
472	#3067	C₂×C₆₇	1	1	yes	characteristic, complemented
473	C₂×#472	C₂×C₆₇	1	1	yes	characteristic, complemented
474	#3021	C₂×C₆₇	1	2	yes	complemented
475	#3019	C₂×C₆₇	1	2	yes	complemented
476	#2957	C₂×C₆₇	1	1	yes	characteristic, complemented
477	#2955	C₂×C₆₇	1	1	yes	characteristic, complemented
478	C₆₇	#61106	1	1	yes	characteristic, direct product factor, Sylow
479	#585	C₂²×C₆₇	1	2	yes	complemented
480	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	2	yes	complemented
481	#578	—	2	1	no	—
482	#578	C₂²×C₆₇	1	2	yes	complemented
483	#577	—	2	4	no	—
484	#577	—	2	2	no	—
485	#577	C₂²×C₆₇	1	8	yes	complemented
486	#577	C₂²×C₆₇	1	4	yes	complemented
487	#576	—	2	4	no	—
488	#576	—	2	2	no	—
489	#576	—	2	2	no	—
490	#576	—	2	1	no	—
491	#576	C₂²×C₆₇	1	4	yes	complemented
492	#576	C₂²×C₆₇	1	4	yes	complemented
493	#576	C₂²×C₆₇	1	8	yes	complemented
494	#576	C₂²×C₆₇	1	2	yes	complemented
495	#575	—	2	4	no	—
496	#575	—	2	2	no	—
497	#575	C₂²×C₆₇	1	1	yes	characteristic
498	#575	C₂²×C₆₇	1	2	yes	complemented
499	#575	C₂²×C₆₇	1	2	yes	complemented
500	C₂×AGL(1,ℤ/8)	—	2	4	no	—
501	C₂×AGL(1,ℤ/8)	—	2	2	no	—
502	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
503	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
504	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
505	C₂×#135	—	2	2	no	—
506	C₂×#135	—	2	1	no	—
507	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
508	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic, complemented
509	C₂²×D₈	—	2	1	no	—
510	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
511	#568	C₂²×C₆₇	1	2	yes	complemented
512	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
513	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
514	#535	C₂²×C₆₇	1	2	yes	complemented
515	#496	C₂²×C₆₇	1	4	yes	complemented
516	#495	C₂²×C₆₇	1	2	yes	complemented
517	#493	C₂²×C₆₇	1	2	yes	complemented
518	#473	C₂²×C₆₇	1	2	yes	complemented
519	#472	C₂²×C₆₇	1	2	yes	complemented
520	#472	C₂²×C₆₇	1	4	yes	complemented
521	#472	C₂²×C₆₇	1	4	yes	complemented
522	#472	C₂²×C₆₇	1	8	yes	complemented
523	#471	C₂²×C₆₇	1	4	yes	complemented
524	#471	C₂²×C₆₇	1	8	yes	complemented
525	#455	C₂²×C₆₇	1	8	yes	complemented
526	#454	C₂²×C₆₇	1	8	yes	complemented
527	#453	C₂²×C₆₇	1	8	yes	complemented
528	#453	C₂²×C₆₇	1	8	yes	complemented
529	#444	C₂²×C₆₇	1	4	yes	complemented
530	#444	C₂²×C₆₇	1	4	yes	complemented
531	#443	C₂²×C₆₇	1	4	yes	complemented
532	#443	C₂²×C₆₇	1	4	yes	complemented
533	#430	C₂²×C₆₇	1	1	yes	characteristic, complemented
534	C₂×#108	C₂²×C₆₇	1	1	yes	characteristic, complemented
535	#421	C₂²×C₆₇	1	1	yes	characteristic, complemented
536	#421	C₂²×C₆₇	1	1	yes	characteristic, complemented
537	#421	C₂²×C₆₇	1	2	yes	complemented
538	#413	C₂²×C₆₇	1	2	yes	complemented
539	C₂×#100	C₂²×C₆₇	1	2	yes	complemented
540	#405	C₂²×C₆₇	1	1	yes	characteristic, complemented
541	2₋¹⁺⁴	—	2	2	no	—
542	2₋¹⁺⁴	—	2	2	no	—
543	2₋¹⁺⁴	C₂³×C₆₇	1	4	yes	complemented
544	H(5,𝔽₂)	—	2	4	no	—
545	H(5,𝔽₂)	—	2	4	no	—
546	H(5,𝔽₂)	—	2	2	no	—
547	H(5,𝔽₂)	—	2	2	no	—
548	H(5,𝔽₂)	—	4	2	no	—
549	H(5,𝔽₂)	—	4	2	no	—
550	H(5,𝔽₂)	C₂³×C₆₇	1	8	yes	—
551	H(5,𝔽₂)	C₂³×C₆₇	1	4	yes	complemented
552	C₂×#41	—	2	4	no	—
553	C₂×#41	—	2	4	no	—
554	C₂×#41	—	2	2	no	—
555	C₂×#41	—	2	2	no	—
556	C₂×#41	—	4	2	no	—
557	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
558	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
559	C₂×#41	C₂³×C₆₇	1	2	yes	—
560	C₂×#41	C₂³×C₆₇	1	2	yes	—
561	C₂²×D₄	—	2	2	no	—
562	C₂²×D₄	—	2	2	no	—
563	C₂²×D₄	—	4	2	no	—
564	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
565	#137	—	2	2	no	—
566	#137	—	2	2	no	—
567	#137	—	2	8	no	—
568	#137	—	2	4	no	—
569	#137	—	2	4	no	—
570	#137	D₄×C₆₇	1	2	yes	complemented
571	#137	D₄×C₆₇	1	2	yes	complemented
572	#137	C₂³×C₆₇	1	4	yes	—
573	#137	C₂³×C₆₇	1	4	yes	complemented
574	AGL(1,ℤ/8)	—	2	4	no	—
575	AGL(1,ℤ/8)	—	2	4	no	—
576	AGL(1,ℤ/8)	—	2	2	no	—
577	AGL(1,ℤ/8)	—	2	2	no	—
578	AGL(1,ℤ/8)	—	2	8	no	—
579	AGL(1,ℤ/8)	—	2	8	no	—
580	AGL(1,ℤ/8)	—	2	8	no	—
581	AGL(1,ℤ/8)	—	2	8	no	—
582	AGL(1,ℤ/8)	—	2	4	no	—
583	AGL(1,ℤ/8)	—	2	8	no	—
584	AGL(1,ℤ/8)	—	2	4	no	—
585	AGL(1,ℤ/8)	—	2	4	no	—
586	AGL(1,ℤ/8)	—	2	4	no	—
587	AGL(1,ℤ/8)	D₄×C₆₇	1	2	yes	complemented
588	AGL(1,ℤ/8)	D₄×C₆₇	1	2	yes	complemented
589	AGL(1,ℤ/8)	C₂³×C₆₇	1	8	yes	—
590	AGL(1,ℤ/8)	C₂³×C₆₇	1	4	yes	—
591	AGL(1,ℤ/8)	C₂³×C₆₇	1	8	yes	complemented
592	AGL(1,ℤ/8)	C₂³×C₆₇	1	4	yes	complemented
593	#135	—	2	4	no	—
594	#135	—	2	4	no	—
595	#135	—	2	4	no	—
596	#135	—	2	4	no	—
597	#135	—	2	2	no	—
598	#135	—	2	8	no	—
599	#135	—	2	4	no	—
600	#135	—	2	8	no	—
601	#135	—	2	2	no	—
602	#135	—	2	1	no	—
603	#135	—	2	1	no	—
604	#135	—	2	1	no	—
605	#135	—	2	1	no	—
606	#135	D₄×C₆₇	1	2	yes	complemented
607	#135	D₄×C₆₇	1	2	yes	complemented
608	#135	C₂³×C₆₇	1	2	yes	—
609	#135	C₂³×C₆₇	1	2	yes	—
610	#135	C₂³×C₆₇	1	4	yes	—
611	C₂×Q₁₆	—	2	2	no	—
612	C₂×Q₁₆	D₄×C₆₇	1	1	yes	characteristic, complemented
613	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic, complemented
614	C₂×SD₁₆	—	2	2	no	—
615	C₂×SD₁₆	—	2	2	no	—
616	C₂×SD₁₆	—	2	4	no	—
617	C₂×SD₁₆	—	2	8	no	—
618	C₂×SD₁₆	D₄×C₆₇	1	2	yes	complemented
619	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	complemented
620	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	complemented
621	C₂×D₈	—	2	2	no	—
622	C₂×D₈	—	2	2	no	—
623	C₂×D₈	—	2	4	no	—
624	C₂×D₈	—	2	4	no	—
625	C₂×D₈	—	2	2	no	—
626	C₂×D₈	—	2	8	no	—
627	C₂×D₈	—	2	1	no	—
628	C₂×D₈	—	2	1	no	—
629	C₂×D₈	—	2	1	no	—
630	C₂×D₈	—	2	1	no	—
631	C₂×D₈	D₄×C₆₇	1	1	yes	characteristic, complemented
632	C₂×D₈	C₂³×C₆₇	1	2	yes	—
633	C₂×D₈	C₂³×C₆₇	1	2	yes	—
634	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
635	C₂×D₈	C₂³×C₆₇	1	4	yes	complemented
636	#131	—	2	4	no	—
637	#131	—	2	1	no	—
638	#131	—	2	1	no	—
639	#131	—	2	1	no	—
640	#131	—	2	1	no	—
641	#131	C₂³×C₆₇	1	2	yes	—
642	#131	C₂³×C₆₇	1	2	yes	—
643	#131	C₂³×C₆₇	1	2	yes	complemented
644	#131	C₂³×C₆₇	1	2	yes	complemented
645	#131	C₂³×C₆₇	1	8	yes	complemented
646	C₂×M₁₆	—	2	4	no	—
647	C₂×M₁₆	—	2	1	no	—
648	C₂×M₁₆	—	2	1	no	—
649	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
650	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
651	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
652	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
653	C₂²×C₈	—	2	1	no	—
654	C₂²×C₈	—	2	1	no	—
655	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
656	#127	C₂³×C₆₇	1	4	yes	complemented
657	#124	C₂³×C₆₇	1	4	yes	complemented
658	#121	—	4	2	no	—
659	#120	—	4	2	no	—
660	#117	C₂³×C₆₇	1	1	yes	characteristic
661	#108	C₂³×C₆₇	1	2	yes	complemented
662	#108	C₂³×C₆₇	1	2	yes	complemented
663	#108	C₂³×C₆₇	1	4	yes	complemented
664	#104	C₂³×C₆₇	1	4	yes	—
665	#104	C₂³×C₆₇	1	4	yes	complemented
666	#104	C₂³×C₆₇	1	8	yes	complemented
667	#101	C₂³×C₆₇	1	4	yes	complemented
668	#100	C₂³×C₆₇	1	8	yes	complemented
669	#100	C₂³×C₆₇	1	4	yes	complemented
670	#97	C₂³×C₆₇	1	2	yes	complemented
671	C₄×C₈	C₂³×C₆₇	1	2	yes	complemented
672	C₂⁴	—	2	2	no	—
673	C₂⁴	—	4	2	no	—
674	#41	—	2	1	no	—
675	#41	—	2	2	no	—
676	#41	—	2	1	no	—
677	#41	—	2	1	no	—
678	#41	—	2	2	no	—
679	#41	—	2	1	no	—
680	#41	—	2	8	no	—
681	#41	—	2	4	no	—
682	#41	—	2	8	no	—
683	#41	—	2	4	no	—
684	#41	—	2	4	no	—
685	#41	—	2	4	no	—
686	#41	—	2	2	no	—
687	#41	—	2	2	no	—
688	#41	—	2	2	no	—
689	#41	—	2	2	no	—
690	#41	—	4	4	no	—
691	#41	—	4	4	no	—
692	#41	—	4	4	no	—
693	#41	—	4	4	no	—
694	#41	—	4	4	no	—
695	#41	—	4	4	no	—
696	#41	—	4	2	no	—
697	#41	—	4	2	no	—
698	#41	C₂×D₄×C₆₇	1	2	yes	—
699	#41	C₂×D₄×C₆₇	1	4	yes	—
700	#41	C₂×D₄×C₆₇	1	2	yes	—
701	#41	C₂⁴×C₆₇	1	2	yes	—
702	#41	C₂⁴×C₆₇	1	4	yes	—
703	#41	C₂⁴×C₆₇	1	2	yes	—
704	C₂×Q₈	—	2	4	no	—
705	C₂×Q₈	—	2	4	no	—
706	C₂×Q₈	—	4	2	no	—
707	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
708	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
709	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
710	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
711	C₂×D₄	—	2	1	no	—
712	C₂×D₄	—	2	2	no	—
713	C₂×D₄	—	2	1	no	—
714	C₂×D₄	—	2	8	no	—
715	C₂×D₄	—	2	4	no	—
716	C₂×D₄	—	2	8	no	—
717	C₂×D₄	—	2	4	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	—	4	4	no	—
725	C₂×D₄	—	4	4	no	—
726	C₂×D₄	—	4	2	no	—
727	C₂×D₄	—	4	2	no	—
728	C₂×D₄	—	4	4	no	—
729	C₂×D₄	—	4	8	no	—
730	C₂×D₄	—	4	4	no	—
731	C₂×D₄	—	4	8	no	—
732	C₂×D₄	—	4	2	no	—
733	C₂×D₄	—	4	4	no	—
734	C₂×D₄	—	4	4	no	—
735	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
736	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
737	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
738	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
739	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
740	C₂²×C₄	—	2	1	no	—
741	C₂²×C₄	—	2	1	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	4	2	no	—
745	C₂²×C₄	—	4	4	no	—
746	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
747	Q₁₆	—	2	4	no	—
748	Q₁₆	—	2	4	no	—
749	Q₁₆	—	2	1	no	—
750	Q₁₆	—	2	1	no	—
751	Q₁₆	C₂×D₄×C₆₇	1	2	yes	—
752	Q₁₆	C₂×D₄×C₆₇	1	2	yes	—
753	Q₁₆	C₂×D₄×C₆₇	1	4	yes	—
754	SD₁₆	—	2	8	no	—
755	SD₁₆	—	2	8	no	—
756	SD₁₆	—	2	4	no	—
757	SD₁₆	—	2	4	no	—
758	SD₁₆	—	2	4	no	—
759	SD₁₆	—	2	4	no	—
760	SD₁₆	—	2	2	no	—
761	SD₁₆	—	2	8	no	—
762	SD₁₆	—	2	2	no	—
763	SD₁₆	C₂×D₄×C₆₇	1	4	yes	—
764	SD₁₆	C₂×D₄×C₆₇	1	4	yes	—
765	SD₁₆	C₂×D₄×C₆₇	1	4	yes	—
766	SD₁₆	C₂×D₄×C₆₇	1	4	yes	—
767	D₈	—	2	8	no	—
768	D₈	—	2	4	no	—
769	D₈	—	2	8	no	—
770	D₈	—	2	4	no	—
771	D₈	—	2	2	no	—
772	D₈	—	2	2	no	—
773	D₈	—	2	2	no	—
774	D₈	—	2	2	no	—
775	D₈	—	2	1	no	—
776	D₈	—	2	8	no	—
777	D₈	—	2	1	no	—
778	D₈	C₂×D₄×C₆₇	1	2	yes	—
779	D₈	C₂×D₄×C₆₇	1	2	yes	—
780	D₈	C₂×D₄×C₆₇	1	4	yes	—
781	M₁₆	—	2	2	no	—
782	M₁₆	—	2	1	no	—
783	M₁₆	—	2	1	no	—
784	M₁₆	—	2	2	no	—
785	M₁₆	—	2	2	no	—
786	M₁₆	—	2	8	no	—
787	M₁₆	—	2	2	no	—
788	M₁₆	—	2	2	no	—
789	M₁₆	C₂×D₄×C₆₇	1	2	yes	—
790	M₁₆	C₂×D₄×C₆₇	1	2	yes	—
791	M₁₆	C₂⁴×C₆₇	1	2	yes	—
792	M₁₆	C₂⁴×C₆₇	1	4	yes	—
793	M₁₆	C₂⁴×C₆₇	1	2	yes	—
794	C₂×C₈	—	2	1	no	—
795	C₂×C₈	—	2	1	no	—
796	C₂×C₈	—	2	2	no	—
797	C₂×C₈	—	2	2	no	—
798	C₂×C₈	—	2	2	no	—
799	C₂×C₈	—	2	2	no	—
800	C₂×C₈	—	2	2	no	—
801	C₂×C₈	—	2	8	no	—
802	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
803	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
804	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
805	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
806	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
807	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
808	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
809	C₄⋊C₄	—	2	1	no	—
810	C₂²⋊C₄	—	2	1	no	—
811	C₂²⋊C₄	—	4	4	no	—
812	C₄²	C₂⁴×C₆₇	1	2	yes	—
813	C₂³	—	2	1	no	—
814	C₂³	—	2	1	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	2	4	no	—
817	C₂³	—	2	2	no	—
818	C₂³	—	4	4	no	—
819	C₂³	—	4	8	no	—
820	C₂³	—	4	2	no	—
821	C₂³	—	4	2	no	—
822	C₂³	—	16	2	no	—
823	C₂³	—	16	4	no	—
824	C₂³	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
825	Q₈	—	2	1	no	—
826	Q₈	—	2	2	no	—
827	Q₈	—	2	1	no	—
828	Q₈	—	2	2	no	—
829	Q₈	—	2	2	no	—
830	Q₈	—	4	4	no	—
831	Q₈	C₂²×D₄×C₆₇	1	2	yes	—
832	Q₈	C₂²×D₄×C₆₇	1	4	yes	—
833	Q₈	C₂²×D₄×C₆₇	1	2	yes	—
834	D₄	—	2	2	no	—
835	D₄	—	2	4	no	—
836	D₄	—	2	2	no	—
837	D₄	—	2	2	no	—
838	D₄	—	2	4	no	—
839	D₄	—	2	2	no	—
840	D₄	—	2	1	no	—
841	D₄	—	2	2	no	—
842	D₄	—	2	1	no	—
843	D₄	—	2	4	no	—
844	D₄	—	2	2	no	—
845	D₄	—	2	4	no	—
846	D₄	—	2	2	no	—
847	D₄	—	4	8	no	—
848	D₄	—	4	8	no	—
849	D₄	—	4	4	no	—
850	D₄	—	4	4	no	—
851	D₄	—	4	4	no	—
852	D₄	—	4	2	no	—
853	D₄	—	4	2	no	—
854	D₄	—	4	2	no	—
855	D₄	—	4	2	no	—
856	D₄	—	16	4	no	—
857	D₄	C₂²×D₄×C₆₇	1	2	yes	—
858	D₄	C₂²×D₄×C₆₇	1	4	yes	—
859	D₄	C₂²×D₄×C₆₇	1	2	yes	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	4	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	4	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	4	8	no	—
872	C₂×C₄	—	4	4	no	—
873	C₂×C₄	—	4	4	no	—
874	C₂×C₄	—	4	4	no	—
875	C₂×C₄	—	4	2	no	—
876	C₂×C₄	—	4	2	no	—
877	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
878	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
879	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
880	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
881	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
882	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
883	C₈	—	2	2	no	—
884	C₈	—	2	4	no	—
885	C₈	—	2	2	no	—
886	C₈	C₂²×D₄×C₆₇	1	1	yes	characteristic
887	C₈	C₂²×D₄×C₆₇	1	1	yes	characteristic
888	C₈	C₂²×D₄×C₆₇	1	1	yes	characteristic
889	C₈	C₂²×D₄×C₆₇	1	4	yes	—
890	C₈	C₂²×D₄×C₆₇	1	1	yes	characteristic
891	C₂²	—	2	2	no	—
892	C₂²	—	2	4	no	—
893	C₂²	—	2	2	no	—
894	C₂²	—	4	1	no	—
895	C₂²	—	4	2	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	4	4	no	—
898	C₂²	—	8	2	no	—
899	C₂²	—	8	1	no	—
900	C₂²	—	8	2	no	—
901	C₂²	—	8	4	no	—
902	C₂²	—	8	4	no	—
903	C₂²	—	16	2	no	—
904	C₂²	—	16	8	no	—
905	C₂²	—	16	4	no	—
906	C₂²	D₄²×C₆₇	1	1	yes	characteristic
907	C₂²	D₄²×C₆₇	1	1	yes	characteristic
908	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
909	C₄	—	2	2	no	—
910	C₄	—	2	4	no	—
911	C₄	—	2	2	no	—
912	C₄	—	4	2	no	—
913	C₄	—	4	2	no	—
914	C₄	D₄²×C₆₇	1	1	yes	characteristic
915	C₄	D₄²×C₆₇	1	1	yes	characteristic
916	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
917	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
918	C₂	—	2	1	no	—
919	C₂	—	2	1	no	—
920	C₂	—	2	1	no	—
921	C₂	—	4	2	no	—
922	C₂	—	4	4	no	—
923	C₂	—	4	2	no	—
924	C₂	—	8	4	no	—
925	C₂	—	8	2	no	—
926	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×#3585	C₂	semidirect
2. C₆₇×#3584	C₂	semidirect
3. C₂×#576×C₆₇	C₂	semidirect
4. C₆₇×#3292	C₂	semidirect
5. C₆₇×#3290	C₂	semidirect
6. C₆₇×#3288	C₂	semidirect
7. C₆₇×#3155	C₂	semidirect
8. C₆₇×#3068	C₂	semidirect
9. C₆₇×#3067	C₂	semidirect
10. C₂×#472×C₆₇	C₂	semidirect
11. C₆₇×#3021	C₂	semidirect
12. C₆₇×#3019	C₂	semidirect
13. C₆₇×#2957	C₂	semidirect
14. C₆₇×#2955	C₂	semidirect
15. #585×C₆₇	C₂²	semidirect
16. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
18. #578×C₆₇	C₂²	semidirect
21. #577×C₆₇	C₂²	semidirect
22. #577×C₆₇	C₂²	semidirect
27. #576×C₆₇	C₂²	semidirect
28. #576×C₆₇	C₂²	semidirect
29. #576×C₆₇	C₂²	semidirect
30. #576×C₆₇	C₂²	semidirect
34. #575×C₆₇	C₂²	semidirect
35. #575×C₆₇	C₂²	semidirect
38. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
39. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
40. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
44. C₂×#135×C₆₇	C₂²	semidirect
46. C₂²×D₈×C₆₇	C₂²	semidirect
47. #568×C₆₇	C₂²	semidirect
48. C₂×#131×C₆₇	C₂²	semidirect
49. C₂×#131×C₆₇	C₂²	semidirect
50. #535×C₆₇	C₂²	semidirect
51. #496×C₆₇	C₂²	semidirect
52. #495×C₆₇	C₂²	semidirect
53. #493×C₆₇	C₂²	semidirect
54. #473×C₆₇	C₂²	semidirect
55. #472×C₆₇	C₂²	semidirect
56. #472×C₆₇	C₂²	semidirect
57. #472×C₆₇	C₂²	semidirect
58. #472×C₆₇	C₂²	semidirect
59. #471×C₆₇	C₂²	semidirect
60. #471×C₆₇	C₂²	semidirect
61. #455×C₆₇	C₂²	semidirect
62. #454×C₆₇	C₂²	semidirect
63. #453×C₆₇	C₂²	semidirect
64. #453×C₆₇	C₂²	semidirect
65. #444×C₆₇	C₂²	semidirect
66. #444×C₆₇	C₂²	semidirect
67. #443×C₆₇	C₂²	semidirect
68. #443×C₆₇	C₂²	semidirect
69. #430×C₆₇	C₂²	semidirect
70. C₂×#108×C₆₇	C₂²	semidirect
71. #421×C₆₇	C₂²	semidirect
72. #421×C₆₇	C₂²	semidirect
73. #421×C₆₇	C₂²	semidirect
74. #413×C₆₇	C₂²	semidirect
75. C₂×#100×C₆₇	C₂²	semidirect
76. #405×C₆₇	C₂²	semidirect
79. 2₋¹⁺⁴×C₆₇	C₂³	semidirect
87. H(5,𝔽₂)×C₆₇	C₂³	semidirect
106. #137×C₆₇	D₄	semidirect
107. #137×C₆₇	D₄	semidirect
109. #137×C₆₇	C₂³	semidirect
123. AGL(1,ℤ/8)×C₆₇	D₄	semidirect
124. AGL(1,ℤ/8)×C₆₇	D₄	semidirect
127. AGL(1,ℤ/8)×C₆₇	C₂³	semidirect
128. AGL(1,ℤ/8)×C₆₇	C₂³	semidirect
142. #135×C₆₇	D₄	semidirect
143. #135×C₆₇	D₄	semidirect
148. C₂×Q₁₆×C₆₇	D₄	semidirect
149. C₂×Q₁₆×C₆₇	C₂³	semidirect
154. C₂×SD₁₆×C₆₇	D₄	semidirect
155. C₂×SD₁₆×C₆₇	C₂³	semidirect
156. C₂×SD₁₆×C₆₇	C₂³	semidirect
167. C₂×D₈×C₆₇	D₄	semidirect
170. C₂×D₈×C₆₇	C₂³	semidirect
171. C₂×D₈×C₆₇	C₂³	semidirect
179. #131×C₆₇	C₂³	semidirect
180. #131×C₆₇	C₂³	semidirect
181. #131×C₆₇	C₂³	semidirect
192. #127×C₆₇	C₂³	semidirect
193. #124×C₆₇	C₂³	semidirect
197. #108×C₆₇	C₂³	semidirect
198. #108×C₆₇	C₂³	semidirect
199. #108×C₆₇	C₂³	semidirect
201. #104×C₆₇	C₂³	semidirect
202. #104×C₆₇	C₂³	semidirect
203. #101×C₆₇	C₂³	semidirect
204. #100×C₆₇	C₂³	semidirect
205. #100×C₆₇	C₂³	semidirect
206. #97×C₆₇	C₂³	semidirect
207. C₄×C₈×C₆₇	C₂³	semidirect
454. #61106	C₆₇	direct (N × H)
464. #3585	C₂×C₆₇	semidirect
465. #3584	C₂×C₆₇	semidirect
466. C₂×#576	C₂×C₆₇	semidirect
467. #3292	C₂×C₆₇	semidirect
468. #3290	C₂×C₆₇	semidirect
469. #3288	C₂×C₆₇	semidirect
470. #3155	C₂×C₆₇	semidirect
471. #3068	C₂×C₆₇	semidirect
472. #3067	C₂×C₆₇	semidirect
473. C₂×#472	C₂×C₆₇	semidirect
474. #3021	C₂×C₆₇	semidirect
475. #3019	C₂×C₆₇	semidirect
476. #2957	C₂×C₆₇	semidirect
477. #2955	C₂×C₆₇	semidirect
478. C₆₇	#61106	direct (N × H)
479. #585	C₂²×C₆₇	semidirect
480. C₂×H(5,𝔽₂)	C₂²×C₆₇	semidirect
482. #578	C₂²×C₆₇	semidirect
485. #577	C₂²×C₆₇	semidirect
486. #577	C₂²×C₆₇	semidirect
491. #576	C₂²×C₆₇	semidirect
492. #576	C₂²×C₆₇	semidirect
493. #576	C₂²×C₆₇	semidirect
494. #576	C₂²×C₆₇	semidirect
498. #575	C₂²×C₆₇	semidirect
499. #575	C₂²×C₆₇	semidirect
502. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
503. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
504. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
508. C₂×#135	C₂²×C₆₇	semidirect
510. C₂²×D₈	C₂²×C₆₇	semidirect
511. #568	C₂²×C₆₇	semidirect
512. C₂×#131	C₂²×C₆₇	semidirect
513. C₂×#131	C₂²×C₆₇	semidirect
514. #535	C₂²×C₆₇	semidirect
515. #496	C₂²×C₆₇	semidirect
516. #495	C₂²×C₆₇	semidirect
517. #493	C₂²×C₆₇	semidirect
518. #473	C₂²×C₆₇	semidirect
519. #472	C₂²×C₆₇	semidirect
520. #472	C₂²×C₆₇	semidirect
521. #472	C₂²×C₆₇	semidirect
522. #472	C₂²×C₆₇	semidirect
523. #471	C₂²×C₆₇	semidirect
524. #471	C₂²×C₆₇	semidirect
525. #455	C₂²×C₆₇	semidirect
526. #454	C₂²×C₆₇	semidirect
527. #453	C₂²×C₆₇	semidirect
528. #453	C₂²×C₆₇	semidirect
529. #444	C₂²×C₆₇	semidirect
530. #444	C₂²×C₆₇	semidirect
531. #443	C₂²×C₆₇	semidirect
532. #443	C₂²×C₆₇	semidirect
533. #430	C₂²×C₆₇	semidirect
534. C₂×#108	C₂²×C₆₇	semidirect
535. #421	C₂²×C₆₇	semidirect
536. #421	C₂²×C₆₇	semidirect
537. #421	C₂²×C₆₇	semidirect
538. #413	C₂²×C₆₇	semidirect
539. C₂×#100	C₂²×C₆₇	semidirect
540. #405	C₂²×C₆₇	semidirect
543. 2₋¹⁺⁴	C₂³×C₆₇	semidirect
551. H(5,𝔽₂)	C₂³×C₆₇	semidirect
570. #137	D₄×C₆₇	semidirect
571. #137	D₄×C₆₇	semidirect
573. #137	C₂³×C₆₇	semidirect
587. AGL(1,ℤ/8)	D₄×C₆₇	semidirect
588. AGL(1,ℤ/8)	D₄×C₆₇	semidirect
591. AGL(1,ℤ/8)	C₂³×C₆₇	semidirect
592. AGL(1,ℤ/8)	C₂³×C₆₇	semidirect
606. #135	D₄×C₆₇	semidirect
607. #135	D₄×C₆₇	semidirect
612. C₂×Q₁₆	D₄×C₆₇	semidirect
613. C₂×Q₁₆	C₂³×C₆₇	semidirect
618. C₂×SD₁₆	D₄×C₆₇	semidirect
619. C₂×SD₁₆	C₂³×C₆₇	semidirect
620. C₂×SD₁₆	C₂³×C₆₇	semidirect
631. C₂×D₈	D₄×C₆₇	semidirect
634. C₂×D₈	C₂³×C₆₇	semidirect
635. C₂×D₈	C₂³×C₆₇	semidirect
643. #131	C₂³×C₆₇	semidirect
644. #131	C₂³×C₆₇	semidirect
645. #131	C₂³×C₆₇	semidirect
656. #127	C₂³×C₆₇	semidirect
657. #124	C₂³×C₆₇	semidirect
661. #108	C₂³×C₆₇	semidirect
662. #108	C₂³×C₆₇	semidirect
663. #108	C₂³×C₆₇	semidirect
665. #104	C₂³×C₆₇	semidirect
666. #104	C₂³×C₆₇	semidirect
667. #101	C₂³×C₆₇	semidirect
668. #100	C₂³×C₆₇	semidirect
669. #100	C₂³×C₆₇	semidirect
670. #97	C₂³×C₆₇	semidirect
671. 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×#3585	2
C₆₇×#3584	2
C₂×#576×C₆₇	2
C₆₇×#3292	2
C₆₇×#3290	2
C₆₇×#3288	2
C₆₇×#3155	2
C₆₇×#3068	2
C₆₇×#3067	2
C₂×#472×C₆₇	2
C₆₇×#3021	2
C₆₇×#3019	2
C₆₇×#2957	2
C₆₇×#2955	2
#61106	67

Subgroups — C67×#61106 #30740357

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61106 #30740357