Subgroups — C₆₇×#61082 #30740333

Order 17152.

2810 conjugacy classes of subgroups.

The subgroup lattice has 1110 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#577×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#576×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3498	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3271	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3268	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3265	C₂	1	4	yes	maximal, complemented
8	C₆₇×#3264	C₂	1	4	yes	maximal, complemented
9	C₂×#496×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3058	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3057	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3040	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3038	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3010	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3009	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3008	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3008	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2943	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2932	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic, complemented
21	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic, complemented
23	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic, complemented
24	#577×C₆₇	—	2	8	no	—
25	#576×C₆₇	—	2	8	no	—
26	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
28	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
30	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
32	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
34	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
36	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
37	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
38	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
41	C₂²×D₈×C₆₇	C₂²	1	2	yes	complemented
42	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
44	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	#550×C₆₇	C₂²	1	4	yes	complemented
46	#548×C₆₇	C₂²	1	4	yes	complemented
47	#546×C₆₇	—	2	4	no	—
48	#546×C₆₇	C₂²	1	4	yes	complemented
49	D₄²×C₆₇	—	2	4	no	—
50	D₄²×C₆₇	C₂²	1	4	yes	complemented
51	#536×C₆₇	—	2	1	no	—
52	#536×C₆₇	C₂²	1	1	yes	characteristic, complemented
53	#535×C₆₇	—	2	1	no	—
54	#535×C₆₇	—	2	1	no	—
55	#535×C₆₇	—	2	1	no	—
56	#535×C₆₇	C₂²	1	1	yes	characteristic
57	#535×C₆₇	C₂²	1	1	yes	characteristic, complemented
58	#535×C₆₇	C₂²	1	1	yes	characteristic, complemented
59	#532×C₆₇	—	2	1	no	—
60	#532×C₆₇	—	2	1	no	—
61	#532×C₆₇	C₂²	1	1	yes	characteristic
62	C₂×#127×C₆₇	—	2	1	no	—
63	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic, complemented
64	C₂×#124×C₆₇	—	2	1	no	—
65	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
66	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	#496×C₆₇	C₂²	1	4	yes	complemented
69	#496×C₆₇	C₂²	1	4	yes	complemented
70	#469×C₆₇	C₂²	1	4	yes	complemented
71	#468×C₆₇	C₂²	1	4	yes	complemented
72	#466×C₆₇	C₂²	1	4	yes	complemented
73	#465×C₆₇	C₂²	1	4	yes	complemented
74	#464×C₆₇	C₂²	1	4	yes	complemented
75	#463×C₆₇	C₂²	1	4	yes	complemented
76	#460×C₆₇	C₂²	1	4	yes	complemented
77	#459×C₆₇	C₂²	1	4	yes	complemented
78	#452×C₆₇	C₂²	1	4	yes	complemented
79	#450×C₆₇	C₂²	1	4	yes	complemented
80	#449×C₆₇	C₂²	1	4	yes	complemented
81	#449×C₆₇	C₂²	1	4	yes	complemented
82	#449×C₆₇	C₂²	1	4	yes	complemented
83	#448×C₆₇	C₂²	1	4	yes	complemented
84	#447×C₆₇	C₂²	1	4	yes	complemented
85	#447×C₆₇	C₂²	1	4	yes	complemented
86	#442×C₆₇	C₂²	1	2	yes	complemented
87	#441×C₆₇	C₂²	1	2	yes	complemented
88	#440×C₆₇	C₂²	1	2	yes	complemented
89	#440×C₆₇	C₂²	1	2	yes	complemented
90	#435×C₆₇	C₂²	1	4	yes	complemented
91	#435×C₆₇	C₂²	1	4	yes	complemented
92	#427×C₆₇	C₂²	1	1	yes	characteristic, complemented
93	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
94	#419×C₆₇	C₂²	1	1	yes	characteristic, complemented
95	#418×C₆₇	C₂²	1	1	yes	characteristic, complemented
96	#418×C₆₇	C₂²	1	1	yes	characteristic, complemented
97	#418×C₆₇	C₂²	1	1	yes	characteristic, complemented
98	#416×C₆₇	C₂²	1	1	yes	characteristic, complemented
99	#416×C₆₇	C₂²	1	1	yes	characteristic, complemented
100	#408×C₆₇	C₂²	1	1	yes	characteristic, complemented
101	#408×C₆₇	C₂²	1	1	yes	characteristic, complemented
102	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic, complemented
103	2₋¹⁺⁴×C₆₇	—	2	4	no	—
104	2₋¹⁺⁴×C₆₇	—	4	2	no	—
105	H(5,𝔽₂)×C₆₇	—	2	4	no	—
106	H(5,𝔽₂)×C₆₇	—	2	4	no	—
107	H(5,𝔽₂)×C₆₇	—	2	4	no	—
108	H(5,𝔽₂)×C₆₇	—	4	2	no	—
109	H(5,𝔽₂)×C₆₇	—	4	2	no	—
110	H(5,𝔽₂)×C₆₇	—	4	2	no	—
111	C₂×#41×C₆₇	—	2	1	no	—
112	C₂×#41×C₆₇	—	2	1	no	—
113	C₂×#41×C₆₇	—	2	1	no	—
114	C₂×#41×C₆₇	—	2	1	no	—
115	C₂×#41×C₆₇	—	2	2	no	—
116	C₂×#41×C₆₇	C₂³	1	2	yes	—
117	C₂×#41×C₆₇	C₂³	1	2	yes	—
118	C₂×#41×C₆₇	C₂³	1	2	yes	—
119	C₂×#41×C₆₇	C₂³	1	2	yes	—
120	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
121	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
122	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
123	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₆₇	—	2	1	no	—
125	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
126	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
127	C₂²×D₄×C₆₇	—	2	1	no	—
128	C₂²×D₄×C₆₇	—	2	1	no	—
129	C₂²×D₄×C₆₇	—	2	1	no	—
130	C₂²×D₄×C₆₇	—	2	2	no	—
131	C₂²×D₄×C₆₇	—	2	2	no	—
132	C₂²×D₄×C₆₇	—	2	2	no	—
133	C₂²×D₄×C₆₇	—	2	4	no	—
134	C₂²×D₄×C₆₇	—	2	2	no	—
135	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
136	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
137	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
139	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
140	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
141	#137×C₆₇	—	2	4	no	—
142	#137×C₆₇	—	2	8	no	—
143	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
144	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
145	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
146	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
147	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
148	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
149	#135×C₆₇	—	2	8	no	—
150	#135×C₆₇	—	2	8	no	—
151	#135×C₆₇	D₄	1	8	yes	complemented
152	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
153	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
154	C₂×SD₁₆×C₆₇	—	2	8	no	—
155	C₂×SD₁₆×C₆₇	—	2	4	no	—
156	C₂×SD₁₆×C₆₇	—	4	2	no	—
157	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
162	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
163	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
164	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
165	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
166	C₂×D₈×C₆₇	—	2	8	no	—
167	C₂×D₈×C₆₇	—	2	4	no	—
168	C₂×D₈×C₆₇	—	4	2	no	—
169	C₂×D₈×C₆₇	C₂³	1	2	yes	—
170	C₂×D₈×C₆₇	C₂³	1	2	yes	—
171	C₂×D₈×C₆₇	C₂³	1	2	yes	—
172	C₂×D₈×C₆₇	C₂³	1	2	yes	—
173	C₂×D₈×C₆₇	C₂³	1	2	yes	—
174	C₂×D₈×C₆₇	C₂³	1	4	yes	—
175	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
176	#131×C₆₇	—	2	4	no	—
177	#131×C₆₇	—	2	4	no	—
178	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
179	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
180	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
181	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
182	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
183	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
184	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
185	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
186	C₄⋊Q₈×C₆₇	—	2	1	no	—
187	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
188	#127×C₆₇	—	2	1	no	—
189	#127×C₆₇	—	2	1	no	—
190	#127×C₆₇	—	2	4	no	—
191	#127×C₆₇	—	2	1	no	—
192	#127×C₆₇	—	2	1	no	—
193	#127×C₆₇	—	2	1	no	—
194	#127×C₆₇	D₄	1	1	yes	characteristic
195	#127×C₆₇	C₂³	1	4	yes	—
196	#124×C₆₇	—	2	1	no	—
197	#124×C₆₇	—	2	1	no	—
198	#124×C₆₇	—	2	1	no	—
199	#124×C₆₇	—	2	1	no	—
200	#124×C₆₇	—	2	4	no	—
201	#124×C₆₇	—	2	1	no	—
202	#124×C₆₇	—	2	1	no	—
203	#124×C₆₇	D₄	1	1	yes	characteristic
204	#124×C₆₇	D₄	1	1	yes	characteristic
205	#124×C₆₇	C₂³	1	4	yes	—
206	#123×C₆₇	—	2	2	no	—
207	#123×C₆₇	—	2	4	no	—
208	C₂²⋊Q₈×C₆₇	—	2	4	no	—
209	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
210	#121×C₆₇	—	2	4	no	—
211	#121×C₆₇	—	2	4	no	—
212	#121×C₆₇	—	2	4	no	—
213	#121×C₆₇	—	2	4	no	—
214	#121×C₆₇	—	2	4	no	—
215	#121×C₆₇	D₄	1	4	yes	—
216	#121×C₆₇	C₂³	1	4	yes	—
217	#121×C₆₇	C₂³	1	4	yes	—
218	#121×C₆₇	C₂³	1	4	yes	—
219	#120×C₆₇	—	2	4	no	—
220	#120×C₆₇	—	2	2	no	—
221	#120×C₆₇	—	2	2	no	—
222	#120×C₆₇	—	2	2	no	—
223	#120×C₆₇	—	2	4	no	—
224	#120×C₆₇	—	2	4	no	—
225	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
226	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
227	C₄×D₄×C₆₇	—	2	2	no	—
228	C₄×D₄×C₆₇	—	2	2	no	—
229	C₄×D₄×C₆₇	—	2	4	no	—
230	C₄×D₄×C₆₇	—	2	4	no	—
231	C₄×D₄×C₆₇	C₂³	1	2	yes	—
232	C₄×D₄×C₆₇	C₂³	1	2	yes	—
233	C₄×D₄×C₆₇	C₂³	1	4	yes	—
234	#117×C₆₇	—	2	1	no	—
235	#117×C₆₇	—	2	1	no	—
236	#117×C₆₇	C₂³	1	1	yes	characteristic
237	#117×C₆₇	C₂³	1	1	yes	characteristic
238	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
239	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
240	C₂×C₄²×C₆₇	—	2	1	no	—
241	C₂×C₄²×C₆₇	—	2	1	no	—
242	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
243	#107×C₆₇	C₂³	1	2	yes	—
244	#106×C₆₇	C₂³	1	2	yes	—
245	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
246	#103×C₆₇	C₂³	1	2	yes	—
247	#103×C₆₇	C₂³	1	4	yes	—
248	#103×C₆₇	C₂³	1	2	yes	—
249	#102×C₆₇	C₂³	1	2	yes	—
250	#102×C₆₇	C₂³	1	4	yes	—
251	#102×C₆₇	C₂³	1	4	yes	—
252	#102×C₆₇	C₂³	1	2	yes	—
253	#102×C₆₇	C₂³	1	4	yes	—
254	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
255	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
256	#97×C₆₇	C₂³	1	2	yes	—
257	#97×C₆₇	C₂³	1	2	yes	—
258	C₂⁴×C₆₇	—	2	2	no	—
259	C₂⁴×C₆₇	—	2	1	no	—
260	C₂⁴×C₆₇	—	2	2	no	—
261	C₂⁴×C₆₇	—	2	2	no	—
262	C₂⁴×C₆₇	—	2	1	no	—
263	C₂⁴×C₆₇	—	2	1	no	—
264	#41×C₆₇	—	2	2	no	—
265	#41×C₆₇	—	2	2	no	—
266	#41×C₆₇	—	2	2	no	—
267	#41×C₆₇	—	2	2	no	—
268	#41×C₆₇	—	2	2	no	—
269	#41×C₆₇	—	2	2	no	—
270	#41×C₆₇	—	2	4	no	—
271	#41×C₆₇	—	2	4	no	—
272	#41×C₆₇	—	2	4	no	—
273	#41×C₆₇	—	2	4	no	—
274	#41×C₆₇	—	4	2	no	—
275	#41×C₆₇	—	4	2	no	—
276	#41×C₆₇	—	4	2	no	—
277	#41×C₆₇	—	4	2	no	—
278	#41×C₆₇	—	4	4	no	—
279	#41×C₆₇	—	4	4	no	—
280	#41×C₆₇	—	4	4	no	—
281	#41×C₆₇	—	4	4	no	—
282	#41×C₆₇	—	4	8	no	—
283	#41×C₆₇	C₂×D₄	1	4	yes	—
284	#41×C₆₇	C₂×D₄	1	4	yes	complemented
285	C₂×Q₈×C₆₇	—	2	2	no	—
286	C₂×Q₈×C₆₇	—	2	1	no	—
287	C₂×Q₈×C₆₇	—	2	4	no	—
288	C₂×Q₈×C₆₇	—	2	2	no	—
289	C₂×Q₈×C₆₇	—	2	2	no	—
290	C₂×Q₈×C₆₇	—	4	2	no	—
291	C₂×Q₈×C₆₇	—	4	4	no	—
292	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
293	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
294	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
295	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
296	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
297	C₂×D₄×C₆₇	—	2	1	no	—
298	C₂×D₄×C₆₇	—	2	1	no	—
299	C₂×D₄×C₆₇	—	2	4	no	—
300	C₂×D₄×C₆₇	—	2	4	no	—
301	C₂×D₄×C₆₇	—	2	4	no	—
302	C₂×D₄×C₆₇	—	2	2	no	—
303	C₂×D₄×C₆₇	—	2	2	no	—
304	C₂×D₄×C₆₇	—	2	2	no	—
305	C₂×D₄×C₆₇	—	2	2	no	—
306	C₂×D₄×C₆₇	—	2	4	no	—
307	C₂×D₄×C₆₇	—	2	4	no	—
308	C₂×D₄×C₆₇	—	2	4	no	—
309	C₂×D₄×C₆₇	—	2	2	no	—
310	C₂×D₄×C₆₇	—	2	2	no	—
311	C₂×D₄×C₆₇	—	2	2	no	—
312	C₂×D₄×C₆₇	—	2	4	no	—
313	C₂×D₄×C₆₇	—	2	2	no	—
314	C₂×D₄×C₆₇	—	2	2	no	—
315	C₂×D₄×C₆₇	—	2	2	no	—
316	C₂×D₄×C₆₇	—	2	1	no	—
317	C₂×D₄×C₆₇	—	2	1	no	—
318	C₂×D₄×C₆₇	—	2	1	no	—
319	C₂×D₄×C₆₇	—	2	4	no	—
320	C₂×D₄×C₆₇	—	2	2	no	—
321	C₂×D₄×C₆₇	—	2	2	no	—
322	C₂×D₄×C₆₇	—	2	2	no	—
323	C₂×D₄×C₆₇	—	4	2	no	—
324	C₂×D₄×C₆₇	—	4	2	no	—
325	C₂×D₄×C₆₇	—	4	2	no	—
326	C₂×D₄×C₆₇	—	4	4	no	—
327	C₂×D₄×C₆₇	—	4	4	no	—
328	C₂×D₄×C₆₇	—	4	4	no	—
329	C₂×D₄×C₆₇	—	4	8	no	—
330	C₂×D₄×C₆₇	—	4	8	no	—
331	C₂×D₄×C₆₇	—	4	8	no	—
332	C₂×D₄×C₆₇	—	8	4	no	—
333	C₂×D₄×C₆₇	—	8	8	no	—
334	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
335	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
336	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
337	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
338	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
339	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
340	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
341	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
342	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
343	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₆₇	—	2	1	no	—
345	C₂²×C₄×C₆₇	—	2	1	no	—
346	C₂²×C₄×C₆₇	—	2	1	no	—
347	C₂²×C₄×C₆₇	—	2	2	no	—
348	C₂²×C₄×C₆₇	—	2	2	no	—
349	C₂²×C₄×C₆₇	—	2	2	no	—
350	C₂²×C₄×C₆₇	—	2	2	no	—
351	C₂²×C₄×C₆₇	—	2	2	no	—
352	C₂²×C₄×C₆₇	—	2	2	no	—
353	C₂²×C₄×C₆₇	—	2	2	no	—
354	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
355	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
356	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
357	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
358	Q₁₆×C₆₇	—	2	4	no	—
359	Q₁₆×C₆₇	C₂×D₄	1	4	yes	complemented
360	SD₁₆×C₆₇	—	2	4	no	—
361	SD₁₆×C₆₇	—	2	4	no	—
362	SD₁₆×C₆₇	—	2	4	no	—
363	SD₁₆×C₆₇	—	2	4	no	—
364	SD₁₆×C₆₇	—	2	4	no	—
365	SD₁₆×C₆₇	—	2	4	no	—
366	SD₁₆×C₆₇	—	4	4	no	—
367	SD₁₆×C₆₇	C₂×D₄	1	4	yes	complemented
368	SD₁₆×C₆₇	C₂×D₄	1	4	yes	complemented
369	D₈×C₆₇	—	2	4	no	—
370	D₈×C₆₇	—	2	4	no	—
371	D₈×C₆₇	—	2	4	no	—
372	D₈×C₆₇	—	2	4	no	—
373	D₈×C₆₇	—	2	4	no	—
374	D₈×C₆₇	—	4	4	no	—
375	D₈×C₆₇	C₂×D₄	1	4	yes	complemented
376	M₁₆×C₆₇	—	2	2	no	—
377	M₁₆×C₆₇	—	2	2	no	—
378	M₁₆×C₆₇	—	2	4	no	—
379	M₁₆×C₆₇	—	2	4	no	—
380	C₂×C₈×C₆₇	—	2	2	no	—
381	C₂×C₈×C₆₇	—	2	4	no	—
382	C₂×C₈×C₆₇	—	2	4	no	—
383	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	complemented
384	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
385	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
386	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
387	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
389	C₄⋊C₄×C₆₇	—	2	2	no	—
390	C₄⋊C₄×C₆₇	—	2	2	no	—
391	C₄⋊C₄×C₆₇	—	2	4	no	—
392	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
393	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
394	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
395	C₂²⋊C₄×C₆₇	—	2	4	no	—
396	C₂²⋊C₄×C₆₇	—	2	1	no	—
397	C₂²⋊C₄×C₆₇	—	2	1	no	—
398	C₂²⋊C₄×C₆₇	—	2	4	no	—
399	C₂²⋊C₄×C₆₇	—	2	4	no	—
400	C₂²⋊C₄×C₆₇	—	2	4	no	—
401	C₂²⋊C₄×C₆₇	—	2	2	no	—
402	C₂²⋊C₄×C₆₇	—	2	2	no	—
403	C₂²⋊C₄×C₆₇	—	2	4	no	—
404	C₂²⋊C₄×C₆₇	—	2	4	no	—
405	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
406	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
407	C₄²×C₆₇	—	2	1	no	—
408	C₄²×C₆₇	—	2	1	no	—
409	C₄²×C₆₇	—	2	2	no	—
410	C₄²×C₆₇	—	2	2	no	—
411	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
412	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
413	C₄²×C₆₇	C₂⁴	1	2	yes	—
414	C₂³×C₆₇	—	2	1	no	—
415	C₂³×C₆₇	—	2	1	no	—
416	C₂³×C₆₇	—	2	2	no	—
417	C₂³×C₆₇	—	2	2	no	—
418	C₂³×C₆₇	—	2	2	no	—
419	C₂³×C₆₇	—	4	4	no	—
420	C₂³×C₆₇	—	4	4	no	—
421	C₂³×C₆₇	—	4	4	no	—
422	C₂³×C₆₇	—	4	2	no	—
423	C₂³×C₆₇	—	4	2	no	—
424	C₂³×C₆₇	—	4	2	no	—
425	C₂³×C₆₇	—	8	2	no	—
426	C₂³×C₆₇	—	8	2	no	—
427	C₂³×C₆₇	—	8	4	no	—
428	C₂³×C₆₇	—	8	4	no	—
429	C₂³×C₆₇	—	8	2	no	—
430	C₂³×C₆₇	—	8	4	no	—
431	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
432	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
433	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
434	Q₈×C₆₇	—	2	2	no	—
435	Q₈×C₆₇	—	2	2	no	—
436	Q₈×C₆₇	—	2	1	no	—
437	Q₈×C₆₇	—	2	1	no	—
438	Q₈×C₆₇	—	2	2	no	—
439	Q₈×C₆₇	—	2	2	no	—
440	Q₈×C₆₇	—	4	4	no	—
441	Q₈×C₆₇	—	4	2	no	—
442	Q₈×C₆₇	C₂²×D₄	1	2	yes	—
443	Q₈×C₆₇	C₂²×D₄	1	2	yes	—
444	D₄×C₆₇	—	2	4	no	—
445	D₄×C₆₇	—	2	4	no	—
446	D₄×C₆₇	—	2	4	no	—
447	D₄×C₆₇	—	2	4	no	—
448	D₄×C₆₇	—	2	2	no	—
449	D₄×C₆₇	—	2	2	no	—
450	D₄×C₆₇	—	2	2	no	—
451	D₄×C₆₇	—	2	2	no	—
452	D₄×C₆₇	—	2	2	no	—
453	D₄×C₆₇	—	2	1	no	—
454	D₄×C₆₇	—	2	1	no	—
455	D₄×C₆₇	—	2	2	no	—
456	D₄×C₆₇	—	2	2	no	—
457	D₄×C₆₇	—	2	2	no	—
458	D₄×C₆₇	—	4	4	no	—
459	D₄×C₆₇	—	4	4	no	—
460	D₄×C₆₇	—	4	4	no	—
461	D₄×C₆₇	—	4	4	no	—
462	D₄×C₆₇	—	4	4	no	—
463	D₄×C₆₇	—	4	4	no	—
464	D₄×C₆₇	—	4	4	no	—
465	D₄×C₆₇	—	4	8	no	—
466	D₄×C₆₇	—	4	4	no	—
467	D₄×C₆₇	—	4	2	no	—
468	D₄×C₆₇	—	4	2	no	—
469	D₄×C₆₇	—	4	2	no	—
470	D₄×C₆₇	—	8	4	no	—
471	D₄×C₆₇	—	8	4	no	—
472	D₄×C₆₇	—	8	4	no	—
473	D₄×C₆₇	—	8	4	no	—
474	D₄×C₆₇	C₂²×D₄	1	2	yes	—
475	D₄×C₆₇	C₂²×D₄	1	2	yes	—
476	C₂×C₄×C₆₇	—	2	1	no	—
477	C₂×C₄×C₆₇	—	2	1	no	—
478	C₂×C₄×C₆₇	—	2	4	no	—
479	C₂×C₄×C₆₇	—	2	4	no	—
480	C₂×C₄×C₆₇	—	2	2	no	—
481	C₂×C₄×C₆₇	—	2	2	no	—
482	C₂×C₄×C₆₇	—	2	2	no	—
483	C₂×C₄×C₆₇	—	2	2	no	—
484	C₂×C₄×C₆₇	—	2	2	no	—
485	C₂×C₄×C₆₇	—	2	2	no	—
486	C₂×C₄×C₆₇	—	2	2	no	—
487	C₂×C₄×C₆₇	—	4	2	no	—
488	C₂×C₄×C₆₇	—	4	4	no	—
489	C₂×C₄×C₆₇	—	4	4	no	—
490	C₂×C₄×C₆₇	—	4	4	no	—
491	C₂×C₄×C₆₇	—	4	4	no	—
492	C₂×C₄×C₆₇	—	4	4	no	—
493	C₂×C₄×C₆₇	—	4	4	no	—
494	C₂×C₄×C₆₇	—	4	2	no	—
495	C₂×C₄×C₆₇	—	8	2	no	—
496	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
497	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
498	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
499	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
500	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
502	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
503	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
504	C₈×C₆₇	—	2	2	no	—
505	C₈×C₆₇	—	2	2	no	—
506	C₈×C₆₇	—	2	2	no	—
507	C₈×C₆₇	C₂²×D₄	1	2	yes	—
508	C₈×C₆₇	C₂²×D₄	1	2	yes	—
509	C₂²×C₆₇	—	2	2	no	—
510	C₂²×C₆₇	—	2	4	no	—
511	C₂²×C₆₇	—	2	4	no	—
512	C₂²×C₆₇	—	2	2	no	—
513	C₂²×C₆₇	—	2	2	no	—
514	C₂²×C₆₇	—	2	2	no	—
515	C₂²×C₆₇	—	2	2	no	—
516	C₂²×C₆₇	—	4	2	no	—
517	C₂²×C₆₇	—	4	2	no	—
518	C₂²×C₆₇	—	4	4	no	—
519	C₂²×C₆₇	—	4	4	no	—
520	C₂²×C₆₇	—	4	4	no	—
521	C₂²×C₆₇	—	4	2	no	—
522	C₂²×C₆₇	—	4	2	no	—
523	C₂²×C₆₇	—	4	2	no	—
524	C₂²×C₆₇	—	16	2	no	—
525	C₂²×C₆₇	—	16	2	no	—
526	C₂²×C₆₇	—	16	2	no	—
527	C₂²×C₆₇	—	16	4	no	—
528	C₂²×C₆₇	—	16	4	no	—
529	C₂²×C₆₇	—	16	4	no	—
530	C₂²×C₆₇	D₄²	1	2	yes	—
531	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
532	C₄×C₆₇	—	2	2	no	—
533	C₄×C₆₇	—	2	2	no	—
534	C₄×C₆₇	—	2	2	no	—
535	C₄×C₆₇	—	2	2	no	—
536	C₄×C₆₇	—	2	2	no	—
537	C₄×C₆₇	—	2	2	no	—
538	C₄×C₆₇	—	4	2	no	—
539	C₄×C₆₇	—	4	2	no	—
540	C₄×C₆₇	—	4	2	no	—
541	C₄×C₆₇	D₄²	1	2	yes	—
542	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
543	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
544	#61082	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
545	C₂×C₆₇	—	2	2	no	—
546	C₂×C₆₇	—	4	2	no	—
547	C₂×C₆₇	—	4	2	no	—
548	C₂×C₆₇	—	4	2	no	—
549	C₂×C₆₇	—	4	2	no	—
550	C₂×C₆₇	—	8	2	no	—
551	C₂×C₆₇	—	8	2	no	—
552	C₂×C₆₇	—	8	2	no	—
553	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
554	C₂×C₆₇	#3585	1	2	yes	—
555	C₂×#577	C₂×C₆₇	1	1	yes	characteristic, complemented
556	C₂×#576	C₂×C₆₇	1	1	yes	characteristic, complemented
557	#3500	C₂×C₆₇	1	1	yes	characteristic, complemented
558	#3498	C₂×C₆₇	1	1	yes	characteristic, complemented
559	#3271	C₂×C₆₇	1	4	yes	complemented
560	#3268	C₂×C₆₇	1	4	yes	complemented
561	#3265	C₂×C₆₇	1	4	yes	complemented
562	#3264	C₂×C₆₇	1	4	yes	complemented
563	C₂×#496	C₂×C₆₇	1	1	yes	characteristic, complemented
564	#3058	C₂×C₆₇	1	1	yes	characteristic, complemented
565	#3057	C₂×C₆₇	1	1	yes	characteristic, complemented
566	#3040	C₂×C₆₇	1	1	yes	characteristic, complemented
567	#3038	C₂×C₆₇	1	1	yes	characteristic, complemented
568	#3010	C₂×C₆₇	1	1	yes	characteristic, complemented
569	#3009	C₂×C₆₇	1	1	yes	characteristic, complemented
570	#3008	C₂×C₆₇	1	1	yes	characteristic, complemented
571	#3008	C₂×C₆₇	1	1	yes	characteristic, complemented
572	#2943	C₂×C₆₇	1	1	yes	characteristic, complemented
573	#2932	C₂×C₆₇	1	1	yes	characteristic, complemented
574	C₆₇	#61082	1	1	yes	characteristic, direct product factor, Sylow
575	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic, complemented
576	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic
577	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic, complemented
578	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic, complemented
579	#577	—	2	8	no	—
580	#576	—	2	8	no	—
581	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic, complemented
582	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
583	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
584	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic, complemented
585	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
586	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
587	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic, complemented
588	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
589	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
590	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
591	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
592	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
593	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
594	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
595	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
596	C₂²×D₈	C₂²×C₆₇	1	2	yes	complemented
597	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
598	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
599	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
600	#550	C₂²×C₆₇	1	4	yes	complemented
601	#548	C₂²×C₆₇	1	4	yes	complemented
602	#546	—	2	4	no	—
603	#546	C₂²×C₆₇	1	4	yes	complemented
604	D₄²	—	2	4	no	—
605	D₄²	C₂²×C₆₇	1	4	yes	complemented
606	#536	—	2	1	no	—
607	#536	C₂²×C₆₇	1	1	yes	characteristic, complemented
608	#535	—	2	1	no	—
609	#535	—	2	1	no	—
610	#535	—	2	1	no	—
611	#535	C₂²×C₆₇	1	1	yes	characteristic
612	#535	C₂²×C₆₇	1	1	yes	characteristic, complemented
613	#535	C₂²×C₆₇	1	1	yes	characteristic, complemented
614	#532	—	2	1	no	—
615	#532	—	2	1	no	—
616	#532	C₂²×C₆₇	1	1	yes	characteristic
617	C₂×#127	—	2	1	no	—
618	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic, complemented
619	C₂×#124	—	2	1	no	—
620	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
621	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
622	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
623	#496	C₂²×C₆₇	1	4	yes	complemented
624	#496	C₂²×C₆₇	1	4	yes	complemented
625	#469	C₂²×C₆₇	1	4	yes	complemented
626	#468	C₂²×C₆₇	1	4	yes	complemented
627	#466	C₂²×C₆₇	1	4	yes	complemented
628	#465	C₂²×C₆₇	1	4	yes	complemented
629	#464	C₂²×C₆₇	1	4	yes	complemented
630	#463	C₂²×C₆₇	1	4	yes	complemented
631	#460	C₂²×C₆₇	1	4	yes	complemented
632	#459	C₂²×C₆₇	1	4	yes	complemented
633	#452	C₂²×C₆₇	1	4	yes	complemented
634	#450	C₂²×C₆₇	1	4	yes	complemented
635	#449	C₂²×C₆₇	1	4	yes	complemented
636	#449	C₂²×C₆₇	1	4	yes	complemented
637	#449	C₂²×C₆₇	1	4	yes	complemented
638	#448	C₂²×C₆₇	1	4	yes	complemented
639	#447	C₂²×C₆₇	1	4	yes	complemented
640	#447	C₂²×C₆₇	1	4	yes	complemented
641	#442	C₂²×C₆₇	1	2	yes	complemented
642	#441	C₂²×C₆₇	1	2	yes	complemented
643	#440	C₂²×C₆₇	1	2	yes	complemented
644	#440	C₂²×C₆₇	1	2	yes	complemented
645	#435	C₂²×C₆₇	1	4	yes	complemented
646	#435	C₂²×C₆₇	1	4	yes	complemented
647	#427	C₂²×C₆₇	1	1	yes	characteristic, complemented
648	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
649	#419	C₂²×C₆₇	1	1	yes	characteristic, complemented
650	#418	C₂²×C₆₇	1	1	yes	characteristic, complemented
651	#418	C₂²×C₆₇	1	1	yes	characteristic, complemented
652	#418	C₂²×C₆₇	1	1	yes	characteristic, complemented
653	#416	C₂²×C₆₇	1	1	yes	characteristic, complemented
654	#416	C₂²×C₆₇	1	1	yes	characteristic, complemented
655	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
656	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
657	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic, complemented
658	2₋¹⁺⁴	—	2	4	no	—
659	2₋¹⁺⁴	—	4	2	no	—
660	H(5,𝔽₂)	—	2	4	no	—
661	H(5,𝔽₂)	—	2	4	no	—
662	H(5,𝔽₂)	—	2	4	no	—
663	H(5,𝔽₂)	—	4	2	no	—
664	H(5,𝔽₂)	—	4	2	no	—
665	H(5,𝔽₂)	—	4	2	no	—
666	C₂×#41	—	2	1	no	—
667	C₂×#41	—	2	1	no	—
668	C₂×#41	—	2	1	no	—
669	C₂×#41	—	2	1	no	—
670	C₂×#41	—	2	2	no	—
671	C₂×#41	C₂³×C₆₇	1	2	yes	—
672	C₂×#41	C₂³×C₆₇	1	2	yes	—
673	C₂×#41	C₂³×C₆₇	1	2	yes	—
674	C₂×#41	C₂³×C₆₇	1	2	yes	—
675	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
676	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
677	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
678	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
679	C₂²×Q₈	—	2	1	no	—
680	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
681	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
682	C₂²×D₄	—	2	1	no	—
683	C₂²×D₄	—	2	1	no	—
684	C₂²×D₄	—	2	1	no	—
685	C₂²×D₄	—	2	2	no	—
686	C₂²×D₄	—	2	2	no	—
687	C₂²×D₄	—	2	2	no	—
688	C₂²×D₄	—	2	4	no	—
689	C₂²×D₄	—	2	2	no	—
690	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
691	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
692	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
693	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
694	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
695	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
696	#137	—	2	4	no	—
697	#137	—	2	8	no	—
698	AGL(1,ℤ/8)	—	2	4	no	—
699	AGL(1,ℤ/8)	—	2	4	no	—
700	AGL(1,ℤ/8)	—	2	4	no	—
701	AGL(1,ℤ/8)	—	2	8	no	—
702	AGL(1,ℤ/8)	—	2	8	no	—
703	AGL(1,ℤ/8)	—	2	8	no	—
704	#135	—	2	8	no	—
705	#135	—	2	8	no	—
706	#135	D₄×C₆₇	1	8	yes	complemented
707	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
708	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
709	C₂×SD₁₆	—	2	8	no	—
710	C₂×SD₁₆	—	2	4	no	—
711	C₂×SD₁₆	—	4	2	no	—
712	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
713	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
714	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
715	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
716	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
717	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
718	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
719	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
720	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
721	C₂×D₈	—	2	8	no	—
722	C₂×D₈	—	2	4	no	—
723	C₂×D₈	—	4	2	no	—
724	C₂×D₈	C₂³×C₆₇	1	2	yes	—
725	C₂×D₈	C₂³×C₆₇	1	2	yes	—
726	C₂×D₈	C₂³×C₆₇	1	2	yes	—
727	C₂×D₈	C₂³×C₆₇	1	2	yes	—
728	C₂×D₈	C₂³×C₆₇	1	2	yes	—
729	C₂×D₈	C₂³×C₆₇	1	4	yes	—
730	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
731	#131	—	2	4	no	—
732	#131	—	2	4	no	—
733	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
734	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
735	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
736	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
737	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
738	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
739	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
740	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
741	C₄⋊Q₈	—	2	1	no	—
742	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
743	#127	—	2	1	no	—
744	#127	—	2	1	no	—
745	#127	—	2	4	no	—
746	#127	—	2	1	no	—
747	#127	—	2	1	no	—
748	#127	—	2	1	no	—
749	#127	D₄×C₆₇	1	1	yes	characteristic
750	#127	C₂³×C₆₇	1	4	yes	—
751	#124	—	2	1	no	—
752	#124	—	2	1	no	—
753	#124	—	2	1	no	—
754	#124	—	2	1	no	—
755	#124	—	2	4	no	—
756	#124	—	2	1	no	—
757	#124	—	2	1	no	—
758	#124	D₄×C₆₇	1	1	yes	characteristic
759	#124	D₄×C₆₇	1	1	yes	characteristic
760	#124	C₂³×C₆₇	1	4	yes	—
761	#123	—	2	2	no	—
762	#123	—	2	4	no	—
763	C₂²⋊Q₈	—	2	4	no	—
764	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
765	#121	—	2	4	no	—
766	#121	—	2	4	no	—
767	#121	—	2	4	no	—
768	#121	—	2	4	no	—
769	#121	—	2	4	no	—
770	#121	D₄×C₆₇	1	4	yes	—
771	#121	C₂³×C₆₇	1	4	yes	—
772	#121	C₂³×C₆₇	1	4	yes	—
773	#121	C₂³×C₆₇	1	4	yes	—
774	#120	—	2	4	no	—
775	#120	—	2	2	no	—
776	#120	—	2	2	no	—
777	#120	—	2	2	no	—
778	#120	—	2	4	no	—
779	#120	—	2	4	no	—
780	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
781	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
782	C₄×D₄	—	2	2	no	—
783	C₄×D₄	—	2	2	no	—
784	C₄×D₄	—	2	4	no	—
785	C₄×D₄	—	2	4	no	—
786	C₄×D₄	C₂³×C₆₇	1	2	yes	—
787	C₄×D₄	C₂³×C₆₇	1	2	yes	—
788	C₄×D₄	C₂³×C₆₇	1	4	yes	—
789	#117	—	2	1	no	—
790	#117	—	2	1	no	—
791	#117	C₂³×C₆₇	1	1	yes	characteristic
792	#117	C₂³×C₆₇	1	1	yes	characteristic
793	C₂×C₂²⋊C₄	—	2	2	no	—
794	C₂×C₂²⋊C₄	—	2	4	no	—
795	C₂×C₄²	—	2	1	no	—
796	C₂×C₄²	—	2	1	no	—
797	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
798	#107	C₂³×C₆₇	1	2	yes	—
799	#106	C₂³×C₆₇	1	2	yes	—
800	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
801	#103	C₂³×C₆₇	1	2	yes	—
802	#103	C₂³×C₆₇	1	2	yes	—
803	#103	C₂³×C₆₇	1	4	yes	—
804	#102	C₂³×C₆₇	1	2	yes	—
805	#102	C₂³×C₆₇	1	2	yes	—
806	#102	C₂³×C₆₇	1	4	yes	—
807	#102	C₂³×C₆₇	1	4	yes	—
808	#102	C₂³×C₆₇	1	4	yes	—
809	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
810	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
811	#97	C₂³×C₆₇	1	2	yes	—
812	#97	C₂³×C₆₇	1	2	yes	—
813	C₂⁴	—	2	2	no	—
814	C₂⁴	—	2	1	no	—
815	C₂⁴	—	2	2	no	—
816	C₂⁴	—	2	2	no	—
817	C₂⁴	—	2	1	no	—
818	C₂⁴	—	2	1	no	—
819	#41	—	2	2	no	—
820	#41	—	2	2	no	—
821	#41	—	2	2	no	—
822	#41	—	2	2	no	—
823	#41	—	2	2	no	—
824	#41	—	2	2	no	—
825	#41	—	2	4	no	—
826	#41	—	2	4	no	—
827	#41	—	2	4	no	—
828	#41	—	2	4	no	—
829	#41	—	4	2	no	—
830	#41	—	4	2	no	—
831	#41	—	4	2	no	—
832	#41	—	4	2	no	—
833	#41	—	4	4	no	—
834	#41	—	4	4	no	—
835	#41	—	4	4	no	—
836	#41	—	4	4	no	—
837	#41	—	4	8	no	—
838	#41	C₂×D₄×C₆₇	1	4	yes	—
839	#41	C₂×D₄×C₆₇	1	4	yes	complemented
840	C₂×Q₈	—	2	2	no	—
841	C₂×Q₈	—	2	1	no	—
842	C₂×Q₈	—	2	4	no	—
843	C₂×Q₈	—	2	2	no	—
844	C₂×Q₈	—	2	2	no	—
845	C₂×Q₈	—	4	2	no	—
846	C₂×Q₈	—	4	4	no	—
847	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
848	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
849	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
850	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
851	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
852	C₂×D₄	—	2	1	no	—
853	C₂×D₄	—	2	1	no	—
854	C₂×D₄	—	2	4	no	—
855	C₂×D₄	—	2	4	no	—
856	C₂×D₄	—	2	4	no	—
857	C₂×D₄	—	2	2	no	—
858	C₂×D₄	—	2	2	no	—
859	C₂×D₄	—	2	2	no	—
860	C₂×D₄	—	2	2	no	—
861	C₂×D₄	—	2	4	no	—
862	C₂×D₄	—	2	4	no	—
863	C₂×D₄	—	2	4	no	—
864	C₂×D₄	—	2	2	no	—
865	C₂×D₄	—	2	2	no	—
866	C₂×D₄	—	2	2	no	—
867	C₂×D₄	—	2	4	no	—
868	C₂×D₄	—	2	2	no	—
869	C₂×D₄	—	2	2	no	—
870	C₂×D₄	—	2	2	no	—
871	C₂×D₄	—	2	1	no	—
872	C₂×D₄	—	2	1	no	—
873	C₂×D₄	—	2	1	no	—
874	C₂×D₄	—	2	4	no	—
875	C₂×D₄	—	2	2	no	—
876	C₂×D₄	—	2	2	no	—
877	C₂×D₄	—	2	2	no	—
878	C₂×D₄	—	4	2	no	—
879	C₂×D₄	—	4	2	no	—
880	C₂×D₄	—	4	2	no	—
881	C₂×D₄	—	4	4	no	—
882	C₂×D₄	—	4	4	no	—
883	C₂×D₄	—	4	4	no	—
884	C₂×D₄	—	4	8	no	—
885	C₂×D₄	—	4	8	no	—
886	C₂×D₄	—	4	8	no	—
887	C₂×D₄	—	8	4	no	—
888	C₂×D₄	—	8	8	no	—
889	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
890	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
891	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
892	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
893	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
894	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
895	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
896	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
897	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
898	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
899	C₂²×C₄	—	2	1	no	—
900	C₂²×C₄	—	2	1	no	—
901	C₂²×C₄	—	2	1	no	—
902	C₂²×C₄	—	2	2	no	—
903	C₂²×C₄	—	2	2	no	—
904	C₂²×C₄	—	2	2	no	—
905	C₂²×C₄	—	2	2	no	—
906	C₂²×C₄	—	2	2	no	—
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
910	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
911	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
912	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
913	Q₁₆	—	2	4	no	—
914	Q₁₆	C₂×D₄×C₆₇	1	4	yes	complemented
915	SD₁₆	—	2	4	no	—
916	SD₁₆	—	2	4	no	—
917	SD₁₆	—	2	4	no	—
918	SD₁₆	—	2	4	no	—
919	SD₁₆	—	2	4	no	—
920	SD₁₆	—	2	4	no	—
921	SD₁₆	—	4	4	no	—
922	SD₁₆	C₂×D₄×C₆₇	1	4	yes	complemented
923	SD₁₆	C₂×D₄×C₆₇	1	4	yes	complemented
924	D₈	—	2	4	no	—
925	D₈	—	2	4	no	—
926	D₈	—	2	4	no	—
927	D₈	—	2	4	no	—
928	D₈	—	2	4	no	—
929	D₈	—	4	4	no	—
930	D₈	C₂×D₄×C₆₇	1	4	yes	complemented
931	M₁₆	—	2	2	no	—
932	M₁₆	—	2	2	no	—
933	M₁₆	—	2	4	no	—
934	M₁₆	—	2	4	no	—
935	C₂×C₈	—	2	2	no	—
936	C₂×C₈	—	2	4	no	—
937	C₂×C₈	—	2	4	no	—
938	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	complemented
939	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
940	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
941	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
942	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
943	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	4	no	—
947	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
948	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
949	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
950	C₂²⋊C₄	—	2	4	no	—
951	C₂²⋊C₄	—	2	1	no	—
952	C₂²⋊C₄	—	2	1	no	—
953	C₂²⋊C₄	—	2	4	no	—
954	C₂²⋊C₄	—	2	4	no	—
955	C₂²⋊C₄	—	2	4	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	2	4	no	—
959	C₂²⋊C₄	—	2	4	no	—
960	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
961	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
962	C₄²	—	2	1	no	—
963	C₄²	—	2	1	no	—
964	C₄²	—	2	2	no	—
965	C₄²	—	2	2	no	—
966	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
967	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
968	C₄²	C₂⁴×C₆₇	1	2	yes	—
969	C₂³	—	2	1	no	—
970	C₂³	—	2	1	no	—
971	C₂³	—	2	2	no	—
972	C₂³	—	2	2	no	—
973	C₂³	—	2	2	no	—
974	C₂³	—	4	4	no	—
975	C₂³	—	4	4	no	—
976	C₂³	—	4	4	no	—
977	C₂³	—	4	2	no	—
978	C₂³	—	4	2	no	—
979	C₂³	—	4	2	no	—
980	C₂³	—	8	2	no	—
981	C₂³	—	8	2	no	—
982	C₂³	—	8	4	no	—
983	C₂³	—	8	4	no	—
984	C₂³	—	8	2	no	—
985	C₂³	—	8	4	no	—
986	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
987	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
988	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
989	Q₈	—	2	2	no	—
990	Q₈	—	2	2	no	—
991	Q₈	—	2	1	no	—
992	Q₈	—	2	1	no	—
993	Q₈	—	2	2	no	—
994	Q₈	—	2	2	no	—
995	Q₈	—	4	4	no	—
996	Q₈	—	4	2	no	—
997	Q₈	C₂²×D₄×C₆₇	1	2	yes	—
998	Q₈	C₂²×D₄×C₆₇	1	2	yes	—
999	D₄	—	2	4	no	—
1000	D₄	—	2	4	no	—
1001	D₄	—	2	4	no	—
1002	D₄	—	2	4	no	—
1003	D₄	—	2	2	no	—
1004	D₄	—	2	2	no	—
1005	D₄	—	2	2	no	—
1006	D₄	—	2	2	no	—
1007	D₄	—	2	2	no	—
1008	D₄	—	2	1	no	—
1009	D₄	—	2	1	no	—
1010	D₄	—	2	2	no	—
1011	D₄	—	2	2	no	—
1012	D₄	—	2	2	no	—
1013	D₄	—	4	4	no	—
1014	D₄	—	4	4	no	—
1015	D₄	—	4	4	no	—
1016	D₄	—	4	4	no	—
1017	D₄	—	4	4	no	—
1018	D₄	—	4	4	no	—
1019	D₄	—	4	4	no	—
1020	D₄	—	4	8	no	—
1021	D₄	—	4	4	no	—
1022	D₄	—	4	2	no	—
1023	D₄	—	4	2	no	—
1024	D₄	—	4	2	no	—
1025	D₄	—	8	4	no	—
1026	D₄	—	8	4	no	—
1027	D₄	—	8	4	no	—
1028	D₄	—	8	4	no	—
1029	D₄	C₂²×D₄×C₆₇	1	2	yes	—
1030	D₄	C₂²×D₄×C₆₇	1	2	yes	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	4	no	—
1034	C₂×C₄	—	2	4	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	2	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	4	2	no	—
1043	C₂×C₄	—	4	4	no	—
1044	C₂×C₄	—	4	4	no	—
1045	C₂×C₄	—	4	4	no	—
1046	C₂×C₄	—	4	4	no	—
1047	C₂×C₄	—	4	4	no	—
1048	C₂×C₄	—	4	4	no	—
1049	C₂×C₄	—	4	2	no	—
1050	C₂×C₄	—	8	2	no	—
1051	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1052	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1053	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1054	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1055	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1056	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1057	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1058	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1059	C₈	—	2	2	no	—
1060	C₈	—	2	2	no	—
1061	C₈	—	2	2	no	—
1062	C₈	C₂²×D₄×C₆₇	1	2	yes	—
1063	C₈	C₂²×D₄×C₆₇	1	2	yes	—
1064	C₂²	—	2	2	no	—
1065	C₂²	—	2	4	no	—
1066	C₂²	—	2	4	no	—
1067	C₂²	—	2	2	no	—
1068	C₂²	—	2	2	no	—
1069	C₂²	—	2	2	no	—
1070	C₂²	—	2	2	no	—
1071	C₂²	—	4	2	no	—
1072	C₂²	—	4	2	no	—
1073	C₂²	—	4	4	no	—
1074	C₂²	—	4	4	no	—
1075	C₂²	—	4	4	no	—
1076	C₂²	—	4	2	no	—
1077	C₂²	—	4	2	no	—
1078	C₂²	—	4	2	no	—
1079	C₂²	—	16	2	no	—
1080	C₂²	—	16	2	no	—
1081	C₂²	—	16	2	no	—
1082	C₂²	—	16	4	no	—
1083	C₂²	—	16	4	no	—
1084	C₂²	—	16	4	no	—
1085	C₂²	D₄²×C₆₇	1	2	yes	—
1086	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1087	C₄	—	2	2	no	—
1088	C₄	—	2	2	no	—
1089	C₄	—	2	2	no	—
1090	C₄	—	2	2	no	—
1091	C₄	—	2	2	no	—
1092	C₄	—	2	2	no	—
1093	C₄	—	4	2	no	—
1094	C₄	—	4	2	no	—
1095	C₄	—	4	2	no	—
1096	C₄	D₄²×C₆₇	1	2	yes	—
1097	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
1098	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1099	C₂	—	2	2	no	—
1100	C₂	—	4	2	no	—
1101	C₂	—	4	2	no	—
1102	C₂	—	4	2	no	—
1103	C₂	—	4	2	no	—
1104	C₂	—	8	2	no	—
1105	C₂	—	8	2	no	—
1106	C₂	—	8	2	no	—
1107	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
1108	C₂	C₆₇×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #532×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#577×C₆₇	C₂	semidirect
2. C₂×#576×C₆₇	C₂	semidirect
3. C₆₇×#3500	C₂	semidirect
4. C₆₇×#3498	C₂	semidirect
5. C₆₇×#3271	C₂	semidirect
6. C₆₇×#3268	C₂	semidirect
7. C₆₇×#3265	C₂	semidirect
8. C₆₇×#3264	C₂	semidirect
9. C₂×#496×C₆₇	C₂	semidirect
10. C₆₇×#3058	C₂	semidirect
11. C₆₇×#3057	C₂	semidirect
12. C₆₇×#3040	C₂	semidirect
13. C₆₇×#3038	C₂	semidirect
14. C₆₇×#3010	C₂	semidirect
15. C₆₇×#3009	C₂	semidirect
16. C₆₇×#3008	C₂	semidirect
17. C₆₇×#3008	C₂	semidirect
18. C₆₇×#2943	C₂	semidirect
19. C₆₇×#2932	C₂	semidirect
20. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
22. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
23. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
26. C₂×#137×C₆₇	C₂²	semidirect
27. C₂×#137×C₆₇	C₂²	semidirect
29. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
30. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
31. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
32. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
33. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
35. C₂×#135×C₆₇	C₂²	semidirect
36. C₂×#135×C₆₇	C₂²	semidirect
37. C₂²×SD₁₆×C₆₇	C₂²	semidirect
38. C₂²×SD₁₆×C₆₇	C₂²	semidirect
39. C₂²×SD₁₆×C₆₇	C₂²	semidirect
40. C₂²×D₈×C₆₇	C₂²	semidirect
41. C₂²×D₈×C₆₇	C₂²	semidirect
42. C₂²×D₈×C₆₇	C₂²	semidirect
43. C₂×#131×C₆₇	C₂²	semidirect
44. C₂×#131×C₆₇	C₂²	semidirect
45. #550×C₆₇	C₂²	semidirect
46. #548×C₆₇	C₂²	semidirect
48. #546×C₆₇	C₂²	semidirect
50. D₄²×C₆₇	C₂²	semidirect
52. #536×C₆₇	C₂²	semidirect
57. #535×C₆₇	C₂²	semidirect
58. #535×C₆₇	C₂²	semidirect
63. C₂×#127×C₆₇	C₂²	semidirect
65. C₂×#124×C₆₇	C₂²	semidirect
66. C₄×#41×C₆₇	C₂²	semidirect
67. C₄×#41×C₆₇	C₂²	semidirect
68. #496×C₆₇	C₂²	semidirect
69. #496×C₆₇	C₂²	semidirect
70. #469×C₆₇	C₂²	semidirect
71. #468×C₆₇	C₂²	semidirect
72. #466×C₆₇	C₂²	semidirect
73. #465×C₆₇	C₂²	semidirect
74. #464×C₆₇	C₂²	semidirect
75. #463×C₆₇	C₂²	semidirect
76. #460×C₆₇	C₂²	semidirect
77. #459×C₆₇	C₂²	semidirect
78. #452×C₆₇	C₂²	semidirect
79. #450×C₆₇	C₂²	semidirect
80. #449×C₆₇	C₂²	semidirect
81. #449×C₆₇	C₂²	semidirect
82. #449×C₆₇	C₂²	semidirect
83. #448×C₆₇	C₂²	semidirect
84. #447×C₆₇	C₂²	semidirect
85. #447×C₆₇	C₂²	semidirect
86. #442×C₆₇	C₂²	semidirect
87. #441×C₆₇	C₂²	semidirect
88. #440×C₆₇	C₂²	semidirect
89. #440×C₆₇	C₂²	semidirect
90. #435×C₆₇	C₂²	semidirect
91. #435×C₆₇	C₂²	semidirect
92. #427×C₆₇	C₂²	semidirect
93. #423×C₆₇	C₂²	semidirect
94. #419×C₆₇	C₂²	semidirect
95. #418×C₆₇	C₂²	semidirect
96. #418×C₆₇	C₂²	semidirect
97. #418×C₆₇	C₂²	semidirect
98. #416×C₆₇	C₂²	semidirect
99. #416×C₆₇	C₂²	semidirect
100. #408×C₆₇	C₂²	semidirect
101. #408×C₆₇	C₂²	semidirect
102. C₂×#97×C₆₇	C₂²	semidirect
151. #135×C₆₇	D₄	semidirect
284. #41×C₆₇	C₂×D₄	semidirect
359. Q₁₆×C₆₇	C₂×D₄	semidirect
367. SD₁₆×C₆₇	C₂×D₄	semidirect
368. SD₁₆×C₆₇	C₂×D₄	semidirect
375. D₈×C₆₇	C₂×D₄	semidirect
383. C₂×C₈×C₆₇	C₂×D₄	semidirect
544. #61082	C₆₇	direct (N × H)
555. C₂×#577	C₂×C₆₇	semidirect
556. C₂×#576	C₂×C₆₇	semidirect
557. #3500	C₂×C₆₇	semidirect
558. #3498	C₂×C₆₇	semidirect
559. #3271	C₂×C₆₇	semidirect
560. #3268	C₂×C₆₇	semidirect
561. #3265	C₂×C₆₇	semidirect
562. #3264	C₂×C₆₇	semidirect
563. C₂×#496	C₂×C₆₇	semidirect
564. #3058	C₂×C₆₇	semidirect
565. #3057	C₂×C₆₇	semidirect
566. #3040	C₂×C₆₇	semidirect
567. #3038	C₂×C₆₇	semidirect
568. #3010	C₂×C₆₇	semidirect
569. #3009	C₂×C₆₇	semidirect
570. #3008	C₂×C₆₇	semidirect
571. #3008	C₂×C₆₇	semidirect
572. #2943	C₂×C₆₇	semidirect
573. #2932	C₂×C₆₇	semidirect
574. C₆₇	#61082	direct (N × H)
575. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
577. C₂×H(5,𝔽₂)	C₂²×C₆₇	semidirect
578. C₂×H(5,𝔽₂)	C₂²×C₆₇	semidirect
581. C₂×#137	C₂²×C₆₇	semidirect
582. C₂×#137	C₂²×C₆₇	semidirect
584. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
585. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
586. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
587. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
588. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
590. C₂×#135	C₂²×C₆₇	semidirect
591. C₂×#135	C₂²×C₆₇	semidirect
592. C₂²×SD₁₆	C₂²×C₆₇	semidirect
593. C₂²×SD₁₆	C₂²×C₆₇	semidirect
594. C₂²×SD₁₆	C₂²×C₆₇	semidirect
595. C₂²×D₈	C₂²×C₆₇	semidirect
596. C₂²×D₈	C₂²×C₆₇	semidirect
597. C₂²×D₈	C₂²×C₆₇	semidirect
598. C₂×#131	C₂²×C₆₇	semidirect
599. C₂×#131	C₂²×C₆₇	semidirect
600. #550	C₂²×C₆₇	semidirect
601. #548	C₂²×C₆₇	semidirect
603. #546	C₂²×C₆₇	semidirect
605. D₄²	C₂²×C₆₇	semidirect
607. #536	C₂²×C₆₇	semidirect
612. #535	C₂²×C₆₇	semidirect
613. #535	C₂²×C₆₇	semidirect
618. C₂×#127	C₂²×C₆₇	semidirect
620. C₂×#124	C₂²×C₆₇	semidirect
621. C₄×#41	C₂²×C₆₇	semidirect
622. C₄×#41	C₂²×C₆₇	semidirect
623. #496	C₂²×C₆₇	semidirect
624. #496	C₂²×C₆₇	semidirect
625. #469	C₂²×C₆₇	semidirect
626. #468	C₂²×C₆₇	semidirect
627. #466	C₂²×C₆₇	semidirect
628. #465	C₂²×C₆₇	semidirect
629. #464	C₂²×C₆₇	semidirect
630. #463	C₂²×C₆₇	semidirect
631. #460	C₂²×C₆₇	semidirect
632. #459	C₂²×C₆₇	semidirect
633. #452	C₂²×C₆₇	semidirect
634. #450	C₂²×C₆₇	semidirect
635. #449	C₂²×C₆₇	semidirect
636. #449	C₂²×C₆₇	semidirect
637. #449	C₂²×C₆₇	semidirect
638. #448	C₂²×C₆₇	semidirect
639. #447	C₂²×C₆₇	semidirect
640. #447	C₂²×C₆₇	semidirect
641. #442	C₂²×C₆₇	semidirect
642. #441	C₂²×C₆₇	semidirect
643. #440	C₂²×C₆₇	semidirect
644. #440	C₂²×C₆₇	semidirect
645. #435	C₂²×C₆₇	semidirect
646. #435	C₂²×C₆₇	semidirect
647. #427	C₂²×C₆₇	semidirect
648. #423	C₂²×C₆₇	semidirect
649. #419	C₂²×C₆₇	semidirect
650. #418	C₂²×C₆₇	semidirect
651. #418	C₂²×C₆₇	semidirect
652. #418	C₂²×C₆₇	semidirect
653. #416	C₂²×C₆₇	semidirect
654. #416	C₂²×C₆₇	semidirect
655. #408	C₂²×C₆₇	semidirect
656. #408	C₂²×C₆₇	semidirect
657. C₂×#97	C₂²×C₆₇	semidirect
706. #135	D₄×C₆₇	semidirect
839. #41	C₂×D₄×C₆₇	semidirect
914. Q₁₆	C₂×D₄×C₆₇	semidirect
922. SD₁₆	C₂×D₄×C₆₇	semidirect
923. SD₁₆	C₂×D₄×C₆₇	semidirect
930. D₈	C₂×D₄×C₆₇	semidirect
938. C₂×C₈	C₂×D₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#577×C₆₇	2
C₂×#576×C₆₇	2
C₆₇×#3500	2
C₆₇×#3498	2
C₆₇×#3271	2
C₆₇×#3268	2
C₆₇×#3265	2
C₆₇×#3264	2
C₂×#496×C₆₇	2
C₆₇×#3058	2
C₆₇×#3057	2
C₆₇×#3040	2
C₆₇×#3038	2
C₆₇×#3010	2
C₆₇×#3009	2
C₆₇×#3008	2
C₆₇×#2943	2
C₆₇×#2932	2
#61082	67

Subgroups — C67×#61082 #30740333

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61082 #30740333