Subgroups — C₆₇×#61340 #30740591

Order 17152.

1792 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3376	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3372	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3372	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3367	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3360	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3359	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3139	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3137	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3082	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3076	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3042	C₂	1	2	yes	maximal
14	C₂×#461×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2949	C₂	1	2	yes	maximal, complemented
17	C₄×AGL(1,ℤ/8)×C₆₇	C₂	1	1	yes	maximal, characteristic
18	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	—
20	#557×C₆₇	C₂²	1	2	yes	complemented
21	#557×C₆₇	C₂²	1	2	yes	complemented
22	#556×C₆₇	C₂²	1	2	yes	complemented
23	#556×C₆₇	C₂²	1	2	yes	complemented
24	#554×C₆₇	—	2	1	no	—
25	#554×C₆₇	—	2	2	no	—
26	#554×C₆₇	C₂²	1	2	yes	—
27	#554×C₆₇	C₂²	1	4	yes	—
28	#552×C₆₇	—	2	2	no	—
29	#552×C₆₇	—	2	2	no	—
30	D₄×Q₈×C₆₇	—	2	1	no	—
31	D₄×Q₈×C₆₇	C₂²	1	2	yes	—
32	#544×C₆₇	C₂²	1	2	yes	—
33	#543×C₆₇	—	2	2	no	—
34	#541×C₆₇	—	2	2	no	—
35	#536×C₆₇	C₂²	1	2	yes	—
36	#533×C₆₇	—	2	1	no	—
37	#533×C₆₇	—	2	1	no	—
38	#533×C₆₇	C₂²	1	1	yes	characteristic
39	#533×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊Q₈×C₆₇	—	2	2	no	—
42	#519×C₆₇	C₂²	1	2	yes	—
43	#518×C₆₇	C₂²	1	2	yes	—
44	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
46	#491×C₆₇	C₂²	1	4	yes	complemented
47	#491×C₆₇	C₂²	1	4	yes	complemented
48	#489×C₆₇	C₂²	1	4	yes	complemented
49	#488×C₆₇	C₂²	1	4	yes	complemented
50	#487×C₆₇	C₂²	1	2	yes	complemented
51	#487×C₆₇	C₂²	1	4	yes	complemented
52	#487×C₆₇	C₂²	1	2	yes	complemented
53	#479×C₆₇	C₂²	1	2	yes	complemented
54	#479×C₆₇	C₂²	1	4	yes	complemented
55	#479×C₆₇	C₂²	1	4	yes	complemented
56	#478×C₆₇	C₂²	1	2	yes	complemented
57	#477×C₆₇	C₂²	1	1	yes	characteristic, complemented
58	#477×C₆₇	C₂²	1	4	yes	complemented
59	#476×C₆₇	C₂²	1	1	yes	characteristic, complemented
60	#475×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	#475×C₆₇	C₂²	1	4	yes	complemented
62	#474×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	#463×C₆₇	C₂²	1	4	yes	—
64	#463×C₆₇	C₂²	1	4	yes	—
65	#461×C₆₇	C₂²	1	2	yes	—
66	#461×C₆₇	C₂²	1	2	yes	—
67	#461×C₆₇	C₂²	1	4	yes	—
68	#461×C₆₇	C₂²	1	4	yes	—
69	#461×C₆₇	C₂²	1	4	yes	—
70	#446×C₆₇	C₂²	1	2	yes	complemented
71	#446×C₆₇	C₂²	1	4	yes	complemented
72	C₈×Q₈×C₆₇	C₂²	1	2	yes	complemented
73	#442×C₆₇	C₂²	1	2	yes	—
74	#440×C₆₇	C₂²	1	4	yes	—
75	#440×C₆₇	C₂²	1	2	yes	—
76	#440×C₆₇	C₂²	1	4	yes	—
77	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
78	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	—
79	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	—
80	C₄×D₈×C₆₇	C₂²	1	2	yes	—
81	#428×C₆₇	C₂²	1	1	yes	characteristic
82	#427×C₆₇	C₂²	1	2	yes	—
83	#424×C₆₇	C₂²	1	2	yes	—
84	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
85	#419×C₆₇	C₂²	1	2	yes	—
86	#419×C₆₇	C₂²	1	2	yes	—
87	#418×C₆₇	C₂²	1	1	yes	characteristic
88	#417×C₆₇	C₂²	1	1	yes	characteristic
89	#416×C₆₇	C₂²	1	2	yes	—
90	C₂×#103×C₆₇	C₂²	1	2	yes	—
91	#405×C₆₇	C₂²	1	2	yes	—
92	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
93	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
94	C₂²×Q₈×C₆₇	—	2	2	no	—
95	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
96	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₆₇	—	2	1	no	—
98	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
99	C₂×SD₁₆×C₆₇	—	2	8	no	—
100	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
101	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
102	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
103	C₂×D₈×C₆₇	C₂³	1	2	yes	—
104	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
105	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
107	C₄⋊Q₈×C₆₇	—	2	2	no	—
108	C₄⋊Q₈×C₆₇	—	2	1	no	—
109	C₄⋊Q₈×C₆₇	—	2	1	no	—
110	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
111	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
112	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
113	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
114	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
115	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
116	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
117	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
118	#126×C₆₇	—	2	4	no	—
119	#126×C₆₇	—	2	4	no	—
120	#125×C₆₇	—	2	2	no	—
121	#125×C₆₇	—	2	2	no	—
122	#125×C₆₇	—	2	4	no	—
123	#125×C₆₇	—	2	4	no	—
124	#125×C₆₇	—	2	2	no	—
125	#125×C₆₇	D₄	1	2	yes	—
126	#125×C₆₇	C₂³	1	2	yes	—
127	#125×C₆₇	C₂³	1	4	yes	—
128	#124×C₆₇	C₂³	1	4	yes	—
129	#123×C₆₇	—	2	4	no	—
130	C₂²⋊Q₈×C₆₇	—	2	2	no	—
131	C₂²⋊Q₈×C₆₇	—	2	2	no	—
132	C₂²⋊Q₈×C₆₇	—	2	2	no	—
133	C₂²⋊Q₈×C₆₇	—	2	4	no	—
134	C₂²⋊Q₈×C₆₇	—	2	1	no	—
135	C₂²⋊Q₈×C₆₇	—	2	1	no	—
136	C₂²⋊Q₈×C₆₇	—	2	2	no	—
137	C₂²⋊Q₈×C₆₇	—	2	4	no	—
138	C₂²⋊Q₈×C₆₇	—	2	2	no	—
139	C₂²⋊Q₈×C₆₇	—	2	2	no	—
140	C₂²⋊Q₈×C₆₇	—	2	4	no	—
141	C₂²⋊Q₈×C₆₇	—	2	4	no	—
142	C₂²⋊Q₈×C₆₇	—	2	4	no	—
143	C₂²⋊Q₈×C₆₇	—	2	4	no	—
144	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
145	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
146	C₄×Q₈×C₆₇	—	2	2	no	—
147	C₄×Q₈×C₆₇	—	2	2	no	—
148	C₄×Q₈×C₆₇	—	2	2	no	—
149	C₄×Q₈×C₆₇	—	2	2	no	—
150	C₄×Q₈×C₆₇	—	2	1	no	—
151	C₄×Q₈×C₆₇	—	2	1	no	—
152	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
153	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
154	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
155	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
156	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
157	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
158	C₄×D₄×C₆₇	—	2	1	no	—
159	C₄×D₄×C₆₇	—	2	1	no	—
160	C₄×D₄×C₆₇	—	2	2	no	—
161	C₄×D₄×C₆₇	—	2	2	no	—
162	C₄×D₄×C₆₇	—	2	1	no	—
163	C₄×D₄×C₆₇	—	2	1	no	—
164	C₄×D₄×C₆₇	C₂³	1	2	yes	—
165	C₄×D₄×C₆₇	C₂³	1	2	yes	—
166	C₄×D₄×C₆₇	C₂³	1	4	yes	—
167	C₄×D₄×C₆₇	C₂³	1	4	yes	—
168	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
169	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
170	#117×C₆₇	—	2	2	no	—
171	#117×C₆₇	—	2	2	no	—
172	#117×C₆₇	—	2	4	no	—
173	#117×C₆₇	—	2	1	no	—
174	#117×C₆₇	C₂³	1	1	yes	characteristic
175	#117×C₆₇	C₂³	1	2	yes	—
176	#117×C₆₇	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
178	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
179	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
180	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
181	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
183	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
184	C₂×C₄²×C₆₇	—	2	1	no	—
185	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
186	#107×C₆₇	C₂³	1	2	yes	—
187	#107×C₆₇	C₂³	1	2	yes	—
188	#107×C₆₇	C₂³	1	2	yes	—
189	#106×C₆₇	C₂³	1	2	yes	—
190	#106×C₆₇	C₂³	1	2	yes	—
191	#106×C₆₇	C₂³	1	2	yes	—
192	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
193	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
194	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
195	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
196	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
197	#103×C₆₇	C₂³	1	2	yes	—
198	#103×C₆₇	C₂³	1	4	yes	—
199	#103×C₆₇	C₂³	1	4	yes	—
200	#103×C₆₇	C₂³	1	2	yes	—
201	#103×C₆₇	C₂³	1	4	yes	—
202	#103×C₆₇	C₂³	1	4	yes	—
203	#103×C₆₇	C₂³	1	4	yes	—
204	#103×C₆₇	C₂³	1	2	yes	—
205	#103×C₆₇	C₂³	1	4	yes	—
206	#102×C₆₇	C₂³	1	2	yes	—
207	#102×C₆₇	C₂³	1	2	yes	—
208	#102×C₆₇	C₂³	1	2	yes	—
209	#102×C₆₇	C₂³	1	2	yes	—
210	#102×C₆₇	C₂³	1	2	yes	—
211	#97×C₆₇	C₂³	1	4	yes	—
212	#97×C₆₇	C₂³	1	2	yes	—
213	C₄×C₈×C₆₇	C₂³	1	2	yes	—
214	C₄×C₈×C₆₇	C₂³	1	4	yes	—
215	C₂⁴×C₆₇	—	2	1	no	—
216	#41×C₆₇	—	2	2	no	—
217	#41×C₆₇	—	2	2	no	—
218	C₂×Q₈×C₆₇	—	2	2	no	—
219	C₂×Q₈×C₆₇	—	2	1	no	—
220	C₂×Q₈×C₆₇	—	2	1	no	—
221	C₂×Q₈×C₆₇	—	2	4	no	—
222	C₂×Q₈×C₆₇	—	2	4	no	—
223	C₂×Q₈×C₆₇	—	2	4	no	—
224	C₂×Q₈×C₆₇	—	8	4	no	—
225	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
226	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
227	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
228	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
229	C₂×D₄×C₆₇	—	2	1	no	—
230	C₂×D₄×C₆₇	—	2	1	no	—
231	C₂×D₄×C₆₇	—	2	2	no	—
232	C₂×D₄×C₆₇	#41	1	4	yes	—
233	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
234	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₆₇	—	2	2	no	—
236	C₂²×C₄×C₆₇	—	2	1	no	—
237	C₂²×C₄×C₆₇	—	2	1	no	—
238	C₂²×C₄×C₆₇	—	2	1	no	—
239	C₂²×C₄×C₆₇	—	2	1	no	—
240	C₂²×C₄×C₆₇	—	2	2	no	—
241	C₂²×C₄×C₆₇	—	2	4	no	—
242	C₂²×C₄×C₆₇	—	2	4	no	—
243	C₂²×C₄×C₆₇	—	2	2	no	—
244	C₂²×C₄×C₆₇	—	8	2	no	—
245	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
248	SD₁₆×C₆₇	—	2	8	no	—
249	SD₁₆×C₆₇	—	2	8	no	—
250	SD₁₆×C₆₇	—	2	4	no	—
251	D₈×C₆₇	—	2	4	no	—
252	M₁₆×C₆₇	—	2	2	no	—
253	M₁₆×C₆₇	—	2	2	no	—
254	C₂×C₈×C₆₇	—	2	4	no	—
255	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
256	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
257	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
258	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
259	C₄⋊C₄×C₆₇	—	2	2	no	—
260	C₄⋊C₄×C₆₇	—	2	1	no	—
261	C₄⋊C₄×C₆₇	—	2	2	no	—
262	C₄⋊C₄×C₆₇	—	2	2	no	—
263	C₄⋊C₄×C₆₇	—	2	4	no	—
264	C₄⋊C₄×C₆₇	—	2	4	no	—
265	C₄⋊C₄×C₆₇	—	2	4	no	—
266	C₄⋊C₄×C₆₇	—	2	2	no	—
267	C₄⋊C₄×C₆₇	—	2	2	no	—
268	C₄⋊C₄×C₆₇	—	2	1	no	—
269	C₄⋊C₄×C₆₇	—	2	1	no	—
270	C₄⋊C₄×C₆₇	—	2	1	no	—
271	C₄⋊C₄×C₆₇	—	2	4	no	—
272	C₄⋊C₄×C₆₇	—	2	4	no	—
273	C₄⋊C₄×C₆₇	—	2	2	no	—
274	C₄⋊C₄×C₆₇	—	2	1	no	—
275	C₄⋊C₄×C₆₇	—	2	4	no	—
276	C₄⋊C₄×C₆₇	—	2	4	no	—
277	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
279	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
280	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
281	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
282	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
283	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
284	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
285	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
286	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
287	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
288	C₂²⋊C₄×C₆₇	—	2	2	no	—
289	C₂²⋊C₄×C₆₇	—	2	1	no	—
290	C₂²⋊C₄×C₆₇	—	2	4	no	—
291	C₂²⋊C₄×C₆₇	—	2	4	no	—
292	C₂²⋊C₄×C₆₇	—	2	2	no	—
293	C₂²⋊C₄×C₆₇	—	2	2	no	—
294	C₂²⋊C₄×C₆₇	—	2	1	no	—
295	C₂²⋊C₄×C₆₇	—	2	1	no	—
296	C₂²⋊C₄×C₆₇	—	2	4	no	—
297	C₂²⋊C₄×C₆₇	—	2	4	no	—
298	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
299	C₄²×C₆₇	—	2	1	no	—
300	C₄²×C₆₇	—	2	1	no	—
301	C₄²×C₆₇	—	2	1	no	—
302	C₄²×C₆₇	—	2	4	no	—
303	C₄²×C₆₇	—	2	4	no	—
304	C₄²×C₆₇	—	2	2	no	—
305	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
306	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
307	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
308	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
309	C₄²×C₆₇	C₂⁴	1	4	yes	—
310	C₂³×C₆₇	—	2	2	no	—
311	C₂³×C₆₇	—	2	4	no	—
312	C₂³×C₆₇	—	2	1	no	—
313	C₂³×C₆₇	—	8	1	no	—
314	C₂³×C₆₇	—	8	1	no	—
315	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
316	Q₈×C₆₇	—	2	4	no	—
317	Q₈×C₆₇	—	2	4	no	—
318	Q₈×C₆₇	—	2	1	no	—
319	Q₈×C₆₇	—	2	4	no	—
320	Q₈×C₆₇	—	2	1	no	—
321	Q₈×C₆₇	—	4	2	no	—
322	Q₈×C₆₇	—	4	4	no	—
323	Q₈×C₆₇	—	4	2	no	—
324	Q₈×C₆₇	—	8	1	no	—
325	Q₈×C₆₇	—	8	4	no	—
326	D₄×C₆₇	—	2	4	no	—
327	D₄×C₆₇	—	2	1	no	—
328	D₄×C₆₇	—	2	2	no	—
329	D₄×C₆₇	—	2	1	no	—
330	D₄×C₆₇	—	4	2	no	—
331	D₄×C₆₇	C₂×#41	1	4	yes	—
332	C₂×C₄×C₆₇	—	2	2	no	—
333	C₂×C₄×C₆₇	—	2	1	no	—
334	C₂×C₄×C₆₇	—	2	1	no	—
335	C₂×C₄×C₆₇	—	2	4	no	—
336	C₂×C₄×C₆₇	—	2	1	no	—
337	C₂×C₄×C₆₇	—	2	2	no	—
338	C₂×C₄×C₆₇	—	2	2	no	—
339	C₂×C₄×C₆₇	—	2	2	no	—
340	C₂×C₄×C₆₇	—	4	1	no	—
341	C₂×C₄×C₆₇	—	4	2	no	—
342	C₂×C₄×C₆₇	—	4	4	no	—
343	C₂×C₄×C₆₇	—	4	2	no	—
344	C₂×C₄×C₆₇	—	4	2	no	—
345	C₂×C₄×C₆₇	—	4	4	no	—
346	C₂×C₄×C₆₇	—	8	4	no	—
347	C₂×C₄×C₆₇	—	8	2	no	—
348	C₂×C₄×C₆₇	—	8	4	no	—
349	C₂×C₄×C₆₇	—	8	1	no	—
350	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
352	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
353	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
355	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
358	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
359	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
360	C₈×C₆₇	—	2	2	no	—
361	C₈×C₆₇	—	2	2	no	—
362	C₈×C₆₇	—	2	2	no	—
363	C₈×C₆₇	—	2	2	no	—
364	C₂²×C₆₇	—	2	1	no	—
365	C₂²×C₆₇	—	2	1	no	—
366	C₂²×C₆₇	—	2	4	no	—
367	C₂²×C₆₇	—	4	2	no	—
368	C₂²×C₆₇	—	4	2	no	—
369	C₂²×C₆₇	—	4	1	no	—
370	C₂²×C₆₇	—	4	1	no	—
371	C₂²×C₆₇	—	4	1	no	—
372	C₂²×C₆₇	—	8	4	no	—
373	C₂²×C₆₇	#548	1	2	yes	—
374	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
375	C₄×C₆₇	—	2	1	no	—
376	C₄×C₆₇	—	2	1	no	—
377	C₄×C₆₇	—	2	4	no	—
378	C₄×C₆₇	—	2	1	no	—
379	C₄×C₆₇	—	2	4	no	—
380	C₄×C₆₇	—	4	1	no	—
381	C₄×C₆₇	—	4	2	no	—
382	C₄×C₆₇	—	4	1	no	—
383	C₄×C₆₇	—	4	4	no	—
384	C₄×C₆₇	—	4	1	no	—
385	C₄×C₆₇	—	4	2	no	—
386	C₄×C₆₇	—	4	2	no	—
387	C₄×C₆₇	#548	1	2	yes	—
388	C₄×C₆₇	#577	1	2	yes	—
389	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
390	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
391	#61340	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
392	C₂×C₆₇	—	2	2	no	—
393	C₂×C₆₇	—	4	4	no	—
394	C₂×C₆₇	—	8	1	no	—
395	C₂×C₆₇	C₂×#548	1	1	yes	characteristic
396	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
397	C₂×C₆₇	#3586	1	1	yes	characteristic
398	#3509	C₂×C₆₇	1	1	yes	characteristic, complemented
399	#3501	C₂×C₆₇	1	1	yes	characteristic, complemented
400	#3376	C₂×C₆₇	1	4	yes	complemented
401	#3372	C₂×C₆₇	1	2	yes	complemented
402	#3372	C₂×C₆₇	1	4	yes	complemented
403	#3367	C₂×C₆₇	1	2	yes	complemented
404	#3360	C₂×C₆₇	1	2	yes	complemented
405	#3359	C₂×C₆₇	1	2	yes	complemented
406	#3139	C₂×C₆₇	1	1	yes	characteristic, complemented
407	#3137	C₂×C₆₇	1	2	yes	complemented
408	#3082	C₂×C₆₇	1	2	yes	complemented
409	#3076	C₂×C₆₇	1	1	yes	characteristic, complemented
410	#3042	C₂×C₆₇	1	2	yes	—
411	C₂×#461	C₂×C₆₇	1	1	yes	characteristic, complemented
412	#2962	C₂×C₆₇	1	1	yes	characteristic, complemented
413	#2949	C₂×C₆₇	1	2	yes	complemented
414	C₄×AGL(1,ℤ/8)	C₂×C₆₇	1	1	yes	characteristic
415	C₆₇	#61340	1	1	yes	characteristic, direct product factor, Sylow
416	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
417	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	—
418	#557	C₂²×C₆₇	1	2	yes	complemented
419	#557	C₂²×C₆₇	1	2	yes	complemented
420	#556	C₂²×C₆₇	1	2	yes	complemented
421	#556	C₂²×C₆₇	1	2	yes	complemented
422	#554	—	2	1	no	—
423	#554	—	2	2	no	—
424	#554	C₂²×C₆₇	1	2	yes	—
425	#554	C₂²×C₆₇	1	4	yes	—
426	#552	—	2	2	no	—
427	#552	—	2	2	no	—
428	D₄×Q₈	—	2	1	no	—
429	D₄×Q₈	C₂²×C₆₇	1	2	yes	—
430	#544	C₂²×C₆₇	1	2	yes	—
431	#543	—	2	2	no	—
432	#541	—	2	2	no	—
433	#536	C₂²×C₆₇	1	2	yes	—
434	#533	—	2	1	no	—
435	#533	—	2	1	no	—
436	#533	C₂²×C₆₇	1	1	yes	characteristic
437	#533	C₂²×C₆₇	1	1	yes	characteristic
438	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
439	C₂×C₂²⋊Q₈	—	2	2	no	—
440	#519	C₂²×C₆₇	1	2	yes	—
441	#518	C₂²×C₆₇	1	2	yes	—
442	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
443	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
444	#491	C₂²×C₆₇	1	4	yes	complemented
445	#491	C₂²×C₆₇	1	4	yes	complemented
446	#489	C₂²×C₆₇	1	4	yes	complemented
447	#488	C₂²×C₆₇	1	4	yes	complemented
448	#487	C₂²×C₆₇	1	2	yes	complemented
449	#487	C₂²×C₆₇	1	4	yes	complemented
450	#487	C₂²×C₆₇	1	2	yes	complemented
451	#479	C₂²×C₆₇	1	2	yes	complemented
452	#479	C₂²×C₆₇	1	4	yes	complemented
453	#479	C₂²×C₆₇	1	4	yes	complemented
454	#478	C₂²×C₆₇	1	2	yes	complemented
455	#477	C₂²×C₆₇	1	1	yes	characteristic, complemented
456	#477	C₂²×C₆₇	1	4	yes	complemented
457	#476	C₂²×C₆₇	1	1	yes	characteristic, complemented
458	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
459	#475	C₂²×C₆₇	1	4	yes	complemented
460	#474	C₂²×C₆₇	1	1	yes	characteristic, complemented
461	#463	C₂²×C₆₇	1	4	yes	—
462	#463	C₂²×C₆₇	1	4	yes	—
463	#461	C₂²×C₆₇	1	2	yes	—
464	#461	C₂²×C₆₇	1	4	yes	—
465	#461	C₂²×C₆₇	1	2	yes	—
466	#461	C₂²×C₆₇	1	4	yes	—
467	#461	C₂²×C₆₇	1	4	yes	—
468	#446	C₂²×C₆₇	1	2	yes	complemented
469	#446	C₂²×C₆₇	1	4	yes	complemented
470	C₈×Q₈	C₂²×C₆₇	1	2	yes	complemented
471	#442	C₂²×C₆₇	1	2	yes	—
472	#440	C₂²×C₆₇	1	4	yes	—
473	#440	C₂²×C₆₇	1	2	yes	—
474	#440	C₂²×C₆₇	1	4	yes	—
475	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
476	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	—
477	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	—
478	C₄×D₈	C₂²×C₆₇	1	2	yes	—
479	#428	C₂²×C₆₇	1	1	yes	characteristic
480	#427	C₂²×C₆₇	1	2	yes	—
481	#424	C₂²×C₆₇	1	2	yes	—
482	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
483	#419	C₂²×C₆₇	1	2	yes	—
484	#419	C₂²×C₆₇	1	2	yes	—
485	#418	C₂²×C₆₇	1	1	yes	characteristic
486	#417	C₂²×C₆₇	1	1	yes	characteristic
487	#416	C₂²×C₆₇	1	2	yes	—
488	C₂×#103	C₂²×C₆₇	1	2	yes	—
489	#405	C₂²×C₆₇	1	2	yes	—
490	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
491	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
492	C₂²×Q₈	—	2	2	no	—
493	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
494	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
495	C₂³×C₄	—	2	1	no	—
496	AGL(1,ℤ/8)	—	2	4	no	—
497	C₂×SD₁₆	—	2	8	no	—
498	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
499	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
500	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
501	C₂×D₈	C₂³×C₆₇	1	2	yes	—
502	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
503	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
504	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
505	C₄⋊Q₈	—	2	2	no	—
506	C₄⋊Q₈	—	2	1	no	—
507	C₄⋊Q₈	—	2	1	no	—
508	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
509	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
510	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
511	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
512	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
513	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
514	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
515	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
516	#126	—	2	4	no	—
517	#126	—	2	4	no	—
518	#125	—	2	2	no	—
519	#125	—	2	2	no	—
520	#125	—	2	4	no	—
521	#125	—	2	4	no	—
522	#125	—	2	2	no	—
523	#125	D₄×C₆₇	1	2	yes	—
524	#125	C₂³×C₆₇	1	2	yes	—
525	#125	C₂³×C₆₇	1	4	yes	—
526	#124	C₂³×C₆₇	1	4	yes	—
527	#123	—	2	4	no	—
528	C₂²⋊Q₈	—	2	2	no	—
529	C₂²⋊Q₈	—	2	2	no	—
530	C₂²⋊Q₈	—	2	2	no	—
531	C₂²⋊Q₈	—	2	4	no	—
532	C₂²⋊Q₈	—	2	1	no	—
533	C₂²⋊Q₈	—	2	1	no	—
534	C₂²⋊Q₈	—	2	2	no	—
535	C₂²⋊Q₈	—	2	4	no	—
536	C₂²⋊Q₈	—	2	2	no	—
537	C₂²⋊Q₈	—	2	2	no	—
538	C₂²⋊Q₈	—	2	4	no	—
539	C₂²⋊Q₈	—	2	4	no	—
540	C₂²⋊Q₈	—	2	4	no	—
541	C₂²⋊Q₈	—	2	4	no	—
542	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
543	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
544	C₄×Q₈	—	2	2	no	—
545	C₄×Q₈	—	2	2	no	—
546	C₄×Q₈	—	2	2	no	—
547	C₄×Q₈	—	2	2	no	—
548	C₄×Q₈	—	2	1	no	—
549	C₄×Q₈	—	2	1	no	—
550	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
551	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
552	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
553	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
554	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
555	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
556	C₄×D₄	—	2	1	no	—
557	C₄×D₄	—	2	1	no	—
558	C₄×D₄	—	2	2	no	—
559	C₄×D₄	—	2	2	no	—
560	C₄×D₄	—	2	1	no	—
561	C₄×D₄	—	2	1	no	—
562	C₄×D₄	C₂³×C₆₇	1	2	yes	—
563	C₄×D₄	C₂³×C₆₇	1	2	yes	—
564	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
565	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
566	C₄×D₄	C₂³×C₆₇	1	4	yes	—
567	C₄×D₄	C₂³×C₆₇	1	4	yes	—
568	#117	—	2	2	no	—
569	#117	—	2	2	no	—
570	#117	—	2	4	no	—
571	#117	—	2	1	no	—
572	#117	C₂³×C₆₇	1	1	yes	characteristic
573	#117	C₂³×C₆₇	1	2	yes	—
574	#117	C₂³×C₆₇	1	2	yes	—
575	C₂×C₄⋊C₄	—	2	1	no	—
576	C₂×C₄⋊C₄	—	2	1	no	—
577	C₂×C₄⋊C₄	—	2	4	no	—
578	C₂×C₄⋊C₄	—	2	2	no	—
579	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
580	C₂×C₂²⋊C₄	—	2	1	no	—
581	C₂×C₂²⋊C₄	—	2	4	no	—
582	C₂×C₄²	—	2	1	no	—
583	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
584	#107	C₂³×C₆₇	1	2	yes	—
585	#107	C₂³×C₆₇	1	2	yes	—
586	#107	C₂³×C₆₇	1	2	yes	—
587	#106	C₂³×C₆₇	1	2	yes	—
588	#106	C₂³×C₆₇	1	2	yes	—
589	#106	C₂³×C₆₇	1	2	yes	—
590	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
591	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
592	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
593	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
594	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
595	#103	C₂³×C₆₇	1	4	yes	—
596	#103	C₂³×C₆₇	1	4	yes	—
597	#103	C₂³×C₆₇	1	2	yes	—
598	#103	C₂³×C₆₇	1	2	yes	—
599	#103	C₂³×C₆₇	1	2	yes	—
600	#103	C₂³×C₆₇	1	4	yes	—
601	#103	C₂³×C₆₇	1	4	yes	—
602	#103	C₂³×C₆₇	1	4	yes	—
603	#103	C₂³×C₆₇	1	4	yes	—
604	#102	C₂³×C₆₇	1	2	yes	—
605	#102	C₂³×C₆₇	1	2	yes	—
606	#102	C₂³×C₆₇	1	2	yes	—
607	#102	C₂³×C₆₇	1	2	yes	—
608	#102	C₂³×C₆₇	1	2	yes	—
609	#97	C₂³×C₆₇	1	2	yes	—
610	#97	C₂³×C₆₇	1	4	yes	—
611	C₄×C₈	C₂³×C₆₇	1	2	yes	—
612	C₄×C₈	C₂³×C₆₇	1	4	yes	—
613	C₂⁴	—	2	1	no	—
614	#41	—	2	2	no	—
615	#41	—	2	2	no	—
616	C₂×Q₈	—	2	2	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	—	2	1	no	—
619	C₂×Q₈	—	2	4	no	—
620	C₂×Q₈	—	2	4	no	—
621	C₂×Q₈	—	2	4	no	—
622	C₂×Q₈	—	8	4	no	—
623	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
624	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
625	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
626	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	2	1	no	—
629	C₂×D₄	—	2	2	no	—
630	C₂×D₄	#41×C₆₇	1	4	yes	—
631	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
632	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	2	1	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	2	4	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	8	2	no	—
643	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
644	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
645	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
646	SD₁₆	—	2	8	no	—
647	SD₁₆	—	2	8	no	—
648	SD₁₆	—	2	4	no	—
649	D₈	—	2	4	no	—
650	M₁₆	—	2	2	no	—
651	M₁₆	—	2	2	no	—
652	C₂×C₈	—	2	4	no	—
653	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
654	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
655	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
656	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
657	C₄⋊C₄	—	2	2	no	—
658	C₄⋊C₄	—	2	1	no	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	4	no	—
671	C₄⋊C₄	—	2	2	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
676	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
677	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
678	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
679	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
680	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
681	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
682	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
683	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
684	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
685	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
686	C₂²⋊C₄	—	2	2	no	—
687	C₂²⋊C₄	—	2	1	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	2	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	1	no	—
693	C₂²⋊C₄	—	2	1	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
697	C₄²	—	2	1	no	—
698	C₄²	—	2	1	no	—
699	C₄²	—	2	1	no	—
700	C₄²	—	2	4	no	—
701	C₄²	—	2	4	no	—
702	C₄²	—	2	2	no	—
703	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
704	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
705	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
706	C₄²	C₂⁴×C₆₇	1	4	yes	—
707	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
708	C₂³	—	2	2	no	—
709	C₂³	—	2	4	no	—
710	C₂³	—	2	1	no	—
711	C₂³	—	8	1	no	—
712	C₂³	—	8	1	no	—
713	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
714	Q₈	—	2	4	no	—
715	Q₈	—	2	4	no	—
716	Q₈	—	2	1	no	—
717	Q₈	—	2	4	no	—
718	Q₈	—	2	1	no	—
719	Q₈	—	4	2	no	—
720	Q₈	—	4	4	no	—
721	Q₈	—	4	2	no	—
722	Q₈	—	8	4	no	—
723	Q₈	—	8	1	no	—
724	D₄	—	2	4	no	—
725	D₄	—	2	1	no	—
726	D₄	—	2	2	no	—
727	D₄	—	2	1	no	—
728	D₄	—	4	2	no	—
729	D₄	C₂×#41×C₆₇	1	4	yes	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	4	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	4	1	no	—
739	C₂×C₄	—	4	2	no	—
740	C₂×C₄	—	4	4	no	—
741	C₂×C₄	—	4	2	no	—
742	C₂×C₄	—	4	4	no	—
743	C₂×C₄	—	4	2	no	—
744	C₂×C₄	—	8	2	no	—
745	C₂×C₄	—	8	4	no	—
746	C₂×C₄	—	8	4	no	—
747	C₂×C₄	—	8	1	no	—
748	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
749	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
750	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
751	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
752	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
753	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
754	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
755	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
756	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
757	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
758	C₈	—	2	2	no	—
759	C₈	—	2	2	no	—
760	C₈	—	2	2	no	—
761	C₈	—	2	2	no	—
762	C₂²	—	2	1	no	—
763	C₂²	—	2	1	no	—
764	C₂²	—	2	4	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	1	no	—
768	C₂²	—	4	1	no	—
769	C₂²	—	4	1	no	—
770	C₂²	—	8	4	no	—
771	C₂²	#548×C₆₇	1	2	yes	—
772	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
773	C₄	—	2	1	no	—
774	C₄	—	2	4	no	—
775	C₄	—	2	1	no	—
776	C₄	—	2	1	no	—
777	C₄	—	2	4	no	—
778	C₄	—	4	2	no	—
779	C₄	—	4	1	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	1	no	—
782	C₄	—	4	2	no	—
783	C₄	—	4	1	no	—
784	C₄	—	4	4	no	—
785	C₄	#548×C₆₇	1	2	yes	—
786	C₄	#577×C₆₇	1	2	yes	—
787	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
788	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
789	C₂	—	2	2	no	—
790	C₂	—	4	4	no	—
791	C₂	—	8	1	no	—
792	C₂	C₂×#548×C₆₇	1	1	yes	characteristic
793	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
794	C₂	C₆₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₂×AGL(1,ℤ/8)×C₆₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #533×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3509	C₂	semidirect
2. C₆₇×#3501	C₂	semidirect
3. C₆₇×#3376	C₂	semidirect
4. C₆₇×#3372	C₂	semidirect
5. C₆₇×#3372	C₂	semidirect
6. C₆₇×#3367	C₂	semidirect
7. C₆₇×#3360	C₂	semidirect
8. C₆₇×#3359	C₂	semidirect
9. C₆₇×#3139	C₂	semidirect
10. C₆₇×#3137	C₂	semidirect
11. C₆₇×#3082	C₂	semidirect
12. C₆₇×#3076	C₂	semidirect
14. C₂×#461×C₆₇	C₂	semidirect
15. C₆₇×#2962	C₂	semidirect
16. C₆₇×#2949	C₂	semidirect
20. #557×C₆₇	C₂²	semidirect
21. #557×C₆₇	C₂²	semidirect
22. #556×C₆₇	C₂²	semidirect
23. #556×C₆₇	C₂²	semidirect
46. #491×C₆₇	C₂²	semidirect
47. #491×C₆₇	C₂²	semidirect
48. #489×C₆₇	C₂²	semidirect
49. #488×C₆₇	C₂²	semidirect
50. #487×C₆₇	C₂²	semidirect
51. #487×C₆₇	C₂²	semidirect
52. #487×C₆₇	C₂²	semidirect
53. #479×C₆₇	C₂²	semidirect
54. #479×C₆₇	C₂²	semidirect
55. #479×C₆₇	C₂²	semidirect
56. #478×C₆₇	C₂²	semidirect
57. #477×C₆₇	C₂²	semidirect
58. #477×C₆₇	C₂²	semidirect
59. #476×C₆₇	C₂²	semidirect
60. #475×C₆₇	C₂²	semidirect
61. #475×C₆₇	C₂²	semidirect
62. #474×C₆₇	C₂²	semidirect
70. #446×C₆₇	C₂²	semidirect
71. #446×C₆₇	C₂²	semidirect
72. C₈×Q₈×C₆₇	C₂²	semidirect
391. #61340	C₆₇	direct (N × H)
398. #3509	C₂×C₆₇	semidirect
399. #3501	C₂×C₆₇	semidirect
400. #3376	C₂×C₆₇	semidirect
401. #3372	C₂×C₆₇	semidirect
402. #3372	C₂×C₆₇	semidirect
403. #3367	C₂×C₆₇	semidirect
404. #3360	C₂×C₆₇	semidirect
405. #3359	C₂×C₆₇	semidirect
406. #3139	C₂×C₆₇	semidirect
407. #3137	C₂×C₆₇	semidirect
408. #3082	C₂×C₆₇	semidirect
409. #3076	C₂×C₆₇	semidirect
411. C₂×#461	C₂×C₆₇	semidirect
412. #2962	C₂×C₆₇	semidirect
413. #2949	C₂×C₆₇	semidirect
415. C₆₇	#61340	direct (N × H)
418. #557	C₂²×C₆₇	semidirect
419. #557	C₂²×C₆₇	semidirect
420. #556	C₂²×C₆₇	semidirect
421. #556	C₂²×C₆₇	semidirect
444. #491	C₂²×C₆₇	semidirect
445. #491	C₂²×C₆₇	semidirect
446. #489	C₂²×C₆₇	semidirect
447. #488	C₂²×C₆₇	semidirect
448. #487	C₂²×C₆₇	semidirect
449. #487	C₂²×C₆₇	semidirect
450. #487	C₂²×C₆₇	semidirect
451. #479	C₂²×C₆₇	semidirect
452. #479	C₂²×C₆₇	semidirect
453. #479	C₂²×C₆₇	semidirect
454. #478	C₂²×C₆₇	semidirect
455. #477	C₂²×C₆₇	semidirect
456. #477	C₂²×C₆₇	semidirect
457. #476	C₂²×C₆₇	semidirect
458. #475	C₂²×C₆₇	semidirect
459. #475	C₂²×C₆₇	semidirect
460. #474	C₂²×C₆₇	semidirect
468. #446	C₂²×C₆₇	semidirect
469. #446	C₂²×C₆₇	semidirect
470. C₈×Q₈	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3509	2
C₆₇×#3501	2
C₆₇×#3376	2
C₆₇×#3372	2
C₆₇×#3367	2
C₆₇×#3360	2
C₆₇×#3359	2
C₆₇×#3139	2
C₆₇×#3137	2
C₆₇×#3082	2
C₆₇×#3076	2
C₆₇×#3042	2
C₂×#461×C₆₇	2
C₆₇×#2962	2
C₆₇×#2949	2
C₄×AGL(1,ℤ/8)×C₆₇	2
#61340	67

Subgroups — C67×#61340 #30740591

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61340 #30740591