Subgroups — C₆₇×#61484 #30740735

Order 17152.

1750 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3523	C₂	1	2	yes	maximal
2	C₆₇×#3395	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3383	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3374	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3342	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#3336	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3328	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3312	C₂	1	4	yes	maximal, complemented
9	D₄×Q₁₆×C₆₇	C₂	1	2	yes	maximal, complemented
10	D₄×Q₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3177	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3170	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3127	C₂	1	4	yes	maximal, complemented
14	C₆₇×#3113	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2966	C₂	1	1	yes	maximal, characteristic
16	C₆₇×#2950	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×Q₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
19	C₂²×Q₁₆×C₆₇	C₂²	1	2	yes	—
20	#557×C₆₇	—	2	2	no	—
21	#557×C₆₇	C₂²	1	2	yes	—
22	#557×C₆₇	C₂²	1	2	yes	—
23	#556×C₆₇	—	2	2	no	—
24	#556×C₆₇	C₂²	1	2	yes	—
25	#552×C₆₇	—	2	4	no	—
26	#552×C₆₇	C₂²	1	4	yes	—
27	D₄×Q₈×C₆₇	C₂²	1	4	yes	—
28	D₄×Q₈×C₆₇	C₂²	1	2	yes	—
29	#541×C₆₇	—	2	4	no	—
30	#541×C₆₇	C₂²	1	4	yes	—
31	#533×C₆₇	—	2	2	no	—
32	#533×C₆₇	C₂²	1	2	yes	—
33	#529×C₆₇	—	2	2	no	—
34	#529×C₆₇	C₂²	1	1	yes	characteristic
35	#519×C₆₇	C₂²	1	4	yes	—
36	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
37	#500×C₆₇	C₂²	1	1	yes	characteristic
38	#499×C₆₇	C₂²	1	2	yes	—
39	#494×C₆₇	C₂²	1	1	yes	characteristic
40	#494×C₆₇	C₂²	1	2	yes	—
41	#491×C₆₇	C₂²	1	4	yes	—
42	#487×C₆₇	C₂²	1	2	yes	—
43	#485×C₆₇	C₂²	1	4	yes	—
44	#485×C₆₇	C₂²	1	4	yes	—
45	#483×C₆₇	C₂²	1	4	yes	—
46	#479×C₆₇	C₂²	1	4	yes	—
47	#479×C₆₇	C₂²	1	4	yes	—
48	#475×C₆₇	C₂²	1	2	yes	—
49	#475×C₆₇	C₂²	1	2	yes	—
50	#470×C₆₇	C₂²	1	4	yes	—
51	#467×C₆₇	C₂²	1	2	yes	—
52	#467×C₆₇	C₂²	1	2	yes	—
53	#467×C₆₇	C₂²	1	2	yes	—
54	#467×C₆₇	C₂²	1	2	yes	—
55	#462×C₆₇	C₂²	1	2	yes	—
56	#462×C₆₇	C₂²	1	4	yes	—
57	#462×C₆₇	C₂²	1	4	yes	—
58	#462×C₆₇	C₂²	1	2	yes	—
59	#451×C₆₇	C₂²	1	4	yes	—
60	#451×C₆₇	C₂²	1	4	yes	—
61	#451×C₆₇	C₂²	1	4	yes	—
62	#446×C₆₇	C₂²	1	1	yes	characteristic
63	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic
64	#441×C₆₇	C₂²	1	4	yes	—
65	#441×C₆₇	C₂²	1	4	yes	—
66	#441×C₆₇	C₂²	1	4	yes	—
67	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
68	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
69	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
70	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
71	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
72	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
73	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
74	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
75	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
76	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
77	#436×C₆₇	C₂²	1	1	yes	characteristic
78	#435×C₆₇	C₂²	1	2	yes	—
79	C₈×D₄×C₆₇	C₂²	1	2	yes	—
80	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
81	#433×C₆₇	C₂²	1	2	yes	—
82	#432×C₆₇	C₂²	1	1	yes	characteristic
83	#427×C₆₇	C₂²	1	2	yes	—
84	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
85	#419×C₆₇	C₂²	1	4	yes	—
86	C₂×#103×C₆₇	C₂²	1	2	yes	—
87	#405×C₆₇	C₂²	1	2	yes	—
88	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
89	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
90	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
91	C₂×Q₁₆×C₆₇	—	2	4	no	—
92	C₂×Q₁₆×C₆₇	—	2	8	no	—
93	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
94	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
95	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
96	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
97	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
98	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
99	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
100	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
101	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
103	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
104	C₄⋊Q₈×C₆₇	—	2	2	no	—
105	C₄⋊Q₈×C₆₇	—	2	2	no	—
106	C₄⋊Q₈×C₆₇	—	2	4	no	—
107	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
108	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
109	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
110	#126×C₆₇	—	2	4	no	—
111	#126×C₆₇	—	2	4	no	—
112	#126×C₆₇	—	2	4	no	—
113	#126×C₆₇	—	2	4	no	—
114	#126×C₆₇	D₄	1	2	yes	—
115	#125×C₆₇	—	2	2	no	—
116	#125×C₆₇	—	2	4	no	—
117	#125×C₆₇	—	2	4	no	—
118	#125×C₆₇	—	2	4	no	—
119	#125×C₆₇	—	2	4	no	—
120	#125×C₆₇	—	2	4	no	—
121	#125×C₆₇	—	2	2	no	—
122	#125×C₆₇	D₄	1	1	yes	characteristic
123	#125×C₆₇	C₂³	1	4	yes	—
124	#124×C₆₇	—	2	2	no	—
125	#124×C₆₇	D₄	1	1	yes	characteristic
126	#123×C₆₇	—	2	4	no	—
127	#123×C₆₇	D₄	1	2	yes	—
128	C₂²⋊Q₈×C₆₇	—	2	2	no	—
129	C₂²⋊Q₈×C₆₇	—	2	4	no	—
130	C₂²⋊Q₈×C₆₇	—	2	4	no	—
131	C₂²⋊Q₈×C₆₇	—	2	4	no	—
132	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
133	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
134	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
135	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
136	#121×C₆₇	D₄	1	1	yes	characteristic
137	C₄×Q₈×C₆₇	—	2	2	no	—
138	C₄×Q₈×C₆₇	—	2	4	no	—
139	C₄×Q₈×C₆₇	—	2	4	no	—
140	C₄×Q₈×C₆₇	—	2	2	no	—
141	C₄×Q₈×C₆₇	—	2	2	no	—
142	C₄×Q₈×C₆₇	—	2	2	no	—
143	C₄×Q₈×C₆₇	—	2	2	no	—
144	C₄×Q₈×C₆₇	—	2	2	no	—
145	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
146	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
147	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
148	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
149	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
150	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
151	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
152	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
153	C₄×D₄×C₆₇	—	2	4	no	—
154	C₄×D₄×C₆₇	—	2	2	no	—
155	C₄×D₄×C₆₇	C₂³	1	2	yes	—
156	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
157	#117×C₆₇	—	2	2	no	—
158	#117×C₆₇	—	2	4	no	—
159	#117×C₆₇	—	2	4	no	—
160	#117×C₆₇	—	2	4	no	—
161	#117×C₆₇	C₂³	1	4	yes	—
162	#117×C₆₇	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
164	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
165	C₂×C₄²×C₆₇	—	2	2	no	—
166	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
167	#107×C₆₇	C₂³	1	1	yes	characteristic
168	#107×C₆₇	C₂³	1	2	yes	—
169	#107×C₆₇	C₂³	1	2	yes	—
170	#107×C₆₇	C₂³	1	2	yes	—
171	#107×C₆₇	C₂³	1	1	yes	characteristic
172	#106×C₆₇	C₂³	1	4	yes	—
173	#106×C₆₇	C₂³	1	4	yes	—
174	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
175	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
176	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
177	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
178	#103×C₆₇	C₂³	1	4	yes	—
179	#103×C₆₇	C₂³	1	2	yes	—
180	#103×C₆₇	C₂³	1	4	yes	—
181	#103×C₆₇	C₂³	1	4	yes	—
182	#103×C₆₇	C₂³	1	4	yes	—
183	#103×C₆₇	C₂³	1	4	yes	—
184	#103×C₆₇	C₂³	1	2	yes	—
185	#103×C₆₇	C₂³	1	4	yes	—
186	#103×C₆₇	C₂³	1	2	yes	—
187	#103×C₆₇	C₂³	1	2	yes	—
188	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
189	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
190	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
191	#97×C₆₇	C₂³	1	2	yes	—
192	#97×C₆₇	C₂³	1	2	yes	—
193	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
194	C₄×C₈×C₆₇	C₂³	1	2	yes	—
195	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
198	C₂×Q₈×C₆₇	—	2	2	no	—
199	C₂×Q₈×C₆₇	—	2	4	no	—
200	C₂×Q₈×C₆₇	—	2	2	no	—
201	C₂×Q₈×C₆₇	—	2	4	no	—
202	C₂×Q₈×C₆₇	—	2	8	no	—
203	C₂×Q₈×C₆₇	—	4	2	no	—
204	C₂×Q₈×C₆₇	—	4	4	no	—
205	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
206	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
207	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
208	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
209	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
210	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₆₇	—	2	2	no	—
212	C₂²×C₄×C₆₇	—	2	2	no	—
213	C₂²×C₄×C₆₇	—	2	4	no	—
214	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
217	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
218	Q₁₆×C₆₇	—	2	4	no	—
219	Q₁₆×C₆₇	—	2	8	no	—
220	Q₁₆×C₆₇	—	2	2	no	—
221	Q₁₆×C₆₇	—	2	4	no	—
222	Q₁₆×C₆₇	—	4	2	no	—
223	Q₁₆×C₆₇	—	4	4	no	—
224	Q₁₆×C₆₇	#41	1	4	yes	—
225	M₁₆×C₆₇	—	4	2	no	—
226	C₂×C₈×C₆₇	—	2	2	no	—
227	C₂×C₈×C₆₇	—	2	4	no	—
228	C₂×C₈×C₆₇	—	4	1	no	—
229	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
230	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
231	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
232	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
233	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
234	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
235	C₄⋊C₄×C₆₇	—	2	2	no	—
236	C₄⋊C₄×C₆₇	—	2	2	no	—
237	C₄⋊C₄×C₆₇	—	2	2	no	—
238	C₄⋊C₄×C₆₇	—	2	2	no	—
239	C₄⋊C₄×C₆₇	—	2	2	no	—
240	C₄⋊C₄×C₆₇	—	2	4	no	—
241	C₄⋊C₄×C₆₇	—	2	4	no	—
242	C₄⋊C₄×C₆₇	—	2	4	no	—
243	C₄⋊C₄×C₆₇	—	2	2	no	—
244	C₄⋊C₄×C₆₇	—	2	4	no	—
245	C₄⋊C₄×C₆₇	—	2	2	no	—
246	C₄⋊C₄×C₆₇	—	2	4	no	—
247	C₄⋊C₄×C₆₇	—	2	2	no	—
248	C₄⋊C₄×C₆₇	—	2	4	no	—
249	C₄⋊C₄×C₆₇	—	2	4	no	—
250	C₄⋊C₄×C₆₇	—	2	4	no	—
251	C₄⋊C₄×C₆₇	—	2	4	no	—
252	C₄⋊C₄×C₆₇	—	2	4	no	—
253	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
254	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
255	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
256	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
257	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
258	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
259	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
260	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
262	C₂²⋊C₄×C₆₇	—	2	4	no	—
263	C₂²⋊C₄×C₆₇	—	2	4	no	—
264	C₂²⋊C₄×C₆₇	—	2	4	no	—
265	C₂²⋊C₄×C₆₇	—	2	4	no	—
266	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
267	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
268	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
269	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
270	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
271	C₄²×C₆₇	—	2	2	no	—
272	C₄²×C₆₇	—	2	2	no	—
273	C₄²×C₆₇	—	2	2	no	—
274	C₄²×C₆₇	—	2	2	no	—
275	C₄²×C₆₇	—	2	4	no	—
276	C₄²×C₆₇	—	2	4	no	—
277	C₄²×C₆₇	—	2	4	no	—
278	C₄²×C₆₇	—	2	4	no	—
279	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
280	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
281	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
282	C₄²×C₆₇	C₂⁴	1	2	yes	—
283	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
284	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
285	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
286	Q₈×C₆₇	—	2	2	no	—
287	Q₈×C₆₇	—	2	2	no	—
288	Q₈×C₆₇	—	2	2	no	—
289	Q₈×C₆₇	—	2	4	no	—
290	Q₈×C₆₇	—	2	4	no	—
291	Q₈×C₆₇	—	2	2	no	—
292	Q₈×C₆₇	—	4	4	no	—
293	Q₈×C₆₇	—	4	8	no	—
294	Q₈×C₆₇	—	4	4	no	—
295	Q₈×C₆₇	C₂×#41	1	4	yes	—
296	D₄×C₆₇	—	2	4	no	—
297	D₄×C₆₇	—	2	2	no	—
298	C₂×C₄×C₆₇	—	2	2	no	—
299	C₂×C₄×C₆₇	—	2	2	no	—
300	C₂×C₄×C₆₇	—	2	2	no	—
301	C₂×C₄×C₆₇	—	2	1	no	—
302	C₂×C₄×C₆₇	—	2	2	no	—
303	C₂×C₄×C₆₇	—	2	1	no	—
304	C₂×C₄×C₆₇	—	2	2	no	—
305	C₂×C₄×C₆₇	—	2	2	no	—
306	C₂×C₄×C₆₇	—	2	4	no	—
307	C₂×C₄×C₆₇	—	2	2	no	—
308	C₂×C₄×C₆₇	—	2	2	no	—
309	C₂×C₄×C₆₇	—	2	4	no	—
310	C₂×C₄×C₆₇	—	4	4	no	—
311	C₂×C₄×C₆₇	—	4	8	no	—
312	C₂×C₄×C₆₇	—	4	4	no	—
313	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
314	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
315	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
316	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
317	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
318	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
322	C₈×C₆₇	—	2	2	no	—
323	C₈×C₆₇	—	2	1	no	—
324	C₈×C₆₇	—	2	1	no	—
325	C₈×C₆₇	—	2	1	no	—
326	C₈×C₆₇	—	2	2	no	—
327	C₈×C₆₇	C₂×#41	1	2	yes	—
328	C₂²×C₆₇	—	2	1	no	—
329	C₂²×C₆₇	—	2	1	no	—
330	C₂²×C₆₇	—	2	2	no	—
331	C₂²×C₆₇	—	2	2	no	—
332	C₂²×C₆₇	—	2	2	no	—
333	C₂²×C₆₇	#578	1	2	yes	—
334	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
335	C₄×C₆₇	—	2	1	no	—
336	C₄×C₆₇	—	2	2	no	—
337	C₄×C₆₇	—	2	4	no	—
338	C₄×C₆₇	—	2	1	no	—
339	C₄×C₆₇	—	2	1	no	—
340	C₄×C₆₇	—	2	1	no	—
341	C₄×C₆₇	—	2	2	no	—
342	C₄×C₆₇	—	2	2	no	—
343	C₄×C₆₇	—	4	2	no	—
344	C₄×C₆₇	—	4	4	no	—
345	C₄×C₆₇	—	4	2	no	—
346	C₄×C₆₇	—	4	2	no	—
347	C₄×C₆₇	—	4	4	no	—
348	C₄×C₆₇	#578	1	2	yes	—
349	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
350	C₄×C₆₇	#585	1	1	yes	characteristic
351	#61484	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
352	C₂×C₆₇	—	2	2	no	—
353	C₂×C₆₇	—	4	2	no	—
354	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
355	C₂×C₆₇	C₂×#578	1	1	yes	characteristic
356	C₂×C₆₇	C₂×#578	1	1	yes	characteristic
357	#3523	C₂×C₆₇	1	2	yes	—
358	#3395	C₂×C₆₇	1	1	yes	characteristic, complemented
359	#3383	C₂×C₆₇	1	1	yes	characteristic, complemented
360	#3374	C₂×C₆₇	1	2	yes	complemented
361	#3342	C₂×C₆₇	1	1	yes	characteristic, complemented
362	#3336	C₂×C₆₇	1	2	yes	complemented
363	#3328	C₂×C₆₇	1	2	yes	complemented
364	#3312	C₂×C₆₇	1	4	yes	complemented
365	D₄×Q₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
366	D₄×Q₁₆	C₂×C₆₇	1	2	yes	complemented
367	#3177	C₂×C₆₇	1	2	yes	complemented
368	#3170	C₂×C₆₇	1	1	yes	characteristic, complemented
369	#3127	C₂×C₆₇	1	4	yes	complemented
370	#3113	C₂×C₆₇	1	2	yes	complemented
371	#2966	C₂×C₆₇	1	1	yes	characteristic
372	#2950	C₂×C₆₇	1	2	yes	complemented
373	C₂×C₄×Q₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
374	C₆₇	#61484	1	1	yes	characteristic, direct product factor, Sylow
375	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
376	C₂²×Q₁₆	C₂²×C₆₇	1	2	yes	—
377	#557	—	2	2	no	—
378	#557	C₂²×C₆₇	1	2	yes	—
379	#557	C₂²×C₆₇	1	2	yes	—
380	#556	—	2	2	no	—
381	#556	C₂²×C₆₇	1	2	yes	—
382	#552	—	2	4	no	—
383	#552	C₂²×C₆₇	1	4	yes	—
384	D₄×Q₈	C₂²×C₆₇	1	2	yes	—
385	D₄×Q₈	C₂²×C₆₇	1	4	yes	—
386	#541	—	2	4	no	—
387	#541	C₂²×C₆₇	1	4	yes	—
388	#533	—	2	2	no	—
389	#533	C₂²×C₆₇	1	2	yes	—
390	#529	—	2	2	no	—
391	#529	C₂²×C₆₇	1	1	yes	characteristic
392	#519	C₂²×C₆₇	1	4	yes	—
393	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
394	#500	C₂²×C₆₇	1	1	yes	characteristic
395	#499	C₂²×C₆₇	1	2	yes	—
396	#494	C₂²×C₆₇	1	1	yes	characteristic
397	#494	C₂²×C₆₇	1	2	yes	—
398	#491	C₂²×C₆₇	1	4	yes	—
399	#487	C₂²×C₆₇	1	2	yes	—
400	#485	C₂²×C₆₇	1	4	yes	—
401	#485	C₂²×C₆₇	1	4	yes	—
402	#483	C₂²×C₆₇	1	4	yes	—
403	#479	C₂²×C₆₇	1	4	yes	—
404	#479	C₂²×C₆₇	1	4	yes	—
405	#475	C₂²×C₆₇	1	2	yes	—
406	#475	C₂²×C₆₇	1	2	yes	—
407	#470	C₂²×C₆₇	1	4	yes	—
408	#467	C₂²×C₆₇	1	2	yes	—
409	#467	C₂²×C₆₇	1	2	yes	—
410	#467	C₂²×C₆₇	1	2	yes	—
411	#467	C₂²×C₆₇	1	2	yes	—
412	#462	C₂²×C₆₇	1	2	yes	—
413	#462	C₂²×C₆₇	1	2	yes	—
414	#462	C₂²×C₆₇	1	4	yes	—
415	#462	C₂²×C₆₇	1	4	yes	—
416	#451	C₂²×C₆₇	1	4	yes	—
417	#451	C₂²×C₆₇	1	4	yes	—
418	#451	C₂²×C₆₇	1	4	yes	—
419	#446	C₂²×C₆₇	1	1	yes	characteristic
420	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic
421	#441	C₂²×C₆₇	1	4	yes	—
422	#441	C₂²×C₆₇	1	4	yes	—
423	#441	C₂²×C₆₇	1	4	yes	—
424	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
425	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
426	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
427	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
428	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
429	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
430	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
431	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
432	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
433	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
434	#436	C₂²×C₆₇	1	1	yes	characteristic
435	#435	C₂²×C₆₇	1	2	yes	—
436	C₈×D₄	C₂²×C₆₇	1	2	yes	—
437	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
438	#433	C₂²×C₆₇	1	2	yes	—
439	#432	C₂²×C₆₇	1	1	yes	characteristic
440	#427	C₂²×C₆₇	1	2	yes	—
441	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
442	#419	C₂²×C₆₇	1	4	yes	—
443	C₂×#103	C₂²×C₆₇	1	2	yes	—
444	#405	C₂²×C₆₇	1	2	yes	—
445	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
446	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
447	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
448	C₂×Q₁₆	—	2	4	no	—
449	C₂×Q₁₆	—	2	8	no	—
450	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
451	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
452	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
453	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
454	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
455	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
456	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
457	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
458	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
459	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
460	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
461	C₄⋊Q₈	—	2	2	no	—
462	C₄⋊Q₈	—	2	2	no	—
463	C₄⋊Q₈	—	2	4	no	—
464	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
465	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
466	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
467	#126	—	2	4	no	—
468	#126	—	2	4	no	—
469	#126	—	2	4	no	—
470	#126	—	2	4	no	—
471	#126	D₄×C₆₇	1	2	yes	—
472	#125	—	2	2	no	—
473	#125	—	2	4	no	—
474	#125	—	2	4	no	—
475	#125	—	2	4	no	—
476	#125	—	2	4	no	—
477	#125	—	2	4	no	—
478	#125	—	2	2	no	—
479	#125	D₄×C₆₇	1	1	yes	characteristic
480	#125	C₂³×C₆₇	1	4	yes	—
481	#124	—	2	2	no	—
482	#124	D₄×C₆₇	1	1	yes	characteristic
483	#123	—	2	4	no	—
484	#123	D₄×C₆₇	1	2	yes	—
485	C₂²⋊Q₈	—	2	2	no	—
486	C₂²⋊Q₈	—	2	4	no	—
487	C₂²⋊Q₈	—	2	4	no	—
488	C₂²⋊Q₈	—	2	4	no	—
489	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
490	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
491	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
492	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
493	#121	D₄×C₆₇	1	1	yes	characteristic
494	C₄×Q₈	—	2	2	no	—
495	C₄×Q₈	—	2	4	no	—
496	C₄×Q₈	—	2	4	no	—
497	C₄×Q₈	—	2	2	no	—
498	C₄×Q₈	—	2	2	no	—
499	C₄×Q₈	—	2	2	no	—
500	C₄×Q₈	—	2	2	no	—
501	C₄×Q₈	—	2	2	no	—
502	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
503	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
504	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
505	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
506	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
507	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
508	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
509	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
510	C₄×D₄	—	2	4	no	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	C₂³×C₆₇	1	2	yes	—
513	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
514	#117	—	2	2	no	—
515	#117	—	2	4	no	—
516	#117	—	2	4	no	—
517	#117	—	2	4	no	—
518	#117	C₂³×C₆₇	1	4	yes	—
519	#117	C₂³×C₆₇	1	2	yes	—
520	C₂×C₄⋊C₄	—	2	2	no	—
521	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
522	C₂×C₄²	—	2	2	no	—
523	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
524	#107	C₂³×C₆₇	1	1	yes	characteristic
525	#107	C₂³×C₆₇	1	1	yes	characteristic
526	#107	C₂³×C₆₇	1	2	yes	—
527	#107	C₂³×C₆₇	1	2	yes	—
528	#107	C₂³×C₆₇	1	2	yes	—
529	#106	C₂³×C₆₇	1	4	yes	—
530	#106	C₂³×C₆₇	1	4	yes	—
531	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
532	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
533	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
534	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
535	#103	C₂³×C₆₇	1	2	yes	—
536	#103	C₂³×C₆₇	1	2	yes	—
537	#103	C₂³×C₆₇	1	2	yes	—
538	#103	C₂³×C₆₇	1	2	yes	—
539	#103	C₂³×C₆₇	1	4	yes	—
540	#103	C₂³×C₆₇	1	4	yes	—
541	#103	C₂³×C₆₇	1	4	yes	—
542	#103	C₂³×C₆₇	1	4	yes	—
543	#103	C₂³×C₆₇	1	4	yes	—
544	#103	C₂³×C₆₇	1	4	yes	—
545	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
546	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
547	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
548	#97	C₂³×C₆₇	1	2	yes	—
549	#97	C₂³×C₆₇	1	2	yes	—
550	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
551	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
552	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
553	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
554	C₄×C₈	C₂³×C₆₇	1	2	yes	—
555	C₂×Q₈	—	2	2	no	—
556	C₂×Q₈	—	2	4	no	—
557	C₂×Q₈	—	2	2	no	—
558	C₂×Q₈	—	2	4	no	—
559	C₂×Q₈	—	2	8	no	—
560	C₂×Q₈	—	4	2	no	—
561	C₂×Q₈	—	4	4	no	—
562	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
563	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
564	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
565	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
566	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
567	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
572	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
573	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
574	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
575	Q₁₆	—	2	4	no	—
576	Q₁₆	—	2	8	no	—
577	Q₁₆	—	2	2	no	—
578	Q₁₆	—	2	4	no	—
579	Q₁₆	—	4	2	no	—
580	Q₁₆	—	4	4	no	—
581	Q₁₆	#41×C₆₇	1	4	yes	—
582	M₁₆	—	4	2	no	—
583	C₂×C₈	—	2	2	no	—
584	C₂×C₈	—	2	4	no	—
585	C₂×C₈	—	4	1	no	—
586	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
587	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
588	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
589	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
590	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
591	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
592	C₄⋊C₄	—	2	2	no	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	2	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	2	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	2	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
611	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
612	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
613	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
614	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
615	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
616	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
617	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
618	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	—	2	4	no	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₂²⋊C₄	—	2	4	no	—
623	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
624	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
625	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
626	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
627	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
628	C₄²	—	2	2	no	—
629	C₄²	—	2	2	no	—
630	C₄²	—	2	2	no	—
631	C₄²	—	2	2	no	—
632	C₄²	—	2	4	no	—
633	C₄²	—	2	4	no	—
634	C₄²	—	2	4	no	—
635	C₄²	—	2	4	no	—
636	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
637	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
638	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
639	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
640	C₄²	C₂⁴×C₆₇	1	2	yes	—
641	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
642	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
643	Q₈	—	2	2	no	—
644	Q₈	—	2	2	no	—
645	Q₈	—	2	2	no	—
646	Q₈	—	2	4	no	—
647	Q₈	—	2	4	no	—
648	Q₈	—	2	2	no	—
649	Q₈	—	4	4	no	—
650	Q₈	—	4	8	no	—
651	Q₈	—	4	4	no	—
652	Q₈	C₂×#41×C₆₇	1	4	yes	—
653	D₄	—	2	4	no	—
654	D₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	4	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	4	no	—
667	C₂×C₄	—	4	4	no	—
668	C₂×C₄	—	4	8	no	—
669	C₂×C₄	—	4	4	no	—
670	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
671	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
672	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
673	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
674	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
675	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
676	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
677	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
678	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
679	C₈	—	2	1	no	—
680	C₈	—	2	2	no	—
681	C₈	—	2	1	no	—
682	C₈	—	2	1	no	—
683	C₈	—	2	2	no	—
684	C₈	C₂×#41×C₆₇	1	2	yes	—
685	C₂²	—	2	1	no	—
686	C₂²	—	2	1	no	—
687	C₂²	—	2	2	no	—
688	C₂²	—	2	2	no	—
689	C₂²	—	2	2	no	—
690	C₂²	#578×C₆₇	1	2	yes	—
691	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
692	C₄	—	2	1	no	—
693	C₄	—	2	1	no	—
694	C₄	—	2	1	no	—
695	C₄	—	2	2	no	—
696	C₄	—	2	2	no	—
697	C₄	—	2	1	no	—
698	C₄	—	2	2	no	—
699	C₄	—	2	4	no	—
700	C₄	—	4	2	no	—
701	C₄	—	4	2	no	—
702	C₄	—	4	4	no	—
703	C₄	—	4	2	no	—
704	C₄	—	4	4	no	—
705	C₄	#578×C₆₇	1	2	yes	—
706	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
707	C₄	#585×C₆₇	1	1	yes	characteristic
708	C₂	—	2	2	no	—
709	C₂	—	4	2	no	—
710	C₂	D₄×#41×C₆₇	1	1	yes	characteristic
711	C₂	C₂×#578×C₆₇	1	1	yes	characteristic
712	C₂	C₂×#578×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	#121×C₆₇	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #529×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#3395	C₂	semidirect
3. C₆₇×#3383	C₂	semidirect
4. C₆₇×#3374	C₂	semidirect
5. C₆₇×#3342	C₂	semidirect
6. C₆₇×#3336	C₂	semidirect
7. C₆₇×#3328	C₂	semidirect
8. C₆₇×#3312	C₂	semidirect
9. D₄×Q₁₆×C₆₇	C₂	semidirect
10. D₄×Q₁₆×C₆₇	C₂	semidirect
11. C₆₇×#3177	C₂	semidirect
12. C₆₇×#3170	C₂	semidirect
13. C₆₇×#3127	C₂	semidirect
14. C₆₇×#3113	C₂	semidirect
16. C₆₇×#2950	C₂	semidirect
17. C₂×C₄×Q₁₆×C₆₇	C₂	semidirect
351. #61484	C₆₇	direct (N × H)
358. #3395	C₂×C₆₇	semidirect
359. #3383	C₂×C₆₇	semidirect
360. #3374	C₂×C₆₇	semidirect
361. #3342	C₂×C₆₇	semidirect
362. #3336	C₂×C₆₇	semidirect
363. #3328	C₂×C₆₇	semidirect
364. #3312	C₂×C₆₇	semidirect
365. D₄×Q₁₆	C₂×C₆₇	semidirect
366. D₄×Q₁₆	C₂×C₆₇	semidirect
367. #3177	C₂×C₆₇	semidirect
368. #3170	C₂×C₆₇	semidirect
369. #3127	C₂×C₆₇	semidirect
370. #3113	C₂×C₆₇	semidirect
372. #2950	C₂×C₆₇	semidirect
373. C₂×C₄×Q₁₆	C₂×C₆₇	semidirect
374. C₆₇	#61484	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#3523	2
C₆₇×#3395	2
C₆₇×#3383	2
C₆₇×#3374	2
C₆₇×#3342	2
C₆₇×#3336	2
C₆₇×#3328	2
C₆₇×#3312	2
D₄×Q₁₆×C₆₇	2
C₆₇×#3177	2
C₆₇×#3170	2
C₆₇×#3127	2
C₆₇×#3113	2
C₆₇×#2966	2
C₆₇×#2950	2
C₂×C₄×Q₁₆×C₆₇	2
#61484	67

Subgroups — C67×#61484 #30740735

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61484 #30740735