Subgroups — C₆₇×#20084 #30699335

Order 17152.

732 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3362	C₂	1	2	yes	maximal, complemented
2	C₆₇×#3274	C₂	1	2	yes	maximal, complemented
3	C₆₇×#1721	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#1697	C₂	1	2	yes	maximal, complemented
5	C₆₇×#1668	C₂	1	2	yes	maximal, complemented
6	C₆₇×#1629	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1623	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#1621	C₂	1	2	yes	maximal, complemented
9	C₆₇×#1588	C₂	1	2	yes	maximal, complemented
10	C₂×AGL(1,ℤ/8)×C₆₇	—	2	2	no	—
11	Q₈²×C₆₇	C₂²	1	1	yes	characteristic, complemented
12	#550×C₆₇	C₂²	1	2	yes	—
13	D₄²×C₆₇	C₂²	1	1	yes	characteristic
14	#493×C₆₇	C₂²	1	2	yes	—
15	#493×C₆₇	C₂²	1	1	yes	characteristic, complemented
16	#492×C₆₇	C₂²	1	1	yes	characteristic
17	#486×C₆₇	—	2	2	no	—
18	#486×C₆₇	C₂²	1	2	yes	complemented
19	#476×C₆₇	—	2	2	no	—
20	#476×C₆₇	C₂²	1	2	yes	—
21	#469×C₆₇	—	2	2	no	—
22	#460×C₆₇	—	2	2	no	—
23	#460×C₆₇	C₂²	1	2	yes	—
24	#460×C₆₇	C₂²	1	2	yes	complemented
25	#459×C₆₇	C₂²	1	2	yes	—
26	#449×C₆₇	—	2	2	no	—
27	#447×C₆₇	—	2	2	no	—
28	C₈×Q₈×C₆₇	C₂²	1	2	yes	complemented
29	C₄×SD₁₆×C₆₇	—	2	2	no	—
30	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
31	#436×C₆₇	C₂²	1	2	yes	—
32	#335×C₆₇	C₂²	1	2	yes	complemented
33	#333×C₆₇	C₂²	1	1	yes	characteristic, complemented
34	#331×C₆₇	C₂²	1	1	yes	characteristic
35	#331×C₆₇	C₂²	1	2	yes	complemented
36	Q₈⋊C₈×C₆₇	C₂²	1	2	yes	complemented
37	D₄⋊C₈×C₆₇	C₂²	1	2	yes	—
38	#322×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	C₂×#41×C₆₇	—	2	2	no	—
40	C₂²×D₄×C₆₇	—	2	2	no	—
41	AGL(1,ℤ/8)×C₆₇	—	4	8	no	—
42	C₂×SD₁₆×C₆₇	—	2	2	no	—
43	C₂×SD₁₆×C₆₇	—	2	2	no	—
44	C₂×SD₁₆×C₆₇	—	4	1	no	—
45	C₂×SD₁₆×C₆₇	D₄	1	2	yes	—
46	C₂×D₈×C₆₇	—	2	2	no	—
47	C₂×D₈×C₆₇	—	2	2	no	—
48	C₂×D₈×C₆₇	—	2	2	no	—
49	C₂×D₈×C₆₇	—	4	1	no	—
50	C₂×M₁₆×C₆₇	—	2	2	no	—
51	C₄⋊Q₈×C₆₇	—	2	2	no	—
52	C₄⋊Q₈×C₆₇	—	4	1	no	—
53	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
54	#127×C₆₇	—	2	2	no	—
55	#127×C₆₇	C₂³	1	2	yes	—
56	#127×C₆₇	C₂³	1	1	yes	characteristic
57	#121×C₆₇	—	2	2	no	—
58	#121×C₆₇	—	2	2	no	—
59	#121×C₆₇	—	4	2	no	—
60	#120×C₆₇	—	4	1	no	—
61	C₄×Q₈×C₆₇	—	2	2	no	—
62	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
63	C₄×D₄×C₆₇	—	2	2	no	—
64	C₄×D₄×C₆₇	C₂³	1	2	yes	—
65	#106×C₆₇	—	2	2	no	—
66	#106×C₆₇	D₄	1	2	yes	—
67	C₄⋊C₈×C₆₇	—	2	2	no	—
68	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
69	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
70	#103×C₆₇	D₄	1	2	yes	—
71	#102×C₆₇	—	2	2	no	—
72	#102×C₆₇	—	2	2	no	—
73	#102×C₆₇	—	2	2	no	—
74	#102×C₆₇	—	2	2	no	—
75	#102×C₆₇	—	2	2	no	—
76	#102×C₆₇	—	2	2	no	—
77	#102×C₆₇	D₄	1	2	yes	—
78	C₂²⋊C₈×C₆₇	—	2	2	no	—
79	C₄×C₈×C₆₇	—	2	2	no	—
80	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
81	C₄×C₈×C₆₇	C₂³	1	2	yes	—
82	C₂⁴×C₆₇	—	4	1	no	—
83	#41×C₆₇	—	4	4	no	—
84	#41×C₆₇	—	8	2	no	—
85	C₂×Q₈×C₆₇	—	2	1	no	—
86	C₂×Q₈×C₆₇	—	4	1	no	—
87	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
88	C₂×D₄×C₆₇	—	2	2	no	—
89	C₂×D₄×C₆₇	—	2	2	no	—
90	C₂×D₄×C₆₇	—	2	2	no	—
91	C₂×D₄×C₆₇	—	2	1	no	—
92	C₂×D₄×C₆₇	—	2	2	no	—
93	C₂×D₄×C₆₇	—	4	2	no	—
94	C₂×D₄×C₆₇	—	4	2	no	—
95	C₂×D₄×C₆₇	—	4	2	no	—
96	C₂×D₄×C₆₇	—	4	4	no	—
97	C₂×D₄×C₆₇	—	8	2	no	—
98	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₆₇	—	2	2	no	—
100	C₂²×C₄×C₆₇	—	4	2	no	—
101	SD₁₆×C₆₇	—	2	4	no	—
102	SD₁₆×C₆₇	—	4	4	no	—
103	SD₁₆×C₆₇	—	4	4	no	—
104	SD₁₆×C₆₇	—	8	2	no	—
105	D₈×C₆₇	—	4	4	no	—
106	D₈×C₆₇	—	4	4	no	—
107	D₈×C₆₇	—	8	2	no	—
108	D₈×C₆₇	—	8	2	no	—
109	M₁₆×C₆₇	—	4	4	no	—
110	C₂×C₈×C₆₇	—	2	1	no	—
111	C₂×C₈×C₆₇	—	2	2	no	—
112	C₂×C₈×C₆₇	—	2	2	no	—
113	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
114	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
115	C₄⋊C₄×C₆₇	—	2	2	no	—
116	C₄⋊C₄×C₆₇	—	2	2	no	—
117	C₄⋊C₄×C₆₇	—	4	2	no	—
118	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
119	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
120	C₂²⋊C₄×C₆₇	—	2	2	no	—
121	C₂²⋊C₄×C₆₇	—	4	2	no	—
122	C₂²⋊C₄×C₆₇	—	4	1	no	—
123	C₄²×C₆₇	—	2	2	no	—
124	C₄²×C₆₇	—	4	1	no	—
125	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
126	C₂³×C₆₇	—	2	2	no	—
127	C₂³×C₆₇	—	4	2	no	—
128	C₂³×C₆₇	—	4	1	no	—
129	C₂³×C₆₇	—	8	4	no	—
130	C₂³×C₆₇	—	16	1	no	—
131	Q₈×C₆₇	—	2	2	no	—
132	Q₈×C₆₇	—	8	1	no	—
133	Q₈×C₆₇	—	16	1	no	—
134	Q₈×C₆₇	AGL(1,ℤ/8)	1	4	yes	complemented
135	D₄×C₆₇	—	2	2	no	—
136	D₄×C₆₇	—	2	2	no	—
137	D₄×C₆₇	—	4	2	no	—
138	D₄×C₆₇	—	4	2	no	—
139	D₄×C₆₇	—	4	2	no	—
140	D₄×C₆₇	—	4	2	no	—
141	D₄×C₆₇	—	4	2	no	—
142	D₄×C₆₇	—	4	2	no	—
143	D₄×C₆₇	—	8	4	no	—
144	D₄×C₆₇	—	8	2	no	—
145	D₄×C₆₇	—	8	1	no	—
146	D₄×C₆₇	—	8	4	no	—
147	D₄×C₆₇	—	16	2	no	—
148	C₂×C₄×C₆₇	—	2	2	no	—
149	C₂×C₄×C₆₇	—	2	2	no	—
150	C₂×C₄×C₆₇	—	2	2	no	—
151	C₂×C₄×C₆₇	—	4	2	no	—
152	C₂×C₄×C₆₇	—	4	2	no	—
153	C₂×C₄×C₆₇	—	4	1	no	—
154	C₂×C₄×C₆₇	—	8	4	no	—
155	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
156	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
157	C₈×C₆₇	—	2	2	no	—
158	C₈×C₆₇	—	2	2	no	—
159	C₈×C₆₇	—	2	2	no	—
160	C₈×C₆₇	—	4	2	no	—
161	C₈×C₆₇	—	4	2	no	—
162	C₂²×C₆₇	—	4	2	no	—
163	C₂²×C₆₇	—	4	2	no	—
164	C₂²×C₆₇	—	4	2	no	—
165	C₂²×C₆₇	—	8	2	no	—
166	C₂²×C₆₇	—	8	2	no	—
167	C₂²×C₆₇	—	8	2	no	—
168	C₂²×C₆₇	—	8	2	no	—
169	C₂²×C₆₇	—	8	1	no	—
170	C₂²×C₆₇	—	16	4	no	—
171	C₂²×C₆₇	D₄²	1	1	yes	characteristic
172	C₄×C₆₇	—	2	4	no	—
173	C₄×C₆₇	—	2	1	no	—
174	C₄×C₆₇	—	4	2	no	—
175	C₄×C₆₇	—	4	2	no	—
176	C₄×C₆₇	—	8	1	no	—
177	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
178	C₄×C₆₇	#577	1	2	yes	—
179	#20084	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂×C₆₇	—	8	2	no	—
181	C₂×C₆₇	—	16	2	no	—
182	C₂×C₆₇	—	16	1	no	—
183	C₂×C₆₇	#3265	1	2	yes	—
184	C₂×C₆₇	#3292	1	1	yes	characteristic
185	#3362	C₂×C₆₇	1	2	yes	complemented
186	#3274	C₂×C₆₇	1	2	yes	complemented
187	#1721	C₂×C₆₇	1	1	yes	characteristic, complemented
188	#1697	C₂×C₆₇	1	2	yes	complemented
189	#1668	C₂×C₆₇	1	2	yes	complemented
190	#1629	C₂×C₆₇	1	1	yes	characteristic, complemented
191	#1623	C₂×C₆₇	1	1	yes	characteristic, complemented
192	#1621	C₂×C₆₇	1	2	yes	complemented
193	#1588	C₂×C₆₇	1	2	yes	complemented
194	C₆₇	#20084	1	1	yes	characteristic, direct product factor, Sylow
195	C₂×AGL(1,ℤ/8)	—	2	2	no	—
196	Q₈²	C₂²×C₆₇	1	1	yes	characteristic, complemented
197	#550	C₂²×C₆₇	1	2	yes	—
198	D₄²	C₂²×C₆₇	1	1	yes	characteristic
199	#493	C₂²×C₆₇	1	2	yes	—
200	#493	C₂²×C₆₇	1	1	yes	characteristic, complemented
201	#492	C₂²×C₆₇	1	1	yes	characteristic
202	#486	—	2	2	no	—
203	#486	C₂²×C₆₇	1	2	yes	complemented
204	#476	—	2	2	no	—
205	#476	C₂²×C₆₇	1	2	yes	—
206	#469	—	2	2	no	—
207	#460	—	2	2	no	—
208	#460	C₂²×C₆₇	1	2	yes	—
209	#460	C₂²×C₆₇	1	2	yes	complemented
210	#459	C₂²×C₆₇	1	2	yes	—
211	#449	—	2	2	no	—
212	#447	—	2	2	no	—
213	C₈×Q₈	C₂²×C₆₇	1	2	yes	complemented
214	C₄×SD₁₆	—	2	2	no	—
215	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
216	#436	C₂²×C₆₇	1	2	yes	—
217	#335	C₂²×C₆₇	1	2	yes	complemented
218	#333	C₂²×C₆₇	1	1	yes	characteristic, complemented
219	#331	C₂²×C₆₇	1	1	yes	characteristic
220	#331	C₂²×C₆₇	1	2	yes	complemented
221	Q₈⋊C₈	C₂²×C₆₇	1	2	yes	complemented
222	D₄⋊C₈	C₂²×C₆₇	1	2	yes	—
223	#322	C₂²×C₆₇	1	1	yes	characteristic, complemented
224	C₂×#41	—	2	2	no	—
225	C₂²×D₄	—	2	2	no	—
226	AGL(1,ℤ/8)	—	4	8	no	—
227	C₂×SD₁₆	—	2	2	no	—
228	C₂×SD₁₆	—	2	2	no	—
229	C₂×SD₁₆	—	4	1	no	—
230	C₂×SD₁₆	D₄×C₆₇	1	2	yes	—
231	C₂×D₈	—	2	2	no	—
232	C₂×D₈	—	2	2	no	—
233	C₂×D₈	—	2	2	no	—
234	C₂×D₈	—	4	1	no	—
235	C₂×M₁₆	—	2	2	no	—
236	C₄⋊Q₈	—	2	2	no	—
237	C₄⋊Q₈	—	4	1	no	—
238	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
239	#127	—	2	2	no	—
240	#127	C₂³×C₆₇	1	1	yes	characteristic
241	#127	C₂³×C₆₇	1	2	yes	—
242	#121	—	2	2	no	—
243	#121	—	2	2	no	—
244	#121	—	4	2	no	—
245	#120	—	4	1	no	—
246	C₄×Q₈	—	2	2	no	—
247	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
248	C₄×D₄	—	2	2	no	—
249	C₄×D₄	C₂³×C₆₇	1	2	yes	—
250	#106	—	2	2	no	—
251	#106	D₄×C₆₇	1	2	yes	—
252	C₄⋊C₈	—	2	2	no	—
253	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
254	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
255	#103	D₄×C₆₇	1	2	yes	—
256	#102	—	2	2	no	—
257	#102	—	2	2	no	—
258	#102	—	2	2	no	—
259	#102	—	2	2	no	—
260	#102	—	2	2	no	—
261	#102	—	2	2	no	—
262	#102	D₄×C₆₇	1	2	yes	—
263	C₂²⋊C₈	—	2	2	no	—
264	C₄×C₈	—	2	2	no	—
265	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
266	C₄×C₈	C₂³×C₆₇	1	2	yes	—
267	C₂⁴	—	4	1	no	—
268	#41	—	4	4	no	—
269	#41	—	8	2	no	—
270	C₂×Q₈	—	2	1	no	—
271	C₂×Q₈	—	4	1	no	—
272	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	2	2	no	—
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	—	2	1	no	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	—	4	2	no	—
280	C₂×D₄	—	4	2	no	—
281	C₂×D₄	—	4	4	no	—
282	C₂×D₄	—	8	2	no	—
283	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	4	2	no	—
286	SD₁₆	—	2	4	no	—
287	SD₁₆	—	4	4	no	—
288	SD₁₆	—	4	4	no	—
289	SD₁₆	—	8	2	no	—
290	D₈	—	4	4	no	—
291	D₈	—	4	4	no	—
292	D₈	—	8	2	no	—
293	D₈	—	8	2	no	—
294	M₁₆	—	4	4	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
299	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	4	2	no	—
303	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
304	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
305	C₂²⋊C₄	—	2	2	no	—
306	C₂²⋊C₄	—	4	2	no	—
307	C₂²⋊C₄	—	4	1	no	—
308	C₄²	—	2	2	no	—
309	C₄²	—	4	1	no	—
310	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
311	C₂³	—	2	2	no	—
312	C₂³	—	4	2	no	—
313	C₂³	—	4	1	no	—
314	C₂³	—	8	4	no	—
315	C₂³	—	16	1	no	—
316	Q₈	—	2	2	no	—
317	Q₈	—	8	1	no	—
318	Q₈	—	16	1	no	—
319	Q₈	AGL(1,ℤ/8)×C₆₇	1	4	yes	complemented
320	D₄	—	2	2	no	—
321	D₄	—	2	2	no	—
322	D₄	—	4	2	no	—
323	D₄	—	4	2	no	—
324	D₄	—	4	2	no	—
325	D₄	—	4	2	no	—
326	D₄	—	4	2	no	—
327	D₄	—	4	2	no	—
328	D₄	—	8	4	no	—
329	D₄	—	8	2	no	—
330	D₄	—	8	1	no	—
331	D₄	—	8	4	no	—
332	D₄	—	16	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	8	4	no	—
340	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
341	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
342	C₈	—	2	2	no	—
343	C₈	—	2	2	no	—
344	C₈	—	2	2	no	—
345	C₈	—	4	2	no	—
346	C₈	—	4	2	no	—
347	C₂²	—	4	2	no	—
348	C₂²	—	4	2	no	—
349	C₂²	—	4	2	no	—
350	C₂²	—	8	2	no	—
351	C₂²	—	8	2	no	—
352	C₂²	—	8	2	no	—
353	C₂²	—	8	2	no	—
354	C₂²	—	8	1	no	—
355	C₂²	—	16	4	no	—
356	C₂²	D₄²×C₆₇	1	1	yes	characteristic
357	C₄	—	2	4	no	—
358	C₄	—	2	1	no	—
359	C₄	—	4	2	no	—
360	C₄	—	4	2	no	—
361	C₄	—	8	1	no	—
362	C₄	C₂×AGL(1,ℤ/8)×C₆₇	1	2	yes	—
363	C₄	#577×C₆₇	1	2	yes	—
364	C₂	—	8	2	no	—
365	C₂	—	16	1	no	—
366	C₂	—	16	2	no	—
367	C₂	C₆₇×#3265	1	2	yes	—
368	C₂	C₆₇×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3362	C₂	semidirect
2. C₆₇×#3274	C₂	semidirect
3. C₆₇×#1721	C₂	semidirect
4. C₆₇×#1697	C₂	semidirect
5. C₆₇×#1668	C₂	semidirect
6. C₆₇×#1629	C₂	semidirect
7. C₆₇×#1623	C₂	semidirect
8. C₆₇×#1621	C₂	semidirect
9. C₆₇×#1588	C₂	semidirect
11. Q₈²×C₆₇	C₂²	semidirect
15. #493×C₆₇	C₂²	semidirect
18. #486×C₆₇	C₂²	semidirect
24. #460×C₆₇	C₂²	semidirect
28. C₈×Q₈×C₆₇	C₂²	semidirect
32. #335×C₆₇	C₂²	semidirect
33. #333×C₆₇	C₂²	semidirect
35. #331×C₆₇	C₂²	semidirect
36. Q₈⋊C₈×C₆₇	C₂²	semidirect
38. #322×C₆₇	C₂²	semidirect
134. Q₈×C₆₇	AGL(1,ℤ/8)	semidirect
179. #20084	C₆₇	direct (N × H)
185. #3362	C₂×C₆₇	semidirect
186. #3274	C₂×C₆₇	semidirect
187. #1721	C₂×C₆₇	semidirect
188. #1697	C₂×C₆₇	semidirect
189. #1668	C₂×C₆₇	semidirect
190. #1629	C₂×C₆₇	semidirect
191. #1623	C₂×C₆₇	semidirect
192. #1621	C₂×C₆₇	semidirect
193. #1588	C₂×C₆₇	semidirect
194. C₆₇	#20084	direct (N × H)
196. Q₈²	C₂²×C₆₇	semidirect
200. #493	C₂²×C₆₇	semidirect
203. #486	C₂²×C₆₇	semidirect
209. #460	C₂²×C₆₇	semidirect
213. C₈×Q₈	C₂²×C₆₇	semidirect
217. #335	C₂²×C₆₇	semidirect
218. #333	C₂²×C₆₇	semidirect
220. #331	C₂²×C₆₇	semidirect
221. Q₈⋊C₈	C₂²×C₆₇	semidirect
223. #322	C₂²×C₆₇	semidirect
319. Q₈	AGL(1,ℤ/8)×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3362	2
C₆₇×#3274	2
C₆₇×#1721	2
C₆₇×#1697	2
C₆₇×#1668	2
C₆₇×#1629	2
C₆₇×#1623	2
C₆₇×#1621	2
C₆₇×#1588	2
#20084	67

Subgroups — C67×#20084 #30699335

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#20084 #30699335