Subgroups — C₆₇×#19959 #30699210

Order 17152.

570 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3393	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#3380	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#3356	C₂	1	2	yes	maximal, complemented
4	C₆₇×#1707	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#1691	C₂	1	2	yes	maximal, complemented
6	C₆₇×#1676	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1670	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#1643	C₂	1	2	yes	maximal, complemented
9	C₆₇×#1638	C₂	1	2	yes	maximal, complemented
10	C₆₇×#1589	C₂	1	1	yes	maximal, characteristic
11	C₈×Q₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	#556×C₆₇	C₂²	1	2	yes	—
13	#554×C₆₇	C₂²	1	2	yes	—
14	#500×C₆₇	C₂²	1	1	yes	characteristic
15	#499×C₆₇	—	2	1	no	—
16	#498×C₆₇	C₂²	1	2	yes	—
17	#495×C₆₇	—	2	1	no	—
18	#494×C₆₇	C₂²	1	1	yes	characteristic
19	#487×C₆₇	C₂²	1	2	yes	—
20	#485×C₆₇	—	2	2	no	—
21	#483×C₆₇	—	2	2	no	—
22	#478×C₆₇	—	2	2	no	—
23	#477×C₆₇	C₂²	1	2	yes	—
24	#476×C₆₇	C₂²	1	2	yes	—
25	#475×C₆₇	C₂²	1	2	yes	—
26	#470×C₆₇	—	2	2	no	—
27	#464×C₆₇	—	2	2	no	—
28	#461×C₆₇	C₂²	1	2	yes	—
29	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic
30	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic
31	C₄×Q₁₆×C₆₇	—	2	1	no	—
32	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
33	C₄×D₈×C₆₇	—	2	1	no	—
34	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
35	#436×C₆₇	C₂²	1	2	yes	—
36	#428×C₆₇	—	2	2	no	—
37	#335×C₆₇	C₂²	1	1	yes	characteristic
38	#335×C₆₇	C₂²	1	1	yes	characteristic
39	#333×C₆₇	C₂²	1	2	yes	—
40	#332×C₆₇	C₂²	1	2	yes	—
41	Q₈⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
42	Q₈⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
43	D₄⋊C₈×C₆₇	C₂²	1	2	yes	—
44	C₈²×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×Q₁₆×C₆₇	—	2	1	no	—
46	C₂×Q₁₆×C₆₇	—	2	1	no	—
47	C₂×Q₁₆×C₆₇	D₄	1	1	yes	characteristic
48	C₂×SD₁₆×C₆₇	—	2	2	no	—
49	C₂×D₈×C₆₇	D₄	1	1	yes	characteristic
50	C₂×M₁₆×C₆₇	—	2	2	no	—
51	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
52	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
53	#126×C₆₇	—	4	2	no	—
54	#125×C₆₇	—	2	2	no	—
55	#124×C₆₇	—	2	2	no	—
56	C₂²⋊Q₈×C₆₇	—	2	2	no	—
57	C₂²⋊Q₈×C₆₇	—	2	2	no	—
58	C₂²⋊Q₈×C₆₇	—	4	2	no	—
59	C₄×Q₈×C₆₇	—	2	2	no	—
60	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
61	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
62	C₄×D₄×C₆₇	—	2	2	no	—
63	C₄×D₄×C₆₇	C₂³	1	2	yes	—
64	#117×C₆₇	—	2	2	no	—
65	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
66	#107×C₆₇	—	2	1	no	—
67	#107×C₆₇	—	2	1	no	—
68	#107×C₆₇	—	2	2	no	—
69	#107×C₆₇	D₄	1	1	yes	characteristic
70	#107×C₆₇	D₄	1	1	yes	characteristic
71	#106×C₆₇	—	2	2	no	—
72	#106×C₆₇	—	2	2	no	—
73	#106×C₆₇	—	2	2	no	—
74	#106×C₆₇	—	2	2	no	—
75	C₄⋊C₈×C₆₇	—	2	1	no	—
76	C₄⋊C₈×C₆₇	—	2	1	no	—
77	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
78	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
79	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
80	#103×C₆₇	—	2	2	no	—
81	#103×C₆₇	—	2	2	no	—
82	#103×C₆₇	—	2	2	no	—
83	#103×C₆₇	—	4	2	no	—
84	#103×C₆₇	D₄	1	1	yes	characteristic
85	#103×C₆₇	D₄	1	1	yes	characteristic
86	#102×C₆₇	—	2	2	no	—
87	#102×C₆₇	D₄	1	2	yes	—
88	C₂²⋊C₈×C₆₇	—	2	2	no	—
89	C₄×C₈×C₆₇	—	2	1	no	—
90	C₄×C₈×C₆₇	—	2	1	no	—
91	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
94	C₂×Q₈×C₆₇	—	2	2	no	—
95	C₂×Q₈×C₆₇	—	2	2	no	—
96	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
97	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
98	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₆₇	—	2	2	no	—
100	C₂²×C₄×C₆₇	—	4	2	no	—
101	Q₁₆×C₆₇	—	2	2	no	—
102	Q₁₆×C₆₇	—	4	2	no	—
103	Q₁₆×C₆₇	—	8	1	no	—
104	SD₁₆×C₆₇	—	8	2	no	—
105	D₈×C₆₇	—	2	2	no	—
106	M₁₆×C₆₇	—	4	4	no	—
107	C₂×C₈×C₆₇	—	2	1	no	—
108	C₂×C₈×C₆₇	—	2	1	no	—
109	C₂×C₈×C₆₇	—	2	2	no	—
110	C₂×C₈×C₆₇	—	2	1	no	—
111	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
115	C₄⋊C₄×C₆₇	—	2	1	no	—
116	C₄⋊C₄×C₆₇	—	2	1	no	—
117	C₄⋊C₄×C₆₇	—	2	2	no	—
118	C₄⋊C₄×C₆₇	—	2	2	no	—
119	C₄⋊C₄×C₆₇	—	2	2	no	—
120	C₄⋊C₄×C₆₇	—	2	2	no	—
121	C₄⋊C₄×C₆₇	—	4	2	no	—
122	C₄⋊C₄×C₆₇	—	4	2	no	—
123	C₄⋊C₄×C₆₇	—	4	2	no	—
124	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
125	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
126	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
127	C₂²⋊C₄×C₆₇	—	2	2	no	—
128	C₂²⋊C₄×C₆₇	—	4	2	no	—
129	C₂²⋊C₄×C₆₇	—	4	2	no	—
130	C₂²⋊C₄×C₆₇	—	4	2	no	—
131	C₄²×C₆₇	—	2	1	no	—
132	C₄²×C₆₇	—	2	1	no	—
133	C₄²×C₆₇	—	4	2	no	—
134	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
135	C₂³×C₆₇	—	2	2	no	—
136	Q₈×C₆₇	—	2	1	no	—
137	Q₈×C₆₇	—	2	1	no	—
138	Q₈×C₆₇	—	2	1	no	—
139	Q₈×C₆₇	—	2	1	no	—
140	Q₈×C₆₇	—	4	2	no	—
141	Q₈×C₆₇	—	4	2	no	—
142	Q₈×C₆₇	—	8	2	no	—
143	D₄×C₆₇	—	2	2	no	—
144	D₄×C₆₇	—	2	2	no	—
145	C₂×C₄×C₆₇	—	2	1	no	—
146	C₂×C₄×C₆₇	—	2	1	no	—
147	C₂×C₄×C₆₇	—	2	1	no	—
148	C₂×C₄×C₆₇	—	2	1	no	—
149	C₂×C₄×C₆₇	—	2	2	no	—
150	C₂×C₄×C₆₇	—	4	2	no	—
151	C₂×C₄×C₆₇	—	4	2	no	—
152	C₂×C₄×C₆₇	—	4	2	no	—
153	C₂×C₄×C₆₇	—	4	2	no	—
154	C₂×C₄×C₆₇	—	16	2	no	—
155	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
158	C₈×C₆₇	—	2	1	no	—
159	C₈×C₆₇	—	2	1	no	—
160	C₈×C₆₇	—	4	1	no	—
161	C₈×C₆₇	—	4	2	no	—
162	C₈×C₆₇	—	4	1	no	—
163	C₈×C₆₇	—	4	1	no	—
164	C₈×C₆₇	#135	1	2	yes	—
165	C₈×C₆₇	#137	1	2	yes	—
166	C₂²×C₆₇	—	4	2	no	—
167	C₂²×C₆₇	—	4	2	no	—
168	C₂²×C₆₇	—	4	2	no	—
169	C₂²×C₆₇	D₄²	1	1	yes	characteristic
170	C₄×C₆₇	—	2	1	no	—
171	C₄×C₆₇	—	4	2	no	—
172	C₄×C₆₇	—	4	1	no	—
173	C₄×C₆₇	—	4	1	no	—
174	C₄×C₆₇	—	4	1	no	—
175	C₄×C₆₇	—	4	1	no	—
176	C₄×C₆₇	—	8	2	no	—
177	C₄×C₆₇	—	8	2	no	—
178	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
179	C₄×C₆₇	C₂×#137	1	1	yes	characteristic
180	C₄×C₆₇	#577	1	1	yes	characteristic
181	C₄×C₆₇	#578	1	1	yes	characteristic
182	#19959	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂×C₆₇	—	8	2	no	—
184	C₂×C₆₇	#3278	1	1	yes	characteristic
185	C₂×C₆₇	#3283	1	1	yes	characteristic
186	C₂×C₆₇	#3290	1	1	yes	characteristic
187	#3393	C₂×C₆₇	1	1	yes	characteristic
188	#3380	C₂×C₆₇	1	1	yes	characteristic
189	#3356	C₂×C₆₇	1	2	yes	complemented
190	#1707	C₂×C₆₇	1	1	yes	characteristic, complemented
191	#1691	C₂×C₆₇	1	2	yes	complemented
192	#1676	C₂×C₆₇	1	1	yes	characteristic, complemented
193	#1670	C₂×C₆₇	1	1	yes	characteristic, complemented
194	#1643	C₂×C₆₇	1	2	yes	complemented
195	#1638	C₂×C₆₇	1	2	yes	complemented
196	#1589	C₂×C₆₇	1	1	yes	characteristic
197	C₈×Q₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
198	C₆₇	#19959	1	1	yes	characteristic, direct product factor, Sylow
199	#556	C₂²×C₆₇	1	2	yes	—
200	#554	C₂²×C₆₇	1	2	yes	—
201	#500	C₂²×C₆₇	1	1	yes	characteristic
202	#499	—	2	1	no	—
203	#498	C₂²×C₆₇	1	2	yes	—
204	#495	—	2	1	no	—
205	#494	C₂²×C₆₇	1	1	yes	characteristic
206	#487	C₂²×C₆₇	1	2	yes	—
207	#485	—	2	2	no	—
208	#483	—	2	2	no	—
209	#478	—	2	2	no	—
210	#477	C₂²×C₆₇	1	2	yes	—
211	#476	C₂²×C₆₇	1	2	yes	—
212	#475	C₂²×C₆₇	1	2	yes	—
213	#470	—	2	2	no	—
214	#464	—	2	2	no	—
215	#461	C₂²×C₆₇	1	2	yes	—
216	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic
217	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic
218	C₄×Q₁₆	—	2	1	no	—
219	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
220	C₄×D₈	—	2	1	no	—
221	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
222	#436	C₂²×C₆₇	1	2	yes	—
223	#428	—	2	2	no	—
224	#335	C₂²×C₆₇	1	1	yes	characteristic
225	#335	C₂²×C₆₇	1	1	yes	characteristic
226	#333	C₂²×C₆₇	1	2	yes	—
227	#332	C₂²×C₆₇	1	2	yes	—
228	Q₈⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
229	Q₈⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
230	D₄⋊C₈	C₂²×C₆₇	1	2	yes	—
231	C₈²	C₂²×C₆₇	1	1	yes	characteristic
232	C₂×Q₁₆	—	2	1	no	—
233	C₂×Q₁₆	—	2	1	no	—
234	C₂×Q₁₆	D₄×C₆₇	1	1	yes	characteristic
235	C₂×SD₁₆	—	2	2	no	—
236	C₂×D₈	D₄×C₆₇	1	1	yes	characteristic
237	C₂×M₁₆	—	2	2	no	—
238	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
239	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
240	#126	—	4	2	no	—
241	#125	—	2	2	no	—
242	#124	—	2	2	no	—
243	C₂²⋊Q₈	—	2	2	no	—
244	C₂²⋊Q₈	—	2	2	no	—
245	C₂²⋊Q₈	—	4	2	no	—
246	C₄×Q₈	—	2	2	no	—
247	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
248	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
249	C₄×D₄	—	2	2	no	—
250	C₄×D₄	C₂³×C₆₇	1	2	yes	—
251	#117	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	#107	—	2	1	no	—
254	#107	—	2	1	no	—
255	#107	—	2	2	no	—
256	#107	D₄×C₆₇	1	1	yes	characteristic
257	#107	D₄×C₆₇	1	1	yes	characteristic
258	#106	—	2	2	no	—
259	#106	—	2	2	no	—
260	#106	—	2	2	no	—
261	#106	—	2	2	no	—
262	C₄⋊C₈	—	2	1	no	—
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
265	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
266	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
267	#103	—	2	2	no	—
268	#103	—	2	2	no	—
269	#103	—	2	2	no	—
270	#103	—	4	2	no	—
271	#103	D₄×C₆₇	1	1	yes	characteristic
272	#103	D₄×C₆₇	1	1	yes	characteristic
273	#102	—	2	2	no	—
274	#102	D₄×C₆₇	1	2	yes	—
275	C₂²⋊C₈	—	2	2	no	—
276	C₄×C₈	—	2	1	no	—
277	C₄×C₈	—	2	1	no	—
278	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
279	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
280	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
284	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
285	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	4	2	no	—
288	Q₁₆	—	2	2	no	—
289	Q₁₆	—	4	2	no	—
290	Q₁₆	—	8	1	no	—
291	SD₁₆	—	8	2	no	—
292	D₈	—	2	2	no	—
293	M₁₆	—	4	4	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
299	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
300	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
301	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
302	C₄⋊C₄	—	2	1	no	—
303	C₄⋊C₄	—	2	1	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	4	2	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
312	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
313	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
314	C₂²⋊C₄	—	2	2	no	—
315	C₂²⋊C₄	—	4	2	no	—
316	C₂²⋊C₄	—	4	2	no	—
317	C₂²⋊C₄	—	4	2	no	—
318	C₄²	—	2	1	no	—
319	C₄²	—	2	1	no	—
320	C₄²	—	4	2	no	—
321	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
322	C₂³	—	2	2	no	—
323	Q₈	—	2	1	no	—
324	Q₈	—	2	1	no	—
325	Q₈	—	2	1	no	—
326	Q₈	—	2	1	no	—
327	Q₈	—	4	2	no	—
328	Q₈	—	4	2	no	—
329	Q₈	—	8	2	no	—
330	D₄	—	2	2	no	—
331	D₄	—	2	2	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	16	2	no	—
342	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
343	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
344	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
345	C₈	—	2	1	no	—
346	C₈	—	2	1	no	—
347	C₈	—	4	1	no	—
348	C₈	—	4	2	no	—
349	C₈	—	4	1	no	—
350	C₈	—	4	1	no	—
351	C₈	#135×C₆₇	1	2	yes	—
352	C₈	#137×C₆₇	1	2	yes	—
353	C₂²	—	4	2	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	4	2	no	—
356	C₂²	D₄²×C₆₇	1	1	yes	characteristic
357	C₄	—	2	1	no	—
358	C₄	—	4	2	no	—
359	C₄	—	4	1	no	—
360	C₄	—	4	1	no	—
361	C₄	—	4	1	no	—
362	C₄	—	4	1	no	—
363	C₄	—	8	2	no	—
364	C₄	—	8	2	no	—
365	C₄	C₂×#135×C₆₇	1	1	yes	characteristic
366	C₄	C₂×#137×C₆₇	1	1	yes	characteristic
367	C₄	#577×C₆₇	1	1	yes	characteristic
368	C₄	#578×C₆₇	1	1	yes	characteristic
369	C₂	—	8	2	no	—
370	C₂	C₆₇×#3278	1	1	yes	characteristic
371	C₂	C₆₇×#3283	1	1	yes	characteristic
372	C₂	C₆₇×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₇
prime radical	C₂×D₈×C₆₇	D₄
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
3. C₆₇×#3356	C₂	semidirect
4. C₆₇×#1707	C₂	semidirect
5. C₆₇×#1691	C₂	semidirect
6. C₆₇×#1676	C₂	semidirect
7. C₆₇×#1670	C₂	semidirect
8. C₆₇×#1643	C₂	semidirect
9. C₆₇×#1638	C₂	semidirect
11. C₈×Q₁₆×C₆₇	C₂	semidirect
182. #19959	C₆₇	direct (N × H)
189. #3356	C₂×C₆₇	semidirect
190. #1707	C₂×C₆₇	semidirect
191. #1691	C₂×C₆₇	semidirect
192. #1676	C₂×C₆₇	semidirect
193. #1670	C₂×C₆₇	semidirect
194. #1643	C₂×C₆₇	semidirect
195. #1638	C₂×C₆₇	semidirect
197. C₈×Q₁₆	C₂×C₆₇	semidirect
198. C₆₇	#19959	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×#3393	2
C₆₇×#3380	2
C₆₇×#3356	2
C₆₇×#1707	2
C₆₇×#1691	2
C₆₇×#1676	2
C₆₇×#1670	2
C₆₇×#1643	2
C₆₇×#1638	2
C₆₇×#1589	2
C₈×Q₁₆×C₆₇	2
#19959	67

Subgroups — C67×#19959 #30699210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#19959 #30699210