Subgroups — C₆₇×#33180 #30712431

Order 17152.

1026 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#494×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#470×C₆₇	C₂	1	2	yes	maximal
3	C₂×#467×C₆₇	C₂	1	2	yes	maximal
4	C₂×#405×C₆₇	C₂	1	1	yes	maximal, characteristic
5	C₆₇×#2621	C₂	1	2	yes	maximal
6	C₆₇×#1971	C₂	1	2	yes	maximal, complemented
7	C₆₇×#1969	C₂	1	2	yes	maximal, complemented
8	C₆₇×#1960	C₂	1	2	yes	maximal, complemented
9	C₆₇×#1846	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×Q₁₆×C₆₇	C₂²	1	2	yes	—
11	C₂²×Q₁₆×C₆₇	C₂²	1	2	yes	—
12	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	—
15	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	—
16	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
17	#494×C₆₇	—	2	4	no	—
18	#470×C₆₇	—	2	8	no	—
19	#467×C₆₇	—	2	8	no	—
20	C₂×#107×C₆₇	C₂²	1	2	yes	—
21	C₂×#106×C₆₇	C₂²	1	2	yes	—
22	C₂×#103×C₆₇	C₂²	1	4	yes	—
23	C₂×#103×C₆₇	C₂²	1	4	yes	—
24	#405×C₆₇	—	2	4	no	—
25	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
29	#398×C₆₇	—	2	4	no	—
30	#397×C₆₇	—	2	4	no	—
31	#391×C₆₇	C₂²	1	4	yes	—
32	#382×C₆₇	C₂²	1	2	yes	—
33	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
34	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
35	C₂×Q₁₆×C₆₇	—	2	4	no	—
36	C₂×Q₁₆×C₆₇	—	2	4	no	—
37	C₂×Q₁₆×C₆₇	—	2	4	no	—
38	C₂×Q₁₆×C₆₇	—	2	4	no	—
39	C₂×Q₁₆×C₆₇	—	2	4	no	—
40	C₂×Q₁₆×C₆₇	—	2	4	no	—
41	C₂×M₁₆×C₆₇	—	2	2	no	—
42	C₂×M₁₆×C₆₇	—	2	2	no	—
43	C₂×M₁₆×C₆₇	D₄	1	4	yes	—
44	C₂²×C₈×C₆₇	—	2	2	no	—
45	C₂²×C₈×C₆₇	—	2	2	no	—
46	C₂²×C₈×C₆₇	D₄	1	4	yes	—
47	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
51	C₄⋊Q₈×C₆₇	—	2	4	no	—
52	C₄⋊Q₈×C₆₇	—	2	4	no	—
53	C₂²⋊Q₈×C₆₇	—	2	8	no	—
54	C₂²⋊Q₈×C₆₇	—	2	8	no	—
55	#117×C₆₇	—	2	2	no	—
56	#117×C₆₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
58	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
59	C₂×C₄⋊C₄×C₆₇	D₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
61	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
62	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
63	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
65	#107×C₆₇	—	2	4	no	—
66	#106×C₆₇	—	2	4	no	—
67	#103×C₆₇	—	2	8	no	—
68	#103×C₆₇	—	2	8	no	—
69	#97×C₆₇	—	2	2	no	—
70	#97×C₆₇	—	2	2	no	—
71	C₄×C₈×C₆₇	—	2	2	no	—
72	C₄×C₈×C₆₇	D₄	1	4	yes	—
73	#95×C₆₇	—	2	4	no	—
74	#95×C₆₇	—	2	8	no	—
75	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
76	C₂×Q₈×C₆₇	—	2	4	no	—
77	C₂×Q₈×C₆₇	—	2	4	no	—
78	C₂×Q₈×C₆₇	—	2	4	no	—
79	C₂×Q₈×C₆₇	—	2	4	no	—
80	C₂×Q₈×C₆₇	—	2	4	no	—
81	C₂×Q₈×C₆₇	—	2	4	no	—
82	C₂²×C₄×C₆₇	—	2	1	no	—
83	C₂²×C₄×C₆₇	—	2	1	no	—
84	C₂²×C₄×C₆₇	—	2	1	no	—
85	C₂²×C₄×C₆₇	—	2	1	no	—
86	C₂²×C₄×C₆₇	—	2	4	no	—
87	C₂²×C₄×C₆₇	—	2	4	no	—
88	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
94	Q₁₆×C₆₇	—	4	8	no	—
95	Q₁₆×C₆₇	—	4	8	no	—
96	M₁₆×C₆₇	—	2	8	no	—
97	C₂×C₈×C₆₇	—	2	1	no	—
98	C₂×C₈×C₆₇	—	2	1	no	—
99	C₂×C₈×C₆₇	—	2	1	no	—
100	C₂×C₈×C₆₇	—	2	1	no	—
101	C₂×C₈×C₆₇	—	2	8	no	—
102	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
103	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
104	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
105	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
106	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
107	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
108	C₂×C₈×C₆₇	#41	1	2	yes	—
109	C₂×C₈×C₆₇	#41	1	2	yes	—
110	C₄⋊C₄×C₆₇	—	2	4	no	—
111	C₄⋊C₄×C₆₇	—	2	4	no	—
112	C₄⋊C₄×C₆₇	—	2	4	no	—
113	C₄⋊C₄×C₆₇	—	4	8	no	—
114	C₄⋊C₄×C₆₇	—	4	8	no	—
115	C₂²⋊C₄×C₆₇	—	2	4	no	—
116	C₂²⋊C₄×C₆₇	—	4	8	no	—
117	C₄²×C₆₇	—	2	1	no	—
118	C₄²×C₆₇	—	2	1	no	—
119	C₄²×C₆₇	C₂×D₄	1	2	yes	—
120	C₄²×C₆₇	#41	1	2	yes	—
121	C₂³×C₆₇	—	2	1	no	—
122	C₂³×C₆₇	—	2	1	no	—
123	C₂³×C₆₇	—	2	4	no	—
124	C₂³×C₆₇	#127	1	2	yes	—
125	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
126	Q₈×C₆₇	—	4	4	no	—
127	Q₈×C₆₇	—	4	4	no	—
128	Q₈×C₆₇	—	4	4	no	—
129	Q₈×C₆₇	—	4	4	no	—
130	C₂×C₄×C₆₇	—	2	1	no	—
131	C₂×C₄×C₆₇	—	2	1	no	—
132	C₂×C₄×C₆₇	—	2	4	no	—
133	C₂×C₄×C₆₇	—	2	2	no	—
134	C₂×C₄×C₆₇	—	2	2	no	—
135	C₂×C₄×C₆₇	—	2	2	no	—
136	C₂×C₄×C₆₇	—	2	2	no	—
137	C₂×C₄×C₆₇	—	2	2	no	—
138	C₂×C₄×C₆₇	—	2	4	no	—
139	C₂×C₄×C₆₇	—	4	4	no	—
140	C₂×C₄×C₆₇	—	4	4	no	—
141	C₂×C₄×C₆₇	—	4	4	no	—
142	C₂×C₄×C₆₇	—	4	4	no	—
143	C₂×C₄×C₆₇	—	4	8	no	—
144	C₂×C₄×C₆₇	#121	1	4	yes	—
145	C₂×C₄×C₆₇	#127	1	2	yes	—
146	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
150	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
151	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
152	C₈×C₆₇	—	2	2	no	—
153	C₈×C₆₇	—	2	2	no	—
154	C₈×C₆₇	#121	1	4	yes	—
155	C₈×C₆₇	#121	1	4	yes	—
156	C₂²×C₆₇	—	2	2	no	—
157	C₂²×C₆₇	—	2	4	no	—
158	C₂²×C₆₇	—	4	2	no	—
159	C₂²×C₆₇	—	4	2	no	—
160	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
161	C₂²×C₆₇	C₂×#127	1	1	yes	characteristic
162	C₂²×C₆₇	#532	1	1	yes	characteristic
163	C₂²×C₆₇	#578	1	4	yes	—
164	C₄×C₆₇	—	2	2	no	—
165	C₄×C₆₇	—	2	4	no	—
166	C₄×C₆₇	—	4	2	no	—
167	C₄×C₆₇	—	8	4	no	—
168	C₄×C₆₇	—	8	4	no	—
169	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
170	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
171	C₄×C₆₇	#532	1	1	yes	characteristic
172	C₄×C₆₇	#532	1	1	yes	characteristic
173	#33180	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂×C₆₇	—	4	2	no	—
175	C₂×C₆₇	#2856	1	1	yes	characteristic
176	C₂×C₆₇	#3059	1	2	yes	—
177	C₂×C₆₇	#3156	1	2	yes	—
178	C₂×C₆₇	#3177	1	2	yes	—
179	C₂×#494	C₂×C₆₇	1	1	yes	characteristic, complemented
180	C₂×#470	C₂×C₆₇	1	2	yes	—
181	C₂×#467	C₂×C₆₇	1	2	yes	—
182	C₂×#405	C₂×C₆₇	1	1	yes	characteristic
183	#2621	C₂×C₆₇	1	2	yes	—
184	#1971	C₂×C₆₇	1	2	yes	complemented
185	#1969	C₂×C₆₇	1	2	yes	complemented
186	#1960	C₂×C₆₇	1	2	yes	complemented
187	#1846	C₂×C₆₇	1	1	yes	characteristic, complemented
188	C₆₇	#33180	1	1	yes	characteristic, direct product factor, Sylow
189	C₂²×Q₁₆	C₂²×C₆₇	1	2	yes	—
190	C₂²×Q₁₆	C₂²×C₆₇	1	2	yes	—
191	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
192	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
193	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	—
194	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	—
195	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
196	#494	—	2	4	no	—
197	#470	—	2	8	no	—
198	#467	—	2	8	no	—
199	C₂×#107	C₂²×C₆₇	1	2	yes	—
200	C₂×#106	C₂²×C₆₇	1	2	yes	—
201	C₂×#103	C₂²×C₆₇	1	4	yes	—
202	C₂×#103	C₂²×C₆₇	1	4	yes	—
203	#405	—	2	4	no	—
204	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
205	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
206	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
207	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
208	#398	—	2	4	no	—
209	#397	—	2	4	no	—
210	#391	C₂²×C₆₇	1	4	yes	—
211	#382	C₂²×C₆₇	1	2	yes	—
212	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
213	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
214	C₂×Q₁₆	—	2	4	no	—
215	C₂×Q₁₆	—	2	4	no	—
216	C₂×Q₁₆	—	2	4	no	—
217	C₂×Q₁₆	—	2	4	no	—
218	C₂×Q₁₆	—	2	4	no	—
219	C₂×Q₁₆	—	2	4	no	—
220	C₂×M₁₆	—	2	2	no	—
221	C₂×M₁₆	—	2	2	no	—
222	C₂×M₁₆	D₄×C₆₇	1	4	yes	—
223	C₂²×C₈	—	2	2	no	—
224	C₂²×C₈	—	2	2	no	—
225	C₂²×C₈	D₄×C₆₇	1	4	yes	—
226	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
227	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
228	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
229	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
230	C₄⋊Q₈	—	2	4	no	—
231	C₄⋊Q₈	—	2	4	no	—
232	C₂²⋊Q₈	—	2	8	no	—
233	C₂²⋊Q₈	—	2	8	no	—
234	#117	—	2	2	no	—
235	#117	—	2	2	no	—
236	C₂×C₄⋊C₄	—	2	4	no	—
237	C₂×C₄⋊C₄	—	2	4	no	—
238	C₂×C₄⋊C₄	D₄×C₆₇	1	2	yes	—
239	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
240	C₂×C₂²⋊C₄	—	2	4	no	—
241	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
242	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
243	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
244	#107	—	2	4	no	—
245	#106	—	2	4	no	—
246	#103	—	2	8	no	—
247	#103	—	2	8	no	—
248	#97	—	2	2	no	—
249	#97	—	2	2	no	—
250	C₄×C₈	—	2	2	no	—
251	C₄×C₈	D₄×C₆₇	1	4	yes	—
252	#95	—	2	4	no	—
253	#95	—	2	8	no	—
254	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
255	C₂×Q₈	—	2	4	no	—
256	C₂×Q₈	—	2	4	no	—
257	C₂×Q₈	—	2	4	no	—
258	C₂×Q₈	—	2	4	no	—
259	C₂×Q₈	—	2	4	no	—
260	C₂×Q₈	—	2	4	no	—
261	C₂²×C₄	—	2	1	no	—
262	C₂²×C₄	—	2	1	no	—
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	2	1	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
268	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
269	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
270	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
271	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
272	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
273	Q₁₆	—	4	8	no	—
274	Q₁₆	—	4	8	no	—
275	M₁₆	—	2	8	no	—
276	C₂×C₈	—	2	1	no	—
277	C₂×C₈	—	2	1	no	—
278	C₂×C₈	—	2	1	no	—
279	C₂×C₈	—	2	1	no	—
280	C₂×C₈	—	2	8	no	—
281	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
282	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
283	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
284	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
285	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
286	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
287	C₂×C₈	#41×C₆₇	1	2	yes	—
288	C₂×C₈	#41×C₆₇	1	2	yes	—
289	C₄⋊C₄	—	2	4	no	—
290	C₄⋊C₄	—	2	4	no	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄⋊C₄	—	4	8	no	—
293	C₄⋊C₄	—	4	8	no	—
294	C₂²⋊C₄	—	2	4	no	—
295	C₂²⋊C₄	—	4	8	no	—
296	C₄²	—	2	1	no	—
297	C₄²	—	2	1	no	—
298	C₄²	C₂×D₄×C₆₇	1	2	yes	—
299	C₄²	#41×C₆₇	1	2	yes	—
300	C₂³	—	2	1	no	—
301	C₂³	—	2	1	no	—
302	C₂³	—	2	4	no	—
303	C₂³	#127×C₆₇	1	2	yes	—
304	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
305	Q₈	—	4	4	no	—
306	Q₈	—	4	4	no	—
307	Q₈	—	4	4	no	—
308	Q₈	—	4	4	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	4	4	no	—
319	C₂×C₄	—	4	4	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	—	4	8	no	—
323	C₂×C₄	#121×C₆₇	1	4	yes	—
324	C₂×C₄	#127×C₆₇	1	2	yes	—
325	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
326	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
327	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
328	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
329	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
330	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
331	C₈	—	2	2	no	—
332	C₈	—	2	2	no	—
333	C₈	#121×C₆₇	1	4	yes	—
334	C₈	#121×C₆₇	1	4	yes	—
335	C₂²	—	2	2	no	—
336	C₂²	—	2	4	no	—
337	C₂²	—	4	2	no	—
338	C₂²	—	4	2	no	—
339	C₂²	C₂×#121×C₆₇	1	1	yes	characteristic
340	C₂²	C₂×#127×C₆₇	1	1	yes	characteristic
341	C₂²	#532×C₆₇	1	1	yes	characteristic
342	C₂²	#578×C₆₇	1	4	yes	—
343	C₄	—	2	4	no	—
344	C₄	—	2	2	no	—
345	C₄	—	4	2	no	—
346	C₄	—	8	4	no	—
347	C₄	—	8	4	no	—
348	C₄	C₂×#121×C₆₇	1	1	yes	characteristic
349	C₄	C₂×#121×C₆₇	1	1	yes	characteristic
350	C₄	#532×C₆₇	1	1	yes	characteristic
351	C₄	#532×C₆₇	1	1	yes	characteristic
352	C₂	—	4	2	no	—
353	C₂	C₆₇×#2856	1	1	yes	characteristic
354	C₂	C₆₇×#3059	1	2	yes	—
355	C₂	C₆₇×#3156	1	2	yes	—
356	C₂	C₆₇×#3177	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂⁴×C₆₇	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂×#117×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#494×C₆₇	C₂	semidirect
6. C₆₇×#1971	C₂	semidirect
7. C₆₇×#1969	C₂	semidirect
8. C₆₇×#1960	C₂	semidirect
9. C₆₇×#1846	C₂	semidirect
173. #33180	C₆₇	direct (N × H)
179. C₂×#494	C₂×C₆₇	semidirect
184. #1971	C₂×C₆₇	semidirect
185. #1969	C₂×C₆₇	semidirect
186. #1960	C₂×C₆₇	semidirect
187. #1846	C₂×C₆₇	semidirect
188. C₆₇	#33180	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#494×C₆₇	2
C₂×#470×C₆₇	2
C₂×#467×C₆₇	2
C₂×#405×C₆₇	2
C₆₇×#2621	2
C₆₇×#1971	2
C₆₇×#1969	2
C₆₇×#1960	2
C₆₇×#1846	2
#33180	67

Subgroups — C67×#33180 #30712431

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#33180 #30712431