Subgroups — C₆₇×#19964 #30699215

Order 17152.

568 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3398	C₂	1	2	yes	maximal
2	C₆₇×#3383	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3342	C₂	1	1	yes	maximal, characteristic
4	C₆₇×#1713	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#1690	C₂	1	2	yes	maximal, complemented
6	C₆₇×#1674	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1673	C₂	1	1	yes	maximal, characteristic
8	C₆₇×#1650	C₂	1	2	yes	maximal
9	C₆₇×#1648	C₂	1	2	yes	maximal, complemented
10	C₆₇×#1591	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×SD₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic
12	#557×C₆₇	C₂²	1	2	yes	—
13	#556×C₆₇	C₂²	1	2	yes	—
14	#500×C₆₇	C₂²	1	1	yes	characteristic
15	#500×C₆₇	C₂²	1	1	yes	characteristic
16	#500×C₆₇	C₂²	1	2	yes	—
17	#499×C₆₇	—	2	1	no	—
18	#497×C₆₇	—	2	2	no	—
19	#494×C₆₇	C₂²	1	2	yes	—
20	#485×C₆₇	—	2	2	no	—
21	#479×C₆₇	—	2	2	no	—
22	#475×C₆₇	C₂²	1	2	yes	—
23	#475×C₆₇	C₂²	1	2	yes	—
24	#467×C₆₇	—	2	1	no	—
25	#464×C₆₇	—	2	2	no	—
26	#462×C₆₇	—	2	2	no	—
27	#462×C₆₇	C₂²	1	2	yes	—
28	#461×C₆₇	C₂²	1	2	yes	—
29	#446×C₆₇	C₂²	1	2	yes	—
30	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic
31	#441×C₆₇	—	2	2	no	—
32	C₄×Q₁₆×C₆₇	—	2	1	no	—
33	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
34	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
35	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
36	#427×C₆₇	—	2	1	no	—
37	#335×C₆₇	C₂²	1	1	yes	characteristic
38	#334×C₆₇	C₂²	1	1	yes	characteristic
39	#332×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	2	yes	—
43	D₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
44	C₈²×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×Q₁₆×C₆₇	—	2	2	no	—
46	C₂×Q₁₆×C₆₇	—	2	2	no	—
47	C₂×Q₁₆×C₆₇	—	2	2	no	—
48	C₂×Q₁₆×C₆₇	D₄	1	1	yes	characteristic
49	C₂×SD₁₆×C₆₇	—	2	2	no	—
50	C₂×SD₁₆×C₆₇	D₄	1	1	yes	characteristic
51	C₂²×C₈×C₆₇	—	2	1	no	—
52	C₄⋊Q₈×C₆₇	—	2	2	no	—
53	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
54	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
55	#126×C₆₇	—	4	2	no	—
56	#125×C₆₇	—	2	2	no	—
57	#125×C₆₇	—	4	2	no	—
58	#124×C₆₇	—	2	2	no	—
59	C₂²⋊Q₈×C₆₇	—	2	2	no	—
60	C₄×Q₈×C₆₇	—	2	2	no	—
61	C₄×Q₈×C₆₇	—	2	2	no	—
62	C₄×Q₈×C₆₇	—	2	2	no	—
63	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
64	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
65	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
66	#117×C₆₇	—	2	2	no	—
67	#107×C₆₇	—	2	1	no	—
68	#107×C₆₇	—	2	1	no	—
69	#107×C₆₇	—	2	1	no	—
70	#107×C₆₇	—	2	1	no	—
71	#107×C₆₇	—	4	2	no	—
72	#107×C₆₇	D₄	1	1	yes	characteristic
73	#106×C₆₇	—	2	2	no	—
74	#106×C₆₇	—	2	2	no	—
75	#106×C₆₇	D₄	1	1	yes	characteristic
76	C₄⋊C₈×C₆₇	—	2	2	no	—
77	C₄⋊C₈×C₆₇	—	2	1	no	—
78	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
79	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
80	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
81	#103×C₆₇	—	2	2	no	—
82	#103×C₆₇	—	2	2	no	—
83	#103×C₆₇	—	2	2	no	—
84	#103×C₆₇	—	2	2	no	—
85	#103×C₆₇	D₄	1	1	yes	characteristic
86	#103×C₆₇	D₄	1	2	yes	—
87	#102×C₆₇	D₄	1	1	yes	characteristic
88	C₂²⋊C₈×C₆₇	—	2	1	no	—
89	#97×C₆₇	—	2	2	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	2	yes	—
97	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
98	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₆₇	—	2	1	no	—
100	Q₁₆×C₆₇	—	2	2	no	—
101	Q₁₆×C₆₇	—	4	4	no	—
102	Q₁₆×C₆₇	—	8	2	no	—
103	Q₁₆×C₆₇	—	8	2	no	—
104	SD₁₆×C₆₇	—	2	2	no	—
105	SD₁₆×C₆₇	—	8	2	no	—
106	C₂×C₈×C₆₇	—	2	1	no	—
107	C₂×C₈×C₆₇	—	2	1	no	—
108	C₂×C₈×C₆₇	—	2	2	no	—
109	C₂×C₈×C₆₇	—	2	1	no	—
110	C₂×C₈×C₆₇	—	4	2	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	2	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	—	4	2	no	—
125	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
126	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
127	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
128	C₂²⋊C₄×C₆₇	—	2	1	no	—
129	C₂²⋊C₄×C₆₇	—	4	2	no	—
130	C₂²⋊C₄×C₆₇	—	4	2	no	—
131	C₄²×C₆₇	—	2	2	no	—
132	C₄²×C₆₇	—	2	1	no	—
133	C₄²×C₆₇	—	4	2	no	—
134	C₄²×C₆₇	—	4	2	no	—
135	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
136	C₂³×C₆₇	—	2	1	no	—
137	Q₈×C₆₇	—	2	1	no	—
138	Q₈×C₆₇	—	2	2	no	—
139	Q₈×C₆₇	—	2	1	no	—
140	Q₈×C₆₇	—	2	2	no	—
141	Q₈×C₆₇	—	4	2	no	—
142	Q₈×C₆₇	—	4	2	no	—
143	Q₈×C₆₇	—	4	2	no	—
144	Q₈×C₆₇	—	4	2	no	—
145	D₄×C₆₇	—	2	1	no	—
146	D₄×C₆₇	—	2	1	no	—
147	C₂×C₄×C₆₇	—	2	1	no	—
148	C₂×C₄×C₆₇	—	2	2	no	—
149	C₂×C₄×C₆₇	—	2	2	no	—
150	C₂×C₄×C₆₇	—	2	1	no	—
151	C₂×C₄×C₆₇	—	2	1	no	—
152	C₂×C₄×C₆₇	—	4	1	no	—
153	C₂×C₄×C₆₇	—	4	1	no	—
154	C₂×C₄×C₆₇	—	4	2	no	—
155	C₂×C₄×C₆₇	—	4	2	no	—
156	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
159	C₈×C₆₇	—	2	2	no	—
160	C₈×C₆₇	—	2	1	no	—
161	C₈×C₆₇	—	2	1	no	—
162	C₈×C₆₇	—	4	1	no	—
163	C₈×C₆₇	—	4	2	no	—
164	C₈×C₆₇	—	4	1	no	—
165	C₈×C₆₇	#135	1	2	yes	—
166	C₈×C₆₇	#137	1	2	yes	—
167	C₂²×C₆₇	—	4	1	no	—
168	C₂²×C₆₇	—	4	1	no	—
169	C₂²×C₆₇	—	4	1	no	—
170	C₂²×C₆₇	D₄²	1	1	yes	characteristic
171	C₄×C₆₇	—	2	1	no	—
172	C₄×C₆₇	—	4	1	no	—
173	C₄×C₆₇	—	4	2	no	—
174	C₄×C₆₇	—	4	1	no	—
175	C₄×C₆₇	—	4	1	no	—
176	C₄×C₆₇	—	4	2	no	—
177	C₄×C₆₇	—	8	2	no	—
178	C₄×C₆₇	—	8	2	no	—
179	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
180	C₄×C₆₇	C₂×#137	1	1	yes	characteristic
181	C₄×C₆₇	#576	1	1	yes	characteristic
182	C₄×C₆₇	#578	1	1	yes	characteristic
183	#19964	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂×C₆₇	—	8	1	no	—
185	C₂×C₆₇	#3276	1	1	yes	characteristic
186	C₂×C₆₇	#3287	1	1	yes	characteristic
187	C₂×C₆₇	#3293	1	1	yes	characteristic
188	#3398	C₂×C₆₇	1	2	yes	—
189	#3383	C₂×C₆₇	1	1	yes	characteristic, complemented
190	#3342	C₂×C₆₇	1	1	yes	characteristic
191	#1713	C₂×C₆₇	1	1	yes	characteristic, complemented
192	#1690	C₂×C₆₇	1	2	yes	complemented
193	#1674	C₂×C₆₇	1	1	yes	characteristic, complemented
194	#1673	C₂×C₆₇	1	1	yes	characteristic
195	#1650	C₂×C₆₇	1	2	yes	—
196	#1648	C₂×C₆₇	1	2	yes	complemented
197	#1591	C₂×C₆₇	1	1	yes	characteristic, complemented
198	C₈×SD₁₆	C₂×C₆₇	1	1	yes	characteristic
199	C₆₇	#19964	1	1	yes	characteristic, direct product factor, Sylow
200	#557	C₂²×C₆₇	1	2	yes	—
201	#556	C₂²×C₆₇	1	2	yes	—
202	#500	C₂²×C₆₇	1	1	yes	characteristic
203	#500	C₂²×C₆₇	1	1	yes	characteristic
204	#500	C₂²×C₆₇	1	2	yes	—
205	#499	—	2	1	no	—
206	#497	—	2	2	no	—
207	#494	C₂²×C₆₇	1	2	yes	—
208	#485	—	2	2	no	—
209	#479	—	2	2	no	—
210	#475	C₂²×C₆₇	1	2	yes	—
211	#475	C₂²×C₆₇	1	2	yes	—
212	#467	—	2	1	no	—
213	#464	—	2	2	no	—
214	#462	—	2	2	no	—
215	#462	C₂²×C₆₇	1	2	yes	—
216	#461	C₂²×C₆₇	1	2	yes	—
217	#446	C₂²×C₆₇	1	2	yes	—
218	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic
219	#441	—	2	2	no	—
220	C₄×Q₁₆	—	2	1	no	—
221	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
222	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
223	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
224	#427	—	2	1	no	—
225	#335	C₂²×C₆₇	1	1	yes	characteristic
226	#334	C₂²×C₆₇	1	1	yes	characteristic
227	#332	C₂²×C₆₇	1	2	yes	—
228	#332	C₂²×C₆₇	1	2	yes	—
229	Q₈⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
230	Q₈⋊C₈	C₂²×C₆₇	1	2	yes	—
231	D₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
232	C₈²	C₂²×C₆₇	1	1	yes	characteristic
233	C₂×Q₁₆	—	2	2	no	—
234	C₂×Q₁₆	—	2	2	no	—
235	C₂×Q₁₆	—	2	2	no	—
236	C₂×Q₁₆	D₄×C₆₇	1	1	yes	characteristic
237	C₂×SD₁₆	—	2	2	no	—
238	C₂×SD₁₆	D₄×C₆₇	1	1	yes	characteristic
239	C₂²×C₈	—	2	1	no	—
240	C₄⋊Q₈	—	2	2	no	—
241	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
242	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
243	#126	—	4	2	no	—
244	#125	—	2	2	no	—
245	#125	—	4	2	no	—
246	#124	—	2	2	no	—
247	C₂²⋊Q₈	—	2	2	no	—
248	C₄×Q₈	—	2	2	no	—
249	C₄×Q₈	—	2	2	no	—
250	C₄×Q₈	—	2	2	no	—
251	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
252	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
253	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
254	#117	—	2	2	no	—
255	#107	—	2	1	no	—
256	#107	—	2	1	no	—
257	#107	—	2	1	no	—
258	#107	—	2	1	no	—
259	#107	—	4	2	no	—
260	#107	D₄×C₆₇	1	1	yes	characteristic
261	#106	—	2	2	no	—
262	#106	—	2	2	no	—
263	#106	D₄×C₆₇	1	1	yes	characteristic
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	—	2	2	no	—
266	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
267	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
268	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
269	#103	—	2	2	no	—
270	#103	—	2	2	no	—
271	#103	—	2	2	no	—
272	#103	—	2	2	no	—
273	#103	D₄×C₆₇	1	1	yes	characteristic
274	#103	D₄×C₆₇	1	2	yes	—
275	#102	D₄×C₆₇	1	1	yes	characteristic
276	C₂²⋊C₈	—	2	1	no	—
277	#97	—	2	2	no	—
278	C₄×C₈	—	2	1	no	—
279	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
280	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
281	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
285	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
286	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
287	C₂²×C₄	—	2	1	no	—
288	Q₁₆	—	2	2	no	—
289	Q₁₆	—	4	4	no	—
290	Q₁₆	—	8	2	no	—
291	Q₁₆	—	8	2	no	—
292	SD₁₆	—	2	2	no	—
293	SD₁₆	—	8	2	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	—	4	2	no	—
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	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
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	—	2	2	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
314	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
315	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
316	C₂²⋊C₄	—	2	1	no	—
317	C₂²⋊C₄	—	4	2	no	—
318	C₂²⋊C₄	—	4	2	no	—
319	C₄²	—	2	1	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	4	2	no	—
322	C₄²	—	4	2	no	—
323	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
324	C₂³	—	2	1	no	—
325	Q₈	—	2	1	no	—
326	Q₈	—	2	2	no	—
327	Q₈	—	2	1	no	—
328	Q₈	—	2	2	no	—
329	Q₈	—	4	2	no	—
330	Q₈	—	4	2	no	—
331	Q₈	—	4	2	no	—
332	Q₈	—	4	2	no	—
333	D₄	—	2	1	no	—
334	D₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
345	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
346	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
347	C₈	—	2	2	no	—
348	C₈	—	2	1	no	—
349	C₈	—	2	1	no	—
350	C₈	—	4	1	no	—
351	C₈	—	4	2	no	—
352	C₈	—	4	1	no	—
353	C₈	#135×C₆₇	1	2	yes	—
354	C₈	#137×C₆₇	1	2	yes	—
355	C₂²	—	4	1	no	—
356	C₂²	—	4	1	no	—
357	C₂²	—	4	1	no	—
358	C₂²	D₄²×C₆₇	1	1	yes	characteristic
359	C₄	—	2	1	no	—
360	C₄	—	4	1	no	—
361	C₄	—	4	2	no	—
362	C₄	—	4	1	no	—
363	C₄	—	4	1	no	—
364	C₄	—	4	2	no	—
365	C₄	—	8	2	no	—
366	C₄	—	8	2	no	—
367	C₄	C₂×#135×C₆₇	1	1	yes	characteristic
368	C₄	C₂×#137×C₆₇	1	1	yes	characteristic
369	C₄	#576×C₆₇	1	1	yes	characteristic
370	C₄	#578×C₆₇	1	1	yes	characteristic
371	C₂	—	8	1	no	—
372	C₂	C₆₇×#3276	1	1	yes	characteristic
373	C₂	C₆₇×#3287	1	1	yes	characteristic
374	C₂	C₆₇×#3293	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₇
prime radical	C₂×D₄×C₆₇	C₂×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
2. C₆₇×#3383	C₂	semidirect
4. C₆₇×#1713	C₂	semidirect
5. C₆₇×#1690	C₂	semidirect
6. C₆₇×#1674	C₂	semidirect
9. C₆₇×#1648	C₂	semidirect
10. C₆₇×#1591	C₂	semidirect
183. #19964	C₆₇	direct (N × H)
189. #3383	C₂×C₆₇	semidirect
191. #1713	C₂×C₆₇	semidirect
192. #1690	C₂×C₆₇	semidirect
193. #1674	C₂×C₆₇	semidirect
196. #1648	C₂×C₆₇	semidirect
197. #1591	C₂×C₆₇	semidirect
199. C₆₇	#19964	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×#3398	2
C₆₇×#3383	2
C₆₇×#3342	2
C₆₇×#1713	2
C₆₇×#1690	2
C₆₇×#1674	2
C₆₇×#1673	2
C₆₇×#1650	2
C₆₇×#1648	2
C₆₇×#1591	2
C₈×SD₁₆×C₆₇	2
#19964	67

Subgroups — C67×#19964 #30699215

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#19964 #30699215