Subgroups — C₆₇×#17886 #30697137

Order 17152.

682 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2965	C₂	1	2	yes	maximal, complemented
2	C₄×#135×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#1591	C₂	1	2	yes	maximal, complemented
4	C₆₇×#1590	C₂	1	4	yes	maximal, complemented
5	C₆₇×#1589	C₂	1	2	yes	maximal, complemented
6	C₆₇×#1564	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1476	C₂	1	2	yes	maximal, complemented
8	C₂×C₈²×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#135×C₆₇	C₄	1	1	yes	characteristic
10	C₄×#41×C₆₇	C₂²	1	2	yes	—
11	#446×C₆₇	C₂²	1	4	yes	—
12	C₄×Q₁₆×C₆₇	C₄	1	1	yes	characteristic
13	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
14	C₄×SD₁₆×C₆₇	C₄	1	2	yes	—
15	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
16	C₄×D₈×C₆₇	C₄	1	1	yes	characteristic
17	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
18	#436×C₆₇	C₂²	1	4	yes	—
19	#435×C₆₇	—	2	4	no	—
20	#431×C₆₇	—	2	2	no	—
21	#431×C₆₇	C₂²	1	2	yes	—
22	#427×C₆₇	C₄	1	1	yes	characteristic
23	#416×C₆₇	C₄	1	2	yes	—
24	C₄×M₁₆×C₆₇	—	2	2	no	—
25	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
28	#335×C₆₇	C₂²	1	2	yes	—
29	#334×C₆₇	C₂²	1	2	yes	—
30	Q₈⋊C₈×C₆₇	C₂²	1	4	yes	—
31	D₄⋊C₈×C₆₇	C₂²	1	4	yes	—
32	C₈²×C₆₇	C₂²	1	2	yes	—
33	C₈²×C₆₇	C₂²	1	2	yes	—
34	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
35	#135×C₆₇	—	2	4	no	—
36	C₂×Q₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
37	C₂×SD₁₆×C₆₇	C₂×C₄	1	2	yes	—
38	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic
39	C₂×M₁₆×C₆₇	—	2	4	no	—
40	C₂²×C₈×C₆₇	—	2	1	no	—
41	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₈×C₆₇	D₄	1	2	yes	—
44	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
45	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
46	C₄×D₄×C₆₇	—	2	2	no	—
47	C₄×D₄×C₆₇	—	2	2	no	—
48	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
49	C₄×D₄×C₆₇	C₂³	1	2	yes	—
50	#117×C₆₇	—	2	2	no	—
51	#117×C₆₇	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₆₇	—	2	2	no	—
53	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
54	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
55	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
56	#106×C₆₇	C₂×C₄	1	2	yes	—
57	C₄⋊C₈×C₆₇	—	2	4	no	—
58	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
59	#103×C₆₇	C₂×C₄	1	2	yes	—
60	#103×C₆₇	C₂×C₄	1	2	yes	—
61	#102×C₆₇	C₂×C₄	1	2	yes	—
62	#102×C₆₇	C₂×C₄	1	2	yes	—
63	C₂²⋊C₈×C₆₇	—	2	2	no	—
64	C₂²⋊C₈×C₆₇	—	2	4	no	—
65	#97×C₆₇	—	2	4	no	—
66	C₄×C₈×C₆₇	—	2	2	no	—
67	C₄×C₈×C₆₇	—	2	1	no	—
68	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
69	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
70	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
71	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
72	C₄×C₈×C₆₇	C₂³	1	2	yes	—
73	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
74	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
75	C₄×C₈×C₆₇	C₂³	1	2	yes	—
76	#41×C₆₇	—	2	4	no	—
77	#41×C₆₇	—	2	4	no	—
78	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
79	C₂×D₄×C₆₇	—	2	2	no	—
80	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₆₇	—	2	2	no	—
82	C₂²×C₄×C₆₇	—	2	2	no	—
83	C₂²×C₄×C₆₇	—	2	2	no	—
84	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
87	Q₁₆×C₆₇	—	2	2	no	—
88	SD₁₆×C₆₇	—	2	4	no	—
89	D₈×C₆₇	—	2	2	no	—
90	M₁₆×C₆₇	—	4	8	no	—
91	C₂×C₈×C₆₇	—	2	4	no	—
92	C₂×C₈×C₆₇	—	2	2	no	—
93	C₂×C₈×C₆₇	—	2	2	no	—
94	C₂×C₈×C₆₇	—	2	4	no	—
95	C₂×C₈×C₆₇	—	2	4	no	—
96	C₂×C₈×C₆₇	M₁₆	1	4	yes	complemented
97	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
102	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
103	C₄⋊C₄×C₆₇	—	2	2	no	—
104	C₄⋊C₄×C₆₇	—	2	2	no	—
105	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
106	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
107	C₂²⋊C₄×C₆₇	—	2	2	no	—
108	C₂²⋊C₄×C₆₇	—	2	2	no	—
109	C₂²⋊C₄×C₆₇	—	2	2	no	—
110	C₄²×C₆₇	—	2	2	no	—
111	C₄²×C₆₇	—	2	2	no	—
112	C₄²×C₆₇	—	2	2	no	—
113	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₆₇	#41	1	1	yes	characteristic
116	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
117	C₂³×C₆₇	—	2	2	no	—
118	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
119	Q₈×C₆₇	—	2	2	no	—
120	Q₈×C₆₇	—	2	2	no	—
121	D₄×C₆₇	—	2	2	no	—
122	D₄×C₆₇	—	2	2	no	—
123	D₄×C₆₇	—	4	4	no	—
124	C₂×C₄×C₆₇	—	2	2	no	—
125	C₂×C₄×C₆₇	—	2	2	no	—
126	C₂×C₄×C₆₇	—	2	2	no	—
127	C₂×C₄×C₆₇	—	2	2	no	—
128	C₂×C₄×C₆₇	—	2	2	no	—
129	C₂×C₄×C₆₇	—	4	4	no	—
130	C₂×C₄×C₆₇	—	4	4	no	—
131	C₂×C₄×C₆₇	—	4	4	no	—
132	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
133	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
134	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
135	C₂×C₄×C₆₇	C₂×M₁₆	1	2	yes	—
136	C₂×C₄×C₆₇	#131	1	2	yes	—
137	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
138	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
139	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
140	C₈×C₆₇	—	2	4	no	—
141	C₈×C₆₇	—	2	1	no	—
142	C₈×C₆₇	—	2	1	no	—
143	C₈×C₆₇	—	2	2	no	—
144	C₈×C₆₇	—	4	4	no	—
145	C₈×C₆₇	C₂×M₁₆	1	2	yes	—
146	C₈×C₆₇	C₂×M₁₆	1	2	yes	—
147	C₈×C₆₇	#135	1	4	yes	complemented
148	C₂²×C₆₇	—	2	1	no	—
149	C₂²×C₆₇	—	2	1	no	—
150	C₂²×C₆₇	—	4	2	no	—
151	C₂²×C₆₇	—	4	2	no	—
152	C₂²×C₆₇	—	4	2	no	—
153	C₂²×C₆₇	#436	1	2	yes	—
154	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
155	C₄×C₆₇	—	2	1	no	—
156	C₄×C₆₇	—	2	1	no	—
157	C₄×C₆₇	—	4	2	no	—
158	C₄×C₆₇	—	4	2	no	—
159	C₄×C₆₇	—	4	2	no	—
160	C₄×C₆₇	#436	1	2	yes	—
161	C₄×C₆₇	#443	1	2	yes	—
162	C₄×C₆₇	C₂²×M₁₆	1	1	yes	characteristic
163	C₄×C₆₇	C₂×#131	1	1	yes	characteristic
164	C₄×C₆₇	C₂×#135	1	2	yes	—
165	#17886	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂×C₆₇	—	2	2	no	—
167	C₂×C₆₇	—	8	2	no	—
168	C₂×C₆₇	C₂×#436	1	1	yes	characteristic
169	C₂×C₆₇	C₄×#135	1	1	yes	characteristic
170	C₂×C₆₇	C₂×#443	1	1	yes	characteristic
171	#2965	C₂×C₆₇	1	2	yes	complemented
172	C₄×#135	C₂×C₆₇	1	1	yes	characteristic
173	#1591	C₂×C₆₇	1	2	yes	complemented
174	#1590	C₂×C₆₇	1	4	yes	complemented
175	#1589	C₂×C₆₇	1	2	yes	complemented
176	#1564	C₂×C₆₇	1	1	yes	characteristic, complemented
177	#1476	C₂×C₆₇	1	2	yes	complemented
178	C₂×C₈²	C₂×C₆₇	1	1	yes	characteristic, complemented
179	C₆₇	#17886	1	1	yes	characteristic, direct product factor, Sylow
180	C₂×#135	C₄×C₆₇	1	1	yes	characteristic
181	C₄×#41	C₂²×C₆₇	1	2	yes	—
182	#446	C₂²×C₆₇	1	4	yes	—
183	C₄×Q₁₆	C₄×C₆₇	1	1	yes	characteristic
184	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
185	C₄×SD₁₆	C₄×C₆₇	1	2	yes	—
186	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
187	C₄×D₈	C₄×C₆₇	1	1	yes	characteristic
188	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
189	#436	C₂²×C₆₇	1	4	yes	—
190	#435	—	2	4	no	—
191	#431	—	2	2	no	—
192	#431	C₂²×C₆₇	1	2	yes	—
193	#427	C₄×C₆₇	1	1	yes	characteristic
194	#416	C₄×C₆₇	1	2	yes	—
195	C₄×M₁₆	—	2	2	no	—
196	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
197	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
198	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
199	#335	C₂²×C₆₇	1	2	yes	—
200	#334	C₂²×C₆₇	1	2	yes	—
201	Q₈⋊C₈	C₂²×C₆₇	1	4	yes	—
202	D₄⋊C₈	C₂²×C₆₇	1	4	yes	—
203	C₈²	C₂²×C₆₇	1	2	yes	—
204	C₈²	C₂²×C₆₇	1	2	yes	—
205	C₂×#41	C₂×C₄×C₆₇	1	2	yes	—
206	#135	—	2	4	no	—
207	C₂×Q₁₆	C₂×C₄×C₆₇	1	1	yes	characteristic
208	C₂×SD₁₆	C₂×C₄×C₆₇	1	2	yes	—
209	C₂×D₈	C₂×C₄×C₆₇	1	1	yes	characteristic
210	C₂×M₁₆	—	2	4	no	—
211	C₂²×C₈	—	2	1	no	—
212	C₂²×C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
213	C₂²×C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
214	C₂²×C₈	D₄×C₆₇	1	2	yes	—
215	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
216	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
217	C₄×D₄	—	2	2	no	—
218	C₄×D₄	—	2	2	no	—
219	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
220	C₄×D₄	C₂³×C₆₇	1	2	yes	—
221	#117	—	2	2	no	—
222	#117	C₂×C₄×C₆₇	1	2	yes	—
223	C₂×C₄²	—	2	2	no	—
224	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
225	#107	C₂×C₄×C₆₇	1	1	yes	characteristic
226	#107	C₂×C₄×C₆₇	1	1	yes	characteristic
227	#106	C₂×C₄×C₆₇	1	2	yes	—
228	C₄⋊C₈	—	2	4	no	—
229	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
230	#103	C₂×C₄×C₆₇	1	2	yes	—
231	#103	C₂×C₄×C₆₇	1	2	yes	—
232	#102	C₂×C₄×C₆₇	1	2	yes	—
233	#102	C₂×C₄×C₆₇	1	2	yes	—
234	C₂²⋊C₈	—	2	2	no	—
235	C₂²⋊C₈	—	2	4	no	—
236	#97	—	2	4	no	—
237	C₄×C₈	—	2	2	no	—
238	C₄×C₈	—	2	1	no	—
239	C₄×C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
240	C₄×C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
241	C₄×C₈	D₄×C₆₇	1	1	yes	characteristic
242	C₄×C₈	D₄×C₆₇	1	1	yes	characteristic
243	C₄×C₈	C₂³×C₆₇	1	2	yes	—
244	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
245	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
246	C₄×C₈	C₂³×C₆₇	1	2	yes	—
247	#41	—	2	4	no	—
248	#41	—	2	4	no	—
249	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
250	C₂×D₄	—	2	2	no	—
251	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
256	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
257	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
258	Q₁₆	—	2	2	no	—
259	SD₁₆	—	2	4	no	—
260	D₈	—	2	2	no	—
261	M₁₆	—	4	8	no	—
262	C₂×C₈	—	2	4	no	—
263	C₂×C₈	—	2	2	no	—
264	C₂×C₈	—	2	2	no	—
265	C₂×C₈	—	2	4	no	—
266	C₂×C₈	—	2	4	no	—
267	C₂×C₈	M₁₆×C₆₇	1	4	yes	complemented
268	C₂×C₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
269	C₂×C₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
270	C₂×C₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
271	C₂×C₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
272	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
273	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
274	C₄⋊C₄	—	2	2	no	—
275	C₄⋊C₄	—	2	2	no	—
276	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
277	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
278	C₂²⋊C₄	—	2	2	no	—
279	C₂²⋊C₄	—	2	2	no	—
280	C₂²⋊C₄	—	2	2	no	—
281	C₄²	—	2	2	no	—
282	C₄²	—	2	2	no	—
283	C₄²	—	2	2	no	—
284	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
285	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
286	C₄²	#41×C₆₇	1	1	yes	characteristic
287	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
288	C₂³	—	2	2	no	—
289	C₂³	C₄×D₄×C₆₇	1	1	yes	characteristic
290	Q₈	—	2	2	no	—
291	Q₈	—	2	2	no	—
292	D₄	—	2	2	no	—
293	D₄	—	2	2	no	—
294	D₄	—	4	4	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	4	4	no	—
301	C₂×C₄	—	4	4	no	—
302	C₂×C₄	—	4	4	no	—
303	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
304	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
305	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
306	C₂×C₄	C₂×M₁₆×C₆₇	1	2	yes	—
307	C₂×C₄	#131×C₆₇	1	2	yes	—
308	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
309	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
310	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
311	C₈	—	2	4	no	—
312	C₈	—	2	1	no	—
313	C₈	—	2	1	no	—
314	C₈	—	2	2	no	—
315	C₈	—	4	4	no	—
316	C₈	C₂×M₁₆×C₆₇	1	2	yes	—
317	C₈	C₂×M₁₆×C₆₇	1	2	yes	—
318	C₈	#135×C₆₇	1	4	yes	complemented
319	C₂²	—	2	1	no	—
320	C₂²	—	2	1	no	—
321	C₂²	—	4	2	no	—
322	C₂²	—	4	2	no	—
323	C₂²	—	4	2	no	—
324	C₂²	#436×C₆₇	1	2	yes	—
325	C₂²	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
326	C₄	—	2	1	no	—
327	C₄	—	2	1	no	—
328	C₄	—	4	2	no	—
329	C₄	—	4	2	no	—
330	C₄	—	4	2	no	—
331	C₄	#436×C₆₇	1	2	yes	—
332	C₄	#443×C₆₇	1	2	yes	—
333	C₄	C₂²×M₁₆×C₆₇	1	1	yes	characteristic
334	C₄	C₂×#131×C₆₇	1	1	yes	characteristic
335	C₄	C₂×#135×C₆₇	1	2	yes	—
336	C₂	—	2	2	no	—
337	C₂	—	8	2	no	—
338	C₂	C₂×#436×C₆₇	1	1	yes	characteristic
339	C₂	C₄×#135×C₆₇	1	1	yes	characteristic
340	C₂	C₂×#443×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄²×C₆₇	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₇
Frattini, cosocle	C₄²	C₂⁴×C₆₇
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂×#135×C₆₇	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₆₇ ◁ C₂×C₄×C₈×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#2965	C₂	semidirect
3. C₆₇×#1591	C₂	semidirect
4. C₆₇×#1590	C₂	semidirect
5. C₆₇×#1589	C₂	semidirect
6. C₆₇×#1564	C₂	semidirect
7. C₆₇×#1476	C₂	semidirect
8. C₂×C₈²×C₆₇	C₂	semidirect
96. C₂×C₈×C₆₇	M₁₆	semidirect
147. C₈×C₆₇	#135	semidirect
165. #17886	C₆₇	direct (N × H)
171. #2965	C₂×C₆₇	semidirect
173. #1591	C₂×C₆₇	semidirect
174. #1590	C₂×C₆₇	semidirect
175. #1589	C₂×C₆₇	semidirect
176. #1564	C₂×C₆₇	semidirect
177. #1476	C₂×C₆₇	semidirect
178. C₂×C₈²	C₂×C₆₇	semidirect
179. C₆₇	#17886	direct (N × H)
267. C₂×C₈	M₁₆×C₆₇	semidirect
318. C₈	#135×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#2965	2
C₄×#135×C₆₇	2
C₆₇×#1591	2
C₆₇×#1590	2
C₆₇×#1589	2
C₆₇×#1564	2
C₆₇×#1476	2
C₂×C₈²×C₆₇	2
#17886	67

Subgroups — C67×#17886 #30697137

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#17886 #30697137