Subgroups — C₆₇×#33011 #30712262

Order 17152.

1346 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#485×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#452×C₆₇	C₂	1	1	yes	maximal, characteristic
4	C₆₇×#2855	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#1878	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#1878	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1877	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#1877	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#1865	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#1864	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#1863	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#1862	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#1825	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#1817	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#1788	C₂	1	1	yes	maximal, characteristic
16	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
20	C₄×#41×C₆₇	—	2	4	no	—
21	C₄×#41×C₆₇	—	2	4	no	—
22	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₆₇	—	2	1	no	—
25	C₂×C₄×D₄×C₆₇	—	2	1	no	—
26	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#117×C₆₇	—	2	1	no	—
29	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₆₇	—	2	1	no	—
31	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
32	#485×C₆₇	—	2	4	no	—
33	#452×C₆₇	—	2	4	no	—
34	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
46	#391×C₆₇	C₂²	1	1	yes	characteristic
47	#391×C₆₇	C₂²	1	1	yes	characteristic
48	#389×C₆₇	C₂²	1	1	yes	characteristic
49	#389×C₆₇	C₂²	1	1	yes	characteristic
50	#387×C₆₇	—	2	1	no	—
51	#387×C₆₇	—	2	1	no	—
52	#385×C₆₇	—	2	1	no	—
53	#381×C₆₇	—	2	1	no	—
54	#380×C₆₇	C₂²	1	1	yes	characteristic
55	#340×C₆₇	C₂²	1	1	yes	characteristic
56	#340×C₆₇	C₂²	1	1	yes	characteristic
57	#340×C₆₇	C₂²	1	1	yes	characteristic
58	#340×C₆₇	C₂²	1	1	yes	characteristic
59	#336×C₆₇	C₂²	1	1	yes	characteristic
60	#336×C₆₇	C₂²	1	1	yes	characteristic
61	#336×C₆₇	C₂²	1	1	yes	characteristic
62	#336×C₆₇	C₂²	1	1	yes	characteristic
63	C₂×#41×C₆₇	—	2	2	no	—
64	C₂×#41×C₆₇	—	2	2	no	—
65	C₂×#41×C₆₇	—	2	2	no	—
66	C₂×#41×C₆₇	—	2	2	no	—
67	C₂×#41×C₆₇	—	2	2	no	—
68	C₂×#41×C₆₇	D₄	1	4	yes	—
69	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
70	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₆₇	—	2	1	no	—
72	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₆₇	—	2	1	no	—
74	C₂³×C₄×C₆₇	—	2	1	no	—
75	C₂³×C₄×C₆₇	—	2	1	no	—
76	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
77	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
78	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
79	C₂×Q₁₆×C₆₇	—	2	2	no	—
80	C₂×Q₁₆×C₆₇	—	2	2	no	—
81	C₂×Q₁₆×C₆₇	—	2	2	no	—
82	C₂×SD₁₆×C₆₇	—	2	2	no	—
83	C₂×SD₁₆×C₆₇	—	2	2	no	—
84	C₂×SD₁₆×C₆₇	—	2	2	no	—
85	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
89	C₂²⋊Q₈×C₆₇	—	2	2	no	—
90	C₂²⋊Q₈×C₆₇	—	2	2	no	—
91	C₄×Q₈×C₆₇	—	2	2	no	—
92	C₄×Q₈×C₆₇	—	2	2	no	—
93	C₄×Q₈×C₆₇	—	2	2	no	—
94	C₄×Q₈×C₆₇	—	2	2	no	—
95	C₄×D₄×C₆₇	—	2	8	no	—
96	C₄×D₄×C₆₇	—	2	8	no	—
97	C₄×D₄×C₆₇	—	2	2	no	—
98	C₄×D₄×C₆₇	—	2	2	no	—
99	C₄×D₄×C₆₇	—	2	2	no	—
100	C₄×D₄×C₆₇	—	2	2	no	—
101	#117×C₆₇	—	2	8	no	—
102	#117×C₆₇	—	2	2	no	—
103	#117×C₆₇	D₄	1	4	yes	—
104	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
105	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
106	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
107	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
108	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
109	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
119	C₂×C₄²×C₆₇	—	2	8	no	—
120	C₂×C₄²×C₆₇	—	2	1	no	—
121	C₂×C₄²×C₆₇	—	2	1	no	—
122	C₂×C₄²×C₆₇	—	2	1	no	—
123	C₂×C₄²×C₆₇	—	2	2	no	—
124	C₂×C₄²×C₆₇	—	2	2	no	—
125	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
126	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
127	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
129	#107×C₆₇	—	2	2	no	—
130	#106×C₆₇	—	2	2	no	—
131	#103×C₆₇	—	2	2	no	—
132	#103×C₆₇	—	2	2	no	—
133	#103×C₆₇	—	2	2	no	—
134	#103×C₆₇	—	2	2	no	—
135	#103×C₆₇	—	2	2	no	—
136	#102×C₆₇	—	2	2	no	—
137	#102×C₆₇	—	2	2	no	—
138	#102×C₆₇	—	2	2	no	—
139	C₂²⋊C₈×C₆₇	—	2	2	no	—
140	C₂²⋊C₈×C₆₇	—	2	2	no	—
141	#95×C₆₇	—	2	1	no	—
142	#95×C₆₇	—	2	1	no	—
143	#95×C₆₇	—	2	1	no	—
144	#95×C₆₇	—	2	1	no	—
145	#95×C₆₇	—	2	1	no	—
146	#95×C₆₇	—	2	1	no	—
147	#95×C₆₇	—	2	1	no	—
148	C₂⁴×C₆₇	—	2	1	no	—
149	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
150	#41×C₆₇	—	2	8	no	—
151	#41×C₆₇	—	2	8	no	—
152	#41×C₆₇	—	2	8	no	—
153	#41×C₆₇	—	2	8	no	—
154	C₂×Q₈×C₆₇	—	2	1	no	—
155	C₂×Q₈×C₆₇	—	2	1	no	—
156	C₂×Q₈×C₆₇	—	2	1	no	—
157	C₂×Q₈×C₆₇	—	2	1	no	—
158	C₂×Q₈×C₆₇	—	2	1	no	—
159	C₂×Q₈×C₆₇	—	2	1	no	—
160	C₂×Q₈×C₆₇	—	2	1	no	—
161	C₂×Q₈×C₆₇	—	2	1	no	—
162	C₂×Q₈×C₆₇	—	2	1	no	—
163	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
164	C₂×Q₈×C₆₇	#41	1	2	yes	—
165	C₂×Q₈×C₆₇	#41	1	2	yes	—
166	C₂×D₄×C₆₇	—	2	4	no	—
167	C₂×D₄×C₆₇	—	2	4	no	—
168	C₂×D₄×C₆₇	—	2	4	no	—
169	C₂×D₄×C₆₇	—	2	1	no	—
170	C₂×D₄×C₆₇	—	2	1	no	—
171	C₂×D₄×C₆₇	—	2	1	no	—
172	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
173	C₂×D₄×C₆₇	#41	1	2	yes	—
174	C₂×D₄×C₆₇	#41	1	2	yes	—
175	C₂²×C₄×C₆₇	—	2	4	no	—
176	C₂²×C₄×C₆₇	—	2	4	no	—
177	C₂²×C₄×C₆₇	—	2	1	no	—
178	C₂²×C₄×C₆₇	—	2	4	no	—
179	C₂²×C₄×C₆₇	—	2	1	no	—
180	C₂²×C₄×C₆₇	—	2	1	no	—
181	C₂²×C₄×C₆₇	—	2	1	no	—
182	C₂²×C₄×C₆₇	—	2	1	no	—
183	C₂²×C₄×C₆₇	—	2	4	no	—
184	C₂²×C₄×C₆₇	—	2	4	no	—
185	C₂²×C₄×C₆₇	—	2	2	no	—
186	C₂²×C₄×C₆₇	—	2	2	no	—
187	C₂²×C₄×C₆₇	—	2	1	no	—
188	C₂²×C₄×C₆₇	—	2	1	no	—
189	C₂²×C₄×C₆₇	—	2	2	no	—
190	C₂²×C₄×C₆₇	—	2	2	no	—
191	C₂²×C₄×C₆₇	—	2	1	no	—
192	C₂²×C₄×C₆₇	—	2	1	no	—
193	C₂²×C₄×C₆₇	—	2	1	no	—
194	C₂²×C₄×C₆₇	—	2	1	no	—
195	C₂²×C₄×C₆₇	—	4	1	no	—
196	C₂²×C₄×C₆₇	—	4	1	no	—
197	C₂²×C₄×C₆₇	—	4	2	no	—
198	C₂²×C₄×C₆₇	—	4	2	no	—
199	C₂²×C₄×C₆₇	—	4	2	no	—
200	C₂²×C₄×C₆₇	—	4	2	no	—
201	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
205	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
206	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
209	Q₁₆×C₆₇	—	4	4	no	—
210	SD₁₆×C₆₇	—	4	4	no	—
211	C₂×C₈×C₆₇	—	2	1	no	—
212	C₂×C₈×C₆₇	—	2	1	no	—
213	C₂×C₈×C₆₇	—	2	1	no	—
214	C₂×C₈×C₆₇	—	2	1	no	—
215	C₂×C₈×C₆₇	—	2	1	no	—
216	C₂×C₈×C₆₇	—	2	1	no	—
217	C₂×C₈×C₆₇	—	2	1	no	—
218	C₂×C₈×C₆₇	—	2	1	no	—
219	C₂×C₈×C₆₇	—	2	1	no	—
220	C₂×C₈×C₆₇	—	2	1	no	—
221	C₂×C₈×C₆₇	—	2	1	no	—
222	C₂×C₈×C₆₇	—	2	1	no	—
223	C₄⋊C₄×C₆₇	—	2	4	no	—
224	C₄⋊C₄×C₆₇	—	2	4	no	—
225	C₄⋊C₄×C₆₇	—	2	1	no	—
226	C₄⋊C₄×C₆₇	—	2	1	no	—
227	C₄⋊C₄×C₆₇	—	2	1	no	—
228	C₄⋊C₄×C₆₇	—	2	1	no	—
229	C₄⋊C₄×C₆₇	—	2	1	no	—
230	C₄⋊C₄×C₆₇	—	2	1	no	—
231	C₄⋊C₄×C₆₇	—	2	1	no	—
232	C₄⋊C₄×C₆₇	—	2	1	no	—
233	C₄⋊C₄×C₆₇	—	4	2	no	—
234	C₄⋊C₄×C₆₇	—	4	2	no	—
235	C₄⋊C₄×C₆₇	—	4	2	no	—
236	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
237	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
238	C₂²⋊C₄×C₆₇	—	2	4	no	—
239	C₂²⋊C₄×C₆₇	—	2	4	no	—
240	C₂²⋊C₄×C₆₇	—	2	4	no	—
241	C₂²⋊C₄×C₆₇	—	4	2	no	—
242	C₂²⋊C₄×C₆₇	—	4	2	no	—
243	C₄²×C₆₇	—	2	4	no	—
244	C₄²×C₆₇	—	2	4	no	—
245	C₄²×C₆₇	—	2	2	no	—
246	C₄²×C₆₇	—	2	4	no	—
247	C₄²×C₆₇	—	2	2	no	—
248	C₄²×C₆₇	—	2	1	no	—
249	C₄²×C₆₇	—	2	1	no	—
250	C₄²×C₆₇	—	2	1	no	—
251	C₄²×C₆₇	—	2	1	no	—
252	C₂³×C₆₇	—	2	2	no	—
253	C₂³×C₆₇	—	2	1	no	—
254	C₂³×C₆₇	—	2	1	no	—
255	C₂³×C₆₇	—	2	2	no	—
256	C₂³×C₆₇	—	2	2	no	—
257	C₂³×C₆₇	—	2	1	no	—
258	C₂³×C₆₇	—	2	1	no	—
259	C₂³×C₆₇	—	2	1	no	—
260	C₂³×C₆₇	—	2	1	no	—
261	C₂³×C₆₇	—	4	1	no	—
262	C₂³×C₆₇	—	4	1	no	—
263	C₂³×C₆₇	—	4	1	no	—
264	C₂³×C₆₇	—	4	1	no	—
265	C₂³×C₆₇	#120	1	2	yes	—
266	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
267	Q₈×C₆₇	—	2	2	no	—
268	Q₈×C₆₇	—	2	2	no	—
269	Q₈×C₆₇	—	2	2	no	—
270	Q₈×C₆₇	—	4	1	no	—
271	Q₈×C₆₇	—	4	1	no	—
272	Q₈×C₆₇	—	4	1	no	—
273	Q₈×C₆₇	—	4	1	no	—
274	Q₈×C₆₇	#123	1	4	yes	—
275	D₄×C₆₇	—	2	16	no	—
276	D₄×C₆₇	—	2	2	no	—
277	D₄×C₆₇	—	2	2	no	—
278	D₄×C₆₇	—	2	2	no	—
279	D₄×C₆₇	#123	1	4	yes	—
280	C₂×C₄×C₆₇	—	2	16	no	—
281	C₂×C₄×C₆₇	—	2	1	no	—
282	C₂×C₄×C₆₇	—	2	1	no	—
283	C₂×C₄×C₆₇	—	2	2	no	—
284	C₂×C₄×C₆₇	—	2	1	no	—
285	C₂×C₄×C₆₇	—	2	1	no	—
286	C₂×C₄×C₆₇	—	2	2	no	—
287	C₂×C₄×C₆₇	—	2	2	no	—
288	C₂×C₄×C₆₇	—	2	1	no	—
289	C₂×C₄×C₆₇	—	2	1	no	—
290	C₂×C₄×C₆₇	—	2	2	no	—
291	C₂×C₄×C₆₇	—	2	2	no	—
292	C₂×C₄×C₆₇	—	2	2	no	—
293	C₂×C₄×C₆₇	—	2	2	no	—
294	C₂×C₄×C₆₇	—	2	1	no	—
295	C₂×C₄×C₆₇	—	2	1	no	—
296	C₂×C₄×C₆₇	—	2	2	no	—
297	C₂×C₄×C₆₇	—	2	2	no	—
298	C₂×C₄×C₆₇	—	2	1	no	—
299	C₂×C₄×C₆₇	—	2	1	no	—
300	C₂×C₄×C₆₇	—	2	1	no	—
301	C₂×C₄×C₆₇	—	2	1	no	—
302	C₂×C₄×C₆₇	—	4	4	no	—
303	C₂×C₄×C₆₇	—	4	4	no	—
304	C₂×C₄×C₆₇	—	4	8	no	—
305	C₂×C₄×C₆₇	—	4	8	no	—
306	C₂×C₄×C₆₇	—	4	1	no	—
307	C₂×C₄×C₆₇	—	4	1	no	—
308	C₂×C₄×C₆₇	—	4	1	no	—
309	C₂×C₄×C₆₇	—	4	1	no	—
310	C₂×C₄×C₆₇	—	4	1	no	—
311	C₂×C₄×C₆₇	—	4	1	no	—
312	C₂×C₄×C₆₇	—	4	1	no	—
313	C₂×C₄×C₆₇	—	4	1	no	—
314	C₂×C₄×C₆₇	—	4	1	no	—
315	C₂×C₄×C₆₇	—	4	1	no	—
316	C₂×C₄×C₆₇	—	4	1	no	—
317	C₂×C₄×C₆₇	—	4	1	no	—
318	C₂×C₄×C₆₇	—	4	1	no	—
319	C₂×C₄×C₆₇	—	4	1	no	—
320	C₂×C₄×C₆₇	—	4	1	no	—
321	C₂×C₄×C₆₇	—	4	1	no	—
322	C₂×C₄×C₆₇	#120	1	2	yes	—
323	C₂×C₄×C₆₇	#135	1	2	yes	—
324	C₂×C₄×C₆₇	#137	1	2	yes	—
325	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
328	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
329	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
330	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
331	C₈×C₆₇	—	4	1	no	—
332	C₈×C₆₇	—	4	1	no	—
333	C₈×C₆₇	—	4	1	no	—
334	C₈×C₆₇	—	4	1	no	—
335	C₂²×C₆₇	—	2	2	no	—
336	C₂²×C₆₇	—	2	4	no	—
337	C₂²×C₆₇	—	2	2	no	—
338	C₂²×C₆₇	—	2	2	no	—
339	C₂²×C₆₇	—	4	1	no	—
340	C₂²×C₆₇	—	4	2	no	—
341	C₂²×C₆₇	—	4	1	no	—
342	C₂²×C₆₇	—	4	2	no	—
343	C₂²×C₆₇	—	4	1	no	—
344	C₂²×C₆₇	—	4	2	no	—
345	C₂²×C₆₇	—	4	1	no	—
346	C₂²×C₆₇	—	4	2	no	—
347	C₂²×C₆₇	—	4	2	no	—
348	C₂²×C₆₇	—	4	2	no	—
349	C₂²×C₆₇	C₂×#120	1	1	yes	characteristic
350	C₂²×C₆₇	#525	1	1	yes	characteristic
351	C₂²×C₆₇	#525	1	1	yes	characteristic
352	C₂²×C₆₇	C₂×#135	1	1	yes	characteristic
353	C₂²×C₆₇	C₂×#137	1	1	yes	characteristic
354	C₂²×C₆₇	#575	1	1	yes	characteristic
355	C₂²×C₆₇	#575	1	1	yes	characteristic
356	C₄×C₆₇	—	2	2	no	—
357	C₄×C₆₇	—	2	4	no	—
358	C₄×C₆₇	—	2	2	no	—
359	C₄×C₆₇	—	2	2	no	—
360	C₄×C₆₇	—	4	1	no	—
361	C₄×C₆₇	—	4	2	no	—
362	C₄×C₆₇	—	4	1	no	—
363	C₄×C₆₇	—	4	2	no	—
364	C₄×C₆₇	—	8	1	no	—
365	C₄×C₆₇	—	8	1	no	—
366	C₄×C₆₇	—	8	1	no	—
367	C₄×C₆₇	—	8	1	no	—
368	C₄×C₆₇	C₂×#123	1	1	yes	characteristic
369	C₄×C₆₇	C₂×#123	1	1	yes	characteristic
370	C₄×C₆₇	#525	1	1	yes	characteristic
371	C₄×C₆₇	#525	1	1	yes	characteristic
372	#33011	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
373	C₂×C₆₇	—	4	2	no	—
374	C₂×C₆₇	—	4	4	no	—
375	C₂×C₆₇	#2849	1	1	yes	characteristic
376	C₂×C₆₇	#3002	1	1	yes	characteristic
377	C₂×C₆₇	#3007	1	1	yes	characteristic
378	C₂×C₆₇	#3102	1	1	yes	characteristic
379	C₂×C₆₇	#3107	1	1	yes	characteristic
380	C₂×C₆₇	#3111	1	1	yes	characteristic
381	C₂×C₆₇	#3116	1	1	yes	characteristic
382	C₂×C₄×#41	C₂×C₆₇	1	1	yes	characteristic
383	C₂×#485	C₂×C₆₇	1	1	yes	characteristic, complemented
384	C₂×#452	C₂×C₆₇	1	1	yes	characteristic
385	#2855	C₂×C₆₇	1	1	yes	characteristic, complemented
386	#1878	C₂×C₆₇	1	1	yes	characteristic, complemented
387	#1878	C₂×C₆₇	1	1	yes	characteristic, complemented
388	#1877	C₂×C₆₇	1	1	yes	characteristic, complemented
389	#1877	C₂×C₆₇	1	1	yes	characteristic, complemented
390	#1865	C₂×C₆₇	1	1	yes	characteristic, complemented
391	#1864	C₂×C₆₇	1	1	yes	characteristic, complemented
392	#1863	C₂×C₆₇	1	1	yes	characteristic, complemented
393	#1862	C₂×C₆₇	1	1	yes	characteristic, complemented
394	#1825	C₂×C₆₇	1	1	yes	characteristic, complemented
395	#1817	C₂×C₆₇	1	1	yes	characteristic, complemented
396	#1788	C₂×C₆₇	1	1	yes	characteristic
397	C₆₇	#33011	1	1	yes	characteristic, direct product factor, Sylow
398	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
399	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
400	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
401	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
402	C₄×#41	—	2	4	no	—
403	C₄×#41	—	2	4	no	—
404	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
405	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
406	C₂×C₄×D₄	—	2	1	no	—
407	C₂×C₄×D₄	—	2	1	no	—
408	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
409	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
410	C₂×#117	—	2	1	no	—
411	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
412	C₂²×C₄²	—	2	1	no	—
413	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
414	#485	—	2	4	no	—
415	#452	—	2	4	no	—
416	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
417	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
418	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
419	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
420	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
421	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
422	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
423	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
424	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
425	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
426	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
427	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
428	#391	C₂²×C₆₇	1	1	yes	characteristic
429	#391	C₂²×C₆₇	1	1	yes	characteristic
430	#389	C₂²×C₆₇	1	1	yes	characteristic
431	#389	C₂²×C₆₇	1	1	yes	characteristic
432	#387	—	2	1	no	—
433	#387	—	2	1	no	—
434	#385	—	2	1	no	—
435	#381	—	2	1	no	—
436	#380	C₂²×C₆₇	1	1	yes	characteristic
437	#340	C₂²×C₆₇	1	1	yes	characteristic
438	#340	C₂²×C₆₇	1	1	yes	characteristic
439	#340	C₂²×C₆₇	1	1	yes	characteristic
440	#340	C₂²×C₆₇	1	1	yes	characteristic
441	#336	C₂²×C₆₇	1	1	yes	characteristic
442	#336	C₂²×C₆₇	1	1	yes	characteristic
443	#336	C₂²×C₆₇	1	1	yes	characteristic
444	#336	C₂²×C₆₇	1	1	yes	characteristic
445	C₂×#41	—	2	2	no	—
446	C₂×#41	—	2	2	no	—
447	C₂×#41	—	2	2	no	—
448	C₂×#41	—	2	2	no	—
449	C₂×#41	—	2	2	no	—
450	C₂×#41	D₄×C₆₇	1	4	yes	—
451	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
452	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
453	C₂²×D₄	—	2	1	no	—
454	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
455	C₂³×C₄	—	2	1	no	—
456	C₂³×C₄	—	2	1	no	—
457	C₂³×C₄	—	2	1	no	—
458	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
459	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
460	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
461	C₂×Q₁₆	—	2	2	no	—
462	C₂×Q₁₆	—	2	2	no	—
463	C₂×Q₁₆	—	2	2	no	—
464	C₂×SD₁₆	—	2	2	no	—
465	C₂×SD₁₆	—	2	2	no	—
466	C₂×SD₁₆	—	2	2	no	—
467	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
468	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
469	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
470	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
471	C₂²⋊Q₈	—	2	2	no	—
472	C₂²⋊Q₈	—	2	2	no	—
473	C₄×Q₈	—	2	2	no	—
474	C₄×Q₈	—	2	2	no	—
475	C₄×Q₈	—	2	2	no	—
476	C₄×Q₈	—	2	2	no	—
477	C₄×D₄	—	2	8	no	—
478	C₄×D₄	—	2	8	no	—
479	C₄×D₄	—	2	2	no	—
480	C₄×D₄	—	2	2	no	—
481	C₄×D₄	—	2	2	no	—
482	C₄×D₄	—	2	2	no	—
483	#117	—	2	8	no	—
484	#117	—	2	2	no	—
485	#117	D₄×C₆₇	1	4	yes	—
486	C₂×C₄⋊C₄	—	2	1	no	—
487	C₂×C₄⋊C₄	—	2	1	no	—
488	C₂×C₄⋊C₄	—	2	1	no	—
489	C₂×C₄⋊C₄	—	2	1	no	—
490	C₂×C₄⋊C₄	—	2	1	no	—
491	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
493	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
494	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
495	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
496	C₂×C₂²⋊C₄	—	2	1	no	—
497	C₂×C₂²⋊C₄	—	2	1	no	—
498	C₂×C₂²⋊C₄	—	2	1	no	—
499	C₂×C₂²⋊C₄	—	2	1	no	—
500	C₂×C₂²⋊C₄	—	2	1	no	—
501	C₂×C₄²	—	2	8	no	—
502	C₂×C₄²	—	2	1	no	—
503	C₂×C₄²	—	2	1	no	—
504	C₂×C₄²	—	2	1	no	—
505	C₂×C₄²	—	2	2	no	—
506	C₂×C₄²	—	2	2	no	—
507	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
508	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
509	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
510	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
511	#107	—	2	2	no	—
512	#106	—	2	2	no	—
513	#103	—	2	2	no	—
514	#103	—	2	2	no	—
515	#103	—	2	2	no	—
516	#103	—	2	2	no	—
517	#103	—	2	2	no	—
518	#102	—	2	2	no	—
519	#102	—	2	2	no	—
520	#102	—	2	2	no	—
521	C₂²⋊C₈	—	2	2	no	—
522	C₂²⋊C₈	—	2	2	no	—
523	#95	—	2	1	no	—
524	#95	—	2	1	no	—
525	#95	—	2	1	no	—
526	#95	—	2	1	no	—
527	#95	—	2	1	no	—
528	#95	—	2	1	no	—
529	#95	—	2	1	no	—
530	C₂⁴	—	2	1	no	—
531	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
532	#41	—	2	8	no	—
533	#41	—	2	8	no	—
534	#41	—	2	8	no	—
535	#41	—	2	8	no	—
536	C₂×Q₈	—	2	1	no	—
537	C₂×Q₈	—	2	1	no	—
538	C₂×Q₈	—	2	1	no	—
539	C₂×Q₈	—	2	1	no	—
540	C₂×Q₈	—	2	1	no	—
541	C₂×Q₈	—	2	1	no	—
542	C₂×Q₈	—	2	1	no	—
543	C₂×Q₈	—	2	1	no	—
544	C₂×Q₈	—	2	1	no	—
545	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
546	C₂×Q₈	#41×C₆₇	1	2	yes	—
547	C₂×Q₈	#41×C₆₇	1	2	yes	—
548	C₂×D₄	—	2	4	no	—
549	C₂×D₄	—	2	4	no	—
550	C₂×D₄	—	2	4	no	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
555	C₂×D₄	#41×C₆₇	1	2	yes	—
556	C₂×D₄	#41×C₆₇	1	2	yes	—
557	C₂²×C₄	—	2	4	no	—
558	C₂²×C₄	—	2	4	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	4	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	4	no	—
566	C₂²×C₄	—	2	4	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	4	1	no	—
578	C₂²×C₄	—	4	1	no	—
579	C₂²×C₄	—	4	2	no	—
580	C₂²×C₄	—	4	2	no	—
581	C₂²×C₄	—	4	2	no	—
582	C₂²×C₄	—	4	2	no	—
583	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
584	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
585	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
586	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
587	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
588	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
589	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
590	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
591	Q₁₆	—	4	4	no	—
592	SD₁₆	—	4	4	no	—
593	C₂×C₈	—	2	1	no	—
594	C₂×C₈	—	2	1	no	—
595	C₂×C₈	—	2	1	no	—
596	C₂×C₈	—	2	1	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	2	1	no	—
599	C₂×C₈	—	2	1	no	—
600	C₂×C₈	—	2	1	no	—
601	C₂×C₈	—	2	1	no	—
602	C₂×C₈	—	2	1	no	—
603	C₂×C₈	—	2	1	no	—
604	C₂×C₈	—	2	1	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	4	2	no	—
616	C₄⋊C₄	—	4	2	no	—
617	C₄⋊C₄	—	4	2	no	—
618	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
619	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
620	C₂²⋊C₄	—	2	4	no	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₂²⋊C₄	—	2	4	no	—
623	C₂²⋊C₄	—	4	2	no	—
624	C₂²⋊C₄	—	4	2	no	—
625	C₄²	—	2	4	no	—
626	C₄²	—	2	4	no	—
627	C₄²	—	2	2	no	—
628	C₄²	—	2	4	no	—
629	C₄²	—	2	2	no	—
630	C₄²	—	2	1	no	—
631	C₄²	—	2	1	no	—
632	C₄²	—	2	1	no	—
633	C₄²	—	2	1	no	—
634	C₂³	—	2	2	no	—
635	C₂³	—	2	1	no	—
636	C₂³	—	2	1	no	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	2	1	no	—
640	C₂³	—	2	1	no	—
641	C₂³	—	2	1	no	—
642	C₂³	—	2	1	no	—
643	C₂³	—	4	1	no	—
644	C₂³	—	4	1	no	—
645	C₂³	—	4	1	no	—
646	C₂³	—	4	1	no	—
647	C₂³	#120×C₆₇	1	2	yes	—
648	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
649	Q₈	—	2	2	no	—
650	Q₈	—	2	2	no	—
651	Q₈	—	2	2	no	—
652	Q₈	—	4	1	no	—
653	Q₈	—	4	1	no	—
654	Q₈	—	4	1	no	—
655	Q₈	—	4	1	no	—
656	Q₈	#123×C₆₇	1	4	yes	—
657	D₄	—	2	16	no	—
658	D₄	—	2	2	no	—
659	D₄	—	2	2	no	—
660	D₄	—	2	2	no	—
661	D₄	#123×C₆₇	1	4	yes	—
662	C₂×C₄	—	2	16	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	4	4	no	—
685	C₂×C₄	—	4	4	no	—
686	C₂×C₄	—	4	8	no	—
687	C₂×C₄	—	4	8	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	#120×C₆₇	1	2	yes	—
705	C₂×C₄	#135×C₆₇	1	2	yes	—
706	C₂×C₄	#137×C₆₇	1	2	yes	—
707	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
708	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
709	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
710	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
711	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
712	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
713	C₈	—	4	1	no	—
714	C₈	—	4	1	no	—
715	C₈	—	4	1	no	—
716	C₈	—	4	1	no	—
717	C₂²	—	2	2	no	—
718	C₂²	—	2	4	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	4	1	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	1	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	1	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	4	2	no	—
730	C₂²	—	4	2	no	—
731	C₂²	C₂×#120×C₆₇	1	1	yes	characteristic
732	C₂²	#525×C₆₇	1	1	yes	characteristic
733	C₂²	#525×C₆₇	1	1	yes	characteristic
734	C₂²	C₂×#135×C₆₇	1	1	yes	characteristic
735	C₂²	C₂×#137×C₆₇	1	1	yes	characteristic
736	C₂²	#575×C₆₇	1	1	yes	characteristic
737	C₂²	#575×C₆₇	1	1	yes	characteristic
738	C₄	—	2	2	no	—
739	C₄	—	2	4	no	—
740	C₄	—	2	2	no	—
741	C₄	—	2	2	no	—
742	C₄	—	4	1	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	1	no	—
745	C₄	—	4	2	no	—
746	C₄	—	8	1	no	—
747	C₄	—	8	1	no	—
748	C₄	—	8	1	no	—
749	C₄	—	8	1	no	—
750	C₄	C₂×#123×C₆₇	1	1	yes	characteristic
751	C₄	C₂×#123×C₆₇	1	1	yes	characteristic
752	C₄	#525×C₆₇	1	1	yes	characteristic
753	C₄	#525×C₆₇	1	1	yes	characteristic
754	C₂	—	4	2	no	—
755	C₂	—	4	4	no	—
756	C₂	C₆₇×#2849	1	1	yes	characteristic
757	C₂	C₆₇×#3002	1	1	yes	characteristic
758	C₂	C₆₇×#3007	1	1	yes	characteristic
759	C₂	C₆₇×#3102	1	1	yes	characteristic
760	C₂	C₆₇×#3107	1	1	yes	characteristic
761	C₂	C₆₇×#3111	1	1	yes	characteristic
762	C₂	C₆₇×#3116	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂²×#41×C₆₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂²×C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#485×C₆₇	C₂	semidirect
4. C₆₇×#2855	C₂	semidirect
5. C₆₇×#1878	C₂	semidirect
6. C₆₇×#1878	C₂	semidirect
7. C₆₇×#1877	C₂	semidirect
8. C₆₇×#1877	C₂	semidirect
9. C₆₇×#1865	C₂	semidirect
10. C₆₇×#1864	C₂	semidirect
11. C₆₇×#1863	C₂	semidirect
12. C₆₇×#1862	C₂	semidirect
13. C₆₇×#1825	C₂	semidirect
14. C₆₇×#1817	C₂	semidirect
372. #33011	C₆₇	direct (N × H)
383. C₂×#485	C₂×C₆₇	semidirect
385. #2855	C₂×C₆₇	semidirect
386. #1878	C₂×C₆₇	semidirect
387. #1878	C₂×C₆₇	semidirect
388. #1877	C₂×C₆₇	semidirect
389. #1877	C₂×C₆₇	semidirect
390. #1865	C₂×C₆₇	semidirect
391. #1864	C₂×C₆₇	semidirect
392. #1863	C₂×C₆₇	semidirect
393. #1862	C₂×C₆₇	semidirect
394. #1825	C₂×C₆₇	semidirect
395. #1817	C₂×C₆₇	semidirect
397. C₆₇	#33011	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×C₄×#41×C₆₇	2
C₂×#485×C₆₇	2
C₂×#452×C₆₇	2
C₆₇×#2855	2
C₆₇×#1878	2
C₆₇×#1877	2
C₆₇×#1865	2
C₆₇×#1864	2
C₆₇×#1863	2
C₆₇×#1862	2
C₆₇×#1825	2
C₆₇×#1817	2
C₆₇×#1788	2
#33011	67

Subgroups — C67×#33011 #30712262

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#33011 #30712262