Subgroups — C₆₇×#33129 #30712380

Order 17152.

1034 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#466×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2854	C₂	1	2	yes	maximal, complemented
4	C₆₇×#1970	C₂	1	2	yes	maximal, complemented
5	C₆₇×#1942	C₂	1	2	yes	maximal, complemented
6	C₆₇×#1934	C₂	1	4	yes	maximal, complemented
7	C₆₇×#1893	C₂	1	2	yes	maximal, complemented
8	C₆₇×#1808	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
12	C₂×#123×C₆₇	—	2	2	no	—
13	C₂×#121×C₆₇	C₂²	1	2	yes	—
14	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
15	#466×C₆₇	—	2	4	no	—
16	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
17	C₂×#107×C₆₇	C₂²	1	2	yes	—
18	C₂×#102×C₆₇	C₂²	1	2	yes	—
19	C₂×#102×C₆₇	C₂²	1	4	yes	—
20	C₂×C₄×C₈×C₆₇	—	2	4	no	—
21	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	—
23	#390×C₆₇	C₂²	1	4	yes	—
24	#389×C₆₇	C₂²	1	4	yes	—
25	#388×C₆₇	—	2	4	no	—
26	#386×C₆₇	—	2	2	no	—
27	#380×C₆₇	C₂²	1	2	yes	—
28	#340×C₆₇	C₂²	1	2	yes	—
29	#340×C₆₇	C₂²	1	4	yes	—
30	C₂²×D₄×C₆₇	—	2	2	no	—
31	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
32	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
35	C₂×D₈×C₆₇	—	2	2	no	—
36	C₂×D₈×C₆₇	—	2	4	no	—
37	C₂²×C₈×C₆₇	—	2	2	no	—
38	C₂²×C₈×C₆₇	—	2	4	no	—
39	C₂²×C₈×C₆₇	—	2	4	no	—
40	C₂²×C₈×C₆₇	D₄	1	4	yes	—
41	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
43	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
44	#123×C₆₇	—	4	8	no	—
45	#121×C₆₇	—	2	4	no	—
46	#121×C₆₇	—	2	4	no	—
47	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
48	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
49	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
50	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
51	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
52	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
53	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
54	C₂×C₄²×C₆₇	—	2	2	no	—
55	C₂×C₄²×C₆₇	—	2	2	no	—
56	C₂×C₄²×C₆₇	D₄	1	2	yes	—
57	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
58	#107×C₆₇	—	2	2	no	—
59	#107×C₆₇	—	2	4	no	—
60	#102×C₆₇	—	2	4	no	—
61	#102×C₆₇	—	2	8	no	—
62	C₄×C₈×C₆₇	—	2	4	no	—
63	C₄×C₈×C₆₇	—	2	4	no	—
64	#95×C₆₇	—	2	2	no	—
65	#95×C₆₇	—	2	4	no	—
66	C₂⁴×C₆₇	—	2	2	no	—
67	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
68	C₂×D₄×C₆₇	—	2	2	no	—
69	C₂×D₄×C₆₇	—	2	4	no	—
70	C₂×D₄×C₆₇	—	2	2	no	—
71	C₂×D₄×C₆₇	—	2	4	no	—
72	C₂×D₄×C₆₇	—	4	4	no	—
73	C₂×D₄×C₆₇	—	4	4	no	—
74	C₂×D₄×C₆₇	—	4	4	no	—
75	C₂²×C₄×C₆₇	—	2	2	no	—
76	C₂²×C₄×C₆₇	—	2	2	no	—
77	C₂²×C₄×C₆₇	—	2	2	no	—
78	C₂²×C₄×C₆₇	—	2	4	no	—
79	C₂²×C₄×C₆₇	—	2	2	no	—
80	C₂²×C₄×C₆₇	—	2	2	no	—
81	C₂²×C₄×C₆₇	—	2	4	no	—
82	C₂²×C₄×C₆₇	—	2	2	no	—
83	C₂²×C₄×C₆₇	D₈	1	4	yes	complemented
84	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
86	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₆₇	#41	1	2	yes	—
89	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
90	D₈×C₆₇	—	4	4	no	—
91	C₂×C₈×C₆₇	—	2	8	no	—
92	C₂×C₈×C₆₇	—	2	2	no	—
93	C₂×C₈×C₆₇	—	2	2	no	—
94	C₂×C₈×C₆₇	—	2	2	no	—
95	C₂×C₈×C₆₇	—	2	8	no	—
96	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
97	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
98	C₂×C₈×C₆₇	#41	1	4	yes	—
99	C₂×C₈×C₆₇	#41	1	4	yes	—
100	C₄⋊C₄×C₆₇	—	2	2	no	—
101	C₄⋊C₄×C₆₇	—	2	4	no	—
102	C₄⋊C₄×C₆₇	—	2	4	no	—
103	C₄⋊C₄×C₆₇	—	2	2	no	—
104	C₄⋊C₄×C₆₇	—	4	8	no	—
105	C₂²⋊C₄×C₆₇	—	4	4	no	—
106	C₂²⋊C₄×C₆₇	—	4	4	no	—
107	C₂²⋊C₄×C₆₇	—	4	8	no	—
108	C₂²⋊C₄×C₆₇	—	4	8	no	—
109	C₄²×C₆₇	—	2	4	no	—
110	C₄²×C₆₇	—	2	2	no	—
111	C₄²×C₆₇	—	2	2	no	—
112	C₂³×C₆₇	—	2	2	no	—
113	C₂³×C₆₇	—	2	2	no	—
114	C₂³×C₆₇	—	4	2	no	—
115	C₂³×C₆₇	—	4	4	no	—
116	C₂³×C₆₇	—	4	2	no	—
117	C₂³×C₆₇	—	4	4	no	—
118	C₂³×C₆₇	—	4	2	no	—
119	C₂³×C₆₇	#121	1	2	yes	—
120	C₂³×C₆₇	C₂×D₈	1	2	yes	—
121	C₂³×C₆₇	#135	1	2	yes	—
122	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
123	D₄×C₆₇	—	4	2	no	—
124	D₄×C₆₇	—	4	2	no	—
125	D₄×C₆₇	—	4	4	no	—
126	D₄×C₆₇	—	8	8	no	—
127	C₂×C₄×C₆₇	—	2	8	no	—
128	C₂×C₄×C₆₇	—	2	2	no	—
129	C₂×C₄×C₆₇	—	2	2	no	—
130	C₂×C₄×C₆₇	—	2	2	no	—
131	C₂×C₄×C₆₇	—	2	2	no	—
132	C₂×C₄×C₆₇	—	2	2	no	—
133	C₂×C₄×C₆₇	—	2	8	no	—
134	C₂×C₄×C₆₇	—	2	2	no	—
135	C₂×C₄×C₆₇	—	2	2	no	—
136	C₂×C₄×C₆₇	—	2	4	no	—
137	C₂×C₄×C₆₇	—	4	2	no	—
138	C₂×C₄×C₆₇	—	4	4	no	—
139	C₂×C₄×C₆₇	—	4	4	no	—
140	C₂×C₄×C₆₇	—	4	2	no	—
141	C₂×C₄×C₆₇	—	4	4	no	—
142	C₂×C₄×C₆₇	—	4	2	no	—
143	C₂×C₄×C₆₇	#121	1	2	yes	—
144	C₂×C₄×C₆₇	C₂×D₈	1	4	yes	—
145	C₂×C₄×C₆₇	#135	1	4	yes	—
146	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
148	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
149	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
150	C₈×C₆₇	—	2	2	no	—
151	C₈×C₆₇	—	2	4	no	—
152	C₈×C₆₇	#123	1	4	yes	complemented
153	C₂²×C₆₇	—	2	2	no	—
154	C₂²×C₆₇	—	2	4	no	—
155	C₂²×C₆₇	—	2	4	no	—
156	C₂²×C₆₇	—	2	2	no	—
157	C₂²×C₆₇	—	8	2	no	—
158	C₂²×C₆₇	—	8	4	no	—
159	C₂²×C₆₇	—	8	4	no	—
160	C₂²×C₆₇	—	8	2	no	—
161	C₂²×C₆₇	—	8	2	no	—
162	C₂²×C₆₇	#466	1	4	yes	—
163	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
164	C₂²×C₆₇	#532	1	2	yes	—
165	C₂²×C₆₇	C₂²×D₈	1	1	yes	characteristic
166	C₂²×C₆₇	C₂×#135	1	1	yes	characteristic
167	C₂²×C₆₇	C₂×#135	1	2	yes	—
168	C₄×C₆₇	—	2	2	no	—
169	C₄×C₆₇	—	2	4	no	—
170	C₄×C₆₇	—	2	4	no	—
171	C₄×C₆₇	—	8	4	no	—
172	C₄×C₆₇	—	8	2	no	—
173	C₄×C₆₇	C₂×#123	1	1	yes	characteristic
174	C₄×C₆₇	#525	1	1	yes	characteristic
175	C₄×C₆₇	#529	1	2	yes	—
176	#33129	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂×C₆₇	—	2	4	no	—
178	C₂×C₆₇	—	16	2	no	—
179	C₂×C₆₇	#2854	1	1	yes	characteristic
180	C₂×C₆₇	C₂×#466	1	1	yes	characteristic
181	C₂×C₆₇	#3050	1	1	yes	characteristic
182	C₂×C₆₇	#3168	1	2	yes	—
183	C₂×C₆₇	#3169	1	2	yes	—
184	C₂×#466	C₂×C₆₇	1	1	yes	characteristic
185	C₂²×C₄×C₈	C₂×C₆₇	1	1	yes	characteristic, complemented
186	#2854	C₂×C₆₇	1	2	yes	complemented
187	#1970	C₂×C₆₇	1	2	yes	complemented
188	#1942	C₂×C₆₇	1	2	yes	complemented
189	#1934	C₂×C₆₇	1	4	yes	complemented
190	#1893	C₂×C₆₇	1	2	yes	complemented
191	#1808	C₂×C₆₇	1	1	yes	characteristic, complemented
192	C₆₇	#33129	1	1	yes	characteristic, direct product factor, Sylow
193	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
194	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
195	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
196	C₂×#123	—	2	2	no	—
197	C₂×#121	C₂²×C₆₇	1	2	yes	—
198	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
199	#466	—	2	4	no	—
200	C₂×#107	C₂²×C₆₇	1	2	yes	—
201	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
202	C₂×#102	C₂²×C₆₇	1	4	yes	—
203	C₂×#102	C₂²×C₆₇	1	2	yes	—
204	C₂×C₄×C₈	—	2	4	no	—
205	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	—
206	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	—
207	#390	C₂²×C₆₇	1	4	yes	—
208	#389	C₂²×C₆₇	1	4	yes	—
209	#388	—	2	4	no	—
210	#386	—	2	2	no	—
211	#380	C₂²×C₆₇	1	2	yes	—
212	#340	C₂²×C₆₇	1	2	yes	—
213	#340	C₂²×C₆₇	1	4	yes	—
214	C₂²×D₄	—	2	2	no	—
215	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
216	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
217	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
218	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
219	C₂×D₈	—	2	2	no	—
220	C₂×D₈	—	2	4	no	—
221	C₂²×C₈	—	2	2	no	—
222	C₂²×C₈	—	2	4	no	—
223	C₂²×C₈	—	2	4	no	—
224	C₂²×C₈	D₄×C₆₇	1	4	yes	—
225	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
226	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
227	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
228	#123	—	4	8	no	—
229	#121	—	2	4	no	—
230	#121	—	2	4	no	—
231	C₂×C₄⋊C₄	—	2	4	no	—
232	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
233	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
234	C₂×C₂²⋊C₄	—	2	2	no	—
235	C₂×C₂²⋊C₄	—	2	2	no	—
236	C₂×C₂²⋊C₄	—	2	4	no	—
237	C₂×C₂²⋊C₄	—	2	4	no	—
238	C₂×C₄²	—	2	2	no	—
239	C₂×C₄²	—	2	2	no	—
240	C₂×C₄²	D₄×C₆₇	1	2	yes	—
241	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
242	#107	—	2	2	no	—
243	#107	—	2	4	no	—
244	#102	—	2	4	no	—
245	#102	—	2	8	no	—
246	C₄×C₈	—	2	4	no	—
247	C₄×C₈	—	2	4	no	—
248	#95	—	2	2	no	—
249	#95	—	2	4	no	—
250	C₂⁴	—	2	2	no	—
251	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
252	C₂×D₄	—	2	2	no	—
253	C₂×D₄	—	2	4	no	—
254	C₂×D₄	—	2	2	no	—
255	C₂×D₄	—	2	4	no	—
256	C₂×D₄	—	4	4	no	—
257	C₂×D₄	—	4	4	no	—
258	C₂×D₄	—	4	4	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	D₈×C₆₇	1	4	yes	complemented
268	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
269	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
270	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
271	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
272	C₂²×C₄	#41×C₆₇	1	2	yes	—
273	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
274	D₈	—	4	4	no	—
275	C₂×C₈	—	2	8	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	8	no	—
280	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
281	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
282	C₂×C₈	#41×C₆₇	1	4	yes	—
283	C₂×C₈	#41×C₆₇	1	4	yes	—
284	C₄⋊C₄	—	2	2	no	—
285	C₄⋊C₄	—	2	4	no	—
286	C₄⋊C₄	—	2	4	no	—
287	C₄⋊C₄	—	2	2	no	—
288	C₄⋊C₄	—	4	8	no	—
289	C₂²⋊C₄	—	4	4	no	—
290	C₂²⋊C₄	—	4	4	no	—
291	C₂²⋊C₄	—	4	8	no	—
292	C₂²⋊C₄	—	4	8	no	—
293	C₄²	—	2	4	no	—
294	C₄²	—	2	2	no	—
295	C₄²	—	2	2	no	—
296	C₂³	—	2	2	no	—
297	C₂³	—	2	2	no	—
298	C₂³	—	4	2	no	—
299	C₂³	—	4	4	no	—
300	C₂³	—	4	2	no	—
301	C₂³	—	4	4	no	—
302	C₂³	—	4	2	no	—
303	C₂³	#121×C₆₇	1	2	yes	—
304	C₂³	C₂×D₈×C₆₇	1	2	yes	—
305	C₂³	#135×C₆₇	1	2	yes	—
306	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
307	D₄	—	4	2	no	—
308	D₄	—	4	2	no	—
309	D₄	—	4	4	no	—
310	D₄	—	8	8	no	—
311	C₂×C₄	—	2	8	no	—
312	C₂×C₄	—	2	8	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	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	4	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	#121×C₆₇	1	2	yes	—
328	C₂×C₄	C₂×D₈×C₆₇	1	4	yes	—
329	C₂×C₄	#135×C₆₇	1	4	yes	—
330	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
331	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
332	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
333	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
334	C₈	—	2	2	no	—
335	C₈	—	2	4	no	—
336	C₈	#123×C₆₇	1	4	yes	complemented
337	C₂²	—	2	2	no	—
338	C₂²	—	2	2	no	—
339	C₂²	—	2	4	no	—
340	C₂²	—	2	4	no	—
341	C₂²	—	8	2	no	—
342	C₂²	—	8	2	no	—
343	C₂²	—	8	2	no	—
344	C₂²	—	8	4	no	—
345	C₂²	—	8	4	no	—
346	C₂²	#466×C₆₇	1	4	yes	—
347	C₂²	C₂×#121×C₆₇	1	1	yes	characteristic
348	C₂²	#532×C₆₇	1	2	yes	—
349	C₂²	C₂²×D₈×C₆₇	1	1	yes	characteristic
350	C₂²	C₂×#135×C₆₇	1	1	yes	characteristic
351	C₂²	C₂×#135×C₆₇	1	2	yes	—
352	C₄	—	2	4	no	—
353	C₄	—	2	4	no	—
354	C₄	—	2	2	no	—
355	C₄	—	8	2	no	—
356	C₄	—	8	4	no	—
357	C₄	C₂×#123×C₆₇	1	1	yes	characteristic
358	C₄	#525×C₆₇	1	1	yes	characteristic
359	C₄	#529×C₆₇	1	2	yes	—
360	C₂	—	2	4	no	—
361	C₂	—	16	2	no	—
362	C₂	C₆₇×#2854	1	1	yes	characteristic
363	C₂	C₂×#466×C₆₇	1	1	yes	characteristic
364	C₂	C₆₇×#3050	1	1	yes	characteristic
365	C₂	C₆₇×#3168	1	2	yes	—
366	C₂	C₆₇×#3169	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂×#466×C₆₇	C₂
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. C₂²×C₄×C₈×C₆₇	C₂	semidirect
3. C₆₇×#2854	C₂	semidirect
4. C₆₇×#1970	C₂	semidirect
5. C₆₇×#1942	C₂	semidirect
6. C₆₇×#1934	C₂	semidirect
7. C₆₇×#1893	C₂	semidirect
8. C₆₇×#1808	C₂	semidirect
83. C₂²×C₄×C₆₇	D₈	semidirect
152. C₈×C₆₇	#123	semidirect
176. #33129	C₆₇	direct (N × H)
185. C₂²×C₄×C₈	C₂×C₆₇	semidirect
186. #2854	C₂×C₆₇	semidirect
187. #1970	C₂×C₆₇	semidirect
188. #1942	C₂×C₆₇	semidirect
189. #1934	C₂×C₆₇	semidirect
190. #1893	C₂×C₆₇	semidirect
191. #1808	C₂×C₆₇	semidirect
192. C₆₇	#33129	direct (N × H)
267. C₂²×C₄	D₈×C₆₇	semidirect
336. C₈	#123×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#466×C₆₇	2
C₂²×C₄×C₈×C₆₇	2
C₆₇×#2854	2
C₆₇×#1970	2
C₆₇×#1942	2
C₆₇×#1934	2
C₆₇×#1893	2
C₆₇×#1808	2
#33129	67

Subgroups — C67×#33129 #30712380

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#33129 #30712380