Subgroups — C₆₇×#33629 #30712880

Order 17152.

574 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×#500×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#135×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#2227	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2226	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2225	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2224	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2159	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2150	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2139	C₂	1	2	yes	maximal
10	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Q₈×C₆₇	—	2	1	no	—
12	C₄×#41×C₆₇	—	2	1	no	—
13	C₂×M₃₂×C₆₇	C₂²	1	2	yes	—
14	#500×C₆₇	—	2	1	no	—
15	#500×C₆₇	—	2	1	no	—
16	#500×C₆₇	C₂²	1	2	yes	—
17	#500×C₆₇	C₂²	1	2	yes	—
18	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
19	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
20	C₄×SD₁₆×C₆₇	—	2	1	no	—
21	C₄×SD₁₆×C₆₇	—	2	1	no	—
22	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
23	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
24	#427×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#107×C₆₇	—	2	1	no	—
26	C₂×#107×C₆₇	C₂²	1	2	yes	—
27	#416×C₆₇	—	2	1	no	—
28	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
29	#367×C₆₇	C₂²	1	4	yes	—
30	#366×C₆₇	C₂²	1	4	yes	—
31	C₄⋊C₁₆×C₆₇	C₂²	1	2	yes	—
32	C₄⋊C₁₆×C₆₇	C₂²	1	2	yes	—
33	#358×C₆₇	C₂²	1	4	yes	—
34	#357×C₆₇	C₂²	1	4	yes	—
35	C₂×#41×C₆₇	—	2	1	no	—
36	C₂²×Q₈×C₆₇	—	4	1	no	—
37	#135×C₆₇	—	2	2	no	—
38	#135×C₆₇	Q₈	1	4	yes	complemented
39	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
40	C₂×SD₁₆×C₆₇	—	2	1	no	—
41	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
43	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
44	C₄⋊Q₈×C₆₇	—	2	2	no	—
45	C₄⋊Q₈×C₆₇	—	2	2	no	—
46	C₄⋊Q₈×C₆₇	—	4	1	no	—
47	C₄⋊Q₈×C₆₇	—	4	1	no	—
48	C₄×Q₈×C₆₇	—	2	1	no	—
49	C₄×Q₈×C₆₇	—	2	1	no	—
50	C₄×D₄×C₆₇	—	2	1	no	—
51	C₄×D₄×C₆₇	—	2	1	no	—
52	C₄×D₄×C₆₇	—	4	1	no	—
53	C₄×D₄×C₆₇	—	4	1	no	—
54	#117×C₆₇	—	2	1	no	—
55	#117×C₆₇	—	4	1	no	—
56	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₆₇	—	4	1	no	—
58	C₂×C₄²×C₆₇	—	4	1	no	—
59	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
60	M₃₂×C₆₇	—	2	4	no	—
61	C₂×C₁₆×C₆₇	C₂³	1	4	yes	—
62	#107×C₆₇	—	2	2	no	—
63	#107×C₆₇	—	2	2	no	—
64	#107×C₆₇	—	2	2	no	—
65	#107×C₆₇	C₂³	1	4	yes	—
66	#107×C₆₇	C₂³	1	1	yes	characteristic
67	#107×C₆₇	C₂³	1	1	yes	characteristic
68	#106×C₆₇	—	2	1	no	—
69	#103×C₆₇	—	2	1	no	—
70	#103×C₆₇	—	2	1	no	—
71	#102×C₆₇	—	2	1	no	—
72	#102×C₆₇	—	2	1	no	—
73	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
74	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
75	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
76	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
77	#41×C₆₇	—	2	4	no	—
78	#41×C₆₇	—	4	2	no	—
79	C₂×Q₈×C₆₇	—	2	1	no	—
80	C₂×Q₈×C₆₇	—	4	2	no	—
81	C₂×Q₈×C₆₇	—	4	2	no	—
82	C₂×Q₈×C₆₇	—	8	4	no	—
83	C₂×D₄×C₆₇	—	2	1	no	—
84	C₂×D₄×C₆₇	—	4	1	no	—
85	C₂²×C₄×C₆₇	—	4	1	no	—
86	C₂²×C₄×C₆₇	—	4	2	no	—
87	C₂²×C₄×C₆₇	—	4	1	no	—
88	C₂²×C₄×C₆₇	—	4	1	no	—
89	C₂²×C₄×C₆₇	D₈	1	1	yes	characteristic
90	C₂²×C₄×C₆₇	D₈	1	1	yes	characteristic
91	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
92	Q₁₆×C₆₇	—	2	1	no	—
93	Q₁₆×C₆₇	C₂×Q₈	1	2	yes	complemented
94	SD₁₆×C₆₇	—	2	4	no	—
95	D₈×C₆₇	—	2	1	no	—
96	D₈×C₆₇	C₂×Q₈	1	2	yes	complemented
97	C₂×C₈×C₆₇	—	2	2	no	—
98	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
99	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
100	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
101	C₂×C₈×C₆₇	C₂×Q₈	1	2	yes	—
102	C₂×C₈×C₆₇	#41	1	2	yes	—
103	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
104	C₄⋊C₄×C₆₇	—	2	1	no	—
105	C₄⋊C₄×C₆₇	—	2	1	no	—
106	C₄⋊C₄×C₆₇	—	2	4	no	—
107	C₄⋊C₄×C₆₇	—	4	2	no	—
108	C₄⋊C₄×C₆₇	—	4	2	no	—
109	C₄⋊C₄×C₆₇	—	4	2	no	—
110	C₄⋊C₄×C₆₇	—	4	1	no	—
111	C₄⋊C₄×C₆₇	—	4	1	no	—
112	C₂²⋊C₄×C₆₇	—	4	1	no	—
113	C₂²⋊C₄×C₆₇	—	4	1	no	—
114	C₂²⋊C₄×C₆₇	—	4	1	no	—
115	C₄²×C₆₇	—	4	1	no	—
116	C₄²×C₆₇	—	4	1	no	—
117	C₄²×C₆₇	—	4	1	no	—
118	C₄²×C₆₇	D₈	1	1	yes	characteristic
119	C₄²×C₆₇	D₈	1	1	yes	characteristic
120	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
122	C₁₆×C₆₇	—	2	4	no	—
123	C₂³×C₆₇	—	4	1	no	—
124	C₂³×C₆₇	C₂×D₈	1	1	yes	characteristic
125	Q₈×C₆₇	—	2	2	no	—
126	Q₈×C₆₇	—	4	1	no	—
127	Q₈×C₆₇	—	8	4	no	—
128	Q₈×C₆₇	—	8	4	no	—
129	D₄×C₆₇	—	2	2	no	—
130	D₄×C₆₇	—	4	4	no	—
131	D₄×C₆₇	—	4	1	no	—
132	C₂×C₄×C₆₇	—	2	2	no	—
133	C₂×C₄×C₆₇	—	2	2	no	—
134	C₂×C₄×C₆₇	—	4	1	no	—
135	C₂×C₄×C₆₇	—	4	4	no	—
136	C₂×C₄×C₆₇	—	4	1	no	—
137	C₂×C₄×C₆₇	—	4	1	no	—
138	C₂×C₄×C₆₇	—	4	4	no	—
139	C₂×C₄×C₆₇	—	8	4	no	—
140	C₂×C₄×C₆₇	—	8	2	no	—
141	C₂×C₄×C₆₇	—	8	2	no	—
142	C₂×C₄×C₆₇	C₂²⋊Q₈	1	2	yes	—
143	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
144	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
145	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
146	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
147	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
148	C₂×C₄×C₆₇	#137	1	2	yes	—
149	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
150	C₈×C₆₇	—	2	1	no	—
151	C₈×C₆₇	—	2	1	no	—
152	C₈×C₆₇	C₂²⋊Q₈	1	2	yes	—
153	C₈×C₆₇	C₂²×Q₈	1	1	yes	characteristic
154	C₈×C₆₇	C₂×#41	1	1	yes	characteristic
155	C₂²×C₆₇	—	2	1	no	—
156	C₂²×C₆₇	—	2	1	no	—
157	C₂²×C₆₇	—	4	2	no	—
158	C₂²×C₆₇	—	8	1	no	—
159	C₂²×C₆₇	—	8	1	no	—
160	C₂²×C₆₇	#474	1	2	yes	—
161	C₂²×C₆₇	C₂²×D₈	1	1	yes	characteristic
162	C₄×C₆₇	—	2	1	no	—
163	C₄×C₆₇	—	2	1	no	—
164	C₄×C₆₇	—	4	2	no	—
165	C₄×C₆₇	—	8	1	no	—
166	C₄×C₆₇	—	8	4	no	—
167	C₄×C₆₇	—	8	1	no	—
168	C₄×C₆₇	#474	1	2	yes	—
169	C₄×C₆₇	#509	1	2	yes	—
170	C₄×C₆₇	#510	1	2	yes	—
171	C₄×C₆₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
172	C₄×C₆₇	C₂×#137	1	1	yes	characteristic
173	#33629	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂×C₆₇	—	2	2	no	—
175	C₂×C₆₇	—	8	2	no	—
176	C₂×C₆₇	C₂×#474	1	1	yes	characteristic
177	C₂×C₆₇	C₂×#509	1	1	yes	characteristic
178	C₂×C₆₇	C₂×#510	1	1	yes	characteristic
179	C₂×#500	C₂×C₆₇	1	1	yes	characteristic, complemented
180	C₄×#135	C₂×C₆₇	1	1	yes	characteristic
181	#2227	C₂×C₆₇	1	2	yes	complemented
182	#2226	C₂×C₆₇	1	2	yes	complemented
183	#2225	C₂×C₆₇	1	2	yes	complemented
184	#2224	C₂×C₆₇	1	2	yes	complemented
185	#2159	C₂×C₆₇	1	2	yes	complemented
186	#2150	C₂×C₆₇	1	1	yes	characteristic, complemented
187	#2139	C₂×C₆₇	1	2	yes	—
188	C₆₇	#33629	1	1	yes	characteristic, direct product factor, Sylow
189	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
190	C₂×C₄⋊Q₈	—	2	1	no	—
191	C₄×#41	—	2	1	no	—
192	C₂×M₃₂	C₂²×C₆₇	1	2	yes	—
193	#500	—	2	1	no	—
194	#500	—	2	1	no	—
195	#500	C₂²×C₆₇	1	2	yes	—
196	#500	C₂²×C₆₇	1	2	yes	—
197	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
198	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
199	C₄×SD₁₆	—	2	1	no	—
200	C₄×SD₁₆	—	2	1	no	—
201	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
202	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
203	#427	C₂²×C₆₇	1	1	yes	characteristic
204	C₂×#107	—	2	1	no	—
205	C₂×#107	C₂²×C₆₇	1	2	yes	—
206	#416	—	2	1	no	—
207	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
208	#367	C₂²×C₆₇	1	4	yes	—
209	#366	C₂²×C₆₇	1	4	yes	—
210	C₄⋊C₁₆	C₂²×C₆₇	1	2	yes	—
211	C₄⋊C₁₆	C₂²×C₆₇	1	2	yes	—
212	#358	C₂²×C₆₇	1	4	yes	—
213	#357	C₂²×C₆₇	1	4	yes	—
214	C₂×#41	—	2	1	no	—
215	C₂²×Q₈	—	4	1	no	—
216	#135	—	2	2	no	—
217	#135	Q₈×C₆₇	1	4	yes	complemented
218	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
219	C₂×SD₁₆	—	2	1	no	—
220	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
221	C₂²×C₈	D₄×C₆₇	1	1	yes	characteristic
222	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
223	C₄⋊Q₈	—	2	2	no	—
224	C₄⋊Q₈	—	2	2	no	—
225	C₄⋊Q₈	—	4	1	no	—
226	C₄⋊Q₈	—	4	1	no	—
227	C₄×Q₈	—	2	1	no	—
228	C₄×Q₈	—	2	1	no	—
229	C₄×D₄	—	2	1	no	—
230	C₄×D₄	—	2	1	no	—
231	C₄×D₄	—	4	1	no	—
232	C₄×D₄	—	4	1	no	—
233	#117	—	2	1	no	—
234	#117	—	4	1	no	—
235	C₂×C₄⋊C₄	—	2	2	no	—
236	C₂×C₄⋊C₄	—	4	1	no	—
237	C₂×C₄²	—	4	1	no	—
238	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
239	M₃₂	—	2	4	no	—
240	C₂×C₁₆	C₂³×C₆₇	1	4	yes	—
241	#107	—	2	2	no	—
242	#107	—	2	2	no	—
243	#107	—	2	2	no	—
244	#107	C₂³×C₆₇	1	4	yes	—
245	#107	C₂³×C₆₇	1	1	yes	characteristic
246	#107	C₂³×C₆₇	1	1	yes	characteristic
247	#106	—	2	1	no	—
248	#103	—	2	1	no	—
249	#103	—	2	1	no	—
250	#102	—	2	1	no	—
251	#102	—	2	1	no	—
252	C₄×C₈	D₄×C₆₇	1	1	yes	characteristic
253	C₄×C₈	D₄×C₆₇	1	1	yes	characteristic
254	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
255	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
256	#41	—	2	4	no	—
257	#41	—	4	2	no	—
258	C₂×Q₈	—	2	1	no	—
259	C₂×Q₈	—	4	2	no	—
260	C₂×Q₈	—	4	2	no	—
261	C₂×Q₈	—	8	4	no	—
262	C₂×D₄	—	2	1	no	—
263	C₂×D₄	—	4	1	no	—
264	C₂²×C₄	—	4	1	no	—
265	C₂²×C₄	—	4	2	no	—
266	C₂²×C₄	—	4	1	no	—
267	C₂²×C₄	—	4	1	no	—
268	C₂²×C₄	D₈×C₆₇	1	1	yes	characteristic
269	C₂²×C₄	D₈×C₆₇	1	1	yes	characteristic
270	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
271	Q₁₆	—	2	1	no	—
272	Q₁₆	C₂×Q₈×C₆₇	1	2	yes	complemented
273	SD₁₆	—	2	4	no	—
274	D₈	—	2	1	no	—
275	D₈	C₂×Q₈×C₆₇	1	2	yes	complemented
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
278	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
279	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
280	C₂×C₈	C₂×Q₈×C₆₇	1	2	yes	—
281	C₂×C₈	#41×C₆₇	1	2	yes	—
282	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
283	C₄⋊C₄	—	2	1	no	—
284	C₄⋊C₄	—	2	1	no	—
285	C₄⋊C₄	—	2	4	no	—
286	C₄⋊C₄	—	4	2	no	—
287	C₄⋊C₄	—	4	2	no	—
288	C₄⋊C₄	—	4	2	no	—
289	C₄⋊C₄	—	4	1	no	—
290	C₄⋊C₄	—	4	1	no	—
291	C₂²⋊C₄	—	4	1	no	—
292	C₂²⋊C₄	—	4	1	no	—
293	C₂²⋊C₄	—	4	1	no	—
294	C₄²	—	4	1	no	—
295	C₄²	—	4	1	no	—
296	C₄²	—	4	1	no	—
297	C₄²	D₈×C₆₇	1	1	yes	characteristic
298	C₄²	D₈×C₆₇	1	1	yes	characteristic
299	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
300	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
301	C₁₆	—	2	4	no	—
302	C₂³	—	4	1	no	—
303	C₂³	C₂×D₈×C₆₇	1	1	yes	characteristic
304	Q₈	—	2	2	no	—
305	Q₈	—	4	1	no	—
306	Q₈	—	8	4	no	—
307	Q₈	—	8	4	no	—
308	D₄	—	2	2	no	—
309	D₄	—	4	4	no	—
310	D₄	—	4	1	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	4	1	no	—
314	C₂×C₄	—	4	4	no	—
315	C₂×C₄	—	4	1	no	—
316	C₂×C₄	—	4	1	no	—
317	C₂×C₄	—	4	4	no	—
318	C₂×C₄	—	8	4	no	—
319	C₂×C₄	—	8	2	no	—
320	C₂×C₄	—	8	2	no	—
321	C₂×C₄	C₂²⋊Q₈×C₆₇	1	2	yes	—
322	C₂×C₄	C₂×D₈×C₆₇	1	1	yes	characteristic
323	C₂×C₄	C₂×D₈×C₆₇	1	1	yes	characteristic
324	C₂×C₄	C₂×D₈×C₆₇	1	1	yes	characteristic
325	C₂×C₄	C₂×D₈×C₆₇	1	1	yes	characteristic
326	C₂×C₄	C₂×D₈×C₆₇	1	1	yes	characteristic
327	C₂×C₄	#137×C₆₇	1	2	yes	—
328	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
329	C₈	—	2	1	no	—
330	C₈	—	2	1	no	—
331	C₈	C₂²⋊Q₈×C₆₇	1	2	yes	—
332	C₈	C₂²×Q₈×C₆₇	1	1	yes	characteristic
333	C₈	C₂×#41×C₆₇	1	1	yes	characteristic
334	C₂²	—	2	1	no	—
335	C₂²	—	2	1	no	—
336	C₂²	—	4	2	no	—
337	C₂²	—	8	1	no	—
338	C₂²	—	8	1	no	—
339	C₂²	#474×C₆₇	1	2	yes	—
340	C₂²	C₂²×D₈×C₆₇	1	1	yes	characteristic
341	C₄	—	2	1	no	—
342	C₄	—	2	1	no	—
343	C₄	—	4	2	no	—
344	C₄	—	8	4	no	—
345	C₄	—	8	1	no	—
346	C₄	—	8	1	no	—
347	C₄	#474×C₆₇	1	2	yes	—
348	C₄	#509×C₆₇	1	2	yes	—
349	C₄	#510×C₆₇	1	2	yes	—
350	C₄	C₂×C₂²⋊Q₈×C₆₇	1	1	yes	characteristic
351	C₄	C₂×#137×C₆₇	1	1	yes	characteristic
352	C₂	—	2	2	no	—
353	C₂	—	8	2	no	—
354	C₂	C₂×#474×C₆₇	1	1	yes	characteristic
355	C₂	C₂×#509×C₆₇	1	1	yes	characteristic
356	C₂	C₂×#510×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₆₇
prime radical	C₂×#135×C₆₇	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂×C₄²×C₆₇ ◁ C₂×C₄×C₈×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#500×C₆₇	C₂	semidirect
3. C₆₇×#2227	C₂	semidirect
4. C₆₇×#2226	C₂	semidirect
5. C₆₇×#2225	C₂	semidirect
6. C₆₇×#2224	C₂	semidirect
7. C₆₇×#2159	C₂	semidirect
8. C₆₇×#2150	C₂	semidirect
38. #135×C₆₇	Q₈	semidirect
93. Q₁₆×C₆₇	C₂×Q₈	semidirect
96. D₈×C₆₇	C₂×Q₈	semidirect
173. #33629	C₆₇	direct (N × H)
179. C₂×#500	C₂×C₆₇	semidirect
181. #2227	C₂×C₆₇	semidirect
182. #2226	C₂×C₆₇	semidirect
183. #2225	C₂×C₆₇	semidirect
184. #2224	C₂×C₆₇	semidirect
185. #2159	C₂×C₆₇	semidirect
186. #2150	C₂×C₆₇	semidirect
188. C₆₇	#33629	direct (N × H)
217. #135	Q₈×C₆₇	semidirect
272. Q₁₆	C₂×Q₈×C₆₇	semidirect
275. D₈	C₂×Q₈×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#500×C₆₇	2
C₄×#135×C₆₇	2
C₆₇×#2227	2
C₆₇×#2226	2
C₆₇×#2225	2
C₆₇×#2224	2
C₆₇×#2159	2
C₆₇×#2150	2
C₆₇×#2139	2
#33629	67

Subgroups — C67×#33629 #30712880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#33629 #30712880