Subgroups — C₆₇×#21789 #30701040

Order 17152.

1374 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#532×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#432×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#431×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#1955	C₂	1	4	yes	maximal, complemented
5	C₆₇×#1954	C₂	1	4	yes	maximal, complemented
6	C₆₇×#1780	C₂	1	4	yes	maximal, complemented
7	C₂²×#41×C₆₇	C₂²	1	2	yes	—
8	#532×C₆₇	—	2	4	no	—
9	#532×C₆₇	—	2	4	no	—
10	C₂×C₄⋊Q₈×C₆₇	C₄	1	1	yes	characteristic
11	C₂×#127×C₆₇	C₄	1	1	yes	characteristic
12	C₂×#124×C₆₇	C₄	1	2	yes	—
13	C₂×#121×C₆₇	C₄	1	2	yes	—
14	C₂×#121×C₆₇	C₄	1	2	yes	—
15	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
17	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
18	#432×C₆₇	—	2	4	no	—
19	#431×C₆₇	—	2	4	no	—
20	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	—
21	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	—
22	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	—
23	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	—
24	C₂×C₂²⋊C₈×C₆₇	C₂²	1	16	yes	—
25	C₂×#97×C₆₇	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	—
27	C₂×#41×C₆₇	—	2	4	no	—
28	C₂×#41×C₆₇	—	2	4	no	—
29	C₂×#41×C₆₇	—	4	8	no	—
30	C₂²×Q₈×C₆₇	C₂×C₄	1	2	yes	—
31	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
32	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
33	C₂²×D₄×C₆₇	C₂×C₄	1	4	yes	—
34	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
38	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
39	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
40	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
41	C₄⋊Q₈×C₆₇	—	2	4	no	—
42	#127×C₆₇	—	2	4	no	—
43	#124×C₆₇	—	2	8	no	—
44	#121×C₆₇	—	2	8	no	—
45	#121×C₆₇	—	2	8	no	—
46	C₄×D₄×C₆₇	—	2	4	no	—
47	C₄×D₄×C₆₇	—	2	4	no	—
48	C₄×D₄×C₆₇	—	2	4	no	—
49	C₄×D₄×C₆₇	—	2	4	no	—
50	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
51	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
52	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	4	yes	—
53	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	4	yes	—
54	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₆₇	D₄	1	4	yes	—
57	C₂×C₄²×C₆₇	D₄	1	4	yes	—
58	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
60	C₄⋊C₈×C₆₇	—	2	4	no	—
61	C₄⋊C₈×C₆₇	—	2	4	no	—
62	C₂²⋊C₈×C₆₇	—	2	4	no	—
63	C₂²⋊C₈×C₆₇	—	2	4	no	—
64	C₂²⋊C₈×C₆₇	—	4	16	no	—
65	#97×C₆₇	—	2	4	no	—
66	C₄×C₈×C₆₇	—	2	4	no	—
67	C₂⁴×C₆₇	C₂²×C₄	1	4	yes	—
68	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
69	#41×C₆₇	—	4	16	no	—
70	#41×C₆₇	—	4	16	no	—
71	C₂×Q₈×C₆₇	—	2	4	no	—
72	C₂×Q₈×C₆₇	—	4	4	no	—
73	C₂×D₄×C₆₇	—	2	8	no	—
74	C₂×D₄×C₆₇	—	2	4	no	—
75	C₂×D₄×C₆₇	—	2	4	no	—
76	C₂×D₄×C₆₇	—	2	4	no	—
77	C₂×D₄×C₆₇	—	2	8	no	—
78	C₂×D₄×C₆₇	—	4	4	no	—
79	C₂×D₄×C₆₇	—	4	4	no	—
80	C₂×D₄×C₆₇	—	4	8	no	—
81	C₂²×C₄×C₆₇	—	2	4	no	—
82	C₂²×C₄×C₆₇	—	2	4	no	—
83	C₂²×C₄×C₆₇	—	2	4	no	—
84	C₂²×C₄×C₆₇	—	2	4	no	—
85	C₂²×C₄×C₆₇	—	2	16	no	—
86	C₂²×C₄×C₆₇	—	4	2	no	—
87	C₂²×C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
88	C₂²×C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
89	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
90	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
98	C₂×C₈×C₆₇	—	2	4	no	—
99	C₂×C₈×C₆₇	—	2	4	no	—
100	C₂×C₈×C₆₇	—	2	8	no	—
101	C₂×C₈×C₆₇	—	2	8	no	—
102	C₄⋊C₄×C₆₇	—	2	4	no	—
103	C₄⋊C₄×C₆₇	—	2	4	no	—
104	C₂²⋊C₄×C₆₇	—	2	8	no	—
105	C₂²⋊C₄×C₆₇	—	2	8	no	—
106	C₄²×C₆₇	C₂²⋊C₄	1	4	yes	—
107	C₄²×C₆₇	C₂²⋊C₄	1	4	yes	—
108	C₄²×C₆₇	C₂×D₄	1	2	yes	—
109	C₄²×C₆₇	C₂×D₄	1	2	yes	—
110	C₄²×C₆₇	C₂×D₄	1	2	yes	—
111	C₄²×C₆₇	C₂×D₄	1	2	yes	—
112	C₂³×C₆₇	—	2	2	no	—
113	C₂³×C₆₇	—	2	2	no	—
114	C₂³×C₆₇	—	2	2	no	—
115	C₂³×C₆₇	—	2	4	no	—
116	C₂³×C₆₇	—	2	8	no	—
117	C₂³×C₆₇	—	2	8	no	—
118	C₂³×C₆₇	—	2	8	no	—
119	C₂³×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
120	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
121	Q₈×C₆₇	—	4	8	no	—
122	D₄×C₆₇	—	4	8	no	—
123	D₄×C₆₇	—	4	8	no	—
124	D₄×C₆₇	—	4	16	no	—
125	D₄×C₆₇	—	4	8	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	—	2	2	no	—
130	C₂×C₄×C₆₇	—	2	4	no	—
131	C₂×C₄×C₆₇	—	2	4	no	—
132	C₂×C₄×C₆₇	—	2	8	no	—
133	C₂×C₄×C₆₇	—	2	4	no	—
134	C₂×C₄×C₆₇	—	2	8	no	—
135	C₂×C₄×C₆₇	—	4	4	no	—
136	C₂×C₄×C₆₇	—	4	8	no	—
137	C₂×C₄×C₆₇	—	4	8	no	—
138	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
139	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
140	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
141	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
142	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
143	C₂×C₄×C₆₇	#131	1	4	yes	—
144	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
145	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
146	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
147	C₈×C₆₇	—	4	4	no	—
148	C₈×C₆₇	—	4	4	no	—
149	C₂²×C₆₇	—	2	2	no	—
150	C₂²×C₆₇	—	2	2	no	—
151	C₂²×C₆₇	—	2	2	no	—
152	C₂²×C₆₇	—	4	4	no	—
153	C₂²×C₆₇	—	4	4	no	—
154	C₂²×C₆₇	—	4	4	no	—
155	C₂²×C₆₇	—	4	4	no	—
156	C₂²×C₆₇	—	4	16	no	—
157	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
158	C₂²×C₆₇	#518	1	2	yes	—
159	C₂²×C₆₇	C₂×#131	1	2	yes	—
160	C₂²×C₆₇	#568	1	2	yes	—
161	C₄×C₆₇	—	2	2	no	—
162	C₄×C₆₇	—	2	2	no	—
163	C₄×C₆₇	—	2	2	no	—
164	C₄×C₆₇	—	2	2	no	—
165	C₄×C₆₇	—	4	4	no	—
166	C₄×C₆₇	#408	1	4	yes	—
167	C₄×C₆₇	#535	1	2	yes	—
168	C₄×C₆₇	#535	1	2	yes	—
169	#21789	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂×C₆₇	—	4	2	no	—
171	C₂×C₆₇	—	8	4	no	—
172	C₂×C₆₇	#2309	1	1	yes	characteristic
173	C₂×C₆₇	C₂×#408	1	1	yes	characteristic
174	C₂×C₆₇	#2879	1	1	yes	characteristic
175	C₂×C₆₇	#2981	1	4	yes	—
176	C₂×#532	C₂×C₆₇	1	1	yes	characteristic
177	C₂×#432	C₂×C₆₇	1	1	yes	characteristic, complemented
178	C₂×#431	C₂×C₆₇	1	1	yes	characteristic, complemented
179	#1955	C₂×C₆₇	1	4	yes	complemented
180	#1954	C₂×C₆₇	1	4	yes	complemented
181	#1780	C₂×C₆₇	1	4	yes	complemented
182	C₆₇	#21789	1	1	yes	characteristic, direct product factor, Sylow
183	C₂²×#41	C₂²×C₆₇	1	2	yes	—
184	#532	—	2	4	no	—
185	#532	—	2	4	no	—
186	C₂×C₄⋊Q₈	C₄×C₆₇	1	1	yes	characteristic
187	C₂×#127	C₄×C₆₇	1	1	yes	characteristic
188	C₂×#124	C₄×C₆₇	1	2	yes	—
189	C₂×#121	C₄×C₆₇	1	2	yes	—
190	C₂×#121	C₄×C₆₇	1	2	yes	—
191	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
192	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
193	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
194	#432	—	2	4	no	—
195	#431	—	2	4	no	—
196	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	—
197	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	—
198	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	—
199	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	—
200	C₂×C₂²⋊C₈	C₂²×C₆₇	1	16	yes	—
201	C₂×#97	C₂²×C₆₇	1	2	yes	—
202	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	—
203	C₂×#41	—	2	4	no	—
204	C₂×#41	—	2	4	no	—
205	C₂×#41	—	4	8	no	—
206	C₂²×Q₈	C₂×C₄×C₆₇	1	2	yes	—
207	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
208	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
209	C₂²×D₄	C₂×C₄×C₆₇	1	4	yes	—
210	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
211	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
212	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
213	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
214	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
215	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
216	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
217	C₄⋊Q₈	—	2	4	no	—
218	#127	—	2	4	no	—
219	#124	—	2	8	no	—
220	#121	—	2	8	no	—
221	#121	—	2	8	no	—
222	C₄×D₄	—	2	4	no	—
223	C₄×D₄	—	2	4	no	—
224	C₄×D₄	—	2	4	no	—
225	C₄×D₄	—	2	4	no	—
226	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
227	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
228	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	4	yes	—
229	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	4	yes	—
230	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
231	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
232	C₂×C₄²	D₄×C₆₇	1	4	yes	—
233	C₂×C₄²	D₄×C₆₇	1	4	yes	—
234	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
235	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
236	C₄⋊C₈	—	2	4	no	—
237	C₄⋊C₈	—	2	4	no	—
238	C₂²⋊C₈	—	2	4	no	—
239	C₂²⋊C₈	—	2	4	no	—
240	C₂²⋊C₈	—	4	16	no	—
241	#97	—	2	4	no	—
242	C₄×C₈	—	2	4	no	—
243	C₂⁴	C₂²×C₄×C₆₇	1	4	yes	—
244	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
245	#41	—	4	16	no	—
246	#41	—	4	16	no	—
247	C₂×Q₈	—	2	4	no	—
248	C₂×Q₈	—	4	4	no	—
249	C₂×D₄	—	2	8	no	—
250	C₂×D₄	—	2	4	no	—
251	C₂×D₄	—	2	4	no	—
252	C₂×D₄	—	2	4	no	—
253	C₂×D₄	—	2	8	no	—
254	C₂×D₄	—	4	4	no	—
255	C₂×D₄	—	4	8	no	—
256	C₂×D₄	—	4	4	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	16	no	—
262	C₂²×C₄	—	4	2	no	—
263	C₂²×C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
264	C₂²×C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
265	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
266	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
267	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
268	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
269	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
270	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
271	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
272	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
273	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
274	C₂×C₈	—	2	4	no	—
275	C₂×C₈	—	2	4	no	—
276	C₂×C₈	—	2	8	no	—
277	C₂×C₈	—	2	8	no	—
278	C₄⋊C₄	—	2	4	no	—
279	C₄⋊C₄	—	2	4	no	—
280	C₂²⋊C₄	—	2	8	no	—
281	C₂²⋊C₄	—	2	8	no	—
282	C₄²	C₂²⋊C₄×C₆₇	1	4	yes	—
283	C₄²	C₂²⋊C₄×C₆₇	1	4	yes	—
284	C₄²	C₂×D₄×C₆₇	1	2	yes	—
285	C₄²	C₂×D₄×C₆₇	1	2	yes	—
286	C₄²	C₂×D₄×C₆₇	1	2	yes	—
287	C₄²	C₂×D₄×C₆₇	1	2	yes	—
288	C₂³	—	2	2	no	—
289	C₂³	—	2	2	no	—
290	C₂³	—	2	2	no	—
291	C₂³	—	2	4	no	—
292	C₂³	—	2	8	no	—
293	C₂³	—	2	8	no	—
294	C₂³	—	2	8	no	—
295	C₂³	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
296	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
297	Q₈	—	4	8	no	—
298	D₄	—	4	8	no	—
299	D₄	—	4	8	no	—
300	D₄	—	4	16	no	—
301	D₄	—	4	8	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	2	8	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	8	no	—
311	C₂×C₄	—	4	4	no	—
312	C₂×C₄	—	4	8	no	—
313	C₂×C₄	—	4	8	no	—
314	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
315	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
316	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
317	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
318	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
319	C₂×C₄	#131×C₆₇	1	4	yes	—
320	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
321	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
322	C₂×C₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
323	C₈	—	4	4	no	—
324	C₈	—	4	4	no	—
325	C₂²	—	2	2	no	—
326	C₂²	—	2	2	no	—
327	C₂²	—	2	2	no	—
328	C₂²	—	4	4	no	—
329	C₂²	—	4	4	no	—
330	C₂²	—	4	4	no	—
331	C₂²	—	4	4	no	—
332	C₂²	—	4	16	no	—
333	C₂²	C₂²×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
334	C₂²	#518×C₆₇	1	2	yes	—
335	C₂²	C₂×#131×C₆₇	1	2	yes	—
336	C₂²	#568×C₆₇	1	2	yes	—
337	C₄	—	2	2	no	—
338	C₄	—	2	2	no	—
339	C₄	—	2	2	no	—
340	C₄	—	2	2	no	—
341	C₄	—	4	4	no	—
342	C₄	#408×C₆₇	1	4	yes	—
343	C₄	#535×C₆₇	1	2	yes	—
344	C₄	#535×C₆₇	1	2	yes	—
345	C₂	—	4	2	no	—
346	C₂	—	8	4	no	—
347	C₂	C₆₇×#2309	1	1	yes	characteristic
348	C₂	C₂×#408×C₆₇	1	1	yes	characteristic
349	C₂	C₆₇×#2879	1	1	yes	characteristic
350	C₂	C₆₇×#2981	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₆₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
socle	C₂³×C₆₇	C₂³×C₄
prime radical	C₂×#532×C₆₇	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#432×C₆₇	C₂	semidirect
3. C₂×#431×C₆₇	C₂	semidirect
4. C₆₇×#1955	C₂	semidirect
5. C₆₇×#1954	C₂	semidirect
6. C₆₇×#1780	C₂	semidirect
169. #21789	C₆₇	direct (N × H)
177. C₂×#432	C₂×C₆₇	semidirect
178. C₂×#431	C₂×C₆₇	semidirect
179. #1955	C₂×C₆₇	semidirect
180. #1954	C₂×C₆₇	semidirect
181. #1780	C₂×C₆₇	semidirect
182. C₆₇	#21789	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×#532×C₆₇	2
C₂×#432×C₆₇	2
C₂×#431×C₆₇	2
C₆₇×#1955	2
C₆₇×#1954	2
C₆₇×#1780	2
#21789	67

Subgroups — C67×#21789 #30701040

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#21789 #30701040