Subgroups — C₄×#399×C₆₇ #30693113

Order 17152.

1966 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×#399×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊C₄×C₆₇	C₂	1	3	yes	maximal, complemented
3	C₂×C₄×C₂²⋊C₄×C₆₇	C₂	1	3	yes	maximal
4	C₆₇×#1445	C₂	1	3	yes	maximal, complemented
5	C₆₇×#1444	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#1439	C₂	1	3	yes	maximal
7	C₄×#95×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊C₄×C₆₇	C₂²	1	3	yes	—
10	C₂²×C₄⋊C₄×C₆₇	C₂²	1	3	yes	—
11	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	3	yes	—
12	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	3	yes	—
13	C₂²×C₄²×C₆₇	C₂²	1	3	yes	—
14	C₂²×C₄²×C₆₇	C₂²	1	3	yes	—
15	#399×C₆₇	C₄	1	8	yes	direct product factor
16	C₄×C₄⋊C₄×C₆₇	—	2	12	no	—
17	C₄×C₂²⋊C₄×C₆₇	—	2	12	no	—
18	C₂×#95×C₆₇	C₂²	1	3	yes	—
19	C₂×#95×C₆₇	C₂²	1	3	yes	—
20	C₂×#95×C₆₇	C₂²	1	6	yes	—
21	C₂×#95×C₆₇	C₂²	1	3	yes	—
22	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
23	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
24	C₂³×C₄×C₆₇	—	2	6	no	—
25	C₂³×C₄×C₆₇	—	2	6	no	—
26	C₂³×C₄×C₆₇	Q₈	1	4	yes	—
27	C₂³×C₄×C₆₇	C₂³	1	3	yes	—
28	C₂³×C₄×C₆₇	C₂³	1	3	yes	—
29	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
30	C₂³×C₄×C₆₇	C₂³	1	3	yes	—
31	C₂³×C₄×C₆₇	C₂³	1	3	yes	—
32	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
33	C₂×C₄⋊C₄×C₆₇	—	2	6	no	—
34	C₂×C₄⋊C₄×C₆₇	—	2	6	no	—
35	C₂×C₄⋊C₄×C₆₇	—	2	12	no	—
36	C₂×C₄⋊C₄×C₆₇	—	2	6	no	—
37	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	12	yes	complemented
38	C₂×C₂²⋊C₄×C₆₇	—	2	6	no	—
39	C₂×C₂²⋊C₄×C₆₇	—	2	6	no	—
40	C₂×C₂²⋊C₄×C₆₇	—	2	6	no	—
41	C₂×C₂²⋊C₄×C₆₇	—	2	6	no	—
42	C₂×C₂²⋊C₄×C₆₇	—	2	6	no	—
43	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	12	yes	—
44	C₂×C₄²×C₆₇	—	2	12	no	—
45	C₂×C₄²×C₆₇	—	2	6	no	—
46	C₂×C₄²×C₆₇	—	2	12	no	—
47	C₂×C₄²×C₆₇	D₄	1	12	yes	—
48	#95×C₆₇	—	2	6	no	—
49	#95×C₆₇	—	2	6	no	—
50	#95×C₆₇	—	2	12	no	—
51	#95×C₆₇	—	2	6	no	—
52	#95×C₆₇	C₂×C₄	1	4	yes	complemented
53	C₂⁴×C₆₇	—	2	3	no	—
54	C₂⁴×C₆₇	—	2	3	no	—
55	C₂⁴×C₆₇	—	2	3	no	—
56	C₂⁴×C₆₇	—	2	3	no	—
57	C₂⁴×C₆₇	C₂²×C₄	1	2	yes	—
58	C₂⁴×C₆₇	C₂×Q₈	1	2	yes	—
59	C₂⁴×C₆₇	#41	1	2	yes	—
60	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
61	C₂²×C₄×C₆₇	—	2	6	no	—
62	C₂²×C₄×C₆₇	—	2	6	no	—
63	C₂²×C₄×C₆₇	—	2	3	no	—
64	C₂²×C₄×C₆₇	—	2	3	no	—
65	C₂²×C₄×C₆₇	—	2	6	no	—
66	C₂²×C₄×C₆₇	—	2	6	no	—
67	C₂²×C₄×C₆₇	—	2	3	no	—
68	C₂²×C₄×C₆₇	—	2	6	no	—
69	C₂²×C₄×C₆₇	—	2	3	no	—
70	C₂²×C₄×C₆₇	—	2	3	no	—
71	C₂²×C₄×C₆₇	—	2	3	no	—
72	C₂²×C₄×C₆₇	—	2	3	no	—
73	C₂²×C₄×C₆₇	—	2	6	no	—
74	C₂²×C₄×C₆₇	—	2	6	no	—
75	C₂²×C₄×C₆₇	—	2	3	no	—
76	C₂²×C₄×C₆₇	—	2	6	no	—
77	C₂²×C₄×C₆₇	—	2	24	no	—
78	C₂²×C₄×C₆₇	—	4	12	no	—
79	C₂²×C₄×C₆₇	—	4	4	no	—
80	C₂²×C₄×C₆₇	C₂²×C₄	1	6	yes	—
81	C₂²×C₄×C₆₇	C₂²×C₄	1	6	yes	—
82	C₂²×C₄×C₆₇	C₂×D₄	1	6	yes	—
83	C₂²×C₄×C₆₇	C₂×D₄	1	6	yes	—
84	C₂²×C₄×C₆₇	C₂×D₄	1	6	yes	—
85	C₂²×C₄×C₆₇	C₂×Q₈	1	2	yes	—
86	C₂²×C₄×C₆₇	C₂×Q₈	1	2	yes	—
87	C₂²×C₄×C₆₇	#41	1	6	yes	—
88	C₂²×C₄×C₆₇	#41	1	6	yes	—
89	C₂²×C₄×C₆₇	#41	1	6	yes	—
90	C₄⋊C₄×C₆₇	—	2	24	no	—
91	C₄⋊C₄×C₆₇	—	2	24	no	—
92	C₂²⋊C₄×C₆₇	—	2	24	no	—
93	C₂²⋊C₄×C₆₇	—	2	24	no	—
94	C₄²×C₆₇	—	2	24	no	—
95	C₄²×C₆₇	—	4	12	no	—
96	C₂³×C₆₇	—	2	6	no	—
97	C₂³×C₆₇	—	2	6	no	—
98	C₂³×C₆₇	—	2	6	no	—
99	C₂³×C₆₇	—	2	6	no	—
100	C₂³×C₆₇	—	2	6	no	—
101	C₂³×C₆₇	—	2	6	no	—
102	C₂³×C₆₇	—	4	3	no	—
103	C₂³×C₆₇	—	4	3	no	—
104	C₂³×C₆₇	—	4	6	no	—
105	C₂³×C₆₇	—	4	1	no	—
106	C₂³×C₆₇	—	4	3	no	—
107	C₂³×C₆₇	C₄×Q₈	1	4	yes	—
108	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
109	C₂³×C₆₇	C₂²×D₄	1	3	yes	—
110	C₂³×C₆₇	C₂²×Q₈	1	1	yes	characteristic
111	C₂³×C₆₇	C₂×#41	1	3	yes	—
112	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
113	C₂³×C₆₇	C₂×#41	1	3	yes	—
114	C₂³×C₆₇	C₂×#41	1	3	yes	—
115	C₂×C₄×C₆₇	—	2	12	no	—
116	C₂×C₄×C₆₇	—	2	6	no	—
117	C₂×C₄×C₆₇	—	2	6	no	—
118	C₂×C₄×C₆₇	—	2	12	no	—
119	C₂×C₄×C₆₇	—	2	6	no	—
120	C₂×C₄×C₆₇	—	2	12	no	—
121	C₂×C₄×C₆₇	—	2	6	no	—
122	C₂×C₄×C₆₇	—	2	6	no	—
123	C₂×C₄×C₆₇	—	2	6	no	—
124	C₂×C₄×C₆₇	—	2	6	no	—
125	C₂×C₄×C₆₇	—	2	12	no	—
126	C₂×C₄×C₆₇	—	2	6	no	—
127	C₂×C₄×C₆₇	—	4	3	no	—
128	C₂×C₄×C₆₇	—	4	6	no	—
129	C₂×C₄×C₆₇	—	4	3	no	—
130	C₂×C₄×C₆₇	—	4	6	no	—
131	C₂×C₄×C₆₇	—	4	6	no	—
132	C₂×C₄×C₆₇	—	4	3	no	—
133	C₂×C₄×C₆₇	—	4	3	no	—
134	C₂×C₄×C₆₇	—	4	1	no	—
135	C₂×C₄×C₆₇	—	4	3	no	—
136	C₂×C₄×C₆₇	—	4	6	no	—
137	C₂×C₄×C₆₇	—	4	16	no	—
138	C₂×C₄×C₆₇	C₄×D₄	1	12	yes	—
139	C₂×C₄×C₆₇	C₂²⋊Q₈	1	12	yes	—
140	C₂×C₄×C₆₇	#123	1	12	yes	—
141	C₂×C₄×C₆₇	#127	1	4	yes	—
142	C₂²×C₆₇	—	2	12	no	—
143	C₂²×C₆₇	—	4	2	no	—
144	C₂²×C₆₇	—	4	2	no	—
145	C₂²×C₆₇	—	4	6	no	—
146	C₂²×C₆₇	—	4	6	no	—
147	C₂²×C₆₇	—	4	2	no	—
148	C₂²×C₆₇	—	4	6	no	—
149	C₂²×C₆₇	C₂×C₄×D₄	1	3	yes	—
150	C₂²×C₆₇	C₂×C₄×Q₈	1	1	yes	characteristic
151	C₂²×C₆₇	C₄×#41	1	3	yes	—
152	C₂²×C₆₇	C₂×C₂²⋊Q₈	1	3	yes	—
153	C₂²×C₆₇	C₂×#123	1	3	yes	—
154	C₂²×C₆₇	#525	1	3	yes	—
155	C₂²×C₆₇	#525	1	3	yes	—
156	C₂²×C₆₇	#529	1	3	yes	—
157	C₂²×C₆₇	#529	1	6	yes	—
158	C₂²×C₆₇	C₂×#127	1	1	yes	characteristic
159	C₂²×C₆₇	#532	1	3	yes	—
160	C₂²×C₆₇	#533	1	3	yes	—
161	C₄×C₆₇	—	2	12	no	—
162	C₄×C₆₇	—	4	6	no	—
163	C₄×C₆₇	—	4	2	no	—
164	C₄×C₆₇	—	4	6	no	—
165	C₄×C₆₇	—	4	6	no	—
166	C₄×C₆₇	#399	1	8	yes	direct product factor
167	C₄×#399	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂×C₆₇	—	4	4	no	—
169	C₂×C₆₇	C₄×#123	1	3	yes	—
170	C₂×C₆₇	C₄×C₂²⋊Q₈	1	3	yes	—
171	C₂×C₆₇	C₄×#127	1	1	yes	characteristic
172	C₂×C₆₇	C₂×#399	1	1	yes	characteristic
173	C₂×C₆₇	#2395	1	3	yes	—
174	C₂×C₆₇	#2396	1	3	yes	—
175	C₂×C₆₇	#2397	1	1	yes	characteristic
176	C₂×#399	C₂×C₆₇	1	1	yes	characteristic
177	C₂×C₄×C₄⋊C₄	C₂×C₆₇	1	3	yes	complemented
178	C₂×C₄×C₂²⋊C₄	C₂×C₆₇	1	3	yes	—
179	#1445	C₂×C₆₇	1	3	yes	complemented
180	#1444	C₂×C₆₇	1	1	yes	characteristic, complemented
181	#1439	C₂×C₆₇	1	3	yes	—
182	C₄×#95	C₂×C₆₇	1	1	yes	characteristic, complemented
183	C₆₇	C₄×#399	1	1	yes	characteristic, direct product factor, Sylow
184	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
185	C₂²×C₄⋊C₄	C₂²×C₆₇	1	3	yes	—
186	C₂²×C₄⋊C₄	C₂²×C₆₇	1	3	yes	—
187	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	3	yes	—
188	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	3	yes	—
189	C₂²×C₄²	C₂²×C₆₇	1	3	yes	—
190	C₂²×C₄²	C₂²×C₆₇	1	3	yes	—
191	#399	C₄×C₆₇	1	8	yes	direct product factor
192	C₄×C₄⋊C₄	—	2	12	no	—
193	C₄×C₂²⋊C₄	—	2	12	no	—
194	C₂×#95	C₂²×C₆₇	1	3	yes	—
195	C₂×#95	C₂²×C₆₇	1	6	yes	—
196	C₂×#95	C₂²×C₆₇	1	3	yes	—
197	C₂×#95	C₂²×C₆₇	1	3	yes	—
198	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
199	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
200	C₂³×C₄	—	2	6	no	—
201	C₂³×C₄	—	2	6	no	—
202	C₂³×C₄	Q₈×C₆₇	1	4	yes	—
203	C₂³×C₄	C₂³×C₆₇	1	3	yes	—
204	C₂³×C₄	C₂³×C₆₇	1	3	yes	—
205	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
206	C₂³×C₄	C₂³×C₆₇	1	3	yes	—
207	C₂³×C₄	C₂³×C₆₇	1	3	yes	—
208	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
209	C₂×C₄⋊C₄	—	2	6	no	—
210	C₂×C₄⋊C₄	—	2	6	no	—
211	C₂×C₄⋊C₄	—	2	12	no	—
212	C₂×C₄⋊C₄	—	2	6	no	—
213	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	12	yes	complemented
214	C₂×C₂²⋊C₄	—	2	6	no	—
215	C₂×C₂²⋊C₄	—	2	6	no	—
216	C₂×C₂²⋊C₄	—	2	6	no	—
217	C₂×C₂²⋊C₄	—	2	6	no	—
218	C₂×C₂²⋊C₄	—	2	6	no	—
219	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	12	yes	—
220	C₂×C₄²	—	2	12	no	—
221	C₂×C₄²	—	2	6	no	—
222	C₂×C₄²	—	2	12	no	—
223	C₂×C₄²	D₄×C₆₇	1	12	yes	—
224	#95	—	2	6	no	—
225	#95	—	2	6	no	—
226	#95	—	2	12	no	—
227	#95	—	2	6	no	—
228	#95	C₂×C₄×C₆₇	1	4	yes	complemented
229	C₂⁴	—	2	3	no	—
230	C₂⁴	—	2	3	no	—
231	C₂⁴	—	2	3	no	—
232	C₂⁴	—	2	3	no	—
233	C₂⁴	C₂²×C₄×C₆₇	1	2	yes	—
234	C₂⁴	C₂×Q₈×C₆₇	1	2	yes	—
235	C₂⁴	#41×C₆₇	1	2	yes	—
236	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
237	C₂²×C₄	—	2	6	no	—
238	C₂²×C₄	—	2	6	no	—
239	C₂²×C₄	—	2	3	no	—
240	C₂²×C₄	—	2	3	no	—
241	C₂²×C₄	—	2	3	no	—
242	C₂²×C₄	—	2	6	no	—
243	C₂²×C₄	—	2	6	no	—
244	C₂²×C₄	—	2	6	no	—
245	C₂²×C₄	—	2	6	no	—
246	C₂²×C₄	—	2	3	no	—
247	C₂²×C₄	—	2	3	no	—
248	C₂²×C₄	—	2	3	no	—
249	C₂²×C₄	—	2	3	no	—
250	C₂²×C₄	—	2	6	no	—
251	C₂²×C₄	—	2	6	no	—
252	C₂²×C₄	—	2	3	no	—
253	C₂²×C₄	—	2	24	no	—
254	C₂²×C₄	—	4	12	no	—
255	C₂²×C₄	—	4	4	no	—
256	C₂²×C₄	C₂²×C₄×C₆₇	1	6	yes	—
257	C₂²×C₄	C₂²×C₄×C₆₇	1	6	yes	—
258	C₂²×C₄	C₂×D₄×C₆₇	1	6	yes	—
259	C₂²×C₄	C₂×D₄×C₆₇	1	6	yes	—
260	C₂²×C₄	C₂×D₄×C₆₇	1	6	yes	—
261	C₂²×C₄	C₂×Q₈×C₆₇	1	2	yes	—
262	C₂²×C₄	C₂×Q₈×C₆₇	1	2	yes	—
263	C₂²×C₄	#41×C₆₇	1	6	yes	—
264	C₂²×C₄	#41×C₆₇	1	6	yes	—
265	C₂²×C₄	#41×C₆₇	1	6	yes	—
266	C₄⋊C₄	—	2	24	no	—
267	C₄⋊C₄	—	2	24	no	—
268	C₂²⋊C₄	—	2	24	no	—
269	C₂²⋊C₄	—	2	24	no	—
270	C₄²	—	2	24	no	—
271	C₄²	—	4	12	no	—
272	C₂³	—	2	6	no	—
273	C₂³	—	2	6	no	—
274	C₂³	—	2	6	no	—
275	C₂³	—	2	6	no	—
276	C₂³	—	2	6	no	—
277	C₂³	—	2	6	no	—
278	C₂³	—	4	3	no	—
279	C₂³	—	4	3	no	—
280	C₂³	—	4	6	no	—
281	C₂³	—	4	1	no	—
282	C₂³	—	4	3	no	—
283	C₂³	C₄×Q₈×C₆₇	1	4	yes	—
284	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
285	C₂³	C₂²×D₄×C₆₇	1	3	yes	—
286	C₂³	C₂²×Q₈×C₆₇	1	1	yes	characteristic
287	C₂³	C₂×#41×C₆₇	1	3	yes	—
288	C₂³	C₂×#41×C₆₇	1	1	yes	characteristic
289	C₂³	C₂×#41×C₆₇	1	3	yes	—
290	C₂³	C₂×#41×C₆₇	1	3	yes	—
291	C₂×C₄	—	2	12	no	—
292	C₂×C₄	—	2	6	no	—
293	C₂×C₄	—	2	6	no	—
294	C₂×C₄	—	2	12	no	—
295	C₂×C₄	—	2	6	no	—
296	C₂×C₄	—	2	12	no	—
297	C₂×C₄	—	2	6	no	—
298	C₂×C₄	—	2	6	no	—
299	C₂×C₄	—	2	6	no	—
300	C₂×C₄	—	2	6	no	—
301	C₂×C₄	—	2	12	no	—
302	C₂×C₄	—	2	6	no	—
303	C₂×C₄	—	4	3	no	—
304	C₂×C₄	—	4	3	no	—
305	C₂×C₄	—	4	6	no	—
306	C₂×C₄	—	4	6	no	—
307	C₂×C₄	—	4	6	no	—
308	C₂×C₄	—	4	3	no	—
309	C₂×C₄	—	4	3	no	—
310	C₂×C₄	—	4	1	no	—
311	C₂×C₄	—	4	3	no	—
312	C₂×C₄	—	4	6	no	—
313	C₂×C₄	—	4	16	no	—
314	C₂×C₄	C₄×D₄×C₆₇	1	12	yes	—
315	C₂×C₄	C₂²⋊Q₈×C₆₇	1	12	yes	—
316	C₂×C₄	#123×C₆₇	1	12	yes	—
317	C₂×C₄	#127×C₆₇	1	4	yes	—
318	C₂²	—	2	12	no	—
319	C₂²	—	4	6	no	—
320	C₂²	—	4	2	no	—
321	C₂²	—	4	2	no	—
322	C₂²	—	4	6	no	—
323	C₂²	—	4	6	no	—
324	C₂²	—	4	2	no	—
325	C₂²	C₂×C₄×D₄×C₆₇	1	3	yes	—
326	C₂²	C₂×C₄×Q₈×C₆₇	1	1	yes	characteristic
327	C₂²	C₄×#41×C₆₇	1	3	yes	—
328	C₂²	C₂×C₂²⋊Q₈×C₆₇	1	3	yes	—
329	C₂²	C₂×#123×C₆₇	1	3	yes	—
330	C₂²	#525×C₆₇	1	3	yes	—
331	C₂²	#525×C₆₇	1	3	yes	—
332	C₂²	#529×C₆₇	1	6	yes	—
333	C₂²	#529×C₆₇	1	3	yes	—
334	C₂²	C₂×#127×C₆₇	1	1	yes	characteristic
335	C₂²	#532×C₆₇	1	3	yes	—
336	C₂²	#533×C₆₇	1	3	yes	—
337	C₄	—	2	12	no	—
338	C₄	—	4	6	no	—
339	C₄	—	4	2	no	—
340	C₄	—	4	6	no	—
341	C₄	—	4	6	no	—
342	C₄	#399×C₆₇	1	8	yes	direct product factor
343	C₂	—	4	4	no	—
344	C₂	C₄×#123×C₆₇	1	3	yes	—
345	C₂	C₄×C₂²⋊Q₈×C₆₇	1	3	yes	—
346	C₂	C₄×#127×C₆₇	1	1	yes	characteristic
347	C₂	C₂×#399×C₆₇	1	1	yes	characteristic
348	C₂	C₆₇×#2395	1	3	yes	—
349	C₂	C₆₇×#2396	1	3	yes	—
350	C₂	C₆₇×#2397	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄×C₆₇	C₂³
commutator	C₂³	C₂³×C₄×C₆₇
Frattini, cosocle	C₂⁴	C₂⁴×C₆₇
socle	C₂⁴×C₆₇	C₂⁴
prime radical	C₂⁵×C₆₇	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₄⋊C₄×C₆₇	C₂	semidirect
4. C₆₇×#1445	C₂	semidirect
5. C₆₇×#1444	C₂	semidirect
7. C₄×#95×C₆₇	C₂	semidirect
15. #399×C₆₇	C₄	direct (N × H)
37. C₂×C₄⋊C₄×C₆₇	C₂×C₄	semidirect
52. #95×C₆₇	C₂×C₄	semidirect
166. C₄×C₆₇	#399	direct (N × H)
167. C₄×#399	C₆₇	direct (N × H)
177. C₂×C₄×C₄⋊C₄	C₂×C₆₇	semidirect
179. #1445	C₂×C₆₇	semidirect
180. #1444	C₂×C₆₇	semidirect
182. C₄×#95	C₂×C₆₇	semidirect
183. C₆₇	C₄×#399	direct (N × H)
191. #399	C₄×C₆₇	direct (N × H)
213. C₂×C₄⋊C₄	C₂×C₄×C₆₇	semidirect
228. #95	C₂×C₄×C₆₇	semidirect
342. C₄	#399×C₆₇	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×#399×C₆₇	2
C₂×C₄×C₄⋊C₄×C₆₇	2
C₂×C₄×C₂²⋊C₄×C₆₇	2
C₆₇×#1445	2
C₆₇×#1444	2
C₆₇×#1439	2
C₄×#95×C₆₇	2
C₄×#399	67

Subgroups — C4×#399×C67 #30693113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#399×C₆₇ #30693113