Subgroups — C₂×C₈×C₄⋊C₄×C₆₇ #30699683

Order 17152.

1438 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊C₈×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₈×C₆₇	C₂	1	2	yes	maximal
3	C₂²×C₄×C₈×C₆₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic
5	C₈×C₄⋊C₄×C₆₇	C₂	1	8	yes	maximal, direct product factor
6	C₂×#336×C₆₇	C₂	1	2	yes	maximal
7	C₂³×C₈×C₆₇	C₂²	1	2	yes	—
8	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
9	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₆₇	C₄	1	2	yes	—
11	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
12	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₈×C₆₇	C₄	1	8	yes	complemented
14	C₂×C₄⋊C₈×C₆₇	C₂²	1	4	yes	—
15	C₂×C₄×C₈×C₆₇	—	2	8	no	—
16	C₂×C₄×C₈×C₆₇	C₄	1	8	yes	complemented
17	C₂×C₄×C₈×C₆₇	C₂²	1	8	yes	—
18	C₂×C₄×C₈×C₆₇	C₂²	1	4	yes	—
19	C₄×C₄⋊C₄×C₆₇	C₄	1	4	yes	—
20	C₄×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
21	C₂×#95×C₆₇	C₄	1	2	yes	—
22	#336×C₆₇	C₂²	1	8	yes	—
23	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₆₇	C₂×C₄	1	4	yes	—
25	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
27	C₂²×C₈×C₆₇	—	2	4	no	—
28	C₂²×C₈×C₆₇	—	2	2	no	—
29	C₂²×C₈×C₆₇	—	2	2	no	—
30	C₂²×C₈×C₆₇	—	2	4	no	—
31	C₂²×C₈×C₆₇	C₂×C₄	1	4	yes	—
32	C₂²×C₈×C₆₇	C₂×C₄	1	8	yes	—
33	C₂²×C₈×C₆₇	C₂×C₄	1	4	yes	—
34	C₂²×C₈×C₆₇	D₄	1	4	yes	—
35	C₂²×C₈×C₆₇	Q₈	1	4	yes	—
36	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
37	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
38	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
39	C₂×C₄⋊C₄×C₆₇	C₈	1	16	yes	direct product factor
40	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	8	yes	—
41	C₂×C₄²×C₆₇	—	2	4	no	—
42	C₂×C₄²×C₆₇	—	2	4	no	—
43	C₂×C₄²×C₆₇	C₂×C₄	1	4	yes	—
44	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₆₇	C₂×C₄	1	4	yes	—
46	C₂×C₄²×C₆₇	C₂×C₄	1	4	yes	—
47	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
48	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
49	C₄⋊C₈×C₆₇	C₂×C₄	1	16	yes	complemented
50	C₄×C₈×C₆₇	—	2	16	no	—
51	C₄×C₈×C₆₇	C₂×C₄	1	16	yes	complemented
52	#95×C₆₇	C₂×C₄	1	8	yes	—
53	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
54	C₂²×C₄×C₆₇	—	2	8	no	—
55	C₂²×C₄×C₆₇	—	2	4	no	—
56	C₂²×C₄×C₆₇	—	2	8	no	—
57	C₂²×C₄×C₆₇	C₄²	1	4	yes	—
58	C₂²×C₄×C₆₇	C₄²	1	4	yes	—
59	C₂²×C₄×C₆₇	C₂×C₈	1	16	yes	—
60	C₂²×C₄×C₆₇	C₂×C₈	1	8	yes	—
61	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
62	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
63	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
65	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
66	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
67	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
68	C₂²×C₄×C₆₇	C₂×Q₈	1	2	yes	—
69	C₂²×C₄×C₆₇	#41	1	2	yes	—
70	C₂²×C₄×C₆₇	#41	1	2	yes	—
71	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
72	C₂×C₈×C₆₇	—	2	8	no	—
73	C₂×C₈×C₆₇	—	2	16	no	—
74	C₂×C₈×C₆₇	—	2	4	no	—
75	C₂×C₈×C₆₇	—	2	2	no	—
76	C₂×C₈×C₆₇	—	2	2	no	—
77	C₂×C₈×C₆₇	—	2	4	no	—
78	C₂×C₈×C₆₇	C₄⋊C₄	1	16	yes	direct product factor
79	C₂×C₈×C₆₇	C₂²×C₄	1	8	yes	—
80	C₂×C₈×C₆₇	C₂²×C₄	1	4	yes	—
81	C₂×C₈×C₆₇	C₂²×C₄	1	4	yes	—
82	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	—
83	C₂×C₈×C₆₇	C₂×Q₈	1	4	yes	—
84	C₄⋊C₄×C₆₇	C₂×C₈	1	32	yes	direct product factor
85	C₄²×C₆₇	—	2	8	no	—
86	C₄²×C₆₇	—	2	4	no	—
87	C₄²×C₆₇	—	2	4	no	—
88	C₄²×C₆₇	C₄²	1	8	yes	—
89	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
90	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
91	C₂³×C₆₇	C₂×C₄²	1	2	yes	—
92	C₂³×C₆₇	C₄×D₄	1	2	yes	—
93	C₂³×C₆₇	C₄×Q₈	1	2	yes	—
94	C₂³×C₆₇	C₂²×C₈	1	4	yes	—
95	C₂³×C₆₇	#131	1	4	yes	—
96	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
97	C₂×C₄×C₆₇	—	2	8	no	—
98	C₂×C₄×C₆₇	—	2	4	no	—
99	C₂×C₄×C₆₇	—	2	8	no	—
100	C₂×C₄×C₆₇	—	2	8	no	—
101	C₂×C₄×C₆₇	—	2	32	no	—
102	C₂×C₄×C₆₇	C₄×C₈	1	16	yes	complemented
103	C₂×C₄×C₆₇	C₂×C₄²	1	4	yes	—
104	C₂×C₄×C₆₇	C₂×C₄²	1	2	yes	—
105	C₂×C₄×C₆₇	C₂×C₄²	1	4	yes	—
106	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	4	yes	—
107	C₂×C₄×C₆₇	#117	1	4	yes	—
108	C₂×C₄×C₆₇	C₄×D₄	1	4	yes	—
109	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
110	C₂×C₄×C₆₇	C₄×Q₈	1	4	yes	—
111	C₂×C₄×C₆₇	C₄×Q₈	1	2	yes	—
112	C₂×C₄×C₆₇	C₂²×C₈	1	16	yes	—
113	C₂×C₄×C₆₇	C₂²×C₈	1	8	yes	—
114	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
115	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
116	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
117	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
118	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
119	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
120	C₈×C₆₇	—	2	4	no	—
121	C₈×C₆₇	—	2	8	no	—
122	C₈×C₆₇	C₂×C₄⋊C₄	1	8	yes	direct product factor
123	C₂²×C₆₇	C₄×C₄⋊C₄	1	4	yes	—
124	C₂²×C₆₇	C₂×C₄×C₈	1	4	yes	—
125	C₂²×C₆₇	#405	1	4	yes	—
126	C₂²×C₆₇	C₈×D₄	1	8	yes	—
127	C₂²×C₆₇	C₈×Q₈	1	8	yes	—
128	C₂²×C₆₇	C₂²×C₄²	1	1	yes	characteristic
129	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
130	C₂²×C₆₇	C₂×C₄×Q₈	1	1	yes	characteristic
131	C₂²×C₆₇	C₂³×C₈	1	2	yes	—
132	C₂²×C₆₇	C₂×#131	1	2	yes	—
133	C₄×C₆₇	—	2	4	no	—
134	C₄×C₆₇	—	2	16	no	—
135	C₄×C₆₇	C₄×C₄⋊C₄	1	4	yes	—
136	C₄×C₆₇	C₂×C₄×C₈	1	8	yes	complemented
137	C₄×C₆₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
138	C₄×C₆₇	C₂×#117	1	1	yes	characteristic
139	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
140	C₄×C₆₇	C₂×C₄×Q₈	1	1	yes	characteristic
141	C₂×C₈×C₄⋊C₄	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
142	C₂×C₆₇	C₈×C₄⋊C₄	1	8	yes	direct product factor
143	C₂×C₆₇	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₆₇	C₂²×C₄×C₈	1	1	yes	characteristic
145	C₂×C₆₇	C₂×#405	1	1	yes	characteristic
146	C₂×C₆₇	C₂×C₈×D₄	1	2	yes	—
147	C₂×C₆₇	C₂×C₈×Q₈	1	2	yes	—
148	C₂²×C₄⋊C₈	C₂×C₆₇	1	1	yes	characteristic
149	C₂²×C₄×C₈	C₂×C₆₇	1	2	yes	—
150	C₂²×C₄×C₈	C₂×C₆₇	1	1	yes	characteristic
151	C₂×C₄×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic
152	C₈×C₄⋊C₄	C₂×C₆₇	1	8	yes	direct product factor
153	C₂×#336	C₂×C₆₇	1	2	yes	—
154	C₆₇	C₂×C₈×C₄⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
155	C₂³×C₈	C₂²×C₆₇	1	2	yes	—
156	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
157	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
158	C₂²×C₄⋊C₄	C₄×C₆₇	1	2	yes	—
159	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
160	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
161	C₂×C₄⋊C₈	C₄×C₆₇	1	8	yes	complemented
162	C₂×C₄⋊C₈	C₂²×C₆₇	1	4	yes	—
163	C₂×C₄×C₈	—	2	8	no	—
164	C₂×C₄×C₈	C₄×C₆₇	1	8	yes	complemented
165	C₂×C₄×C₈	C₂²×C₆₇	1	8	yes	—
166	C₂×C₄×C₈	C₂²×C₆₇	1	4	yes	—
167	C₄×C₄⋊C₄	C₄×C₆₇	1	4	yes	—
168	C₄×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
169	C₂×#95	C₄×C₆₇	1	2	yes	—
170	#336	C₂²×C₆₇	1	8	yes	—
171	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
172	C₂³×C₄	C₂×C₄×C₆₇	1	4	yes	—
173	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
174	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
175	C₂²×C₈	—	2	4	no	—
176	C₂²×C₈	—	2	2	no	—
177	C₂²×C₈	—	2	2	no	—
178	C₂²×C₈	—	2	4	no	—
179	C₂²×C₈	C₂×C₄×C₆₇	1	4	yes	—
180	C₂²×C₈	C₂×C₄×C₆₇	1	8	yes	—
181	C₂²×C₈	C₂×C₄×C₆₇	1	4	yes	—
182	C₂²×C₈	D₄×C₆₇	1	4	yes	—
183	C₂²×C₈	Q₈×C₆₇	1	4	yes	—
184	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
185	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
186	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
187	C₂×C₄⋊C₄	C₈×C₆₇	1	16	yes	direct product factor
188	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	8	yes	—
189	C₂×C₄²	—	2	4	no	—
190	C₂×C₄²	—	2	4	no	—
191	C₂×C₄²	C₂×C₄×C₆₇	1	4	yes	—
192	C₂×C₄²	C₂×C₄×C₆₇	1	2	yes	—
193	C₂×C₄²	C₂×C₄×C₆₇	1	4	yes	—
194	C₂×C₄²	C₂×C₄×C₆₇	1	4	yes	—
195	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
196	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
197	C₄⋊C₈	C₂×C₄×C₆₇	1	16	yes	complemented
198	C₄×C₈	—	2	16	no	—
199	C₄×C₈	C₂×C₄×C₆₇	1	16	yes	complemented
200	#95	C₂×C₄×C₆₇	1	8	yes	—
201	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
202	C₂²×C₄	—	2	8	no	—
203	C₂²×C₄	—	2	4	no	—
204	C₂²×C₄	—	2	8	no	—
205	C₂²×C₄	C₄²×C₆₇	1	4	yes	—
206	C₂²×C₄	C₄²×C₆₇	1	4	yes	—
207	C₂²×C₄	C₂×C₈×C₆₇	1	16	yes	—
208	C₂²×C₄	C₂×C₈×C₆₇	1	8	yes	—
209	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
210	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
211	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
212	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
213	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
214	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
215	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
216	C₂²×C₄	C₂×Q₈×C₆₇	1	2	yes	—
217	C₂²×C₄	#41×C₆₇	1	2	yes	—
218	C₂²×C₄	#41×C₆₇	1	2	yes	—
219	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
220	C₂×C₈	—	2	8	no	—
221	C₂×C₈	—	2	16	no	—
222	C₂×C₈	—	2	4	no	—
223	C₂×C₈	—	2	2	no	—
224	C₂×C₈	—	2	2	no	—
225	C₂×C₈	—	2	4	no	—
226	C₂×C₈	C₄⋊C₄×C₆₇	1	16	yes	direct product factor
227	C₂×C₈	C₂²×C₄×C₆₇	1	4	yes	—
228	C₂×C₈	C₂²×C₄×C₆₇	1	8	yes	—
229	C₂×C₈	C₂²×C₄×C₆₇	1	4	yes	—
230	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	—
231	C₂×C₈	C₂×Q₈×C₆₇	1	4	yes	—
232	C₄⋊C₄	C₂×C₈×C₆₇	1	32	yes	direct product factor
233	C₄²	—	2	8	no	—
234	C₄²	—	2	4	no	—
235	C₄²	—	2	4	no	—
236	C₄²	C₄²×C₆₇	1	8	yes	—
237	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
238	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
239	C₂³	C₂×C₄²×C₆₇	1	2	yes	—
240	C₂³	C₄×D₄×C₆₇	1	2	yes	—
241	C₂³	C₄×Q₈×C₆₇	1	2	yes	—
242	C₂³	C₂²×C₈×C₆₇	1	4	yes	—
243	C₂³	#131×C₆₇	1	4	yes	—
244	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
245	C₂×C₄	—	2	8	no	—
246	C₂×C₄	—	2	4	no	—
247	C₂×C₄	—	2	8	no	—
248	C₂×C₄	—	2	8	no	—
249	C₂×C₄	—	2	32	no	—
250	C₂×C₄	C₄×C₈×C₆₇	1	16	yes	complemented
251	C₂×C₄	C₂×C₄²×C₆₇	1	4	yes	—
252	C₂×C₄	C₂×C₄²×C₆₇	1	2	yes	—
253	C₂×C₄	C₂×C₄²×C₆₇	1	4	yes	—
254	C₂×C₄	C₂×C₄⋊C₄×C₆₇	1	4	yes	—
255	C₂×C₄	#117×C₆₇	1	4	yes	—
256	C₂×C₄	C₄×D₄×C₆₇	1	4	yes	—
257	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
258	C₂×C₄	C₄×Q₈×C₆₇	1	4	yes	—
259	C₂×C₄	C₄×Q₈×C₆₇	1	2	yes	—
260	C₂×C₄	C₂²×C₈×C₆₇	1	16	yes	—
261	C₂×C₄	C₂²×C₈×C₆₇	1	8	yes	—
262	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
263	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
264	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
265	C₂×C₄	C₂²×Q₈×C₆₇	1	1	yes	characteristic
266	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
267	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
268	C₈	—	2	4	no	—
269	C₈	—	2	8	no	—
270	C₈	C₂×C₄⋊C₄×C₆₇	1	8	yes	direct product factor
271	C₂²	C₄×C₄⋊C₄×C₆₇	1	4	yes	—
272	C₂²	C₂×C₄×C₈×C₆₇	1	4	yes	—
273	C₂²	#405×C₆₇	1	4	yes	—
274	C₂²	C₈×D₄×C₆₇	1	8	yes	—
275	C₂²	C₈×Q₈×C₆₇	1	8	yes	—
276	C₂²	C₂²×C₄²×C₆₇	1	1	yes	characteristic
277	C₂²	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
278	C₂²	C₂×C₄×Q₈×C₆₇	1	1	yes	characteristic
279	C₂²	C₂³×C₈×C₆₇	1	2	yes	—
280	C₂²	C₂×#131×C₆₇	1	2	yes	—
281	C₄	—	2	4	no	—
282	C₄	—	2	16	no	—
283	C₄	C₄×C₄⋊C₄×C₆₇	1	4	yes	—
284	C₄	C₂×C₄×C₈×C₆₇	1	8	yes	complemented
285	C₄	C₂²×C₄⋊C₄×C₆₇	1	1	yes	characteristic
286	C₄	C₂×#117×C₆₇	1	1	yes	characteristic
287	C₄	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
288	C₄	C₂×C₄×Q₈×C₆₇	1	1	yes	characteristic
289	C₂	C₈×C₄⋊C₄×C₆₇	1	8	yes	direct product factor
290	C₂	C₂×C₄×C₄⋊C₄×C₆₇	1	1	yes	characteristic
291	C₂	C₂²×C₄×C₈×C₆₇	1	1	yes	characteristic
292	C₂	C₂×#405×C₆₇	1	1	yes	characteristic
293	C₂	C₂×C₈×D₄×C₆₇	1	2	yes	—
294	C₂	C₂×C₈×Q₈×C₆₇	1	2	yes	—

	subgroup	G/H
center	C₂³×C₈×C₆₇	C₂²
commutator	C₂	C₂²×C₄×C₈×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
socle, prime radical	C₂⁴×C₆₇	C₂²×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₈×C₄⋊C₄×C₆₇	C₂	direct (N × H)
13. C₂×C₄⋊C₈×C₆₇	C₄	semidirect
16. C₂×C₄×C₈×C₆₇	C₄	semidirect
39. C₂×C₄⋊C₄×C₆₇	C₈	direct (N × H)
49. C₄⋊C₈×C₆₇	C₂×C₄	semidirect
51. C₄×C₈×C₆₇	C₂×C₄	semidirect
78. C₂×C₈×C₆₇	C₄⋊C₄	direct (N × H)
84. C₄⋊C₄×C₆₇	C₂×C₈	direct (N × H)
102. C₂×C₄×C₆₇	C₄×C₈	semidirect
122. C₈×C₆₇	C₂×C₄⋊C₄	direct (N × H)
136. C₄×C₆₇	C₂×C₄×C₈	semidirect
141. C₂×C₈×C₄⋊C₄	C₆₇	direct (N × H)
142. C₂×C₆₇	C₈×C₄⋊C₄	direct (N × H)
152. C₈×C₄⋊C₄	C₂×C₆₇	direct (N × H)
154. C₆₇	C₂×C₈×C₄⋊C₄	direct (N × H)
161. C₂×C₄⋊C₈	C₄×C₆₇	semidirect
164. C₂×C₄×C₈	C₄×C₆₇	semidirect
187. C₂×C₄⋊C₄	C₈×C₆₇	direct (N × H)
197. C₄⋊C₈	C₂×C₄×C₆₇	semidirect
199. C₄×C₈	C₂×C₄×C₆₇	semidirect
226. C₂×C₈	C₄⋊C₄×C₆₇	direct (N × H)
232. C₄⋊C₄	C₂×C₈×C₆₇	direct (N × H)
250. C₂×C₄	C₄×C₈×C₆₇	semidirect
270. C₈	C₂×C₄⋊C₄×C₆₇	direct (N × H)
284. C₄	C₂×C₄×C₈×C₆₇	semidirect
289. C₂	C₈×C₄⋊C₄×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
C₂²×C₄⋊C₈×C₆₇	2
C₂²×C₄×C₈×C₆₇	2
C₂×C₄×C₄⋊C₄×C₆₇	2
C₈×C₄⋊C₄×C₆₇	2
C₂×#336×C₆₇	2
C₂×C₈×C₄⋊C₄	67

Subgroups — C2×C8×C4⋊C4×C67 #30699683

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×C₄⋊C₄×C₆₇ #30699683