Subgroups — C₂×C₈×Q₈×D₆₇ #31720180

Order 17152.

2478 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Q₈×D₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×Q₈×C₆₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×Dic₁₃₄	C₂	1	3	yes	maximal, complemented
4	C₂×#16863520	C₂	1	3	yes	maximal, complemented
5	C₈×Q₈×D₆₇	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₄⋊C₈×D₆₇	C₂	1	3	yes	maximal
7	C₂×C₄×C₈×D₆₇	C₂	1	3	yes	maximal
8	C₂×C₈×Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×Q₈×D₆₇	C₄	1	1	yes	characteristic
10	C₂²×C₈×D₆₇	C₂²	1	3	yes	—
11	C₂²×C₈×D₆₇	C₂²	1	1	yes	characteristic
12	C₂×Q₈×Dic₆₇	C₄	1	1	yes	characteristic
13	C₂×C₄×Dic₁₃₄	C₂²	1	3	yes	—
14	C₂×#14524008	C₄	1	3	yes	—
15	C₄×Q₈×D₆₇	C₄	1	8	yes	—
16	C₄×Q₈×D₆₇	C₂²	1	8	yes	—
17	C₂×C₄⋊C₄×D₆₇	C₄	1	3	yes	—
18	C₂×C₄²×D₆₇	C₂²	1	3	yes	—
19	Q₈×C₆₇⋊C₈	C₂²	1	8	yes	complemented
20	C₈×Dic₁₃₄	C₂²	1	24	yes	complemented
21	#16863520	C₂²	1	24	yes	complemented
22	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	3	yes	—
23	C₂×Dic₆₇⋊C₈	C₂²	1	6	yes	—
24	C₄⋊C₈×D₆₇	C₂²	1	24	yes	—
25	C₂×C₄×C₆₇⋊C₈	C₂²	1	3	yes	—
26	C₂×C₈×Dic₆₇	C₂²	1	3	yes	—
27	C₂×C₈×Dic₆₇	C₂²	1	3	yes	—
28	C₄×C₈×D₆₇	C₂²	1	24	yes	—
29	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
30	C₈×Q₈×C₆₇	C₂²	1	8	yes	complemented
31	C₂×C₄⋊C₈×C₆₇	C₂²	1	3	yes	—
32	C₂×C₄×C₈×C₆₇	C₂²	1	3	yes	—
33	C₂²×Dic₁₃₄	C₂×C₄	1	3	yes	—
34	C₂×Q₈×D₆₇	C₈	1	16	yes	direct product factor
35	C₂×Q₈×D₆₇	C₂×C₄	1	8	yes	—
36	C₂²×C₄×D₆₇	C₂×C₄	1	3	yes	—
37	C₂²×C₄×D₆₇	C₂×C₄	1	3	yes	—
38	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
39	C₂²×C₆₇⋊C₈	C₂³	1	3	yes	—
40	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
41	C₂×C₈×D₆₇	—	2	12	no	—
42	C₂×C₈×D₆₇	Q₈	1	8	yes	direct product factor
43	C₂×C₈×D₆₇	C₂³	1	12	yes	—
44	C₂×C₈×D₆₇	C₂³	1	4	yes	—
45	Q₈×Dic₆₇	C₂×C₄	1	8	yes	—
46	C₄×Dic₁₃₄	C₂×C₄	1	12	yes	—
47	C₄×Dic₁₃₄	C₂³	1	12	yes	—
48	#14524008	C₂×C₄	1	24	yes	—
49	C₂×C₄⋊Dic₆₇	C₂×C₄	1	3	yes	—
50	C₂×Dic₆₇⋊C₄	C₂×C₄	1	6	yes	—
51	C₄⋊C₄×D₆₇	C₂×C₄	1	24	yes	—
52	C₂×C₄×Dic₆₇	C₂×C₄	1	3	yes	—
53	C₂×C₄×Dic₆₇	C₂×C₄	1	3	yes	—
54	C₂×C₄×Dic₆₇	C₂³	1	3	yes	—
55	C₄²×D₆₇	C₂×C₄	1	12	yes	—
56	C₄²×D₆₇	C₂³	1	12	yes	—
57	C₄⋊(C₆₇⋊C₈)	C₂³	1	12	yes	—
58	Dic₆₇⋊C₈	C₂³	1	24	yes	—
59	C₄×C₆₇⋊C₈	C₂³	1	12	yes	—
60	C₈×Dic₆₇	C₂³	1	12	yes	—
61	C₈×Dic₆₇	C₂³	1	12	yes	—
62	C₂²×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₈×C₆₇	C₂³	1	3	yes	—
64	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
65	C₄×Q₈×C₆₇	C₂×C₄	1	4	yes	—
66	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
67	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	3	yes	—
68	C₂×C₄²×C₆₇	C₂³	1	3	yes	—
69	C₄⋊C₈×C₆₇	C₂³	1	12	yes	—
70	C₄×C₈×C₆₇	C₂³	1	12	yes	—
71	C₂³×D₆₇	C₂²×C₄	1	1	yes	characteristic
72	C₂×Dic₁₃₄	C₂×C₈	1	24	yes	complemented
73	C₂×Dic₁₃₄	C₂²×C₄	1	12	yes	—
74	Q₈×D₆₇	C₂×C₈	1	64	yes	direct product factor
75	C₂²×Dic₆₇	C₂²×C₄	1	3	yes	—
76	C₂²×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
77	C₂²×Dic₆₇	C₂²×C₄	1	3	yes	—
78	C₂×C₄×D₆₇	—	2	12	no	—
79	C₂×C₄×D₆₇	C₂×C₈	1	24	yes	—
80	C₂×C₄×D₆₇	C₂²×C₄	1	12	yes	—
81	C₂×C₄×D₆₇	C₂²×C₄	1	2	yes	—
82	C₂×C₄×D₆₇	C₂²×C₄	1	12	yes	—
83	C₂×C₄×D₆₇	C₂×Q₈	1	4	yes	—
84	C₂×C₄×D₆₇	#41	1	4	yes	—
85	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
86	C₂×C₆₇⋊C₈	—	2	6	no	—
87	C₂×C₆₇⋊C₈	C₂×Q₈	1	4	yes	complemented
88	C₂×C₆₇⋊C₈	C₂⁴	1	6	yes	—
89	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
90	C₈×D₆₇	—	2	24	no	—
91	C₈×D₆₇	C₂×Q₈	1	16	yes	direct product factor
92	C₄⋊Dic₆₇	C₂²×C₄	1	12	yes	—
93	Dic₆₇⋊C₄	C₂²×C₄	1	24	yes	—
94	C₄×Dic₆₇	C₂²×C₄	1	6	yes	—
95	C₄×Dic₆₇	C₂²×C₄	1	12	yes	—
96	C₄×Dic₆₇	C₂²×C₄	1	12	yes	—
97	C₄×Dic₆₇	C₂⁴	1	6	yes	—
98	C₂×Q₈×C₆₇	C₂×C₈	1	8	yes	complemented
99	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
100	C₂²×C₄×C₆₇	C₂²×C₄	1	3	yes	—
101	C₂²×C₄×C₆₇	C₂²×C₄	1	3	yes	—
102	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
103	C₂×C₈×C₆₇	—	2	6	no	—
104	C₂×C₈×C₆₇	C₂×Q₈	1	4	yes	complemented
105	C₂×C₈×C₆₇	C₂⁴	1	6	yes	—
106	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
107	C₄⋊C₄×C₆₇	C₂²×C₄	1	12	yes	—
108	C₄²×C₆₇	C₂²×C₄	1	6	yes	—
109	C₄²×C₆₇	C₂⁴	1	6	yes	—
110	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
111	C₂²×D₆₇	C₄×Q₈	1	4	yes	—
112	C₂²×D₆₇	C₂²×C₈	1	4	yes	—
113	C₂²×D₆₇	#131	1	4	yes	—
114	C₂²×D₆₇	C₂³×C₄	1	2	yes	—
115	Q₈×C₆₇	C₂²×C₈	1	16	yes	complemented
116	C₂×C₄×C₆₇	—	2	6	no	—
117	C₂×C₄×C₆₇	C₂²×C₈	1	12	yes	—
118	C₂×C₄×C₆₇	C₂³×C₄	1	6	yes	—
119	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
120	C₂×C₄×C₆₇	C₂³×C₄	1	6	yes	—
121	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
122	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
123	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
124	C₂×Dic₆₇	—	2	6	no	—
125	C₂×Dic₆₇	C₄×Q₈	1	4	yes	—
126	C₂×Dic₆₇	C₂²×C₈	1	12	yes	—
127	C₂×Dic₆₇	C₂³×C₄	1	6	yes	—
128	C₂×Dic₆₇	C₂³×C₄	1	2	yes	—
129	C₂×Dic₆₇	C₂³×C₄	1	6	yes	—
130	C₄×D₆₇	—	2	24	no	—
131	C₄×D₆₇	C₄×Q₈	1	8	yes	—
132	C₄×D₆₇	C₂²×C₈	1	48	yes	—
133	C₄×D₆₇	C₂²×Q₈	1	4	yes	—
134	C₄×D₆₇	C₂×#41	1	4	yes	—
135	Dic₁₃₄	C₂²×C₈	1	48	yes	complemented
136	C₈×C₆₇	—	2	6	no	—
137	C₈×C₆₇	C₂²×Q₈	1	4	yes	complemented
138	C₆₇⋊C₈	—	2	6	no	—
139	C₆₇⋊C₈	C₂²×Q₈	1	4	yes	complemented
140	C₂²×C₆₇	C₂×C₄×Q₈	1	2	yes	—
141	C₂²×C₆₇	C₂³×C₈	1	2	yes	—
142	C₂²×C₆₇	C₂×#131	1	2	yes	—
143	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
144	C₂×D₆₇	C₈×Q₈	1	16	yes	direct product factor
145	C₂×D₆₇	C₂×C₄×Q₈	1	4	yes	—
146	C₂×D₆₇	C₂³×C₈	1	4	yes	—
147	C₂×D₆₇	C₂×#131	1	4	yes	—
148	C₄×C₆₇	—	2	6	no	—
149	C₄×C₆₇	C₂×C₄×Q₈	1	2	yes	—
150	C₄×C₆₇	C₂³×C₈	1	12	yes	—
151	C₄×C₆₇	C₂³×Q₈	1	1	yes	characteristic
152	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
153	Dic₆₇	—	2	6	no	—
154	Dic₆₇	C₂×C₄×Q₈	1	4	yes	—
155	Dic₆₇	C₂³×C₈	1	12	yes	—
156	C₂²×C₈×Q₈	—	67	1	no	maximal, Sylow
157	C₂×C₆₇	C₂×C₈×Q₈	1	4	yes	complemented
158	C₂×C₆₇	C₂²×C₄×Q₈	1	1	yes	characteristic
159	C₂×C₆₇	C₂⁴×C₈	1	1	yes	characteristic
160	C₂×C₆₇	C₂²×#131	1	1	yes	characteristic
161	D₆₇	C₂×C₈×Q₈	1	8	yes	direct product factor
162	C₂²×C₄×Q₈	—	67	1	no	—
163	C₂×C₈×Q₈	—	67	16	no	—
164	C₂×C₈×Q₈	—	67	3	no	—
165	C₂×C₈×Q₈	—	67	3	no	—
166	C₂×C₈×Q₈	—	67	1	no	—
167	C₂×C₈×Q₈	D₆₇	1	1	yes	characteristic, direct product factor
168	C₂²×C₄⋊C₈	—	67	3	no	—
169	C₂²×C₄×C₈	—	67	3	no	—
170	C₆₇	C₂²×C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
171	C₂³×Q₈	—	67	1	no	—
172	C₂³×C₈	—	67	1	no	—
173	C₂³×C₈	—	67	3	no	—
174	C₂×C₄×Q₈	—	67	1	no	—
175	C₂×C₄×Q₈	—	67	8	no	—
176	C₂×C₄×Q₈	—	67	8	no	—
177	C₂×C₄×Q₈	—	67	3	no	—
178	C₂×C₄×Q₈	—	67	3	no	—
179	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic
180	C₂²×C₄⋊C₄	—	67	3	no	—
181	C₂²×C₄²	—	67	3	no	—
182	C₈×Q₈	—	67	8	no	—
183	C₈×Q₈	—	67	24	no	—
184	C₈×Q₈	—	67	24	no	—
185	C₈×Q₈	C₂×D₆₇	1	8	yes	direct product factor
186	C₂×C₄⋊C₈	—	67	6	no	—
187	C₂×C₄⋊C₈	—	67	3	no	—
188	C₂×C₄⋊C₈	—	67	24	no	—
189	C₂×C₄⋊C₈	C₂×D₆₇	1	3	yes	—
190	C₂×C₄×C₈	—	67	3	no	—
191	C₂×C₄×C₈	—	67	3	no	—
192	C₂×C₄×C₈	—	67	3	no	—
193	C₂×C₄×C₈	—	67	24	no	—
194	C₂×C₄×C₈	C₂×D₆₇	1	3	yes	—
195	C₂²×Q₈	—	67	16	no	—
196	C₂²×Q₈	—	67	8	no	—
197	C₂²×Q₈	—	67	3	no	—
198	C₂²×Q₈	C₄×D₆₇	1	1	yes	characteristic
199	C₂³×C₄	—	67	3	no	—
200	C₂³×C₄	—	67	1	no	—
201	C₂³×C₄	—	67	3	no	—
202	C₂²×C₈	—	67	1	no	—
203	C₂²×C₈	—	67	8	no	—
204	C₂²×C₈	—	67	4	no	—
205	C₂²×C₈	—	67	3	no	—
206	C₂²×C₈	—	67	12	no	—
207	C₂²×C₈	—	134	12	no	—
208	C₂²×C₈	C₂²×D₆₇	1	3	yes	—
209	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
210	C₄×Q₈	—	67	8	no	—
211	C₄×Q₈	—	67	24	no	—
212	C₄×Q₈	—	67	12	no	—
213	C₄×Q₈	—	67	12	no	—
214	C₄×Q₈	C₄×D₆₇	1	4	yes	—
215	C₄×Q₈	C₂²×D₆₇	1	4	yes	—
216	C₂×C₄⋊C₄	—	67	6	no	—
217	C₂×C₄⋊C₄	—	67	3	no	—
218	C₂×C₄⋊C₄	—	67	24	no	—
219	C₂×C₄⋊C₄	C₄×D₆₇	1	3	yes	—
220	C₂×C₄²	—	67	3	no	—
221	C₂×C₄²	—	67	3	no	—
222	C₂×C₄²	—	67	3	no	—
223	C₂×C₄²	—	67	12	no	—
224	C₂×C₄²	—	67	12	no	—
225	C₂×C₄²	C₂²×D₆₇	1	3	yes	—
226	C₄⋊C₈	—	67	24	no	—
227	C₄⋊C₈	—	67	12	no	—
228	C₄⋊C₈	C₂²×D₆₇	1	12	yes	—
229	C₄×C₈	—	67	12	no	—
230	C₄×C₈	—	67	12	no	—
231	C₄×C₈	—	67	12	no	—
232	C₄×C₈	C₂²×D₆₇	1	12	yes	—
233	C₂⁴	—	67	1	no	—
234	C₂×Q₈	—	67	64	no	—
235	C₂×Q₈	—	67	24	no	—
236	C₂×Q₈	—	67	12	no	—
237	C₂×Q₈	C₈×D₆₇	1	8	yes	direct product factor
238	C₂×Q₈	C₂×C₄×D₆₇	1	4	yes	—
239	C₂²×C₄	—	67	1	no	—
240	C₂²×C₄	—	67	3	no	—
241	C₂²×C₄	—	67	24	no	—
242	C₂²×C₄	—	67	2	no	—
243	C₂²×C₄	—	67	12	no	—
244	C₂²×C₄	—	67	4	no	—
245	C₂²×C₄	—	67	4	no	—
246	C₂²×C₄	—	67	2	no	—
247	C₂²×C₄	—	67	3	no	—
248	C₂²×C₄	—	67	12	no	—
249	C₂²×C₄	—	134	12	no	—
250	C₂²×C₄	C₂×C₄×D₆₇	1	3	yes	—
251	C₂²×C₄	C₂×C₄×D₆₇	1	3	yes	—
252	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
253	C₂×C₈	—	2	6	no	—
254	C₂×C₈	—	67	4	no	—
255	C₂×C₈	—	67	2	no	—
256	C₂×C₈	—	67	16	no	—
257	C₂×C₈	—	67	6	no	—
258	C₂×C₈	—	134	24	no	—
259	C₂×C₈	—	134	6	no	—
260	C₂×C₈	Q₈×D₆₇	1	4	yes	direct product factor
261	C₂×C₈	C₂³×D₆₇	1	6	yes	—
262	C₂×C₈	C₂³×D₆₇	1	2	yes	—
263	C₄⋊C₄	—	67	24	no	—
264	C₄⋊C₄	—	67	12	no	—
265	C₄⋊C₄	C₂×C₄×D₆₇	1	12	yes	—
266	C₄²	—	67	12	no	—
267	C₄²	—	67	12	no	—
268	C₄²	—	67	6	no	—
269	C₄²	—	67	6	no	—
270	C₄²	C₂×C₄×D₆₇	1	6	yes	—
271	C₄²	C₂³×D₆₇	1	6	yes	—
272	C₂³	—	67	4	no	—
273	C₂³	—	67	4	no	—
274	C₂³	—	67	4	no	—
275	C₂³	—	67	2	no	—
276	C₂³	C₂²×C₄×D₆₇	1	1	yes	characteristic
277	Q₈	—	67	48	no	—
278	Q₈	C₂×C₈×D₆₇	1	16	yes	direct product factor
279	C₂×C₄	—	2	6	no	—
280	C₂×C₄	—	67	4	no	—
281	C₂×C₄	—	67	12	no	—
282	C₂×C₄	—	67	2	no	—
283	C₂×C₄	—	67	6	no	—
284	C₂×C₄	—	67	8	no	—
285	C₂×C₄	—	67	48	no	—
286	C₂×C₄	—	67	4	no	—
287	C₂×C₄	—	67	4	no	—
288	C₂×C₄	—	67	6	no	—
289	C₂×C₄	—	134	24	no	—
290	C₂×C₄	—	134	6	no	—
291	C₂×C₄	C₂×C₈×D₆₇	1	12	yes	—
292	C₂×C₄	C₂²×C₄×D₆₇	1	6	yes	—
293	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
294	C₂×C₄	C₂²×C₄×D₆₇	1	6	yes	—
295	C₂×C₄	C₂×Q₈×D₆₇	1	2	yes	—
296	C₂×C₄	#41×D₆₇	1	2	yes	—
297	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
298	C₈	—	2	6	no	—
299	C₈	—	67	4	no	—
300	C₈	—	134	6	no	—
301	C₈	C₂×Q₈×D₆₇	1	4	yes	direct product factor
302	C₂²	—	67	4	no	—
303	C₂²	—	67	4	no	—
304	C₂²	—	67	4	no	—
305	C₂²	—	67	16	no	—
306	C₂²	C₄×Q₈×D₆₇	1	2	yes	—
307	C₂²	C₂²×C₈×D₆₇	1	2	yes	—
308	C₂²	#131×D₆₇	1	2	yes	—
309	C₂²	C₂³×C₄×D₆₇	1	1	yes	characteristic
310	C₄	—	2	6	no	—
311	C₄	—	67	12	no	—
312	C₄	—	67	4	no	—
313	C₄	—	134	6	no	—
314	C₄	C₄×Q₈×D₆₇	1	2	yes	—
315	C₄	C₂²×C₈×D₆₇	1	12	yes	—
316	C₄	C₂²×Q₈×D₆₇	1	1	yes	characteristic
317	C₄	C₂×#41×D₆₇	1	1	yes	characteristic
318	C₂	—	67	8	no	—
319	C₂	C₈×Q₈×D₆₇	1	4	yes	direct product factor
320	C₂	C₂×C₄×Q₈×D₆₇	1	1	yes	characteristic
321	C₂	C₂³×C₈×D₆₇	1	1	yes	characteristic
322	C₂	C₂×#131×D₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈	C₂²×D₆₇
commutator	C₂×C₆₇	C₂⁴×C₈
Frattini	C₂×C₄	C₂⁴×D₆₇
Fitting	C₂×C₈×Q₈×C₆₇	C₂
socle	C₂³×C₆₇	C₂³×C₄
prime radical	C₂³×D₆₇	C₂²×C₄
cosocle	C₂×C₄×C₆₇	C₂⁵
hypercenter	C₂×C₈×Q₈	D₆₇
hypocenter	C₆₇	C₂²×C₈×Q₈
LCS	G ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₈×Q₈

Complements

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

N	H ≅ G/N	type
2. C₂×Q₈×C₆₇⋊C₈	C₂	semidirect
3. C₂×C₈×Dic₁₃₄	C₂	semidirect
4. C₂×#16863520	C₂	semidirect
5. C₈×Q₈×D₆₇	C₂	direct (N × H)
8. C₂×C₈×Q₈×C₆₇	C₂	semidirect
19. Q₈×C₆₇⋊C₈	C₂²	semidirect
20. C₈×Dic₁₃₄	C₂²	semidirect
21. #16863520	C₂²	semidirect
30. C₈×Q₈×C₆₇	C₂²	semidirect
34. C₂×Q₈×D₆₇	C₈	direct (N × H)
42. C₂×C₈×D₆₇	Q₈	direct (N × H)
72. C₂×Dic₁₃₄	C₂×C₈	semidirect
74. Q₈×D₆₇	C₂×C₈	direct (N × H)
87. C₂×C₆₇⋊C₈	C₂×Q₈	semidirect
91. C₈×D₆₇	C₂×Q₈	direct (N × H)
98. C₂×Q₈×C₆₇	C₂×C₈	semidirect
104. C₂×C₈×C₆₇	C₂×Q₈	semidirect
115. Q₈×C₆₇	C₂²×C₈	semidirect
135. Dic₁₃₄	C₂²×C₈	semidirect
137. C₈×C₆₇	C₂²×Q₈	semidirect
139. C₆₇⋊C₈	C₂²×Q₈	semidirect
144. C₂×D₆₇	C₈×Q₈	direct (N × H)
157. C₂×C₆₇	C₂×C₈×Q₈	semidirect
161. D₆₇	C₂×C₈×Q₈	direct (N × H)
167. C₂×C₈×Q₈	D₆₇	direct (N × H)
170. C₆₇	C₂²×C₈×Q₈	semidirect
185. C₈×Q₈	C₂×D₆₇	direct (N × H)
237. C₂×Q₈	C₈×D₆₇	direct (N × H)
260. C₂×C₈	Q₈×D₆₇	direct (N × H)
278. Q₈	C₂×C₈×D₆₇	direct (N × H)
301. C₈	C₂×Q₈×D₆₇	direct (N × H)
319. C₂	C₈×Q₈×D₆₇	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×C₄×Q₈×D₆₇	2
C₂×Q₈×C₆₇⋊C₈	2
C₂×C₈×Dic₁₃₄	2
C₂×#16863520	2
C₈×Q₈×D₆₇	2
C₂×C₄⋊C₈×D₆₇	2
C₂×C₄×C₈×D₆₇	2
C₂×C₈×Q₈×C₆₇	2
C₂²×C₈×Q₈	67

Subgroups — C2×C8×Q8×D67 #31720180

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×Q₈×D₆₇ #31720180