Subgroups — C₄×D₄×C₆₇⋊C₈ #30854145

Order 17152.

1422 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×D₄×C₆₇⋊C₈	C₂	1	2	yes	maximal
2	C₂²×C₄×C₆₇⋊C₈	C₂	1	2	yes	maximal, complemented
3	C₄⋊C₄×C₆₇⋊C₈	C₂	1	2	yes	maximal, complemented
4	C₄×C₄⋊(C₆₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²⋊C₄×C₆₇⋊C₈	C₂	1	4	yes	maximal, complemented
6	C₄×C₂²⋊(C₆₇⋊C₈)	C₂	1	2	yes	maximal, complemented
7	C₄²×C₆₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄²×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic
9	C₂³×C₆₇⋊C₈	C₂²	1	4	yes	—
10	D₄×C₆₇⋊C₈	C₄	1	16	yes	direct product factor
11	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
12	C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	1	4	yes	—
13	C₂×C₄×C₆₇⋊C₈	—	2	8	no	—
14	C₂×C₄×C₆₇⋊C₈	C₂²	1	2	yes	—
15	C₂×C₄×C₆₇⋊C₈	C₂²	1	4	yes	—
16	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₆₇⋊C₈	C₂²	1	2	yes	—
18	C₂×C₄×C₆₇⋊C₈	C₂²	1	2	yes	—
19	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
20	#16863151	C₂²	1	2	yes	—
21	#16863151	C₂²	1	4	yes	—
22	C₂×C₄×D₄×C₆₇	C₄	1	2	yes	—
23	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
25	C₄×C₄⋊C₄×C₆₇	C₄	1	2	yes	—
26	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
27	C₄×C₂²⋊C₄×C₆₇	C₄	1	4	yes	—
28	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
29	C₄³×C₆₇	C₂²	1	1	yes	characteristic
30	C₂²×C₆₇⋊C₈	—	2	8	no	—
31	C₂²×C₆₇⋊C₈	—	2	8	no	—
32	C₂²×C₆₇⋊C₈	C₂×C₄	1	16	yes	complemented
33	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
34	C₂²×C₆₇⋊C₈	C₂³	1	4	yes	—
35	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
36	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	8	yes	complemented
37	C₂²⋊(C₆₇⋊C₈)	C₂×C₄	1	16	yes	complemented
38	C₄×C₆₇⋊C₈	—	2	8	no	—
39	C₄×C₆₇⋊C₈	—	2	4	no	—
40	C₄×C₆₇⋊C₈	—	2	4	no	—
41	C₄×C₆₇⋊C₈	—	2	2	no	—
42	C₄×C₆₇⋊C₈	C₂×C₄	1	8	yes	complemented
43	C₄×C₆₇⋊C₈	D₄	1	4	yes	direct product factor
44	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₆₇	C₂×C₄	1	4	yes	—
46	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
47	C₄×D₄×C₆₇	C₈	1	16	yes	complemented
48	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	—
49	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
51	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
52	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	4	yes	—
53	C₂×C₄²×C₆₇	—	2	4	no	—
54	C₂×C₄²×C₆₇	—	2	4	no	—
55	C₂×C₄²×C₆₇	C₂×C₄	1	4	yes	—
56	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
59	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
62	#95×C₆₇	C₂×C₄	1	2	yes	—
63	#95×C₆₇	C₂×C₄	1	4	yes	—
64	C₂×C₆₇⋊C₈	—	2	4	no	—
65	C₂×C₆₇⋊C₈	—	2	2	no	—
66	C₂×C₆₇⋊C₈	—	2	2	no	—
67	C₂×C₆₇⋊C₈	—	2	4	no	—
68	C₂×C₆₇⋊C₈	—	2	32	no	—
69	C₂×C₆₇⋊C₈	C₂²×C₄	1	4	yes	—
70	C₂×C₆₇⋊C₈	C₂²×C₄	1	8	yes	—
71	C₂×C₆₇⋊C₈	C₂²×C₄	1	4	yes	—
72	C₂×C₆₇⋊C₈	C₂×D₄	1	4	yes	—
73	C₂×C₆₇⋊C₈	#41	1	4	yes	—
74	C₂⁴×C₆₇	C₂²×C₄	1	2	yes	—
75	C₂×D₄×C₆₇	C₄²	1	4	yes	—
76	C₂×D₄×C₆₇	C₂×C₈	1	8	yes	—
77	C₂²×C₄×C₆₇	—	2	8	no	—
78	C₂²×C₄×C₆₇	—	2	8	no	—
79	C₂²×C₄×C₆₇	—	2	2	no	—
80	C₂²×C₄×C₆₇	—	2	2	no	—
81	C₂²×C₄×C₆₇	—	2	4	no	—
82	C₂²×C₄×C₆₇	C₂×C₈	1	16	yes	complemented
83	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
84	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
88	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
91	C₄⋊C₄×C₆₇	C₄²	1	4	yes	—
92	C₄⋊C₄×C₆₇	C₂×C₈	1	8	yes	complemented
93	C₂²⋊C₄×C₆₇	C₄²	1	8	yes	—
94	C₂²⋊C₄×C₆₇	C₂×C₈	1	16	yes	complemented
95	C₄²×C₆₇	—	2	8	no	—
96	C₄²×C₆₇	—	2	4	no	—
97	C₄²×C₆₇	—	2	2	no	—
98	C₄²×C₆₇	—	2	2	no	—
99	C₄²×C₆₇	—	2	2	no	—
100	C₄²×C₆₇	C₂×C₈	1	8	yes	complemented
101	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
102	C₄²×C₆₇	C₂×D₄	1	2	yes	—
103	C₄²×C₆₇	#41	1	2	yes	—
104	C₂³×C₆₇	—	2	2	no	—
105	C₂³×C₆₇	—	2	2	no	—
106	C₂³×C₆₇	—	2	4	no	—
107	C₂³×C₆₇	C₂×C₄²	1	4	yes	—
108	C₂³×C₆₇	C₂²×C₈	1	8	yes	—
109	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
110	D₄×C₆₇	C₄×C₈	1	16	yes	complemented
111	C₂×C₄×C₆₇	—	2	4	no	—
112	C₂×C₄×C₆₇	—	2	2	no	—
113	C₂×C₄×C₆₇	—	2	2	no	—
114	C₂×C₄×C₆₇	—	2	2	no	—
115	C₂×C₄×C₆₇	—	2	2	no	—
116	C₂×C₄×C₆₇	—	2	2	no	—
117	C₂×C₄×C₆₇	—	2	4	no	—
118	C₂×C₄×C₆₇	—	2	8	no	—
119	C₂×C₄×C₆₇	—	2	8	no	—
120	C₂×C₄×C₆₇	—	2	32	no	—
121	C₂×C₄×C₆₇	C₂×C₄²	1	2	yes	—
122	C₂×C₄×C₆₇	C₂×C₄²	1	4	yes	—
123	C₂×C₄×C₆₇	C₂×C₄²	1	2	yes	—
124	C₂×C₄×C₆₇	C₄×D₄	1	4	yes	—
125	C₂×C₄×C₆₇	C₂²×C₈	1	4	yes	—
126	C₂×C₄×C₆₇	C₂²×C₈	1	8	yes	—
127	C₂×C₄×C₆₇	C₂²×C₈	1	4	yes	—
128	C₂×C₄×C₆₇	C₂²×C₈	1	4	yes	—
129	C₂×C₄×C₆₇	#131	1	4	yes	—
130	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
131	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
132	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
133	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
134	C₆₇⋊C₈	—	2	8	no	—
135	C₆₇⋊C₈	—	2	4	no	—
136	C₆₇⋊C₈	C₄×D₄	1	8	yes	direct product factor
137	C₂²×C₆₇	—	2	4	no	—
138	C₂²×C₆₇	—	2	8	no	—
139	C₂²×C₆₇	—	2	8	no	—
140	C₂²×C₆₇	—	2	4	no	—
141	C₂²×C₆₇	C₂×C₄×C₈	1	8	yes	complemented
142	C₂²×C₆₇	C₂²×C₄²	1	1	yes	characteristic
143	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
144	C₂²×C₆₇	C₄×#41	1	1	yes	characteristic
145	C₂²×C₆₇	C₂³×C₈	1	2	yes	—
146	C₂²×C₆₇	C₂×#131	1	2	yes	—
147	C₄×C₆₇	—	2	2	no	—
148	C₄×C₆₇	—	2	8	no	—
149	C₄×C₆₇	—	2	4	no	—
150	C₄×C₆₇	—	2	4	no	—
151	C₄×C₆₇	C₂×C₄×C₈	1	4	yes	complemented
152	C₄×C₆₇	C₈×D₄	1	8	yes	complemented
153	C₄×C₆₇	C₂×C₄×D₄	1	2	yes	—
154	C₄×C₆₇	C₄×#41	1	2	yes	—
155	C₄×C₈×D₄	—	67	1	no	maximal, Sylow
156	C₂×C₆₇	—	2	8	no	—
157	C₂×C₆₇	C₄²×D₄	1	1	yes	characteristic
158	C₂×C₆₇	C₂²×C₄×C₈	1	1	yes	characteristic
159	C₂×C₆₇	C₄×#131	1	1	yes	characteristic
160	C₂×C₆₇	C₂×C₈×D₄	1	2	yes	—
161	C₂×C₆₇	C₈×#41	1	2	yes	—
162	C₂×C₈×D₄	—	67	2	no	—
163	C₂²×C₄×C₈	—	67	2	no	—
164	C₄²×D₄	D₆₇	1	1	yes	characteristic
165	C₈×C₄⋊C₄	—	67	2	no	—
166	C₄×C₄⋊C₈	—	67	1	no	—
167	C₈×C₂²⋊C₄	—	67	4	no	—
168	C₄×C₂²⋊C₈	—	67	2	no	—
169	C₄²×C₈	—	67	1	no	—
170	C₆₇	C₄×C₈×D₄	1	1	yes	characteristic, complemented, Sylow
171	C₂³×C₈	—	67	4	no	—
172	C₂×C₄×D₄	Dic₆₇	1	2	yes	—
173	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
174	C₂²×C₄²	C₂×D₆₇	1	2	yes	—
175	C₈×D₄	—	67	16	no	—
176	C₂×C₄⋊C₈	—	67	2	no	—
177	C₂×C₂²⋊C₈	—	67	4	no	—
178	C₂×C₄×C₈	—	67	2	no	—
179	C₂×C₄×C₈	—	67	1	no	—
180	C₂×C₄×C₈	—	67	4	no	—
181	C₂×C₄×C₈	—	67	2	no	—
182	C₂×C₄×C₈	—	67	2	no	—
183	C₂×C₄×C₈	—	67	1	no	—
184	C₂×C₄×C₈	—	134	8	no	—
185	C₄×C₄⋊C₄	Dic₆₇	1	2	yes	—
186	C₄×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic
187	C₄×C₂²⋊C₄	Dic₆₇	1	4	yes	—
188	C₄×C₂²⋊C₄	C₂×D₆₇	1	2	yes	—
189	C₄³	C₂×D₆₇	1	1	yes	characteristic
190	#336	—	67	4	no	—
191	#336	—	67	2	no	—
192	C₂²×D₄	C₂×Dic₆₇	1	1	yes	characteristic
193	C₂³×C₄	C₂×Dic₆₇	1	4	yes	—
194	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
195	C₂²×C₈	—	67	2	no	—
196	C₂²×C₈	—	67	16	no	—
197	C₂²×C₈	—	67	4	no	—
198	C₂²×C₈	—	67	2	no	—
199	C₂²×C₈	—	134	8	no	—
200	C₂²×C₈	—	134	8	no	—
201	C₄×D₄	C₆₇⋊C₈	1	16	yes	direct product factor
202	C₄×D₄	C₄×D₆₇	1	8	yes	—
203	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
204	C₂×C₄⋊C₄	C₂×Dic₆₇	1	2	yes	—
205	C₂×C₂²⋊C₄	C₂×Dic₆₇	1	2	yes	—
206	C₂×C₂²⋊C₄	C₂×Dic₆₇	1	4	yes	—
207	C₂×C₄²	—	2	4	no	—
208	C₂×C₄²	—	2	4	no	—
209	C₂×C₄²	C₂×Dic₆₇	1	2	yes	—
210	C₂×C₄²	C₂×Dic₆₇	1	4	yes	—
211	C₂×C₄²	C₂×Dic₆₇	1	2	yes	—
212	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
213	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
214	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
215	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
216	C₄⋊C₈	—	67	8	no	—
217	C₂²⋊C₈	—	67	16	no	—
218	C₄×C₈	—	67	8	no	—
219	C₄×C₈	—	67	4	no	—
220	C₄×C₈	—	134	4	no	—
221	C₄×C₈	—	134	8	no	—
222	C₄×C₈	—	134	4	no	—
223	C₄×C₈	—	134	2	no	—
224	#95	C₂×Dic₆₇	1	2	yes	—
225	#95	C₂×Dic₆₇	1	4	yes	—
226	C₂⁴	C₂²×Dic₆₇	1	2	yes	—
227	C₂×D₄	C₄×Dic₆₇	1	4	yes	—
228	C₂×D₄	C₂×C₆₇⋊C₈	1	8	yes	—
229	C₂²×C₄	—	2	8	no	—
230	C₂²×C₄	—	2	8	no	—
231	C₂²×C₄	—	2	2	no	—
232	C₂²×C₄	—	2	4	no	—
233	C₂²×C₄	—	2	2	no	—
234	C₂²×C₄	C₂×C₆₇⋊C₈	1	16	yes	complemented
235	C₂²×C₄	C₂×C₄×D₆₇	1	8	yes	—
236	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
237	C₂²×C₄	C₂²×Dic₆₇	1	2	yes	—
238	C₂²×C₄	C₂²×Dic₆₇	1	2	yes	—
239	C₂²×C₄	C₂²×Dic₆₇	1	4	yes	—
240	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
241	C₂²×C₄	C₂²×Dic₆₇	1	2	yes	—
242	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
243	C₂×C₈	—	67	4	no	—
244	C₂×C₈	—	67	4	no	—
245	C₂×C₈	—	67	4	no	—
246	C₂×C₈	—	67	4	no	—
247	C₂×C₈	—	67	8	no	—
248	C₂×C₈	—	134	32	no	—
249	C₂×C₈	—	134	4	no	—
250	C₂×C₈	—	134	2	no	—
251	C₂×C₈	—	134	4	no	—
252	C₂×C₈	—	134	2	no	—
253	C₄⋊C₄	C₄×Dic₆₇	1	4	yes	—
254	C₄⋊C₄	C₂×C₆₇⋊C₈	1	8	yes	complemented
255	C₂²⋊C₄	C₄×Dic₆₇	1	8	yes	—
256	C₂²⋊C₄	C₂×C₆₇⋊C₈	1	16	yes	complemented
257	C₄²	—	2	8	no	—
258	C₄²	—	2	4	no	—
259	C₄²	—	2	2	no	—
260	C₄²	—	2	2	no	—
261	C₄²	—	2	2	no	—
262	C₄²	C₂×C₆₇⋊C₈	1	8	yes	complemented
263	C₄²	C₂×C₄×D₆₇	1	4	yes	—
264	C₄²	D₄×D₆₇	1	2	yes	—
265	C₄²	#11761627	1	2	yes	—
266	C₂³	—	2	2	no	—
267	C₂³	—	2	2	no	—
268	C₂³	—	2	4	no	—
269	C₂³	C₂×C₄×Dic₆₇	1	4	yes	—
270	C₂³	C₂²×C₆₇⋊C₈	1	8	yes	—
271	C₂³	C₂³×Dic₆₇	1	1	yes	characteristic
272	D₄	C₄×C₆₇⋊C₈	1	16	yes	direct product factor
273	C₂×C₄	—	2	4	no	—
274	C₂×C₄	—	2	2	no	—
275	C₂×C₄	—	2	2	no	—
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	2	2	no	—
278	C₂×C₄	—	2	2	no	—
279	C₂×C₄	—	2	4	no	—
280	C₂×C₄	—	2	8	no	—
281	C₂×C₄	—	2	8	no	—
282	C₂×C₄	—	2	32	no	—
283	C₂×C₄	C₂×C₄×Dic₆₇	1	2	yes	—
284	C₂×C₄	C₂×C₄×Dic₆₇	1	4	yes	—
285	C₂×C₄	C₂×C₄×Dic₆₇	1	2	yes	—
286	C₂×C₄	D₄×Dic₆₇	1	4	yes	—
287	C₂×C₄	C₂²×C₆₇⋊C₈	1	4	yes	—
288	C₂×C₄	C₂²×C₆₇⋊C₈	1	8	yes	—
289	C₂×C₄	C₂²×C₆₇⋊C₈	1	4	yes	—
290	C₂×C₄	C₂²×C₆₇⋊C₈	1	4	yes	—
291	C₂×C₄	#14524050	1	4	yes	—
292	C₂×C₄	C₂²×C₄×D₆₇	1	2	yes	—
293	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
294	C₂×C₄	#41×D₆₇	1	2	yes	—
295	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
296	C₈	—	67	8	no	—
297	C₈	—	134	8	no	—
298	C₈	—	134	4	no	—
299	C₂²	—	2	8	no	—
300	C₂²	—	2	4	no	—
301	C₂²	—	2	8	no	—
302	C₂²	—	2	4	no	—
303	C₂²	C₂×C₄×C₆₇⋊C₈	1	8	yes	complemented
304	C₂²	C₂²×C₄×Dic₆₇	1	1	yes	characteristic
305	C₂²	C₂×D₄×Dic₆₇	1	1	yes	characteristic
306	C₂²	#41×Dic₆₇	1	1	yes	characteristic
307	C₂²	C₂³×C₆₇⋊C₈	1	2	yes	—
308	C₂²	C₂×#14524050	1	2	yes	—
309	C₄	—	2	8	no	—
310	C₄	—	2	2	no	—
311	C₄	—	2	4	no	—
312	C₄	—	2	4	no	—
313	C₄	C₂×C₄×C₆₇⋊C₈	1	4	yes	complemented
314	C₄	D₄×C₆₇⋊C₈	1	8	yes	direct product factor
315	C₄	C₄×D₄×D₆₇	1	2	yes	—
316	C₄	C₄×#11761627	1	2	yes	—
317	C₂	—	2	8	no	—
318	C₂	C₄×D₄×Dic₆₇	1	1	yes	characteristic
319	C₂	C₂²×C₄×C₆₇⋊C₈	1	1	yes	characteristic
320	C₂	C₄×#14524050	1	1	yes	characteristic
321	C₂	C₂×D₄×C₆₇⋊C₈	1	2	yes	—
322	C₂	#41×C₆₇⋊C₈	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²	C₂²×D₆₇
commutator	C₂×C₆₇	C₂²×C₄×C₈
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₄²×D₄×C₆₇	C₂
socle	C₂³×C₆₇	C₂³×C₄
prime radical	C₂²×D₄×C₆₇	C₂×C₄
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	C₄²×D₄	D₆₇
hypocenter	C₆₇	C₄×C₈×D₄
LCS	G ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄² ◁ C₄²×D₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×C₆₇⋊C₈	C₂	semidirect
3. C₄⋊C₄×C₆₇⋊C₈	C₂	semidirect
4. C₄×C₄⋊(C₆₇⋊C₈)	C₂	semidirect
5. C₂²⋊C₄×C₆₇⋊C₈	C₂	semidirect
6. C₄×C₂²⋊(C₆₇⋊C₈)	C₂	semidirect
7. C₄²×C₆₇⋊C₈	C₂	semidirect
10. D₄×C₆₇⋊C₈	C₄	direct (N × H)
32. C₂²×C₆₇⋊C₈	C₂×C₄	semidirect
36. C₄⋊(C₆₇⋊C₈)	C₂×C₄	semidirect
37. C₂²⋊(C₆₇⋊C₈)	C₂×C₄	semidirect
42. C₄×C₆₇⋊C₈	C₂×C₄	semidirect
43. C₄×C₆₇⋊C₈	D₄	direct (N × H)
47. C₄×D₄×C₆₇	C₈	semidirect
82. C₂²×C₄×C₆₇	C₂×C₈	semidirect
92. C₄⋊C₄×C₆₇	C₂×C₈	semidirect
94. C₂²⋊C₄×C₆₇	C₂×C₈	semidirect
100. C₄²×C₆₇	C₂×C₈	semidirect
110. D₄×C₆₇	C₄×C₈	semidirect
136. C₆₇⋊C₈	C₄×D₄	direct (N × H)
141. C₂²×C₆₇	C₂×C₄×C₈	semidirect
151. C₄×C₆₇	C₂×C₄×C₈	semidirect
152. C₄×C₆₇	C₈×D₄	semidirect
170. C₆₇	C₄×C₈×D₄	semidirect
201. C₄×D₄	C₆₇⋊C₈	direct (N × H)
234. C₂²×C₄	C₂×C₆₇⋊C₈	semidirect
254. C₄⋊C₄	C₂×C₆₇⋊C₈	semidirect
256. C₂²⋊C₄	C₂×C₆₇⋊C₈	semidirect
262. C₄²	C₂×C₆₇⋊C₈	semidirect
272. D₄	C₄×C₆₇⋊C₈	direct (N × H)
303. C₂²	C₂×C₄×C₆₇⋊C₈	semidirect
313. C₄	C₂×C₄×C₆₇⋊C₈	semidirect
314. C₄	D₄×C₆₇⋊C₈	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×D₄×C₆₇⋊C₈	2
C₂²×C₄×C₆₇⋊C₈	2
C₄⋊C₄×C₆₇⋊C₈	2
C₄×C₄⋊(C₆₇⋊C₈)	2
C₂²⋊C₄×C₆₇⋊C₈	2
C₄×C₂²⋊(C₆₇⋊C₈)	2
C₄²×C₆₇⋊C₈	2
C₄²×D₄×C₆₇	2
C₄×C₈×D₄	67

Subgroups — C4×D4×C67⋊C8 #30854145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₄×C₆₇⋊C₈ #30854145