Subgroups — C₂×C₄×Q₈×#64408 #34030515

Order 18688.

3966 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₈×#64408	C₂	1	2	yes	maximal
2	C₄×Q₈×#64408	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₄⋊C₄×#64408	C₂	1	6	yes	maximal
4	C₂×C₄×C₄⋊#64408	C₂	1	3	yes	maximal
5	C₂×C₄²×#64408	C₂	1	3	yes	maximal
6	C₂×C₄×Q₈×D₇₃	C₂	1	1	yes	maximal, characteristic
7	C₂×Q₈×#64408	C₄	1	32	yes	direct product factor
8	C₂×Q₈×#64408	C₂²	1	16	yes	—
9	C₂²×C₄⋊#64408	C₂²	1	6	yes	—
10	C₂²×C₄×#64408	C₂²	1	3	yes	—
11	C₂²×C₄×#64408	C₂²	1	6	yes	—
12	C₂²×C₄×#64408	C₂²	1	6	yes	—
13	C₂²×C₄×#64408	C₂²	1	1	yes	characteristic
14	C₄⋊C₄×#64408	C₂²	1	48	yes	—
15	C₄×C₄⋊#64408	C₂²	1	24	yes	—
16	C₂×(C₂×#64408)⋊C₄	C₂²	1	6	yes	—
17	C₄²×#64408	C₂²	1	24	yes	—
18	C₂²×Q₈×D₇₃	C₂²	1	1	yes	characteristic
19	C₂×Q₈×Dic₇₃	C₄	1	1	yes	characteristic, complemented
20	C₂×C₄×Dic₁₄₆	C₄	1	3	yes	complemented
21	C₂×#14556556	C₄	1	3	yes	complemented
22	C₄×Q₈×D₇₃	C₄	1	8	yes	complemented
23	C₄×Q₈×D₇₃	C₂²	1	8	yes	—
24	C₂×C₄⋊C₄×D₇₃	C₂²	1	3	yes	—
25	C₂×C₄²×D₇₃	C₂²	1	3	yes	—
26	C₂×C₄×Q₈×C₇₃	C₄	1	1	yes	characteristic, complemented
27	C₂³×#64408	C₂³	1	6	yes	—
28	C₂³×#64408	C₂³	1	2	yes	—
29	Q₈×#64408	C₂×C₄	1	128	yes	direct product factor
30	C₂×C₄⋊#64408	C₂×C₄	1	48	yes	—
31	C₂×C₄⋊#64408	C₂³	1	24	yes	—
32	C₂×C₄×#64408	—	2	24	no	—
33	C₂×C₄×#64408	—	2	12	no	—
34	C₂×C₄×#64408	C₂×C₄	1	48	yes	—
35	C₂×C₄×#64408	Q₈	1	8	yes	direct product factor
36	C₂×C₄×#64408	C₂³	1	12	yes	—
37	C₂×C₄×#64408	C₂³	1	24	yes	—
38	C₂×C₄×#64408	C₂³	1	24	yes	—
39	C₂×C₄×#64408	C₂³	1	4	yes	—
40	(C₂×#64408)⋊C₄	C₂³	1	24	yes	—
41	C₂²×Dic₁₄₆	C₂×C₄	1	3	yes	—
42	C₂×Q₈×D₇₃	C₂×C₄	1	16	yes	—
43	C₂×Q₈×D₇₃	C₂×C₄	1	4	yes	—
44	C₂×Q₈×D₇₃	C₂³	1	4	yes	—
45	C₂²×C₄×D₇₃	C₂³	1	3	yes	—
46	C₂²×C₄×D₇₃	C₂³	1	3	yes	—
47	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
48	Q₈×Dic₇₃	C₂×C₄	1	8	yes	complemented
49	C₄×Dic₁₄₆	C₂×C₄	1	24	yes	complemented
50	#14556556	C₂×C₄	1	24	yes	complemented
51	C₂×C₄⋊Dic₇₃	C₂×C₄	1	3	yes	—
52	C₂×#11924007	C₂×C₄	1	6	yes	—
53	C₄⋊C₄×D₇₃	C₂×C₄	1	12	yes	—
54	C₄⋊C₄×D₇₃	C₂³	1	12	yes	—
55	C₂×C₄×Dic₇₃	C₂×C₄	1	3	yes	—
56	C₂×C₄×Dic₇₃	C₂×C₄	1	3	yes	—
57	C₂×C₄×Dic₇₃	C₂×C₄	1	3	yes	—
58	C₄²×D₇₃	C₂×C₄	1	12	yes	—
59	C₄²×D₇₃	C₂³	1	12	yes	—
60	C₂²×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
61	C₄×Q₈×C₇₃	C₂×C₄	1	8	yes	complemented
62	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	3	yes	—
63	C₂×C₄²×C₇₃	C₂×C₄	1	3	yes	—
64	C₂²×#64408	—	2	12	no	—
65	C₂²×#64408	—	2	12	no	—
66	C₂²×#64408	C₂²×C₄	1	24	yes	—
67	C₂²×#64408	C₂²×C₄	1	8	yes	—
68	C₂²×#64408	C₂×Q₈	1	8	yes	—
69	C₂²×#64408	#41	1	8	yes	—
70	C₂²×#64408	C₂⁴	1	12	yes	—
71	C₂²×#64408	C₂⁴	1	4	yes	—
72	C₄⋊#64408	C₂²×C₄	1	96	yes	—
73	C₄×#64408	—	2	48	no	—
74	C₄×#64408	—	2	24	no	—
75	C₄×#64408	C₂²×C₄	1	96	yes	—
76	C₄×#64408	C₂×Q₈	1	16	yes	direct product factor
77	C₂³×D₇₃	C₂⁴	1	1	yes	characteristic
78	C₂×Dic₁₄₆	C₄²	1	24	yes	complemented
79	C₂×Dic₁₄₆	C₂²×C₄	1	12	yes	—
80	Q₈×D₇₃	C₄²	1	32	yes	complemented
81	Q₈×D₇₃	C₂²×C₄	1	32	yes	—
82	C₂²×Dic₇₃	C₂²×C₄	1	3	yes	—
83	C₂²×Dic₇₃	C₂²×C₄	1	3	yes	—
84	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
85	C₂×C₄×D₇₃	—	2	12	no	—
86	C₂×C₄×D₇₃	C₂²×C₄	1	6	yes	—
87	C₂×C₄×D₇₃	C₂²×C₄	1	6	yes	—
88	C₂×C₄×D₇₃	C₂²×C₄	1	24	yes	—
89	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
90	C₂×C₄×D₇₃	C₂×Q₈	1	4	yes	—
91	C₂×C₄×D₇₃	#41	1	4	yes	—
92	C₂×C₄×D₇₃	C₂⁴	1	6	yes	—
93	C₂×C₄×D₇₃	C₂⁴	1	6	yes	—
94	C₂×C₄×D₇₃	C₂⁴	1	2	yes	—
95	C₄⋊Dic₇₃	C₂²×C₄	1	12	yes	—
96	#11924007	C₂²×C₄	1	24	yes	—
97	C₄×Dic₇₃	C₂²×C₄	1	12	yes	—
98	C₄×Dic₇₃	C₂²×C₄	1	12	yes	—
99	C₄×Dic₇₃	C₂²×C₄	1	12	yes	—
100	C₂×Q₈×C₇₃	C₄²	1	8	yes	complemented
101	C₂×Q₈×C₇₃	C₂²×C₄	1	4	yes	—
102	C₂²×C₄×C₇₃	C₂²×C₄	1	3	yes	—
103	C₂²×C₄×C₇₃	C₂²×C₄	1	3	yes	—
104	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
105	C₄⋊C₄×C₇₃	C₂²×C₄	1	12	yes	—
106	C₄²×C₇₃	C₂²×C₄	1	12	yes	—
107	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
108	C₂²×D₇₃	C₂³×C₄	1	4	yes	—
109	C₂²×D₇₃	C₂³×C₄	1	1	yes	characteristic
110	C₂²×D₇₃	C₂²×Q₈	1	2	yes	—
111	C₂²×D₇₃	C₂×#41	1	4	yes	—
112	C₂²×D₇₃	C₂×#41	1	2	yes	—
113	C₂²×D₇₃	C₂⁵	1	1	yes	characteristic
114	C₂×#64408	—	2	48	no	—
115	C₂×#64408	—	2	12	no	—
116	C₂×#64408	—	2	12	no	—
117	C₂×#64408	C₄×Q₈	1	32	yes	direct product factor
118	C₂×#64408	C₂³×C₄	1	24	yes	—
119	C₂×#64408	C₂³×C₄	1	8	yes	—
120	C₂×#64408	C₂²×Q₈	1	8	yes	—
121	C₂×#64408	C₂×#41	1	8	yes	—
122	Q₈×C₇₃	C₂×C₄²	1	16	yes	complemented
123	C₂×C₄×C₇₃	—	2	6	no	—
124	C₂×C₄×C₇₃	C₂×C₄²	1	12	yes	—
125	C₂×C₄×C₇₃	C₄×Q₈	1	4	yes	complemented
126	C₂×C₄×C₇₃	C₂³×C₄	1	6	yes	—
127	C₂×C₄×C₇₃	C₂³×C₄	1	2	yes	—
128	C₂×C₄×C₇₃	C₂³×C₄	1	6	yes	—
129	C₂×Dic₇₃	—	2	6	no	—
130	C₂×Dic₇₃	C₂×C₄²	1	12	yes	—
131	C₂×Dic₇₃	C₄×Q₈	1	4	yes	complemented
132	C₂×Dic₇₃	C₂³×C₄	1	6	yes	—
133	C₂×Dic₇₃	C₂³×C₄	1	2	yes	—
134	C₂×Dic₇₃	C₂³×C₄	1	6	yes	—
135	C₄×D₇₃	—	2	12	no	—
136	C₄×D₇₃	—	2	12	no	—
137	C₄×D₇₃	C₂×C₄²	1	24	yes	—
138	C₄×D₇₃	C₄×Q₈	1	8	yes	complemented
139	C₄×D₇₃	C₂³×C₄	1	24	yes	—
140	C₄×D₇₃	C₂²×Q₈	1	4	yes	—
141	C₄×D₇₃	C₂×#41	1	4	yes	—
142	Dic₁₄₆	C₂×C₄²	1	48	yes	complemented
143	C₂²×C₇₃	C₂²×C₄²	1	2	yes	—
144	C₂²×C₇₃	C₂×C₄×Q₈	1	2	yes	—
145	C₂²×C₇₃	C₄×#41	1	2	yes	—
146	C₂²×C₇₃	C₂⁴×C₄	1	1	yes	characteristic
147	C₂×D₇₃	C₂²×C₄²	1	2	yes	—
148	C₂×D₇₃	C₂×C₄×Q₈	1	8	yes	—
149	C₂×D₇₃	C₂×C₄×Q₈	1	2	yes	—
150	C₂×D₇₃	C₄×#41	1	8	yes	—
151	C₂×D₇₃	C₄×#41	1	2	yes	—
152	C₂×D₇₃	C₂⁴×C₄	1	2	yes	—
153	C₂×D₇₃	C₂³×Q₈	1	1	yes	characteristic
154	C₂×D₇₃	C₂²×#41	1	2	yes	—
155	C₂×D₇₃	C₂²×#41	1	1	yes	characteristic
156	#64408	—	2	24	no	—
157	#64408	C₂×C₄×Q₈	1	16	yes	direct product factor
158	C₄×C₇₃	—	2	6	no	—
159	C₄×C₇₃	C₂²×C₄²	1	12	yes	—
160	C₄×C₇₃	C₂×C₄×Q₈	1	4	yes	complemented
161	Dic₇₃	—	2	6	no	—
162	Dic₇₃	C₂²×C₄²	1	12	yes	—
163	Dic₇₃	C₂×C₄×Q₈	1	4	yes	complemented
164	C₂×C₄²×Q₈	—	73	1	no	maximal, Sylow
165	C₂×C₇₃	C₄²×Q₈	1	4	yes	complemented
166	C₂×C₇₃	C₂³×C₄²	1	1	yes	characteristic
167	C₂×C₇₃	C₂²×C₄×Q₈	1	1	yes	characteristic
168	C₂×C₇₃	C₂×C₄×#41	1	1	yes	characteristic
169	D₇₃	C₄²×Q₈	1	4	yes	complemented
170	D₇₃	C₂²×C₄×Q₈	1	2	yes	—
171	D₇₃	C₂×C₄×#41	1	2	yes	—
172	C₂²×C₄×Q₈	—	73	2	no	—
173	C₂²×C₄×Q₈	—	73	1	no	—
174	C₄²×Q₈	—	73	16	no	—
175	C₂×C₄×C₄⋊C₄	—	73	3	no	—
176	C₂×C₄×C₄⋊C₄	—	73	6	no	—
177	C₂×C₄³	—	73	3	no	—
178	C₇₃	C₂×C₄²×Q₈	1	1	yes	characteristic, complemented, Sylow
179	C₂³×Q₈	—	73	1	no	—
180	C₂×C₄×Q₈	—	73	32	no	—
181	C₂×C₄×Q₈	—	73	16	no	—
182	C₂×C₄×Q₈	—	73	1	no	—
183	C₂×C₄×Q₈	—	73	8	no	—
184	C₂×C₄×Q₈	—	73	8	no	—
185	C₂×C₄×Q₈	—	73	3	no	—
186	C₂×C₄×Q₈	—	73	3	no	—
187	C₂×C₄×Q₈	#64408	1	1	yes	characteristic, direct product factor
188	C₂²×C₄⋊C₄	—	73	6	no	—
189	C₂²×C₄⋊C₄	—	73	3	no	—
190	C₂²×C₄²	—	73	6	no	—
191	C₂²×C₄²	—	73	1	no	—
192	C₂²×C₄²	—	73	3	no	—
193	C₂²×C₄²	—	73	6	no	—
194	C₂²×C₄²	—	73	3	no	—
195	C₄×C₄⋊C₄	—	73	24	no	—
196	C₄×C₄⋊C₄	—	73	48	no	—
197	C₂×#95	—	73	6	no	—
198	C₄³	—	73	24	no	—
199	C₂²×Q₈	—	73	16	no	—
200	C₂²×Q₈	—	73	4	no	—
201	C₂²×Q₈	—	73	4	no	—
202	C₂²×Q₈	—	73	3	no	—
203	C₂²×Q₈	C₂×#64408	1	1	yes	characteristic
204	C₂³×C₄	—	73	2	no	—
205	C₂³×C₄	—	73	3	no	—
206	C₂³×C₄	—	73	1	no	—
207	C₂³×C₄	—	73	6	no	—
208	C₂³×C₄	—	73	3	no	—
209	C₄×Q₈	—	73	128	no	—
210	C₄×Q₈	—	73	8	no	—
211	C₄×Q₈	—	73	24	no	—
212	C₄×Q₈	—	73	24	no	—
213	C₄×Q₈	C₂×#64408	1	8	yes	direct product factor
214	C₂×C₄⋊C₄	—	73	24	no	—
215	C₂×C₄⋊C₄	—	73	48	no	—
216	C₂×C₄⋊C₄	—	73	6	no	—
217	C₂×C₄⋊C₄	—	73	3	no	—
218	C₂×C₄⋊C₄	—	73	12	no	—
219	C₂×C₄⋊C₄	—	73	12	no	—
220	C₂×C₄⋊C₄	C₂×#64408	1	3	yes	—
221	C₂×C₄²	—	73	24	no	—
222	C₂×C₄²	—	73	48	no	—
223	C₂×C₄²	—	73	4	no	—
224	C₂×C₄²	—	73	8	no	—
225	C₂×C₄²	—	73	3	no	—
226	C₂×C₄²	—	73	3	no	—
227	C₂×C₄²	—	73	3	no	—
228	C₂×C₄²	—	73	12	no	—
229	C₂×C₄²	—	73	12	no	—
230	C₂×C₄²	—	73	24	no	—
231	C₂×C₄²	—	73	12	no	—
232	C₂×C₄²	—	146	24	no	—
233	C₂×C₄²	—	146	12	no	—
234	C₂×C₄²	C₂×#64408	1	3	yes	—
235	#95	—	73	24	no	—
236	C₂⁴	—	73	1	no	—
237	C₂×Q₈	—	73	32	no	—
238	C₂×Q₈	—	73	32	no	—
239	C₂×Q₈	—	73	12	no	—
240	C₂×Q₈	—	73	24	no	—
241	C₂×Q₈	C₄×#64408	1	8	yes	direct product factor
242	C₂×Q₈	C₂²×#64408	1	4	yes	—
243	C₂²×C₄	—	73	8	no	—
244	C₂²×C₄	—	73	8	no	—
245	C₂²×C₄	—	73	8	no	—
246	C₂²×C₄	—	73	4	no	—
247	C₂²×C₄	—	73	1	no	—
248	C₂²×C₄	—	73	3	no	—
249	C₂²×C₄	—	73	4	no	—
250	C₂²×C₄	—	73	4	no	—
251	C₂²×C₄	—	73	2	no	—
252	C₂²×C₄	—	73	6	no	—
253	C₂²×C₄	—	73	2	no	—
254	C₂²×C₄	—	73	6	no	—
255	C₂²×C₄	—	73	24	no	—
256	C₂²×C₄	—	73	24	no	—
257	C₂²×C₄	—	73	12	no	—
258	C₂²×C₄	—	73	3	no	—
259	C₂²×C₄	—	73	6	no	—
260	C₂²×C₄	—	73	6	no	—
261	C₂²×C₄	—	146	12	no	—
262	C₂²×C₄	—	146	12	no	—
263	C₂²×C₄	—	146	12	no	—
264	C₂²×C₄	C₂²×#64408	1	3	yes	—
265	C₂²×C₄	C₂²×#64408	1	3	yes	—
266	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
267	C₄⋊C₄	—	73	96	no	—
268	C₄⋊C₄	—	73	24	no	—
269	C₄⋊C₄	—	73	12	no	—
270	C₄⋊C₄	C₂²×#64408	1	12	yes	—
271	C₄²	—	73	96	no	—
272	C₄²	—	73	16	no	—
273	C₄²	—	73	12	no	—
274	C₄²	—	73	12	no	—
275	C₄²	—	73	12	no	—
276	C₄²	—	146	48	no	—
277	C₄²	—	146	24	no	—
278	C₄²	C₂²×#64408	1	12	yes	—
279	C₂³	—	73	4	no	—
280	C₂³	—	73	2	no	—
281	C₂³	—	73	2	no	—
282	C₂³	—	73	4	no	—
283	C₂³	—	73	1	no	—
284	C₂³	—	73	1	no	—
285	C₂³	C₂³×#64408	1	1	yes	characteristic
286	Q₈	—	73	48	no	—
287	Q₈	C₂×C₄×#64408	1	16	yes	direct product factor
288	C₂×C₄	—	2	6	no	—
289	C₂×C₄	—	73	8	no	—
290	C₂×C₄	—	73	8	no	—
291	C₂×C₄	—	73	8	no	—
292	C₂×C₄	—	73	32	no	—
293	C₂×C₄	—	73	12	no	—
294	C₂×C₄	—	73	4	no	—
295	C₂×C₄	—	73	2	no	—
296	C₂×C₄	—	73	6	no	—
297	C₂×C₄	—	73	24	no	—
298	C₂×C₄	—	73	24	no	—
299	C₂×C₄	—	73	4	no	—
300	C₂×C₄	—	73	4	no	—
301	C₂×C₄	—	73	8	no	—
302	C₂×C₄	—	73	24	no	—
303	C₂×C₄	—	73	6	no	—
304	C₂×C₄	—	146	12	no	—
305	C₂×C₄	—	146	12	no	—
306	C₂×C₄	—	146	12	no	—
307	C₂×C₄	—	146	12	no	—
308	C₂×C₄	—	146	48	no	—
309	C₂×C₄	—	146	6	no	—
310	C₂×C₄	C₂×C₄×#64408	1	12	yes	—
311	C₂×C₄	Q₈×#64408	1	4	yes	direct product factor
312	C₂×C₄	C₂³×#64408	1	6	yes	—
313	C₂×C₄	C₂³×#64408	1	6	yes	—
314	C₂×C₄	C₂³×#64408	1	2	yes	—
315	C₂²	—	73	8	no	—
316	C₂²	—	73	8	no	—
317	C₂²	—	73	2	no	—
318	C₂²	—	73	2	no	—
319	C₂²	—	73	1	no	—
320	C₂²	—	73	1	no	—
321	C₂²	—	73	2	no	—
322	C₂²	—	73	2	no	—
323	C₂²	—	73	2	no	—
324	C₂²	C₂²×C₄×#64408	1	2	yes	—
325	C₂²	C₂×Q₈×#64408	1	2	yes	—
326	C₂²	#41×#64408	1	2	yes	—
327	C₂²	C₂⁴×#64408	1	1	yes	characteristic
328	C₄	—	2	6	no	—
329	C₄	—	73	16	no	—
330	C₄	—	73	12	no	—
331	C₄	—	73	4	no	—
332	C₄	—	146	24	no	—
333	C₄	—	146	6	no	—
334	C₄	C₂²×C₄×#64408	1	12	yes	—
335	C₄	C₂×Q₈×#64408	1	4	yes	direct product factor
336	C₂	—	73	2	no	—
337	C₂	—	73	2	no	—
338	C₂	—	73	4	no	—
339	C₂	C₄×Q₈×#64408	1	4	yes	direct product factor
340	C₂	C₂³×C₄×#64408	1	1	yes	characteristic
341	C₂	C₂²×Q₈×#64408	1	1	yes	characteristic
342	C₂	C₂×#41×#64408	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×#64408
commutator	C₂×C₇₃	C₂³×C₄²
Frattini	C₂²	C₂⁴×#64408
Fitting	C₂×C₄×Q₈×C₇₃	C₄
socle	C₂³×C₇₃	C₂³×C₄
prime radical	C₂³×D₇₃	C₂⁴
cosocle	C₂²×D₇₃	C₂⁵
hypercenter	C₂×C₄×Q₈	#64408
hypocenter	C₇₃	C₂×C₄²×Q₈
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×Q₈

Complements

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

N	H ≅ G/N	type
2. C₄×Q₈×#64408	C₂	direct (N × H)
7. C₂×Q₈×#64408	C₄	direct (N × H)
19. C₂×Q₈×Dic₇₃	C₄	semidirect
20. C₂×C₄×Dic₁₄₆	C₄	semidirect
21. C₂×#14556556	C₄	semidirect
22. C₄×Q₈×D₇₃	C₄	semidirect
26. C₂×C₄×Q₈×C₇₃	C₄	semidirect
29. Q₈×#64408	C₂×C₄	direct (N × H)
35. C₂×C₄×#64408	Q₈	direct (N × H)
48. Q₈×Dic₇₃	C₂×C₄	semidirect
49. C₄×Dic₁₄₆	C₂×C₄	semidirect
50. #14556556	C₂×C₄	semidirect
61. C₄×Q₈×C₇₃	C₂×C₄	semidirect
76. C₄×#64408	C₂×Q₈	direct (N × H)
78. C₂×Dic₁₄₆	C₄²	semidirect
80. Q₈×D₇₃	C₄²	semidirect
100. C₂×Q₈×C₇₃	C₄²	semidirect
117. C₂×#64408	C₄×Q₈	direct (N × H)
122. Q₈×C₇₃	C₂×C₄²	semidirect
125. C₂×C₄×C₇₃	C₄×Q₈	semidirect
131. C₂×Dic₇₃	C₄×Q₈	semidirect
138. C₄×D₇₃	C₄×Q₈	semidirect
142. Dic₁₄₆	C₂×C₄²	semidirect
157. #64408	C₂×C₄×Q₈	direct (N × H)
160. C₄×C₇₃	C₂×C₄×Q₈	semidirect
163. Dic₇₃	C₂×C₄×Q₈	semidirect
165. C₂×C₇₃	C₄²×Q₈	semidirect
169. D₇₃	C₄²×Q₈	semidirect
178. C₇₃	C₂×C₄²×Q₈	semidirect
187. C₂×C₄×Q₈	#64408	direct (N × H)
213. C₄×Q₈	C₂×#64408	direct (N × H)
241. C₂×Q₈	C₄×#64408	direct (N × H)
287. Q₈	C₂×C₄×#64408	direct (N × H)
311. C₂×C₄	Q₈×#64408	direct (N × H)
335. C₄	C₂×Q₈×#64408	direct (N × H)
339. C₂	C₄×Q₈×#64408	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×Q₈×#64408	2
C₄×Q₈×#64408	2
C₂×C₄⋊C₄×#64408	2
C₂×C₄×C₄⋊#64408	2
C₂×C₄²×#64408	2
C₂×C₄×Q₈×D₇₃	2
C₂×C₄²×Q₈	73

Subgroups — C2×C4×Q8×#64408 #34030515

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×Q₈×#64408 #34030515