Subgroups — C₄⋊C₄×D₆₃₂ #34306664

Order 20224.

1134 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₆₃₂	C₂	1	2	yes	maximal
2	C₂×C₄×D₆₃₂	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₄×D₃₁₆	C₂	1	2	yes	maximal, complemented
4	#23764133	C₂	1	2	yes	maximal, complemented
5	#23763650	C₂	1	4	yes	maximal, complemented
6	#23763560	C₂	1	1	yes	maximal, characteristic, complemented
7	#23763401	C₂	1	2	yes	maximal, complemented
8	C₈×C₄⋊C₄×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₆₃₂	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₃₁₆	C₂²	1	4	yes	—
11	C₂×C₄×D₃₁₆	C₂²	1	2	yes	—
12	C₂×C₄⋊C₄×D₇₉	—	2	2	no	—
13	C₄×D₆₃₂	—	2	8	no	—
14	C₄×D₆₃₂	C₄	1	8	yes	complemented
15	C₂×#14579095	C₂²	1	2	yes	—
16	C₂×#14579095	C₂²	1	2	yes	—
17	C₂×#14579095	C₂²	1	1	yes	characteristic
18	C₂×#14579083	C₂²	1	4	yes	—
19	C₂×#14579083	C₂²	1	2	yes	—
20	#19098461	C₂²	1	4	yes	—
21	#19098437	—	2	4	no	—
22	#19098433	C₂²	1	2	yes	—
23	#19098420	—	2	2	no	—
24	#19098326	C₂²	1	4	yes	—
25	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₇₉	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
29	#336×C₇₉	C₂²	1	2	yes	—
30	C₂²×D₃₁₆	C₂³	1	2	yes	—
31	C₂²×C₄×D₇₉	—	2	2	no	—
32	C₂²×C₄×D₇₉	—	2	4	no	—
33	C₂×D₆₃₂	C₂×C₄	1	4	yes	—
34	C₂×D₆₃₂	D₄	1	4	yes	—
35	C₂×D₆₃₂	Q₈	1	4	yes	—
36	C₄×D₃₁₆	—	2	4	no	—
37	C₄×D₃₁₆	—	2	8	no	—
38	C₄×D₃₁₆	—	4	4	no	—
39	C₄×D₃₁₆	C₂×C₄	1	8	yes	complemented
40	C₂×C₄⋊Dic₇₉	—	2	2	no	—
41	C₂×C₄⋊Dic₇₉	—	2	2	no	—
42	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	—
43	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
44	C₂×Dic₇₉⋊C₄	—	2	4	no	—
45	C₄⋊C₄×D₇₉	—	4	8	no	—
46	C₂×(C₂×D₇₉)⋊C₄	—	2	2	no	—
47	C₂×(C₂×D₇₉)⋊C₄	—	2	4	no	—
48	#14579095	—	2	4	no	—
49	#14579095	—	4	2	no	—
50	#14579095	C₂×C₄	1	4	yes	complemented
51	#14579083	—	2	8	no	—
52	#14579083	C₂×C₄	1	8	yes	complemented
53	C₇₉⋊#95	—	2	4	no	—
54	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
55	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
60	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
61	C₄⋊C₈×C₇₉	—	2	2	no	—
62	C₄×C₈×C₇₉	—	2	4	no	—
63	C₄×C₈×C₇₉	C₂×C₄	1	4	yes	complemented
64	#95×C₇₉	D₄	1	2	yes	—
65	C₂³×D₇₉	—	2	2	no	—
66	C₂×D₃₁₆	—	2	2	no	—
67	C₂×D₃₁₆	—	2	2	no	—
68	C₂×D₃₁₆	—	2	2	no	—
69	C₂×D₃₁₆	C₂²×C₄	1	4	yes	—
70	C₂×D₃₁₆	C₂×D₄	1	4	yes	—
71	C₂×D₃₁₆	C₂×Q₈	1	4	yes	—
72	C₂²×Dic₇₉	—	2	2	no	—
73	C₂²×Dic₇₉	—	2	4	no	—
74	C₂×C₄×D₇₉	—	2	8	no	—
75	C₂×C₄×D₇₉	—	4	8	no	—
76	C₂×C₄×D₇₉	—	4	4	no	—
77	C₂×C₄×D₇₉	—	4	8	no	—
78	C₂×C₄×D₇₉	—	4	4	no	—
79	C₂×C₄×D₇₉	—	8	4	no	—
80	D₆₃₂	C₄⋊C₄	1	16	yes	direct product factor
81	C₄⋊Dic₇₉	—	2	4	no	—
82	C₄⋊Dic₇₉	—	2	2	no	—
83	C₄⋊Dic₇₉	—	2	4	no	—
84	C₄⋊Dic₇₉	—	4	4	no	—
85	C₄⋊Dic₇₉	—	8	2	no	—
86	C₄⋊Dic₇₉	C₂²×C₄	1	4	yes	—
87	Dic₇₉⋊C₄	—	4	8	no	—
88	(C₂×D₇₉)⋊C₄	—	2	8	no	—
89	(C₂×D₇₉)⋊C₄	—	4	8	no	—
90	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
95	C₂×C₈×C₇₉	—	2	2	no	—
96	C₂×C₈×C₇₉	—	2	2	no	—
97	C₂×C₈×C₇₉	—	2	1	no	—
98	C₂×C₈×C₇₉	—	2	1	no	—
99	C₂×C₈×C₇₉	—	2	2	no	—
100	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
101	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
102	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
103	C₂×C₈×C₇₉	C₂×Q₈	1	2	yes	—
104	C₄⋊C₄×C₇₉	—	2	2	no	—
105	C₄⋊C₄×C₇₉	D₈	1	4	yes	complemented
106	C₄²×C₇₉	—	2	2	no	—
107	C₄²×C₇₉	—	2	2	no	—
108	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
109	C₄²×C₇₉	#41	1	2	yes	—
110	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
111	C₂²×D₇₉	—	2	4	no	—
112	C₂²×D₇₉	—	2	4	no	—
113	C₂²×D₇₉	—	2	4	no	—
114	C₂²×D₇₉	—	4	2	no	—
115	C₂²×D₇₉	—	4	2	no	—
116	C₂²×D₇₉	—	4	2	no	—
117	C₂²×D₇₉	—	4	2	no	—
118	C₂×C₄×C₇₉	—	2	2	no	—
119	C₂×C₄×C₇₉	—	2	1	no	—
120	C₂×C₄×C₇₉	—	2	2	no	—
121	C₂×C₄×C₇₉	—	2	1	no	—
122	C₂×C₄×C₇₉	—	2	2	no	—
123	C₂×C₄×C₇₉	—	2	2	no	—
124	C₂×C₄×C₇₉	—	2	2	no	—
125	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
126	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
127	C₂×C₄×C₇₉	C₂×D₈	1	4	yes	—
128	C₂×C₄×C₇₉	C₂×D₈	1	2	yes	—
129	C₂×C₄×C₇₉	#135	1	2	yes	—
130	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
131	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
132	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
133	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
134	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
135	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
136	C₂×Dic₇₉	—	2	4	no	—
137	C₂×Dic₇₉	—	4	2	no	—
138	C₂×Dic₇₉	—	4	2	no	—
139	C₂×Dic₇₉	—	4	4	no	—
140	C₂×Dic₇₉	—	4	4	no	—
141	C₂×Dic₇₉	—	4	4	no	—
142	D₃₁₆	—	2	4	no	—
143	D₃₁₆	—	2	4	no	—
144	D₃₁₆	—	2	4	no	—
145	D₃₁₆	C₂×C₄⋊C₄	1	8	yes	complemented
146	C₄×D₇₉	—	4	16	no	—
147	C₄×D₇₉	—	8	16	no	—
148	C₈×C₇₉	—	2	2	no	—
149	C₈×C₇₉	—	4	2	no	—
150	C₈×C₇₉	C₂×C₄⋊C₄	1	4	yes	complemented
151	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
152	C₂²×C₇₉	D₄²	1	1	yes	characteristic
153	C₂²×C₇₉	D₄×Q₈	1	1	yes	characteristic
154	C₂²×C₇₉	C₂²×D₈	1	1	yes	characteristic
155	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
156	C₂²×C₇₉	#576	1	1	yes	characteristic
157	C₂²×C₇₉	#578	1	1	yes	characteristic
158	C₂×D₇₉	—	2	8	no	—
159	C₂×D₇₉	—	4	4	no	—
160	C₂×D₇₉	—	4	4	no	—
161	C₂×D₇₉	—	4	4	no	—
162	C₂×D₇₉	—	4	4	no	—
163	C₂×D₇₉	—	4	4	no	—
164	C₂×D₇₉	—	4	4	no	—
165	C₄×C₇₉	—	2	2	no	—
166	C₄×C₇₉	—	2	4	no	—
167	C₄×C₇₉	—	4	2	no	—
168	C₄×C₇₉	C₄×D₈	1	4	yes	complemented
169	C₄×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
170	C₄×C₇₉	#520	1	1	yes	characteristic
171	C₄×C₇₉	#547	1	1	yes	characteristic
172	C₄×C₇₉	#554	1	1	yes	characteristic
173	Dic₇₉	—	4	4	no	—
174	Dic₇₉	—	8	4	no	—
175	C₄⋊C₄×D₈	—	79	1	no	maximal, Sylow
176	C₂×C₇₉	D₄×C₄⋊C₄	1	1	yes	characteristic
177	C₂×C₇₉	C₂×C₄×D₈	1	1	yes	characteristic
178	C₂×C₇₉	#2951	1	1	yes	characteristic
179	C₂×C₇₉	D₄×D₈	1	1	yes	characteristic
180	C₂×C₇₉	#3283	1	1	yes	characteristic
181	C₂×C₇₉	Q₈×D₈	1	1	yes	characteristic
182	C₂×C₇₉	#3380	1	1	yes	characteristic
183	D₇₉	—	4	8	no	—
184	C₂×C₄×D₈	—	79	1	no	—
185	C₂×C₄×D₈	—	79	2	no	—
186	D₄×C₄⋊C₄	—	79	2	no	—
187	#1942	—	79	2	no	—
188	#1862	—	79	4	no	—
189	#1845	—	79	1	no	—
190	#1802	—	79	2	no	—
191	C₈×C₄⋊C₄	D₇₉	1	1	yes	characteristic, complemented
192	C₇₉	C₄⋊C₄×D₈	1	1	yes	characteristic, complemented, Sylow
193	C₂²×D₈	—	79	1	no	—
194	C₂×C₄×D₄	—	79	4	no	—
195	C₂×C₄×D₄	—	79	2	no	—
196	C₂²×C₄⋊C₄	—	158	2	no	—
197	C₄×D₈	—	79	8	no	—
198	C₄×D₈	—	158	8	no	—
199	C₂×#107	—	79	2	no	—
200	C₂×#107	—	79	1	no	—
201	C₂×#107	—	79	2	no	—
202	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
203	C₂×#102	—	79	2	no	—
204	C₂×#102	—	79	4	no	—
205	C₂×C₄×C₈	C₂×D₇₉	1	2	yes	—
206	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
207	#389	—	79	4	no	—
208	#385	—	158	4	no	—
209	#384	—	79	2	no	—
210	#380	—	158	2	no	—
211	C₄×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
212	#340	—	79	4	no	—
213	#336	C₂×D₇₉	1	2	yes	—
214	C₂²×D₄	—	79	2	no	—
215	C₂³×C₄	—	158	4	no	—
216	C₂³×C₄	—	158	2	no	—
217	C₂×D₈	—	79	4	no	—
218	C₂×D₈	—	79	4	no	—
219	C₂×D₈	—	79	4	no	—
220	C₂²×C₈	C₂²×D₇₉	1	2	yes	—
221	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
222	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
223	C₄×D₄	—	316	4	no	—
224	C₄×D₄	—	79	8	no	—
225	C₄×D₄	—	158	8	no	—
226	C₄×D₄	—	158	4	no	—
227	C₂×C₄⋊C₄	—	316	8	no	—
228	C₂×C₄⋊C₄	—	79	2	no	—
229	C₂×C₄⋊C₄	—	79	4	no	—
230	C₂×C₄⋊C₄	—	158	2	no	—
231	C₂×C₄⋊C₄	—	158	4	no	—
232	C₂×C₄⋊C₄	—	158	2	no	—
233	C₂×C₄⋊C₄	D₃₁₆	1	1	yes	characteristic
234	C₂×C₄⋊C₄	D₃₁₆	1	1	yes	characteristic
235	C₂×C₂²⋊C₄	—	158	4	no	—
236	C₂×C₂²⋊C₄	—	158	2	no	—
237	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
238	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
239	#107	—	316	2	no	—
240	#107	—	79	4	no	—
241	#107	—	158	4	no	—
242	C₄⋊C₈	—	2	2	no	—
243	#102	—	79	8	no	—
244	#102	—	158	8	no	—
245	C₄×C₈	—	2	4	no	—
246	C₄×C₈	C₄×D₇₉	1	4	yes	complemented
247	#95	—	158	4	no	—
248	#95	D₃₁₆	1	2	yes	—
249	C₂⁴	—	158	2	no	—
250	C₂×D₄	—	79	4	no	—
251	C₂×D₄	—	79	4	no	—
252	C₂×D₄	—	79	4	no	—
253	C₂×D₄	—	158	2	no	—
254	C₂×D₄	—	158	2	no	—
255	C₂×D₄	—	158	2	no	—
256	C₂²×C₄	—	316	8	no	—
257	C₂²×C₄	—	316	4	no	—
258	C₂²×C₄	—	316	4	no	—
259	C₂²×C₄	—	316	8	no	—
260	C₂²×C₄	—	632	4	no	—
261	C₂²×C₄	—	158	4	no	—
262	C₂²×C₄	—	158	2	no	—
263	C₂²×C₄	—	158	8	no	—
264	C₂²×C₄	C₂×D₃₁₆	1	2	yes	—
265	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
266	C₂²×C₄	C₂×D₃₁₆	1	2	yes	—
267	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
268	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
269	D₈	—	79	16	no	—
270	C₂×C₈	—	2	1	no	—
271	C₂×C₈	—	2	1	no	—
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	—	2	2	no	—
274	C₂×C₈	—	2	2	no	—
275	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
276	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
277	C₂×C₈	D₄×D₇₉	1	2	yes	—
278	C₂×C₈	Q₈×D₇₉	1	2	yes	—
279	C₄⋊C₄	—	2	2	no	—
280	C₄⋊C₄	—	316	8	no	—
281	C₄⋊C₄	—	316	4	no	—
282	C₄⋊C₄	—	79	4	no	—
283	C₄⋊C₄	—	632	2	no	—
284	C₄⋊C₄	—	158	4	no	—
285	C₄⋊C₄	—	158	4	no	—
286	C₄⋊C₄	—	158	2	no	—
287	C₄⋊C₄	D₆₃₂	1	4	yes	direct product factor
288	C₂²⋊C₄	—	316	8	no	—
289	C₂²⋊C₄	—	158	8	no	—
290	C₄²	—	2	2	no	—
291	C₄²	—	2	2	no	—
292	C₄²	C₂×C₄×D₇₉	1	2	yes	—
293	C₄²	#11929624	1	2	yes	—
294	C₂³	—	316	2	no	—
295	C₂³	—	316	2	no	—
296	C₂³	—	316	2	no	—
297	C₂³	—	316	2	no	—
298	C₂³	—	158	4	no	—
299	C₂³	—	158	4	no	—
300	C₂³	—	158	4	no	—
301	C₂³	C₂²×D₃₁₆	1	1	yes	characteristic
302	D₄	—	79	8	no	—
303	D₄	—	158	4	no	—
304	D₄	—	158	4	no	—
305	D₄	—	158	4	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	316	2	no	—
314	C₂×C₄	—	316	2	no	—
315	C₂×C₄	—	316	16	no	—
316	C₂×C₄	—	316	4	no	—
317	C₂×C₄	—	316	4	no	—
318	C₂×C₄	—	316	4	no	—
319	C₂×C₄	—	632	16	no	—
320	C₂×C₄	—	158	4	no	—
321	C₂×C₄	C₄×D₃₁₆	1	2	yes	—
322	C₂×C₄	C₄×D₃₁₆	1	2	yes	—
323	C₂×C₄	C₂×D₆₃₂	1	4	yes	—
324	C₂×C₄	C₂×D₆₃₂	1	2	yes	—
325	C₂×C₄	#14579183	1	2	yes	—
326	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
327	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
328	C₂×C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
329	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
330	C₂×C₄	#14579207	1	1	yes	characteristic
331	C₂×C₄	#14579208	1	1	yes	characteristic
332	C₈	—	2	2	no	—
333	C₈	—	4	2	no	—
334	C₈	C₄⋊C₄×D₇₉	1	4	yes	complemented
335	C₂²	—	316	4	no	—
336	C₂²	—	316	4	no	—
337	C₂²	—	316	4	no	—
338	C₂²	—	316	4	no	—
339	C₂²	—	316	4	no	—
340	C₂²	—	316	4	no	—
341	C₂²	—	158	8	no	—
342	C₂²	C₂×C₄×D₃₁₆	1	1	yes	characteristic
343	C₂²	D₄×D₃₁₆	1	1	yes	characteristic
344	C₂²	Q₈×D₃₁₆	1	1	yes	characteristic
345	C₂²	C₂²×D₆₃₂	1	1	yes	characteristic
346	C₂²	C₂×#14579183	1	1	yes	characteristic
347	C₂²	#19099368	1	1	yes	characteristic
348	C₂²	#19099380	1	1	yes	characteristic
349	C₄	—	2	4	no	—
350	C₄	—	2	2	no	—
351	C₄	—	4	2	no	—
352	C₄	—	316	4	no	—
353	C₄	—	632	4	no	—
354	C₄	C₄×D₆₃₂	1	4	yes	complemented
355	C₄	C₂×C₄⋊C₄×D₇₉	1	1	yes	characteristic
356	C₄	#19099043	1	1	yes	characteristic
357	C₄	#19099218	1	1	yes	characteristic
358	C₄	#19099273	1	1	yes	characteristic
359	C₂	—	316	8	no	—
360	C₂	C₄⋊C₄×D₃₁₆	1	1	yes	characteristic
361	C₂	C₂×C₄×D₆₃₂	1	1	yes	characteristic
362	C₂	#23772277	1	1	yes	characteristic
363	C₂	D₄×D₆₃₂	1	1	yes	characteristic
364	C₂	#23775122	1	1	yes	characteristic
365	C₂	Q₈×D₆₃₂	1	1	yes	characteristic
366	C₂	#23776268	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₃₁₆
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₈×C₄⋊C₄×C₇₉	C₂
socle	C₂³×C₇₉	C₂²×D₄
prime radical	C₂²×D₆₃₂	C₂²
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₈×C₄⋊C₄	D₇₉
hypocenter	C₇₉	C₄⋊C₄×D₈
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₄×C₄⋊C₄ ◁ C₈×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. C₄⋊C₄×D₃₁₆	C₂	semidirect
4. #23764133	C₂	semidirect
5. #23763650	C₂	semidirect
6. #23763560	C₂	semidirect
7. #23763401	C₂	semidirect
8. C₈×C₄⋊C₄×C₇₉	C₂	semidirect
14. C₄×D₆₃₂	C₄	semidirect
39. C₄×D₃₁₆	C₂×C₄	semidirect
50. #14579095	C₂×C₄	semidirect
52. #14579083	C₂×C₄	semidirect
63. C₄×C₈×C₇₉	C₂×C₄	semidirect
80. D₆₃₂	C₄⋊C₄	direct (N × H)
105. C₄⋊C₄×C₇₉	D₈	semidirect
145. D₃₁₆	C₂×C₄⋊C₄	semidirect
150. C₈×C₇₉	C₂×C₄⋊C₄	semidirect
168. C₄×C₇₉	C₄×D₈	semidirect
191. C₈×C₄⋊C₄	D₇₉	semidirect
192. C₇₉	C₄⋊C₄×D₈	semidirect
246. C₄×C₈	C₄×D₇₉	semidirect
287. C₄⋊C₄	D₆₃₂	direct (N × H)
334. C₈	C₄⋊C₄×D₇₉	semidirect
354. C₄	C₄×D₆₃₂	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₄×D₆₃₂	2
C₄⋊C₄×D₃₁₆	2
#23764133	2
#23763650	2
#23763560	2
#23763401	2
C₈×C₄⋊C₄×C₇₉	2
C₄⋊C₄×D₈	79

Subgroups — C4⋊C4×D632 #34306664

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊C₄×D₆₃₂ #34306664