Subgroups — #34441805

Order 20224.

526 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23765309	C₂	1	1	yes	maximal, characteristic, complemented
2	Q₈×C₇₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#23765232	C₂	1	1	yes	maximal, characteristic, complemented
4	#23765226	C₂	1	2	yes	maximal, complemented
5	D₄×C₇₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×C₇₉⋊C₁₆	C₂	1	2	yes	maximal, complemented
7	#23765207	C₂	1	2	yes	maximal, complemented
8	#23765203	C₂	1	1	yes	maximal, characteristic, complemented
9	#23764997	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₇₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#2966	C₂	1	1	yes	maximal, characteristic
12	C₂×#14579101	C₂²	1	2	yes	—
13	C₂²×C₇₉⋊C₁₆	C₂²	1	2	yes	—
14	C₂²×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
16	C₄⋊(C₇₉⋊C₁₆)	C₂²	1	1	yes	characteristic
17	C₄⋊(C₇₉⋊C₁₆)	C₂²	1	2	yes	—
18	C₄⋊(C₇₉⋊C₁₆)	C₂²	1	1	yes	characteristic
19	C₄⋊(C₇₉⋊C₁₆)	C₂²	1	2	yes	—
20	C₂²⋊(C₇₉⋊C₁₆)	C₂²	1	2	yes	—
21	C₂²⋊(C₇₉⋊C₁₆)	C₂²	1	2	yes	—
22	C₂²⋊(C₇₉⋊C₁₆)	C₂²	1	2	yes	—
23	#19098339	C₂²	1	2	yes	—
24	#19098339	C₂²	1	2	yes	—
25	C₄×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
26	C₄×C₇₉⋊C₁₆	C₂²	1	2	yes	—
27	C₄×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
28	C₄×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
29	C₄×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
30	#529×C₇₉	C₄	1	1	yes	characteristic
31	#446×C₇₉	C₄	1	1	yes	characteristic
32	C₈×Q₈×C₇₉	C₂²	1	1	yes	characteristic
33	#436×C₇₉	C₄	1	1	yes	characteristic
34	#435×C₇₉	C₄	1	2	yes	—
35	C₈×D₄×C₇₉	C₂²	1	2	yes	—
36	C₈×D₄×C₇₉	C₂²	1	1	yes	characteristic
37	#433×C₇₉	C₄	1	2	yes	—
38	#432×C₇₉	C₄	1	1	yes	characteristic
39	#405×C₇₉	C₂²	1	2	yes	—
40	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
41	#14579101	—	2	4	no	—
42	C₂×C₇₉⋊C₁₆	—	2	4	no	—
43	C₂×C₇₉⋊C₁₆	—	2	2	no	—
44	C₂×C₇₉⋊C₁₆	—	2	2	no	—
45	C₂×C₇₉⋊C₁₆	C₂³	1	1	yes	characteristic
46	C₂×C₇₉⋊C₁₆	C₂³	1	1	yes	characteristic
47	C₂×C₇₉⋊C₁₆	C₂³	1	2	yes	—
48	C₂×C₇₉⋊C₁₆	C₂³	1	2	yes	—
49	C₂×C₇₉⋊C₁₆	C₂³	1	1	yes	characteristic
50	C₂×C₇₉⋊C₁₆	C₂³	1	1	yes	characteristic
51	C₂×M₁₆×C₇₉	C₂×C₄	1	2	yes	—
52	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
55	#126×C₇₉	C₈	1	2	yes	—
56	#125×C₇₉	C₈	1	1	yes	characteristic
57	#124×C₇₉	C₈	1	1	yes	characteristic
58	#123×C₇₉	C₈	1	2	yes	—
59	C₂²⋊Q₈×C₇₉	C₈	1	1	yes	characteristic
60	#121×C₇₉	C₈	1	1	yes	characteristic
61	C₄×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
62	C₄×D₄×C₇₉	C₂×C₄	1	2	yes	—
63	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
64	#117×C₇₉	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
66	C₄⋊C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
67	C₄⋊C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
68	C₄⋊C₈×C₇₉	C₂×C₄	1	2	yes	—
69	C₄⋊C₈×C₇₉	C₂×C₄	1	2	yes	—
70	C₂²⋊C₈×C₇₉	C₂×C₄	1	2	yes	—
71	C₂²⋊C₈×C₇₉	C₂×C₄	1	2	yes	—
72	C₂²⋊C₈×C₇₉	C₂×C₄	1	2	yes	—
73	#97×C₇₉	C₂×C₄	1	2	yes	—
74	#97×C₇₉	C₂×C₄	1	2	yes	—
75	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
76	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
77	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
78	C₄×C₈×C₇₉	C₂³	1	2	yes	—
79	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
80	C₇₉⋊C₁₆	—	2	1	no	—
81	C₇₉⋊C₁₆	—	2	1	no	—
82	C₇₉⋊C₁₆	—	2	2	no	—
83	C₇₉⋊C₁₆	—	2	2	no	—
84	C₇₉⋊C₁₆	#41	1	2	yes	—
85	C₇₉⋊C₁₆	#41	1	2	yes	—
86	C₂×Q₈×C₇₉	C₂×C₈	1	1	yes	characteristic
87	C₂×D₄×C₇₉	C₂×C₈	1	2	yes	—
88	C₂×D₄×C₇₉	C₂×C₈	1	1	yes	characteristic
89	C₂²×C₄×C₇₉	C₂×C₈	1	1	yes	characteristic
90	C₂²×C₄×C₇₉	C₂×C₈	1	1	yes	characteristic
91	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
93	M₁₆×C₇₉	—	2	4	no	—
94	C₂×C₈×C₇₉	—	2	2	no	—
95	C₂×C₈×C₇₉	—	2	1	no	—
96	C₂×C₈×C₇₉	—	2	1	no	—
97	C₂×C₈×C₇₉	—	2	2	no	—
98	C₂×C₈×C₇₉	—	2	2	no	—
99	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
102	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
103	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
105	C₄⋊C₄×C₇₉	C₂×C₈	1	2	yes	—
106	C₄⋊C₄×C₇₉	C₂×C₈	1	2	yes	—
107	C₄⋊C₄×C₇₉	C₂×C₈	1	1	yes	characteristic
108	C₄⋊C₄×C₇₉	C₂×C₈	1	2	yes	—
109	C₄⋊C₄×C₇₉	C₂×C₈	1	1	yes	characteristic
110	C₄⋊C₄×C₇₉	C₂×C₈	1	2	yes	—
111	C₂²⋊C₄×C₇₉	C₂×C₈	1	2	yes	—
112	C₂²⋊C₄×C₇₉	C₂×C₈	1	2	yes	—
113	C₂²⋊C₄×C₇₉	C₂×C₈	1	2	yes	—
114	C₂²⋊C₄×C₇₉	C₂×C₈	1	2	yes	—
115	C₂²⋊C₄×C₇₉	C₂×C₈	1	2	yes	—
116	C₄²×C₇₉	C₂×C₈	1	1	yes	characteristic
117	C₄²×C₇₉	C₂×C₈	1	1	yes	characteristic
118	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
121	C₂³×C₇₉	C₂²×C₈	1	2	yes	—
122	C₂³×C₇₉	C₂²×C₈	1	1	yes	characteristic
123	Q₈×C₇₉	—	2	2	no	—
124	D₄×C₇₉	—	2	4	no	—
125	D₄×C₇₉	—	2	2	no	—
126	C₂×C₄×C₇₉	—	2	2	no	—
127	C₂×C₄×C₇₉	—	2	1	no	—
128	C₂×C₄×C₇₉	—	2	2	no	—
129	C₂×C₄×C₇₉	—	2	1	no	—
130	C₂×C₄×C₇₉	—	2	2	no	—
131	C₂×C₄×C₇₉	—	2	2	no	—
132	C₂×C₄×C₇₉	C₂²×C₈	1	1	yes	characteristic
133	C₂×C₄×C₇₉	C₂²×C₈	1	1	yes	characteristic
134	C₂×C₄×C₇₉	C₂²×C₈	1	1	yes	characteristic
135	C₂×C₄×C₇₉	C₂²×C₈	1	1	yes	characteristic
136	C₂×C₄×C₇₉	C₂²×C₈	1	2	yes	—
137	C₂×C₄×C₇₉	C₂²×C₈	1	2	yes	—
138	C₂×C₄×C₇₉	C₂²×C₈	1	2	yes	—
139	C₂×C₄×C₇₉	C₂²×C₈	1	1	yes	characteristic
140	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
141	C₈×C₇₉	—	2	1	no	—
142	C₈×C₇₉	—	2	2	no	—
143	C₈×C₇₉	—	2	1	no	—
144	C₈×C₇₉	—	2	2	no	—
145	C₈×C₇₉	#131	1	2	yes	—
146	C₈×C₇₉	C₂×#41	1	1	yes	characteristic
147	C₈×C₇₉	C₂×#41	1	1	yes	characteristic
148	C₂²×C₇₉	—	2	1	no	—
149	C₂²×C₇₉	—	2	1	no	—
150	C₂²×C₇₉	—	2	2	no	—
151	C₂²×C₇₉	—	2	2	no	—
152	C₂²×C₇₉	—	2	2	no	—
153	C₂²×C₇₉	#504	1	2	yes	—
154	C₂²×C₇₉	C₂³×C₈	1	1	yes	characteristic
155	C₄×C₇₉	—	2	1	no	—
156	C₄×C₇₉	—	2	1	no	—
157	C₄×C₇₉	—	2	1	no	—
158	C₄×C₇₉	—	2	2	no	—
159	C₄×C₇₉	—	2	2	no	—
160	C₄×C₇₉	—	2	1	no	—
161	C₄×C₇₉	—	2	2	no	—
162	C₄×C₇₉	#504	1	2	yes	—
163	C₄×C₇₉	C₄×#41	1	1	yes	characteristic
164	C₄×C₇₉	C₂×#131	1	1	yes	characteristic
165	#33480	—	79	1	no	maximal, Sylow
166	C₂×C₇₉	—	2	2	no	—
167	C₂×C₇₉	—	4	2	no	—
168	C₂×C₇₉	C₈×#41	1	1	yes	characteristic
169	C₂×C₇₉	C₂×#504	1	1	yes	characteristic
170	C₂×C₇₉	C₂×#504	1	1	yes	characteristic
171	#2966	D₇₉	1	1	yes	characteristic
172	#2183	—	79	1	no	—
173	Q₈×C₁₆	—	79	1	no	—
174	#2169	—	79	1	no	—
175	#2168	—	79	2	no	—
176	D₄×C₁₆	—	79	1	no	—
177	D₄×C₁₆	—	79	2	no	—
178	#2164	—	79	2	no	—
179	#2163	—	79	1	no	—
180	#2108	—	79	2	no	—
181	C₂×C₄×C₁₆	—	79	1	no	—
182	C₇₉	#33480	1	1	yes	characteristic, complemented, Sylow
183	#529	Dic₇₉	1	1	yes	characteristic
184	C₂×M₃₂	—	79	2	no	—
185	C₂²×C₁₆	—	79	1	no	—
186	C₂²×C₁₆	—	79	1	no	—
187	C₂²×C₁₆	—	79	2	no	—
188	#446	Dic₇₉	1	1	yes	characteristic
189	C₈×Q₈	C₂×D₇₉	1	1	yes	characteristic
190	#436	Dic₇₉	1	1	yes	characteristic
191	#435	Dic₇₉	1	2	yes	—
192	C₈×D₄	C₂×D₇₉	1	2	yes	—
193	C₈×D₄	C₂×D₇₉	1	1	yes	characteristic
194	#433	Dic₇₉	1	2	yes	—
195	#432	Dic₇₉	1	1	yes	characteristic
196	#405	C₂×D₇₉	1	2	yes	—
197	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
198	C₄⋊C₁₆	—	79	1	no	—
199	C₄⋊C₁₆	—	79	1	no	—
200	C₄⋊C₁₆	—	79	2	no	—
201	C₄⋊C₁₆	—	79	2	no	—
202	C₂²⋊C₁₆	—	79	2	no	—
203	C₂²⋊C₁₆	—	79	2	no	—
204	C₂²⋊C₁₆	—	79	2	no	—
205	#346	—	79	2	no	—
206	#346	—	79	2	no	—
207	C₄×C₁₆	—	79	1	no	—
208	C₄×C₁₆	—	79	1	no	—
209	C₄×C₁₆	—	79	1	no	—
210	C₄×C₁₆	—	79	1	no	—
211	C₄×C₁₆	—	79	2	no	—
212	C₂×M₁₆	C₂×Dic₇₉	1	2	yes	—
213	C₂²×C₈	C₂×Dic₇₉	1	1	yes	characteristic
214	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
215	C₂²×C₈	C₂²×D₇₉	1	2	yes	—
216	#126	C₇₉⋊C₈	1	2	yes	—
217	#125	C₇₉⋊C₈	1	1	yes	characteristic
218	#124	C₇₉⋊C₈	1	1	yes	characteristic
219	#123	C₇₉⋊C₈	1	2	yes	—
220	C₂²⋊Q₈	C₇₉⋊C₈	1	1	yes	characteristic
221	#121	C₇₉⋊C₈	1	1	yes	characteristic
222	C₄×Q₈	C₂×Dic₇₉	1	1	yes	characteristic
223	C₄×D₄	C₂×Dic₇₉	1	2	yes	—
224	C₄×D₄	C₂×Dic₇₉	1	1	yes	characteristic
225	#117	C₂×Dic₇₉	1	2	yes	—
226	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
227	M₃₂	—	158	4	no	—
228	C₂×C₁₆	—	79	1	no	—
229	C₂×C₁₆	—	79	1	no	—
230	C₂×C₁₆	—	79	1	no	—
231	C₂×C₁₆	—	79	1	no	—
232	C₂×C₁₆	—	79	2	no	—
233	C₂×C₁₆	—	79	2	no	—
234	C₂×C₁₆	—	158	2	no	—
235	C₂×C₁₆	—	158	4	no	—
236	C₂×C₁₆	—	158	2	no	—
237	C₄⋊C₈	C₂×Dic₇₉	1	1	yes	characteristic
238	C₄⋊C₈	C₂×Dic₇₉	1	1	yes	characteristic
239	C₄⋊C₈	C₂×Dic₇₉	1	2	yes	—
240	C₄⋊C₈	C₂×Dic₇₉	1	2	yes	—
241	C₂²⋊C₈	C₂×Dic₇₉	1	2	yes	—
242	C₂²⋊C₈	C₂×Dic₇₉	1	2	yes	—
243	C₂²⋊C₈	C₂×Dic₇₉	1	2	yes	—
244	#97	C₂×Dic₇₉	1	2	yes	—
245	#97	C₂×Dic₇₉	1	2	yes	—
246	C₄×C₈	C₂×Dic₇₉	1	1	yes	characteristic
247	C₄×C₈	C₂×Dic₇₉	1	1	yes	characteristic
248	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
249	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
250	C₄×C₈	C₂²×D₇₉	1	2	yes	—
251	C₂×Q₈	C₂×C₇₉⋊C₈	1	1	yes	characteristic
252	C₂×D₄	C₂×C₇₉⋊C₈	1	2	yes	—
253	C₂×D₄	C₂×C₇₉⋊C₈	1	1	yes	characteristic
254	C₂²×C₄	C₂×C₇₉⋊C₈	1	1	yes	characteristic
255	C₂²×C₄	C₂×C₇₉⋊C₈	1	1	yes	characteristic
256	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
257	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
258	M₁₆	—	2	4	no	—
259	C₂×C₈	—	2	1	no	—
260	C₂×C₈	—	2	1	no	—
261	C₂×C₈	—	2	2	no	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	2	2	no	—
264	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
265	C₂×C₈	C₂²×Dic₇₉	1	2	yes	—
266	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
267	C₂×C₈	C₂²×Dic₇₉	1	2	yes	—
268	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
269	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
270	C₄⋊C₄	C₂×C₇₉⋊C₈	1	2	yes	—
271	C₄⋊C₄	C₂×C₇₉⋊C₈	1	2	yes	—
272	C₄⋊C₄	C₂×C₇₉⋊C₈	1	1	yes	characteristic
273	C₄⋊C₄	C₂×C₇₉⋊C₈	1	2	yes	—
274	C₄⋊C₄	C₂×C₇₉⋊C₈	1	1	yes	characteristic
275	C₄⋊C₄	C₂×C₇₉⋊C₈	1	2	yes	—
276	C₂²⋊C₄	C₂×C₇₉⋊C₈	1	2	yes	—
277	C₂²⋊C₄	C₂×C₇₉⋊C₈	1	2	yes	—
278	C₂²⋊C₄	C₂×C₇₉⋊C₈	1	2	yes	—
279	C₂²⋊C₄	C₂×C₇₉⋊C₈	1	2	yes	—
280	C₂²⋊C₄	C₂×C₇₉⋊C₈	1	2	yes	—
281	C₄²	C₂×C₇₉⋊C₈	1	1	yes	characteristic
282	C₄²	C₂×C₇₉⋊C₈	1	1	yes	characteristic
283	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
284	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
285	C₄²	C₂²×Dic₇₉	1	2	yes	—
286	C₁₆	—	79	2	no	—
287	C₁₆	—	79	2	no	—
288	C₁₆	—	158	1	no	—
289	C₁₆	—	158	1	no	—
290	C₁₆	—	158	2	no	—
291	C₁₆	—	158	2	no	—
292	C₂³	C₂²×C₇₉⋊C₈	1	2	yes	—
293	C₂³	C₂²×C₇₉⋊C₈	1	1	yes	characteristic
294	Q₈	—	2	2	no	—
295	D₄	—	2	4	no	—
296	D₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	C₂²×C₇₉⋊C₈	1	1	yes	characteristic
304	C₂×C₄	C₂²×C₇₉⋊C₈	1	1	yes	characteristic
305	C₂×C₄	C₂²×C₇₉⋊C₈	1	1	yes	characteristic
306	C₂×C₄	C₂²×C₇₉⋊C₈	1	1	yes	characteristic
307	C₂×C₄	C₂²×C₇₉⋊C₈	1	2	yes	—
308	C₂×C₄	C₂²×C₇₉⋊C₈	1	2	yes	—
309	C₂×C₄	C₂²×C₇₉⋊C₈	1	2	yes	—
310	C₂×C₄	C₂²×C₇₉⋊C₈	1	1	yes	characteristic
311	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
312	C₈	—	2	1	no	—
313	C₈	—	2	2	no	—
314	C₈	—	2	1	no	—
315	C₈	—	2	2	no	—
316	C₈	#14579168	1	2	yes	—
317	C₈	#41×D₇₉	1	1	yes	characteristic
318	C₈	#41×D₇₉	1	1	yes	characteristic
319	C₂²	—	2	1	no	—
320	C₂²	—	2	1	no	—
321	C₂²	—	2	2	no	—
322	C₂²	—	2	2	no	—
323	C₂²	—	2	2	no	—
324	C₂²	#19098980	1	2	yes	—
325	C₂²	C₂³×C₇₉⋊C₈	1	1	yes	characteristic
326	C₄	—	2	1	no	—
327	C₄	—	2	2	no	—
328	C₄	—	2	1	no	—
329	C₄	—	2	1	no	—
330	C₄	—	2	1	no	—
331	C₄	—	2	2	no	—
332	C₄	—	2	2	no	—
333	C₄	#19098980	1	2	yes	—
334	C₄	#41×Dic₇₉	1	1	yes	characteristic
335	C₄	C₂×#14579168	1	1	yes	characteristic
336	C₂	—	2	2	no	—
337	C₂	—	4	2	no	—
338	C₂	#41×C₇₉⋊C₈	1	1	yes	characteristic
339	C₂	C₂×#19098980	1	1	yes	characteristic
340	C₂	C₂×#19098980	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₇₉
commutator, socle	C₂²×C₇₉	C₂³×C₈
Fitting	C₇₉×#2966	C₂
prime radical	#121×C₇₉	C₈
cosocle	C₂×C₈×C₇₉	C₂⁴
hypercenter	#2966	D₇₉
hypocenter	C₇₉	#33480
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₈ ◁ #2966

Complements

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

N	H ≅ G/N	type
1. #23765309	C₂	semidirect
2. Q₈×C₇₉⋊C₁₆	C₂	semidirect
3. #23765232	C₂	semidirect
4. #23765226	C₂	semidirect
5. D₄×C₇₉⋊C₁₆	C₂	semidirect
6. D₄×C₇₉⋊C₁₆	C₂	semidirect
7. #23765207	C₂	semidirect
8. #23765203	C₂	semidirect
9. #23764997	C₂	semidirect
10. C₂×C₄×C₇₉⋊C₁₆	C₂	semidirect
182. C₇₉	#33480	semidirect

Maximal subgroups

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

subgroup	index
#23765309	2
Q₈×C₇₉⋊C₁₆	2
#23765232	2
#23765226	2
D₄×C₇₉⋊C₁₆	2
#23765207	2
#23765203	2
#23764997	2
C₂×C₄×C₇₉⋊C₁₆	2
C₇₉×#2966	2
#33480	79