Subgroups — C₂×C₄⋊C₈×Dic₇₉ #34286142

Order 20224.

1550 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊(C₇₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×Dic₇₉	C₂	1	2	yes	maximal
3	C₂×C₄²×Dic₇₉	C₂	1	1	yes	maximal, characteristic
4	C₄⋊C₈×Dic₇₉	C₂	1	8	yes	maximal, direct product factor
5	C₂×#19098317	C₂	1	2	yes	maximal
6	C₂²×C₄⋊C₈×C₇₉	C₂	1	1	yes	maximal, characteristic
7	C₂³×C₇₉⋊C₈	C₂²	1	2	yes	—
8	C₂²×C₄×Dic₇₉	C₄	1	2	yes	—
9	C₂²×C₄×Dic₇₉	C₄	1	2	yes	—
10	C₂²×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊(C₇₉⋊C₈)	C₄	1	8	yes	complemented
13	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	4	yes	—
14	C₂×C₈×Dic₇₉	—	2	8	no	—
15	C₂×C₈×Dic₇₉	C₂²	1	8	yes	—
16	C₄²×Dic₇₉	C₄	1	4	yes	—
17	C₄²×Dic₇₉	C₂²	1	4	yes	—
18	#19098317	C₂²	1	8	yes	—
19	C₂³×C₈×C₇₉	C₂²	1	2	yes	—
20	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₇₉	C₄	1	8	yes	complemented
22	C₂×C₄⋊C₈×C₇₉	C₂²	1	4	yes	—
23	C₂³×Dic₇₉	C₂×C₄	1	2	yes	—
24	C₂³×Dic₇₉	C₂×C₄	1	2	yes	—
25	C₂²×C₇₉⋊C₈	—	2	4	no	—
26	C₂²×C₇₉⋊C₈	—	2	4	no	—
27	C₂²×C₇₉⋊C₈	C₂×C₄	1	8	yes	—
28	C₂²×C₇₉⋊C₈	C₂³	1	4	yes	—
29	C₂×C₄×Dic₇₉	—	2	2	no	—
30	C₂×C₄×Dic₇₉	—	2	2	no	—
31	C₂×C₄×Dic₇₉	—	2	8	no	—
32	C₂×C₄×Dic₇₉	C₈	1	16	yes	complemented
33	C₂×C₄×Dic₇₉	C₂×C₄	1	2	yes	—
34	C₂×C₄×Dic₇₉	C₂×C₄	1	8	yes	—
35	C₂×C₄×Dic₇₉	C₂×C₄	1	2	yes	—
36	C₂×C₄×Dic₇₉	C₂×C₄	1	8	yes	—
37	C₂×C₄×Dic₇₉	D₄	1	4	yes	—
38	C₂×C₄×Dic₇₉	Q₈	1	4	yes	—
39	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
40	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
41	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	16	yes	complemented
42	C₈×Dic₇₉	—	2	16	no	—
43	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₇₉	—	2	4	no	—
47	C₂²×C₈×C₇₉	—	2	4	no	—
48	C₂²×C₈×C₇₉	C₂×C₄	1	8	yes	—
49	C₂²×C₈×C₇₉	C₂³	1	4	yes	—
50	C₂×C₄²×C₇₉	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₇₉	C₂×C₄	1	4	yes	—
52	C₂×C₄²×C₇₉	C₂×C₄	1	4	yes	—
53	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
54	C₄⋊C₈×C₇₉	C₂×C₄	1	16	yes	complemented
55	C₂²×Dic₇₉	—	2	4	no	—
56	C₂²×Dic₇₉	—	2	4	no	—
57	C₂²×Dic₇₉	C₄⋊C₄	1	8	yes	—
58	C₂²×Dic₇₉	C₂×C₈	1	8	yes	—
59	C₂²×Dic₇₉	C₂×C₈	1	8	yes	—
60	C₂²×Dic₇₉	M₁₆	1	8	yes	—
61	C₂²×Dic₇₉	C₂²×C₄	1	4	yes	—
62	C₂²×Dic₇₉	C₂²×C₄	1	4	yes	—
63	C₂×C₇₉⋊C₈	—	2	16	no	—
64	C₂×C₇₉⋊C₈	—	2	4	no	—
65	C₂×C₇₉⋊C₈	—	2	4	no	—
66	C₂×C₇₉⋊C₈	C₂²×C₄	1	8	yes	—
67	C₄×Dic₇₉	—	2	16	no	—
68	C₄×Dic₇₉	—	2	4	no	—
69	C₄×Dic₇₉	—	2	2	no	—
70	C₄×Dic₇₉	—	2	2	no	—
71	C₄×Dic₇₉	C₄⋊C₄	1	8	yes	—
72	C₄×Dic₇₉	C₂×C₈	1	32	yes	complemented
73	C₄×Dic₇₉	C₂×D₄	1	4	yes	—
74	C₄×Dic₇₉	C₂×Q₈	1	4	yes	—
75	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₇₉	—	2	4	no	—
77	C₂²×C₄×C₇₉	C₄²	1	4	yes	—
78	C₂²×C₄×C₇₉	C₄²	1	4	yes	—
79	C₂²×C₄×C₇₉	C₂×C₈	1	8	yes	—
80	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
86	C₂²×C₄×C₇₉	C₂×Q₈	1	2	yes	—
87	C₂²×C₄×C₇₉	#41	1	2	yes	—
88	C₂²×C₄×C₇₉	#41	1	2	yes	—
89	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
90	C₂×C₈×C₇₉	—	2	16	no	—
91	C₂×C₈×C₇₉	—	2	4	no	—
92	C₂×C₈×C₇₉	—	2	4	no	—
93	C₂×C₈×C₇₉	C₂²×C₄	1	8	yes	—
94	C₄²×C₇₉	C₄²	1	8	yes	—
95	C₄²×C₇₉	C₂²×C₄	1	4	yes	—
96	C₄²×C₇₉	C₂²×C₄	1	4	yes	—
97	C₂³×C₇₉	C₂×C₄²	1	2	yes	—
98	C₂³×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
99	C₂³×C₇₉	#117	1	2	yes	—
100	C₂³×C₇₉	C₂²×C₈	1	4	yes	—
101	C₂³×C₇₉	C₂×M₁₆	1	4	yes	—
102	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
103	C₂×C₄×C₇₉	—	2	4	no	—
104	C₂×C₄×C₇₉	—	2	8	no	—
105	C₂×C₄×C₇₉	C₄×C₈	1	16	yes	complemented
106	C₂×C₄×C₇₉	C₂×C₄²	1	4	yes	—
107	C₂×C₄×C₇₉	C₂×C₄²	1	2	yes	—
108	C₂×C₄×C₇₉	C₂×C₄²	1	4	yes	—
109	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
110	C₂×C₄×C₇₉	#117	1	2	yes	—
111	C₂×C₄×C₇₉	C₄×D₄	1	4	yes	—
112	C₂×C₄×C₇₉	C₄×D₄	1	4	yes	—
113	C₂×C₄×C₇₉	C₄×Q₈	1	4	yes	—
114	C₂×C₄×C₇₉	C₄×Q₈	1	4	yes	—
115	C₂×C₄×C₇₉	C₂²×C₈	1	8	yes	—
116	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
117	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
118	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
119	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
120	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
121	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
122	C₂×Dic₇₉	—	2	4	no	—
123	C₂×Dic₇₉	—	2	4	no	—
124	C₂×Dic₇₉	—	2	16	no	—
125	C₂×Dic₇₉	C₄⋊C₈	1	32	yes	direct product factor
126	C₂×Dic₇₉	C₂×C₄⋊C₄	1	8	yes	—
127	C₂×Dic₇₉	C₂²×C₈	1	8	yes	—
128	C₂×Dic₇₉	C₂²×C₈	1	8	yes	—
129	C₂×Dic₇₉	C₂×M₁₆	1	8	yes	—
130	C₈×C₇₉	—	2	8	no	—
131	C₇₉⋊C₈	—	2	8	no	—
132	C₂²×C₇₉	C₄×C₄⋊C₄	1	4	yes	—
133	C₂²×C₇₉	C₂×C₄×C₈	1	4	yes	—
134	C₂²×C₇₉	C₄×M₁₆	1	4	yes	—
135	C₂²×C₇₉	C₂×C₄⋊C₈	1	8	yes	—
136	C₂²×C₇₉	#431	1	8	yes	—
137	C₂²×C₇₉	C₂²×C₄²	1	1	yes	characteristic
138	C₂²×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
139	C₂²×C₇₉	C₂×#117	1	1	yes	characteristic
140	C₂²×C₇₉	C₂³×C₈	1	2	yes	—
141	C₂²×C₇₉	C₂²×M₁₆	1	2	yes	—
142	C₄×C₇₉	—	2	4	no	—
143	C₄×C₇₉	C₄×C₄⋊C₄	1	4	yes	—
144	C₄×C₇₉	C₂×C₄×C₈	1	8	yes	complemented
145	C₄×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
146	C₄×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
147	C₄×C₇₉	C₂×C₄×Q₈	1	1	yes	characteristic
148	C₄×C₇₉	C₂×C₄×Q₈	1	1	yes	characteristic
149	Dic₇₉	—	2	8	no	—
150	Dic₇₉	C₂×C₄⋊C₈	1	16	yes	direct product factor
151	C₂×C₄×C₄⋊C₈	—	79	1	no	maximal, Sylow
152	C₂×C₇₉	C₄×C₄⋊C₈	1	8	yes	complemented
153	C₂×C₇₉	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₇₉	C₂²×C₄×C₈	1	1	yes	characteristic
155	C₂×C₇₉	C₂×C₄×M₁₆	1	1	yes	characteristic
156	C₂×C₇₉	C₂²×C₄⋊C₈	1	2	yes	—
157	C₂×C₇₉	C₂×#431	1	2	yes	—
158	C₂²×C₄⋊C₈	—	79	1	no	—
159	C₂²×C₄⋊C₈	D₇₉	1	1	yes	characteristic
160	C₂²×C₄×C₈	—	79	2	no	—
161	C₂×C₄³	—	79	1	no	—
162	C₄×C₄⋊C₈	—	79	8	no	—
163	C₂×#336	—	79	2	no	—
164	C₇₉	C₂×C₄×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
165	C₂³×C₈	—	79	2	no	—
166	C₂³×C₈	C₂×D₇₉	1	2	yes	—
167	C₂²×C₄²	—	79	1	no	—
168	C₂²×C₄²	—	79	2	no	—
169	C₂²×C₄²	—	79	1	no	—
170	C₂²×C₄²	—	79	2	no	—
171	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
172	C₂×C₄⋊C₈	—	79	4	no	—
173	C₂×C₄⋊C₈	—	79	8	no	—
174	C₂×C₄⋊C₈	Dic₇₉	1	8	yes	direct product factor
175	C₂×C₄⋊C₈	C₂×D₇₉	1	4	yes	—
176	C₂×C₄×C₈	—	79	8	no	—
177	C₂×C₄×C₈	—	158	8	no	—
178	C₄³	—	79	4	no	—
179	C₄³	—	79	4	no	—
180	#336	—	79	8	no	—
181	C₂³×C₄	—	79	2	no	—
182	C₂³×C₄	—	79	2	no	—
183	C₂³×C₄	C₄×D₇₉	1	1	yes	characteristic
184	C₂³×C₄	C₄×D₇₉	1	1	yes	characteristic
185	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
186	C₂²×C₈	—	2	4	no	—
187	C₂²×C₈	—	2	4	no	—
188	C₂²×C₈	—	79	8	no	—
189	C₂²×C₈	—	79	4	no	—
190	C₂²×C₈	—	158	4	no	—
191	C₂²×C₈	—	158	4	no	—
192	C₂²×C₈	C₂×Dic₇₉	1	8	yes	—
193	C₂²×C₈	C₂²×D₇₉	1	4	yes	—
194	C₂×C₄²	—	79	16	no	—
195	C₂×C₄²	—	79	2	no	—
196	C₂×C₄²	—	79	8	no	—
197	C₂×C₄²	—	79	4	no	—
198	C₂×C₄²	—	79	4	no	—
199	C₂×C₄²	—	79	2	no	—
200	C₂×C₄²	—	79	8	no	—
201	C₂×C₄²	—	79	2	no	—
202	C₂×C₄²	—	79	2	no	—
203	C₂×C₄²	—	158	8	no	—
204	C₂×C₄²	—	158	2	no	—
205	C₂×C₄²	—	158	2	no	—
206	C₂×C₄²	C₄×D₇₉	1	2	yes	—
207	C₂×C₄²	C₄×D₇₉	1	4	yes	—
208	C₂×C₄²	C₂×Dic₇₉	1	4	yes	—
209	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
210	C₄⋊C₈	—	79	16	no	—
211	C₄⋊C₈	C₂×Dic₇₉	1	16	yes	direct product factor
212	C₄×C₈	—	158	16	no	—
213	C₂⁴	C₂×C₄×D₇₉	1	1	yes	characteristic
214	C₂²×C₄	—	2	4	no	—
215	C₂²×C₄	—	79	8	no	—
216	C₂²×C₄	—	79	8	no	—
217	C₂²×C₄	—	79	8	no	—
218	C₂²×C₄	—	79	4	no	—
219	C₂²×C₄	—	79	8	no	—
220	C₂²×C₄	—	79	4	no	—
221	C₂²×C₄	—	158	4	no	—
222	C₂²×C₄	—	158	4	no	—
223	C₂²×C₄	C₄×Dic₇₉	1	4	yes	—
224	C₂²×C₄	C₄×Dic₇₉	1	4	yes	—
225	C₂²×C₄	C₈×D₇₉	1	8	yes	—
226	C₂²×C₄	C₂×C₄×D₇₉	1	2	yes	—
227	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
228	C₂²×C₄	C₂×C₄×D₇₉	1	2	yes	—
229	C₂²×C₄	C₂×C₄×D₇₉	1	2	yes	—
230	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
231	C₂²×C₄	D₄×D₇₉	1	2	yes	—
232	C₂²×C₄	Q₈×D₇₉	1	2	yes	—
233	C₂²×C₄	#11929623	1	2	yes	—
234	C₂²×C₄	#11929625	1	2	yes	—
235	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
236	C₂×C₈	—	2	4	no	—
237	C₂×C₈	—	2	16	no	—
238	C₂×C₈	—	2	4	no	—
239	C₂×C₈	—	79	8	no	—
240	C₂×C₈	—	158	4	no	—
241	C₂×C₈	—	158	16	no	—
242	C₂×C₈	—	158	4	no	—
243	C₂×C₈	C₂²×Dic₇₉	1	8	yes	—
244	C₄²	—	79	4	no	—
245	C₄²	—	79	8	no	—
246	C₄²	—	79	32	no	—
247	C₄²	—	79	4	no	—
248	C₄²	—	158	16	no	—
249	C₄²	—	158	2	no	—
250	C₄²	—	158	2	no	—
251	C₄²	—	158	4	no	—
252	C₄²	C₄×Dic₇₉	1	8	yes	—
253	C₄²	C₂×C₄×D₇₉	1	4	yes	—
254	C₄²	C₂²×Dic₇₉	1	4	yes	—
255	C₂³	C₂×C₄×Dic₇₉	1	2	yes	—
256	C₂³	C₄⋊C₄×D₇₉	1	2	yes	—
257	C₂³	#14579119	1	2	yes	—
258	C₂³	C₂×C₈×D₇₉	1	4	yes	—
259	C₂³	M₁₆×D₇₉	1	4	yes	—
260	C₂³	C₂²×C₄×D₇₉	1	1	yes	characteristic
261	C₂×C₄	—	2	8	no	—
262	C₂×C₄	—	2	4	no	—
263	C₂×C₄	—	79	8	no	—
264	C₂×C₄	—	79	8	no	—
265	C₂×C₄	—	79	8	no	—
266	C₂×C₄	—	79	32	no	—
267	C₂×C₄	—	79	8	no	—
268	C₂×C₄	—	158	4	no	—
269	C₂×C₄	—	158	4	no	—
270	C₂×C₄	—	158	16	no	—
271	C₂×C₄	C₈×Dic₇₉	1	16	yes	complemented
272	C₂×C₄	C₂×C₄×Dic₇₉	1	4	yes	—
273	C₂×C₄	C₂×C₄×Dic₇₉	1	2	yes	—
274	C₂×C₄	C₂×C₄×Dic₇₉	1	4	yes	—
275	C₂×C₄	C₄⋊C₄×D₇₉	1	2	yes	—
276	C₂×C₄	#14579119	1	2	yes	—
277	C₂×C₄	#14579123	1	4	yes	—
278	C₂×C₄	D₄×Dic₇₉	1	4	yes	—
279	C₂×C₄	#14579126	1	4	yes	—
280	C₂×C₄	Q₈×Dic₇₉	1	4	yes	—
281	C₂×C₄	C₂×C₈×D₇₉	1	8	yes	—
282	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
283	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
284	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
285	C₂×C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
286	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
287	C₂×C₄	C₂×#11929625	1	1	yes	characteristic
288	C₈	—	2	8	no	—
289	C₈	—	158	8	no	—
290	C₂²	C₄⋊C₄×Dic₇₉	1	4	yes	—
291	C₂²	C₂×C₈×Dic₇₉	1	4	yes	—
292	C₂²	M₁₆×Dic₇₉	1	4	yes	—
293	C₂²	C₄⋊C₈×D₇₉	1	8	yes	—
294	C₂²	#19098615	1	8	yes	—
295	C₂²	C₂²×C₄×Dic₇₉	1	1	yes	characteristic
296	C₂²	C₂×C₄⋊C₄×D₇₉	1	1	yes	characteristic
297	C₂²	C₂×#14579119	1	1	yes	characteristic
298	C₂²	C₂²×C₈×D₇₉	1	2	yes	—
299	C₂²	C₂×M₁₆×D₇₉	1	2	yes	—
300	C₄	—	2	4	no	—
301	C₄	—	79	16	no	—
302	C₄	—	158	8	no	—
303	C₄	C₄⋊C₄×Dic₇₉	1	4	yes	—
304	C₄	C₂×C₈×Dic₇₉	1	8	yes	complemented
305	C₄	C₂×#14579123	1	1	yes	characteristic
306	C₄	C₂×D₄×Dic₇₉	1	1	yes	characteristic
307	C₄	C₂×#14579126	1	1	yes	characteristic
308	C₄	C₂×Q₈×Dic₇₉	1	1	yes	characteristic
309	C₂	C₄⋊C₈×Dic₇₉	1	8	yes	direct product factor
310	C₂	C₂×C₄⋊C₄×Dic₇₉	1	1	yes	characteristic
311	C₂	C₂²×C₈×Dic₇₉	1	1	yes	characteristic
312	C₂	C₂×M₁₆×Dic₇₉	1	1	yes	characteristic
313	C₂	C₂×C₄⋊C₈×D₇₉	1	2	yes	—
314	C₂	C₂×#19098615	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
4. C₄⋊C₈×Dic₇₉	C₂	direct (N × H)
12. C₂×C₄⋊(C₇₉⋊C₈)	C₄	semidirect
21. C₂×C₄⋊C₈×C₇₉	C₄	semidirect
32. C₂×C₄×Dic₇₉	C₈	semidirect
41. C₄⋊(C₇₉⋊C₈)	C₂×C₄	semidirect
54. C₄⋊C₈×C₇₉	C₂×C₄	semidirect
72. C₄×Dic₇₉	C₂×C₈	semidirect
105. C₂×C₄×C₇₉	C₄×C₈	semidirect
125. C₂×Dic₇₉	C₄⋊C₈	direct (N × H)
144. C₄×C₇₉	C₂×C₄×C₈	semidirect
150. Dic₇₉	C₂×C₄⋊C₈	direct (N × H)
152. C₂×C₇₉	C₄×C₄⋊C₈	semidirect
164. C₇₉	C₂×C₄×C₄⋊C₈	semidirect
174. C₂×C₄⋊C₈	Dic₇₉	direct (N × H)
211. C₄⋊C₈	C₂×Dic₇₉	direct (N × H)
271. C₂×C₄	C₈×Dic₇₉	semidirect
304. C₄	C₂×C₈×Dic₇₉	semidirect
309. C₂	C₄⋊C₈×Dic₇₉	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×C₄⋊(C₇₉⋊C₈)	2
C₂²×C₈×Dic₇₉	2
C₂×C₄²×Dic₇₉	2
C₄⋊C₈×Dic₇₉	2
C₂×#19098317	2
C₂²×C₄⋊C₈×C₇₉	2
C₂×C₄×C₄⋊C₈	79

Subgroups — C2×C4⋊C8×Dic79 #34286142

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄⋊C₈×Dic₇₉ #34286142