Subgroups — C₂²⋊(C₇₉⋊C₆₄) #34176078

Order 20224.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇₉⋊C₆₄	C₂	1	2	yes	maximal, complemented
2	C₂²×C₃₂×C₇₉	C₂	1	1	yes	maximal, characteristic
3	C₇₉⋊C₆₄	—	2	2	no	—
4	C₂²×C₁₆×C₇₉	C₄	1	1	yes	characteristic
5	C₂×C₃₂×C₇₉	—	2	2	no	—
6	C₂×C₃₂×C₇₉	C₄	1	1	yes	characteristic
7	C₂×C₃₂×C₇₉	C₂²	1	1	yes	characteristic
8	C₂²×C₈×C₇₉	C₈	1	1	yes	characteristic
9	C₂×C₁₆×C₇₉	—	2	1	no	—
10	C₂×C₁₆×C₇₉	—	2	1	no	—
11	C₂×C₁₆×C₇₉	C₈	1	1	yes	characteristic
12	C₂×C₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
13	C₃₂×C₇₉	—	2	1	no	—
14	C₃₂×C₇₉	D₄	1	2	yes	—
15	C₂²×C₄×C₇₉	C₁₆	1	1	yes	characteristic
16	C₂×C₈×C₇₉	—	2	1	no	—
17	C₂×C₈×C₇₉	—	2	1	no	—
18	C₂×C₈×C₇₉	C₁₆	1	1	yes	characteristic
19	C₂×C₈×C₇₉	C₂×C₈	1	1	yes	characteristic
20	C₁₆×C₇₉	—	2	1	no	—
21	C₁₆×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
22	C₁₆×C₇₉	M₁₆	1	1	yes	characteristic
23	C₂³×C₇₉	C₃₂	1	1	yes	characteristic
24	C₂×C₄×C₇₉	—	2	1	no	—
25	C₂×C₄×C₇₉	—	2	1	no	—
26	C₂×C₄×C₇₉	C₃₂	1	1	yes	characteristic
27	C₂×C₄×C₇₉	C₂×C₁₆	1	1	yes	characteristic
28	C₈×C₇₉	—	2	1	no	—
29	C₈×C₇₉	C₂²⋊C₈	1	1	yes	characteristic
30	C₈×C₇₉	M₃₂	1	1	yes	characteristic
31	C₂²×C₇₉	—	2	1	no	—
32	C₂²×C₇₉	—	2	1	no	—
33	C₂²×C₇₉	C₆₄	1	2	yes	complemented
34	C₂²×C₇₉	C₂×C₃₂	1	1	yes	characteristic
35	C₄×C₇₉	—	2	1	no	—
36	C₄×C₇₉	C₂²⋊C₁₆	1	1	yes	characteristic
37	C₄×C₇₉	M₆₄	1	1	yes	characteristic
38	C₂²⋊C₆₄	—	79	1	no	maximal, Sylow
39	C₂×C₇₉	—	2	2	no	—
40	C₂×C₇₉	C₂²⋊C₃₂	1	1	yes	characteristic
41	C₂×C₇₉	C₂×C₆₄	1	1	yes	characteristic
42	C₂×C₇₉	M₁₂₈	1	1	yes	characteristic
43	C₂²×C₃₂	D₇₉	1	1	yes	characteristic
44	C₂×C₆₄	—	79	2	no	—
45	C₇₉	C₂²⋊C₆₄	1	1	yes	characteristic, complemented, Sylow
46	C₂²×C₁₆	Dic₇₉	1	1	yes	characteristic
47	C₂×C₃₂	—	2	2	no	—
48	C₂×C₃₂	Dic₇₉	1	1	yes	characteristic
49	C₂×C₃₂	C₂×D₇₉	1	1	yes	characteristic
50	C₆₄	—	158	2	no	—
51	C₂²×C₈	C₇₉⋊C₈	1	1	yes	characteristic
52	C₂×C₁₆	—	2	1	no	—
53	C₂×C₁₆	—	2	1	no	—
54	C₂×C₁₆	C₇₉⋊C₈	1	1	yes	characteristic
55	C₂×C₁₆	C₂×Dic₇₉	1	1	yes	characteristic
56	C₃₂	—	2	1	no	—
57	C₃₂	C₂²⋊D₇₉	1	2	yes	—
58	C₂²×C₄	C₇₉⋊C₁₆	1	1	yes	characteristic
59	C₂×C₈	—	2	1	no	—
60	C₂×C₈	—	2	1	no	—
61	C₂×C₈	C₇₉⋊C₁₆	1	1	yes	characteristic
62	C₂×C₈	C₂×C₇₉⋊C₈	1	1	yes	characteristic
63	C₁₆	—	2	1	no	—
64	C₁₆	C₂²⋊Dic₇₉	1	1	yes	characteristic
65	C₁₆	#11929608	1	1	yes	characteristic
66	C₂³	C₇₉⋊C₃₂	1	1	yes	characteristic
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	C₇₉⋊C₃₂	1	1	yes	characteristic
70	C₂×C₄	C₂×C₇₉⋊C₁₆	1	1	yes	characteristic
71	C₈	—	2	1	no	—
72	C₈	C₂²⋊(C₇₉⋊C₈)	1	1	yes	characteristic
73	C₈	#14579101	1	1	yes	characteristic
74	C₂²	—	2	1	no	—
75	C₂²	—	2	1	no	—
76	C₂²	C₇₉⋊C₆₄	1	2	yes	complemented
77	C₂²	C₂×C₇₉⋊C₃₂	1	1	yes	characteristic
78	C₄	—	2	1	no	—
79	C₄	C₂²⋊(C₇₉⋊C₁₆)	1	1	yes	characteristic
80	C₄	#19098397	1	1	yes	characteristic
81	C₂	—	2	2	no	—
82	C₂	C₂²⋊(C₇₉⋊C₃₂)	1	1	yes	characteristic
83	C₂	C₂×C₇₉⋊C₆₄	1	1	yes	characteristic
84	C₂	#23761611	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₃₂	C₂×D₇₉
commutator	C₂×C₇₉	C₂×C₆₄
Fitting	C₂²×C₃₂×C₇₉	C₂
socle	C₂²×C₇₉	C₂×C₃₂
prime radical	C₂³×C₇₉	C₃₂
cosocle	C₂×C₃₂×C₇₉	C₂²
hypercenter	C₂²×C₃₂	D₇₉
hypocenter	C₇₉	C₂²⋊C₆₄
LCS	G ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₃₂ ◁ C₂²×C₃₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₇₉⋊C₆₄	C₂	semidirect
33. C₂²×C₇₉	C₆₄	semidirect
45. C₇₉	C₂²⋊C₆₄	semidirect
76. C₂²	C₇₉⋊C₆₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇₉⋊C₆₄	2
C₂²×C₃₂×C₇₉	2
C₂²⋊C₆₄	79

Subgroups — C22⋊(C79⋊C64) #34176078

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊(C₇₉⋊C₆₄) #34176078