Group #34446382 — subgroups

Subgroups — #34446382

Order 20224.

462 conjugacy classes of subgroups; only the 391 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 391 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23765694	C₂	1	8	yes	maximal, complemented
2	C₂×#19098397	C₂	1	6	yes	maximal, complemented
3	C₂×#504×C₇₉	C₂	1	1	yes	maximal, characteristic
4	#19098397	C₂²	1	4	yes	—
5	#19098397	C₂²	1	12	yes	complemented
6	C₂×C₇₉⋊C₃₂	C₂²	1	12	yes	complemented
7	C₂×#131×C₇₉	C₄	1	1	yes	characteristic
8	#504×C₇₉	C₄	1	4	yes	—
9	#504×C₇₉	C₂²	1	4	yes	—
10	C₂×M₃₂×C₇₉	C₄	1	3	yes	—
11	C₂²×C₁₆×C₇₉	C₂²	1	3	yes	—
12	C₇₉⋊C₃₂	C₂³	1	8	yes	—
13	C₂×#41×C₇₉	C₈	1	1	yes	characteristic
14	#131×C₇₉	C₈	1	4	yes	—
15	#131×C₇₉	C₂×C₄	1	4	yes	—
16	C₂×M₁₆×C₇₉	C₈	1	3	yes	—
17	C₂²×C₈×C₇₉	C₂×C₄	1	3	yes	—
18	M₃₂×C₇₉	C₂×C₄	1	12	yes	—
19	C₂×C₁₆×C₇₉	C₂×C₄	1	3	yes	—
20	C₂×C₁₆×C₇₉	C₂×C₄	1	6	yes	—
21	C₂×C₁₆×C₇₉	C₂³	1	6	yes	—
22	C₂×C₁₆×C₇₉	C₂³	1	1	yes	characteristic
23	#41×C₇₉	C₁₆	1	4	yes	—
24	#41×C₇₉	C₂×C₈	1	4	yes	—
25	C₂×Q₈×C₇₉	C₁₆	1	1	yes	characteristic
26	C₂×D₄×C₇₉	C₁₆	1	3	yes	—
27	C₂²×C₄×C₇₉	C₂×C₈	1	3	yes	—
28	M₁₆×C₇₉	C₂×C₈	1	12	yes	—
29	C₂×C₈×C₇₉	C₂×C₈	1	3	yes	—
30	C₂×C₈×C₇₉	C₂×C₈	1	6	yes	—
31	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₈×C₇₉	C₂²×C₄	1	6	yes	—
33	C₁₆×C₇₉	C₂²×C₄	1	1	yes	characteristic
34	C₁₆×C₇₉	C₂²×C₄	1	6	yes	—
35	C₁₆×C₇₉	C₂⁴	1	1	yes	characteristic
36	C₂³×C₇₉	C₂×C₁₆	1	3	yes	—
37	Q₈×C₇₉	C₂×C₁₆	1	4	yes	—
38	D₄×C₇₉	C₂×C₁₆	1	12	yes	—
39	C₂×C₄×C₇₉	C₂×C₁₆	1	3	yes	—
40	C₂×C₄×C₇₉	C₂×C₁₆	1	6	yes	—
41	C₂×C₄×C₇₉	C₂²×C₈	1	1	yes	characteristic
42	C₂×C₄×C₇₉	C₂²×C₈	1	6	yes	—
43	C₈×C₇₉	C₂²×C₈	1	1	yes	characteristic
44	C₈×C₇₉	C₂²×C₈	1	6	yes	—
45	C₈×C₇₉	C₂³×C₄	1	1	yes	characteristic
46	C₂²×C₇₉	—	4	3	no	—
47	C₂²×C₇₉	C₂²×C₁₆	1	1	yes	characteristic
48	C₂²×C₇₉	C₂²×C₁₆	1	6	yes	—
49	C₄×C₇₉	C₂²×C₁₆	1	1	yes	characteristic
50	C₄×C₇₉	C₂²×C₁₆	1	6	yes	—
51	C₄×C₇₉	C₂³×C₈	1	1	yes	characteristic
52	#33974	—	79	1	no	maximal, Sylow
53	C₂×C₇₉	—	2	1	no	—
54	C₂×C₇₉	—	2	6	no	—
55	C₂×C₇₉	C₂³×C₁₆	1	1	yes	characteristic
56	C₂×#504	D₇₉	1	1	yes	characteristic
57	#2258	—	79	8	no	—
58	C₂×M₆₄	—	79	6	no	—
59	C₇₉	#33974	1	1	yes	characteristic, complemented, Sylow
60	C₂×#131	Dic₇₉	1	1	yes	characteristic
61	#504	Dic₇₉	1	4	yes	—
62	#504	C₂×D₇₉	1	4	yes	—
63	C₂×M₃₂	Dic₇₉	1	3	yes	—
64	C₂²×C₁₆	C₂×D₇₉	1	3	yes	—
65	M₆₄	—	79	4	no	—
66	M₆₄	—	79	12	no	—
67	C₂×C₃₂	—	79	12	no	—
68	C₂×#41	C₇₉⋊C₈	1	1	yes	characteristic
69	#131	C₇₉⋊C₈	1	4	yes	—
70	#131	C₂×Dic₇₉	1	4	yes	—
71	C₂×M₁₆	C₇₉⋊C₈	1	3	yes	—
72	C₂²×C₈	C₂×Dic₇₉	1	3	yes	—
73	M₃₂	C₂×Dic₇₉	1	12	yes	—
74	C₂×C₁₆	C₂×Dic₇₉	1	3	yes	—
75	C₂×C₁₆	C₂×Dic₇₉	1	6	yes	—
76	C₂×C₁₆	C₂²×D₇₉	1	6	yes	—
77	C₂×C₁₆	C₂²×D₇₉	1	1	yes	characteristic
78	C₃₂	—	79	8	no	—
79	#41	C₇₉⋊C₁₆	1	4	yes	—
80	#41	C₂×C₇₉⋊C₈	1	4	yes	—
81	C₂×Q₈	C₇₉⋊C₁₆	1	1	yes	characteristic
82	C₂×D₄	C₇₉⋊C₁₆	1	3	yes	—
83	C₂²×C₄	C₂×C₇₉⋊C₈	1	3	yes	—
84	M₁₆	C₂×C₇₉⋊C₈	1	12	yes	—
85	C₂×C₈	C₂×C₇₉⋊C₈	1	3	yes	—
86	C₂×C₈	C₂×C₇₉⋊C₈	1	6	yes	—
87	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
88	C₂×C₈	C₂²×Dic₇₉	1	6	yes	—
89	C₁₆	C₂²×Dic₇₉	1	1	yes	characteristic
90	C₁₆	C₂²×Dic₇₉	1	6	yes	—
91	C₁₆	C₂³×D₇₉	1	1	yes	characteristic
92	C₂³	C₂×C₇₉⋊C₁₆	1	3	yes	—
93	Q₈	C₂×C₇₉⋊C₁₆	1	4	yes	—
94	D₄	C₂×C₇₉⋊C₁₆	1	12	yes	—
95	C₂×C₄	C₂×C₇₉⋊C₁₆	1	3	yes	—
96	C₂×C₄	C₂×C₇₉⋊C₁₆	1	6	yes	—
97	C₂×C₄	C₂²×C₇₉⋊C₈	1	1	yes	characteristic
98	C₂×C₄	C₂²×C₇₉⋊C₈	1	6	yes	—
99	C₈	C₂²×C₇₉⋊C₈	1	1	yes	characteristic
100	C₈	C₂²×C₇₉⋊C₈	1	6	yes	—
101	C₈	C₂³×Dic₇₉	1	1	yes	characteristic
102	C₂²	—	4	3	no	—
103	C₂²	C₂²×C₇₉⋊C₁₆	1	1	yes	characteristic
104	C₂²	C₂²×C₇₉⋊C₁₆	1	6	yes	—
105	C₄	C₂²×C₇₉⋊C₁₆	1	1	yes	characteristic
106	C₄	C₂²×C₇₉⋊C₁₆	1	6	yes	—
107	C₄	C₂³×C₇₉⋊C₈	1	1	yes	characteristic
108	C₂	—	2	1	no	—
109	C₂	—	2	6	no	—
110	C₂	C₂³×C₇₉⋊C₁₆	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23765694

C₂

yes

maximal, complemented

C₂×#19098397

C₂

yes

maximal, complemented

C₂×#504×C₇₉

C₂

yes

maximal, characteristic

#19098397

C₂²

yes

—

#19098397

C₂²

yes

complemented

C₂×C₇₉⋊C₃₂

C₂²

yes

complemented

C₂×#131×C₇₉

C₄

yes

characteristic

#504×C₇₉

C₄

yes

—

#504×C₇₉

C₂²

yes

—

C₂×M₃₂×C₇₉

C₄

yes

—

C₂²×C₁₆×C₇₉

C₂²

yes

—

C₇₉⋊C₃₂

C₂³

yes

—

C₂×#41×C₇₉

C₈

yes

characteristic

#131×C₇₉

C₈

yes

—

#131×C₇₉

C₂×C₄

yes

—

C₂×M₁₆×C₇₉

C₈

yes

—

C₂²×C₈×C₇₉

C₂×C₄

yes

—

M₃₂×C₇₉

C₂×C₄

yes

—

C₂×C₁₆×C₇₉

C₂×C₄

yes

—

C₂×C₁₆×C₇₉

C₂×C₄

yes

—

C₂×C₁₆×C₇₉

C₂³

yes

—

C₂×C₁₆×C₇₉

C₂³

yes

characteristic

#41×C₇₉

C₁₆

yes

—

#41×C₇₉

C₂×C₈

yes

—

C₂×Q₈×C₇₉

C₁₆

yes

characteristic

C₂×D₄×C₇₉

C₁₆

yes

—

C₂²×C₄×C₇₉

C₂×C₈

yes

—

M₁₆×C₇₉

C₂×C₈

yes

—

C₂×C₈×C₇₉

C₂×C₈

yes

—

C₂×C₈×C₇₉

C₂×C₈

yes

—

C₂×C₈×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₉

C₂²×C₄

yes

—

C₁₆×C₇₉

C₂²×C₄

yes

characteristic

C₁₆×C₇₉

C₂²×C₄

yes

—

C₁₆×C₇₉

C₂⁴

yes

characteristic

C₂³×C₇₉

C₂×C₁₆

yes

—

Q₈×C₇₉

C₂×C₁₆

yes

—

D₄×C₇₉

C₂×C₁₆

yes

—

C₂×C₄×C₇₉

C₂×C₁₆

yes

—

C₂×C₄×C₇₉

C₂×C₁₆

yes

—

C₂×C₄×C₇₉

C₂²×C₈

yes

characteristic

C₂×C₄×C₇₉

C₂²×C₈

yes

—

C₈×C₇₉

C₂²×C₈

yes

characteristic

C₈×C₇₉

C₂²×C₈

yes

—

C₈×C₇₉

C₂³×C₄

yes

characteristic

C₂²×C₇₉

—

C₂²×C₇₉

C₂²×C₁₆

yes

characteristic

C₂²×C₇₉

C₂²×C₁₆

yes

—

C₄×C₇₉

C₂²×C₁₆

yes

characteristic

C₄×C₇₉

C₂²×C₁₆

yes

—

C₄×C₇₉

C₂³×C₈

yes

characteristic

#33974

—

maximal, Sylow

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

C₂³×C₁₆

yes

characteristic

C₂×#504

D₇₉

yes

characteristic

#2258

—

C₂×M₆₄

—

C₇₉

#33974

yes

characteristic, complemented, Sylow

C₂×#131

Dic₇₉

yes

characteristic

#504

Dic₇₉

yes

—

#504

C₂×D₇₉

yes

—

C₂×M₃₂

Dic₇₉

yes

—

C₂²×C₁₆

C₂×D₇₉

yes

—

M₆₄

—

M₆₄

—

C₂×C₃₂

—

C₂×#41

C₇₉⋊C₈

yes

characteristic

#131

C₇₉⋊C₈

yes

—

#131

C₂×Dic₇₉

yes

—

C₂×M₁₆

C₇₉⋊C₈

yes

—

C₂²×C₈

C₂×Dic₇₉

yes

—

M₃₂

C₂×Dic₇₉

yes

—

C₂×C₁₆

C₂×Dic₇₉

yes

—

C₂×C₁₆

C₂×Dic₇₉

yes

—

C₂×C₁₆

C₂²×D₇₉

yes

—

C₂×C₁₆

C₂²×D₇₉

yes

characteristic

C₃₂

—

#41

C₇₉⋊C₁₆

yes

—

#41

C₂×C₇₉⋊C₈

yes

—

C₂×Q₈

C₇₉⋊C₁₆

yes

characteristic

C₂×D₄

C₇₉⋊C₁₆

yes

—

C₂²×C₄

C₂×C₇₉⋊C₈

yes

—

M₁₆

C₂×C₇₉⋊C₈

yes

—

C₂×C₈

C₂×C₇₉⋊C₈

yes

—

C₂×C₈

C₂×C₇₉⋊C₈

yes

—

C₂×C₈

C₂²×Dic₇₉

yes

characteristic

C₂×C₈

C₂²×Dic₇₉

yes

—

C₁₆

C₂²×Dic₇₉

yes

characteristic

C₁₆

C₂²×Dic₇₉

yes

—

C₁₆

C₂³×D₇₉

yes

characteristic

C₂³

C₂×C₇₉⋊C₁₆

yes

—

Q₈

C₂×C₇₉⋊C₁₆

yes

—

D₄

C₂×C₇₉⋊C₁₆

yes

—

C₂×C₄

C₂×C₇₉⋊C₁₆

yes

—

C₂×C₄

C₂×C₇₉⋊C₁₆

yes

—

C₂×C₄

C₂²×C₇₉⋊C₈

yes

characteristic

C₂×C₄

C₂²×C₇₉⋊C₈

yes

—

C₈

C₂²×C₇₉⋊C₈

yes

characteristic

100

C₈

C₂²×C₇₉⋊C₈

yes

—

101

C₈

C₂³×Dic₇₉

yes

characteristic

102

C₂²

—

103

C₂²

C₂²×C₇₉⋊C₁₆

yes

characteristic

104

C₂²

C₂²×C₇₉⋊C₁₆

yes

—

105

C₄

C₂²×C₇₉⋊C₁₆

yes

characteristic

106

C₄

C₂²×C₇₉⋊C₁₆

yes

—

107

C₄

C₂³×C₇₉⋊C₈

yes

characteristic

108

C₂

—

109

C₂

—

110

C₂

C₂³×C₇₉⋊C₁₆

yes

characteristic

	subgroup	G/H
center, Frattini	C₁₆	C₂³×D₇₉
commutator, socle	C₂×C₇₉	C₂³×C₁₆
Fitting	C₂×#504×C₇₉	C₂
prime radical	C₂×#41×C₇₉	C₈
cosocle	C₁₆×C₇₉	C₂⁴
hypercenter	C₂×#504	D₇₉
hypocenter	C₇₉	#33974
LCS	G ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₁₆ ◁ C₂×#504

subgroup

G/H

center, Frattini

C₁₆

C₂³×D₇₉

commutator, socle

C₂×C₇₉

C₂³×C₁₆

Fitting

C₂×#504×C₇₉

C₂

prime radical

C₂×#41×C₇₉

C₈

cosocle

C₁₆×C₇₉

C₂⁴

D₇₉

C₇₉

G ▷ C₂×C₇₉ ▷ C₇₉

C₁ ◁ C₁₆ ◁ C₂×#504

N	H ≅ G/N	type
1. #23765694	C₂	semidirect
2. C₂×#19098397	C₂	semidirect
5. #19098397	C₂²	semidirect
6. C₂×C₇₉⋊C₃₂	C₂²	semidirect
59. C₇₉	#33974	semidirect

H ≅ G/N

type

1. #23765694

C₂

semidirect

2. C₂×#19098397

C₂

semidirect

5. #19098397

C₂²

semidirect

6. C₂×C₇₉⋊C₃₂

C₂²

semidirect

59. C₇₉

#33974

semidirect

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

subgroup	index
#23765694	2
C₂×#19098397	2
C₂×#504×C₇₉	2
#33974	79

subgroup

index

#23765694

C₂×#19098397

C₂×#504×C₇₉

#33974

Subgroups — #34446382

Conjugacy classes of subgroups

Complements

Maximal subgroups