Group #23762923 — subgroups

Subgroups — #23762923

Order 10112.

154 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 57 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	#19098968	C₂	1	1	yes	maximal, characteristic, complemented
2	#19098853	C₂	1	2	yes	maximal
3	#19098314	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098311	C₂	1	2	yes	maximal, complemented
5	#436×C₇₉	C₂	1	1	yes	maximal, characteristic
6	#14579161	C₂²	1	2	yes	—
7	#14579095	—	2	1	no	—
8	#14579095	—	2	1	no	—
9	#14579092	—	2	2	no	—
10	C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
11	#14579082	—	2	2	no	—
12	C₂×M₁₆×C₇₉	—	2	1	no	—
13	C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
14	C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
15	C₂²⋊C₈×C₇₉	—	2	1	no	—
16	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×Dic₁₅₈	—	2	2	no	—
18	C₂×C₇₉⋊C₈	—	2	2	no	—
19	C₄⋊Dic₇₉	—	2	2	no	—
20	C₄⋊Dic₇₉	—	2	2	no	—
21	C₂×D₄×C₇₉	D₄	1	1	yes	characteristic
22	C₂²×C₄×C₇₉	—	2	1	no	—
23	M₁₆×C₇₉	—	4	2	no	—
24	C₂×C₈×C₇₉	—	2	1	no	—
25	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
26	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
27	C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
28	C₂²⋊C₄×C₇₉	—	2	1	no	—
29	C₄²×C₇₉	C₂³	1	1	yes	characteristic
30	C₂³×C₇₉	—	2	1	no	—
31	D₄×C₇₉	—	2	2	no	—
32	C₂×C₄×C₇₉	—	2	1	no	—
33	C₂×C₄×C₇₉	—	4	1	no	—
34	C₂×C₄×C₇₉	—	4	1	no	—
35	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
38	C₂×Dic₇₉	—	4	2	no	—
39	Dic₁₅₈	—	8	2	no	—
40	C₈×C₇₉	—	2	1	no	—
41	C₈×C₇₉	—	4	1	no	—
42	C₈×C₇₉	SD₁₆	1	2	yes	—
43	C₇₉⋊C₈	—	4	2	no	—
44	C₂²×C₇₉	—	4	1	no	—
45	C₂²×C₇₉	—	4	1	no	—
46	C₂²×C₇₉	—	4	1	no	—
47	C₂²×C₇₉	#121	1	1	yes	characteristic
48	C₄×C₇₉	—	2	1	no	—
49	C₄×C₇₉	—	4	1	no	—
50	C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
51	C₄×C₇₉	#137	1	1	yes	characteristic
52	C₄×C₇₉	#137	1	2	yes	—
53	Dic₇₉	—	8	2	no	—
54	C₂×C₇₉	—	8	1	no	—
55	C₂×C₇₉	#461	1	1	yes	characteristic
56	C₂×C₇₉	#470	1	1	yes	characteristic
57	C₂×C₇₉	#472	1	1	yes	characteristic
58	#1695	—	79	1	no	maximal, Sylow
59	C₇₉	#1695	1	1	yes	characteristic, complemented, Sylow
60	#500	—	79	1	no	—
61	#476	—	79	2	no	—
62	#436	D₇₉	1	1	yes	characteristic
63	#334	—	79	1	no	—
64	#333	—	79	2	no	—
65	C₂×M₁₆	—	2	1	no	—
66	C₄⋊Q₈	—	79	2	no	—
67	C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
68	#107	—	158	1	no	—
69	#107	—	158	1	no	—
70	#106	—	158	2	no	—
71	C₄⋊C₈	—	79	2	no	—
72	C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
73	#102	—	158	2	no	—
74	C₂²⋊C₈	—	2	1	no	—
75	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
76	C₂×Q₈	—	158	2	no	—
77	C₂×D₄	D₃₁₆	1	1	yes	characteristic
78	C₂²×C₄	—	2	1	no	—
79	M₁₆	—	4	2	no	—
80	C₂×C₈	—	2	1	no	—
81	C₂×C₈	—	158	2	no	—
82	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
83	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
84	C₄⋊C₄	—	158	2	no	—
85	C₄⋊C₄	—	158	2	no	—
86	C₄⋊C₄	D₃₁₆	1	1	yes	characteristic
87	C₂²⋊C₄	—	2	1	no	—
88	C₄²	C₂²×D₇₉	1	1	yes	characteristic
89	C₂³	—	2	1	no	—
90	Q₈	—	632	2	no	—
91	D₄	—	2	2	no	—
92	C₂×C₄	—	2	1	no	—
93	C₂×C₄	—	4	1	no	—
94	C₂×C₄	—	4	1	no	—
95	C₂×C₄	—	316	2	no	—
96	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
97	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
98	C₂×C₄	#11929624	1	1	yes	characteristic
99	C₈	—	2	1	no	—
100	C₈	—	4	1	no	—
101	C₈	—	316	2	no	—
102	C₈	#11929612	1	2	yes	—
103	C₂²	—	4	1	no	—
104	C₂²	—	4	1	no	—
105	C₂²	—	4	1	no	—
106	C₂²	#14579135	1	1	yes	characteristic
107	C₄	—	2	1	no	—
108	C₄	—	4	1	no	—
109	C₄	—	632	2	no	—
110	C₄	C₂×#11929612	1	1	yes	characteristic
111	C₄	#14579191	1	1	yes	characteristic
112	C₄	#14579194	1	2	yes	—
113	C₂	—	8	1	no	—
114	C₂	#19098768	1	1	yes	characteristic
115	C₂	#19098821	1	1	yes	characteristic
116	C₂	#19098833	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098968

C₂

yes

maximal, characteristic, complemented

#19098853

C₂

yes

maximal

#19098314

C₂

yes

maximal, characteristic, complemented

#19098311

C₂

yes

maximal, complemented

#436×C₇₉

C₂

yes

maximal, characteristic

#14579161

C₂²

yes

—

#14579095

—

#14579095

—

#14579092

—

C₄⋊(C₇₉⋊C₈)

C₂²

yes

—

#14579082

—

C₂×M₁₆×C₇₉

—

C₄×D₄×C₇₉

C₂²

yes

characteristic

C₄⋊C₈×C₇₉

C₂²

yes

characteristic

C₂²⋊C₈×C₇₉

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₂×D₄×C₇₉

D₄

yes

characteristic

C₂²×C₄×C₇₉

—

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

D₄

yes

characteristic

C₄⋊C₄×C₇₉

D₄

yes

characteristic

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

C₂³

yes

characteristic

C₂³×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

#41

yes

characteristic

C₂×Dic₇₉

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

SD₁₆

yes

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#121

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂×SD₁₆

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

#500

—

#476

—

#436

D₇₉

yes

characteristic

#334

—

#333

—

C₂×M₁₆

—

C₄⋊Q₈

—

C₄×D₄

C₂×D₇₉

yes

characteristic

#107

—

158

—

#107

—

158

—

#106

—

158

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₇₉

yes

characteristic

#102

—

158

—

C₂²⋊C₈

—

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂×Q₈

—

158

—

C₂×D₄

D₃₁₆

yes

characteristic

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

C₂²⋊D₇₉

yes

characteristic

C₂×C₈

C₂²⋊D₇₉

yes

characteristic

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄⋊C₄

D₃₁₆

yes

characteristic

C₂²⋊C₄

—

C₄²

C₂²×D₇₉

yes

characteristic

C₂³

—

Q₈

—

632

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

316

—

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

C₂×C₄

C₂×D₃₁₆

yes

characteristic

C₂×C₄

#11929624

yes

characteristic

C₈

—

100

C₈

—

101

C₈

—

316

—

102

C₈

#11929612

yes

—

103

C₂²

—

104

C₂²

—

105

C₂²

—

106

C₂²

#14579135

yes

characteristic

107

C₄

—

108

C₄

—

109

C₄

—

632

—

110

C₄

C₂×#11929612

yes

characteristic

111

C₄

#14579191

yes

characteristic

112

C₄

#14579194

yes

—

113

C₂

—

114

C₂

#19098768

yes

characteristic

115

C₂

#19098821

yes

characteristic

116

C₂

#19098833

yes

characteristic

	subgroup	G/H
center	C₂²	#14579135
commutator, cosocle	C₄²×C₇₉	C₂³
Frattini	C₄²	C₂²×D₇₉
Fitting	#436×C₇₉	C₂
socle	C₂²×C₇₉	#121
prime radical	C₂×D₄×C₇₉	D₄
hypercenter	#436	D₇₉
hypocenter	C₇₉	#1695
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #436

subgroup

G/H

center

C₂²

#14579135

commutator, cosocle

C₄²×C₇₉

C₂³

Frattini

C₄²

C₂²×D₇₉

Fitting

#436×C₇₉

C₂

socle

C₂²×C₇₉

#121

prime radical

C₂×D₄×C₇₉

D₄

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #436

N	H ≅ G/N	type
1. #19098968	C₂	semidirect
3. #19098314	C₂	semidirect
4. #19098311	C₂	semidirect
59. C₇₉	#1695	semidirect

H ≅ G/N

type

1. #19098968

C₂

semidirect

3. #19098314

C₂

semidirect

4. #19098311

C₂

semidirect

59. C₇₉

#1695

semidirect

Subgroups — #23762923

Conjugacy classes of subgroups

Complements