Group #23762890 — subgroups

Subgroups — #23762890

Order 10112.

166 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 55 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	#19098943	C₂	1	1	yes	maximal, characteristic, complemented
2	#19098844	C₂	1	2	yes	maximal
3	#19098642	C₂	1	1	yes	maximal, characteristic
4	#19098308	C₂	1	2	yes	maximal, complemented
5	#334×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₃₁₆	—	2	1	no	—
7	C₂×Dic₃₁₆	—	2	1	no	—
8	C₂×#11929607	—	2	1	no	—
9	#14579161	C₂²	1	2	yes	—
10	C₄×D₃₁₆	C₂²	1	1	yes	characteristic
11	#14579095	—	2	2	no	—
12	C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
13	#14579083	—	2	2	no	—
14	(C₂×D₇₉)⋊C₈	—	2	1	no	—
15	C₄⋊C₈×C₇₉	C₂²	1	2	yes	—
16	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×Dic₁₅₈	—	2	2	no	—
18	C₂×D₃₁₆	D₄	1	1	yes	characteristic
19	C₂×C₄×D₇₉	—	2	1	no	—
20	Dic₃₁₆	—	4	2	no	—
21	Dic₃₁₆	—	4	2	no	—
22	#11929607	—	4	2	no	—
23	C₂×C₇₉⋊C₈	—	2	1	no	—
24	C₄⋊Dic₇₉	—	2	2	no	—
25	C₄⋊Dic₇₉	—	2	2	no	—
26	C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
27	(C₂×D₇₉)⋊C₄	—	2	1	no	—
28	C₂×C₈×C₇₉	—	2	2	no	—
29	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
30	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
31	C₄²×C₇₉	C₂³	1	1	yes	characteristic
32	C₂²×D₇₉	—	2	1	no	—
33	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
36	C₂×Dic₇₉	—	2	1	no	—
37	C₂×Dic₇₉	—	4	2	no	—
38	D₃₁₆	—	2	2	no	—
39	C₄×D₇₉	—	4	1	no	—
40	C₄×D₇₉	—	4	1	no	—
41	Dic₁₅₈	—	4	2	no	—
42	Dic₁₅₈	—	4	2	no	—
43	C₈×C₇₉	—	2	1	no	—
44	C₈×C₇₉	—	4	2	no	—
45	C₈×C₇₉	D₈	1	2	yes	—
46	C₇₉⋊C₈	—	4	1	no	—
47	C₂²×C₇₉	#121	1	1	yes	characteristic
48	C₂×D₇₉	—	4	1	no	—
49	C₂×D₇₉	—	4	1	no	—
50	C₂×D₇₉	—	4	1	no	—
51	C₄×C₇₉	—	2	1	no	—
52	C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
53	C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
54	C₄×C₇₉	#137	1	2	yes	—
55	Dic₇₉	—	4	1	no	—
56	Dic₇₉	—	8	2	no	—
57	C₂×C₇₉	#459	1	1	yes	characteristic
58	C₂×C₇₉	#470	1	1	yes	characteristic
59	C₂×C₇₉	#473	1	1	yes	characteristic
60	D₇₉	—	8	1	no	—
61	#1689	—	79	1	no	maximal, Sylow
62	C₇₉	#1689	1	1	yes	characteristic, complemented, Sylow
63	#494	—	79	1	no	—
64	#474	—	79	2	no	—
65	#436	—	79	1	no	—
66	#334	D₇₉	1	1	yes	characteristic, complemented
67	#332	—	79	2	no	—
68	C₂×Q₁₆	—	158	1	no	—
69	C₂×Q₁₆	—	158	1	no	—
70	C₂×M₁₆	—	158	1	no	—
71	C₄⋊Q₈	—	79	2	no	—
72	C₄×D₄	—	79	1	no	—
73	#107	—	158	2	no	—
74	C₄⋊C₈	—	79	1	no	—
75	C₄⋊C₈	C₂×D₇₉	1	2	yes	—
76	#102	—	158	2	no	—
77	C₂²⋊C₈	—	158	1	no	—
78	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
79	C₂×Q₈	—	158	2	no	—
80	C₂×D₄	—	79	1	no	—
81	C₂²×C₄	—	158	1	no	—
82	Q₁₆	—	316	2	no	—
83	Q₁₆	—	316	2	no	—
84	M₁₆	—	316	2	no	—
85	C₂×C₈	—	2	2	no	—
86	C₂×C₈	—	158	1	no	—
87	C₂×C₈	D₃₁₆	1	1	yes	characteristic
88	C₂×C₈	D₃₁₆	1	1	yes	characteristic
89	C₄⋊C₄	—	79	1	no	—
90	C₄⋊C₄	—	158	2	no	—
91	C₄⋊C₄	—	158	2	no	—
92	C₂²⋊C₄	—	158	1	no	—
93	C₄²	C₂²×D₇₉	1	1	yes	characteristic
94	C₂³	—	158	1	no	—
95	Q₈	—	316	2	no	—
96	Q₈	—	316	2	no	—
97	D₄	—	158	2	no	—
98	C₂×C₄	—	316	1	no	—
99	C₂×C₄	—	316	1	no	—
100	C₂×C₄	—	316	2	no	—
101	C₂×C₄	—	158	1	no	—
102	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
103	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
104	C₂×C₄	#11929625	1	1	yes	characteristic
105	C₈	—	2	1	no	—
106	C₈	—	4	2	no	—
107	C₈	—	316	1	no	—
108	C₈	D₆₃₂	1	2	yes	—
109	C₂²	—	316	1	no	—
110	C₂²	—	316	1	no	—
111	C₂²	—	316	1	no	—
112	C₂²	#14579136	1	1	yes	characteristic
113	C₄	—	2	1	no	—
114	C₄	—	316	1	no	—
115	C₄	—	632	2	no	—
116	C₄	C₂×D₆₃₂	1	1	yes	characteristic
117	C₄	#14579189	1	1	yes	characteristic
118	C₄	#14579190	1	2	yes	—
119	C₂	—	632	1	no	—
120	C₂	#19098759	1	1	yes	characteristic
121	C₂	#19098822	1	1	yes	characteristic
122	C₂	#19098839	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098943

C₂

yes

maximal, characteristic, complemented

#19098844

C₂

yes

maximal

#19098642

C₂

yes

maximal, characteristic

#19098308

C₂

yes

maximal, complemented

#334×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

—

C₂×#11929607

—

#14579161

C₂²

yes

—

C₄×D₃₁₆

C₂²

yes

characteristic

#14579095

—

C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

#14579083

—

(C₂×D₇₉)⋊C₈

—

C₄⋊C₈×C₇₉

C₂²

yes

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

C₂×D₃₁₆

D₄

yes

characteristic

C₂×C₄×D₇₉

—

Dic₃₁₆

—

Dic₃₁₆

—

#11929607

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

D₄

yes

characteristic

(C₂×D₇₉)⋊C₄

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

D₄

yes

characteristic

C₄²×C₇₉

C₂³

yes

characteristic

C₂²×D₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

#41

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

D₃₁₆

—

C₄×D₇₉

—

C₄×D₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

D₈

yes

—

C₇₉⋊C₈

—

C₂²×C₇₉

#121

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂×D₈

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

D₇₉

—

#1689

—

maximal, Sylow

C₇₉

#1689

yes

characteristic, complemented, Sylow

—

—

—

D₇₉

yes

characteristic, complemented

#332

—

C₂×Q₁₆

—

158

—

C₂×Q₁₆

—

158

—

C₂×M₁₆

—

158

—

C₄⋊Q₈

—

C₄×D₄

—

#107

—

158

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₇₉

yes

—

#102

—

158

—

C₂²⋊C₈

—

158

—

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂×Q₈

—

158

—

C₂×D₄

—

C₂²×C₄

—

158

—

Q₁₆

—

316

—

Q₁₆

—

316

—

M₁₆

—

316

—

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

D₃₁₆

yes

characteristic

C₂×C₈

D₃₁₆

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₂²⋊C₄

—

158

—

C₄²

C₂²×D₇₉

yes

characteristic

C₂³

—

158

—

Q₈

—

316

—

Q₈

—

316

—

D₄

—

158

—

C₂×C₄

—

316

—

C₂×C₄

—

316

—

100

C₂×C₄

—

316

—

101

C₂×C₄

—

158

—

102

C₂×C₄

D₄×D₇₉

yes

characteristic

103

C₂×C₄

C₂×D₃₁₆

yes

characteristic

104

C₂×C₄

#11929625

yes

characteristic

105

C₈

—

106

C₈

—

107

C₈

—

316

—

108

C₈

D₆₃₂

yes

—

109

C₂²

—

316

—

110

C₂²

—

316

—

111

C₂²

—

316

—

112

C₂²

#14579136

yes

characteristic

113

C₄

—

114

C₄

—

316

—

115

C₄

—

632

—

116

C₄

C₂×D₆₃₂

yes

characteristic

117

C₄

#14579189

yes

characteristic

118

C₄

#14579190

yes

—

119

C₂

—

632

—

120

C₂

#19098759

yes

characteristic

121

C₂

#19098822

yes

characteristic

122

C₂

#19098839

yes

characteristic

	subgroup	G/H
center	C₂²	#14579136
commutator, cosocle	C₄²×C₇₉	C₂³
Frattini	C₄²	C₂²×D₇₉
Fitting	#334×C₇₉	C₂
socle	C₂²×C₇₉	#121
prime radical	C₂×D₃₁₆	D₄
hypercenter	#334	D₇₉
hypocenter	C₇₉	#1689
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #334

subgroup

G/H

center

C₂²

#14579136

commutator, cosocle

C₄²×C₇₉

C₂³

Frattini

C₄²

C₂²×D₇₉

Fitting

#334×C₇₉

C₂

socle

C₂²×C₇₉

#121

prime radical

C₂×D₃₁₆

D₄

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #334

N	H ≅ G/N	type
1. #19098943	C₂	semidirect
4. #19098308	C₂	semidirect
5. #334×C₇₉	C₂	semidirect
62. C₇₉	#1689	semidirect
66. #334	D₇₉	semidirect

H ≅ G/N

type

1. #19098943

C₂

semidirect

4. #19098308

C₂

semidirect

5. #334×C₇₉

C₂

semidirect

62. C₇₉

#1689

semidirect

66. #334

D₇₉

semidirect

Subgroups — #23762890

Conjugacy classes of subgroups

Complements