Group #23762522 — subgroups

Subgroups — #23762522

Order 10112.

218 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 53 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	#19099299	C₂	1	1	yes	maximal, characteristic
2	#19098935	C₂	1	1	yes	maximal, characteristic
3	#19098859	C₂	1	2	yes	maximal, complemented
4	#19098293	C₂	1	2	yes	maximal, complemented
5	#331×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#11929612	—	2	2	no	—
7	#14579161	C₂²	1	1	yes	characteristic
8	#14579148	—	2	2	no	—
9	#14579142	—	2	2	no	—
10	C₄×Dic₁₅₈	C₂²	1	2	yes	—
11	D₄×Dic₇₉	—	2	2	no	—
12	#14579095	—	2	2	no	—
13	#14579086	—	2	2	no	—
14	C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
15	#127×C₇₉	C₂²	1	1	yes	characteristic
16	C₄⋊C₈×C₇₉	C₂²	1	2	yes	—
17	C₂×Dic₁₅₈	—	2	1	no	—
18	C₂×Dic₁₅₈	D₄	1	2	yes	—
19	C₂²×Dic₇₉	—	2	2	no	—
20	#11929612	—	4	4	no	—
21	C₂×C₇₉⋊C₈	—	2	1	no	—
22	C₄⋊Dic₇₉	—	2	2	no	—
23	C₄⋊Dic₇₉	D₄	1	2	yes	—
24	Dic₇₉⋊C₄	—	2	2	no	—
25	C₂²⋊Dic₇₉	—	2	4	no	—
26	C₂²⋊Dic₇₉	—	2	2	no	—
27	C₄×Dic₇₉	—	2	2	no	—
28	C₂×D₄×C₇₉	—	2	2	no	—
29	C₂×D₄×C₇₉	D₄	1	2	yes	—
30	C₂×C₈×C₇₉	—	2	2	no	—
31	C₄²×C₇₉	C₂³	1	1	yes	characteristic
32	C₂³×C₇₉	—	2	2	no	—
33	D₄×C₇₉	—	4	2	no	—
34	D₄×C₇₉	—	4	2	no	—
35	D₄×C₇₉	—	4	2	no	—
36	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
37	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
38	C₂×Dic₇₉	—	2	2	no	—
39	C₂×Dic₇₉	—	2	2	no	—
40	C₂×Dic₇₉	—	4	1	no	—
41	C₂×Dic₇₉	—	8	2	no	—
42	Dic₁₅₈	—	2	2	no	—
43	Dic₁₅₈	—	2	2	no	—
44	Dic₁₅₈	—	4	2	no	—
45	C₈×C₇₉	—	4	2	no	—
46	C₇₉⋊C₈	—	2	2	no	—
47	C₂²×C₇₉	—	4	4	no	—
48	C₂²×C₇₉	—	4	2	no	—
49	C₂²×C₇₉	#120	1	1	yes	characteristic
50	C₄×C₇₉	—	2	1	no	—
51	C₄×C₇₉	#135	1	2	yes	—
52	C₄×C₇₉	#137	1	2	yes	—
53	Dic₇₉	—	4	2	no	—
54	Dic₇₉	—	4	2	no	—
55	Dic₇₉	—	8	1	no	—
56	C₂×C₇₉	—	8	2	no	—
57	C₂×C₇₉	#452	1	2	yes	—
58	C₂×C₇₉	#453	1	1	yes	characteristic
59	#1630	—	79	1	no	maximal, Sylow
60	C₇₉	#1630	1	1	yes	characteristic, complemented, Sylow
61	#559	—	79	1	no	—
62	#492	—	79	1	no	—
63	#477	—	79	2	no	—
64	#331	D₇₉	1	1	yes	characteristic
65	Q₈⋊C₈	—	79	2	no	—
66	C₂×SD₁₆	—	158	2	no	—
67	C₄⋊Q₈	—	79	1	no	—
68	#127	C₂×D₇₉	1	1	yes	characteristic
69	#124	—	158	2	no	—
70	#123	—	158	2	no	—
71	C₄×Q₈	—	79	2	no	—
72	C₄×D₄	—	158	2	no	—
73	#107	—	158	2	no	—
74	C₄⋊C₈	C₂×D₇₉	1	2	yes	—
75	#103	—	158	2	no	—
76	C₄×C₈	—	79	1	no	—
77	C₂×Q₈	—	79	2	no	—
78	C₂×Q₈	—	158	1	no	—
79	C₂×D₄	—	2	2	no	—
80	C₂×D₄	D₃₁₆	1	2	yes	—
81	C₂²×C₄	—	158	2	no	—
82	SD₁₆	—	316	4	no	—
83	C₂×C₈	—	2	2	no	—
84	C₂×C₈	—	158	1	no	—
85	C₄⋊C₄	—	79	2	no	—
86	C₄⋊C₄	—	158	2	no	—
87	C₄⋊C₄	—	158	2	no	—
88	C₂²⋊C₄	—	158	4	no	—
89	C₂²⋊C₄	—	158	2	no	—
90	C₄²	—	158	2	no	—
91	C₄²	C₂²×D₇₉	1	1	yes	characteristic
92	C₂³	—	2	2	no	—
93	Q₈	—	316	2	no	—
94	Q₈	—	158	2	no	—
95	Q₈	—	158	2	no	—
96	D₄	—	4	2	no	—
97	D₄	—	4	2	no	—
98	D₄	—	4	2	no	—
99	C₂×C₄	—	316	1	no	—
100	C₂×C₄	—	632	2	no	—
101	C₂×C₄	—	158	2	no	—
102	C₂×C₄	—	158	2	no	—
103	C₂×C₄	D₄×D₇₉	1	2	yes	—
104	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
105	C₈	—	4	2	no	—
106	C₈	—	158	2	no	—
107	C₂²	—	4	4	no	—
108	C₂²	—	4	2	no	—
109	C₂²	#14579131	1	1	yes	characteristic
110	C₄	—	2	1	no	—
111	C₄	—	316	2	no	—
112	C₄	—	316	2	no	—
113	C₄	—	632	1	no	—
114	C₄	#14579180	1	2	yes	—
115	C₄	#14579190	1	2	yes	—
116	C₂	—	8	2	no	—
117	C₂	#19098726	1	2	yes	—
118	C₂	#19098733	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19099299

C₂

yes

maximal, characteristic

#19098935

C₂

yes

maximal, characteristic

#19098859

C₂

yes

maximal, complemented

#19098293

C₂

yes

maximal, complemented

#331×C₇₉

C₂

yes

maximal, characteristic

C₂×#11929612

—

#14579161

C₂²

yes

characteristic

#14579148

—

#14579142

—

C₄×Dic₁₅₈

C₂²

yes

—

D₄×Dic₇₉

—

#14579095

—

#14579086

—

C₄×C₇₉⋊C₈

C₂²

yes

characteristic

#127×C₇₉

C₂²

yes

characteristic

C₄⋊C₈×C₇₉

C₂²

yes

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

D₄

yes

—

C₂²×Dic₇₉

—

#11929612

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

D₄

yes

—

Dic₇₉⋊C₄

—

C₂²⋊Dic₇₉

—

C₂²⋊Dic₇₉

—

C₄×Dic₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

D₄

yes

—

C₂×C₈×C₇₉

—

C₄²×C₇₉

C₂³

yes

characteristic

C₂³×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#120

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

#135

yes

—

C₄×C₇₉

#137

yes

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

#452

yes

—

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

—

—

—

D₇₉

yes

characteristic

Q₈⋊C₈

—

C₂×SD₁₆

—

158

—

C₄⋊Q₈

—

#127

C₂×D₇₉

yes

characteristic

#124

—

158

—

#123

—

158

—

C₄×Q₈

—

C₄×D₄

—

158

—

#107

—

158

—

C₄⋊C₈

C₂×D₇₉

yes

—

#103

—

158

—

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

158

—

C₂×D₄

—

C₂×D₄

D₃₁₆

yes

—

C₂²×C₄

—

158

—

SD₁₆

—

316

—

C₂×C₈

—

C₂×C₈

—

158

—

C₄⋊C₄

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₂²⋊C₄

—

158

—

C₂²⋊C₄

—

158

—

C₄²

—

158

—

C₄²

C₂²×D₇₉

yes

characteristic

C₂³

—

Q₈

—

316

—

Q₈

—

158

—

Q₈

—

158

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

316

—

100

C₂×C₄

—

632

—

101

C₂×C₄

—

158

—

102

C₂×C₄

—

158

—

103

C₂×C₄

D₄×D₇₉

yes

—

104

C₂×C₄

C₂×D₃₁₆

yes

characteristic

105

C₈

—

106

C₈

—

158

—

107

C₂²

—

108

C₂²

—

109

C₂²

#14579131

yes

characteristic

110

C₄

—

111

C₄

—

316

—

112

C₄

—

316

—

113

C₄

—

632

—

114

C₄

#14579180

yes

—

115

C₄

#14579190

yes

—

116

C₂

—

117

C₂

#19098726

yes

—

118

C₂

#19098733

yes

characteristic

	subgroup	G/H
center	C₂²	#14579131
commutator, cosocle	C₄²×C₇₉	C₂³
Frattini	C₄²	C₂²×D₇₉
Fitting	#331×C₇₉	C₂
socle	C₂²×C₇₉	#120
prime radical	#127×C₇₉	C₂²
hypercenter	#331	D₇₉
hypocenter	C₇₉	#1630
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #331

subgroup

G/H

center

C₂²

#14579131

commutator, cosocle

C₄²×C₇₉

C₂³

Frattini

C₄²

C₂²×D₇₉

Fitting

#331×C₇₉

C₂

socle

C₂²×C₇₉

#120

prime radical

#127×C₇₉

C₂²

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #331

N	H ≅ G/N	type
3. #19098859	C₂	semidirect
4. #19098293	C₂	semidirect
60. C₇₉	#1630	semidirect

H ≅ G/N

type

3. #19098859

C₂

semidirect

4. #19098293

C₂

semidirect

60. C₇₉

#1630

semidirect

Subgroups — #23762522

Conjugacy classes of subgroups

Complements