Group #23762885 — subgroups

Subgroups — #23762885

Order 10112.

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

normal subgroups only

This group has 184 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	#19098940	C₂	1	1	yes	maximal, characteristic
2	#19098764	C₂	1	2	yes	maximal, complemented
3	#19098693	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098306	C₂	1	2	yes	maximal, complemented
5	#334×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11929613	—	2	2	no	—
7	C₂×D₆₃₂	—	2	1	no	—
8	C₂×D₆₃₂	—	2	1	no	—
9	#14579158	C₂²	1	2	yes	—
10	C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
11	C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
12	Dic₇₉⋊C₈	—	2	1	no	—
13	#14579083	—	2	2	no	—
14	#14579071	—	2	1	no	—
15	C₄⋊C₈×C₇₉	C₂²	1	2	yes	—
16	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×Dic₁₅₈	D₄	1	1	yes	characteristic
18	C₂×D₃₁₆	—	2	2	no	—
19	C₂×D₃₁₆	—	2	2	no	—
20	C₂×D₃₁₆	—	2	2	no	—
21	#11929613	—	4	4	no	—
22	D₆₃₂	—	4	2	no	—
23	D₆₃₂	—	4	2	no	—
24	C₂×C₇₉⋊C₈	—	2	1	no	—
25	C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
26	Dic₇₉⋊C₄	—	2	1	no	—
27	C₄×Dic₇₉	—	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	—	4	2	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	—	2	1	no	—
38	D₃₁₆	—	4	2	no	—
39	D₃₁₆	—	4	2	no	—
40	D₃₁₆	—	4	2	no	—
41	D₃₁₆	—	4	2	no	—
42	D₃₁₆	—	8	2	no	—
43	Dic₁₅₈	—	2	2	no	—
44	C₈×C₇₉	—	2	1	no	—
45	C₈×C₇₉	—	4	2	no	—
46	C₈×C₇₉	SD₁₆	1	2	yes	complemented
47	C₇₉⋊C₈	—	4	1	no	—
48	C₂²×C₇₉	#121	1	1	yes	characteristic
49	C₂×D₇₉	—	8	2	no	—
50	C₂×D₇₉	—	8	2	no	—
51	C₂×D₇₉	—	8	2	no	—
52	C₄×C₇₉	—	2	1	no	—
53	C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
54	C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
55	C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
56	Dic₇₉	—	4	1	no	—
57	Dic₇₉	—	4	1	no	—
58	C₂×C₇₉	#460	1	1	yes	characteristic
59	C₂×C₇₉	#469	1	1	yes	characteristic
60	C₂×C₇₉	#472	1	1	yes	characteristic
61	D₇₉	—	16	2	no	—
62	#1688	—	79	1	no	maximal, Sylow
63	C₇₉	#1688	1	1	yes	characteristic, complemented, Sylow
64	#493	—	79	1	no	—
65	#460	—	79	2	no	—
66	#446	—	79	1	no	—
67	#334	D₇₉	1	1	yes	characteristic, complemented
68	#331	—	79	2	no	—
69	C₂×SD₁₆	—	158	2	no	—
70	C₂×D₈	—	158	1	no	—
71	C₂×D₈	—	158	1	no	—
72	#127	—	79	2	no	—
73	C₄×Q₈	—	79	1	no	—
74	C₄⋊C₈	—	79	1	no	—
75	C₄⋊C₈	—	158	1	no	—
76	C₄⋊C₈	C₂×D₇₉	1	2	yes	—
77	#102	—	158	2	no	—
78	#97	—	158	1	no	—
79	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
80	C₂×Q₈	—	79	1	no	—
81	C₂×D₄	—	158	2	no	—
82	C₂×D₄	—	158	2	no	—
83	C₂×D₄	—	158	2	no	—
84	SD₁₆	—	316	4	no	—
85	D₈	—	316	2	no	—
86	D₈	—	316	2	no	—
87	C₂×C₈	—	2	2	no	—
88	C₂×C₈	—	158	1	no	—
89	C₂×C₈	D₃₁₆	1	1	yes	characteristic
90	C₂×C₈	D₃₁₆	1	1	yes	characteristic
91	C₄⋊C₄	—	79	1	no	—
92	C₄⋊C₄	—	158	1	no	—
93	C₄²	—	158	1	no	—
94	C₄²	C₂²×D₇₉	1	1	yes	characteristic
95	C₂³	—	316	2	no	—
96	Q₈	—	158	2	no	—
97	D₄	—	316	2	no	—
98	D₄	—	316	2	no	—
99	D₄	—	316	2	no	—
100	D₄	—	316	2	no	—
101	D₄	—	632	2	no	—
102	C₂×C₄	—	158	1	no	—
103	C₂×C₄	—	158	1	no	—
104	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
105	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
106	C₂×C₄	#11929625	1	1	yes	characteristic
107	C₈	—	2	1	no	—
108	C₈	—	4	2	no	—
109	C₈	—	316	1	no	—
110	C₈	#11929613	1	2	yes	complemented
111	C₂²	—	632	2	no	—
112	C₂²	—	632	2	no	—
113	C₂²	—	632	2	no	—
114	C₂²	#14579136	1	1	yes	characteristic
115	C₄	—	2	1	no	—
116	C₄	—	316	1	no	—
117	C₄	—	316	1	no	—
118	C₄	C₂×#11929613	1	1	yes	characteristic
119	C₄	#14579188	1	2	yes	—
120	C₄	#14579189	1	1	yes	characteristic
121	C₂	—	1264	2	no	—
122	C₂	#19098764	1	1	yes	characteristic
123	C₂	#19098817	1	1	yes	characteristic
124	C₂	#19098834	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098940

C₂

yes

maximal, characteristic

#19098764

C₂

yes

maximal, complemented

#19098693

C₂

yes

maximal, characteristic, complemented

#19098306

C₂

yes

maximal, complemented

#334×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×#11929613

—

C₂×D₆₃₂

—

C₂×D₆₃₂

—

#14579158

C₂²

yes

—

C₄×Dic₁₅₈

C₂²

yes

characteristic

C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

Dic₇₉⋊C₈

—

#14579083

—

#14579071

—

C₄⋊C₈×C₇₉

C₂²

yes

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

D₄

yes

characteristic

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

#11929613

—

D₆₃₂

—

D₆₃₂

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

D₄

yes

characteristic

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

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

—

D₃₁₆

—

D₃₁₆

—

D₃₁₆

—

D₃₁₆

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

SD₁₆

yes

complemented

C₇₉⋊C₈

—

C₂²×C₇₉

#121

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂×SD₁₆

yes

characteristic

C₄×C₇₉

AGL(1,ℤ/8)

yes

—

C₄×C₇₉

AGL(1,ℤ/8)

yes

characteristic

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

D₇₉

—

#1688

—

maximal, Sylow

C₇₉

#1688

yes

characteristic, complemented, Sylow

—

—

—

D₇₉

yes

characteristic, complemented

#331

—

C₂×SD₁₆

—

158

—

C₂×D₈

—

158

—

C₂×D₈

—

158

—

#127

—

C₄×Q₈

—

C₄⋊C₈

—

C₄⋊C₈

—

158

—

C₄⋊C₈

C₂×D₇₉

yes

—

#102

—

158

—

#97

—

158

—

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂×Q₈

—

C₂×D₄

—

158

—

C₂×D₄

—

158

—

C₂×D₄

—

158

—

SD₁₆

—

316

—

D₈

—

316

—

D₈

—

316

—

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

D₃₁₆

yes

characteristic

C₂×C₈

D₃₁₆

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

158

—

C₄²

—

158

—

C₄²

C₂²×D₇₉

yes

characteristic

C₂³

—

316

—

Q₈

—

158

—

D₄

—

316

—

D₄

—

316

—

D₄

—

316

—

100

D₄

—

316

—

101

D₄

—

632

—

102

C₂×C₄

—

158

—

103

C₂×C₄

—

158

—

104

C₂×C₄

D₄×D₇₉

yes

characteristic

105

C₂×C₄

C₂×D₃₁₆

yes

characteristic

106

C₂×C₄

#11929625

yes

characteristic

107

C₈

—

108

C₈

—

109

C₈

—

316

—

110

C₈

#11929613

yes

complemented

111

C₂²

—

632

—

112

C₂²

—

632

—

113

C₂²

—

632

—

114

C₂²

#14579136

yes

characteristic

115

C₄

—

116

C₄

—

316

—

117

C₄

—

316

—

118

C₄

C₂×#11929613

yes

characteristic

119

C₄

#14579188

yes

—

120

C₄

#14579189

yes

characteristic

121

C₂

—

1264

—

122

C₂

#19098764

yes

characteristic

123

C₂

#19098817

yes

characteristic

124

C₂

#19098834

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	#19098940	C₂
hypercenter	#334	D₇₉
hypocenter	C₇₉	#1688
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

C₂²×C₇₉

C₂

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #334

N	H ≅ G/N	type
2. #19098764	C₂	semidirect
3. #19098693	C₂	semidirect
4. #19098306	C₂	semidirect
5. #334×C₇₉	C₂	semidirect
46. C₈×C₇₉	SD₁₆	semidirect
63. C₇₉	#1688	semidirect
67. #334	D₇₉	semidirect
110. C₈	#11929613	semidirect

H ≅ G/N

type

2. #19098764

C₂

semidirect

3. #19098693

C₂

semidirect

4. #19098306

C₂

semidirect

5. #334×C₇₉

C₂

semidirect

46. C₈×C₇₉

SD₁₆

semidirect

63. C₇₉

#1688

semidirect

67. #334

D₇₉

semidirect

110. C₈

#11929613

semidirect

Subgroups — #23762885

Conjugacy classes of subgroups

Complements