Group #23765630 — subgroups

Subgroups — #23765630

Order 10112.

138 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 47 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	#19098964	C₂	1	1	yes	maximal, characteristic, complemented
2	#19098946	C₂	1	1	yes	maximal, characteristic
3	#19098368	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098366	C₂	1	1	yes	maximal, characteristic, complemented
5	#19098364	C₂	1	1	yes	maximal, characteristic
6	C₁₆×Dic₇₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#357×C₇₉	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₃₁₆	C₂²	1	1	yes	characteristic
9	C₂×#11929612	—	2	1	no	—
10	#14579152	—	2	1	no	—
11	#14579148	—	2	1	no	—
12	C₂×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
13	#14579095	C₂²	1	1	yes	characteristic
14	#14579092	—	2	1	no	—
15	C₈×Dic₇₉	C₂²	1	1	yes	characteristic
16	C₂×D₈×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
18	#107×C₇₉	C₂²	1	1	yes	characteristic
19	C₂×Dic₁₅₈	—	2	1	no	—
20	Dic₃₁₆	—	2	1	no	—
21	Dic₃₁₆	—	2	1	no	—
22	#11929612	—	4	2	no	—
23	C₂×C₇₉⋊C₈	D₄	1	1	yes	characteristic
24	C₄⋊Dic₇₉	—	2	1	no	—
25	C₄⋊Dic₇₉	—	4	1	no	—
26	Dic₇₉⋊C₄	—	4	1	no	—
27	C₂²⋊Dic₇₉	—	4	1	no	—
28	C₂²⋊Dic₇₉	—	4	1	no	—
29	C₄×Dic₇₉	D₄	1	1	yes	characteristic
30	C₇₉⋊C₁₆	—	2	1	no	—
31	C₂×D₄×C₇₉	—	2	1	no	—
32	D₈×C₇₉	—	2	1	no	—
33	D₈×C₇₉	—	2	1	no	—
34	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
35	C₄⋊C₄×C₇₉	—	2	1	no	—
36	C₁₆×C₇₉	—	2	1	no	—
37	C₂³×C₇₉	—	4	1	no	—
38	D₄×C₇₉	—	4	1	no	—
39	D₄×C₇₉	—	4	1	no	—
40	C₂×C₄×C₇₉	—	4	1	no	—
41	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
42	C₂×Dic₇₉	—	4	1	no	—
43	C₂×Dic₇₉	—	4	1	no	—
44	C₂×Dic₇₉	D₈	1	1	yes	characteristic
45	C₂×Dic₇₉	D₈	1	1	yes	characteristic
46	Dic₁₅₈	—	4	1	no	—
47	Dic₁₅₈	—	4	1	no	—
48	C₈×C₇₉	#41	1	1	yes	characteristic
49	C₈×C₇₉	#41	1	1	yes	characteristic
50	C₇₉⋊C₈	SD₁₆	1	2	yes	—
51	C₂²×C₇₉	—	8	1	no	—
52	C₂²×C₇₉	—	8	1	no	—
53	C₂²×C₇₉	—	8	1	no	—
54	C₂²×C₇₉	C₂×D₈	1	1	yes	characteristic
55	C₄×C₇₉	—	8	1	no	—
56	C₄×C₇₉	#124	1	1	yes	characteristic
57	C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
58	Dic₇₉	—	2	1	no	—
59	Dic₇₉	—	2	1	no	—
60	Dic₇₉	—	8	1	no	—
61	Dic₇₉	—	8	1	no	—
62	C₂×C₇₉	—	16	1	no	—
63	C₂×C₇₉	#486	1	1	yes	characteristic
64	C₂×C₇₉	#508	1	1	yes	characteristic
65	C₂×C₇₉	#508	1	1	yes	characteristic
66	#2242	—	79	1	no	maximal, Sylow
67	C₇₉	#2242	1	1	yes	characteristic, complemented, Sylow
68	#499	—	79	1	no	—
69	#495	—	79	1	no	—
70	#358	—	79	1	no	—
71	#358	—	79	1	no	—
72	#357	—	79	1	no	—
73	#357	D₇₉	1	1	yes	characteristic
74	C₄×C₁₆	—	79	1	no	—
75	C₂×Q₁₆	—	79	1	no	—
76	C₂×SD₁₆	—	158	1	no	—
77	C₂×D₈	C₂×D₇₉	1	1	yes	characteristic
78	#125	—	158	1	no	—
79	#124	—	158	1	no	—
80	C₂×C₁₆	—	79	1	no	—
81	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
82	#107	—	79	1	no	—
83	#107	C₂×D₇₉	1	1	yes	characteristic
84	#106	—	158	1	no	—
85	C₄×C₈	—	79	1	no	—
86	C₂×Q₈	—	158	1	no	—
87	C₂×D₄	—	2	1	no	—
88	Q₁₆	—	158	1	no	—
89	Q₁₆	—	158	1	no	—
90	SD₁₆	—	316	2	no	—
91	D₈	—	2	1	no	—
92	D₈	—	2	1	no	—
93	C₂×C₈	—	79	1	no	—
94	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
95	C₄⋊C₄	—	2	1	no	—
96	C₄⋊C₄	—	316	1	no	—
97	C₄⋊C₄	—	316	1	no	—
98	C₄⋊C₄	—	158	1	no	—
99	C₂²⋊C₄	—	316	1	no	—
100	C₂²⋊C₄	—	316	1	no	—
101	C₄²	—	79	1	no	—
102	C₁₆	—	2	1	no	—
103	C₁₆	—	158	1	no	—
104	C₂³	—	4	1	no	—
105	Q₈	—	316	1	no	—
106	Q₈	—	316	1	no	—
107	D₄	—	4	1	no	—
108	D₄	—	4	1	no	—
109	C₂×C₄	—	4	1	no	—
110	C₂×C₄	—	316	1	no	—
111	C₂×C₄	—	316	1	no	—
112	C₂×C₄	—	79	1	no	—
113	C₂×C₄	—	79	1	no	—
114	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
115	C₈	—	79	2	no	—
116	C₈	#11929623	1	1	yes	characteristic
117	C₈	#11929624	1	1	yes	characteristic
118	C₂²	—	8	1	no	—
119	C₂²	—	8	1	no	—
120	C₂²	—	8	1	no	—
121	C₂²	D₈×D₇₉	1	1	yes	characteristic
122	C₄	—	8	1	no	—
123	C₄	—	632	1	no	—
124	C₄	—	632	1	no	—
125	C₄	—	158	1	no	—
126	C₄	—	158	1	no	—
127	C₄	#14579147	1	1	yes	characteristic
128	C₄	SD₁₆×D₇₉	1	1	yes	characteristic
129	C₂	—	16	1	no	—
130	C₂	#19098908	1	1	yes	characteristic
131	C₂	#19098992	1	1	yes	characteristic
132	C₂	#19098994	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098964

C₂

yes

maximal, characteristic, complemented

#19098946

C₂

yes

maximal, characteristic

#19098368

C₂

yes

maximal, characteristic, complemented

#19098366

C₂

yes

maximal, characteristic, complemented

#19098364

C₂

yes

maximal, characteristic

C₁₆×Dic₇₉

C₂

yes

maximal, characteristic, complemented

#357×C₇₉

C₂

yes

maximal, characteristic

C₂×Dic₃₁₆

C₂²

yes

—

—

—

C₂×C₇₉⋊C₁₆

C₂²

yes

characteristic

#14579095

C₂²

yes

characteristic

#14579092

—

C₈×Dic₇₉

C₂²

yes

characteristic

C₂×D₈×C₇₉

C₂²

yes

characteristic

C₂×C₁₆×C₇₉

C₂²

yes

characteristic

#107×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

Dic₃₁₆

—

Dic₃₁₆

—

#11929612

—

C₂×C₇₉⋊C₈

D₄

yes

characteristic

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

C₂²⋊Dic₇₉

—

C₂²⋊Dic₇₉

—

C₄×Dic₇₉

D₄

yes

characteristic

C₇₉⋊C₁₆

—

C₂×D₄×C₇₉

—

D₈×C₇₉

—

D₈×C₇₉

—

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₄⋊C₄×C₇₉

—

C₁₆×C₇₉

—

C₂³×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

D₈

yes

characteristic

C₂×Dic₇₉

D₈

yes

characteristic

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

yes

C₈×C₇₉

yes

C₇₉⋊C₈

SD₁₆

yes

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂×D₈

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

#124

yes

characteristic

C₄×C₇₉

C₂×SD₁₆

yes

characteristic

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

—

—

—

—

—

D₇₉

yes

characteristic

C₄×C₁₆

—

C₂×Q₁₆

—

C₂×SD₁₆

—

158

—

C₂×D₈

C₂×D₇₉

yes

characteristic

#125

—

158

—

#124

—

158

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₉

yes

characteristic

#107

—

#107

C₂×D₇₉

yes

characteristic

#106

—

158

—

C₄×C₈

—

C₂×Q₈

—

158

—

C₂×D₄

—

Q₁₆

—

158

—

Q₁₆

—

158

—

SD₁₆

—

316

—

D₈

—

D₈

—

C₂×C₈

—

C₂×C₈

C₂²×D₇₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

316

—

C₄⋊C₄

—

316

—

C₄⋊C₄

—

158

—

C₂²⋊C₄

—

316

—

100

C₂²⋊C₄

—

316

—

101

C₄²

—

102

C₁₆

—

103

C₁₆

—

158

—

104

C₂³

—

105

Q₈

—

316

—

106

Q₈

—

316

—

107

D₄

—

108

D₄

—

109

C₂×C₄

—

110

C₂×C₄

—

316

—

111

C₂×C₄

—

316

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

D₄×D₇₉

yes

characteristic

115

C₈

—

116

C₈

#11929623

yes

characteristic

117

C₈

#11929624

yes

characteristic

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

D₈×D₇₉

yes

characteristic

122

C₄

—

123

C₄

—

632

—

124

C₄

—

632

—

125

C₄

—

158

—

126

C₄

—

158

—

127

C₄

#14579147

yes

characteristic

128

C₄

SD₁₆×D₇₉

yes

characteristic

129

C₂

—

130

C₂

#19098908

yes

characteristic

131

C₂

#19098992

yes

characteristic

132

C₂

#19098994

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₇₉
commutator, cosocle	C₂×C₈×C₇₉	C₂³
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	#357×C₇₉	C₂
socle	C₂²×C₇₉	C₂×D₈
prime radical	C₂×D₈×C₇₉	C₂²
hypercenter	#357	D₇₉
hypocenter	C₇₉	#2242
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

subgroup

G/H

center

C₂²

D₈×D₇₉

commutator, cosocle

C₂×C₈×C₇₉

C₂³

Frattini

C₂×C₈

C₂²×D₇₉

Fitting

#357×C₇₉

C₂

socle

C₂²×C₇₉

C₂×D₈

prime radical

C₂×D₈×C₇₉

C₂²

D₇₉

C₇₉

G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

N	H ≅ G/N	type
1. #19098964	C₂	semidirect
3. #19098368	C₂	semidirect
4. #19098366	C₂	semidirect
6. C₁₆×Dic₇₉	C₂	semidirect
67. C₇₉	#2242	semidirect

H ≅ G/N

type

1. #19098964

C₂

semidirect

3. #19098368

C₂

semidirect

4. #19098366

C₂

semidirect

6. C₁₆×Dic₇₉

C₂

semidirect

67. C₇₉

#2242

semidirect

Subgroups — #23765630

Conjugacy classes of subgroups

Complements