Group #23765613 — subgroups

Subgroups — #23765613

Order 10112.

134 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 41 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	#19098813	C₂	1	1	yes	maximal, characteristic
2	#19098610	C₂	1	1	yes	maximal, characteristic, complemented
3	#19098387	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098386	C₂	1	1	yes	maximal, characteristic, complemented
5	#19098376	C₂	1	1	yes	maximal, characteristic, complemented
6	#19098344	C₂	1	1	yes	maximal, characteristic, complemented
7	#361×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#11929607	C₂²	1	1	yes	characteristic
9	M₁₆×D₇₉	—	2	1	no	—
10	#14579132	—	2	1	no	—
11	#14579101	C₂²	1	1	yes	characteristic
12	#14579097	C₂²	1	1	yes	characteristic
13	#14579096	—	2	1	no	—
14	#14579093	C₂²	1	1	yes	characteristic
15	#14579082	—	2	1	no	—
16	C₂×D₈×C₇₉	C₂²	1	1	yes	characteristic
17	M₃₂×C₇₉	C₂²	1	1	yes	characteristic
18	#108×C₇₉	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊D₇₉	—	4	1	no	—
20	C₂×C₄×D₇₉	D₄	1	1	yes	characteristic
21	#11929608	—	2	1	no	—
22	#11929607	—	2	1	no	—
23	#11929607	—	2	1	no	—
24	#11929607	—	4	1	no	—
25	C₂×C₇₉⋊C₈	D₄	1	1	yes	characteristic
26	C₈×D₇₉	—	4	1	no	—
27	C₄⋊Dic₇₉	—	2	1	no	—
28	C₂²⋊Dic₇₉	—	4	1	no	—
29	C₇₉⋊C₁₆	—	2	1	no	—
30	C₂×D₄×C₇₉	—	2	1	no	—
31	D₈×C₇₉	—	2	1	no	—
32	D₈×C₇₉	—	2	1	no	—
33	M₁₆×C₇₉	—	2	1	no	—
34	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
35	C₁₆×C₇₉	—	2	1	no	—
36	C₂³×C₇₉	—	4	1	no	—
37	C₂²×D₇₉	SD₁₆	1	1	yes	characteristic
38	D₄×C₇₉	—	4	1	no	—
39	D₄×C₇₉	—	4	1	no	—
40	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
41	C₂²⋊D₇₉	—	8	2	no	—
42	C₂×Dic₇₉	—	4	1	no	—
43	C₂×Dic₇₉	SD₁₆	1	1	yes	characteristic
44	C₄×D₇₉	—	2	1	no	—
45	C₄×D₇₉	—	2	1	no	—
46	C₈×C₇₉	—	4	1	no	—
47	C₈×C₇₉	#41	1	1	yes	characteristic
48	C₈×C₇₉	#41	1	1	yes	characteristic
49	C₇₉⋊C₈	—	2	1	no	—
50	C₇₉⋊C₈	—	4	1	no	—
51	C₂²×C₇₉	—	8	1	no	—
52	C₂²×C₇₉	—	8	1	no	—
53	C₂²×C₇₉	—	8	1	no	—
54	C₂²×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
55	C₂×D₇₉	—	2	1	no	—
56	C₂×D₇₉	—	4	1	no	—
57	C₄×C₇₉	#123	1	1	yes	characteristic
58	C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
59	Dic₇₉	—	2	1	no	—
60	Dic₇₉	—	8	1	no	—
61	C₂×C₇₉	—	2	1	no	—
62	C₂×C₇₉	—	16	1	no	—
63	C₂×C₇₉	#481	1	1	yes	characteristic
64	D₇₉	—	4	1	no	—
65	#2238	—	79	1	no	maximal, Sylow
66	C₇₉	#2238	1	1	yes	characteristic, complemented, Sylow
67	#469	—	79	1	no	—
68	#430	—	79	1	no	—
69	#365	—	79	1	no	—
70	#365	—	79	1	no	—
71	#361	—	79	1	no	—
72	#361	D₇₉	1	1	yes	characteristic, complemented
73	#349	—	79	1	no	—
74	C₂×D₈	C₂×D₇₉	1	1	yes	characteristic
75	C₂×M₁₆	—	79	1	no	—
76	C₂×M₁₆	—	158	1	no	—
77	#121	—	158	1	no	—
78	M₃₂	—	79	1	no	—
79	M₃₂	C₂×D₇₉	1	1	yes	characteristic
80	#108	—	79	1	no	—
81	#108	—	158	1	no	—
82	#108	C₂×D₇₉	1	1	yes	characteristic
83	#106	—	79	1	no	—
84	#102	—	158	1	no	—
85	C₂×D₄	—	2	1	no	—
86	C₂×D₄	—	316	1	no	—
87	C₂²×C₄	—	79	1	no	—
88	D₈	—	2	1	no	—
89	D₈	—	2	1	no	—
90	M₁₆	—	2	1	no	—
91	M₁₆	—	316	1	no	—
92	M₁₆	—	158	1	no	—
93	M₁₆	—	158	1	no	—
94	M₁₆	—	158	1	no	—
95	C₂×C₈	—	316	1	no	—
96	C₂×C₈	—	79	1	no	—
97	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
98	C₄⋊C₄	—	158	1	no	—
99	C₂²⋊C₄	—	316	1	no	—
100	C₁₆	—	2	1	no	—
101	C₁₆	—	158	1	no	—
102	C₂³	—	4	1	no	—
103	C₂³	—	79	1	no	—
104	D₄	—	4	1	no	—
105	D₄	—	4	1	no	—
106	D₄	—	632	2	no	—
107	C₂×C₄	—	316	1	no	—
108	C₂×C₄	—	79	1	no	—
109	C₂×C₄	—	158	1	no	—
110	C₂×C₄	—	158	1	no	—
111	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
112	C₈	—	4	1	no	—
113	C₈	—	316	1	no	—
114	C₈	—	158	1	no	—
115	C₈	#11929623	1	1	yes	characteristic
116	C₈	#11929624	1	1	yes	characteristic
117	C₂²	—	8	1	no	—
118	C₂²	—	8	1	no	—
119	C₂²	—	8	1	no	—
120	C₂²	—	316	1	no	—
121	C₂²	—	158	1	no	—
122	C₂²	SD₁₆×D₇₉	1	1	yes	characteristic
123	C₄	—	632	1	no	—
124	C₄	—	158	1	no	—
125	C₄	#14579143	1	1	yes	characteristic
126	C₄	#14579185	1	1	yes	characteristic
127	C₂	—	2	1	no	—
128	C₂	—	16	1	no	—
129	C₂	—	316	1	no	—
130	C₂	#19098880	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098813

C₂

yes

maximal, characteristic

#19098610

C₂

yes

maximal, characteristic, complemented

#19098387

C₂

yes

maximal, characteristic, complemented

#19098386

C₂

yes

maximal, characteristic, complemented

#19098376

C₂

yes

maximal, characteristic, complemented

#19098344

C₂

yes

maximal, characteristic, complemented

#361×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×#11929607

C₂²

yes

characteristic

M₁₆×D₇₉

—

#14579132

—

#14579101

C₂²

yes

characteristic

#14579097

C₂²

yes

characteristic

#14579096

—

#14579093

C₂²

yes

characteristic

#14579082

—

C₂×D₈×C₇₉

C₂²

yes

characteristic

M₃₂×C₇₉

C₂²

yes

characteristic

#108×C₇₉

C₂²

yes

characteristic

C₂×C₂²⋊D₇₉

—

C₂×C₄×D₇₉

D₄

yes

—

—

—

—

C₂×C₇₉⋊C₈

D₄

yes

characteristic

C₈×D₇₉

—

C₄⋊Dic₇₉

—

C₂²⋊Dic₇₉

—

C₇₉⋊C₁₆

—

C₂×D₄×C₇₉

—

D₈×C₇₉

—

D₈×C₇₉

—

M₁₆×C₇₉

—

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₁₆×C₇₉

—

C₂³×C₇₉

—

C₂²×D₇₉

SD₁₆

yes

characteristic

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²⋊D₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

SD₁₆

yes

characteristic

C₄×D₇₉

—

C₄×D₇₉

—

C₈×C₇₉

—

C₈×C₇₉

yes

C₈×C₇₉

yes

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂×SD₁₆

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

yes

C₄×C₇₉

yes

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

#481

yes

characteristic

D₇₉

—

#2238

—

maximal, Sylow

C₇₉

#2238

yes

characteristic, complemented, Sylow

—

—

—

—

—

D₇₉

yes

characteristic, complemented

#349

—

C₂×D₈

C₂×D₇₉

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

158

—

#121

—

158

—

M₃₂

—

M₃₂

C₂×D₇₉

yes

characteristic

#108

—

#108

—

158

—

#108

C₂×D₇₉

yes

characteristic

#106

—

#102

—

158

—

C₂×D₄

—

C₂×D₄

—

316

—

C₂²×C₄

—

D₈

—

D₈

—

M₁₆

—

M₁₆

—

316

—

M₁₆

—

158

—

M₁₆

—

158

—

M₁₆

—

158

—

C₂×C₈

—

316

—

C₂×C₈

—

C₂×C₈

C₂²×D₇₉

yes

characteristic

C₄⋊C₄

—

158

—

C₂²⋊C₄

—

316

—

100

C₁₆

—

101

C₁₆

—

158

—

102

C₂³

—

103

C₂³

—

104

D₄

—

105

D₄

—

106

D₄

—

632

—

107

C₂×C₄

—

316

—

108

C₂×C₄

—

109

C₂×C₄

—

158

—

110

C₂×C₄

—

158

—

111

C₂×C₄

D₄×D₇₉

yes

characteristic

112

C₈

—

113

C₈

—

316

—

114

C₈

—

158

—

115

C₈

#11929623

yes

characteristic

116

C₈

#11929624

yes

characteristic

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

316

—

121

C₂²

—

158

—

122

C₂²

SD₁₆×D₇₉

yes

characteristic

123

C₄

—

632

—

124

C₄

—

158

—

125

C₄

#14579143

yes

characteristic

126

C₄

#14579185

yes

characteristic

127

C₂

—

128

C₂

—

129

C₂

—

316

—

130

C₂

#19098880

yes

characteristic

	subgroup	G/H
center	C₂	#19098880
commutator, cosocle	C₂×C₈×C₇₉	C₂³
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	#361×C₇₉	C₂
socle	C₂×C₇₉	#481
prime radical	#19098813	C₂
hypercenter	#361	D₇₉
hypocenter	C₇₉	#2238
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #361

subgroup

G/H

center

C₂

#19098880

commutator, cosocle

C₂×C₈×C₇₉

C₂³

Frattini

C₂×C₈

C₂²×D₇₉

Fitting

#361×C₇₉

C₂

C₂×C₇₉

C₂

D₇₉

C₇₉

G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #361

N	H ≅ G/N	type
2. #19098610	C₂	semidirect
3. #19098387	C₂	semidirect
4. #19098386	C₂	semidirect
5. #19098376	C₂	semidirect
6. #19098344	C₂	semidirect
7. #361×C₇₉	C₂	semidirect
66. C₇₉	#2238	semidirect
72. #361	D₇₉	semidirect

H ≅ G/N

type

2. #19098610

C₂

semidirect

3. #19098387

C₂

semidirect

4. #19098386

C₂

semidirect

5. #19098376

C₂

semidirect

6. #19098344

C₂

semidirect

7. #361×C₇₉

C₂

semidirect

66. C₇₉

#2238

semidirect

72. #361

D₇₉

semidirect

Subgroups — #23765613

Conjugacy classes of subgroups

Complements