Group #23765291 — subgroups

Subgroups — #23765291

Order 10112.

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

normal subgroups only

This group has 142 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	#19099003	C₂	1	1	yes	maximal, characteristic
2	#19098671	C₂	1	1	yes	maximal, characteristic, complemented
3	#19098387	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098378	C₂	1	1	yes	maximal, characteristic, complemented
5	#19098373	C₂	1	1	yes	maximal, characteristic
6	#19098341	C₂	1	1	yes	maximal, characteristic, complemented
7	#444×C₇₉	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₃₁₆	C₂²	1	1	yes	characteristic
9	C₄×Dic₁₅₈	—	2	1	no	—
10	#14579107	C₄	1	2	yes	complemented
11	#14579105	C₄	1	2	yes	complemented
12	#14579101	C₂²	1	1	yes	characteristic
13	#14579101	C₂²	1	1	yes	characteristic
14	#14579093	C₂²	1	1	yes	characteristic
15	#14579086	—	2	1	no	—
16	#135×C₇₉	C₂²	1	1	yes	characteristic
17	#131×C₇₉	—	2	1	no	—
18	#108×C₇₉	C₂²	1	1	yes	characteristic
19	#104×C₇₉	—	2	1	no	—
20	#97×C₇₉	C₂²	1	1	yes	characteristic
21	C₂×Dic₁₅₈	—	2	1	no	—
22	Dic₃₁₆	—	2	1	no	—
23	Dic₃₁₆	C₂×C₄	1	2	yes	—
24	C₄⋊Dic₇₉	—	2	1	no	—
25	Dic₇₉⋊C₄	—	4	1	no	—
26	C₄×Dic₇₉	—	4	1	no	—
27	C₇₉⋊C₁₆	—	2	1	no	—
28	C₇₉⋊C₁₆	C₂×C₄	1	2	yes	—
29	#41×C₇₉	—	2	1	no	—
30	Q₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
31	SD₁₆×C₇₉	—	2	1	no	—
32	D₈×C₇₉	C₂×C₄	1	1	yes	characteristic
33	M₁₆×C₇₉	—	2	1	no	—
34	M₁₆×C₇₉	—	4	1	no	—
35	C₂×C₈×C₇₉	—	4	1	no	—
36	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
37	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
38	C₄²×C₇₉	D₄	1	1	yes	characteristic
39	Q₈×C₇₉	—	2	1	no	—
40	D₄×C₇₉	—	2	1	no	—
41	D₄×C₇₉	—	4	1	no	—
42	C₂×C₄×C₇₉	—	2	1	no	—
43	C₂×C₄×C₇₉	—	4	1	no	—
44	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
45	C₂×Dic₇₉	—	4	1	no	—
46	C₂×Dic₇₉	—	4	1	no	—
47	Dic₁₅₈	—	2	2	no	—
48	Dic₁₅₈	—	4	1	no	—
49	C₈×C₇₉	—	2	1	no	—
50	C₈×C₇₉	—	4	1	no	—
51	C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
52	C₈×C₇₉	#41	1	1	yes	characteristic
53	C₂²×C₇₉	—	4	1	no	—
54	C₂²×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
55	C₄×C₇₉	—	4	1	no	—
56	C₄×C₇₉	—	4	1	no	—
57	C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
58	C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
59	Dic₇₉	—	4	2	no	—
60	Dic₇₉	—	8	1	no	—
61	C₂×C₇₉	—	2	1	no	—
62	C₂×C₇₉	—	8	1	no	—
63	C₂×C₇₉	#442	1	1	yes	characteristic
64	#2180	—	79	1	no	maximal, Sylow
65	C₇₉	#2180	1	1	yes	characteristic, complemented, Sylow
66	#510	—	79	1	no	—
67	#444	D₇₉	1	1	yes	characteristic
68	#441	—	79	1	no	—
69	#365	—	79	1	no	—
70	#362	—	79	1	no	—
71	#360	—	79	1	no	—
72	#347	—	79	1	no	—
73	#135	C₂×D₇₉	1	1	yes	characteristic
74	C₂×Q₁₆	—	79	1	no	—
75	#131	—	2	1	no	—
76	C₄×Q₈	—	158	1	no	—
77	Q₃₂	—	79	2	no	—
78	SD₃₂	—	79	2	no	—
79	M₃₂	—	79	1	no	—
80	M₃₂	—	79	1	no	—
81	#108	C₂×D₇₉	1	1	yes	characteristic
82	#106	—	79	1	no	—
83	#104	—	2	1	no	—
84	#103	—	158	1	no	—
85	#97	C₂×D₇₉	1	1	yes	characteristic
86	#41	—	2	1	no	—
87	C₂×Q₈	—	158	1	no	—
88	Q₁₆	—	79	2	no	—
89	Q₁₆	—	158	1	no	—
90	Q₁₆	C₄×D₇₉	1	1	yes	characteristic
91	SD₁₆	—	2	1	no	—
92	D₈	C₄×D₇₉	1	1	yes	characteristic
93	M₁₆	—	2	1	no	—
94	M₁₆	—	4	1	no	—
95	C₂×C₈	—	4	1	no	—
96	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
97	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
98	C₄⋊C₄	—	316	1	no	—
99	C₄⋊C₄	—	158	1	no	—
100	C₄²	—	316	1	no	—
101	C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
102	C₁₆	—	79	2	no	—
103	C₁₆	—	158	1	no	—
104	Q₈	—	2	1	no	—
105	Q₈	—	316	1	no	—
106	Q₈	—	158	2	no	—
107	D₄	—	2	1	no	—
108	D₄	—	4	1	no	—
109	C₂×C₄	—	2	1	no	—
110	C₂×C₄	—	4	1	no	—
111	C₂×C₄	—	316	1	no	—
112	C₂×C₄	—	316	1	no	—
113	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
114	C₈	—	2	1	no	—
115	C₈	—	4	1	no	—
116	C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
117	C₈	#11929624	1	1	yes	characteristic
118	C₂²	—	4	1	no	—
119	C₂²	#14579186	1	1	yes	characteristic
120	C₄	—	4	1	no	—
121	C₄	—	4	1	no	—
122	C₄	—	316	2	no	—
123	C₄	—	632	1	no	—
124	C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
125	C₄	#14579187	1	1	yes	characteristic
126	C₂	—	2	1	no	—
127	C₂	—	8	1	no	—
128	C₂	#19098673	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19099003

C₂

yes

maximal, characteristic

#19098671

C₂

yes

maximal, characteristic, complemented

#19098387

C₂

yes

maximal, characteristic, complemented

#19098378

C₂

yes

maximal, characteristic, complemented

#19098373

C₂

yes

maximal, characteristic

#19098341

C₂

yes

maximal, characteristic, complemented

#444×C₇₉

C₂

yes

maximal, characteristic

C₂×Dic₃₁₆

C₂²

yes

characteristic

C₄×Dic₁₅₈

—

#14579107

C₄

yes

complemented

#14579105

C₄

yes

complemented

#14579101

C₂²

yes

characteristic

#14579101

C₂²

yes

characteristic

#14579093

C₂²

yes

characteristic

#14579086

—

#135×C₇₉

C₂²

yes

characteristic

#131×C₇₉

—

#108×C₇₉

C₂²

yes

characteristic

#104×C₇₉

—

#97×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

Dic₃₁₆

—

Dic₃₁₆

C₂×C₄

yes

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₇₉⋊C₁₆

—

C₇₉⋊C₁₆

C₂×C₄

yes

—

#41×C₇₉

—

Q₁₆×C₇₉

C₂×C₄

yes

characteristic

SD₁₆×C₇₉

—

D₈×C₇₉

C₂×C₄

yes

characteristic

M₁₆×C₇₉

—

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₄²×C₇₉

D₄

yes

characteristic

Q₈×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

C₂²×C₄

yes

characteristic

C₈×C₇₉

#41

yes

characteristic

C₂²×C₇₉

—

C₂²×C₇₉

AGL(1,ℤ/8)

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₄×D₄

yes

characteristic

C₄×C₇₉

AGL(1,ℤ/8)

yes

characteristic

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

#510

—

#444

D₇₉

yes

—

—

—

—

—

C₂×D₇₉

yes

characteristic

C₂×Q₁₆

—

#131

—

C₄×Q₈

—

158

—

Q₃₂

—

SD₃₂

—

M₃₂

—

M₃₂

—

#108

C₂×D₇₉

yes

—

—

—

158

—

#97

C₂×D₇₉

yes

characteristic

#41

—

C₂×Q₈

—

158

—

Q₁₆

—

Q₁₆

—

158

—

Q₁₆

C₄×D₇₉

yes

characteristic

SD₁₆

—

D₈

C₄×D₇₉

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₇₉

yes

characteristic

C₂×C₈

C₂²×D₇₉

yes

characteristic

C₄⋊C₄

—

316

—

C₄⋊C₄

—

158

—

100

C₄²

—

316

—

101

C₄²

C₂²⋊D₇₉

yes

characteristic

102

C₁₆

—

103

C₁₆

—

158

—

104

Q₈

—

105

Q₈

—

316

—

106

Q₈

—

158

—

107

D₄

—

108

D₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

316

—

112

C₂×C₄

—

316

—

113

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

114

C₈

—

115

C₈

—

116

C₈

C₂×C₄×D₇₉

yes

characteristic

117

C₈

#11929624

yes

characteristic

118

C₂²

—

119

C₂²

#14579186

yes

characteristic

120

C₄

—

121

C₄

—

122

C₄

—

316

—

123

C₄

—

632

—

124

C₄

C₄×C₂²⋊D₇₉

yes

characteristic

125

C₄

#14579187

yes

characteristic

126

C₂

—

127

C₂

—

128

C₂

#19098673

yes

characteristic

	subgroup	G/H
center	C₂	#19098673
commutator	C₈×C₇₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	#444×C₇₉	C₂
socle	C₂×C₇₉	#442
prime radical	#135×C₇₉	C₂²
cosocle	C₂×C₈×C₇₉	C₂³
hypercenter	#444	D₇₉
hypocenter	C₇₉	#2180
LCS	G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #97 ◁ #444

subgroup

G/H

center

C₂

#19098673

commutator

C₈×C₇₉

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₇₉

Fitting

#444×C₇₉

C₂

socle

C₂×C₇₉

#442

prime radical

#135×C₇₉

C₂²

cosocle

C₂×C₈×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ #97 ◁ #444

N	H ≅ G/N	type
2. #19098671	C₂	semidirect
3. #19098387	C₂	semidirect
4. #19098378	C₂	semidirect
6. #19098341	C₂	semidirect
10. #14579107	C₄	semidirect
11. #14579105	C₄	semidirect
65. C₇₉	#2180	semidirect

H ≅ G/N

type

2. #19098671

C₂

semidirect

3. #19098387

C₂

semidirect

4. #19098378

C₂

semidirect

6. #19098341

C₂

semidirect

10. #14579107

C₄

semidirect

11. #14579105

C₄

semidirect

65. C₇₉

#2180

semidirect

Subgroups — #23765291

Conjugacy classes of subgroups

Complements