Group #23765476 — subgroups

Subgroups — #23765476

Order 10112.

170 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 49 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	#19098998	C₂	1	2	yes	maximal, complemented
2	#19098940	C₂	1	1	yes	maximal, characteristic, complemented
3	#19098384	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098375	C₂	1	2	yes	maximal, complemented
5	#443×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₆₃₂	—	2	1	no	—
7	C₂×D₆₃₂	C₂²	1	2	yes	—
8	#14579158	—	2	1	no	—
9	#14579104	—	2	2	no	—
10	#14579102	—	2	2	no	—
11	#14579101	C₂²	1	2	yes	—
12	#135×C₇₉	C₂²	1	1	yes	characteristic
13	#131×C₇₉	—	2	1	no	—
14	#108×C₇₉	C₂²	1	1	yes	characteristic
15	#104×C₇₉	—	2	1	no	—
16	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×D₃₁₆	—	2	2	no	—
18	C₂×D₃₁₆	—	4	2	no	—
19	D₆₃₂	—	2	2	no	—
20	D₆₃₂	—	2	2	no	—
21	D₆₃₂	—	4	1	no	—
22	D₆₃₂	—	4	1	no	—
23	C₇₉⋊C₁₆	—	2	2	no	—
24	#41×C₇₉	—	2	1	no	—
25	Q₁₆×C₇₉	D₄	1	1	yes	characteristic, complemented
26	SD₁₆×C₇₉	—	2	1	no	—
27	D₈×C₇₉	D₄	1	1	yes	characteristic, complemented
28	M₁₆×C₇₉	—	2	1	no	—
29	M₁₆×C₇₉	—	4	1	no	—
30	C₂×C₈×C₇₉	—	4	1	no	—
31	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
32	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
33	C₄²×C₇₉	D₄	1	1	yes	characteristic
34	C₂²×D₇₉	—	4	2	no	—
35	Q₈×C₇₉	—	2	1	no	—
36	D₄×C₇₉	—	2	1	no	—
37	D₄×C₇₉	—	4	1	no	—
38	C₂×C₄×C₇₉	—	2	1	no	—
39	C₂×C₄×C₇₉	—	4	1	no	—
40	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
41	D₃₁₆	—	4	2	no	—
42	D₃₁₆	—	4	2	no	—
43	D₃₁₆	—	8	4	no	—
44	C₈×C₇₉	—	4	1	no	—
45	C₈×C₇₉	D₈	1	1	yes	characteristic
46	C₈×C₇₉	D₈	1	1	yes	characteristic
47	C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
48	C₈×C₇₉	#41	1	1	yes	characteristic
49	C₂²×C₇₉	—	4	1	no	—
50	C₂²×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
51	C₂×D₇₉	—	8	4	no	—
52	C₂×D₇₉	—	8	2	no	—
53	C₄×C₇₉	—	2	2	no	—
54	C₄×C₇₉	—	4	1	no	—
55	C₄×C₇₉	#121	1	1	yes	characteristic
56	C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
57	C₂×C₇₉	—	2	1	no	—
58	C₂×C₇₉	—	8	1	no	—
59	C₂×C₇₉	#459	1	1	yes	characteristic
60	D₇₉	—	16	2	no	—
61	#2213	—	79	1	no	maximal, Sylow
62	C₇₉	#2213	1	1	yes	characteristic, complemented, Sylow
63	#509	—	79	2	no	—
64	#493	—	79	1	no	—
65	#443	D₇₉	1	1	yes	characteristic, complemented
66	#364	—	79	1	no	—
67	#361	—	79	2	no	—
68	#135	C₂×D₇₉	1	1	yes	characteristic
69	C₂×D₈	—	79	2	no	—
70	C₂×D₈	—	158	1	no	—
71	#131	—	2	1	no	—
72	#127	—	158	1	no	—
73	SD₃₂	—	158	2	no	—
74	D₁₆	—	158	2	no	—
75	M₃₂	—	79	2	no	—
76	#108	C₂×D₇₉	1	1	yes	characteristic
77	#104	—	2	1	no	—
78	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
79	#41	—	2	1	no	—
80	C₂×D₄	—	316	2	no	—
81	C₂×D₄	—	158	2	no	—
82	Q₁₆	D₃₁₆	1	1	yes	characteristic, complemented
83	SD₁₆	—	2	1	no	—
84	D₈	—	316	1	no	—
85	D₈	—	316	1	no	—
86	D₈	—	158	2	no	—
87	D₈	—	158	2	no	—
88	D₈	D₃₁₆	1	1	yes	characteristic, complemented
89	M₁₆	—	2	1	no	—
90	M₁₆	—	4	1	no	—
91	C₂×C₈	—	4	1	no	—
92	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
93	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
94	C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
95	C₁₆	—	158	2	no	—
96	C₂³	—	316	2	no	—
97	Q₈	—	2	1	no	—
98	D₄	—	2	1	no	—
99	D₄	—	4	1	no	—
100	D₄	—	316	2	no	—
101	D₄	—	316	2	no	—
102	D₄	—	632	4	no	—
103	C₂×C₄	—	2	1	no	—
104	C₂×C₄	—	4	1	no	—
105	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
106	C₈	—	4	1	no	—
107	C₈	#11929609	1	1	yes	characteristic
108	C₈	#11929609	1	1	yes	characteristic
109	C₈	C₂×D₃₁₆	1	1	yes	characteristic
110	C₈	#11929624	1	1	yes	characteristic
111	C₂²	—	4	1	no	—
112	C₂²	—	632	4	no	—
113	C₂²	—	632	2	no	—
114	C₂²	#14579186	1	1	yes	characteristic
115	C₄	—	2	2	no	—
116	C₄	—	4	1	no	—
117	C₄	#14579135	1	1	yes	characteristic
118	C₄	C₂×#11929609	1	1	yes	characteristic
119	C₂	—	2	1	no	—
120	C₂	—	8	1	no	—
121	C₂	—	1264	2	no	—
122	C₂	#19098758	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098998

C₂

yes

maximal, complemented

#19098940

C₂

yes

maximal, characteristic, complemented

#19098384

C₂

yes

maximal, characteristic, complemented

#19098375

C₂

yes

maximal, complemented

#443×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×D₆₃₂

—

C₂×D₆₃₂

C₂²

yes

—

—

—

—

C₂²

yes

—

#135×C₇₉

C₂²

yes

characteristic

#131×C₇₉

—

#108×C₇₉

C₂²

yes

characteristic

#104×C₇₉

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×D₃₁₆

—

C₂×D₃₁₆

—

D₆₃₂

—

D₆₃₂

—

D₆₃₂

—

D₆₃₂

—

C₇₉⋊C₁₆

—

#41×C₇₉

—

Q₁₆×C₇₉

D₄

yes

characteristic, complemented

SD₁₆×C₇₉

—

D₈×C₇₉

D₄

yes

characteristic, complemented

M₁₆×C₇₉

—

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₄²×C₇₉

D₄

yes

characteristic

C₂²×D₇₉

—

Q₈×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

D₃₁₆

—

D₃₁₆

—

D₃₁₆

—

C₈×C₇₉

—

C₈×C₇₉

D₈

yes

characteristic

C₈×C₇₉

D₈

yes

characteristic

C₈×C₇₉

C₂×D₄

yes

characteristic

C₈×C₇₉

#41

yes

characteristic

C₂²×C₇₉

—

C₂²×C₇₉

AGL(1,ℤ/8)

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

#121

yes

characteristic

C₄×C₇₉

C₂×D₈

yes

characteristic

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

#459

yes

characteristic

D₇₉

—

#2213

—

maximal, Sylow

C₇₉

#2213

yes

characteristic, complemented, Sylow

#509

—

#493

—

#443

D₇₉

yes

characteristic, complemented

#364

—

#361

—

#135

C₂×D₇₉

yes

characteristic

C₂×D₈

—

C₂×D₈

—

158

—

#131

—

#127

—

158

—

SD₃₂

—

158

—

D₁₆

—

158

—

M₃₂

—

#108

C₂×D₇₉

yes

characteristic

#104

—

C₄×C₈

C₂×D₇₉

yes

characteristic

#41

—

C₂×D₄

—

316

—

C₂×D₄

—

158

—

Q₁₆

D₃₁₆

yes

characteristic, complemented

SD₁₆

—

D₈

—

316

—

D₈

—

316

—

D₈

—

158

—

D₈

—

158

—

D₈

D₃₁₆

yes

characteristic, complemented

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₇₉

yes

characteristic

C₂×C₈

C₂²×D₇₉

yes

characteristic

C₄²

C₂²⋊D₇₉

yes

characteristic

C₁₆

—

158

—

C₂³

—

316

—

Q₈

—

D₄

—

D₄

—

100

D₄

—

316

—

101

D₄

—

316

—

102

D₄

—

632

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

106

C₈

—

107

C₈

#11929609

yes

characteristic

108

C₈

#11929609

yes

characteristic

109

C₈

C₂×D₃₁₆

yes

characteristic

110

C₈

#11929624

yes

characteristic

111

C₂²

—

112

C₂²

—

632

—

113

C₂²

—

632

—

114

C₂²

#14579186

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

#14579135

yes

characteristic

118

C₄

C₂×#11929609

yes

characteristic

119

C₂

—

120

C₂

—

121

C₂

—

1264

—

122

C₂

#19098758

yes

characteristic

	subgroup	G/H
center	C₂	#19098758
commutator, cosocle	C₂×C₈×C₇₉	C₂³
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	#443×C₇₉	C₂
socle	C₂×C₇₉	#459
hypercenter	#443	D₇₉
hypocenter	C₇₉	#2213
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #443

subgroup

G/H

center

C₂

#19098758

commutator, cosocle

C₂×C₈×C₇₉

C₂³

Frattini

C₂×C₈

C₂²×D₇₉

Fitting

#443×C₇₉

C₂

C₂×C₇₉

D₇₉

C₇₉

G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #443

N	H ≅ G/N	type
1. #19098998	C₂	semidirect
2. #19098940	C₂	semidirect
3. #19098384	C₂	semidirect
4. #19098375	C₂	semidirect
5. #443×C₇₉	C₂	semidirect
25. Q₁₆×C₇₉	D₄	semidirect
27. D₈×C₇₉	D₄	semidirect
62. C₇₉	#2213	semidirect
65. #443	D₇₉	semidirect
82. Q₁₆	D₃₁₆	semidirect
88. D₈	D₃₁₆	semidirect

H ≅ G/N

type

1. #19098998

C₂

semidirect

2. #19098940

C₂

semidirect

3. #19098384

C₂

semidirect

4. #19098375

C₂

semidirect

5. #443×C₇₉

C₂

semidirect

25. Q₁₆×C₇₉

D₄

semidirect

27. D₈×C₇₉

D₄

semidirect

62. C₇₉

#2213

semidirect

65. #443

D₇₉

semidirect

82. Q₁₆

D₃₁₆

semidirect

88. D₈

D₃₁₆

semidirect

Subgroups — #23765476

Conjugacy classes of subgroups

Complements