Group #23765569 — subgroups

Subgroups — #23765569

Order 10112.

126 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 45 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	#19098960	C₂	1	1	yes	maximal, characteristic, complemented
2	#19098680	C₂	1	1	yes	maximal, characteristic
3	#19098386	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098385	C₂	1	1	yes	maximal, characteristic, complemented
5	#19098383	C₂	1	1	yes	maximal, characteristic, complemented
6	#19098373	C₂	1	1	yes	maximal, characteristic
7	#360×C₇₉	C₂	1	1	yes	maximal, characteristic
8	#14579168	—	2	1	no	—
9	#14579160	—	2	1	no	—
10	#14579101	C₂²	1	1	yes	characteristic
11	#14579097	C₂²	1	1	yes	characteristic
12	#14579093	C₂²	1	1	yes	characteristic
13	#14579092	—	2	1	no	—
14	#14579088	—	2	1	no	—
15	C₈×Dic₇₉	C₂²	1	1	yes	characteristic
16	#135×C₇₉	C₂²	1	1	yes	characteristic
17	M₃₂×C₇₉	C₂²	1	1	yes	characteristic
18	#106×C₇₉	C₂²	1	1	yes	characteristic
19	C₂×Dic₁₅₈	—	4	1	no	—
20	#11929608	—	2	1	no	—
21	#11929608	—	4	1	no	—
22	C₂×C₇₉⋊C₈	—	4	1	no	—
23	C₂×C₇₉⋊C₈	D₄	1	1	yes	characteristic
24	C₄⋊Dic₇₉	—	2	1	no	—
25	Dic₇₉⋊C₄	—	4	1	no	—
26	C₄×Dic₇₉	D₄	1	1	yes	characteristic
27	C₇₉⋊C₁₆	—	2	1	no	—
28	#41×C₇₉	—	2	1	no	—
29	Q₁₆×C₇₉	Q₈	1	1	yes	characteristic, complemented
30	SD₁₆×C₇₉	—	2	1	no	—
31	D₈×C₇₉	Q₈	1	1	yes	characteristic, complemented
32	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
33	C₄⋊C₄×C₇₉	—	2	1	no	—
34	C₁₆×C₇₉	—	2	1	no	—
35	Q₈×C₇₉	—	2	1	no	—
36	D₄×C₇₉	—	2	1	no	—
37	D₄×C₇₉	—	4	1	no	—
38	C₂×C₄×C₇₉	—	4	1	no	—
39	C₂×C₄×C₇₉	—	4	1	no	—
40	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
41	C₂×Dic₇₉	—	2	1	no	—
42	C₂×Dic₇₉	—	4	1	no	—
43	Dic₁₅₈	—	8	2	no	—
44	C₈×C₇₉	C₂×Q₈	1	1	yes	characteristic
45	C₈×C₇₉	#41	1	1	yes	characteristic
46	C₇₉⋊C₈	—	4	1	no	—
47	C₇₉⋊C₈	SD₁₆	1	1	yes	characteristic
48	C₇₉⋊C₈	SD₁₆	1	1	yes	characteristic
49	C₂²×C₇₉	—	4	1	no	—
50	C₂²×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
51	C₄×C₇₉	—	4	1	no	—
52	C₄×C₇₉	—	8	1	no	—
53	C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
54	C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
55	Dic₇₉	—	2	2	no	—
56	Dic₇₉	—	8	1	no	—
57	C₂×C₇₉	—	2	1	no	—
58	C₂×C₇₉	—	8	1	no	—
59	C₂×C₇₉	#476	1	1	yes	characteristic
60	#2230	—	79	1	no	maximal, Sylow
61	C₇₉	#2230	1	1	yes	characteristic, complemented, Sylow
62	#498	—	79	1	no	—
63	#443	—	79	1	no	—
64	#365	—	79	1	no	—
65	#365	—	79	1	no	—
66	#364	—	79	1	no	—
67	#360	—	79	1	no	—
68	#360	D₇₉	1	1	yes	characteristic
69	#135	C₂×D₇₉	1	1	yes	characteristic
70	#131	—	158	1	no	—
71	C₄⋊Q₈	—	158	1	no	—
72	M₃₂	—	79	1	no	—
73	M₃₂	C₂×D₇₉	1	1	yes	characteristic
74	#108	—	79	1	no	—
75	#106	—	79	1	no	—
76	#106	—	158	1	no	—
77	#106	C₂×D₇₉	1	1	yes	characteristic
78	#104	—	158	1	no	—
79	C₄×C₈	—	79	1	no	—
80	#41	—	2	1	no	—
81	C₂×Q₈	—	316	1	no	—
82	Q₁₆	Dic₁₅₈	1	1	yes	characteristic, complemented
83	SD₁₆	—	2	1	no	—
84	D₈	Dic₁₅₈	1	1	yes	characteristic, complemented
85	M₁₆	—	316	1	no	—
86	M₁₆	—	158	1	no	—
87	C₂×C₈	—	316	1	no	—
88	C₂×C₈	—	79	1	no	—
89	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
90	C₄⋊C₄	—	2	1	no	—
91	C₄⋊C₄	—	316	1	no	—
92	C₄⋊C₄	—	158	1	no	—
93	C₄²	—	79	1	no	—
94	C₁₆	—	2	1	no	—
95	C₁₆	—	158	1	no	—
96	Q₈	—	2	1	no	—
97	Q₈	—	632	2	no	—
98	D₄	—	2	1	no	—
99	D₄	—	4	1	no	—
100	C₂×C₄	—	4	1	no	—
101	C₂×C₄	—	4	1	no	—
102	C₂×C₄	—	316	1	no	—
103	C₂×C₄	—	158	1	no	—
104	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
105	C₈	—	316	1	no	—
106	C₈	—	79	1	no	—
107	C₈	—	79	1	no	—
108	C₈	C₂×Dic₁₅₈	1	1	yes	characteristic
109	C₈	#11929623	1	1	yes	characteristic
110	C₂²	—	4	1	no	—
111	C₂²	#14579185	1	1	yes	characteristic
112	C₄	—	4	1	no	—
113	C₄	—	8	1	no	—
114	C₄	—	632	1	no	—
115	C₄	—	158	2	no	—
116	C₄	#14579138	1	1	yes	characteristic
117	C₄	SD₁₆×D₇₉	1	1	yes	characteristic
118	C₂	—	2	1	no	—
119	C₂	—	8	1	no	—
120	C₂	#19098851	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098960

C₂

yes

maximal, characteristic, complemented

#19098680

C₂

yes

maximal, characteristic

#19098386

C₂

yes

maximal, characteristic, complemented

#19098385

C₂

yes

maximal, characteristic, complemented

#19098383

C₂

yes

maximal, characteristic, complemented

#19098373

C₂

yes

maximal, characteristic

#360×C₇₉

C₂

yes

maximal, characteristic

#14579168

—

#14579160

—

#14579101

C₂²

yes

characteristic

#14579097

C₂²

yes

characteristic

#14579093

C₂²

yes

characteristic

#14579092

—

#14579088

—

C₈×Dic₇₉

C₂²

yes

characteristic

#135×C₇₉

C₂²

yes

characteristic

M₃₂×C₇₉

C₂²

yes

characteristic

#106×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

#11929608

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

D₄

yes

characteristic

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

D₄

yes

characteristic

C₇₉⋊C₁₆

—

#41×C₇₉

—

Q₁₆×C₇₉

Q₈

yes

characteristic, complemented

SD₁₆×C₇₉

—

D₈×C₇₉

Q₈

yes

characteristic, complemented

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₄⋊C₄×C₇₉

—

C₁₆×C₇₉

—

Q₈×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

C₈×C₇₉

C₂×Q₈

yes

characteristic

C₈×C₇₉

#41

yes

characteristic

C₇₉⋊C₈

—

C₇₉⋊C₈

SD₁₆

yes

characteristic

C₇₉⋊C₈

SD₁₆

yes

characteristic

C₂²×C₇₉

—

C₂²×C₇₉

AGL(1,ℤ/8)

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂²⋊Q₈

yes

characteristic

C₄×C₇₉

C₂×SD₁₆

yes

characteristic

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

—

—

—

—

—

—

D₇₉

yes

characteristic

#135

C₂×D₇₉

yes

characteristic

#131

—

158

—

C₄⋊Q₈

—

158

—

M₃₂

—

M₃₂

C₂×D₇₉

yes

—

—

—

158

—

#106

C₂×D₇₉

yes

characteristic

#104

—

158

—

C₄×C₈

—

#41

—

C₂×Q₈

—

316

—

Q₁₆

Dic₁₅₈

yes

characteristic, complemented

SD₁₆

—

D₈

Dic₁₅₈

yes

characteristic, complemented

M₁₆

—

316

—

M₁₆

—

158

—

C₂×C₈

—

316

—

C₂×C₈

—

C₂×C₈

C₂²×D₇₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

316

—

C₄⋊C₄

—

158

—

C₄²

—

C₁₆

—

C₁₆

—

158

—

Q₈

—

Q₈

—

632

—

D₄

—

D₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

316

—

103

C₂×C₄

—

158

—

104

C₂×C₄

D₄×D₇₉

yes

characteristic

105

C₈

—

316

—

106

C₈

—

107

C₈

—

108

C₈

C₂×Dic₁₅₈

yes

characteristic

109

C₈

#11929623

yes

characteristic

110

C₂²

—

111

C₂²

#14579185

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

—

632

—

115

C₄

—

158

—

116

C₄

#14579138

yes

characteristic

117

C₄

SD₁₆×D₇₉

yes

characteristic

118

C₂

—

119

C₂

—

120

C₂

#19098851

yes

characteristic

	subgroup	G/H
center	C₂	#19098851
commutator, cosocle	C₂×C₈×C₇₉	C₂³
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	#360×C₇₉	C₂
socle	C₂×C₇₉	#476
prime radical	#135×C₇₉	C₂²
hypercenter	#360	D₇₉
hypocenter	C₇₉	#2230
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #360

subgroup

G/H

center

C₂

#19098851

commutator, cosocle

C₂×C₈×C₇₉

C₂³

Frattini

C₂×C₈

C₂²×D₇₉

Fitting

#360×C₇₉

C₂

socle

C₂×C₇₉

#476

prime radical

#135×C₇₉

C₂²

D₇₉

C₇₉

G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #360

N	H ≅ G/N	type
1. #19098960	C₂	semidirect
3. #19098386	C₂	semidirect
4. #19098385	C₂	semidirect
5. #19098383	C₂	semidirect
29. Q₁₆×C₇₉	Q₈	semidirect
31. D₈×C₇₉	Q₈	semidirect
61. C₇₉	#2230	semidirect
82. Q₁₆	Dic₁₅₈	semidirect
84. D₈	Dic₁₅₈	semidirect

H ≅ G/N

type

1. #19098960

C₂

semidirect

3. #19098386

C₂

semidirect

4. #19098385

C₂

semidirect

5. #19098383

C₂

semidirect

29. Q₁₆×C₇₉

Q₈

semidirect

31. D₈×C₇₉

Q₈

semidirect

61. C₇₉

#2230

semidirect

82. Q₁₆

Dic₁₅₈

semidirect

84. D₈

Dic₁₅₈

semidirect

Subgroups — #23765569

Conjugacy classes of subgroups

Complements