Group #23765446 — subgroups

Subgroups — #23765446

Order 10112.

166 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 55 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	C₂×#14579106	C₂	1	2	yes	maximal
2	#19098943	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₆₃₂	C₂	1	1	yes	maximal, characteristic
4	#19098368	C₂	1	2	yes	maximal, complemented
5	C₄⋊C₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₃₁₆	—	2	1	no	—
7	C₂×Dic₃₁₆	C₂²	1	2	yes	—
8	C₂×D₆₃₂	C₂²	1	1	yes	characteristic
9	#14579161	—	2	1	no	—
10	C₄×D₃₁₆	—	2	1	no	—
11	#14579106	—	2	4	no	—
12	#14579095	C₂²	1	1	yes	characteristic
13	#14579083	—	2	1	no	—
14	C₂×C₁₆×C₇₉	C₂²	1	2	yes	—
15	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
16	C₂×Dic₁₅₈	—	2	2	no	—
17	C₂×D₃₁₆	—	2	1	no	—
18	C₂×C₄×D₇₉	—	4	1	no	—
19	Dic₃₁₆	—	2	2	no	—
20	Dic₃₁₆	—	2	2	no	—
21	Dic₃₁₆	—	4	2	no	—
22	D₆₃₂	—	2	1	no	—
23	D₆₃₂	D₄	1	2	yes	—
24	C₄⋊Dic₇₉	—	2	1	no	—
25	C₄⋊Dic₇₉	—	4	1	no	—
26	C₄⋊Dic₇₉	—	4	1	no	—
27	(C₂×D₇₉)⋊C₄	—	4	1	no	—
28	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
29	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
30	C₄²×C₇₉	D₄	1	1	yes	characteristic
31	C₁₆×C₇₉	—	2	2	no	—
32	C₂²×D₇₉	—	4	1	no	—
33	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
34	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
35	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
36	C₂×Dic₇₉	—	4	1	no	—
37	C₂×Dic₇₉	—	4	2	no	—
38	D₃₁₆	—	2	2	no	—
39	D₃₁₆	—	4	1	no	—
40	C₄×D₇₉	—	8	2	no	—
41	Dic₁₅₈	—	4	2	no	—
42	Dic₁₅₈	—	4	2	no	—
43	C₈×C₇₉	—	2	1	no	—
44	C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
45	C₈×C₇₉	#41	1	1	yes	characteristic
46	C₂²×C₇₉	C₂×D₈	1	1	yes	characteristic
47	C₂×D₇₉	—	4	2	no	—
48	C₂×D₇₉	—	8	1	no	—
49	C₂×D₇₉	—	8	1	no	—
50	C₄×C₇₉	—	2	1	no	—
51	C₄×C₇₉	SD₃₂	1	2	yes	complemented
52	C₄×C₇₉	#121	1	1	yes	characteristic
53	C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
54	Dic₇₉	—	8	2	no	—
55	Dic₇₉	—	8	1	no	—
56	C₂×C₇₉	#459	1	1	yes	characteristic
57	C₂×C₇₉	C₂×SD₃₂	1	1	yes	characteristic
58	C₂×C₇₉	#510	1	1	yes	characteristic
59	D₇₉	—	8	2	no	—
60	#2208	—	79	1	no	maximal, Sylow
61	C₇₉	#2208	1	1	yes	characteristic, complemented, Sylow
62	C₂×SD₃₂	—	79	2	no	—
63	#494	—	79	1	no	—
64	C₄×D₈	—	79	1	no	—
65	C₄⋊C₁₆	D₇₉	1	1	yes	characteristic, complemented
66	#358	—	79	2	no	—
67	C₂×Q₁₆	—	79	2	no	—
68	C₂×Q₁₆	—	158	1	no	—
69	C₂×D₈	—	79	1	no	—
70	C₄⋊Q₈	—	158	1	no	—
71	C₄×D₄	—	158	1	no	—
72	SD₃₂	—	158	4	no	—
73	C₂×C₁₆	C₂×D₇₉	1	2	yes	—
74	#107	—	79	1	no	—
75	#102	—	158	1	no	—
76	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
77	C₂×Q₈	—	158	2	no	—
78	C₂×D₄	—	158	1	no	—
79	C₂²×C₄	—	316	1	no	—
80	Q₁₆	—	316	2	no	—
81	Q₁₆	—	158	2	no	—
82	Q₁₆	—	158	2	no	—
83	D₈	—	79	2	no	—
84	D₈	—	158	1	no	—
85	C₂×C₈	D₃₁₆	1	1	yes	characteristic
86	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
87	C₄⋊C₄	—	316	1	no	—
88	C₄⋊C₄	—	316	1	no	—
89	C₄⋊C₄	—	158	1	no	—
90	C₂²⋊C₄	—	316	1	no	—
91	C₄²	D₃₁₆	1	1	yes	characteristic
92	C₁₆	—	2	2	no	—
93	C₂³	—	316	1	no	—
94	Q₈	—	316	2	no	—
95	Q₈	—	316	2	no	—
96	D₄	—	316	1	no	—
97	D₄	—	158	2	no	—
98	C₂×C₄	—	316	1	no	—
99	C₂×C₄	—	316	2	no	—
100	C₂×C₄	—	632	2	no	—
101	C₂×C₄	D₆₃₂	1	1	yes	characteristic
102	C₂×C₄	D₆₃₂	1	1	yes	characteristic
103	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
104	C₈	—	2	1	no	—
105	C₈	D₄×D₇₉	1	1	yes	characteristic
106	C₈	#11929625	1	1	yes	characteristic
107	C₂²	—	316	2	no	—
108	C₂²	—	632	1	no	—
109	C₂²	—	632	1	no	—
110	C₂²	C₂×D₆₃₂	1	1	yes	characteristic
111	C₄	—	2	1	no	—
112	C₄	—	632	1	no	—
113	C₄	—	632	2	no	—
114	C₄	#14579106	1	2	yes	complemented
115	C₄	#14579136	1	1	yes	characteristic
116	C₄	#14579189	1	1	yes	characteristic
117	C₂	—	632	2	no	—
118	C₂	#19098759	1	1	yes	characteristic
119	C₂	C₂×#14579106	1	1	yes	characteristic
120	C₂	#19099006	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579106

C₂

yes

maximal

#19098943

C₂

yes

maximal, characteristic, complemented

C₄×D₆₃₂

C₂

yes

maximal, characteristic

#19098368

C₂

yes

maximal, complemented

C₄⋊C₁₆×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

C₂²

yes

—

C₂×D₆₃₂

C₂²

yes

characteristic

#14579161

—

C₄×D₃₁₆

—

#14579106

—

#14579095

C₂²

yes

characteristic

#14579083

—

C₂×C₁₆×C₇₉

C₂²

yes

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

C₂×D₃₁₆

—

C₂×C₄×D₇₉

—

Dic₃₁₆

—

Dic₃₁₆

—

Dic₃₁₆

—

D₆₃₂

—

D₆₃₂

D₄

yes

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

(C₂×D₇₉)⋊C₄

—

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₄²×C₇₉

D₄

yes

characteristic

C₁₆×C₇₉

—

C₂²×D₇₉

—

C₂×C₄×C₇₉

D₈

yes

characteristic

C₂×C₄×C₇₉

D₈

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

D₃₁₆

—

D₃₁₆

—

C₄×D₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

C₂×D₄

yes

characteristic

C₈×C₇₉

#41

yes

characteristic

C₂²×C₇₉

C₂×D₈

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

SD₃₂

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

#459

yes

characteristic

C₂×C₇₉

C₂×SD₃₂

yes

characteristic

C₂×C₇₉

#510

yes

characteristic

D₇₉

—

#2208

—

maximal, Sylow

C₇₉

#2208

yes

characteristic, complemented, Sylow

C₂×SD₃₂

—

#494

—

C₄×D₈

—

C₄⋊C₁₆

D₇₉

yes

characteristic, complemented

#358

—

C₂×Q₁₆

—

C₂×Q₁₆

—

158

—

C₂×D₈

—

C₄⋊Q₈

—

158

—

C₄×D₄

—

158

—

SD₃₂

—

158

—

C₂×C₁₆

C₂×D₇₉

yes

—

#107

—

#102

—

158

—

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂×Q₈

—

158

—

C₂×D₄

—

158

—

C₂²×C₄

—

316

—

Q₁₆

—

316

—

Q₁₆

—

158

—

Q₁₆

—

158

—

D₈

—

D₈

—

158

—

C₂×C₈

D₃₁₆

yes

characteristic

C₂×C₈

C₂²×D₇₉

yes

characteristic

C₄⋊C₄

—

316

—

C₄⋊C₄

—

316

—

C₄⋊C₄

—

158

—

C₂²⋊C₄

—

316

—

C₄²

D₃₁₆

yes

characteristic

C₁₆

—

C₂³

—

316

—

Q₈

—

316

—

Q₈

—

316

—

D₄

—

316

—

D₄

—

158

—

C₂×C₄

—

316

—

C₂×C₄

—

316

—

100

C₂×C₄

—

632

—

101

C₂×C₄

D₆₃₂

yes

characteristic

102

C₂×C₄

D₆₃₂

yes

characteristic

103

C₂×C₄

C₂×D₃₁₆

yes

characteristic

104

C₈

—

105

C₈

D₄×D₇₉

yes

characteristic

106

C₈

#11929625

yes

characteristic

107

C₂²

—

316

—

108

C₂²

—

632

—

109

C₂²

—

632

—

110

C₂²

C₂×D₆₃₂

yes

characteristic

111

C₄

—

112

C₄

—

632

—

113

C₄

—

632

—

114

C₄

#14579106

yes

complemented

115

C₄

#14579136

yes

characteristic

116

C₄

#14579189

yes

characteristic

117

C₂

—

632

—

118

C₂

#19098759

yes

characteristic

119

C₂

C₂×#14579106

yes

characteristic

120

C₂

#19099006

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₆₃₂
commutator, cosocle	C₂×C₈×C₇₉	C₂³
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	C₄⋊C₁₆×C₇₉	C₂
socle	C₂²×C₇₉	C₂×D₈
prime radical	C₂×D₆₃₂	C₂²
hypercenter	C₄⋊C₁₆	D₇₉
hypocenter	C₇₉	#2208
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

subgroup

G/H

center

C₂²

C₂×D₆₃₂

commutator, cosocle

C₂×C₈×C₇₉

C₂³

Frattini

C₂×C₈

C₂²×D₇₉

Fitting

C₄⋊C₁₆×C₇₉

C₂

socle

C₂²×C₇₉

C₂×D₈

prime radical

C₂×D₆₃₂

C₂²

hypercenter

C₄⋊C₁₆

D₇₉

hypocenter

C₇₉

#2208

LCS

G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

N	H ≅ G/N	type
2. #19098943	C₂	semidirect
4. #19098368	C₂	semidirect
5. C₄⋊C₁₆×C₇₉	C₂	semidirect
51. C₄×C₇₉	SD₃₂	semidirect
61. C₇₉	#2208	semidirect
65. C₄⋊C₁₆	D₇₉	semidirect
114. C₄	#14579106	semidirect

H ≅ G/N

type

2. #19098943

C₂

semidirect

4. #19098368

C₂

semidirect

5. C₄⋊C₁₆×C₇₉

C₂

semidirect

51. C₄×C₇₉

SD₃₂

semidirect

61. C₇₉

#2208

semidirect

65. C₄⋊C₁₆

D₇₉

semidirect

114. C₄

#14579106

semidirect

Subgroups — #23765446

Conjugacy classes of subgroups

Complements