Group #23761409 — subgroups

Subgroups — #23761409

Order 10112.

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

normal subgroups only

This group has 126 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	C₂²⋊(C₇₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
2	#19098326	C₂	1	1	yes	maximal, characteristic, complemented
3	#466×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊Dic₇₉	—	2	1	no	—
5	C₂×C₇₉⋊C₁₆	—	2	1	no	—
6	C₂×D₈×C₇₉	C₄	1	1	yes	characteristic, complemented
7	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
8	#121×C₇₉	—	2	1	no	—
9	#107×C₇₉	C₄	1	1	yes	characteristic, complemented
10	#102×C₇₉	—	2	1	no	—
11	C₂²×Dic₇₉	—	4	1	no	—
12	C₄⋊Dic₇₉	—	2	2	no	—
13	C₄⋊Dic₇₉	—	4	1	no	—
14	C₇₉⋊C₁₆	—	4	1	no	—
15	C₂×D₄×C₇₉	—	2	1	no	—
16	C₂×D₄×C₇₉	—	4	1	no	—
17	C₂²×C₄×C₇₉	D₄	1	1	yes	characteristic
18	D₈×C₇₉	—	4	1	no	—
19	C₂×C₈×C₇₉	—	4	1	no	—
20	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
22	C₄⋊C₄×C₇₉	—	2	1	no	—
23	C₂²⋊C₄×C₇₉	—	4	1	no	—
24	C₂³×C₇₉	—	4	1	no	—
25	C₂³×C₇₉	D₈	1	1	yes	characteristic
26	D₄×C₇₉	—	4	1	no	—
27	D₄×C₇₉	—	4	1	no	—
28	D₄×C₇₉	—	8	1	no	—
29	D₄×C₇₉	—	8	1	no	—
30	C₂×C₄×C₇₉	—	2	1	no	—
31	C₂×C₄×C₇₉	—	2	1	no	—
32	C₂×C₄×C₇₉	—	4	1	no	—
33	C₂×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₇₉	SD₁₆	1	1	yes	characteristic
35	C₂×Dic₇₉	—	4	2	no	—
36	C₂×Dic₇₉	—	8	1	no	—
37	C₂×Dic₇₉	—	8	1	no	—
38	C₈×C₇₉	—	2	1	no	—
39	C₈×C₇₉	—	2	1	no	—
40	C₂²×C₇₉	—	2	1	no	—
41	C₂²×C₇₉	—	2	1	no	—
42	C₂²×C₇₉	—	8	1	no	—
43	C₂²×C₇₉	—	8	1	no	—
44	C₂²×C₇₉	—	8	1	no	—
45	C₂²×C₇₉	#102	1	1	yes	characteristic
46	C₂²×C₇₉	D₁₆	1	1	yes	characteristic
47	C₂²×C₇₉	SD₃₂	1	1	yes	characteristic
48	C₄×C₇₉	—	2	1	no	—
49	C₄×C₇₉	—	8	1	no	—
50	C₄×C₇₉	#99	1	1	yes	characteristic
51	C₄×C₇₉	#104	1	1	yes	characteristic
52	Dic₇₉	—	8	2	no	—
53	C₂×C₇₉	—	2	1	no	—
54	C₂×C₇₉	—	2	1	no	—
55	C₂×C₇₉	—	16	1	no	—
56	C₂×C₇₉	#327	1	1	yes	characteristic
57	C₂×C₇₉	#357	1	1	yes	characteristic
58	C₂×C₇₉	#360	1	1	yes	characteristic
59	#1347	—	79	1	no	maximal, Sylow
60	C₇₉	#1347	1	1	yes	characteristic, complemented, Sylow
61	#466	D₇₉	1	1	yes	characteristic
62	C₂²⋊C₁₆	—	79	1	no	—
63	#340	—	79	1	no	—
64	C₂×D₈	Dic₇₉	1	1	yes	characteristic, complemented
65	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
66	#121	—	2	1	no	—
67	C₂×C₄⋊C₄	—	158	1	no	—
68	C₂×C₁₆	—	158	1	no	—
69	#107	Dic₇₉	1	1	yes	characteristic, complemented
70	#102	—	2	1	no	—
71	C₂×D₄	—	2	1	no	—
72	C₂×D₄	—	4	1	no	—
73	C₂²×C₄	—	316	1	no	—
74	C₂²×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
75	D₈	—	4	1	no	—
76	C₂×C₈	—	4	1	no	—
77	C₂×C₈	C₂×Dic₇₉	1	1	yes	characteristic
78	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
79	C₄⋊C₄	—	2	1	no	—
80	C₄⋊C₄	—	316	1	no	—
81	C₄⋊C₄	—	158	2	no	—
82	C₂²⋊C₄	—	4	1	no	—
83	C₁₆	—	316	1	no	—
84	C₂³	—	4	1	no	—
85	C₂³	#11929609	1	1	yes	characteristic
86	D₄	—	4	1	no	—
87	D₄	—	4	1	no	—
88	D₄	—	8	1	no	—
89	D₄	—	8	1	no	—
90	C₂×C₄	—	2	1	no	—
91	C₂×C₄	—	2	1	no	—
92	C₂×C₄	—	4	1	no	—
93	C₂×C₄	—	316	2	no	—
94	C₂×C₄	—	632	1	no	—
95	C₂×C₄	—	632	1	no	—
96	C₂×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
97	C₂×C₄	#11929612	1	1	yes	characteristic
98	C₈	—	2	1	no	—
99	C₈	—	2	1	no	—
100	C₂²	—	2	1	no	—
101	C₂²	—	2	1	no	—
102	C₂²	—	8	1	no	—
103	C₂²	—	8	1	no	—
104	C₂²	—	8	1	no	—
105	C₂²	#14579082	1	1	yes	characteristic
106	C₂²	#14579102	1	1	yes	characteristic
107	C₂²	#14579105	1	1	yes	characteristic
108	C₄	—	2	1	no	—
109	C₄	—	8	1	no	—
110	C₄	—	632	2	no	—
111	C₄	#14579076	1	1	yes	characteristic
112	C₄	#14579088	1	1	yes	characteristic
113	C₂	—	2	1	no	—
114	C₂	—	2	1	no	—
115	C₂	—	16	1	no	—
116	C₂	#19098297	1	1	yes	characteristic
117	C₂	#19098364	1	1	yes	characteristic
118	C₂	#19098373	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²⋊(C₇₉⋊C₁₆)

C₂

yes

maximal, characteristic, complemented

#19098326

C₂

yes

maximal, characteristic, complemented

#466×C₇₉

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₇₉

—

C₂×C₇₉⋊C₁₆

—

C₂×D₈×C₇₉

C₄

yes

characteristic, complemented

C₂²×C₈×C₇₉

C₂²

yes

characteristic

#121×C₇₉

—

#107×C₇₉

C₄

yes

characteristic, complemented

#102×C₇₉

—

C₂²×Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₇₉⋊C₁₆

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂²×C₄×C₇₉

D₄

yes

characteristic

D₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

D₄

yes

characteristic

C₄⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

D₈

yes

characteristic

D₄×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

SD₁₆

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₈×C₇₉

—

C₈×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#102

yes

characteristic

C₂²×C₇₉

D₁₆

yes

characteristic

C₂²×C₇₉

SD₃₂

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

yes

C₄×C₇₉

yes

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

#466

D₇₉

yes

characteristic

C₂²⋊C₁₆

—

#340

—

C₂×D₈

Dic₇₉

yes

characteristic, complemented

C₂²×C₈

C₂×D₇₉

yes

characteristic

#121

—

C₂×C₄⋊C₄

—

158

—

C₂×C₁₆

—

158

—

#107

Dic₇₉

yes

characteristic, complemented

#102

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

316

—

C₂²×C₄

C₂²⋊D₇₉

yes

characteristic

D₈

—

C₂×C₈

—

C₂×C₈

C₂×Dic₇₉

yes

characteristic

C₂×C₈

C₂²⋊D₇₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

316

—

C₄⋊C₄

—

158

—

C₂²⋊C₄

—

C₁₆

—

316

—

C₂³

—

C₂³

#11929609

yes

characteristic

D₄

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

316

—

C₂×C₄

—

632

—

C₂×C₄

—

632

—

C₂×C₄

C₂²⋊Dic₇₉

yes

characteristic

C₂×C₄

#11929612

yes

characteristic

C₈

—

C₈

—

100

C₂²

—

101

C₂²

—

102

C₂²

—

103

C₂²

—

104

C₂²

—

105

C₂²

#14579082

yes

characteristic

106

C₂²

#14579102

yes

characteristic

107

C₂²

#14579105

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

632

—

111

C₄

#14579076

yes

characteristic

112

C₄

#14579088

yes

characteristic

113

C₂

—

114

C₂

—

115

C₂

—

116

C₂

#19098297

yes

characteristic

117

C₂

#19098364

yes

characteristic

118

C₂

#19098373

yes

characteristic

	subgroup	G/H
center	C₂²	#14579082
commutator	C₂×C₈×C₇₉	C₂×C₄
Frattini	C₂²×C₈	C₂×D₇₉
Fitting, prime radical	#466×C₇₉	C₂
socle	C₂²×C₇₉	#102
cosocle	C₂²×C₈×C₇₉	C₂²
hypercenter	#466	D₇₉
hypocenter	C₇₉	#1347
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #466

subgroup

G/H

center

C₂²

#14579082

commutator

C₂×C₈×C₇₉

C₂×C₄

Frattini

C₂²×C₈

C₂×D₇₉

Fitting, prime radical

#466×C₇₉

C₂

socle

C₂²×C₇₉

#102

cosocle

C₂²×C₈×C₇₉

C₂²

D₇₉

C₇₉

G ▷ C₂×C₈×C₇₉ ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #466

N	H ≅ G/N	type
1. C₂²⋊(C₇₉⋊C₁₆)	C₂	semidirect
2. #19098326	C₂	semidirect
6. C₂×D₈×C₇₉	C₄	semidirect
9. #107×C₇₉	C₄	semidirect
60. C₇₉	#1347	semidirect
64. C₂×D₈	Dic₇₉	semidirect
69. #107	Dic₇₉	semidirect

H ≅ G/N

type

1. C₂²⋊(C₇₉⋊C₁₆)

C₂

semidirect

2. #19098326

C₂

semidirect

6. C₂×D₈×C₇₉

C₄

semidirect

9. #107×C₇₉

C₄

semidirect

60. C₇₉

#1347

semidirect

64. C₂×D₈

Dic₇₉

semidirect

69. #107

Dic₇₉

semidirect

Subgroups — #23761409

Conjugacy classes of subgroups

Complements