Group #23761506 — subgroups

Subgroups — #23761506

Order 10112.

140 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 73 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	#19098601	C₂	1	1	yes	maximal, characteristic
2	C₂×#14579093	C₂	1	1	yes	maximal, characteristic
3	C₂×M₃₂×C₇₉	C₂	1	1	yes	maximal, characteristic
4	#14579120	—	2	1	no	—
5	C₂×C₄⋊Dic₇₉	—	2	1	no	—
6	#14579095	C₄	1	2	yes	complemented
7	#14579093	—	2	1	no	—
8	#14579093	—	2	1	no	—
9	#14579093	C₄	1	2	yes	complemented
10	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
11	M₃₂×C₇₉	—	2	1	no	—
12	M₃₂×C₇₉	C₄	1	2	yes	complemented
13	C₂×C₁₆×C₇₉	—	2	1	no	—
14	C₂²×Dic₇₉	—	4	1	no	—
15	C₄⋊Dic₇₉	—	2	2	no	—
16	C₄⋊Dic₇₉	—	2	2	no	—
17	C₄⋊Dic₇₉	—	4	1	no	—
18	C₂²⋊Dic₇₉	—	4	1	no	—
19	C₄×Dic₇₉	—	4	1	no	—
20	C₂²×C₄×C₇₉	D₄	1	1	yes	characteristic
21	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
25	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
26	C₂×C₈×C₇₉	Q₈	1	1	yes	characteristic
27	C₁₆×C₇₉	—	2	2	no	—
28	C₂³×C₇₉	D₈	1	1	yes	characteristic
29	C₂×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₇₉	SD₁₆	1	1	yes	characteristic
33	C₂×C₄×C₇₉	SD₁₆	1	1	yes	characteristic
34	C₂×C₄×C₇₉	Q₁₆	1	1	yes	characteristic
35	C₂×Dic₇₉	—	4	2	no	—
36	C₂×Dic₇₉	—	4	2	no	—
37	C₂×Dic₇₉	—	8	2	no	—
38	C₈×C₇₉	C₄²	1	1	yes	characteristic
39	C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
40	C₈×C₇₉	C₄⋊C₄	1	1	yes	characteristic
41	C₈×C₇₉	C₄⋊C₄	1	1	yes	characteristic
42	C₂²×C₇₉	—	2	2	no	—
43	C₂²×C₇₉	#102	1	1	yes	characteristic
44	C₂²×C₇₉	#102	1	1	yes	characteristic
45	C₂²×C₇₉	#107	1	1	yes	characteristic
46	C₄×C₇₉	#95	1	1	yes	characteristic
47	C₄×C₇₉	#103	1	1	yes	characteristic
48	C₄×C₇₉	#103	1	1	yes	characteristic
49	C₄×C₇₉	#106	1	1	yes	characteristic
50	Dic₇₉	—	8	2	no	—
51	Dic₇₉	—	8	2	no	—
52	C₂×C₇₉	—	2	1	no	—
53	C₂×C₇₉	—	2	1	no	—
54	C₂×C₇₉	#340	1	1	yes	characteristic
55	C₂×C₇₉	#360	1	2	yes	—
56	#1386	—	79	1	no	maximal, Sylow
57	C₇₉	#1386	1	1	yes	characteristic, complemented, Sylow
58	C₂×M₃₂	D₇₉	1	1	yes	characteristic
59	#427	—	79	1	no	—
60	C₂×#106	—	79	1	no	—
61	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
62	#117	—	158	1	no	—
63	C₂×C₄⋊C₄	—	158	1	no	—
64	M₃₂	—	2	1	no	—
65	M₃₂	Dic₇₉	1	2	yes	complemented
66	C₂×C₁₆	—	2	1	no	—
67	#107	—	79	2	no	—
68	#106	—	79	2	no	—
69	#106	—	158	1	no	—
70	#106	—	158	1	no	—
71	C₂²×C₄	—	316	1	no	—
72	C₂²×C₄	D₃₁₆	1	1	yes	characteristic
73	C₂×C₈	Dic₁₅₈	1	1	yes	characteristic
74	C₂×C₈	C₄×D₇₉	1	1	yes	characteristic
75	C₂×C₈	C₄×D₇₉	1	1	yes	characteristic
76	C₂×C₈	C₂×Dic₇₉	1	1	yes	characteristic
77	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
78	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
79	C₄⋊C₄	—	316	1	no	—
80	C₄⋊C₄	—	158	2	no	—
81	C₄⋊C₄	—	158	2	no	—
82	C₂²⋊C₄	—	316	1	no	—
83	C₄²	—	316	1	no	—
84	C₁₆	—	2	2	no	—
85	C₂³	D₆₃₂	1	1	yes	characteristic
86	C₂×C₄	—	316	2	no	—
87	C₂×C₄	—	316	2	no	—
88	C₂×C₄	—	632	2	no	—
89	C₂×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
90	C₂×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
91	C₂×C₄	C₄⋊Dic₇₉	1	1	yes	characteristic
92	C₂×C₄	#11929613	1	1	yes	characteristic
93	C₂×C₄	#11929613	1	1	yes	characteristic
94	C₂×C₄	Dic₃₁₆	1	1	yes	characteristic
95	C₈	C₄×Dic₇₉	1	1	yes	characteristic
96	C₈	C₂²⋊Dic₇₉	1	1	yes	characteristic
97	C₈	Dic₇₉⋊C₄	1	1	yes	characteristic
98	C₈	Dic₇₉⋊C₄	1	1	yes	characteristic
99	C₂²	—	2	2	no	—
100	C₂²	#14579083	1	1	yes	characteristic
101	C₂²	#14579083	1	1	yes	characteristic
102	C₂²	#14579095	1	1	yes	characteristic
103	C₄	—	632	2	no	—
104	C₄	—	632	2	no	—
105	C₄	C₇₉⋊#95	1	1	yes	characteristic
106	C₄	#14579086	1	1	yes	characteristic
107	C₄	#14579086	1	1	yes	characteristic
108	C₄	#14579093	1	1	yes	characteristic
109	C₂	—	2	1	no	—
110	C₂	—	2	1	no	—
111	C₂	#19098326	1	1	yes	characteristic
112	C₂	#19098374	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19098601

C₂

yes

maximal, characteristic

C₂×#14579093

C₂

yes

maximal, characteristic

C₂×M₃₂×C₇₉

C₂

yes

maximal, characteristic

#14579120

—

C₂×C₄⋊Dic₇₉

—

#14579095

C₄

yes

—

—

C₄

yes

complemented

C₂²×C₈×C₇₉

C₂²

yes

characteristic

M₃₂×C₇₉

—

M₃₂×C₇₉

C₄

yes

complemented

C₂×C₁₆×C₇₉

—

C₂²×Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₂²⋊Dic₇₉

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

Q₈

yes

characteristic

C₁₆×C₇₉

—

C₂³×C₇₉

D₈

yes

characteristic

C₂×C₄×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₉

SD₁₆

yes

characteristic

C₂×C₄×C₇₉

SD₁₆

yes

characteristic

C₂×C₄×C₇₉

Q₁₆

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₈×C₇₉

C₄²

yes

characteristic

C₈×C₇₉

C₂²⋊C₄

yes

characteristic

C₈×C₇₉

C₄⋊C₄

yes

characteristic

C₈×C₇₉

C₄⋊C₄

yes

characteristic

C₂²×C₇₉

—

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

#340

yes

characteristic

C₂×C₇₉

#360

yes

—

#1386

—

maximal, Sylow

C₇₉

#1386

yes

characteristic, complemented, Sylow

C₂×M₃₂

D₇₉

yes

characteristic

#427

—

C₂×#106

—

C₂²×C₈

C₂×D₇₉

yes

characteristic

#117

—

158

—

C₂×C₄⋊C₄

—

158

—

M₃₂

—

M₃₂

Dic₇₉

yes

complemented

C₂×C₁₆

—

#107

—

#106

—

#106

—

158

—

#106

—

158

—

C₂²×C₄

—

316

—

C₂²×C₄

D₃₁₆

yes

characteristic

C₂×C₈

Dic₁₅₈

yes

characteristic

C₂×C₈

C₄×D₇₉

yes

characteristic

C₂×C₈

C₄×D₇₉

yes

characteristic

C₂×C₈

C₂×Dic₇₉

yes

characteristic

C₂×C₈

C₂²⋊D₇₉

yes

characteristic

C₂×C₈

C₂²⋊D₇₉

yes

characteristic

C₄⋊C₄

—

316

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₂²⋊C₄

—

316

—

C₄²

—

316

—

C₁₆

—

C₂³

D₆₃₂

yes

characteristic

C₂×C₄

—

316

—

C₂×C₄

—

316

—

C₂×C₄

—

632

—

C₂×C₄

(C₂×D₇₉)⋊C₄

yes

characteristic

C₂×C₄

(C₂×D₇₉)⋊C₄

yes

characteristic

C₂×C₄

C₄⋊Dic₇₉

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

Dic₃₁₆

yes

characteristic

C₈

C₄×Dic₇₉

yes

characteristic

C₈

C₂²⋊Dic₇₉

yes

characteristic

C₈

Dic₇₉⋊C₄

yes

characteristic

C₈

Dic₇₉⋊C₄

yes

characteristic

C₂²

—

100

C₂²

#14579083

yes

characteristic

101

C₂²

#14579083

yes

characteristic

102

C₂²

#14579095

yes

characteristic

103

C₄

—

632

—

104

C₄

—

632

—

105

C₄

C₇₉⋊#95

yes

characteristic

106

C₄

#14579086

yes

characteristic

107

C₄

#14579086

yes

characteristic

108

C₄

#14579093

yes

characteristic

109

C₂

—

110

C₂

—

111

C₂

#19098326

yes

characteristic

112

C₂

#19098374

yes

—

	subgroup	G/H
center	C₂²	#14579083
commutator	C₈×C₇₉	C₄²
Frattini	C₂²×C₈	C₂×D₇₉
Fitting	C₂×M₃₂×C₇₉	C₂
socle	C₂²×C₇₉	#102
prime radical	C₂³×C₇₉	D₈
cosocle	C₂²×C₈×C₇₉	C₂²
hypercenter	C₂×M₃₂	D₇₉
hypocenter	C₇₉	#1386
LCS	G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

subgroup

G/H

center

C₂²

#14579083

commutator

C₈×C₇₉

C₄²

Frattini

C₂²×C₈

C₂×D₇₉

Fitting

C₂×M₃₂×C₇₉

C₂

socle

C₂²×C₇₉

#102

prime radical

C₂³×C₇₉

D₈

cosocle

C₂²×C₈×C₇₉

C₂²

hypercenter

C₂×M₃₂

D₇₉

hypocenter

C₇₉

#1386

LCS

G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
6. #14579095	C₄	semidirect
9. #14579093	C₄	semidirect
12. M₃₂×C₇₉	C₄	semidirect
57. C₇₉	#1386	semidirect
65. M₃₂	Dic₇₉	semidirect

H ≅ G/N

type

6. #14579095

C₄

semidirect

9. #14579093

C₄

semidirect

12. M₃₂×C₇₉

C₄

semidirect

57. C₇₉

#1386

semidirect

65. M₃₂

Dic₇₉

semidirect

Subgroups — #23761506

Conjugacy classes of subgroups

Complements