Group #23763508 — subgroups

Subgroups — #23763508

Order 10112.

296 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 89 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×#14579076	C₂	1	2	yes	maximal
2	#19098329	C₂	1	4	yes	maximal, complemented
3	#518×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂²⋊Dic₇₉	C₂²	1	4	yes	—
5	#14579076	—	2	4	no	—
6	C₂²×D₄×C₇₉	C₂²	1	1	yes	characteristic
7	C₄×D₄×C₇₉	—	2	4	no	—
8	#117×C₇₉	C₄	1	2	yes	complemented
9	C₂×C₂²⋊C₄×C₇₉	C₄	1	2	yes	complemented
10	C₂×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
11	C₂²×Dic₇₉	—	2	4	no	—
12	C₂²⋊Dic₇₉	—	2	4	no	—
13	C₂²⋊Dic₇₉	—	2	4	no	—
14	C₂⁴×C₇₉	C₂×C₄	1	1	yes	characteristic
15	C₂⁴×C₇₉	C₂³	1	1	yes	characteristic
16	C₂×D₄×C₇₉	—	2	4	no	—
17	C₂×D₄×C₇₉	D₄	1	4	yes	—
18	C₂²×C₄×C₇₉	—	2	2	no	—
19	C₂²×C₄×C₇₉	—	2	2	no	—
20	C₂²×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
21	C₄⋊C₄×C₇₉	—	2	2	no	—
22	C₂²⋊C₄×C₇₉	—	2	2	no	—
23	C₂²⋊C₄×C₇₉	—	2	2	no	—
24	C₂²⋊C₄×C₇₉	C₂×C₄	1	4	yes	—
25	C₄²×C₇₉	—	2	2	no	—
26	C₂³×C₇₉	—	2	2	no	—
27	C₂³×C₇₉	—	8	1	no	—
28	C₂³×C₇₉	—	8	1	no	—
29	C₂³×C₇₉	C₂²⋊C₄	1	2	yes	—
30	C₂³×C₇₉	C₂²×C₄	1	1	yes	characteristic
31	C₂³×C₇₉	C₂×D₄	1	2	yes	—
32	C₂³×C₇₉	#41	1	4	yes	—
33	D₄×C₇₉	—	2	8	no	—
34	C₂×C₄×C₇₉	—	2	2	no	—
35	C₂×C₄×C₇₉	—	2	4	no	—
36	C₂×C₄×C₇₉	—	8	2	no	—
37	C₂×C₄×C₇₉	—	8	2	no	—
38	C₂×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
39	C₂×Dic₇₉	—	4	4	no	—
40	C₂×Dic₇₉	—	8	4	no	—
41	C₂²×C₇₉	—	2	2	no	—
42	C₂²×C₇₉	—	4	2	no	—
43	C₂²×C₇₉	—	4	1	no	—
44	C₂²×C₇₉	—	4	4	no	—
45	C₂²×C₇₉	—	4	2	no	—
46	C₂²×C₇₉	—	8	2	no	—
47	C₂²×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
48	C₂²×C₇₉	#117	1	2	yes	—
49	C₂²×C₇₉	#123	1	4	yes	—
50	C₄×C₇₉	—	2	2	no	—
51	C₄×C₇₉	—	4	4	no	—
52	Dic₇₉	—	8	4	no	—
53	C₂×C₇₉	—	2	4	no	—
54	C₂×C₇₉	—	2	1	no	—
55	C₂×C₇₉	—	2	2	no	—
56	C₂×C₇₉	—	4	2	no	—
57	C₂×C₇₉	#381	1	1	yes	characteristic
58	#1828	—	79	1	no	maximal, Sylow
59	C₇₉	#1828	1	1	yes	characteristic, complemented, Sylow
60	#518	D₇₉	1	1	yes	characteristic
61	C₂×#99	—	79	2	no	—
62	#342	—	79	4	no	—
63	C₂²×D₄	C₂×D₇₉	1	1	yes	characteristic
64	C₄×D₄	—	2	4	no	—
65	#117	Dic₇₉	1	2	yes	complemented
66	C₂×C₂²⋊C₄	—	79	4	no	—
67	C₂×C₂²⋊C₄	Dic₇₉	1	2	yes	complemented
68	C₂×C₂²⋊C₄	C₂×D₇₉	1	2	yes	—
69	#99	—	158	4	no	—
70	C₂⁴	C₂×Dic₇₉	1	1	yes	characteristic
71	C₂⁴	C₂²×D₇₉	1	1	yes	characteristic
72	C₂×D₄	—	2	4	no	—
73	C₂×D₄	C₂²⋊D₇₉	1	4	yes	—
74	C₂²×C₄	—	2	2	no	—
75	C₂²×C₄	—	2	2	no	—
76	C₂²×C₄	—	158	4	no	—
77	C₂²×C₄	C₂×Dic₇₉	1	1	yes	characteristic
78	C₄⋊C₄	—	2	2	no	—
79	C₂²⋊C₄	—	2	2	no	—
80	C₂²⋊C₄	—	2	2	no	—
81	C₂²⋊C₄	—	158	4	no	—
82	C₂²⋊C₄	—	158	4	no	—
83	C₂²⋊C₄	C₂×Dic₇₉	1	4	yes	—
84	C₄²	—	2	2	no	—
85	C₂³	—	2	2	no	—
86	C₂³	—	8	1	no	—
87	C₂³	—	8	1	no	—
88	C₂³	C₂²⋊Dic₇₉	1	2	yes	—
89	C₂³	C₂²×Dic₇₉	1	1	yes	characteristic
90	C₂³	C₂×C₂²⋊D₇₉	1	2	yes	—
91	C₂³	#11929624	1	4	yes	—
92	D₄	—	2	8	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	2	4	no	—
95	C₂×C₄	—	8	2	no	—
96	C₂×C₄	—	8	2	no	—
97	C₂×C₄	—	316	4	no	—
98	C₂×C₄	—	632	4	no	—
99	C₂×C₄	C₂²⋊Dic₇₉	1	2	yes	—
100	C₂²	—	2	2	no	—
101	C₂²	—	4	2	no	—
102	C₂²	—	4	4	no	—
103	C₂²	—	4	1	no	—
104	C₂²	—	4	2	no	—
105	C₂²	—	8	2	no	—
106	C₂²	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
107	C₂²	#14579120	1	2	yes	—
108	C₂²	#14579144	1	4	yes	—
109	C₄	—	2	2	no	—
110	C₄	—	4	4	no	—
111	C₄	—	632	4	no	—
112	C₂	—	2	1	no	—
113	C₂	—	2	4	no	—
114	C₂	—	2	2	no	—
115	C₂	—	4	2	no	—
116	C₂	#19098426	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579076

C₂

yes

maximal

#19098329

C₂

yes

maximal, complemented

#518×C₇₉

C₂

yes

maximal, characteristic

C₂×C₂²⋊Dic₇₉

C₂²

yes

—

#14579076

—

C₂²×D₄×C₇₉

C₂²

yes

characteristic

C₄×D₄×C₇₉

—

#117×C₇₉

C₄

yes

complemented

C₂×C₂²⋊C₄×C₇₉

C₄

yes

complemented

C₂×C₂²⋊C₄×C₇₉

C₂²

yes

—

C₂²×Dic₇₉

—

C₂²⋊Dic₇₉

—

C₂²⋊Dic₇₉

—

C₂⁴×C₇₉

C₂×C₄

yes

characteristic

C₂⁴×C₇₉

C₂³

yes

characteristic

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

D₄

yes

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂×C₄

yes

characteristic

C₄⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

C₂×C₄

yes

—

C₄²×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

C₂²⋊C₄

yes

—

C₂³×C₇₉

C₂²×C₄

yes

characteristic

C₂³×C₇₉

C₂×D₄

yes

—

C₂³×C₇₉

#41

yes

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²⋊C₄

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₇₉

#117

yes

—

C₂²×C₇₉

#123

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

#518

D₇₉

yes

characteristic

C₂×#99

—

#342

—

C₂²×D₄

C₂×D₇₉

yes

characteristic

C₄×D₄

—

#117

Dic₇₉

yes

complemented

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

Dic₇₉

yes

complemented

C₂×C₂²⋊C₄

C₂×D₇₉

yes

—

#99

—

158

—

C₂⁴

C₂×Dic₇₉

yes

characteristic

C₂⁴

C₂²×D₇₉

yes

characteristic

C₂×D₄

—

C₂×D₄

C₂²⋊D₇₉

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

158

—

C₂²×C₄

C₂×Dic₇₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

158

—

C₂²⋊C₄

—

158

—

C₂²⋊C₄

C₂×Dic₇₉

yes

—

C₄²

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂²⋊Dic₇₉

yes

—

C₂³

C₂²×Dic₇₉

yes

characteristic

C₂³

C₂×C₂²⋊D₇₉

yes

—

C₂³

#11929624

yes

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

316

—

C₂×C₄

—

632

—

C₂×C₄

C₂²⋊Dic₇₉

yes

—

100

C₂²

—

101

C₂²

—

102

C₂²

—

103

C₂²

—

104

C₂²

—

105

C₂²

—

106

C₂²

C₂×C₂²⋊Dic₇₉

yes

characteristic

107

C₂²

#14579120

yes

—

108

C₂²

#14579144

yes

—

109

C₄

—

110

C₄

—

111

C₄

—

632

—

112

C₂

—

113

C₂

—

114

C₂

—

115

C₂

—

116

C₂

#19098426

yes

characteristic

	subgroup	G/H
center	C₂	#19098426
commutator	C₂³×C₇₉	C₂²×C₄
Frattini	C₂⁴	C₂²×D₇₉
Fitting	#518×C₇₉	C₂
socle	C₂×C₇₉	#381
prime radical	C₂²×D₄×C₇₉	C₂²
cosocle	C₂⁴×C₇₉	C₂³
hypercenter	#518	D₇₉
hypocenter	C₇₉	#1828
LCS	G ▷ C₂³×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ #518

subgroup

G/H

center

C₂

#19098426

commutator

C₂³×C₇₉

C₂²×C₄

Frattini

C₂⁴

C₂²×D₇₉

Fitting

#518×C₇₉

C₂

socle

C₂×C₇₉

#381

prime radical

C₂²×D₄×C₇₉

C₂²

cosocle

C₂⁴×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂³×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂ ◁ C₂⁴ ◁ #518

N	H ≅ G/N	type
2. #19098329	C₂	semidirect
8. #117×C₇₉	C₄	semidirect
9. C₂×C₂²⋊C₄×C₇₉	C₄	semidirect
59. C₇₉	#1828	semidirect
65. #117	Dic₇₉	semidirect
67. C₂×C₂²⋊C₄	Dic₇₉	semidirect

H ≅ G/N

type

2. #19098329

C₂

semidirect

8. #117×C₇₉

C₄

semidirect

9. C₂×C₂²⋊C₄×C₇₉

C₄

semidirect

59. C₇₉

#1828

semidirect

65. #117

Dic₇₉

semidirect

67. C₂×C₂²⋊C₄

Dic₇₉

semidirect

Subgroups — #23763508

Conjugacy classes of subgroups

Complements