Group #23762479 — subgroups

Subgroups — #23762479

Order 10112.

228 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 57 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	#19099293	C₂	1	1	yes	maximal, characteristic, complemented
2	#19098937	C₂	1	1	yes	maximal, characteristic
3	#19098764	C₂	1	2	yes	maximal
4	#19098293	C₂	1	2	yes	maximal, complemented
5	#333×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11929613	—	2	2	no	—
7	C₂×#11929611	—	2	2	no	—
8	#14579160	—	2	2	no	—
9	#14579159	—	2	2	no	—
10	#14579158	C₂²	1	1	yes	characteristic
11	C₄×Dic₁₅₈	C₂²	1	2	yes	—
12	#14579126	—	2	2	no	—
13	#14579083	—	2	2	no	—
14	C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
15	C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
16	C₄⋊C₈×C₇₉	C₂²	1	2	yes	—
17	C₂×Dic₁₅₈	—	2	2	no	—
18	C₂×Dic₁₅₈	D₄	1	2	yes	—
19	C₂×D₃₁₆	—	2	2	no	—
20	C₂×D₃₁₆	—	2	1	no	—
21	#11929613	—	4	4	no	—
22	#11929611	—	4	4	no	—
23	C₂×C₇₉⋊C₈	—	2	1	no	—
24	C₄⋊Dic₇₉	D₄	1	2	yes	—
25	Dic₇₉⋊C₄	—	2	4	no	—
26	Dic₇₉⋊C₄	—	2	2	no	—
27	C₄×Dic₇₉	—	2	2	no	—
28	C₄×Dic₇₉	—	2	2	no	—
29	C₂×Q₈×C₇₉	D₄	1	2	yes	—
30	C₂×C₈×C₇₉	—	2	2	no	—
31	C₄⋊C₄×C₇₉	—	2	2	no	—
32	C₄²×C₇₉	C₂³	1	1	yes	characteristic
33	C₂²×D₇₉	—	4	1	no	—
34	Q₈×C₇₉	—	4	2	no	—
35	C₂×C₄×C₇₉	—	2	2	no	—
36	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
37	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
38	C₂×Dic₇₉	—	2	2	no	—
39	C₂×Dic₇₉	—	2	2	no	—
40	D₃₁₆	—	4	2	no	—
41	D₃₁₆	—	4	2	no	—
42	D₃₁₆	—	4	2	no	—
43	Dic₁₅₈	—	2	2	no	—
44	Dic₁₅₈	—	8	2	no	—
45	Dic₁₅₈	SD₁₆	1	4	yes	complemented
46	C₈×C₇₉	—	4	2	no	—
47	C₇₉⋊C₈	—	2	2	no	—
48	C₂²×C₇₉	#120	1	1	yes	characteristic
49	C₂×D₇₉	—	8	2	no	—
50	C₂×D₇₉	—	8	1	no	—
51	C₄×C₇₉	—	2	1	no	—
52	C₄×C₇₉	—	4	2	no	—
53	C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
54	C₄×C₇₉	#137	1	2	yes	—
55	Dic₇₉	—	2	4	no	—
56	Dic₇₉	—	4	2	no	—
57	C₂×C₇₉	#448	1	2	yes	—
58	C₂×C₇₉	#453	1	1	yes	characteristic
59	D₇₉	—	16	1	no	—
60	#1623	—	79	1	no	maximal, Sylow
61	C₇₉	#1623	1	1	yes	characteristic, complemented, Sylow
62	Q₈²	—	79	1	no	—
63	#492	—	79	1	no	—
64	#460	—	79	2	no	—
65	#333	D₇₉	1	1	yes	characteristic, complemented
66	Q₈⋊C₈	—	79	2	no	—
67	C₂×SD₁₆	—	158	2	no	—
68	C₂×SD₁₆	—	158	2	no	—
69	C₄⋊Q₈	—	158	2	no	—
70	C₄⋊Q₈	—	158	2	no	—
71	C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
72	#127	—	79	1	no	—
73	C₄×Q₈	—	79	2	no	—
74	C₄×Q₈	—	158	2	no	—
75	C₄⋊C₈	C₂×D₇₉	1	2	yes	—
76	#102	—	158	2	no	—
77	C₄×C₈	—	79	1	no	—
78	C₂×Q₈	—	79	2	no	—
79	C₂×Q₈	—	158	2	no	—
80	C₂×Q₈	D₃₁₆	1	2	yes	—
81	C₂×D₄	—	158	2	no	—
82	C₂×D₄	—	158	1	no	—
83	SD₁₆	—	316	4	no	—
84	SD₁₆	—	316	4	no	—
85	C₂×C₈	—	2	2	no	—
86	C₂×C₈	—	158	1	no	—
87	C₄⋊C₄	—	2	2	no	—
88	C₄⋊C₄	—	79	2	no	—
89	C₄⋊C₄	—	158	4	no	—
90	C₄⋊C₄	—	158	2	no	—
91	C₄²	—	158	2	no	—
92	C₄²	—	158	2	no	—
93	C₄²	C₂²×D₇₉	1	1	yes	characteristic
94	C₂³	—	316	1	no	—
95	Q₈	—	4	2	no	—
96	Q₈	—	79	4	no	—
97	Q₈	—	632	2	no	—
98	Q₈	—	158	2	no	—
99	D₄	—	316	2	no	—
100	D₄	—	316	2	no	—
101	D₄	—	316	2	no	—
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	158	2	no	—
104	C₂×C₄	—	158	2	no	—
105	C₂×C₄	D₄×D₇₉	1	2	yes	—
106	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
107	C₈	—	4	2	no	—
108	C₈	—	158	2	no	—
109	C₂²	—	632	2	no	—
110	C₂²	—	632	1	no	—
111	C₂²	#14579131	1	1	yes	characteristic
112	C₄	—	2	1	no	—
113	C₄	—	4	2	no	—
114	C₄	—	316	2	no	—
115	C₄	—	158	4	no	—
116	C₄	SD₁₆×D₇₉	1	2	yes	—
117	C₄	#14579193	1	2	yes	—
118	C₂	—	1264	1	no	—
119	C₂	#19098703	1	2	yes	—
120	C₂	#19098733	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19099293

C₂

yes

maximal, characteristic, complemented

#19098937

C₂

yes

maximal, characteristic

#19098764

C₂

yes

maximal

#19098293

C₂

yes

maximal, complemented

#333×C₇₉

C₂

yes

maximal, characteristic, complemented

—

—

—

—

C₂²

yes

characteristic

C₄×Dic₁₅₈

C₂²

yes

—

#14579126

—

#14579083

—

C₄×C₇₉⋊C₈

C₂²

yes

characteristic

C₄⋊Q₈×C₇₉

C₂²

yes

characteristic

C₄⋊C₈×C₇₉

C₂²

yes

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

D₄

yes

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

#11929613

—

#11929611

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

D₄

yes

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂×Q₈×C₇₉

D₄

yes

—

C₂×C₈×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

C₂³

yes

characteristic

C₂²×D₇₉

—

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

D₃₁₆

—

D₃₁₆

—

D₃₁₆

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

SD₁₆

yes

complemented

C₈×C₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

#120

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂×SD₁₆

yes

—

C₄×C₇₉

#137

yes

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

#448

yes

—

C₂×C₇₉

#453

yes

characteristic

D₇₉

—

#1623

—

maximal, Sylow

C₇₉

#1623

yes

characteristic, complemented, Sylow

Q₈²

—

#492

—

#460

—

#333

D₇₉

yes

characteristic, complemented

Q₈⋊C₈

—

C₂×SD₁₆

—

158

—

C₂×SD₁₆

—

158

—

C₄⋊Q₈

—

158

—

C₄⋊Q₈

—

158

—

C₄⋊Q₈

C₂×D₇₉

yes

characteristic

#127

—

C₄×Q₈

—

C₄×Q₈

—

158

—

C₄⋊C₈

C₂×D₇₉

yes

—

#102

—

158

—

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

158

—

C₂×Q₈

D₃₁₆

yes

—

C₂×D₄

—

158

—

C₂×D₄

—

158

—

SD₁₆

—

316

—

SD₁₆

—

316

—

C₂×C₈

—

C₂×C₈

—

158

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄²

—

158

—

C₄²

—

158

—

C₄²

C₂²×D₇₉

yes

characteristic

C₂³

—

316

—

Q₈

—

Q₈

—

Q₈

—

632

—

Q₈

—

158

—

D₄

—

316

—

100

D₄

—

316

—

101

D₄

—

316

—

102

C₂×C₄

—

103

C₂×C₄

—

158

—

104

C₂×C₄

—

158

—

105

C₂×C₄

D₄×D₇₉

yes

—

106

C₂×C₄

C₂×D₃₁₆

yes

characteristic

107

C₈

—

108

C₈

—

158

—

109

C₂²

—

632

—

110

C₂²

—

632

—

111

C₂²

#14579131

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

—

316

—

115

C₄

—

158

—

116

C₄

SD₁₆×D₇₉

yes

—

117

C₄

#14579193

yes

—

118

C₂

—

1264

—

119

C₂

#19098703

yes

—

120

C₂

#19098733

yes

characteristic

	subgroup	G/H
center	C₂²	#14579131
commutator, cosocle	C₄²×C₇₉	C₂³
Frattini	C₄²	C₂²×D₇₉
Fitting	#333×C₇₉	C₂
socle	C₂²×C₇₉	#120
prime radical	#14579158	C₂²
hypercenter	#333	D₇₉
hypocenter	C₇₉	#1623
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #333

subgroup

G/H

center

C₂²

#14579131

commutator, cosocle

C₄²×C₇₉

C₂³

Frattini

C₄²

C₂²×D₇₉

Fitting

#333×C₇₉

C₂

C₂²×C₇₉

C₂²

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #333

N	H ≅ G/N	type
1. #19099293	C₂	semidirect
4. #19098293	C₂	semidirect
5. #333×C₇₉	C₂	semidirect
45. Dic₁₅₈	SD₁₆	semidirect
61. C₇₉	#1623	semidirect
65. #333	D₇₉	semidirect

H ≅ G/N

type

1. #19099293

C₂

semidirect

4. #19098293

C₂

semidirect

5. #333×C₇₉

C₂

semidirect

45. Dic₁₅₈

SD₁₆

semidirect

61. C₇₉

#1623

semidirect

65. #333

D₇₉

semidirect

Subgroups — #23762479

Conjugacy classes of subgroups

Complements