Group #23762910 — subgroups

Subgroups — #23762910

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	#19098765	C₂	1	2	yes	maximal
2	#19098642	C₂	1	1	yes	maximal, characteristic
3	#19098314	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098309	C₂	1	2	yes	maximal, complemented
5	#500×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11929611	—	2	2	no	—
7	C₂×#11929607	—	2	1	no	—
8	C₄×D₃₁₆	C₂²	1	1	yes	characteristic
9	C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
10	C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
11	#14579085	—	2	2	no	—
12	(C₂×D₇₉)⋊C₈	—	2	1	no	—
13	C₄⋊Q₈×C₇₉	C₂²	1	2	yes	—
14	#107×C₇₉	—	2	1	no	—
15	#107×C₇₉	—	2	1	no	—
16	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×D₃₁₆	D₄	1	1	yes	characteristic
18	C₂×C₄×D₇₉	—	2	1	no	—
19	#11929611	—	4	4	no	—
20	#11929607	—	4	2	no	—
21	C₂×C₇₉⋊C₈	—	2	1	no	—
22	C₂×C₇₉⋊C₈	—	2	2	no	—
23	C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
24	(C₂×D₇₉)⋊C₄	—	2	1	no	—
25	C₂×Q₈×C₇₉	—	2	2	no	—
26	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
27	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
28	C₄⋊C₄×C₇₉	—	2	2	no	—
29	C₄⋊C₄×C₇₉	—	2	2	no	—
30	C₄²×C₇₉	C₂³	1	1	yes	characteristic
31	C₂²×D₇₉	—	2	1	no	—
32	Q₈×C₇₉	—	4	2	no	—
33	Q₈×C₇₉	—	4	2	no	—
34	C₂×C₄×C₇₉	—	4	2	no	—
35	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
38	C₂×Dic₇₉	—	2	1	no	—
39	D₃₁₆	—	2	2	no	—
40	C₄×D₇₉	—	4	1	no	—
41	C₄×D₇₉	—	4	1	no	—
42	C₈×C₇₉	—	2	1	no	—
43	C₈×C₇₉	SD₁₆	1	2	yes	complemented
44	C₇₉⋊C₈	—	4	1	no	—
45	C₇₉⋊C₈	—	4	2	no	—
46	C₂²×C₇₉	#121	1	1	yes	characteristic
47	C₂×D₇₉	—	4	1	no	—
48	C₂×D₇₉	—	4	1	no	—
49	C₂×D₇₉	—	4	1	no	—
50	C₄×C₇₉	—	2	1	no	—
51	C₄×C₇₉	—	8	2	no	—
52	C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
53	C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
54	C₄×C₇₉	#137	1	1	yes	characteristic
55	Dic₇₉	—	4	1	no	—
56	C₂×C₇₉	#461	1	1	yes	characteristic
57	C₂×C₇₉	#469	1	1	yes	characteristic
58	C₂×C₇₉	#473	1	1	yes	characteristic
59	D₇₉	—	8	1	no	—
60	#1693	—	79	1	no	maximal, Sylow
61	C₇₉	#1693	1	1	yes	characteristic, complemented, Sylow
62	#500	D₇₉	1	1	yes	characteristic, complemented
63	#461	—	79	2	no	—
64	#436	—	79	1	no	—
65	#334	—	79	1	no	—
66	#332	—	79	2	no	—
67	C₂×SD₁₆	—	158	2	no	—
68	C₂×M₁₆	—	158	1	no	—
69	C₄⋊Q₈	C₂×D₇₉	1	2	yes	—
70	C₄×D₄	—	79	1	no	—
71	#107	—	2	1	no	—
72	#107	—	2	1	no	—
73	C₄⋊C₈	—	79	1	no	—
74	C₄⋊C₈	—	79	2	no	—
75	#103	—	158	2	no	—
76	C₂²⋊C₈	—	158	1	no	—
77	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
78	C₂×Q₈	—	2	2	no	—
79	C₂×D₄	—	79	1	no	—
80	C₂²×C₄	—	158	1	no	—
81	SD₁₆	—	316	4	no	—
82	M₁₆	—	316	2	no	—
83	C₂×C₈	—	158	2	no	—
84	C₂×C₈	—	158	1	no	—
85	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
86	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
87	C₄⋊C₄	—	2	2	no	—
88	C₄⋊C₄	—	2	2	no	—
89	C₄⋊C₄	—	79	1	no	—
90	C₂²⋊C₄	—	158	1	no	—
91	C₄²	C₂²×D₇₉	1	1	yes	characteristic
92	C₂³	—	158	1	no	—
93	Q₈	—	4	2	no	—
94	Q₈	—	4	2	no	—
95	D₄	—	158	2	no	—
96	C₂×C₄	—	4	2	no	—
97	C₂×C₄	—	316	1	no	—
98	C₂×C₄	—	316	1	no	—
99	C₂×C₄	—	158	1	no	—
100	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
101	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
102	C₂×C₄	#11929623	1	1	yes	characteristic
103	C₈	—	2	1	no	—
104	C₈	—	316	1	no	—
105	C₈	—	316	2	no	—
106	C₈	#11929611	1	2	yes	complemented
107	C₂²	—	316	1	no	—
108	C₂²	—	316	1	no	—
109	C₂²	—	316	1	no	—
110	C₂²	#14579132	1	1	yes	characteristic
111	C₄	—	2	1	no	—
112	C₄	—	8	2	no	—
113	C₄	—	316	1	no	—
114	C₄	C₂×#11929611	1	1	yes	characteristic
115	C₄	#14579185	1	2	yes	—
116	C₄	#14579192	1	1	yes	characteristic
117	C₂	—	632	1	no	—
118	C₂	#19098765	1	1	yes	characteristic
119	C₂	#19098813	1	1	yes	characteristic
120	C₂	#19098835	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098765

C₂

yes

maximal

#19098642

C₂

yes

maximal, characteristic

#19098314

C₂

yes

maximal, characteristic, complemented

#19098309

C₂

yes

maximal, complemented

#500×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×#11929611

—

C₂×#11929607

—

C₄×D₃₁₆

C₂²

yes

characteristic

C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₇₉⋊C₈)

C₂²

yes

—

#14579085

—

(C₂×D₇₉)⋊C₈

—

C₄⋊Q₈×C₇₉

C₂²

yes

—

#107×C₇₉

—

#107×C₇₉

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×D₃₁₆

D₄

yes

characteristic

C₂×C₄×D₇₉

—

#11929611

—

#11929607

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

D₄

yes

characteristic

(C₂×D₇₉)⋊C₄

—

C₂×Q₈×C₇₉

—

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

D₄

yes

characteristic

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

C₂³

yes

characteristic

C₂²×D₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

#41

yes

characteristic

C₂×Dic₇₉

—

D₃₁₆

—

C₄×D₇₉

—

C₄×D₇₉

—

C₈×C₇₉

—

C₈×C₇₉

SD₁₆

yes

complemented

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

#121

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂×SD₁₆

yes

characteristic

C₄×C₇₉

AGL(1,ℤ/8)

yes

—

C₄×C₇₉

#137

yes

characteristic

Dic₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

D₇₉

—

#1693

—

maximal, Sylow

C₇₉

#1693

yes

characteristic, complemented, Sylow

#500

D₇₉

yes

characteristic, complemented

—

—

—

—

C₂×SD₁₆

—

158

—

C₂×M₁₆

—

158

—

C₄⋊Q₈

C₂×D₇₉

yes

—

C₄×D₄

—

#107

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

#103

—

158

—

C₂²⋊C₈

—

158

—

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂×Q₈

—

C₂×D₄

—

C₂²×C₄

—

158

—

SD₁₆

—

316

—

M₁₆

—

316

—

C₂×C₈

—

158

—

C₂×C₈

—

158

—

C₂×C₈

C₂²⋊D₇₉

yes

characteristic

C₂×C₈

C₂²⋊D₇₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

158

—

C₄²

C₂²×D₇₉

yes

characteristic

C₂³

—

158

—

Q₈

—

Q₈

—

D₄

—

158

—

C₂×C₄

—

C₂×C₄

—

316

—

C₂×C₄

—

316

—

C₂×C₄

—

158

—

100

C₂×C₄

D₄×D₇₉

yes

characteristic

101

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

102

C₂×C₄

#11929623

yes

characteristic

103

C₈

—

104

C₈

—

316

—

105

C₈

—

316

—

106

C₈

#11929611

yes

complemented

107

C₂²

—

316

—

108

C₂²

—

316

—

109

C₂²

—

316

—

110

C₂²

#14579132

yes

characteristic

111

C₄

—

112

C₄

—

113

C₄

—

316

—

114

C₄

C₂×#11929611

yes

characteristic

115

C₄

#14579185

yes

—

116

C₄

#14579192

yes

characteristic

117

C₂

—

632

—

118

C₂

#19098765

yes

characteristic

119

C₂

#19098813

yes

characteristic

120

C₂

#19098835

yes

characteristic

	subgroup	G/H
center	C₂²	#14579132
commutator, cosocle	C₄²×C₇₉	C₂³
Frattini	C₄²	C₂²×D₇₉
Fitting	#500×C₇₉	C₂
socle	C₂²×C₇₉	#121
prime radical	C₂×D₃₁₆	D₄
hypercenter	#500	D₇₉
hypocenter	C₇₉	#1693
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #500

subgroup

G/H

center

C₂²

#14579132

commutator, cosocle

C₄²×C₇₉

C₂³

Frattini

C₄²

C₂²×D₇₉

Fitting

#500×C₇₉

C₂

socle

C₂²×C₇₉

#121

prime radical

C₂×D₃₁₆

D₄

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #500

N	H ≅ G/N	type
3. #19098314	C₂	semidirect
4. #19098309	C₂	semidirect
5. #500×C₇₉	C₂	semidirect
43. C₈×C₇₉	SD₁₆	semidirect
61. C₇₉	#1693	semidirect
62. #500	D₇₉	semidirect
106. C₈	#11929611	semidirect

H ≅ G/N

type

3. #19098314

C₂

semidirect

4. #19098309

C₂

semidirect

5. #500×C₇₉

C₂

semidirect

43. C₈×C₇₉

SD₁₆

semidirect

61. C₇₉

#1693

semidirect

62. #500

D₇₉

semidirect

106. C₈

#11929611

semidirect

Subgroups — #23762910

Conjugacy classes of subgroups

Complements