Group #23762765 — subgroups

Subgroups — #23762765

Order 10112.

172 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 61 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	#19098943	C₂	1	1	yes	maximal, characteristic, complemented
2	#19098843	C₂	1	2	yes	maximal
3	#19098316	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098310	C₂	1	2	yes	maximal, complemented
5	C₈×D₄×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₃₁₆	—	2	1	no	—
7	C₂×Dic₃₁₆	—	2	1	no	—
8	#14579161	C₂²	1	2	yes	—
9	#14579094	—	2	2	no	—
10	C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
11	#14579082	—	2	2	no	—
12	C₂²×C₈×C₇₉	—	2	1	no	—
13	C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
14	C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
15	C₂²⋊C₈×C₇₉	—	2	1	no	—
16	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×Dic₁₅₈	—	2	2	no	—
18	Dic₃₁₆	—	4	2	no	—
19	Dic₃₁₆	—	4	2	no	—
20	C₂×C₇₉⋊C₈	—	2	2	no	—
21	C₄⋊Dic₇₉	—	2	2	no	—
22	C₄⋊Dic₇₉	—	2	2	no	—
23	C₂×D₄×C₇₉	D₄	1	1	yes	characteristic
24	C₂²×C₄×C₇₉	—	2	1	no	—
25	C₂×C₈×C₇₉	—	2	1	no	—
26	C₂×C₈×C₇₉	—	4	2	no	—
27	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
28	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
29	C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
30	C₂²⋊C₄×C₇₉	—	2	1	no	—
31	C₄²×C₇₉	C₂³	1	1	yes	characteristic
32	C₂³×C₇₉	—	2	1	no	—
33	D₄×C₇₉	—	2	1	no	—
34	D₄×C₇₉	Q₁₆	1	2	yes	complemented
35	C₂×C₄×C₇₉	—	2	1	no	—
36	C₂×C₄×C₇₉	—	4	1	no	—
37	C₂×C₄×C₇₉	—	4	1	no	—
38	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
41	C₂×Dic₇₉	—	4	2	no	—
42	Dic₁₅₈	—	4	2	no	—
43	Dic₁₅₈	—	4	2	no	—
44	C₈×C₇₉	—	2	1	no	—
45	C₈×C₇₉	—	4	1	no	—
46	C₈×C₇₉	D₈	1	2	yes	—
47	C₇₉⋊C₈	—	4	2	no	—
48	C₂²×C₇₉	—	2	2	no	—
49	C₂²×C₇₉	—	4	1	no	—
50	C₂²×C₇₉	—	4	1	no	—
51	C₂²×C₇₉	#121	1	1	yes	characteristic
52	C₄×C₇₉	—	2	1	no	—
53	C₄×C₇₉	—	4	1	no	—
54	C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
55	C₄×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
56	C₄×C₇₉	#135	1	1	yes	characteristic
57	C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
58	Dic₇₉	—	8	2	no	—
59	C₂×C₇₉	—	4	2	no	—
60	C₂×C₇₉	#459	1	1	yes	characteristic
61	C₂×C₇₉	#467	1	1	yes	characteristic
62	C₂×C₇₉	#473	1	1	yes	characteristic
63	#1669	—	79	1	no	maximal, Sylow
64	C₇₉	#1669	1	1	yes	characteristic, complemented, Sylow
65	#494	—	79	1	no	—
66	#474	—	79	2	no	—
67	C₈×D₄	D₇₉	1	1	yes	characteristic
68	#335	—	79	1	no	—
69	#332	—	79	2	no	—
70	C₂×Q₁₆	—	158	1	no	—
71	C₂×Q₁₆	—	158	1	no	—
72	C₂²×C₈	—	2	1	no	—
73	C₄⋊Q₈	—	79	2	no	—
74	C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
75	#107	—	158	2	no	—
76	C₄⋊C₈	—	79	2	no	—
77	C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
78	#102	—	158	2	no	—
79	C₂²⋊C₈	—	2	1	no	—
80	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
81	C₂×Q₈	—	158	2	no	—
82	C₂×D₄	D₃₁₆	1	1	yes	characteristic
83	C₂²×C₄	—	2	1	no	—
84	Q₁₆	—	316	2	no	—
85	Q₁₆	—	316	2	no	—
86	C₂×C₈	—	2	1	no	—
87	C₂×C₈	—	4	2	no	—
88	C₂×C₈	—	158	2	no	—
89	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
90	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
91	C₄⋊C₄	—	158	2	no	—
92	C₄⋊C₄	—	158	2	no	—
93	C₄⋊C₄	D₃₁₆	1	1	yes	characteristic
94	C₂²⋊C₄	—	2	1	no	—
95	C₄²	C₂²×D₇₉	1	1	yes	characteristic
96	C₂³	—	2	1	no	—
97	Q₈	—	316	2	no	—
98	Q₈	—	316	2	no	—
99	D₄	—	2	1	no	—
100	D₄	Dic₃₁₆	1	2	yes	complemented
101	C₂×C₄	—	2	1	no	—
102	C₂×C₄	—	4	1	no	—
103	C₂×C₄	—	4	1	no	—
104	C₂×C₄	—	316	2	no	—
105	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
106	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
107	C₂×C₄	#11929624	1	1	yes	characteristic
108	C₈	—	2	1	no	—
109	C₈	—	4	1	no	—
110	C₈	—	316	2	no	—
111	C₈	#11929609	1	2	yes	—
112	C₂²	—	2	2	no	—
113	C₂²	—	4	1	no	—
114	C₂²	—	4	1	no	—
115	C₂²	#14579135	1	1	yes	characteristic
116	C₄	—	2	1	no	—
117	C₄	—	4	1	no	—
118	C₄	—	632	2	no	—
119	C₄	C₂×#11929609	1	1	yes	characteristic
120	C₄	C₂×Dic₃₁₆	1	1	yes	characteristic
121	C₄	#14579183	1	1	yes	characteristic
122	C₄	#14579186	1	1	yes	characteristic
123	C₂	—	4	2	no	—
124	C₂	#19098758	1	1	yes	characteristic
125	C₂	#19098804	1	1	yes	characteristic
126	C₂	#19098838	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098943

C₂

yes

maximal, characteristic, complemented

#19098843

C₂

yes

maximal

#19098316

C₂

yes

maximal, characteristic, complemented

#19098310

C₂

yes

maximal, complemented

C₈×D₄×C₇₉

C₂

yes

maximal, characteristic

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

—

#14579161

C₂²

yes

—

#14579094

—

C₄⋊(C₇₉⋊C₈)

C₂²

yes

—

#14579082

—

C₂²×C₈×C₇₉

—

C₄×D₄×C₇₉

C₂²

yes

characteristic

C₄⋊C₈×C₇₉

C₂²

yes

characteristic

C₂²⋊C₈×C₇₉

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

Dic₃₁₆

—

Dic₃₁₆

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₂×D₄×C₇₉

D₄

yes

characteristic

C₂²×C₄×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

D₄

yes

characteristic

C₄⋊C₄×C₇₉

D₄

yes

characteristic

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

C₂³

yes

characteristic

C₂³×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

Q₁₆

yes

complemented

C₂×C₄×C₇₉

—

C₂×C₄×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

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

D₈

yes

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#121

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂×D₈

yes

characteristic

C₄×C₇₉

C₂×Q₁₆

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

#494

—

#474

—

C₈×D₄

D₇₉

yes

characteristic

#335

—

#332

—

C₂×Q₁₆

—

158

—

C₂×Q₁₆

—

158

—

C₂²×C₈

—

C₄⋊Q₈

—

C₄×D₄

C₂×D₇₉

yes

characteristic

#107

—

158

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₇₉

yes

characteristic

#102

—

158

—

C₂²⋊C₈

—

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂×Q₈

—

158

—

C₂×D₄

D₃₁₆

yes

characteristic

C₂²×C₄

—

Q₁₆

—

316

—

Q₁₆

—

316

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

C₂²⋊D₇₉

yes

characteristic

C₂×C₈

C₂²⋊D₇₉

yes

characteristic

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄⋊C₄

D₃₁₆

yes

characteristic

C₂²⋊C₄

—

C₄²

C₂²×D₇₉

yes

characteristic

C₂³

—

Q₈

—

316

—

Q₈

—

316

—

D₄

—

100

D₄

Dic₃₁₆

yes

complemented

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

316

—

105

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

106

C₂×C₄

C₂×D₃₁₆

yes

characteristic

107

C₂×C₄

#11929624

yes

characteristic

108

C₈

—

109

C₈

—

110

C₈

—

316

—

111

C₈

#11929609

yes

—

112

C₂²

—

113

C₂²

—

114

C₂²

—

115

C₂²

#14579135

yes

characteristic

116

C₄

—

117

C₄

—

118

C₄

—

632

—

119

C₄

C₂×#11929609

yes

characteristic

120

C₄

C₂×Dic₃₁₆

yes

characteristic

121

C₄

#14579183

yes

characteristic

122

C₄

#14579186

yes

characteristic

123

C₂

—

124

C₂

#19098758

yes

characteristic

125

C₂

#19098804

yes

characteristic

126

C₂

#19098838

yes

characteristic

	subgroup	G/H
center	C₂²	#14579135
commutator, cosocle	C₄²×C₇₉	C₂³
Frattini	C₄²	C₂²×D₇₉
Fitting	C₈×D₄×C₇₉	C₂
socle	C₂²×C₇₉	#121
prime radical	C₂×D₄×C₇₉	D₄
hypercenter	C₈×D₄	D₇₉
hypocenter	C₇₉	#1669
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈×D₄

subgroup

G/H

center

C₂²

#14579135

commutator, cosocle

C₄²×C₇₉

C₂³

Frattini

C₄²

C₂²×D₇₉

Fitting

C₈×D₄×C₇₉

C₂

socle

C₂²×C₇₉

#121

prime radical

C₂×D₄×C₇₉

D₄

hypercenter

C₈×D₄

D₇₉

hypocenter

C₇₉

#1669

LCS

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₈×D₄

N	H ≅ G/N	type
1. #19098943	C₂	semidirect
3. #19098316	C₂	semidirect
4. #19098310	C₂	semidirect
34. D₄×C₇₉	Q₁₆	semidirect
64. C₇₉	#1669	semidirect
100. D₄	Dic₃₁₆	semidirect

H ≅ G/N

type

1. #19098943

C₂

semidirect

3. #19098316

C₂

semidirect

4. #19098310

C₂

semidirect

34. D₄×C₇₉

Q₁₆

semidirect

64. C₇₉

#1669

semidirect

100. D₄

Dic₃₁₆

semidirect

Subgroups — #23762765

Conjugacy classes of subgroups

Complements