Group #23773909 — subgroups

Subgroups — #23773909

Order 10112.

356 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 145 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	#19099118	C₂	1	2	yes	maximal
2	#19098966	C₂	1	2	yes	maximal, complemented
3	#19098963	C₂	1	4	yes	maximal, complemented
4	#19098961	C₂	1	1	yes	maximal, characteristic, complemented
5	#19098598	C₂	1	4	yes	maximal
6	C₄×C₈×D₇₉	C₂	1	1	yes	maximal, characteristic
7	#498×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₈×D₇₉	C₂²	1	2	yes	—
9	#14579161	C₂²	1	2	yes	—
10	#14579152	C₂²	1	4	yes	—
11	#14579141	—	2	2	no	—
12	#14579137	—	2	2	no	—
13	Q₈×Dic₇₉	—	2	2	no	—
14	#14579126	—	2	2	no	—
15	#14579119	C₂²	1	4	yes	—
16	C₄²×D₇₉	C₂²	1	1	yes	characteristic
17	#14579094	C₂²	1	8	yes	—
18	#14579093	C₂²	1	4	yes	—
19	C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
20	C₈×Dic₇₉	C₂²	1	2	yes	—
21	C₄⋊Q₈×C₇₉	C₂²	1	2	yes	—
22	#106×C₇₉	C₂²	1	4	yes	—
23	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
24	C₂×Dic₁₅₈	—	2	2	no	—
25	C₂×C₄×D₇₉	D₄	1	2	yes	—
26	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
27	C₂×C₇₉⋊C₈	C₂³	1	2	yes	—
28	C₈×D₇₉	Q₈	1	8	yes	complemented
29	C₄⋊Dic₇₉	—	2	4	no	—
30	C₄⋊Dic₇₉	—	2	2	no	—
31	C₄⋊Dic₇₉	C₂³	1	4	yes	—
32	Dic₇₉⋊C₄	—	2	4	no	—
33	(C₂×D₇₉)⋊C₄	—	2	4	no	—
34	C₄×Dic₇₉	—	2	4	no	—
35	C₄×Dic₇₉	D₄	1	2	yes	—
36	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
37	C₂×Q₈×C₇₉	—	2	2	no	—
38	C₂×C₈×C₇₉	C₂³	1	2	yes	—
39	C₄⋊C₄×C₇₉	—	2	2	no	—
40	C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
41	C₄²×C₇₉	C₂³	1	1	yes	characteristic
42	C₂²×D₇₉	C₂×D₄	1	1	yes	characteristic
43	Q₈×C₇₉	—	4	4	no	—
44	C₂×C₄×C₇₉	—	2	4	no	—
45	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
46	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
47	C₂×Dic₇₉	—	2	4	no	—
48	C₂×Dic₇₉	C₂×D₄	1	2	yes	—
49	C₂×Dic₇₉	C₂×D₄	1	1	yes	characteristic
50	C₄×D₇₉	—	2	4	no	—
51	C₄×D₇₉	C₂×Q₈	1	4	yes	—
52	Dic₁₅₈	—	4	4	no	—
53	C₈×C₇₉	C₂×Q₈	1	4	yes	—
54	C₇₉⋊C₈	C₂×Q₈	1	4	yes	—
55	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
56	C₂×D₇₉	—	2	2	no	—
57	C₂×D₇₉	C₄⋊Q₈	1	2	yes	—
58	C₄×C₇₉	—	4	4	no	—
59	C₄×C₇₉	#135	1	4	yes	—
60	C₄×C₇₉	C₂²×Q₈	1	2	yes	—
61	Dic₇₉	—	2	2	no	—
62	Dic₇₉	—	4	4	no	—
63	Dic₇₉	C₄⋊Q₈	1	2	yes	—
64	C₂×C₇₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
65	C₂×C₇₉	C₂×#135	1	2	yes	—
66	D₇₉	—	2	2	no	—
67	#3160	—	79	1	no	maximal, Sylow
68	C₇₉	#3160	1	1	yes	characteristic, complemented, Sylow
69	#533	—	79	2	no	—
70	#500	—	79	2	no	—
71	#499	—	79	4	no	—
72	#498	—	79	1	no	—
73	#498	D₇₉	1	1	yes	characteristic, complemented
74	#427	—	79	4	no	—
75	C₂×C₄×C₈	—	79	1	no	—
76	C₂²×C₈	—	79	2	no	—
77	C₄⋊Q₈	—	79	2	no	—
78	C₄⋊Q₈	C₂×D₇₉	1	2	yes	—
79	#125	—	79	4	no	—
80	C₂²⋊Q₈	—	158	2	no	—
81	C₂²⋊Q₈	—	158	2	no	—
82	C₄×Q₈	—	158	2	no	—
83	C₄×Q₈	—	158	2	no	—
84	#117	—	79	4	no	—
85	C₂×C₄²	—	79	1	no	—
86	#107	—	79	8	no	—
87	#106	—	79	4	no	—
88	#106	C₂×D₇₉	1	4	yes	—
89	C₄×C₈	—	79	2	no	—
90	C₄×C₈	—	79	1	no	—
91	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
92	C₂×Q₈	—	2	2	no	—
93	C₂×Q₈	—	158	2	no	—
94	C₂²×C₄	—	79	1	no	—
95	C₂²×C₄	—	79	2	no	—
96	C₂×C₈	—	79	2	no	—
97	C₂×C₈	—	79	8	no	—
98	C₂×C₈	C₂²×D₇₉	1	2	yes	—
99	C₄⋊C₄	—	2	2	no	—
100	C₄⋊C₄	—	79	4	no	—
101	C₄⋊C₄	—	158	4	no	—
102	C₄⋊C₄	—	158	4	no	—
103	C₄⋊C₄	—	158	2	no	—
104	C₄⋊C₄	C₂²×D₇₉	1	4	yes	—
105	C₂²⋊C₄	—	158	4	no	—
106	C₄²	—	79	2	no	—
107	C₄²	—	79	1	no	—
108	C₄²	—	158	4	no	—
109	C₄²	C₂²×D₇₉	1	1	yes	characteristic
110	C₂³	—	79	1	no	—
111	Q₈	—	4	4	no	—
112	Q₈	—	316	4	no	—
113	C₂×C₄	—	2	4	no	—
114	C₂×C₄	—	79	1	no	—
115	C₂×C₄	—	79	4	no	—
116	C₂×C₄	—	79	2	no	—
117	C₂×C₄	—	158	4	no	—
118	C₂×C₄	—	158	4	no	—
119	C₂×C₄	D₄×D₇₉	1	2	yes	—
120	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
121	C₈	—	79	4	no	—
122	C₈	Q₈×D₇₉	1	4	yes	—
123	C₂²	—	79	2	no	—
124	C₂²	—	158	2	no	—
125	C₂²	C₂×D₄×D₇₉	1	1	yes	characteristic
126	C₄	—	4	4	no	—
127	C₄	—	316	4	no	—
128	C₄	—	79	2	no	—
129	C₄	—	158	2	no	—
130	C₄	#14579182	1	4	yes	—
131	C₄	C₂×Q₈×D₇₉	1	2	yes	—
132	C₂	—	158	2	no	—
133	C₂	C₄⋊Q₈×D₇₉	1	1	yes	characteristic
134	C₂	C₂×#14579182	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19099118

C₂

yes

maximal

#19098966

C₂

yes

maximal, complemented

#19098963

C₂

yes

maximal, complemented

#19098961

C₂

yes

maximal, characteristic, complemented

#19098598

C₂

yes

maximal

C₄×C₈×D₇₉

C₂

yes

maximal, characteristic

#498×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₇₉

C₂²

yes

—

#14579161

C₂²

yes

—

#14579152

C₂²

yes

—

#14579141

—

#14579137

—

Q₈×Dic₇₉

—

#14579126

—

#14579119

C₂²

yes

—

C₄²×D₇₉

C₂²

yes

characteristic

#14579094

C₂²

yes

—

#14579093

C₂²

yes

—

C₄×C₇₉⋊C₈

C₂²

yes

characteristic

C₈×Dic₇₉

C₂²

yes

—

C₄⋊Q₈×C₇₉

C₂²

yes

—

#106×C₇₉

C₂²

yes

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

C₂×C₄×D₇₉

D₄

yes

—

C₂×C₄×D₇₉

C₂³

yes

characteristic

C₂×C₇₉⋊C₈

C₂³

yes

—

C₈×D₇₉

Q₈

yes

complemented

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

C₂³

yes

—

Dic₇₉⋊C₄

—

(C₂×D₇₉)⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

D₄

yes

—

C₄×Dic₇₉

C₂³

yes

characteristic

C₂×Q₈×C₇₉

—

C₂×C₈×C₇₉

C₂³

yes

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

C₂³

yes

—

C₄²×C₇₉

C₂³

yes

characteristic

C₂²×D₇₉

C₂×D₄

yes

characteristic

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂⁴

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

C₂×D₄

yes

—

C₂×Dic₇₉

C₂×D₄

yes

characteristic

C₄×D₇₉

—

C₄×D₇₉

C₂×Q₈

yes

—

Dic₁₅₈

—

C₈×C₇₉

C₂×Q₈

yes

—

C₇₉⋊C₈

C₂×Q₈

yes

—

C₂²×C₇₉

C₂²×D₄

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

C₄⋊Q₈

yes

—

C₄×C₇₉

—

C₄×C₇₉

#135

yes

—

C₄×C₇₉

C₂²×Q₈

yes

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

C₄⋊Q₈

yes

—

C₂×C₇₉

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₇₉

C₂×#135

yes

—

D₇₉

—

#3160

—

maximal, Sylow

C₇₉

#3160

yes

characteristic, complemented, Sylow

—

—

—

—

D₇₉

yes

characteristic, complemented

#427

—

C₂×C₄×C₈

—

C₂²×C₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₇₉

yes

—

#125

—

C₂²⋊Q₈

—

158

—

C₂²⋊Q₈

—

158

—

C₄×Q₈

—

158

—

C₄×Q₈

—

158

—

#117

—

C₂×C₄²

—

#107

—

#106

—

#106

C₂×D₇₉

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

158

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²×D₇₉

yes

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

158

—

102

C₄⋊C₄

—

158

—

103

C₄⋊C₄

—

158

—

104

C₄⋊C₄

C₂²×D₇₉

yes

—

105

C₂²⋊C₄

—

158

—

106

C₄²

—

107

C₄²

—

108

C₄²

—

158

—

109

C₄²

C₂²×D₇₉

yes

characteristic

110

C₂³

—

111

Q₈

—

112

Q₈

—

316

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

158

—

118

C₂×C₄

—

158

—

119

C₂×C₄

D₄×D₇₉

yes

—

120

C₂×C₄

C₂³×D₇₉

yes

characteristic

121

C₈

—

122

C₈

Q₈×D₇₉

yes

—

123

C₂²

—

124

C₂²

—

158

—

125

C₂²

C₂×D₄×D₇₉

yes

characteristic

126

C₄

—

127

C₄

—

316

—

128

C₄

—

129

C₄

—

158

—

130

C₄

#14579182

yes

—

131

C₄

C₂×Q₈×D₇₉

yes

—

132

C₂

—

158

—

133

C₂

C₄⋊Q₈×D₇₉

yes

characteristic

134

C₂

C₂×#14579182

yes

—

	subgroup	G/H
center	C₂²	C₂×D₄×D₇₉
commutator, cosocle	C₂×C₄×C₇₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₇₉
Fitting	#498×C₇₉	C₂
socle	C₂²×C₇₉	C₂²×D₄
prime radical	C₂²×D₇₉	C₂×D₄
hypercenter	#498	D₇₉
hypocenter	C₇₉	#3160
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #498

subgroup

G/H

center

C₂²

C₂×D₄×D₇₉

commutator, cosocle

C₂×C₄×C₇₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₇₉

Fitting

#498×C₇₉

C₂

socle

C₂²×C₇₉

C₂²×D₄

prime radical

C₂²×D₇₉

C₂×D₄

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #498

N	H ≅ G/N	type
2. #19098966	C₂	semidirect
3. #19098963	C₂	semidirect
4. #19098961	C₂	semidirect
7. #498×C₇₉	C₂	semidirect
28. C₈×D₇₉	Q₈	semidirect
68. C₇₉	#3160	semidirect
73. #498	D₇₉	semidirect

H ≅ G/N

type

2. #19098966

C₂

semidirect

3. #19098963

C₂

semidirect

4. #19098961

C₂

semidirect

7. #498×C₇₉

C₂

semidirect

28. C₈×D₇₉

Q₈

semidirect

68. C₇₉

#3160

semidirect

73. #498

D₇₉

semidirect

Subgroups — #23773909

Conjugacy classes of subgroups

Complements