Group #23773829 — subgroups

Subgroups — #23773829

Order 10112.

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

normal subgroups only

This group has 572 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	C₂×#14579184	C₂	1	4	yes	maximal, complemented
2	#19099114	C₂	1	2	yes	maximal, complemented
3	#19098948	C₂	1	4	yes	maximal, complemented
4	#19098940	C₂	1	1	yes	maximal, characteristic, complemented
5	#19098937	C₂	1	2	yes	maximal, complemented
6	C₄×C₈×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#494×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#11929625	C₂²	1	4	yes	—
9	#14579184	—	2	16	no	—
10	C₂×#11929611	C₂²	1	8	yes	—
11	C₂×D₆₃₂	C₂²	1	4	yes	—
12	C₂×C₈×D₇₉	C₂²	1	2	yes	—
13	#14579158	C₂²	1	2	yes	—
14	#14579150	C₂²	1	4	yes	—
15	#14579136	—	2	4	no	—
16	#14579123	—	2	4	no	—
17	C₄²×D₇₉	C₂²	1	1	yes	characteristic
18	C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
19	C₈×Dic₇₉	C₂²	1	2	yes	—
20	C₂×Q₁₆×C₇₉	C₂²	1	4	yes	—
21	C₄⋊Q₈×C₇₉	C₂²	1	2	yes	—
22	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
23	#11929625	—	2	16	no	—
24	C₂×D₃₁₆	—	2	4	no	—
25	C₂×D₃₁₆	—	2	4	no	—
26	C₂×D₃₁₆	C₂³	1	4	yes	—
27	C₂×C₄×D₇₉	—	2	4	no	—
28	C₂×C₄×D₇₉	D₄	1	2	yes	—
29	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
30	#11929611	—	2	16	no	—
31	D₆₃₂	—	2	8	no	—
32	C₂×C₇₉⋊C₈	C₂³	1	2	yes	—
33	C₈×D₇₉	D₄	1	8	yes	complemented
34	(C₂×D₇₉)⋊C₄	—	2	8	no	—
35	C₄×Dic₇₉	D₄	1	2	yes	—
36	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
37	C₂×Q₈×C₇₉	C₂³	1	4	yes	—
38	Q₁₆×C₇₉	—	2	8	no	—
39	C₂×C₈×C₇₉	C₂³	1	2	yes	—
40	C₄⋊C₄×C₇₉	—	2	4	no	—
41	C₄²×C₇₉	C₂³	1	1	yes	characteristic
42	C₂²×D₇₉	—	2	4	no	—
43	C₂²×D₇₉	C₂×D₄	1	1	yes	characteristic
44	Q₈×C₇₉	—	2	8	no	—
45	C₂×C₄×C₇₉	—	2	4	no	—
46	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
47	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
48	C₂×Dic₇₉	C₂×D₄	1	2	yes	—
49	C₂×Dic₇₉	C₂×D₄	1	1	yes	characteristic
50	D₃₁₆	—	2	8	no	—
51	D₃₁₆	—	4	8	no	—
52	D₃₁₆	—	4	8	no	—
53	C₄×D₇₉	—	2	4	no	—
54	C₄×D₇₉	—	4	8	no	—
55	C₄×D₇₉	C₂×D₄	1	4	yes	—
56	C₈×C₇₉	C₂×D₄	1	4	yes	—
57	C₇₉⋊C₈	C₂×D₄	1	4	yes	—
58	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
59	C₂×D₇₉	—	2	2	no	—
60	C₂×D₇₉	—	4	4	no	—
61	C₂×D₇₉	—	4	8	no	—
62	C₂×D₇₉	#127	1	2	yes	—
63	C₄×C₇₉	—	4	4	no	—
64	C₄×C₇₉	#135	1	4	yes	complemented
65	C₄×C₇₉	C₂²×D₄	1	2	yes	—
66	Dic₇₉	—	2	2	no	—
67	Dic₇₉	#127	1	2	yes	—
68	C₂×C₇₉	C₂×#127	1	1	yes	characteristic
69	C₂×C₇₉	C₂×#135	1	2	yes	—
70	D₇₉	—	2	2	no	—
71	D₇₉	—	8	4	no	—
72	#3147	—	79	1	no	maximal, Sylow
73	C₇₉	#3147	1	1	yes	characteristic, complemented, Sylow
74	C₂×#135	—	79	4	no	—
75	#532	—	79	2	no	—
76	#495	—	79	4	no	—
77	#494	D₇₉	1	1	yes	characteristic, complemented
78	#493	—	79	1	no	—
79	#492	—	79	2	no	—
80	C₂×C₄×C₈	—	79	1	no	—
81	C₂×#41	—	79	4	no	—
82	#135	—	158	16	no	—
83	C₂×Q₁₆	C₂×D₇₉	1	4	yes	—
84	C₂×SD₁₆	—	79	8	no	—
85	C₂×D₈	—	79	4	no	—
86	C₂²×C₈	—	79	2	no	—
87	C₄⋊Q₈	C₂×D₇₉	1	2	yes	—
88	#127	—	79	2	no	—
89	#124	—	79	4	no	—
90	#121	—	158	4	no	—
91	C₄×D₄	—	158	4	no	—
92	C₂×C₄²	—	79	1	no	—
93	C₄×C₈	—	79	2	no	—
94	C₄×C₈	—	79	1	no	—
95	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
96	#41	—	158	16	no	—
97	C₂×Q₈	C₂²×D₇₉	1	4	yes	—
98	C₂×D₄	—	79	4	no	—
99	C₂×D₄	—	158	4	no	—
100	C₂×D₄	—	158	4	no	—
101	C₂²×C₄	—	79	1	no	—
102	C₂²×C₄	—	79	2	no	—
103	C₂²×C₄	—	158	4	no	—
104	Q₁₆	—	2	8	no	—
105	SD₁₆	—	158	16	no	—
106	D₈	—	158	8	no	—
107	C₂×C₈	—	79	2	no	—
108	C₂×C₈	—	79	8	no	—
109	C₂×C₈	C₂²×D₇₉	1	2	yes	—
110	C₄⋊C₄	—	2	4	no	—
111	C₂²⋊C₄	—	158	8	no	—
112	C₄²	—	79	2	no	—
113	C₄²	—	79	1	no	—
114	C₄²	C₂²×D₇₉	1	1	yes	characteristic
115	C₂³	—	79	1	no	—
116	C₂³	—	158	4	no	—
117	Q₈	—	2	8	no	—
118	D₄	—	316	8	no	—
119	D₄	—	316	8	no	—
120	D₄	—	158	8	no	—
121	C₂×C₄	—	2	4	no	—
122	C₂×C₄	—	316	8	no	—
123	C₂×C₄	—	79	1	no	—
124	C₂×C₄	—	79	4	no	—
125	C₂×C₄	—	79	2	no	—
126	C₂×C₄	—	158	4	no	—
127	C₂×C₄	D₄×D₇₉	1	2	yes	—
128	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
129	C₈	—	79	4	no	—
130	C₈	D₄×D₇₉	1	4	yes	—
131	C₂²	—	316	8	no	—
132	C₂²	—	316	4	no	—
133	C₂²	—	79	2	no	—
134	C₂²	—	158	2	no	—
135	C₂²	C₂×D₄×D₇₉	1	1	yes	characteristic
136	C₄	—	4	4	no	—
137	C₄	—	79	2	no	—
138	C₄	—	158	2	no	—
139	C₄	#14579184	1	4	yes	complemented
140	C₄	C₂×D₄×D₇₉	1	2	yes	—
141	C₂	—	632	4	no	—
142	C₂	—	158	2	no	—
143	C₂	#127×D₇₉	1	1	yes	characteristic
144	C₂	C₂×#14579184	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579184

C₂

yes

maximal, complemented

#19099114

C₂

yes

maximal, complemented

#19098948

C₂

yes

maximal, complemented

#19098940

C₂

yes

maximal, characteristic, complemented

#19098937

C₂

yes

maximal, complemented

C₄×C₈×D₇₉

C₂

yes

maximal, characteristic, complemented

#494×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×#11929625

C₂²

yes

—

#14579184

—

C₂×#11929611

C₂²

yes

—

C₂×D₆₃₂

C₂²

yes

—

C₂×C₈×D₇₉

C₂²

yes

—

#14579158

C₂²

yes

—

#14579150

C₂²

yes

—

#14579136

—

#14579123

—

C₄²×D₇₉

C₂²

yes

characteristic

C₄×C₇₉⋊C₈

C₂²

yes

characteristic

C₈×Dic₇₉

C₂²

yes

—

C₂×Q₁₆×C₇₉

C₂²

yes

—

C₄⋊Q₈×C₇₉

C₂²

yes

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

#11929625

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

C₂³

yes

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

D₄

yes

—

C₂×C₄×D₇₉

C₂³

yes

characteristic

#11929611

—

D₆₃₂

—

C₂×C₇₉⋊C₈

C₂³

yes

—

C₈×D₇₉

D₄

yes

complemented

(C₂×D₇₉)⋊C₄

—

C₄×Dic₇₉

D₄

yes

—

C₄×Dic₇₉

C₂³

yes

characteristic

C₂×Q₈×C₇₉

C₂³

yes

—

Q₁₆×C₇₉

—

C₂×C₈×C₇₉

C₂³

yes

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

C₂³

yes

characteristic

C₂²×D₇₉

—

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×D₄

yes

—

C₂×Dic₇₉

C₂×D₄

yes

characteristic

D₃₁₆

—

D₃₁₆

—

D₃₁₆

—

C₄×D₇₉

—

C₄×D₇₉

—

C₄×D₇₉

C₂×D₄

yes

—

C₈×C₇₉

C₂×D₄

yes

—

C₇₉⋊C₈

C₂×D₄

yes

—

C₂²×C₇₉

C₂²×D₄

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

#127

yes

—

C₄×C₇₉

—

C₄×C₇₉

#135

yes

complemented

C₄×C₇₉

C₂²×D₄

yes

—

Dic₇₉

—

Dic₇₉

#127

yes

—

C₂×C₇₉

C₂×#127

yes

characteristic

C₂×C₇₉

C₂×#135

yes

—

D₇₉

—

D₇₉

—

#3147

—

maximal, Sylow

C₇₉

#3147

yes

characteristic, complemented, Sylow

—

—

—

D₇₉

yes

characteristic, complemented

#493

—

#492

—

C₂×C₄×C₈

—

C₂×#41

—

#135

—

158

—

C₂×Q₁₆

C₂×D₇₉

yes

—

C₂×SD₁₆

—

C₂×D₈

—

C₂²×C₈

—

C₄⋊Q₈

C₂×D₇₉

yes

—

#127

—

#124

—

#121

—

158

—

C₄×D₄

—

158

—

C₂×C₄²

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₇₉

yes

characteristic

#41

—

158

—

C₂×Q₈

C₂²×D₇₉

yes

—

C₂×D₄

—

C₂×D₄

—

158

—

100

C₂×D₄

—

158

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

158

—

104

Q₁₆

—

105

SD₁₆

—

158

—

106

D₈

—

158

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

C₂²×D₇₉

yes

—

110

C₄⋊C₄

—

111

C₂²⋊C₄

—

158

—

112

C₄²

—

113

C₄²

—

114

C₄²

C₂²×D₇₉

yes

characteristic

115

C₂³

—

116

C₂³

—

158

—

117

Q₈

—

118

D₄

—

316

—

119

D₄

—

316

—

120

D₄

—

158

—

121

C₂×C₄

—

122

C₂×C₄

—

316

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

158

—

127

C₂×C₄

D₄×D₇₉

yes

—

128

C₂×C₄

C₂³×D₇₉

yes

characteristic

129

C₈

—

130

C₈

D₄×D₇₉

yes

—

131

C₂²

—

316

—

132

C₂²

—

316

—

133

C₂²

—

134

C₂²

—

158

—

135

C₂²

C₂×D₄×D₇₉

yes

characteristic

136

C₄

—

137

C₄

—

138

C₄

—

158

—

139

C₄

#14579184

yes

complemented

140

C₄

C₂×D₄×D₇₉

yes

—

141

C₂

—

632

—

142

C₂

—

158

—

143

C₂

#127×D₇₉

yes

characteristic

144

C₂

C₂×#14579184

yes

—

	subgroup	G/H
center	C₂²	C₂×D₄×D₇₉
commutator, cosocle	C₂×C₄×C₇₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₇₉
Fitting	#494×C₇₉	C₂
socle	C₂²×C₇₉	C₂²×D₄
hypercenter	#494	D₇₉
hypocenter	C₇₉	#3147
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

subgroup

G/H

center

C₂²

C₂×D₄×D₇₉

commutator, cosocle

C₂×C₄×C₇₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₇₉

Fitting

#494×C₇₉

C₂

socle

C₂²×C₇₉

C₂²×D₄

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #494

N	H ≅ G/N	type
1. C₂×#14579184	C₂	semidirect
2. #19099114	C₂	semidirect
3. #19098948	C₂	semidirect
4. #19098940	C₂	semidirect
5. #19098937	C₂	semidirect
6. C₄×C₈×D₇₉	C₂	semidirect
7. #494×C₇₉	C₂	semidirect
33. C₈×D₇₉	D₄	semidirect
64. C₄×C₇₉	#135	semidirect
73. C₇₉	#3147	semidirect
77. #494	D₇₉	semidirect
139. C₄	#14579184	semidirect

H ≅ G/N

type

1. C₂×#14579184

C₂

semidirect

2. #19099114

C₂

semidirect

3. #19098948

C₂

semidirect

4. #19098940

C₂

semidirect

5. #19098937

C₂

semidirect

6. C₄×C₈×D₇₉

C₂

semidirect

7. #494×C₇₉

C₂

semidirect

33. C₈×D₇₉

D₄

semidirect

64. C₄×C₇₉

#135

semidirect

73. C₇₉

#3147

semidirect

77. #494

D₇₉

semidirect

139. C₄

#14579184

semidirect

Subgroups — #23773829

Conjugacy classes of subgroups

Complements