Group #23765444 — subgroups

Subgroups — #23765444

Order 10112.

166 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 49 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×#14579106	C₂	1	1	yes	maximal, characteristic
2	C₂×#14579104	C₂	1	1	yes	maximal, characteristic
3	#19098941	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098645	C₂	1	1	yes	maximal, characteristic
5	Dic₇₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	#19098366	C₂	1	1	yes	maximal, characteristic, complemented
7	#358×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₃₁₆	C₂²	1	1	yes	characteristic
9	C₂×#11929614	—	2	1	no	—
10	C₂×D₆₃₂	C₂²	1	1	yes	characteristic
11	#14579159	—	2	1	no	—
12	#14579123	—	2	1	no	—
13	#14579106	—	2	2	no	—
14	#14579104	—	2	2	no	—
15	C₂×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
16	#14579081	—	2	1	no	—
17	C₈×Dic₇₉	C₂²	1	1	yes	characteristic
18	C₂×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
20	#107×C₇₉	C₂²	1	1	yes	characteristic
21	C₂×Dic₁₅₈	—	2	1	no	—
22	C₂×D₃₁₆	—	2	1	no	—
23	C₂×C₄×D₇₉	—	4	1	no	—
24	Dic₃₁₆	—	2	1	no	—
25	Dic₃₁₆	—	2	1	no	—
26	#11929614	—	4	2	no	—
27	D₆₃₂	—	2	1	no	—
28	D₆₃₂	D₄	1	2	yes	—
29	C₂×C₇₉⋊C₈	D₄	1	1	yes	characteristic
30	Dic₇₉⋊C₄	—	4	1	no	—
31	Dic₇₉⋊C₄	—	4	1	no	—
32	(C₂×D₇₉)⋊C₄	—	4	1	no	—
33	C₄×Dic₇₉	D₄	1	1	yes	characteristic
34	C₇₉⋊C₁₆	—	2	1	no	—
35	C₂×Q₈×C₇₉	—	2	1	no	—
36	Q₁₆×C₇₉	—	2	1	no	—
37	Q₁₆×C₇₉	—	2	1	no	—
38	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
39	C₄⋊C₄×C₇₉	—	2	1	no	—
40	C₁₆×C₇₉	—	2	1	no	—
41	C₂²×D₇₉	—	4	1	no	—
42	Q₈×C₇₉	—	4	1	no	—
43	Q₈×C₇₉	—	4	1	no	—
44	C₂×C₄×C₇₉	—	4	1	no	—
45	C₂×C₄×C₇₉	—	4	1	no	—
46	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
47	C₂×Dic₇₉	—	4	1	no	—
48	C₂×Dic₇₉	D₈	1	1	yes	characteristic
49	C₂×Dic₇₉	D₈	1	1	yes	characteristic
50	D₃₁₆	—	2	2	no	—
51	D₃₁₆	—	4	1	no	—
52	C₄×D₇₉	—	8	2	no	—
53	Dic₁₅₈	—	4	1	no	—
54	Dic₁₅₈	—	4	1	no	—
55	C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
56	C₈×C₇₉	#41	1	1	yes	characteristic
57	C₇₉⋊C₈	—	2	1	no	—
58	C₂²×C₇₉	C₂×D₈	1	1	yes	characteristic
59	C₂×D₇₉	—	4	2	no	—
60	C₂×D₇₉	—	8	1	no	—
61	C₂×D₇₉	—	8	1	no	—
62	C₄×C₇₉	—	8	1	no	—
63	C₄×C₇₉	—	8	1	no	—
64	C₄×C₇₉	#121	1	1	yes	characteristic
65	C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
66	Dic₇₉	—	2	1	no	—
67	Dic₇₉	—	8	1	no	—
68	Dic₇₉	SD₃₂	1	2	yes	complemented
69	C₂×C₇₉	#459	1	1	yes	characteristic
70	C₂×C₇₉	C₂×SD₃₂	1	1	yes	characteristic
71	C₂×C₇₉	#510	1	1	yes	characteristic
72	D₇₉	—	8	2	no	—
73	#2208	—	79	1	no	maximal, Sylow
74	C₇₉	#2208	1	1	yes	characteristic, complemented, Sylow
75	C₂×SD₃₂	—	79	1	no	—
76	C₂×SD₃₂	—	79	1	no	—
77	#494	—	79	1	no	—
78	C₄×D₈	—	79	1	no	—
79	C₄⋊C₁₆	—	79	1	no	—
80	#358	—	79	1	no	—
81	#358	D₇₉	1	1	yes	characteristic, complemented
82	C₂×Q₁₆	—	79	1	no	—
83	C₂×Q₁₆	—	158	1	no	—
84	C₂×Q₁₆	C₂×D₇₉	1	1	yes	characteristic
85	C₂×D₈	—	79	1	no	—
86	C₄⋊Q₈	—	158	1	no	—
87	C₄×D₄	—	158	1	no	—
88	SD₃₂	—	158	2	no	—
89	SD₃₂	—	158	2	no	—
90	C₂×C₁₆	—	79	1	no	—
91	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
92	#107	C₂×D₇₉	1	1	yes	characteristic
93	#102	—	158	1	no	—
94	C₄×C₈	—	79	1	no	—
95	C₂×Q₈	—	2	1	no	—
96	C₂×Q₈	—	158	1	no	—
97	C₂×D₄	—	158	1	no	—
98	C₂²×C₄	—	316	1	no	—
99	Q₁₆	—	2	1	no	—
100	Q₁₆	—	2	1	no	—
101	Q₁₆	—	316	2	no	—
102	Q₁₆	—	158	1	no	—
103	Q₁₆	—	158	1	no	—
104	D₈	—	79	2	no	—
105	D₈	—	158	1	no	—
106	C₂×C₈	—	79	1	no	—
107	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
108	C₄⋊C₄	—	2	1	no	—
109	C₄⋊C₄	—	316	1	no	—
110	C₄⋊C₄	—	316	1	no	—
111	C₂²⋊C₄	—	316	1	no	—
112	C₄²	—	79	1	no	—
113	C₁₆	—	2	1	no	—
114	C₁₆	—	158	1	no	—
115	C₂³	—	316	1	no	—
116	Q₈	—	4	1	no	—
117	Q₈	—	4	1	no	—
118	Q₈	—	316	1	no	—
119	Q₈	—	316	1	no	—
120	D₄	—	316	1	no	—
121	D₄	—	158	2	no	—
122	C₂×C₄	—	4	1	no	—
123	C₂×C₄	—	4	1	no	—
124	C₂×C₄	—	316	1	no	—
125	C₂×C₄	—	79	1	no	—
126	C₂×C₄	—	79	1	no	—
127	C₂×C₄	—	632	2	no	—
128	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
129	C₈	—	158	1	no	—
130	C₈	D₄×D₇₉	1	1	yes	characteristic
131	C₈	#11929624	1	1	yes	characteristic
132	C₂²	—	316	2	no	—
133	C₂²	—	632	1	no	—
134	C₂²	—	632	1	no	—
135	C₂²	D₈×D₇₉	1	1	yes	characteristic
136	C₄	—	8	1	no	—
137	C₄	—	8	1	no	—
138	C₄	—	79	2	no	—
139	C₄	—	632	1	no	—
140	C₄	—	158	1	no	—
141	C₄	#14579134	1	1	yes	characteristic
142	C₄	#14579188	1	1	yes	characteristic
143	C₂	—	632	2	no	—
144	C₂	#19098757	1	1	yes	characteristic
145	C₂	SD₃₂×D₇₉	1	1	yes	characteristic
146	C₂	#19099005	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579106

C₂

yes

maximal, characteristic

C₂×#14579104

C₂

yes

maximal, characteristic

#19098941

C₂

yes

maximal, characteristic, complemented

#19098645

C₂

yes

maximal, characteristic

Dic₇₉⋊C₁₆

C₂

yes

maximal, characteristic, complemented

#19098366

C₂

yes

maximal, characteristic, complemented

#358×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×Dic₃₁₆

C₂²

yes

characteristic

C₂×#11929614

—

C₂×D₆₃₂

C₂²

yes

—

—

—

—

C₂×C₇₉⋊C₁₆

C₂²

yes

characteristic

#14579081

—

C₈×Dic₇₉

C₂²

yes

characteristic

C₂×Q₁₆×C₇₉

C₂²

yes

characteristic

C₂×C₁₆×C₇₉

C₂²

yes

characteristic

#107×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

C₂×D₃₁₆

—

C₂×C₄×D₇₉

—

Dic₃₁₆

—

Dic₃₁₆

—

#11929614

—

D₆₃₂

—

D₆₃₂

D₄

yes

—

C₂×C₇₉⋊C₈

D₄

yes

characteristic

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

(C₂×D₇₉)⋊C₄

—

C₄×Dic₇₉

D₄

yes

characteristic

C₇₉⋊C₁₆

—

C₂×Q₈×C₇₉

—

Q₁₆×C₇₉

—

Q₁₆×C₇₉

—

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₄⋊C₄×C₇₉

—

C₁₆×C₇₉

—

C₂²×D₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

D₈

yes

characteristic

C₂×Dic₇₉

D₈

yes

characteristic

D₃₁₆

—

D₃₁₆

—

C₄×D₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

C₂×D₄

yes

characteristic

C₈×C₇₉

#41

yes

characteristic

C₇₉⋊C₈

—

C₂²×C₇₉

C₂×D₈

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

yes

C₄×C₇₉

yes

Dic₇₉

—

Dic₇₉

—

Dic₇₉

SD₃₂

yes

complemented

C₂×C₇₉

#459

yes

characteristic

C₂×C₇₉

C₂×SD₃₂

yes

characteristic

C₂×C₇₉

#510

yes

characteristic

D₇₉

—

#2208

—

maximal, Sylow

C₇₉

#2208

yes

characteristic, complemented, Sylow

C₂×SD₃₂

—

C₂×SD₃₂

—

#494

—

C₄×D₈

—

C₄⋊C₁₆

—

#358

—

#358

D₇₉

yes

characteristic, complemented

C₂×Q₁₆

—

C₂×Q₁₆

—

158

—

C₂×Q₁₆

C₂×D₇₉

yes

characteristic

C₂×D₈

—

C₄⋊Q₈

—

158

—

C₄×D₄

—

158

—

SD₃₂

—

158

—

SD₃₂

—

158

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₉

yes

characteristic

#107

C₂×D₇₉

yes

characteristic

#102

—

158

—

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

158

—

C₂×D₄

—

158

—

C₂²×C₄

—

316

—

Q₁₆

—

100

Q₁₆

—

101

Q₁₆

—

316

—

102

Q₁₆

—

158

—

103

Q₁₆

—

158

—

104

D₈

—

105

D₈

—

158

—

106

C₂×C₈

—

107

C₂×C₈

C₂²×D₇₉

yes

characteristic

108

C₄⋊C₄

—

109

C₄⋊C₄

—

316

—

110

C₄⋊C₄

—

316

—

111

C₂²⋊C₄

—

316

—

112

C₄²

—

113

C₁₆

—

114

C₁₆

—

158

—

115

C₂³

—

316

—

116

Q₈

—

117

Q₈

—

118

Q₈

—

316

—

119

Q₈

—

316

—

120

D₄

—

316

—

121

D₄

—

158

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

316

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

632

—

128

C₂×C₄

D₄×D₇₉

yes

characteristic

129

C₈

—

158

—

130

C₈

D₄×D₇₉

yes

characteristic

131

C₈

#11929624

yes

characteristic

132

C₂²

—

316

—

133

C₂²

—

632

—

134

C₂²

—

632

—

135

C₂²

D₈×D₇₉

yes

characteristic

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

632

—

140

C₄

—

158

—

141

C₄

#14579134

yes

characteristic

142

C₄

#14579188

yes

characteristic

143

C₂

—

632

—

144

C₂

#19098757

yes

characteristic

145

C₂

SD₃₂×D₇₉

yes

characteristic

146

C₂

#19099005

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₇₉
commutator, cosocle	C₂×C₈×C₇₉	C₂³
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	#358×C₇₉	C₂
socle	C₂²×C₇₉	C₂×D₈
prime radical	C₂×D₆₃₂	C₂²
hypercenter	#358	D₇₉
hypocenter	C₇₉	#2208
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #358

subgroup

G/H

center

C₂²

D₈×D₇₉

commutator, cosocle

C₂×C₈×C₇₉

C₂³

Frattini

C₂×C₈

C₂²×D₇₉

Fitting

#358×C₇₉

C₂

socle

C₂²×C₇₉

C₂×D₈

prime radical

C₂×D₆₃₂

C₂²

D₇₉

C₇₉

G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #358

N	H ≅ G/N	type
3. #19098941	C₂	semidirect
5. Dic₇₉⋊C₁₆	C₂	semidirect
6. #19098366	C₂	semidirect
7. #358×C₇₉	C₂	semidirect
68. Dic₇₉	SD₃₂	semidirect
74. C₇₉	#2208	semidirect
81. #358	D₇₉	semidirect

H ≅ G/N

type

3. #19098941

C₂

semidirect

5. Dic₇₉⋊C₁₆

C₂

semidirect

6. #19098366

C₂

semidirect

7. #358×C₇₉

C₂

semidirect

68. Dic₇₉

SD₃₂

semidirect

74. C₇₉

#2208

semidirect

81. #358

D₇₉

semidirect

Subgroups — #23765444

Conjugacy classes of subgroups

Complements