Group #23762797 — subgroups

Subgroups — #23762797

Order 10112.

160 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 57 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	#19098966	C₂	1	1	yes	maximal, characteristic, complemented
2	#19098853	C₂	1	1	yes	maximal, characteristic
3	D₄×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#19098315	C₂	1	1	yes	maximal, characteristic, complemented
5	#19098312	C₂	1	1	yes	maximal, characteristic, complemented
6	#19098311	C₂	1	1	yes	maximal, characteristic, complemented
7	#476×C₇₉	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₇₉⋊C₈	—	2	1	no	—
9	#14579161	C₂²	1	1	yes	characteristic
10	#14579094	—	2	1	no	—
11	#14579094	—	2	1	no	—
12	#14579092	—	2	1	no	—
13	C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
15	#14579082	—	2	1	no	—
16	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
17	C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
18	C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
19	C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
20	#106×C₇₉	—	2	1	no	—
21	C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
22	#102×C₇₉	—	2	1	no	—
23	C₂×Dic₁₅₈	—	2	1	no	—
24	C₂×C₇₉⋊C₈	—	2	1	no	—
25	C₂×C₇₉⋊C₈	—	2	1	no	—
26	C₂×C₇₉⋊C₈	—	4	2	no	—
27	C₂×C₇₉⋊C₈	D₄	1	1	yes	characteristic
28	C₂×C₇₉⋊C₈	D₄	1	1	yes	characteristic
29	C₄⋊Dic₇₉	—	2	1	no	—
30	C₄⋊Dic₇₉	—	2	1	no	—
31	C₂×Q₈×C₇₉	—	2	1	no	—
32	C₂×D₄×C₇₉	D₄	1	1	yes	characteristic
33	C₂²×C₄×C₇₉	—	2	1	no	—
34	C₂×C₈×C₇₉	—	2	1	no	—
35	C₄⋊C₄×C₇₉	—	2	1	no	—
36	C₄⋊C₄×C₇₉	—	2	1	no	—
37	C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
38	C₂²⋊C₄×C₇₉	—	2	1	no	—
39	C₄²×C₇₉	C₂³	1	1	yes	characteristic
40	C₂³×C₇₉	—	2	1	no	—
41	Q₈×C₇₉	—	8	1	no	—
42	D₄×C₇₉	—	2	1	no	—
43	D₄×C₇₉	Q₁₆	1	2	yes	—
44	C₂×C₄×C₇₉	—	2	1	no	—
45	C₂×C₄×C₇₉	—	4	1	no	—
46	C₂×C₄×C₇₉	—	4	1	no	—
47	C₂×C₄×C₇₉	—	4	1	no	—
48	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
51	C₂×Dic₇₉	—	4	1	no	—
52	Dic₁₅₈	—	8	1	no	—
53	C₈×C₇₉	—	4	1	no	—
54	C₇₉⋊C₈	—	2	1	no	—
55	C₇₉⋊C₈	—	4	1	no	—
56	C₇₉⋊C₈	—	4	1	no	—
57	C₇₉⋊C₈	SD₁₆	1	2	yes	—
58	C₂²×C₇₉	—	2	2	no	—
59	C₂²×C₇₉	—	4	1	no	—
60	C₂²×C₇₉	—	4	1	no	—
61	C₂²×C₇₉	#121	1	1	yes	characteristic
62	C₄×C₇₉	—	2	1	no	—
63	C₄×C₇₉	—	4	1	no	—
64	C₄×C₇₉	—	8	1	no	—
65	C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
66	C₄×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
67	C₄×C₇₉	#135	1	1	yes	characteristic
68	C₄×C₇₉	#137	1	1	yes	characteristic
69	Dic₇₉	—	8	1	no	—
70	C₂×C₇₉	—	4	2	no	—
71	C₂×C₇₉	#461	1	1	yes	characteristic
72	C₂×C₇₉	#467	1	1	yes	characteristic
73	C₂×C₇₉	#472	1	1	yes	characteristic
74	#1675	—	79	1	no	maximal, Sylow
75	C₇₉	#1675	1	1	yes	characteristic, complemented, Sylow
76	#500	—	79	1	no	—
77	#476	—	79	1	no	—
78	#476	D₇₉	1	1	yes	characteristic
79	C₈×D₄	—	79	1	no	—
80	#335	—	79	1	no	—
81	#333	—	79	1	no	—
82	#333	—	79	1	no	—
83	C₂²×C₈	—	158	1	no	—
84	C₄⋊Q₈	—	79	1	no	—
85	C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
86	C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
87	#107	—	158	1	no	—
88	#107	—	158	1	no	—
89	#106	—	2	1	no	—
90	#106	—	158	1	no	—
91	C₄⋊C₈	—	79	1	no	—
92	C₄⋊C₈	—	79	1	no	—
93	C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
94	#102	—	2	1	no	—
95	#102	—	158	1	no	—
96	C₂²⋊C₈	—	158	1	no	—
97	C₄×C₈	—	79	1	no	—
98	C₂×Q₈	—	2	1	no	—
99	C₂×Q₈	—	158	1	no	—
100	C₂×D₄	C₂²⋊D₇₉	1	1	yes	characteristic
101	C₂²×C₄	—	2	1	no	—
102	C₂×C₈	—	2	1	no	—
103	C₂×C₈	—	316	2	no	—
104	C₂×C₈	—	79	1	no	—
105	C₂×C₈	—	79	1	no	—
106	C₂×C₈	—	158	1	no	—
107	C₂×C₈	—	158	1	no	—
108	C₄⋊C₄	—	2	1	no	—
109	C₄⋊C₄	—	2	1	no	—
110	C₄⋊C₄	—	158	1	no	—
111	C₄⋊C₄	—	158	1	no	—
112	C₄⋊C₄	C₂²⋊D₇₉	1	1	yes	characteristic
113	C₂²⋊C₄	—	2	1	no	—
114	C₄²	C₂²×D₇₉	1	1	yes	characteristic
115	C₂³	—	2	1	no	—
116	Q₈	—	8	1	no	—
117	Q₈	—	632	1	no	—
118	D₄	—	2	1	no	—
119	D₄	#11929614	1	2	yes	—
120	C₂×C₄	—	2	1	no	—
121	C₂×C₄	—	4	1	no	—
122	C₂×C₄	—	4	1	no	—
123	C₂×C₄	—	4	1	no	—
124	C₂×C₄	—	316	1	no	—
125	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
126	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
127	C₂×C₄	#11929623	1	1	yes	characteristic
128	C₈	—	4	1	no	—
129	C₈	—	316	1	no	—
130	C₈	—	316	1	no	—
131	C₈	—	79	2	no	—
132	C₈	—	158	1	no	—
133	C₂²	—	2	2	no	—
134	C₂²	—	4	1	no	—
135	C₂²	—	4	1	no	—
136	C₂²	#14579133	1	1	yes	characteristic
137	C₄	—	2	1	no	—
138	C₄	—	4	1	no	—
139	C₄	—	8	1	no	—
140	C₄	—	632	1	no	—
141	C₄	SD₁₆×D₇₉	1	1	yes	characteristic
142	C₄	C₂×#11929614	1	1	yes	characteristic
143	C₄	#14579181	1	1	yes	characteristic
144	C₄	#14579190	1	1	yes	characteristic
145	C₂	—	4	2	no	—
146	C₂	#19098766	1	1	yes	characteristic
147	C₂	#19098802	1	1	yes	characteristic
148	C₂	#19098831	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098966

C₂

yes

maximal, characteristic, complemented

#19098853

C₂

yes

maximal, characteristic

D₄×C₇₉⋊C₈

C₂

yes

maximal, characteristic

#19098315

C₂

yes

maximal, characteristic, complemented

#19098312

C₂

yes

maximal, characteristic, complemented

#19098311

C₂

yes

maximal, characteristic, complemented

#476×C₇₉

C₂

yes

maximal, characteristic

C₂²×C₇₉⋊C₈

—

#14579161

C₂²

yes

—

—

—

C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

#14579082

—

C₂²⋊(C₇₉⋊C₈)

—

C₄×C₇₉⋊C₈

C₂²

yes

characteristic

C₄⋊Q₈×C₇₉

C₂²

yes

characteristic

C₄×D₄×C₇₉

C₂²

yes

characteristic

#106×C₇₉

—

C₄⋊C₈×C₇₉

C₂²

yes

characteristic

#102×C₇₉

—

C₂×Dic₁₅₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

D₄

yes

characteristic

C₂×C₇₉⋊C₈

D₄

yes

characteristic

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₂×Q₈×C₇₉

—

C₂×D₄×C₇₉

D₄

yes

characteristic

C₂²×C₄×C₇₉

—

C₂×C₈×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

D₄

yes

characteristic

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

C₂³

yes

characteristic

C₂³×C₇₉

—

Q₈×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

Q₁₆

yes

—

C₂×C₄×C₇₉

—

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

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₇₉⋊C₈

SD₁₆

yes

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#121

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂×SD₁₆

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

#500

—

#476

—

#476

D₇₉

yes

characteristic

C₈×D₄

—

#335

—

#333

—

#333

—

C₂²×C₈

—

158

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₇₉

yes

characteristic

C₄×D₄

C₂×D₇₉

yes

characteristic

#107

—

158

—

#107

—

158

—

#106

—

#106

—

158

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₇₉

yes

characteristic

#102

—

#102

—

158

—

C₂²⋊C₈

—

158

—

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

158

—

100

C₂×D₄

C₂²⋊D₇₉

yes

characteristic

101

C₂²×C₄

—

102

C₂×C₈

—

103

C₂×C₈

—

316

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

158

—

107

C₂×C₈

—

158

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

158

—

111

C₄⋊C₄

—

158

—

112

C₄⋊C₄

C₂²⋊D₇₉

yes

characteristic

113

C₂²⋊C₄

—

114

C₄²

C₂²×D₇₉

yes

characteristic

115

C₂³

—

116

Q₈

—

117

Q₈

—

632

—

118

D₄

—

119

D₄

#11929614

yes

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

316

—

125

C₂×C₄

D₄×D₇₉

yes

characteristic

126

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

127

C₂×C₄

#11929623

yes

characteristic

128

C₈

—

129

C₈

—

316

—

130

C₈

—

316

—

131

C₈

—

132

C₈

—

158

—

133

C₂²

—

134

C₂²

—

135

C₂²

—

136

C₂²

#14579133

yes

characteristic

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

—

632

—

141

C₄

SD₁₆×D₇₉

yes

characteristic

142

C₄

C₂×#11929614

yes

characteristic

143

C₄

#14579181

yes

characteristic

144

C₄

#14579190

yes

characteristic

145

C₂

—

146

C₂

#19098766

yes

characteristic

147

C₂

#19098802

yes

characteristic

148

C₂

#19098831

yes

characteristic

	subgroup	G/H
center	C₂²	#14579133
commutator, cosocle	C₄²×C₇₉	C₂³
Frattini	C₄²	C₂²×D₇₉
Fitting	#476×C₇₉	C₂
socle	C₂²×C₇₉	#121
prime radical	C₂×D₄×C₇₉	D₄
hypercenter	#476	D₇₉
hypocenter	C₇₉	#1675
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #476

subgroup

G/H

center

C₂²

#14579133

commutator, cosocle

C₄²×C₇₉

C₂³

Frattini

C₄²

C₂²×D₇₉

Fitting

#476×C₇₉

C₂

socle

C₂²×C₇₉

#121

prime radical

C₂×D₄×C₇₉

D₄

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #476

N	H ≅ G/N	type
1. #19098966	C₂	semidirect
4. #19098315	C₂	semidirect
5. #19098312	C₂	semidirect
6. #19098311	C₂	semidirect
75. C₇₉	#1675	semidirect

H ≅ G/N

type

1. #19098966

C₂

semidirect

4. #19098315

C₂

semidirect

5. #19098312

C₂

semidirect

6. #19098311

C₂

semidirect

75. C₇₉

#1675

semidirect

Subgroups — #23762797

Conjugacy classes of subgroups

Complements