Group #23765204 — subgroups

Subgroups — #23765204

Order 10112.

138 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 67 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	#19098518	C₂	1	1	yes	maximal, characteristic
2	Dic₇₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₇₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²⋊(C₇₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
5	#19098338	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₆×Dic₇₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²⋊C₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic
8	C₂×#11929608	C₄	1	1	yes	characteristic
9	#14579120	C₄	1	1	yes	characteristic
10	C₂×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
12	#14579071	C₄	1	1	yes	characteristic
13	#14579071	C₄	1	1	yes	characteristic
14	C₈×Dic₇₉	C₂²	1	1	yes	characteristic
15	C₈×Dic₇₉	C₂²	1	1	yes	characteristic
16	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
19	#11929608	—	2	2	no	—
20	C₂×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
21	C₂×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
22	C₄⋊Dic₇₉	C₈	1	1	yes	characteristic
23	C₄⋊Dic₇₉	C₈	1	1	yes	characteristic
24	C₂²⋊Dic₇₉	C₈	1	1	yes	characteristic
25	C₂²⋊Dic₇₉	C₈	1	1	yes	characteristic
26	C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
27	C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
28	C₇₉⋊C₁₆	—	2	1	no	—
29	C₇₉⋊C₁₆	—	2	1	no	—
30	C₂²×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
31	C₂×C₈×C₇₉	—	2	1	no	—
32	C₂×C₈×C₇₉	—	2	1	no	—
33	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
34	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
35	C₁₆×C₇₉	—	2	1	no	—
36	C₁₆×C₇₉	—	2	1	no	—
37	C₂³×C₇₉	C₂×C₈	1	1	yes	characteristic
38	C₂×C₄×C₇₉	—	2	1	no	—
39	C₂×C₄×C₇₉	—	2	1	no	—
40	C₂×C₄×C₇₉	C₂×C₈	1	1	yes	characteristic
41	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
42	C₂×Dic₇₉	C₂×C₈	1	1	yes	characteristic
43	C₂×Dic₇₉	C₂×C₈	1	1	yes	characteristic
44	C₂×Dic₇₉	C₂×C₈	1	1	yes	characteristic
45	C₂×Dic₇₉	C₂×C₈	1	1	yes	characteristic
46	C₈×C₇₉	—	2	1	no	—
47	C₈×C₇₉	#41	1	1	yes	characteristic
48	C₈×C₇₉	#41	1	1	yes	characteristic
49	C₇₉⋊C₈	—	2	1	no	—
50	C₇₉⋊C₈	M₁₆	1	2	yes	—
51	C₂²×C₇₉	—	2	1	no	—
52	C₂²×C₇₉	—	2	1	no	—
53	C₂²×C₇₉	—	2	1	no	—
54	C₂²×C₇₉	C₂²×C₈	1	1	yes	characteristic
55	C₄×C₇₉	—	2	1	no	—
56	C₄×C₇₉	#117	1	1	yes	characteristic
57	C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
58	Dic₇₉	—	2	1	no	—
59	Dic₇₉	—	2	1	no	—
60	Dic₇₉	—	2	1	no	—
61	Dic₇₉	—	2	1	no	—
62	C₂×C₇₉	—	4	1	no	—
63	C₂×C₇₉	#431	1	1	yes	characteristic
64	C₂×C₇₉	#504	1	1	yes	characteristic
65	C₂×C₇₉	#504	1	1	yes	characteristic
66	#2164	—	79	1	no	maximal, Sylow
67	C₇₉	#2164	1	1	yes	characteristic, complemented, Sylow
68	#405	—	79	1	no	—
69	C₄⋊C₁₆	—	79	1	no	—
70	C₄⋊C₁₆	—	79	1	no	—
71	C₂²⋊C₁₆	—	79	1	no	—
72	C₂²⋊C₁₆	D₇₉	1	1	yes	characteristic
73	#346	—	79	1	no	—
74	C₄×C₁₆	—	79	1	no	—
75	C₂×M₁₆	—	79	1	no	—
76	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
77	#117	—	79	1	no	—
78	C₂×C₁₆	—	79	1	no	—
79	C₂×C₁₆	—	79	1	no	—
80	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
81	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
82	#97	—	79	1	no	—
83	#97	—	79	1	no	—
84	C₄×C₈	—	79	1	no	—
85	C₄×C₈	—	79	1	no	—
86	C₂²×C₄	C₄×D₇₉	1	1	yes	characteristic
87	M₁₆	—	158	2	no	—
88	C₂×C₈	—	2	1	no	—
89	C₂×C₈	—	2	1	no	—
90	C₂×C₈	—	79	1	no	—
91	C₂×C₈	—	79	1	no	—
92	C₂×C₈	C₄×D₇₉	1	1	yes	characteristic
93	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
94	C₄⋊C₄	—	79	1	no	—
95	C₄⋊C₄	—	79	1	no	—
96	C₂²⋊C₄	—	79	1	no	—
97	C₂²⋊C₄	—	79	1	no	—
98	C₄²	—	79	1	no	—
99	C₄²	—	79	1	no	—
100	C₁₆	—	2	1	no	—
101	C₁₆	—	2	1	no	—
102	C₁₆	—	158	1	no	—
103	C₁₆	—	158	1	no	—
104	C₂³	C₈×D₇₉	1	1	yes	characteristic
105	C₂×C₄	—	2	1	no	—
106	C₂×C₄	—	2	1	no	—
107	C₂×C₄	—	79	1	no	—
108	C₂×C₄	—	79	1	no	—
109	C₂×C₄	—	79	1	no	—
110	C₂×C₄	—	79	1	no	—
111	C₂×C₄	C₈×D₇₉	1	1	yes	characteristic
112	C₂×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
113	C₈	—	2	1	no	—
114	C₈	—	79	2	no	—
115	C₈	—	158	1	no	—
116	C₈	#11929623	1	1	yes	characteristic
117	C₈	#11929623	1	1	yes	characteristic
118	C₂²	—	2	1	no	—
119	C₂²	—	2	1	no	—
120	C₂²	—	2	1	no	—
121	C₂²	C₂×C₈×D₇₉	1	1	yes	characteristic
122	C₄	—	2	1	no	—
123	C₄	—	158	1	no	—
124	C₄	—	158	1	no	—
125	C₄	—	158	1	no	—
126	C₄	—	158	1	no	—
127	C₄	#14579117	1	1	yes	characteristic
128	C₄	M₁₆×D₇₉	1	1	yes	characteristic
129	C₂	—	4	1	no	—
130	C₂	#19098613	1	1	yes	characteristic
131	C₂	#19098979	1	1	yes	characteristic
132	C₂	#19098981	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098518

C₂

yes

maximal, characteristic

Dic₇₉⋊C₁₆

C₂

yes

maximal, characteristic, complemented

Dic₇₉⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₂²⋊(C₇₉⋊C₁₆)

C₂

yes

maximal, characteristic

#19098338

C₂

yes

maximal, characteristic, complemented

C₁₆×Dic₇₉

C₂

yes

maximal, characteristic, complemented

C₂²⋊C₁₆×C₇₉

C₂

yes

maximal, characteristic

C₂×#11929608

C₄

yes

characteristic

#14579120

C₄

yes

characteristic

C₂×C₇₉⋊C₁₆

C₂²

yes

characteristic

C₂×C₇₉⋊C₁₆

C₂²

yes

characteristic

#14579071

C₄

yes

characteristic

#14579071

C₄

yes

characteristic

C₈×Dic₇₉

C₂²

yes

characteristic

C₈×Dic₇₉

C₂²

yes

characteristic

C₂²×C₈×C₇₉

C₂²

yes

characteristic

C₂×C₁₆×C₇₉

C₂²

yes

characteristic

C₂×C₁₆×C₇₉

C₂²

yes

characteristic

#11929608

—

C₂×C₇₉⋊C₈

C₂×C₄

yes

characteristic

C₂×C₇₉⋊C₈

C₂×C₄

yes

characteristic

C₄⋊Dic₇₉

C₈

yes

characteristic

C₄⋊Dic₇₉

C₈

yes

characteristic

C₂²⋊Dic₇₉

C₈

yes

characteristic

C₂²⋊Dic₇₉

C₈

yes

characteristic

C₄×Dic₇₉

C₂×C₄

yes

characteristic

C₄×Dic₇₉

C₂×C₄

yes

characteristic

C₇₉⋊C₁₆

—

C₇₉⋊C₁₆

—

C₂²×C₄×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₁₆×C₇₉

—

C₁₆×C₇₉

—

C₂³×C₇₉

C₂×C₈

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×C₈

yes

characteristic

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×Dic₇₉

C₂×C₈

yes

characteristic

C₂×Dic₇₉

C₂×C₈

yes

characteristic

C₂×Dic₇₉

C₂×C₈

yes

characteristic

C₂×Dic₇₉

C₂×C₈

yes

characteristic

C₈×C₇₉

—

C₈×C₇₉

yes

C₈×C₇₉

yes

C₇₉⋊C₈

—

C₇₉⋊C₈

M₁₆

yes

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂²×C₈

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

#117

yes

characteristic

C₄×C₇₉

C₂×M₁₆

yes

characteristic

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

#405

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

C₂²⋊C₁₆

D₇₉

yes

characteristic

#346

—

C₄×C₁₆

—

C₂×M₁₆

—

C₂²×C₈

C₂×D₇₉

yes

characteristic

#117

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₉

yes

characteristic

C₂×C₁₆

C₂×D₇₉

yes

characteristic

#97

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

C₄×D₇₉

yes

characteristic

M₁₆

—

158

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₇₉

yes

characteristic

C₂×C₈

C₂²×D₇₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

100

C₁₆

—

101

C₁₆

—

102

C₁₆

—

158

—

103

C₁₆

—

158

—

104

C₂³

C₈×D₇₉

yes

characteristic

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

C₈×D₇₉

yes

characteristic

112

C₂×C₄

C₂×C₄×D₇₉

yes

characteristic

113

C₈

—

114

C₈

—

115

C₈

—

158

—

116

C₈

#11929623

yes

characteristic

117

C₈

#11929623

yes

characteristic

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

C₂×C₈×D₇₉

yes

characteristic

122

C₄

—

123

C₄

—

158

—

124

C₄

—

158

—

125

C₄

—

158

—

126

C₄

—

158

—

127

C₄

#14579117

yes

characteristic

128

C₄

M₁₆×D₇₉

yes

characteristic

129

C₂

—

130

C₂

#19098613

yes

characteristic

131

C₂

#19098979

yes

characteristic

132

C₂

#19098981

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₇₉
commutator, socle	C₂²×C₇₉	C₂²×C₈
Fitting	C₂²⋊C₁₆×C₇₉	C₂
prime radical	C₂³×C₇₉	C₂×C₈
cosocle	C₂×C₈×C₇₉	C₂³
hypercenter	C₂²⋊C₁₆	D₇₉
hypocenter	C₇₉	#2164
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂²⋊C₁₆

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₇₉

commutator, socle

C₂²×C₇₉

C₂²×C₈

Fitting

C₂²⋊C₁₆×C₇₉

C₂

prime radical

C₂³×C₇₉

C₂×C₈

cosocle

C₂×C₈×C₇₉

C₂³

hypercenter

C₂²⋊C₁₆

D₇₉

C₇₉

G ▷ C₂²×C₇₉ ▷ C₇₉

C₁ ◁ C₂×C₈ ◁ C₂²⋊C₁₆

N	H ≅ G/N	type
2. Dic₇₉⋊C₁₆	C₂	semidirect
3. Dic₇₉⋊C₁₆	C₂	semidirect
5. #19098338	C₂	semidirect
6. C₁₆×Dic₇₉	C₂	semidirect
67. C₇₉	#2164	semidirect

H ≅ G/N

type

2. Dic₇₉⋊C₁₆

C₂

semidirect

3. Dic₇₉⋊C₁₆

C₂

semidirect

5. #19098338

C₂

semidirect

6. C₁₆×Dic₇₉

C₂

semidirect

67. C₇₉

#2164

semidirect

Subgroups — #23765204

Conjugacy classes of subgroups

Complements