Group #23764982 — subgroups

Subgroups — #23764982

Order 10112.

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

normal subgroups only

This group has 148 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	#19098611	C₂	1	1	yes	maximal, characteristic
2	#19098589	C₂	1	1	yes	maximal, characteristic
3	#19098335	C₂	1	1	yes	maximal, characteristic
4	#19098334	C₂	1	1	yes	maximal, characteristic
5	#19098328	C₂	1	1	yes	maximal, characteristic
6	C₇₉⋊#338	C₂	1	1	yes	maximal, characteristic
7	#341×C₇₉	C₂	1	1	yes	maximal, characteristic
8	C₂×#11929608	C₂²	1	1	yes	characteristic
9	C₂×#11929608	C₂²	1	1	yes	characteristic
10	C₂×#11929608	C₂²	1	1	yes	characteristic
11	#14579120	C₂²	1	1	yes	characteristic
12	#14579096	—	2	2	no	—
13	Dic₇₉⋊C₈	—	2	2	no	—
14	C₂×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
15	C₂×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
16	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
17	#11929608	—	2	1	no	—
18	#11929608	—	2	1	no	—
19	#11929608	—	2	1	no	—
20	#11929608	—	2	1	no	—
21	#11929608	—	2	1	no	—
22	#11929608	—	2	1	no	—
23	C₂×C₇₉⋊C₈	—	2	1	no	—
24	C₂×C₇₉⋊C₈	—	2	1	no	—
25	C₂×C₇₉⋊C₈	D₄	1	2	yes	—
26	C₄⋊Dic₇₉	—	2	1	no	—
27	C₂²⋊Dic₇₉	Q₈	1	2	yes	—
28	C₄×Dic₇₉	—	2	1	no	—
29	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
30	M₁₆×C₇₉	—	2	1	no	—
31	M₁₆×C₇₉	—	2	1	no	—
32	M₁₆×C₇₉	—	2	1	no	—
33	M₁₆×C₇₉	—	2	1	no	—
34	C₂×C₈×C₇₉	—	2	1	no	—
35	C₂×C₈×C₇₉	—	2	1	no	—
36	C₂×C₈×C₇₉	—	2	1	no	—
37	C₂×C₈×C₇₉	—	2	1	no	—
38	C₂×C₈×C₇₉	—	2	1	no	—
39	C₂³×C₇₉	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
42	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
43	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
44	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
45	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
46	C₂×Dic₇₉	—	2	2	no	—
47	C₈×C₇₉	—	4	1	no	—
48	C₈×C₇₉	—	4	1	no	—
49	C₈×C₇₉	—	4	1	no	—
50	C₇₉⋊C₈	—	2	2	no	—
51	C₇₉⋊C₈	—	4	1	no	—
52	C₇₉⋊C₈	—	4	1	no	—
53	C₂²×C₇₉	—	4	1	no	—
54	C₂²×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
55	C₂²×C₇₉	#125	1	1	yes	characteristic
56	C₂²×C₇₉	#125	1	1	yes	characteristic
57	C₄×C₇₉	#123	1	1	yes	characteristic
58	C₄×C₇₉	#124	1	1	yes	characteristic
59	C₄×C₇₉	#126	1	1	yes	characteristic
60	C₄×C₇₉	#126	1	1	yes	characteristic
61	Dic₇₉	—	4	2	no	—
62	C₂×C₇₉	—	2	1	no	—
63	C₂×C₇₉	—	2	1	no	—
64	C₂×C₇₉	—	2	1	no	—
65	C₂×C₇₉	#400	1	1	yes	characteristic
66	#2103	—	79	1	no	maximal, Sylow
67	C₇₉	#2103	1	1	yes	characteristic, complemented, Sylow
68	#430	—	79	1	no	—
69	#424	—	79	1	no	—
70	#344	—	79	1	no	—
71	#344	—	79	1	no	—
72	#341	—	79	1	no	—
73	#341	D₇₉	1	1	yes	characteristic
74	#338	—	79	1	no	—
75	C₂×M₁₆	—	79	1	no	—
76	C₂×M₁₆	—	79	1	no	—
77	C₂×M₁₆	—	79	1	no	—
78	C₂×M₁₆	C₂×D₇₉	1	1	yes	characteristic
79	C₂×M₁₆	C₂×D₇₉	1	1	yes	characteristic
80	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
81	#117	—	79	1	no	—
82	#108	—	158	2	no	—
83	C₄⋊C₈	—	158	2	no	—
84	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
85	M₁₆	—	2	1	no	—
86	M₁₆	—	2	1	no	—
87	M₁₆	—	2	1	no	—
88	M₁₆	—	2	1	no	—
89	M₁₆	—	158	1	no	—
90	M₁₆	—	158	1	no	—
91	M₁₆	—	158	1	no	—
92	M₁₆	—	158	1	no	—
93	M₁₆	—	158	1	no	—
94	M₁₆	—	158	1	no	—
95	C₂×C₈	—	2	1	no	—
96	C₂×C₈	—	2	1	no	—
97	C₂×C₈	—	2	1	no	—
98	C₂×C₈	—	2	1	no	—
99	C₂×C₈	—	2	1	no	—
100	C₂×C₈	—	79	2	no	—
101	C₂×C₈	—	158	1	no	—
102	C₂×C₈	—	158	1	no	—
103	C₄⋊C₄	—	158	1	no	—
104	C₂²⋊C₄	—	79	2	no	—
105	C₄²	—	158	1	no	—
106	C₂³	Q₈×D₇₉	1	1	yes	characteristic
107	C₂×C₄	—	158	2	no	—
108	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
109	C₂×C₄	#11929623	1	1	yes	characteristic
110	C₂×C₄	#11929623	1	1	yes	characteristic
111	C₂×C₄	#11929624	1	1	yes	characteristic
112	C₂×C₄	#11929624	1	1	yes	characteristic
113	C₂×C₄	#11929624	1	1	yes	characteristic
114	C₈	—	4	1	no	—
115	C₈	—	4	1	no	—
116	C₈	—	4	1	no	—
117	C₈	—	316	1	no	—
118	C₈	—	316	1	no	—
119	C₈	—	158	2	no	—
120	C₂²	—	4	1	no	—
121	C₂²	#14579139	1	1	yes	characteristic
122	C₂²	#14579151	1	1	yes	characteristic
123	C₂²	#14579151	1	1	yes	characteristic
124	C₄	—	316	2	no	—
125	C₄	#14579143	1	1	yes	characteristic
126	C₄	#14579147	1	1	yes	characteristic
127	C₄	#14579154	1	1	yes	characteristic
128	C₄	#14579155	1	1	yes	characteristic
129	C₂	—	2	1	no	—
130	C₂	—	2	1	no	—
131	C₂	—	2	1	no	—
132	C₂	#19098504	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098611

C₂

yes

maximal, characteristic

#19098589

C₂

yes

maximal, characteristic

#19098335

C₂

yes

maximal, characteristic

#19098334

C₂

yes

maximal, characteristic

#19098328

C₂

yes

maximal, characteristic

C₇₉⋊#338

C₂

yes

maximal, characteristic

#341×C₇₉

C₂

yes

maximal, characteristic

C₂×#11929608

C₂²

yes

characteristic

C₂×#11929608

C₂²

yes

characteristic

C₂×#11929608

C₂²

yes

characteristic

#14579120

C₂²

yes

characteristic

#14579096

—

Dic₇₉⋊C₈

—

C₂×M₁₆×C₇₉

C₂²

yes

characteristic

C₂×M₁₆×C₇₉

C₂²

yes

characteristic

C₂²×C₈×C₇₉

C₂²

yes

—

—

—

—

—

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

D₄

yes

—

C₄⋊Dic₇₉

—

C₂²⋊Dic₇₉

Q₈

yes

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

M₁₆×C₇₉

—

M₁₆×C₇₉

—

M₁₆×C₇₉

—

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂³×C₇₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×Dic₇₉

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂²⋊Q₈

yes

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

—

—

—

—

—

D₇₉

yes

characteristic

#338

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₉

yes

characteristic

C₂×M₁₆

C₂×D₇₉

yes

characteristic

C₂²×C₈

C₂×D₇₉

yes

characteristic

#117

—

#108

—

158

—

C₄⋊C₈

—

158

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

158

—

M₁₆

—

158

—

M₁₆

—

158

—

M₁₆

—

158

—

M₁₆

—

158

—

M₁₆

—

158

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

158

—

102

C₂×C₈

—

158

—

103

C₄⋊C₄

—

158

—

104

C₂²⋊C₄

—

105

C₄²

—

158

—

106

C₂³

Q₈×D₇₉

yes

characteristic

107

C₂×C₄

—

158

—

108

C₂×C₄

D₄×D₇₉

yes

characteristic

109

C₂×C₄

#11929623

yes

characteristic

110

C₂×C₄

#11929623

yes

characteristic

111

C₂×C₄

#11929624

yes

characteristic

112

C₂×C₄

#11929624

yes

characteristic

113

C₂×C₄

#11929624

yes

characteristic

114

C₈

—

115

C₈

—

116

C₈

—

117

C₈

—

316

—

118

C₈

—

316

—

119

C₈

—

158

—

120

C₂²

—

121

C₂²

#14579139

yes

characteristic

122

C₂²

#14579151

yes

characteristic

123

C₂²

#14579151

yes

characteristic

124

C₄

—

316

—

125

C₄

#14579143

yes

characteristic

126

C₄

#14579147

yes

characteristic

127

C₄

#14579154

yes

characteristic

128

C₄

#14579155

yes

characteristic

129

C₂

—

130

C₂

—

131

C₂

—

132

C₂

#19098504

yes

characteristic

	subgroup	G/H
center	C₄	#14579147
commutator, cosocle	C₂²×C₄×C₇₉	C₂³
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	#341×C₇₉	C₂
socle	C₂×C₇₉	#400
prime radical	C₂³×C₇₉	C₂×Q₈
hypercenter	#341	D₇₉
hypocenter	C₇₉	#2103
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #341

subgroup

G/H

center

C₄

#14579147

commutator, cosocle

C₂²×C₄×C₇₉

C₂³

Frattini

C₂²×C₄

C₂²×D₇₉

Fitting

#341×C₇₉

C₂

socle

C₂×C₇₉

#400

prime radical

C₂³×C₇₉

C₂×Q₈

D₇₉

C₇₉

G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #341

N	H ≅ G/N	type
67. C₇₉	#2103	semidirect

H ≅ G/N

type

67. C₇₉

#2103

semidirect

Subgroups — #23764982

Conjugacy classes of subgroups

Complements