Group #23763437 — subgroups

Subgroups — #23763437

Order 10112.

292 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 89 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	C₂²×C₈×D₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#14579096	C₂	1	2	yes	maximal, complemented
3	#19098526	C₂	1	2	yes	maximal
4	#19098328	C₂	1	1	yes	maximal, characteristic, complemented
5	#341×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×D₇₉	C₂²	1	1	yes	characteristic
7	C₂×#11929608	C₂²	1	2	yes	—
8	C₂²×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
9	C₂×C₈×D₇₉	—	2	4	no	—
10	C₂×C₈×D₇₉	C₄	1	4	yes	—
11	#14579096	—	2	4	no	—
12	(C₂×D₇₉)⋊C₈	—	2	4	no	—
13	C₂×M₁₆×C₇₉	C₂²	1	2	yes	—
14	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
15	C₂³×D₇₉	Q₈	1	1	yes	characteristic
16	C₂²×Dic₇₉	Q₈	1	1	yes	characteristic
17	C₂×C₄×D₇₉	—	2	2	no	—
18	C₂×C₄×D₇₉	—	2	2	no	—
19	C₂×C₄×D₇₉	C₂×C₄	1	2	yes	—
20	C₂×C₄×D₇₉	D₄	1	2	yes	—
21	#11929608	—	2	2	no	—
22	#11929608	—	2	2	no	—
23	C₂×C₇₉⋊C₈	—	2	2	no	—
24	C₂×C₇₉⋊C₈	C₂×C₄	1	2	yes	—
25	C₂×C₇₉⋊C₈	D₄	1	4	yes	—
26	C₈×D₇₉	—	2	8	no	—
27	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
28	M₁₆×C₇₉	—	2	2	no	—
29	M₁₆×C₇₉	—	2	2	no	—
30	C₂×C₈×C₇₉	—	2	2	no	—
31	C₂×C₈×C₇₉	—	2	2	no	—
32	C₂×C₈×C₇₉	C₂×C₄	1	2	yes	—
33	C₂³×C₇₉	C₂×Q₈	1	1	yes	characteristic
34	C₂²×D₇₉	—	2	2	no	—
35	C₂²×D₇₉	—	2	4	no	—
36	C₂²×D₇₉	C₄⋊C₄	1	2	yes	—
37	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
39	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₇₉	#41	1	2	yes	—
41	C₂×Dic₇₉	—	2	2	no	—
42	C₂×Dic₇₉	C₄⋊C₄	1	2	yes	—
43	C₄×D₇₉	—	2	2	no	—
44	C₄×D₇₉	—	2	2	no	—
45	C₄×D₇₉	—	2	4	no	—
46	C₈×C₇₉	—	2	2	no	—
47	C₈×C₇₉	—	4	2	no	—
48	C₇₉⋊C₈	—	4	2	no	—
49	C₇₉⋊C₈	C₂²⋊C₄	1	4	yes	—
50	C₂²×C₇₉	—	2	2	no	—
51	C₂²×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
52	C₂²×C₇₉	C₂²⋊Q₈	1	2	yes	—
53	C₂×D₇₉	—	2	8	no	—
54	C₂×D₇₉	—	2	2	no	—
55	C₂×D₇₉	—	2	2	no	—
56	C₂×D₇₉	#108	1	4	yes	complemented
57	C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
58	C₄×C₇₉	#117	1	1	yes	characteristic
59	C₄×C₇₉	#121	1	2	yes	—
60	Dic₇₉	—	2	2	no	—
61	C₂×C₇₉	—	2	2	no	—
62	C₂×C₇₉	#380	1	1	yes	characteristic
63	C₂×C₇₉	C₂×#108	1	2	yes	—
64	D₇₉	—	2	4	no	—
65	#1810	—	79	1	no	maximal, Sylow
66	C₇₉	#1810	1	1	yes	characteristic, complemented, Sylow
67	C₂³×C₈	—	79	1	no	—
68	C₂×#108	—	79	2	no	—
69	#407	—	79	2	no	—
70	#341	—	79	1	no	—
71	#341	D₇₉	1	1	yes	characteristic, complemented
72	C₂³×C₄	—	79	1	no	—
73	C₂×M₁₆	—	79	2	no	—
74	C₂×M₁₆	C₂×D₇₉	1	2	yes	—
75	C₂²×C₈	—	79	1	no	—
76	C₂²×C₈	—	79	4	no	—
77	C₂²×C₈	—	158	4	no	—
78	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
79	#108	—	158	4	no	—
80	C₂²⋊C₈	—	158	4	no	—
81	C₂⁴	—	79	1	no	—
82	C₂²×C₄	—	79	1	no	—
83	C₂²×C₄	—	79	2	no	—
84	C₂²×C₄	—	79	2	no	—
85	C₂²×C₄	—	158	2	no	—
86	C₂²×C₄	—	158	2	no	—
87	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
88	M₁₆	—	2	2	no	—
89	M₁₆	—	2	2	no	—
90	M₁₆	—	158	2	no	—
91	M₁₆	—	158	2	no	—
92	C₂×C₈	—	2	2	no	—
93	C₂×C₈	—	2	2	no	—
94	C₂×C₈	—	79	2	no	—
95	C₂×C₈	—	79	4	no	—
96	C₂×C₈	—	158	8	no	—
97	C₂×C₈	—	158	2	no	—
98	C₂×C₈	C₄×D₇₉	1	2	yes	—
99	C₂³	—	79	2	no	—
100	C₂³	—	158	4	no	—
101	C₂³	—	158	2	no	—
102	C₂³	Q₈×D₇₉	1	1	yes	characteristic
103	C₂×C₄	—	79	2	no	—
104	C₂×C₄	—	158	2	no	—
105	C₂×C₄	—	158	2	no	—
106	C₂×C₄	—	158	2	no	—
107	C₂×C₄	—	158	4	no	—
108	C₂×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
109	C₂×C₄	D₄×D₇₉	1	2	yes	—
110	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
111	C₂×C₄	#11929624	1	2	yes	—
112	C₈	—	2	2	no	—
113	C₈	—	4	2	no	—
114	C₈	—	316	2	no	—
115	C₈	—	79	4	no	—
116	C₂²	—	2	2	no	—
117	C₂²	—	79	4	no	—
118	C₂²	—	158	8	no	—
119	C₂²	—	158	2	no	—
120	C₂²	—	158	2	no	—
121	C₂²	C₄⋊C₄×D₇₉	1	1	yes	characteristic
122	C₂²	#14579139	1	2	yes	—
123	C₄	—	158	2	no	—
124	C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
125	C₄	#14579118	1	1	yes	characteristic
126	C₄	#14579134	1	2	yes	—
127	C₂	—	2	2	no	—
128	C₂	—	158	4	no	—
129	C₂	#19098422	1	1	yes	characteristic
130	C₂	#108×D₇₉	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₈×D₇₉

C₂

yes

maximal, characteristic

C₂×#14579096

C₂

yes

maximal, complemented

#19098526

C₂

yes

maximal

#19098328

C₂

yes

maximal, characteristic, complemented

#341×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₇₉

C₂²

yes

characteristic

C₂×#11929608

C₂²

yes

—

C₂²×C₇₉⋊C₈

C₂²

yes

characteristic

C₂×C₈×D₇₉

—

C₂×C₈×D₇₉

C₄

yes

—

#14579096

—

(C₂×D₇₉)⋊C₈

—

C₂×M₁₆×C₇₉

C₂²

yes

—

C₂²×C₈×C₇₉

C₂²

yes

characteristic

C₂³×D₇₉

Q₈

yes

characteristic

C₂²×Dic₇₉

Q₈

yes

characteristic

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

C₂×C₄

yes

—

C₂×C₄×D₇₉

D₄

yes

—

#11929608

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

C₂×C₄

yes

—

C₂×C₇₉⋊C₈

D₄

yes

—

C₈×D₇₉

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

M₁₆×C₇₉

—

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂×C₄

yes

—

C₂³×C₇₉

C₂×Q₈

yes

characteristic

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂²×D₇₉

C₄⋊C₄

yes

—

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

#41

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

C₄⋊C₄

yes

—

C₄×D₇₉

—

C₄×D₇₉

—

C₄×D₇₉

—

C₈×C₇₉

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₇₉⋊C₈

C₂²⋊C₄

yes

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₇₉

C₂²⋊Q₈

yes

—

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

#108

yes

complemented

C₄×C₇₉

C₂×C₂²⋊C₄

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

#380

yes

characteristic

C₂×C₇₉

C₂×#108

yes

—

D₇₉

—

#1810

—

maximal, Sylow

C₇₉

#1810

yes

characteristic, complemented, Sylow

C₂³×C₈

—

—

—

—

D₇₉

yes

characteristic, complemented

C₂³×C₄

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₉

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

158

—

C₂²×C₈

C₂×D₇₉

yes

characteristic

#108

—

158

—

C₂²⋊C₈

—

158

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

158

—

C₂²×C₄

—

158

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

158

—

M₁₆

—

158

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

—

158

—

C₂×C₈

C₄×D₇₉

yes

—

C₂³

—

100

C₂³

—

158

—

101

C₂³

—

158

—

102

C₂³

Q₈×D₇₉

yes

characteristic

103

C₂×C₄

—

104

C₂×C₄

—

158

—

105

C₂×C₄

—

158

—

106

C₂×C₄

—

158

—

107

C₂×C₄

—

158

—

108

C₂×C₄

C₂×C₄×D₇₉

yes

characteristic

109

C₂×C₄

D₄×D₇₉

yes

—

110

C₂×C₄

D₄×D₇₉

yes

characteristic

111

C₂×C₄

#11929624

yes

—

112

C₈

—

113

C₈

—

114

C₈

—

316

—

115

C₈

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

158

—

119

C₂²

—

158

—

120

C₂²

—

158

—

121

C₂²

C₄⋊C₄×D₇₉

yes

characteristic

122

C₂²

#14579139

yes

—

123

C₄

—

158

—

124

C₄

C₂²⋊C₄×D₇₉

yes

characteristic

125

C₄

#14579118

yes

characteristic

126

C₄

#14579134

yes

—

127

C₂

—

128

C₂

—

158

—

129

C₂

#19098422

yes

characteristic

130

C₂

#108×D₇₉

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	#341×C₇₉	C₂
socle	C₂²×C₇₉	C₂×C₄⋊C₄
prime radical	C₂³×D₇₉	Q₈
cosocle	C₂²×C₄×C₇₉	C₂³
hypercenter	#341	D₇₉
hypocenter	C₇₉	#1810
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #341

subgroup

G/H

center

C₂×C₄

D₄×D₇₉

commutator

C₂×C₄×C₇₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₉

Fitting

#341×C₇₉

C₂

socle

C₂²×C₇₉

C₂×C₄⋊C₄

prime radical

C₂³×D₇₉

Q₈

cosocle

C₂²×C₄×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #341

N	H ≅ G/N	type
2. C₂×#14579096	C₂	semidirect
4. #19098328	C₂	semidirect
5. #341×C₇₉	C₂	semidirect
56. C₂×D₇₉	#108	semidirect
66. C₇₉	#1810	semidirect
71. #341	D₇₉	semidirect

H ≅ G/N

type

2. C₂×#14579096

C₂

semidirect

4. #19098328

C₂

semidirect

5. #341×C₇₉

C₂

semidirect

56. C₂×D₇₉

#108

semidirect

66. C₇₉

#1810

semidirect

71. #341

D₇₉

semidirect

Subgroups — #23763437

Conjugacy classes of subgroups

Complements