Group #23765015 — subgroups

Subgroups — #23765015

Order 10112.

228 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 93 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×#14579167	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₇₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	(C₂×D₇₉)⋊C₁₆	C₂	1	4	yes	maximal, complemented
4	C₂×M₃₂×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11929624	C₄	1	1	yes	characteristic
6	#14579167	—	2	2	no	—
7	#14579167	—	2	2	no	—
8	C₂×#11929608	C₄	1	1	yes	characteristic
9	C₂×#11929607	C₄	1	2	yes	—
10	C₂×C₈×D₇₉	C₂²	1	2	yes	—
11	C₂×C₇₉⋊C₁₆	—	2	2	no	—
12	C₂×C₇₉⋊C₁₆	C₂²	1	2	yes	—
13	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
14	M₃₂×C₇₉	—	2	2	no	—
15	C₂×C₁₆×C₇₉	C₂²	1	2	yes	—
16	#11929624	—	2	2	no	—
17	#11929624	—	2	2	no	—
18	C₂×Dic₁₅₈	C₈	1	1	yes	characteristic
19	C₂×D₃₁₆	C₈	1	1	yes	characteristic
20	C₂×C₂²⋊D₇₉	C₈	1	2	yes	—
21	C₂×C₄×D₇₉	C₂×C₄	1	2	yes	—
22	#11929608	—	2	2	no	—
23	#11929607	—	2	4	no	—
24	C₂×C₇₉⋊C₈	C₂×C₄	1	2	yes	—
25	C₈×D₇₉	—	2	2	no	—
26	C₈×D₇₉	—	2	2	no	—
27	C₇₉⋊C₁₆	—	2	2	no	—
28	C₂²×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
29	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
30	C₂×C₈×C₇₉	D₄	1	2	yes	—
31	C₂×C₈×C₇₉	D₄	1	2	yes	—
32	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
33	C₁₆×C₇₉	—	2	2	no	—
34	C₂³×C₇₉	C₂×C₈	1	1	yes	characteristic
35	C₂²×D₇₉	C₂×C₈	1	2	yes	—
36	C₂×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
37	C₂×C₄×C₇₉	C₂×C₈	1	1	yes	characteristic
38	C₂×C₄×C₇₉	M₁₆	1	2	yes	—
39	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
40	C₂²⋊D₇₉	—	2	4	no	—
41	C₂×Dic₇₉	C₂×C₈	1	2	yes	—
42	D₃₁₆	—	2	2	no	—
43	C₄×D₇₉	—	2	2	no	—
44	C₄×D₇₉	—	2	2	no	—
45	Dic₁₅₈	—	2	2	no	—
46	C₈×C₇₉	C₂²⋊C₄	1	2	yes	—
47	C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
48	C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
49	C₇₉⋊C₈	—	2	2	no	—
50	C₂²×C₇₉	—	2	2	no	—
51	C₂²×C₇₉	C₂²⋊C₈	1	2	yes	—
52	C₂²×C₇₉	C₂²×C₈	1	1	yes	characteristic
53	C₂×D₇₉	—	2	2	no	—
54	C₂×D₇₉	—	2	4	no	—
55	C₄×C₇₉	C₂²⋊C₈	1	2	yes	—
56	C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
57	C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
58	Dic₇₉	—	2	2	no	—
59	C₂×C₇₉	—	2	2	no	—
60	C₂×C₇₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
61	C₂×C₇₉	#504	1	2	yes	—
62	D₇₉	—	4	2	no	—
63	#2113	—	79	1	no	maximal, Sylow
64	C₇₉	#2113	1	1	yes	characteristic, complemented, Sylow
65	C₂×#131	—	79	1	no	—
66	C₂×M₃₂	D₇₉	1	1	yes	characteristic, complemented
67	C₂²×C₁₆	—	79	1	no	—
68	C₂²⋊C₁₆	—	79	4	no	—
69	C₂×#41	—	79	1	no	—
70	#131	—	158	2	no	—
71	#131	—	158	2	no	—
72	C₂×M₁₆	—	79	1	no	—
73	C₂×M₁₆	—	79	2	no	—
74	C₂²×C₈	—	79	2	no	—
75	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
76	M₃₂	—	2	2	no	—
77	C₂×C₁₆	—	79	2	no	—
78	C₂×C₁₆	—	158	2	no	—
79	C₂×C₁₆	C₂×D₇₉	1	2	yes	—
80	#41	—	158	2	no	—
81	#41	—	158	2	no	—
82	C₂×Q₈	—	79	1	no	—
83	C₂×D₄	—	79	2	no	—
84	C₂×D₄	—	79	1	no	—
85	C₂²×C₄	—	79	2	no	—
86	C₂²×C₄	C₄×D₇₉	1	1	yes	characteristic
87	M₁₆	—	158	2	no	—
88	M₁₆	—	158	4	no	—
89	C₂×C₈	—	79	2	no	—
90	C₂×C₈	—	158	2	no	—
91	C₂×C₈	—	158	2	no	—
92	C₂×C₈	C₄×D₇₉	1	1	yes	characteristic
93	C₂×C₈	D₃₁₆	1	2	yes	—
94	C₂×C₈	C₂²⋊D₇₉	1	2	yes	—
95	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
96	C₁₆	—	2	2	no	—
97	C₁₆	—	158	2	no	—
98	C₂³	—	79	2	no	—
99	C₂³	C₈×D₇₉	1	1	yes	characteristic
100	Q₈	—	158	2	no	—
101	D₄	—	158	4	no	—
102	D₄	—	158	2	no	—
103	C₂×C₄	—	79	2	no	—
104	C₂×C₄	—	158	2	no	—
105	C₂×C₄	—	158	2	no	—
106	C₂×C₄	(C₂×D₇₉)⋊C₄	1	2	yes	—
107	C₂×C₄	C₈×D₇₉	1	1	yes	characteristic
108	C₂×C₄	#11929607	1	2	yes	—
109	C₂×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
110	C₈	—	158	2	no	—
111	C₈	(C₂×D₇₉)⋊C₄	1	2	yes	—
112	C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
113	C₈	C₂×D₃₁₆	1	1	yes	characteristic
114	C₂²	—	2	2	no	—
115	C₂²	—	158	4	no	—
116	C₂²	—	158	2	no	—
117	C₂²	(C₂×D₇₉)⋊C₈	1	2	yes	—
118	C₂²	C₂×C₈×D₇₉	1	1	yes	characteristic
119	C₄	—	158	2	no	—
120	C₄	(C₂×D₇₉)⋊C₈	1	2	yes	—
121	C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
122	C₄	C₂×#11929607	1	1	yes	characteristic
123	C₂	—	2	2	no	—
124	C₂	—	316	2	no	—
125	C₂	C₂×(C₂×D₇₉)⋊C₈	1	1	yes	characteristic
126	C₂	#19098981	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579167

C₂

yes

maximal, characteristic

C₂²×C₇₉⋊C₁₆

C₂

yes

maximal, characteristic, complemented

(C₂×D₇₉)⋊C₁₆

C₂

yes

maximal, complemented

C₂×M₃₂×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×#11929624

C₄

yes

—

—

C₄

yes

characteristic

C₂×#11929607

C₄

yes

—

C₂×C₈×D₇₉

C₂²

yes

—

C₂×C₇₉⋊C₁₆

—

C₂×C₇₉⋊C₁₆

C₂²

yes

—

C₂²×C₈×C₇₉

C₂²

yes

characteristic

M₃₂×C₇₉

—

C₂×C₁₆×C₇₉

C₂²

yes

—

#11929624

—

#11929624

—

C₂×Dic₁₅₈

C₈

yes

characteristic

C₂×D₃₁₆

C₈

yes

characteristic

C₂×C₂²⋊D₇₉

C₈

yes

—

C₂×C₄×D₇₉

C₂×C₄

yes

—

#11929608

—

#11929607

—

C₂×C₇₉⋊C₈

C₂×C₄

yes

—

C₈×D₇₉

—

C₈×D₇₉

—

C₇₉⋊C₁₆

—

C₂²×C₄×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

D₄

yes

—

C₂×C₈×C₇₉

D₄

yes

—

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₁₆×C₇₉

—

C₂³×C₇₉

C₂×C₈

yes

characteristic

C₂²×D₇₉

C₂×C₈

yes

—

C₂×C₄×C₇₉

C₂²⋊C₄

yes

—

C₂×C₄×C₇₉

C₂×C₈

yes

characteristic

C₂×C₄×C₇₉

M₁₆

yes

—

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂²⋊D₇₉

—

C₂×Dic₇₉

C₂×C₈

yes

—

D₃₁₆

—

C₄×D₇₉

—

C₄×D₇₉

—

Dic₁₅₈

—

C₈×C₇₉

C₂²⋊C₄

yes

—

C₈×C₇₉

C₂×D₄

yes

characteristic

C₈×C₇₉

C₂×D₄

yes

characteristic

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂²⋊C₈

yes

—

C₂²×C₇₉

C₂²×C₈

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

C₂²⋊C₈

yes

—

C₄×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₇₉

C₂×M₁₆

yes

characteristic

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

C₂×C₂²⋊C₈

yes

characteristic

C₂×C₇₉

#504

yes

—

D₇₉

—

#2113

—

maximal, Sylow

C₇₉

#2113

yes

characteristic, complemented, Sylow

C₂×#131

—

C₂×M₃₂

D₇₉

yes

characteristic, complemented

C₂²×C₁₆

—

C₂²⋊C₁₆

—

C₂×#41

—

#131

—

158

—

#131

—

158

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

C₂×D₇₉

yes

characteristic

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

158

—

C₂×C₁₆

C₂×D₇₉

yes

—

#41

—

158

—

#41

—

158

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₇₉

yes

characteristic

M₁₆

—

158

—

M₁₆

—

158

—

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

—

158

—

C₂×C₈

C₄×D₇₉

yes

characteristic

C₂×C₈

D₃₁₆

yes

—

C₂×C₈

C₂²⋊D₇₉

yes

—

C₂×C₈

C₂²×D₇₉

yes

characteristic

C₁₆

—

C₁₆

—

158

—

C₂³

—

C₂³

C₈×D₇₉

yes

characteristic

100

Q₈

—

158

—

101

D₄

—

158

—

102

D₄

—

158

—

103

C₂×C₄

—

104

C₂×C₄

—

158

—

105

C₂×C₄

—

158

—

106

C₂×C₄

(C₂×D₇₉)⋊C₄

yes

—

107

C₂×C₄

C₈×D₇₉

yes

characteristic

108

C₂×C₄

#11929607

yes

—

109

C₂×C₄

C₂×C₄×D₇₉

yes

characteristic

110

C₈

—

158

—

111

C₈

(C₂×D₇₉)⋊C₄

yes

—

112

C₈

C₂×C₂²⋊D₇₉

yes

characteristic

113

C₈

C₂×D₃₁₆

yes

characteristic

114

C₂²

—

115

C₂²

—

158

—

116

C₂²

—

158

—

117

C₂²

(C₂×D₇₉)⋊C₈

yes

—

118

C₂²

C₂×C₈×D₇₉

yes

characteristic

119

C₄

—

158

—

120

C₄

(C₂×D₇₉)⋊C₈

yes

—

121

C₄

C₂×(C₂×D₇₉)⋊C₄

yes

characteristic

122

C₄

C₂×#11929607

yes

characteristic

123

C₂

—

124

C₂

—

316

—

125

C₂

C₂×(C₂×D₇₉)⋊C₈

yes

characteristic

126

C₂

#19098981

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₇₉
commutator, socle	C₂²×C₇₉	C₂²×C₈
Fitting	C₂×M₃₂×C₇₉	C₂
prime radical	C₂×#11929624	C₄
cosocle	C₂×C₈×C₇₉	C₂³
hypercenter	C₂×M₃₂	D₇₉
hypocenter	C₇₉	#2113
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×M₃₂

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₇₉

commutator, socle

C₂²×C₇₉

C₂²×C₈

Fitting

C₂×M₃₂×C₇₉

C₂

prime radical

C₂×#11929624

C₄

cosocle

C₂×C₈×C₇₉

C₂³

hypercenter

C₂×M₃₂

D₇₉

C₇₉

G ▷ C₂²×C₇₉ ▷ C₇₉

C₁ ◁ C₂×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
2. C₂²×C₇₉⋊C₁₆	C₂	semidirect
3. (C₂×D₇₉)⋊C₁₆	C₂	semidirect
4. C₂×M₃₂×C₇₉	C₂	semidirect
64. C₇₉	#2113	semidirect
66. C₂×M₃₂	D₇₉	semidirect

H ≅ G/N

type

2. C₂²×C₇₉⋊C₁₆

C₂

semidirect

3. (C₂×D₇₉)⋊C₁₆

C₂

semidirect

4. C₂×M₃₂×C₇₉

C₂

semidirect

64. C₇₉

#2113

semidirect

66. C₂×M₃₂

D₇₉

semidirect

Subgroups — #23765015

Conjugacy classes of subgroups

Complements