Group #23763512 — subgroups

Subgroups — #23763512

Order 10112.

236 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 81 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	#19099041	C₂	1	1	yes	maximal, characteristic
2	C₂×#14579080	C₂	1	1	yes	maximal, characteristic
3	#19098335	C₂	1	2	yes	maximal
4	#19098334	C₂	1	2	yes	maximal
5	C₂×#101×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#11929608	C₂²	1	2	yes	—
7	Q₈×Dic₇₉	—	2	2	no	—
8	Q₈×Dic₇₉	—	2	2	no	—
9	#14579120	C₄	1	4	yes	—
10	#14579120	C₂²	1	1	yes	characteristic
11	#14579120	C₂²	1	1	yes	characteristic
12	#14579080	—	2	2	no	—
13	C₂²×Q₈×C₇₉	C₂²	1	1	yes	characteristic
14	C₂×M₁₆×C₇₉	C₂²	1	2	yes	—
15	#101×C₇₉	—	2	2	no	—
16	#11929608	—	2	2	no	—
17	#11929608	—	2	2	no	—
18	C₂×C₇₉⋊C₈	—	2	2	no	—
19	C₄⋊Dic₇₉	—	2	4	no	—
20	C₄⋊Dic₇₉	—	2	1	no	—
21	C₄⋊Dic₇₉	—	2	1	no	—
22	C₂²⋊Dic₇₉	C₂×C₄	1	2	yes	—
23	C₂²⋊Dic₇₉	C₂×C₄	1	2	yes	—
24	C₄×Dic₇₉	—	2	4	no	—
25	C₄×Dic₇₉	—	2	1	no	—
26	C₄×Dic₇₉	—	2	1	no	—
27	C₂×Q₈×C₇₉	—	2	2	no	—
28	C₂×Q₈×C₇₉	—	2	2	no	—
29	C₂×Q₈×C₇₉	D₄	1	2	yes	—
30	C₂×Q₈×C₇₉	D₄	1	2	yes	—
31	C₂²×C₄×C₇₉	C₂×C₄	1	2	yes	—
32	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
33	M₁₆×C₇₉	—	2	2	no	—
34	M₁₆×C₇₉	—	2	2	no	—
35	C₂×C₈×C₇₉	—	2	2	no	—
36	C₂³×C₇₉	C₂²×C₄	1	1	yes	characteristic
37	Q₈×C₇₉	—	2	4	no	—
38	Q₈×C₇₉	—	2	4	no	—
39	C₂×C₄×C₇₉	—	2	2	no	—
40	C₂×C₄×C₇₉	—	2	2	no	—
41	C₂×C₄×C₇₉	C₂²⋊C₄	1	4	yes	—
42	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₇₉	#41	1	2	yes	—
45	C₂×C₄×C₇₉	#41	1	2	yes	—
46	C₂×Dic₇₉	—	2	2	no	—
47	C₂×Dic₇₉	—	2	2	no	—
48	C₈×C₇₉	—	4	2	no	—
49	C₇₉⋊C₈	—	4	2	no	—
50	C₂²×C₇₉	—	4	1	no	—
51	C₂²×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
52	C₂²×C₇₉	#117	1	1	yes	characteristic
53	C₂²×C₇₉	#117	1	1	yes	characteristic
54	C₄×C₇₉	—	2	4	no	—
55	C₄×C₇₉	#123	1	2	yes	—
56	C₄×C₇₉	#123	1	2	yes	—
57	Dic₇₉	—	4	2	no	—
58	Dic₇₉	—	4	2	no	—
59	C₂×C₇₉	—	2	1	no	—
60	C₂×C₇₉	—	2	1	no	—
61	C₂×C₇₉	—	2	1	no	—
62	C₂×C₇₉	#381	1	1	yes	characteristic
63	#1830	—	79	1	no	maximal, Sylow
64	C₇₉	#1830	1	1	yes	characteristic, complemented, Sylow
65	#519	—	79	1	no	—
66	C₂×#101	—	79	1	no	—
67	C₂×#101	D₇₉	1	1	yes	characteristic
68	#344	—	79	2	no	—
69	#344	—	79	2	no	—
70	C₂²×Q₈	C₂×D₇₉	1	1	yes	characteristic
71	C₂×M₁₆	—	79	2	no	—
72	C₂×M₁₆	C₂×D₇₉	1	2	yes	—
73	C₄×Q₈	—	158	2	no	—
74	C₄×Q₈	—	158	2	no	—
75	#117	—	79	1	no	—
76	#117	—	79	1	no	—
77	#117	—	79	4	no	—
78	#101	—	2	2	no	—
79	#101	—	158	2	no	—
80	C₂×Q₈	—	2	2	no	—
81	C₂×Q₈	—	2	2	no	—
82	C₂×Q₈	D₃₁₆	1	2	yes	—
83	C₂×Q₈	C₂²⋊D₇₉	1	2	yes	—
84	C₂²×C₄	C₄×D₇₉	1	2	yes	—
85	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
86	M₁₆	—	2	2	no	—
87	M₁₆	—	2	2	no	—
88	M₁₆	—	158	2	no	—
89	M₁₆	—	158	2	no	—
90	C₂×C₈	—	2	2	no	—
91	C₂×C₈	—	158	2	no	—
92	C₄⋊C₄	—	158	4	no	—
93	C₄⋊C₄	—	158	1	no	—
94	C₄⋊C₄	—	158	1	no	—
95	C₂²⋊C₄	—	79	2	no	—
96	C₂²⋊C₄	—	79	2	no	—
97	C₄²	—	158	4	no	—
98	C₄²	—	158	1	no	—
99	C₄²	—	158	1	no	—
100	C₂³	C₂×C₄×D₇₉	1	1	yes	characteristic
101	Q₈	—	2	4	no	—
102	Q₈	—	2	4	no	—
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	—	158	2	no	—
106	C₂×C₄	—	158	2	no	—
107	C₂×C₄	(C₂×D₇₉)⋊C₄	1	4	yes	—
108	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
109	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
110	C₂×C₄	#11929623	1	2	yes	—
111	C₂×C₄	#11929623	1	2	yes	—
112	C₈	—	4	2	no	—
113	C₈	—	316	2	no	—
114	C₂²	—	4	1	no	—
115	C₂²	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
116	C₂²	#14579117	1	1	yes	characteristic
117	C₂²	#14579117	1	1	yes	characteristic
118	C₄	—	2	4	no	—
119	C₄	—	316	2	no	—
120	C₄	—	316	2	no	—
121	C₄	#14579142	1	2	yes	—
122	C₄	#14579145	1	2	yes	—
123	C₂	—	2	1	no	—
124	C₂	—	2	1	no	—
125	C₂	—	2	1	no	—
126	C₂	#19098424	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19099041

C₂

yes

maximal, characteristic

C₂×#14579080

C₂

yes

maximal, characteristic

#19098335

C₂

yes

maximal

#19098334

C₂

yes

maximal

C₂×#101×C₇₉

C₂

yes

maximal, characteristic

C₂×#11929608

C₂²

yes

—

Q₈×Dic₇₉

—

Q₈×Dic₇₉

—

#14579120

C₄

yes

—

#14579120

C₂²

yes

characteristic

#14579120

C₂²

yes

characteristic

#14579080

—

C₂²×Q₈×C₇₉

C₂²

yes

characteristic

C₂×M₁₆×C₇₉

C₂²

yes

—

#101×C₇₉

—

#11929608

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₂²⋊Dic₇₉

C₂×C₄

yes

—

C₂²⋊Dic₇₉

C₂×C₄

yes

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

D₄

yes

—

C₂×Q₈×C₇₉

D₄

yes

—

C₂²×C₄×C₇₉

C₂×C₄

yes

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

M₁₆×C₇₉

—

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂³×C₇₉

C₂²×C₄

yes

characteristic

Q₈×C₇₉

—

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²⋊C₄

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

#41

yes

—

C₂×C₄×C₇₉

#41

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂×C₂²⋊C₄

yes

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₄×C₇₉

—

C₄×C₇₉

#123

yes

—

C₄×C₇₉

#123

yes

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

#519

—

C₂×#101

—

C₂×#101

D₇₉

yes

characteristic

#344

—

#344

—

C₂²×Q₈

C₂×D₇₉

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₉

yes

—

C₄×Q₈

—

158

—

C₄×Q₈

—

158

—

—

—

—

—

—

158

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

D₃₁₆

yes

—

C₂×Q₈

C₂²⋊D₇₉

yes

—

C₂²×C₄

C₄×D₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

158

—

M₁₆

—

158

—

C₂×C₈

—

C₂×C₈

—

158

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

158

—

C₄²

—

158

—

C₄²

—

158

—

100

C₂³

C₂×C₄×D₇₉

yes

characteristic

101

Q₈

—

102

Q₈

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

158

—

106

C₂×C₄

—

158

—

107

C₂×C₄

(C₂×D₇₉)⋊C₄

yes

—

108

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

109

C₂×C₄

C₂×D₃₁₆

yes

characteristic

110

C₂×C₄

#11929623

yes

—

111

C₂×C₄

#11929623

yes

—

112

C₈

—

113

C₈

—

316

—

114

C₂²

—

115

C₂²

C₂×(C₂×D₇₉)⋊C₄

yes

characteristic

116

C₂²

#14579117

yes

characteristic

117

C₂²

#14579117

yes

characteristic

118

C₄

—

119

C₄

—

316

—

120

C₄

—

316

—

121

C₄

#14579142

yes

—

122

C₄

#14579145

yes

—

123

C₂

—

124

C₂

—

125

C₂

—

126

C₂

#19098424

yes

characteristic

	subgroup	G/H
center	C₂	#19098424
commutator, prime radical	C₂³×C₇₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	C₂×#101×C₇₉	C₂
socle	C₂×C₇₉	#381
cosocle	C₂²×C₄×C₇₉	C₂³
hypercenter	C₂×#101	D₇₉
hypocenter	C₇₉	#1830
LCS	G ▷ C₂³×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#101

subgroup

G/H

center

C₂

#19098424

commutator, prime radical

C₂³×C₇₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₉

Fitting

C₂×#101×C₇₉

C₂

socle

C₂×C₇₉

#381

cosocle

C₂²×C₄×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂³×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#101

N	H ≅ G/N	type
64. C₇₉	#1830	semidirect

H ≅ G/N

type

64. C₇₉

#1830

semidirect

Subgroups — #23763512

Conjugacy classes of subgroups

Complements