Group #23761297 — subgroups

Subgroups — #23761297

Order 10112.

148 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 77 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	#19098616	C₂	1	1	yes	maximal, characteristic
2	#19098587	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊C₈×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#11929608	—	2	1	no	—
5	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
6	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
7	C₄⋊(C₇₉⋊C₈)	C₄	1	2	yes	—
8	C₂²⋊(C₇₉⋊C₈)	C₄	1	2	yes	—
9	C₄×C₇₉⋊C₈	—	2	1	no	—
10	C₂²×C₈×C₇₉	—	2	1	no	—
11	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
12	C₄⋊C₈×C₇₉	—	2	1	no	—
13	C₄⋊C₈×C₇₉	C₄	1	2	yes	—
14	#11929608	—	4	1	no	—
15	#11929608	—	4	1	no	—
16	C₂×C₇₉⋊C₈	—	2	2	no	—
17	C₂×C₇₉⋊C₈	—	2	2	no	—
18	C₂²×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₇₉	D₄	1	1	yes	characteristic
20	C₂²×C₄×C₇₉	Q₈	1	1	yes	characteristic
21	C₂×C₈×C₇₉	—	2	2	no	—
22	C₂×C₈×C₇₉	—	4	1	no	—
23	C₂×C₈×C₇₉	—	4	1	no	—
24	C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
25	C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
26	C₄²×C₇₉	D₄	1	1	yes	characteristic
27	C₄²×C₇₉	D₄	1	1	yes	characteristic
28	C₂³×C₇₉	C₄⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₇₉	—	2	2	no	—
30	C₂×C₄×C₇₉	—	4	1	no	—
31	C₂×C₄×C₇₉	C₄²	1	1	yes	characteristic
32	C₂×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
38	C₂×C₄×C₇₉	SD₁₆	1	1	yes	characteristic
39	C₂×C₄×C₇₉	SD₁₆	1	1	yes	characteristic
40	C₂×C₄×C₇₉	Q₁₆	1	1	yes	characteristic
41	C₈×C₇₉	—	4	2	no	—
42	C₇₉⋊C₈	—	4	2	no	—
43	C₇₉⋊C₈	—	4	2	no	—
44	C₂²×C₇₉	—	2	1	no	—
45	C₂²×C₇₉	—	2	1	no	—
46	C₂²×C₇₉	#95	1	1	yes	characteristic
47	C₂²×C₇₉	#106	1	1	yes	characteristic
48	C₂²×C₇₉	#107	1	1	yes	characteristic
49	C₄×C₇₉	—	2	1	no	—
50	C₄×C₇₉	—	2	1	no	—
51	C₄×C₇₉	—	2	1	no	—
52	C₄×C₇₉	#102	1	1	yes	characteristic
53	C₄×C₇₉	#102	1	1	yes	characteristic
54	C₄×C₇₉	#103	1	1	yes	characteristic
55	C₄×C₇₉	#103	1	1	yes	characteristic
56	C₄×C₇₉	#108	1	2	yes	—
57	C₂×C₇₉	—	2	1	no	—
58	C₂×C₇₉	—	2	1	no	—
59	C₂×C₇₉	#340	1	1	yes	characteristic
60	C₂×C₇₉	#341	1	1	yes	characteristic
61	C₂×C₇₉	#344	1	1	yes	characteristic
62	#1301	—	79	1	no	maximal, Sylow
63	C₇₉	#1301	1	1	yes	characteristic, complemented, Sylow
64	#431	—	79	1	no	—
65	#423	—	79	1	no	—
66	C₂×C₄⋊C₈	D₇₉	1	1	yes	characteristic
67	C₂×M₁₆	—	158	1	no	—
68	C₂²×C₈	—	2	1	no	—
69	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
70	C₄⋊C₈	—	2	1	no	—
71	C₄⋊C₈	—	79	2	no	—
72	C₄⋊C₈	—	158	1	no	—
73	C₄⋊C₈	—	158	1	no	—
74	C₄⋊C₈	Dic₇₉	1	2	yes	—
75	C₂²⋊C₈	—	79	2	no	—
76	C₄×C₈	—	158	1	no	—
77	C₂²×C₄	Dic₁₅₈	1	1	yes	characteristic
78	C₂²×C₄	C₄×D₇₉	1	1	yes	characteristic
79	C₂²×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
80	M₁₆	—	316	1	no	—
81	M₁₆	—	316	1	no	—
82	C₂×C₈	—	2	2	no	—
83	C₂×C₈	—	4	1	no	—
84	C₂×C₈	—	4	1	no	—
85	C₂×C₈	—	158	2	no	—
86	C₂×C₈	—	158	2	no	—
87	C₄²	C₄×D₇₉	1	1	yes	characteristic
88	C₄²	D₃₁₆	1	1	yes	characteristic
89	C₄²	C₂×Dic₇₉	1	1	yes	characteristic
90	C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
91	C₂³	Dic₇₉⋊C₄	1	1	yes	characteristic
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	—	4	1	no	—
94	C₂×C₄	C₄×Dic₇₉	1	1	yes	characteristic
95	C₂×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
96	C₂×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
97	C₂×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
98	C₂×C₄	Dic₇₉⋊C₄	1	1	yes	characteristic
99	C₂×C₄	C₄⋊Dic₇₉	1	1	yes	characteristic
100	C₂×C₄	#11929609	1	1	yes	characteristic
101	C₂×C₄	#11929611	1	1	yes	characteristic
102	C₂×C₄	#11929612	1	1	yes	characteristic
103	C₂×C₄	#11929614	1	1	yes	characteristic
104	C₈	—	4	2	no	—
105	C₈	—	316	2	no	—
106	C₈	—	316	2	no	—
107	C₂²	—	2	1	no	—
108	C₂²	—	2	1	no	—
109	C₂²	C₇₉⋊#95	1	1	yes	characteristic
110	C₂²	#14579092	1	1	yes	characteristic
111	C₂²	#14579094	1	1	yes	characteristic
112	C₄	—	2	1	no	—
113	C₄	—	2	1	no	—
114	C₄	—	2	1	no	—
115	C₄	#14579081	1	1	yes	characteristic
116	C₄	#14579082	1	1	yes	characteristic
117	C₄	#14579084	1	1	yes	characteristic
118	C₄	#14579085	1	1	yes	characteristic
119	C₄	#14579097	1	2	yes	—
120	C₂	—	2	1	no	—
121	C₂	—	2	1	no	—
122	C₂	#19098325	1	1	yes	characteristic
123	C₂	#19098328	1	1	yes	characteristic
124	C₂	#19098335	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098616

C₂

yes

maximal, characteristic

#19098587

C₂

yes

maximal, characteristic

C₂×C₄⋊C₈×C₇₉

C₂

yes

maximal, characteristic

C₂×#11929608

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

C₄

yes

—

C₂²⋊(C₇₉⋊C₈)

C₄

yes

—

C₄×C₇₉⋊C₈

—

C₂²×C₈×C₇₉

—

C₂×C₄²×C₇₉

C₂²

yes

characteristic

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

C₄

yes

—

#11929608

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂²×C₄×C₇₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₉

D₄

yes

characteristic

C₂²×C₄×C₇₉

Q₈

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₄²×C₇₉

C₂×C₄

yes

characteristic

C₄²×C₇₉

C₂×C₄

yes

characteristic

C₄²×C₇₉

D₄

yes

characteristic

C₄²×C₇₉

D₄

yes

characteristic

C₂³×C₇₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₄²

yes

characteristic

C₂×C₄×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₉

D₈

yes

characteristic

C₂×C₄×C₇₉

SD₁₆

yes

characteristic

C₂×C₄×C₇₉

SD₁₆

yes

characteristic

C₂×C₄×C₇₉

Q₁₆

yes

characteristic

C₈×C₇₉

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

#431

—

#423

—

C₂×C₄⋊C₈

D₇₉

yes

characteristic

C₂×M₁₆

—

158

—

C₂²×C₈

—

C₂×C₄²

C₂×D₇₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

158

—

C₄⋊C₈

—

158

—

C₄⋊C₈

Dic₇₉

yes

—

C₂²⋊C₈

—

C₄×C₈

—

158

—

C₂²×C₄

Dic₁₅₈

yes

characteristic

C₂²×C₄

C₄×D₇₉

yes

characteristic

C₂²×C₄

C₂²⋊D₇₉

yes

characteristic

M₁₆

—

316

—

M₁₆

—

316

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

—

158

—

C₄²

C₄×D₇₉

yes

characteristic

C₄²

D₃₁₆

yes

characteristic

C₄²

C₂×Dic₇₉

yes

characteristic

C₄²

C₂²⋊D₇₉

yes

characteristic

C₂³

Dic₇₉⋊C₄

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×Dic₇₉

yes

characteristic

C₂×C₄

(C₂×D₇₉)⋊C₄

yes

characteristic

C₂×C₄

(C₂×D₇₉)⋊C₄

yes

characteristic

C₂×C₄

C₂²⋊Dic₇₉

yes

characteristic

C₂×C₄

Dic₇₉⋊C₄

yes

characteristic

C₂×C₄

C₄⋊Dic₇₉

yes

characteristic

100

C₂×C₄

#11929609

yes

characteristic

101

C₂×C₄

#11929611

yes

characteristic

102

C₂×C₄

#11929612

yes

characteristic

103

C₂×C₄

#11929614

yes

characteristic

104

C₈

—

105

C₈

—

316

—

106

C₈

—

316

—

107

C₂²

—

108

C₂²

—

109

C₂²

C₇₉⋊#95

yes

characteristic

110

C₂²

#14579092

yes

characteristic

111

C₂²

#14579094

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

—

115

C₄

#14579081

yes

characteristic

116

C₄

#14579082

yes

characteristic

117

C₄

#14579084

yes

characteristic

118

C₄

#14579085

yes

characteristic

119

C₄

#14579097

yes

—

120

C₂

—

121

C₂

—

122

C₂

#19098325

yes

characteristic

123

C₂

#19098328

yes

characteristic

124

C₂

#19098335

yes

characteristic

	subgroup	G/H
center	C₂×C₄	(C₂×D₇₉)⋊C₄
commutator	C₂×C₄×C₇₉	C₄²
Frattini	C₂×C₄²	C₂×D₇₉
Fitting	C₂×C₄⋊C₈×C₇₉	C₂
socle	C₂²×C₇₉	#95
prime radical	C₂³×C₇₉	C₄⋊C₄
cosocle	C₂×C₄²×C₇₉	C₂²
hypercenter	C₂×C₄⋊C₈	D₇₉
hypocenter	C₇₉	#1301
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

subgroup

G/H

center

C₂×C₄

(C₂×D₇₉)⋊C₄

commutator

C₂×C₄×C₇₉

C₄²

Frattini

C₂×C₄²

C₂×D₇₉

Fitting

C₂×C₄⋊C₈×C₇₉

C₂

socle

C₂²×C₇₉

#95

prime radical

C₂³×C₇₉

C₄⋊C₄

cosocle

C₂×C₄²×C₇₉

C₂²

hypercenter

C₂×C₄⋊C₈

D₇₉

hypocenter

C₇₉

#1301

LCS

G ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
63. C₇₉	#1301	semidirect

H ≅ G/N

type

63. C₇₉

#1301

semidirect

Subgroups — #23761297

Conjugacy classes of subgroups

Complements