Group #34175669 — subgroups

Subgroups — #34175669

Order 20224.

124 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 49 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	#23765158	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊(C₇₉⋊C₃₂)	C₂	1	1	yes	maximal, characteristic
3	C₇₉×C₂²⋊C₃₂	C₂	1	1	yes	maximal, characteristic
4	C₂×#14579101	C₄	1	1	yes	characteristic
5	#19098518	C₄	1	1	yes	characteristic
6	C₂×C₇₉⋊C₃₂	—	2	1	no	—
7	Dic₇₉⋊C₁₆	—	2	1	no	—
8	Dic₇₉⋊C₁₆	—	2	1	no	—
9	C₂²×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
10	C₂×C₃₂×C₇₉	—	2	1	no	—
11	C₂×#11929608	C₈	1	1	yes	characteristic
12	#14579120	C₈	1	1	yes	characteristic
13	#14579101	—	4	1	no	—
14	C₂×C₇₉⋊C₁₆	—	2	1	no	—
15	#14579071	—	2	1	no	—
16	C₈×Dic₇₉	—	2	1	no	—
17	C₇₉⋊C₃₂	—	4	1	no	—
18	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₁₆×C₇₉	—	4	1	no	—
20	C₂×C₁₆×C₇₉	D₄	1	1	yes	characteristic
21	C₂×C₁₆×C₇₉	D₄	1	1	yes	characteristic
22	C₃₂×C₇₉	—	4	1	no	—
23	#11929608	—	4	1	no	—
24	C₂×C₇₉⋊C₈	—	2	1	no	—
25	C₄⋊Dic₇₉	C₁₆	1	1	yes	characteristic
26	C₄⋊Dic₇₉	C₁₆	1	1	yes	characteristic
27	C₂²⋊Dic₇₉	—	2	1	no	—
28	C₄×Dic₇₉	—	2	1	no	—
29	C₇₉⋊C₁₆	—	4	1	no	—
30	C₂²×C₄×C₇₉	C₂×C₈	1	1	yes	characteristic
31	C₂×C₈×C₇₉	—	2	1	no	—
32	C₂×C₈×C₇₉	—	2	1	no	—
33	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₈×C₇₉	M₁₆	1	1	yes	characteristic
35	C₁₆×C₇₉	—	2	1	no	—
36	C₁₆×C₇₉	—	2	1	no	—
37	C₂³×C₇₉	M₃₂	1	1	yes	characteristic
38	C₂×C₄×C₇₉	—	2	1	no	—
39	C₂×C₄×C₇₉	—	2	1	no	—
40	C₂×C₄×C₇₉	C₂²⋊C₈	1	1	yes	characteristic
41	C₂×C₄×C₇₉	C₂×C₁₆	1	1	yes	characteristic
42	C₂×Dic₇₉	—	2	1	no	—
43	C₂×Dic₇₉	—	2	1	no	—
44	C₈×C₇₉	—	2	1	no	—
45	C₈×C₇₉	#99	1	1	yes	characteristic
46	C₈×C₇₉	#101	1	1	yes	characteristic
47	C₇₉⋊C₈	—	4	1	no	—
48	C₂²×C₇₉	—	2	1	no	—
49	C₂²×C₇₉	—	2	1	no	—
50	C₂²×C₇₉	—	2	1	no	—
51	C₂²×C₇₉	C₂²⋊C₁₆	1	1	yes	characteristic
52	C₄×C₇₉	—	2	1	no	—
53	C₄×C₇₉	#324	1	1	yes	characteristic
54	C₄×C₇₉	#349	1	1	yes	characteristic
55	Dic₇₉	—	4	1	no	—
56	Dic₇₉	—	4	1	no	—
57	#7363	—	79	1	no	maximal, Sylow
58	C₂×C₇₉	—	4	1	no	—
59	C₂×C₇₉	#1322	1	1	yes	characteristic
60	C₂×C₇₉	#1401	1	1	yes	characteristic
61	C₂×C₇₉	#1401	1	1	yes	characteristic
62	#2151	—	79	1	no	—
63	C₂²⋊C₃₂	—	79	1	no	—
64	C₂²⋊C₃₂	D₇₉	1	1	yes	characteristic
65	C₇₉	#7363	1	1	yes	characteristic, complemented, Sylow
66	C₂×M₃₂	—	79	1	no	—
67	C₂²×C₁₆	C₂×D₇₉	1	1	yes	characteristic
68	#405	—	79	1	no	—
69	C₂×C₃₂	—	2	1	no	—
70	C₂×C₃₂	—	158	1	no	—
71	C₄⋊C₁₆	—	158	1	no	—
72	C₄⋊C₁₆	—	158	1	no	—
73	C₂×M₁₆	—	79	1	no	—
74	C₂²×C₈	C₄×D₇₉	1	1	yes	characteristic
75	#117	—	79	1	no	—
76	M₃₂	—	316	1	no	—
77	C₂×C₁₆	—	4	1	no	—
78	C₂×C₁₆	—	158	1	no	—
79	C₂×C₁₆	D₃₁₆	1	1	yes	characteristic
80	C₂×C₁₆	C₂²⋊D₇₉	1	1	yes	characteristic
81	#97	—	158	1	no	—
82	C₄×C₈	—	158	1	no	—
83	C₃₂	—	4	1	no	—
84	C₃₂	—	316	1	no	—
85	C₂²×C₄	C₈×D₇₉	1	1	yes	characteristic
86	M₁₆	—	316	1	no	—
87	C₂×C₈	—	2	1	no	—
88	C₂×C₈	—	2	1	no	—
89	C₂×C₈	—	158	1	no	—
90	C₂×C₈	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
91	C₂×C₈	#11929607	1	1	yes	characteristic
92	C₄⋊C₄	—	79	1	no	—
93	C₄⋊C₄	—	79	1	no	—
94	C₂²⋊C₄	—	158	1	no	—
95	C₄²	—	158	1	no	—
96	C₁₆	—	2	1	no	—
97	C₁₆	—	2	1	no	—
98	C₁₆	—	316	1	no	—
99	C₂³	#14579100	1	1	yes	characteristic
100	C₂×C₄	—	2	1	no	—
101	C₂×C₄	—	2	1	no	—
102	C₂×C₄	—	158	1	no	—
103	C₂×C₄	—	158	1	no	—
104	C₂×C₄	(C₂×D₇₉)⋊C₈	1	1	yes	characteristic
105	C₂×C₄	C₁₆×D₇₉	1	1	yes	characteristic
106	C₈	—	2	1	no	—
107	C₈	—	316	1	no	—
108	C₈	#14579075	1	1	yes	characteristic
109	C₈	#14579079	1	1	yes	characteristic
110	C₂²	—	2	1	no	—
111	C₂²	—	2	1	no	—
112	C₂²	—	2	1	no	—
113	C₂²	(C₂×D₇₉)⋊C₁₆	1	1	yes	characteristic
114	C₄	—	2	1	no	—
115	C₄	—	316	1	no	—
116	C₄	—	316	1	no	—
117	C₄	#19098288	1	1	yes	characteristic
118	C₄	#19098344	1	1	yes	characteristic
119	C₂	—	4	1	no	—
120	C₂	#23761339	1	1	yes	characteristic
121	C₂	#23761541	1	1	yes	characteristic
122	C₂	#23761543	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23765158

C₂

yes

maximal, characteristic

C₂²⋊(C₇₉⋊C₃₂)

C₂

yes

maximal, characteristic

C₇₉×C₂²⋊C₃₂

C₂

yes

maximal, characteristic

C₂×#14579101

C₄

yes

characteristic

#19098518

C₄

yes

characteristic

C₂×C₇₉⋊C₃₂

—

Dic₇₉⋊C₁₆

—

Dic₇₉⋊C₁₆

—

C₂²×C₁₆×C₇₉

C₂²

yes

characteristic

C₂×C₃₂×C₇₉

—

C₂×#11929608

C₈

yes

characteristic

#14579120

C₈

yes

characteristic

#14579101

—

C₂×C₇₉⋊C₁₆

—

#14579071

—

C₈×Dic₇₉

—

C₇₉⋊C₃₂

—

C₂²×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₇₉

—

C₂×C₁₆×C₇₉

D₄

yes

characteristic

C₂×C₁₆×C₇₉

D₄

yes

characteristic

C₃₂×C₇₉

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

C₁₆

yes

characteristic

C₄⋊Dic₇₉

C₁₆

yes

characteristic

C₂²⋊Dic₇₉

—

C₄×Dic₇₉

—

C₇₉⋊C₁₆

—

C₂²×C₄×C₇₉

C₂×C₈

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₉

M₁₆

yes

characteristic

C₁₆×C₇₉

—

C₁₆×C₇₉

—

C₂³×C₇₉

M₃₂

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₇₉

C₂×C₁₆

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₈×C₇₉

—

C₈×C₇₉

yes

C₈×C₇₉

yes

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂²⋊C₁₆

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

yes

C₄×C₇₉

yes

Dic₇₉

—

Dic₇₉

—

#7363

—

maximal, Sylow

C₂×C₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₂²⋊C₃₂

—

C₂²⋊C₃₂

D₇₉

yes

characteristic

C₇₉

#7363

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂²×C₁₆

C₂×D₇₉

yes

characteristic

#405

—

C₂×C₃₂

—

C₂×C₃₂

—

158

—

C₄⋊C₁₆

—

158

—

C₄⋊C₁₆

—

158

—

C₂×M₁₆

—

C₂²×C₈

C₄×D₇₉

yes

characteristic

#117

—

M₃₂

—

316

—

C₂×C₁₆

—

C₂×C₁₆

—

158

—

C₂×C₁₆

D₃₁₆

yes

characteristic

C₂×C₁₆

C₂²⋊D₇₉

yes

characteristic

#97

—

158

—

C₄×C₈

—

158

—

C₃₂

—

C₃₂

—

316

—

C₂²×C₄

C₈×D₇₉

yes

characteristic

M₁₆

—

316

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

characteristic

C₂×C₈

#11929607

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

158

—

C₄²

—

158

—

C₁₆

—

C₁₆

—

C₁₆

—

316

—

C₂³

#14579100

yes

characteristic

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

158

—

103

C₂×C₄

—

158

—

104

C₂×C₄

(C₂×D₇₉)⋊C₈

yes

characteristic

105

C₂×C₄

C₁₆×D₇₉

yes

characteristic

106

C₈

—

107

C₈

—

316

—

108

C₈

#14579075

yes

characteristic

109

C₈

#14579079

yes

characteristic

110

C₂²

—

111

C₂²

—

112

C₂²

—

113

C₂²

(C₂×D₇₉)⋊C₁₆

yes

characteristic

114

C₄

—

115

C₄

—

316

—

116

C₄

—

316

—

117

C₄

#19098288

yes

characteristic

118

C₄

#19098344

yes

characteristic

119

C₂

—

120

C₂

#23761339

yes

characteristic

121

C₂

#23761541

yes

characteristic

122

C₂

#23761543

yes

characteristic

	subgroup	G/H
center	C₂×C₈	(C₂×D₇₉)⋊C₄
commutator	C₂×C₄×C₇₉	C₂×C₁₆
Frattini	C₂²×C₁₆	C₂×D₇₉
Fitting	C₇₉×C₂²⋊C₃₂	C₂
socle	C₂²×C₇₉	C₂²⋊C₁₆
prime radical	C₂³×C₇₉	M₃₂
cosocle	C₂²×C₁₆×C₇₉	C₂²
hypercenter	C₂²⋊C₃₂	D₇₉
hypocenter	C₇₉	#7363
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₁₆ ◁ C₂²⋊C₃₂

subgroup

G/H

center

C₂×C₈

(C₂×D₇₉)⋊C₄

commutator

C₂×C₄×C₇₉

C₂×C₁₆

Frattini

C₂²×C₁₆

C₂×D₇₉

Fitting

C₇₉×C₂²⋊C₃₂

C₂

socle

C₂²×C₇₉

C₂²⋊C₁₆

prime radical

C₂³×C₇₉

M₃₂

cosocle

C₂²×C₁₆×C₇₉

C₂²

hypercenter

C₂²⋊C₃₂

D₇₉

hypocenter

C₇₉

#7363

LCS

G ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₈ ◁ C₂²×C₁₆ ◁ C₂²⋊C₃₂

N	H ≅ G/N	type
65. C₇₉	#7363	semidirect

H ≅ G/N

type

65. C₇₉

#7363

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#23765158	2
C₂²⋊(C₇₉⋊C₃₂)	2
C₇₉×C₂²⋊C₃₂	2
#7363	79

subgroup

index

#23765158

C₂²⋊(C₇₉⋊C₃₂)

C₇₉×C₂²⋊C₃₂

#7363

Subgroups — #34175669

Conjugacy classes of subgroups

Complements

Maximal subgroups