Group #34203271 — subgroups

Subgroups — #34203271

Order 20224.

390 conjugacy classes of subgroups; only the 227 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 227 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×#19098339	C₂	1	2	yes	maximal
2	#23761478	C₂	1	4	yes	maximal
3	C₄²×C₈×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₇₉⋊C₁₆	C₂²	1	4	yes	—
5	#19098339	C₄	1	8	yes	complemented
6	C₂×C₄×C₈×C₇₉	C₄	1	2	yes	—
7	C₂×C₄×C₈×C₇₉	C₄	1	1	yes	characteristic
8	C₂×C₄×C₈×C₇₉	C₂²	1	2	yes	—
9	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
10	C₄³×C₇₉	C₄	1	1	yes	characteristic
11	C₂×C₇₉⋊C₁₆	—	2	8	no	—
12	C₂×C₇₉⋊C₁₆	C₂×C₄	1	8	yes	—
13	C₂²×C₈×C₇₉	C₂×C₄	1	2	yes	—
14	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
16	C₂×C₄²×C₇₉	C₈	1	4	yes	—
17	C₂×C₄²×C₇₉	C₂×C₄	1	2	yes	—
18	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
19	C₄×C₈×C₇₉	—	2	4	no	—
20	C₄×C₈×C₇₉	—	2	4	no	—
21	C₄×C₈×C₇₉	C₈	1	4	yes	—
22	C₄×C₈×C₇₉	C₂×C₄	1	4	yes	—
23	C₇₉⋊C₁₆	—	2	8	no	—
24	C₂²×C₄×C₇₉	C₂×C₈	1	2	yes	—
25	C₂²×C₄×C₇₉	C₂×C₈	1	4	yes	—
26	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₈×C₇₉	—	2	2	no	—
28	C₂×C₈×C₇₉	—	2	2	no	—
29	C₂×C₈×C₇₉	C₄²	1	2	yes	—
30	C₂×C₈×C₇₉	C₂×C₈	1	4	yes	—
31	C₂×C₈×C₇₉	M₁₆	1	4	yes	—
32	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
33	C₂×C₈×C₇₉	#41	1	4	yes	—
34	C₄²×C₇₉	—	2	8	no	—
35	C₄²×C₇₉	—	2	2	no	—
36	C₄²×C₇₉	—	2	2	no	—
37	C₄²×C₇₉	C₄²	1	2	yes	—
38	C₄²×C₇₉	C₂×C₈	1	2	yes	—
39	C₂³×C₇₉	C₂²×C₈	1	1	yes	characteristic
40	C₂×C₄×C₇₉	—	2	4	no	—
41	C₂×C₄×C₇₉	—	2	4	no	—
42	C₂×C₄×C₇₉	—	2	4	no	—
43	C₂×C₄×C₇₉	C₄×C₈	1	4	yes	—
44	C₂×C₄×C₇₉	M₃₂	1	8	yes	—
45	C₂×C₄×C₇₉	C₂×C₄²	1	1	yes	characteristic
46	C₂×C₄×C₇₉	#117	1	2	yes	—
47	C₂×C₄×C₇₉	C₂²×C₈	1	1	yes	characteristic
48	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
49	C₈×C₇₉	—	2	4	no	—
50	C₈×C₇₉	#97	1	4	yes	—
51	C₈×C₇₉	#117	1	4	yes	—
52	C₂²×C₇₉	C₂×C₄×C₈	1	1	yes	characteristic
53	C₂²×C₇₉	#431	1	2	yes	—
54	C₂²×C₇₉	C₂×M₃₂	1	4	yes	—
55	C₄×C₇₉	—	2	4	no	—
56	C₄×C₇₉	—	2	8	no	—
57	C₄×C₇₉	#376	1	1	yes	characteristic
58	C₄×C₇₉	C₂×#97	1	1	yes	characteristic
59	C₄×C₇₉	#431	1	2	yes	—
60	#12591	—	79	1	no	maximal, Sylow
61	C₂×C₇₉	#1744	1	1	yes	characteristic
62	C₂×C₇₉	C₄×M₃₂	1	2	yes	—
63	C₂×C₇₉	#2163	1	4	yes	—
64	C₂×#346	—	79	2	no	—
65	C₄²×C₈	D₇₉	1	1	yes	characteristic
66	#1374	—	79	4	no	—
67	C₇₉	#12591	1	1	yes	characteristic, complemented, Sylow
68	C₂²×C₁₆	—	79	4	no	—
69	C₂×C₄×C₈	Dic₇₉	1	2	yes	—
70	C₂×C₄×C₈	Dic₇₉	1	1	yes	characteristic
71	C₂×C₄×C₈	C₂×D₇₉	1	2	yes	—
72	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
73	C₄³	Dic₇₉	1	1	yes	characteristic
74	#346	—	79	8	no	—
75	C₂²×C₈	C₂×Dic₇₉	1	2	yes	—
76	C₂²×C₈	C₂×Dic₇₉	1	1	yes	characteristic
77	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
78	C₂×C₄²	C₇₉⋊C₈	1	4	yes	—
79	C₂×C₄²	C₂×Dic₇₉	1	2	yes	—
80	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
81	C₂×C₁₆	—	79	8	no	—
82	C₂×C₁₆	—	158	8	no	—
83	C₄×C₈	—	2	4	no	—
84	C₄×C₈	—	2	4	no	—
85	C₄×C₈	C₇₉⋊C₈	1	4	yes	—
86	C₄×C₈	C₄×D₇₉	1	4	yes	—
87	C₂²×C₄	C₂×C₇₉⋊C₈	1	2	yes	—
88	C₂²×C₄	C₂×C₇₉⋊C₈	1	4	yes	—
89	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
90	C₂×C₈	—	2	2	no	—
91	C₂×C₈	—	2	2	no	—
92	C₂×C₈	C₄×Dic₇₉	1	2	yes	—
93	C₂×C₈	C₂×C₇₉⋊C₈	1	4	yes	—
94	C₂×C₈	#11929608	1	4	yes	—
95	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
96	C₂×C₈	#11929624	1	4	yes	—
97	C₄²	—	2	8	no	—
98	C₄²	—	2	2	no	—
99	C₄²	—	2	2	no	—
100	C₄²	C₄×Dic₇₉	1	2	yes	—
101	C₄²	C₂×C₇₉⋊C₈	1	2	yes	—
102	C₁₆	—	158	8	no	—
103	C₂³	C₂²×C₇₉⋊C₈	1	1	yes	characteristic
104	C₂×C₄	—	2	4	no	—
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	—	2	4	no	—
107	C₂×C₄	C₄×C₇₉⋊C₈	1	4	yes	—
108	C₂×C₄	#14579101	1	8	yes	—
109	C₂×C₄	C₂×C₄×Dic₇₉	1	1	yes	characteristic
110	C₂×C₄	#14579120	1	2	yes	—
111	C₂×C₄	C₂²×C₇₉⋊C₈	1	1	yes	characteristic
112	C₂×C₄	C₂×#11929608	1	2	yes	—
113	C₈	—	2	4	no	—
114	C₈	#14579072	1	4	yes	—
115	C₈	#14579118	1	4	yes	—
116	C₂²	C₂×C₄×C₇₉⋊C₈	1	1	yes	characteristic
117	C₂²	#19098616	1	2	yes	—
118	C₂²	C₂×#14579101	1	4	yes	—
119	C₄	—	2	4	no	—
120	C₄	—	2	8	no	—
121	C₄	#19098409	1	1	yes	characteristic
122	C₄	C₂×#14579072	1	1	yes	characteristic
123	C₄	#19098616	1	2	yes	—
124	C₂	#23763146	1	1	yes	characteristic
125	C₂	C₄×#14579101	1	2	yes	—
126	C₂	#23765203	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19098339

C₂

yes

maximal

#23761478

C₂

yes

maximal

C₄²×C₈×C₇₉

C₂

yes

maximal, characteristic

C₂²×C₇₉⋊C₁₆

C₂²

yes

—

#19098339

C₄

yes

complemented

C₂×C₄×C₈×C₇₉

C₄

yes

—

C₂×C₄×C₈×C₇₉

C₄

yes

characteristic

C₂×C₄×C₈×C₇₉

C₂²

yes

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

C₄³×C₇₉

C₄

yes

characteristic

C₂×C₇₉⋊C₁₆

—

C₂×C₇₉⋊C₁₆

C₂×C₄

yes

—

C₂²×C₈×C₇₉

C₂×C₄

yes

—

C₂²×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₇₉

C₂³

yes

characteristic

C₂×C₄²×C₇₉

C₈

yes

—

C₂×C₄²×C₇₉

C₂×C₄

yes

—

C₂×C₄²×C₇₉

C₂×C₄

yes

characteristic

C₄×C₈×C₇₉

—

C₄×C₈×C₇₉

—

C₄×C₈×C₇₉

C₈

yes

—

C₄×C₈×C₇₉

C₂×C₄

yes

—

C₇₉⋊C₁₆

—

C₂²×C₄×C₇₉

C₂×C₈

yes

—

C₂²×C₄×C₇₉

C₂×C₈

yes

—

C₂²×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₄²

yes

—

C₂×C₈×C₇₉

C₂×C₈

yes

—

C₂×C₈×C₇₉

M₁₆

yes

—

C₂×C₈×C₇₉

C₂²×C₄

yes

—

C₂×C₈×C₇₉

#41

yes

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

C₄²

yes

—

C₄²×C₇₉

C₂×C₈

yes

—

C₂³×C₇₉

C₂²×C₈

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₄×C₈

yes

—

C₂×C₄×C₇₉

M₃₂

yes

—

C₂×C₄×C₇₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₇₉

#117

yes

—

C₂×C₄×C₇₉

C₂²×C₈

yes

characteristic

C₂×C₄×C₇₉

C₂×M₁₆

yes

—

C₈×C₇₉

—

C₈×C₇₉

#97

yes

—

C₈×C₇₉

#117

yes

—

C₂²×C₇₉

C₂×C₄×C₈

yes

characteristic

C₂²×C₇₉

#431

yes

—

C₂²×C₇₉

C₂×M₃₂

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

#376

yes

characteristic

C₄×C₇₉

C₂×#97

yes

characteristic

C₄×C₇₉

#431

yes

—

—

C₂×C₇₉

yes

C₂×C₇₉

C₄×M₃₂

yes

—

C₂×C₇₉

#2163

yes

—

C₂×#346

—

C₄²×C₈

D₇₉

yes

characteristic

#1374

—

C₇₉

#12591

yes

characteristic, complemented, Sylow

C₂²×C₁₆

—

C₂×C₄×C₈

Dic₇₉

yes

—

C₂×C₄×C₈

Dic₇₉

yes

characteristic

C₂×C₄×C₈

C₂×D₇₉

yes

—

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

C₄³

Dic₇₉

yes

characteristic

#346

—

C₂²×C₈

C₂×Dic₇₉

yes

—

C₂²×C₈

C₂×Dic₇₉

yes

characteristic

C₂²×C₈

C₂²×D₇₉

yes

characteristic

C₂×C₄²

C₇₉⋊C₈

yes

—

C₂×C₄²

C₂×Dic₇₉

yes

—

C₂×C₄²

C₂×Dic₇₉

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

158

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₇₉⋊C₈

yes

—

C₄×C₈

C₄×D₇₉

yes

—

C₂²×C₄

C₂×C₇₉⋊C₈

yes

—

C₂²×C₄

C₂×C₇₉⋊C₈

yes

—

C₂²×C₄

C₂²×Dic₇₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×Dic₇₉

yes

—

C₂×C₈

C₂×C₇₉⋊C₈

yes

—

C₂×C₈

#11929608

yes

—

C₂×C₈

C₂×C₄×D₇₉

yes

—

C₂×C₈

#11929624

yes

—

C₄²

—

C₄²

—

C₄²

—

100

C₄²

C₄×Dic₇₉

yes

—

101

C₄²

C₂×C₇₉⋊C₈

yes

—

102

C₁₆

—

158

—

103

C₂³

C₂²×C₇₉⋊C₈

yes

characteristic

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

C₄×C₇₉⋊C₈

yes

—

108

C₂×C₄

#14579101

yes

—

109

C₂×C₄

C₂×C₄×Dic₇₉

yes

characteristic

110

C₂×C₄

#14579120

yes

—

111

C₂×C₄

C₂²×C₇₉⋊C₈

yes

characteristic

112

C₂×C₄

C₂×#11929608

yes

—

113

C₈

—

114

C₈

#14579072

yes

—

115

C₈

#14579118

yes

—

116

C₂²

C₂×C₄×C₇₉⋊C₈

yes

characteristic

117

C₂²

#19098616

yes

—

118

C₂²

C₂×#14579101

yes

—

119

C₄

—

120

C₄

—

121

C₄

#19098409

yes

characteristic

122

C₄

C₂×#14579072

yes

characteristic

123

C₄

#19098616

yes

—

124

C₂

#23763146

yes

characteristic

125

C₂

C₄×#14579101

yes

—

126

C₂

#23765203

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₇₉
commutator	C₂²×C₇₉	C₂×C₄×C₈
Fitting	C₄²×C₈×C₇₉	C₂
socle, prime radical	C₂³×C₇₉	C₂²×C₈
cosocle	C₂²×C₈×C₇₉	C₂³
hypercenter	C₄²×C₈	D₇₉
hypocenter	C₇₉	#12591
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₈ ◁ C₄²×C₈

subgroup

G/H

center, Frattini

C₂²×C₈

C₂²×D₇₉

commutator

C₂²×C₇₉

C₂×C₄×C₈

Fitting

C₄²×C₈×C₇₉

C₂

socle, prime radical

C₂³×C₇₉

C₂²×C₈

cosocle

C₂²×C₈×C₇₉

C₂³

hypercenter

C₄²×C₈

D₇₉

C₇₉

G ▷ C₂²×C₇₉ ▷ C₇₉

C₁ ◁ C₂²×C₈ ◁ C₄²×C₈

N	H ≅ G/N	type
5. #19098339	C₄	semidirect
67. C₇₉	#12591	semidirect

H ≅ G/N

type

5. #19098339

C₄

semidirect

67. C₇₉

#12591

semidirect

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

subgroup	index
C₂×#19098339	2
#23761478	2
C₄²×C₈×C₇₉	2
#12591	79

subgroup

index

C₂×#19098339

#23761478

C₄²×C₈×C₇₉

#12591

Subgroups — #34203271

Conjugacy classes of subgroups

Complements

Maximal subgroups