Group #22627011 — subgroups

Subgroups — #22627011

Order 9344.

136 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 53 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×#14556688	C₂	1	1	yes	maximal, characteristic
2	C₂×#14556686	C₂	1	1	yes	maximal, characteristic
3	#17989552	C₂	1	1	yes	maximal, characteristic
4	#14556688	—	2	1	no	—
5	#14556688	C₄	1	2	yes	complemented
6	#14556686	—	2	1	no	—
7	#14556686	C₄	1	2	yes	complemented
8	C₂×#11924040	—	2	1	no	—
9	C₂×#11924040	—	2	1	no	—
10	C₂×#11924038	C₄	1	1	yes	characteristic
11	C₂×#11924036	C₂²	1	1	yes	characteristic
12	#14556646	—	2	1	no	—
13	C₄×#10596833	—	2	1	no	—
14	#14556549	C₄	1	1	yes	characteristic
15	#11924040	—	2	2	no	—
16	#11924040	—	2	2	no	—
17	#11924038	—	2	1	no	—
18	#11924038	C₈	1	2	yes	—
19	#11924036	C₂×C₄	1	1	yes	characteristic
20	#11924036	C₂×C₄	1	1	yes	characteristic
21	#11924036	D₄	1	1	yes	characteristic
22	#11924036	Q₈	1	1	yes	characteristic
23	C₂×#10596833	—	2	1	no	—
24	C₂×#10596833	D₄	1	1	yes	characteristic
25	C₂×#10596833	D₄	1	1	yes	characteristic
26	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
27	C₄⋊Dic₇₃	C₈	1	1	yes	characteristic
28	#11924005	—	2	1	no	—
29	C₄×Dic₇₃	—	2	1	no	—
30	C₄⋊C₄×C₇₃	C₈	1	1	yes	characteristic
31	C₂²×D₇₃	M₁₆	1	1	yes	characteristic
32	C₂×C₄×C₇₃	—	2	1	no	—
33	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
34	C₂×Dic₇₃	—	2	1	no	—
35	C₂×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
36	C₄×D₇₃	C₄²	1	1	yes	characteristic
37	C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
38	C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
39	C₄×D₇₃	M₁₆	1	1	yes	characteristic
40	#10596833	—	2	2	no	—
41	#10596833	C₂²⋊C₄	1	1	yes	characteristic
42	#10596833	C₂²⋊C₄	1	1	yes	characteristic
43	#10596833	C₄⋊C₄	1	1	yes	characteristic
44	#10596833	C₄⋊C₄	1	1	yes	characteristic
45	C₂²×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
46	C₂×D₇₃	—	2	1	no	—
47	C₂×D₇₃	—	2	1	no	—
48	C₂×D₇₃	#97	1	1	yes	characteristic
49	C₂×D₇₃	C₄⋊C₈	1	1	yes	characteristic
50	C₄×C₇₃	—	4	1	no	—
51	C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
52	C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
53	Dic₇₃	—	4	1	no	—
54	Dic₇₃	#95	1	1	yes	characteristic
55	Dic₇₃	C₂²⋊C₈	1	1	yes	characteristic
56	C₂×C₇₃	#336	1	1	yes	characteristic
57	C₂×C₇₃	#350	1	1	yes	characteristic
58	C₂×C₇₃	#350	1	1	yes	characteristic
59	D₇₃	—	2	1	no	—
60	D₇₃	—	2	1	no	—
61	#1379	—	73	1	no	maximal, Sylow
62	C₇₃	#1379	1	1	yes	characteristic, complemented, Sylow
63	C₂×M₃₂	—	73	1	no	—
64	C₂²×C₁₆	—	73	1	no	—
65	#405	—	73	1	no	—
66	C₂×M₁₆	—	73	1	no	—
67	C₂²×C₈	—	73	1	no	—
68	#117	—	73	1	no	—
69	M₃₂	—	73	2	no	—
70	M₃₂	—	146	1	no	—
71	C₂×C₁₆	—	73	2	no	—
72	C₂×C₁₆	—	146	1	no	—
73	C₂×C₁₆	—	146	1	no	—
74	C₂×C₁₆	—	146	1	no	—
75	#97	—	146	1	no	—
76	C₄×C₈	—	146	1	no	—
77	C₂²×C₄	—	73	1	no	—
78	M₁₆	—	73	2	no	—
79	M₁₆	—	146	1	no	—
80	C₂×C₈	—	73	1	no	—
81	C₂×C₈	—	73	1	no	—
82	C₂×C₈	—	73	1	no	—
83	C₂×C₈	—	73	1	no	—
84	C₂×C₈	—	73	1	no	—
85	C₂×C₈	—	73	1	no	—
86	C₂×C₈	—	146	1	no	—
87	C₄⋊C₄	—	73	1	no	—
88	C₄⋊C₄	#10596842	1	1	yes	characteristic
89	C₂²⋊C₄	—	146	1	no	—
90	C₄²	—	146	1	no	—
91	C₁₆	—	146	2	no	—
92	C₁₆	—	146	2	no	—
93	C₂³	—	73	1	no	—
94	C₂×C₄	—	2	1	no	—
95	C₂×C₄	—	73	1	no	—
96	C₂×C₄	—	73	1	no	—
97	C₂×C₄	—	73	1	no	—
98	C₂×C₄	—	73	1	no	—
99	C₂×C₄	—	73	1	no	—
100	C₂×C₄	—	146	1	no	—
101	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
102	C₈	—	73	1	no	—
103	C₈	—	73	1	no	—
104	C₈	—	73	1	no	—
105	C₈	—	73	1	no	—
106	C₈	—	146	2	no	—
107	C₂²	—	73	1	no	—
108	C₂²	—	73	1	no	—
109	C₂²	—	146	1	no	—
110	C₂²	—	146	1	no	—
111	C₂²	C₂²⋊#10596842	1	1	yes	characteristic
112	C₄	—	4	1	no	—
113	C₄	—	292	1	no	—
114	C₄	—	73	1	no	—
115	C₄	—	73	1	no	—
116	C₄	C₄×#10596842	1	1	yes	characteristic
117	C₄	C₄⋊#10596842	1	1	yes	characteristic
118	C₂	—	146	1	no	—
119	C₂	—	146	1	no	—
120	C₂	(C₂×#10596842)⋊C₄	1	1	yes	characteristic
121	C₂	#17989687	1	1	yes	characteristic
122	C₂	#17989688	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556688

C₂

yes

maximal, characteristic

C₂×#14556686

C₂

yes

maximal, characteristic

#17989552

C₂

yes

maximal, characteristic

#14556688

—

#14556688

C₄

yes

complemented

#14556686

—

#14556686

C₄

yes

—

—

C₄

yes

characteristic

C₂×#11924036

C₂²

yes

—

—

C₄

yes

—

—

—

C₈

yes

—

#11924036

C₂×C₄

yes

characteristic

#11924036

C₂×C₄

yes

characteristic

#11924036

D₄

yes

characteristic

#11924036

Q₈

yes

characteristic

C₂×#10596833

—

C₂×#10596833

D₄

yes

characteristic

C₂×#10596833

D₄

yes

characteristic

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₄⋊Dic₇₃

C₈

yes

characteristic

#11924005

—

C₄×Dic₇₃

—

C₄⋊C₄×C₇₃

C₈

yes

characteristic

C₂²×D₇₃

M₁₆

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂²⋊C₄

yes

characteristic

C₄×D₇₃

C₄²

yes

characteristic

C₄×D₇₃

C₄⋊C₄

yes

characteristic

C₄×D₇₃

C₂×C₈

yes

characteristic

C₄×D₇₃

M₁₆

yes

characteristic

#10596833

—

#10596833

C₂²⋊C₄

yes

characteristic

#10596833

C₂²⋊C₄

yes

characteristic

#10596833

C₄⋊C₄

yes

characteristic

#10596833

C₄⋊C₄

yes

characteristic

C₂²×C₇₃

C₂²⋊C₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

#97

yes

characteristic

C₂×D₇₃

C₄⋊C₈

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

C₄×C₈

yes

characteristic

C₄×C₇₃

C₄⋊C₈

yes

characteristic

Dic₇₃

—

Dic₇₃

#95

yes

characteristic

Dic₇₃

C₂²⋊C₈

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

D₇₃

—

D₇₃

—

#1379

—

maximal, Sylow

C₇₃

#1379

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂²×C₁₆

—

#405

—

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

M₃₂

—

146

—

C₂×C₁₆

—

C₂×C₁₆

—

146

—

C₂×C₁₆

—

146

—

C₂×C₁₆

—

146

—

#97

—

146

—

C₄×C₈

—

146

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₄⋊C₄

—

C₄⋊C₄

#10596842

yes

characteristic

C₂²⋊C₄

—

146

—

C₄²

—

146

—

C₁₆

—

146

—

C₁₆

—

146

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

146

—

101

C₂×C₄

C₂×#10596842

yes

characteristic

102

C₈

—

103

C₈

—

104

C₈

—

105

C₈

—

106

C₈

—

146

—

107

C₂²

—

108

C₂²

—

109

C₂²

—

146

—

110

C₂²

—

146

—

111

C₂²

C₂²⋊#10596842

yes

characteristic

112

C₄

—

113

C₄

—

292

—

114

C₄

—

115

C₄

—

116

C₄

C₄×#10596842

yes

characteristic

117

C₄

C₄⋊#10596842

yes

characteristic

118

C₂

—

146

—

119

C₂

—

146

—

120

C₂

(C₂×#10596842)⋊C₄

yes

characteristic

121

C₂

#17989687

yes

characteristic

122

C₂

#17989688

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#10596842
commutator	C₄×C₇₃	C₄×C₈
Frattini	C₂×C₄	C₂×#10596842
Fitting	C₄⋊C₄×C₇₃	C₈
socle	C₂²×C₇₃	C₂²⋊C₈
hypercenter	C₄⋊C₄	#10596842
hypocenter	C₇₃	#1379
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

subgroup

G/H

center

C₂²

C₂²⋊#10596842

commutator

C₄×C₇₃

C₄×C₈

Frattini

C₂×C₄

C₂×#10596842

Fitting

C₄⋊C₄×C₇₃

C₈

socle

C₂²×C₇₃

C₂²⋊C₈

C₄⋊C₄

C₇₃

G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

N	H ≅ G/N	type
5. #14556688	C₄	semidirect
7. #14556686	C₄	semidirect
62. C₇₃	#1379	semidirect

H ≅ G/N

type

5. #14556688

C₄

semidirect

7. #14556686

C₄

semidirect

62. C₇₃

#1379

semidirect

Subgroups — #22627011

Conjugacy classes of subgroups

Complements