Group #22627129 — subgroups

Subgroups — #22627129

Order 9344.

160 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 73 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	#17989690	C₂	1	2	yes	maximal, complemented
2	C₂²⋊#11924040	C₂	1	2	yes	maximal
3	C₄×#11924040	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×#10596833	C₂	1	1	yes	maximal, characteristic
5	C₂×#11924040	C₂²	1	4	yes	—
6	C₂²×#10596833	C₄	1	1	yes	characteristic
7	C₂²×#10596833	C₂²	1	1	yes	characteristic
8	C₄×#10596833	C₄	1	1	yes	characteristic
9	C₄×#10596833	C₄	1	1	yes	characteristic
10	C₄×#10596833	C₂²	1	1	yes	characteristic
11	C₄×#10596833	C₂²	1	1	yes	characteristic
12	C₂×C₄×Dic₇₃	C₄	1	1	yes	characteristic
13	#11924040	—	2	4	no	—
14	C₂×#10596833	—	2	2	no	—
15	C₂×#10596833	—	2	2	no	—
16	C₂×#10596833	C₂×C₄	1	1	yes	characteristic
17	C₂×#10596833	C₂×C₄	1	1	yes	characteristic
18	C₂×#10596833	C₂×C₄	1	1	yes	characteristic
19	C₂×#10596833	C₂³	1	1	yes	characteristic
20	C₂²×Dic₇₃	C₈	1	1	yes	characteristic
21	C₂²×Dic₇₃	C₂×C₄	1	1	yes	characteristic
22	C₄×Dic₇₃	C₈	1	1	yes	characteristic
23	C₄×Dic₇₃	C₈	1	1	yes	characteristic
24	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
25	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄×C₇₃	C₈	1	1	yes	characteristic
27	C₂³×C₇₃	C₂×C₈	1	1	yes	characteristic
28	C₂×C₄×C₇₃	—	2	2	no	—
29	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
31	C₂×Dic₇₃	—	2	1	no	—
32	C₂×Dic₇₃	—	2	1	no	—
33	C₂×Dic₇₃	C₁₆	1	4	yes	complemented
34	C₂×Dic₇₃	C₂×C₈	1	1	yes	characteristic
35	C₂×Dic₇₃	C₂×C₈	1	1	yes	characteristic
36	C₂×Dic₇₃	C₂×C₈	1	1	yes	characteristic
37	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
38	#10596833	—	2	1	no	—
39	#10596833	—	2	1	no	—
40	#10596833	M₁₆	1	2	yes	—
41	#10596833	#41	1	2	yes	—
42	C₂²×C₇₃	—	2	1	no	—
43	C₂²×C₇₃	—	2	1	no	—
44	C₂²×C₇₃	C₂×C₁₆	1	2	yes	—
45	C₂²×C₇₃	C₂²×C₈	1	1	yes	characteristic
46	C₄×C₇₃	—	2	1	no	—
47	C₄×C₇₃	M₃₂	1	2	yes	—
48	Dic₇₃	—	2	1	no	—
49	Dic₇₃	C₂×C₁₆	1	2	yes	—
50	Dic₇₃	C₂×C₁₆	1	2	yes	—
51	Dic₇₃	#117	1	1	yes	characteristic
52	Dic₇₃	C₂×M₁₆	1	1	yes	characteristic
53	C₂×C₇₃	—	2	2	no	—
54	C₂×C₇₃	#431	1	1	yes	characteristic
55	C₂×C₇₃	C₂²×C₁₆	1	1	yes	characteristic
56	C₂×C₇₃	C₂×M₃₂	1	1	yes	characteristic
57	#2162	—	73	1	no	maximal, Sylow
58	C₇₃	#2162	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₄×C₈	—	73	1	no	—
60	C₄⋊C₁₆	—	73	2	no	—
61	C₂²⋊C₁₆	—	73	2	no	—
62	C₄×C₁₆	—	73	2	no	—
63	C₂²×C₈	—	73	1	no	—
64	C₂²×C₈	—	73	1	no	—
65	C₂×C₄²	—	73	1	no	—
66	C₂×C₁₆	—	73	4	no	—
67	C₄×C₈	—	73	1	no	—
68	C₄×C₈	—	73	1	no	—
69	C₄×C₈	—	73	1	no	—
70	C₄×C₈	—	73	1	no	—
71	C₂²×C₄	—	73	1	no	—
72	C₂²×C₄	—	73	1	no	—
73	C₂²×C₄	#10596842	1	1	yes	characteristic
74	C₂×C₈	—	73	1	no	—
75	C₂×C₈	—	73	1	no	—
76	C₂×C₈	—	73	1	no	—
77	C₂×C₈	—	73	1	no	—
78	C₂×C₈	—	146	2	no	—
79	C₂×C₈	—	146	2	no	—
80	C₄²	—	73	1	no	—
81	C₄²	—	73	1	no	—
82	C₄²	—	73	1	no	—
83	C₄²	—	73	1	no	—
84	C₁₆	—	146	4	no	—
85	C₂³	C₂×#10596842	1	1	yes	characteristic
86	C₂×C₄	—	2	2	no	—
87	C₂×C₄	—	73	4	no	—
88	C₂×C₄	—	73	1	no	—
89	C₂×C₄	—	73	1	no	—
90	C₂×C₄	—	73	1	no	—
91	C₂×C₄	—	73	1	no	—
92	C₂×C₄	—	146	1	no	—
93	C₂×C₄	—	146	1	no	—
94	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
95	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
96	C₈	—	73	2	no	—
97	C₈	—	73	2	no	—
98	C₈	—	146	1	no	—
99	C₈	—	146	1	no	—
100	C₂²	—	2	1	no	—
101	C₂²	—	2	1	no	—
102	C₂²	#14556686	1	2	yes	—
103	C₂²	C₂²×#10596842	1	1	yes	characteristic
104	C₄	—	2	1	no	—
105	C₄	—	73	1	no	—
106	C₄	—	73	1	no	—
107	C₄	—	73	2	no	—
108	C₄	—	73	2	no	—
109	C₄	—	146	1	no	—
110	C₄	#14556687	1	2	yes	—
111	C₂	—	2	2	no	—
112	C₂	#17989700	1	1	yes	characteristic
113	C₂	C₂×#14556686	1	1	yes	characteristic
114	C₂	C₂×#14556687	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989690

C₂

yes

maximal, complemented

C₂²⋊#11924040

C₂

yes

maximal

C₄×#11924040

C₂

yes

maximal, complemented

C₂×C₄×#10596833

C₂

yes

maximal, characteristic

C₂×#11924040

C₂²

yes

—

C₂²×#10596833

C₄

yes

characteristic

C₂²×#10596833

C₂²

yes

characteristic

C₄×#10596833

C₄

yes

characteristic

C₄×#10596833

C₄

yes

characteristic

C₄×#10596833

C₂²

yes

characteristic

C₄×#10596833

C₂²

yes

characteristic

C₂×C₄×Dic₇₃

C₄

yes

—

—

—

C₂×C₄

yes

characteristic

C₂×#10596833

C₂×C₄

yes

characteristic

C₂×#10596833

C₂×C₄

yes

characteristic

C₂×#10596833

C₂³

yes

characteristic

C₂²×Dic₇₃

C₈

yes

characteristic

C₂²×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

C₈

yes

characteristic

C₄×Dic₇₃

C₈

yes

characteristic

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₃

C₈

yes

characteristic

C₂³×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₁₆

yes

complemented

C₂×Dic₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

C₂²×C₄

yes

—

—

M₁₆

yes

—

#10596833

#41

yes

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂×C₁₆

yes

—

C₂²×C₇₃

C₂²×C₈

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

M₃₂

yes

—

Dic₇₃

—

Dic₇₃

C₂×C₁₆

yes

—

Dic₇₃

C₂×C₁₆

yes

—

Dic₇₃

#117

yes

characteristic

Dic₇₃

C₂×M₁₆

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

#431

yes

characteristic

C₂×C₇₃

C₂²×C₁₆

yes

characteristic

C₂×C₇₃

C₂×M₃₂

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂×C₄×C₈

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

C₄×C₁₆

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₁₆

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

#10596842

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₁₆

—

146

—

C₂³

C₂×#10596842

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

yes

C₂×C₄

yes

C₈

—

C₈

—

C₈

—

146

—

C₈

—

146

—

100

C₂²

—

101

C₂²

—

102

C₂²

#14556686

yes

—

103

C₂²

C₂²×#10596842

yes

characteristic

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

146

—

110

C₄

#14556687

yes

—

111

C₂

—

112

C₂

#17989700

yes

characteristic

113

C₂

C₂×#14556686

yes

characteristic

114

C₂

C₂×#14556687

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#10596842
commutator	C₂×C₇₃	C₂²×C₁₆
Frattini	C₂²	C₂²×#10596842
Fitting	C₂²×C₄×C₇₃	C₈
socle	C₂²×C₇₃	C₂²×C₈
hypercenter	C₂²×C₄	#10596842
hypocenter	C₇₃	#2162
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄

subgroup

G/H

center

C₂×C₄

C₂×#10596842

commutator

C₂×C₇₃

C₂²×C₁₆

Frattini

C₂²

C₂²×#10596842

Fitting

C₂²×C₄×C₇₃

C₈

socle

C₂²×C₇₃

C₂²×C₈

C₂²×C₄

C₇₃

G ▷ C₂×C₇₃ ▷ C₇₃

C₁ ◁ C₂×C₄ ◁ C₂²×C₄

N	H ≅ G/N	type
1. #17989690	C₂	semidirect
3. C₄×#11924040	C₂	semidirect
33. C₂×Dic₇₃	C₁₆	semidirect
58. C₇₃	#2162	semidirect

H ≅ G/N

type

1. #17989690

C₂

semidirect

3. C₄×#11924040

C₂

semidirect

33. C₂×Dic₇₃

C₁₆

semidirect

58. C₇₃

#2162

semidirect

Subgroups — #22627129

Conjugacy classes of subgroups

Complements