Group #22627127 — subgroups

Subgroups — #22627127

Order 9344.

152 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 67 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	#17989706	C₂	1	1	yes	maximal, characteristic
3	#17989692	C₂	1	2	yes	maximal, complemented
4	#17989691	C₂	1	2	yes	maximal, complemented
5	#17989553	C₂	1	1	yes	maximal, characteristic
6	#14556688	—	2	1	no	—
7	#14556688	C₂²	1	1	yes	characteristic
8	#14556688	C₂²	1	2	yes	—
9	#14556688	C₂²	1	1	yes	characteristic
10	#14556687	—	2	1	no	—
11	#14556686	—	2	1	no	—
12	C₂×#11924040	—	2	1	no	—
13	C₂×#11924036	C₂²	1	1	yes	characteristic
14	#14556670	C₄	1	1	yes	characteristic
15	#14556645	C₄	1	2	yes	—
16	C₈×#64408	C₂²	1	2	yes	—
17	M₁₆×D₇₃	C₄	1	1	yes	characteristic
18	#11924040	—	2	2	no	—
19	#11924040	—	2	1	no	—
20	#11924040	—	2	1	no	—
21	#11924036	C₂×C₄	1	1	yes	characteristic
22	#11924036	D₄	1	1	yes	characteristic
23	#11924036	Q₈	1	1	yes	characteristic
24	#11924036	C₂³	1	1	yes	characteristic
25	C₂×#10596833	D₄	1	1	yes	characteristic
26	C₂×#10596833	Q₈	1	1	yes	characteristic
27	C₄⋊#64408	—	2	1	no	—
28	C₂²⋊#64408	—	2	1	no	—
29	C₄×#64408	C₂×C₄	1	2	yes	—
30	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
31	#11924012	C₈	1	1	yes	characteristic
32	#11924011	C₈	1	2	yes	—
33	C₈×D₇₃	C₂×C₄	1	2	yes	—
34	M₁₆×C₇₃	C₈	1	1	yes	characteristic
35	C₂²×D₇₃	M₁₆	1	1	yes	characteristic
36	C₂×#64408	—	2	2	no	—
37	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
38	C₂×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
39	C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
40	C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
41	C₄×D₇₃	M₁₆	1	1	yes	characteristic
42	C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
43	#10596833	C₄⋊C₄	1	1	yes	characteristic
44	#10596833	C₄⋊C₄	1	1	yes	characteristic
45	#10596833	C₂×D₄	1	1	yes	characteristic
46	#10596833	C₂×Q₈	1	1	yes	characteristic
47	C₈×C₇₃	C₂×C₈	1	2	yes	—
48	#10596831	C₂×C₈	1	2	yes	—
49	C₂²×C₇₃	C₄⋊C₈	1	1	yes	characteristic
50	C₂×D₇₃	—	4	1	no	—
51	C₂×D₇₃	C₄⋊C₈	1	1	yes	characteristic
52	C₂×D₇₃	C₂×M₁₆	1	1	yes	characteristic
53	#64408	—	4	2	no	—
54	C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
55	C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
56	Dic₇₃	C₄⋊C₈	1	1	yes	characteristic
57	Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
58	C₂×C₇₃	—	2	1	no	—
59	C₂×C₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
60	D₇₃	—	2	1	no	—
61	D₇₃	—	2	1	no	—
62	#2153	—	73	1	no	maximal, Sylow
63	C₇₃	#2153	1	1	yes	characteristic, complemented, Sylow
64	C₂×M₃₂	—	73	1	no	—
65	C₂×M₃₂	—	73	1	no	—
66	#405	—	73	1	no	—
67	#364	—	73	2	no	—
68	#364	—	73	2	no	—
69	C₂×M₁₆	—	73	1	no	—
70	C₂²×C₈	—	73	1	no	—
71	#117	—	73	1	no	—
72	M₃₂	—	73	1	no	—
73	M₃₂	—	73	2	no	—
74	M₃₂	—	73	1	no	—
75	M₃₂	—	146	1	no	—
76	M₃₂	—	146	1	no	—
77	C₂×C₁₆	—	146	1	no	—
78	C₂×C₁₆	—	146	1	no	—
79	#97	—	73	2	no	—
80	C₄×C₈	—	73	2	no	—
81	C₂²×C₄	—	73	1	no	—
82	M₁₆	—	73	1	no	—
83	M₁₆	—	73	2	no	—
84	M₁₆	#10596842	1	1	yes	characteristic
85	C₂×C₈	—	73	1	no	—
86	C₂×C₈	—	73	1	no	—
87	C₂×C₈	—	73	1	no	—
88	C₂×C₈	—	73	1	no	—
89	C₂×C₈	—	73	1	no	—
90	C₂×C₈	—	73	1	no	—
91	C₂×C₈	—	73	2	no	—
92	C₄⋊C₄	—	146	1	no	—
93	C₂²⋊C₄	—	146	1	no	—
94	C₄²	—	73	2	no	—
95	C₁₆	—	146	2	no	—
96	C₁₆	—	146	1	no	—
97	C₁₆	—	146	1	no	—
98	C₂³	—	73	1	no	—
99	C₂×C₄	—	73	1	no	—
100	C₂×C₄	—	73	1	no	—
101	C₂×C₄	—	73	1	no	—
102	C₂×C₄	—	73	1	no	—
103	C₂×C₄	—	73	1	no	—
104	C₂×C₄	—	146	2	no	—
105	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
106	C₈	—	73	1	no	—
107	C₈	—	73	1	no	—
108	C₈	—	73	1	no	—
109	C₈	—	73	1	no	—
110	C₈	—	73	2	no	—
111	C₈	C₂×#10596842	1	2	yes	—
112	C₂²	—	292	1	no	—
113	C₂²	—	73	1	no	—
114	C₂²	—	73	1	no	—
115	C₂²	C₄⋊#10596842	1	1	yes	characteristic
116	C₄	—	292	2	no	—
117	C₄	—	73	1	no	—
118	C₄	—	73	1	no	—
119	C₄	C₄⋊#10596842	1	1	yes	characteristic
120	C₄	C₂²×#10596842	1	1	yes	characteristic
121	C₂	—	2	1	no	—
122	C₂	—	146	1	no	—
123	C₂	—	146	1	no	—
124	C₂	C₂×C₄⋊#10596842	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556688

C₂

yes

maximal, characteristic

#17989706

C₂

yes

maximal, characteristic

#17989692

C₂

yes

maximal, complemented

#17989691

C₂

yes

maximal, complemented

#17989553

C₂

yes

maximal, characteristic

#14556688

—

#14556688

C₂²

yes

characteristic

#14556688

C₂²

yes

—

#14556688

C₂²

yes

—

—

—

C₂²

yes

characteristic

#14556670

C₄

yes

characteristic

#14556645

C₄

yes

—

C₈×#64408

C₂²

yes

—

M₁₆×D₇₃

C₄

yes

—

—

—

C₂×C₄

yes

characteristic

#11924036

D₄

yes

characteristic

#11924036

Q₈

yes

characteristic

#11924036

C₂³

yes

characteristic

C₂×#10596833

D₄

yes

characteristic

C₂×#10596833

Q₈

yes

—

—

C₂×C₄

yes

—

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

#11924012

C₈

yes

characteristic

#11924011

C₈

yes

—

C₈×D₇₃

C₂×C₄

yes

—

M₁₆×C₇₃

C₈

yes

characteristic

C₂²×D₇₃

M₁₆

yes

characteristic

C₂×#64408

—

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

C₄⋊C₄

yes

characteristic

C₄×D₇₃

C₄⋊C₄

yes

characteristic

C₄×D₇₃

C₂×C₈

yes

characteristic

C₄×D₇₃

M₁₆

yes

characteristic

C₄×D₇₃

C₂²×C₄

yes

characteristic

#10596833

C₄⋊C₄

yes

characteristic

#10596833

C₄⋊C₄

yes

characteristic

#10596833

C₂×D₄

yes

characteristic

#10596833

C₂×Q₈

yes

characteristic

C₈×C₇₃

C₂×C₈

yes

—

#10596831

C₂×C₈

yes

—

C₂²×C₇₃

C₄⋊C₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

C₄⋊C₈

yes

characteristic

C₂×D₇₃

C₂×M₁₆

yes

characteristic

#64408

—

C₄×C₇₃

C₄⋊C₈

yes

characteristic

C₄×C₇₃

C₂²×C₈

yes

characteristic

Dic₇₃

C₄⋊C₈

yes

characteristic

Dic₇₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

C₂×C₄⋊C₈

yes

characteristic

D₇₃

—

D₇₃

—

#2153

—

maximal, Sylow

C₇₃

#2153

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂×M₃₂

—

#405

—

#364

—

#364

—

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

M₃₂

—

M₃₂

—

M₃₂

—

146

—

M₃₂

—

146

—

C₂×C₁₆

—

146

—

C₂×C₁₆

—

146

—

#97

—

C₄×C₈

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

M₁₆

#10596842

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

146

—

C₂²⋊C₄

—

146

—

C₄²

—

C₁₆

—

146

—

C₁₆

—

146

—

C₁₆

—

146

—

C₂³

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

146

—

105

C₂×C₄

C₂×#10596842

yes

characteristic

106

C₈

—

107

C₈

—

108

C₈

—

109

C₈

—

110

C₈

—

111

C₈

C₂×#10596842

yes

—

112

C₂²

—

292

—

113

C₂²

—

114

C₂²

—

115

C₂²

C₄⋊#10596842

yes

characteristic

116

C₄

—

292

—

117

C₄

—

118

C₄

—

119

C₄

C₄⋊#10596842

yes

characteristic

120

C₄

C₂²×#10596842

yes

characteristic

121

C₂

—

122

C₂

—

146

—

123

C₂

—

146

—

124

C₂

C₂×C₄⋊#10596842

yes

characteristic

	subgroup	G/H
center	C₂	C₂×C₄⋊#10596842
commutator	C₄×C₇₃	C₂²×C₈
Frattini	C₄	C₂²×#10596842
Fitting	M₁₆×C₇₃	C₈
socle	C₂×C₇₃	C₂×C₄⋊C₈
hypercenter	M₁₆	#10596842
hypocenter	C₇₃	#2153
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ M₁₆

subgroup

G/H

center

C₂

C₂×C₄⋊#10596842

commutator

C₄×C₇₃

C₂²×C₈

Frattini

C₄

C₂²×#10596842

Fitting

M₁₆×C₇₃

C₈

socle

C₂×C₇₃

C₂×C₄⋊C₈

M₁₆

C₇₃

G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ M₁₆

N	H ≅ G/N	type
3. #17989692	C₂	semidirect
4. #17989691	C₂	semidirect
63. C₇₃	#2153	semidirect

H ≅ G/N

type

3. #17989692

C₂

semidirect

4. #17989691

C₂

semidirect

63. C₇₃

#2153

semidirect

Subgroups — #22627127

Conjugacy classes of subgroups

Complements