Group #22609437 — subgroups

Subgroups — #22609437

Order 9344.

146 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 57 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	#17988985	C₂	1	1	yes	maximal, characteristic
2	#17988882	C₂	1	1	yes	maximal, characteristic
3	#17988797	C₂	1	1	yes	maximal, characteristic
4	#17988340	C₂	1	1	yes	maximal, characteristic
5	#17988335	C₂	1	1	yes	maximal, characteristic
6	#17988332	C₂	1	1	yes	maximal, characteristic
7	#446×C₇₃	C₂	1	1	yes	maximal, characteristic
8	C₂×#11924018	—	2	1	no	—
9	#14556591	C₂²	1	1	yes	characteristic
10	#14556591	C₂²	1	1	yes	characteristic
11	#14556524	—	2	1	no	—
12	#14556523	—	2	1	no	—
13	#14556523	—	2	1	no	—
14	C₄⋊#10596831	C₂²	1	1	yes	characteristic
15	C₄⋊#10596831	C₂²	1	1	yes	characteristic
16	#14556515	—	2	1	no	—
17	#14556514	—	2	1	no	—
18	C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
19	C₄⋊C₈×C₇₃	—	2	1	no	—
20	C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
21	#97×C₇₃	—	2	1	no	—
22	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
23	C₂×Dic₁₄₆	—	2	1	no	—
24	C₂×Dic₁₄₆	—	2	1	no	—
25	#11924018	—	4	2	no	—
26	C₂×#10596831	—	2	1	no	—
27	C₂×#10596831	—	2	1	no	—
28	C₄⋊Dic₇₃	—	2	1	no	—
29	C₄⋊Dic₇₃	—	2	1	no	—
30	C₄⋊Dic₇₃	—	2	1	no	—
31	C₄⋊Dic₇₃	—	2	1	no	—
32	C₂×Q₈×C₇₃	D₄	1	1	yes	characteristic
33	C₂×C₈×C₇₃	—	2	1	no	—
34	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
35	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
36	C₄⋊C₄×C₇₃	—	2	1	no	—
37	C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
38	C₄²×C₇₃	—	2	1	no	—
39	C₄²×C₇₃	C₂³	1	1	yes	characteristic
40	Q₈×C₇₃	—	2	1	no	—
41	Q₈×C₇₃	—	2	1	no	—
42	C₂×C₄×C₇₃	—	2	1	no	—
43	C₂×C₄×C₇₃	—	2	1	no	—
44	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
47	C₂×Dic₇₃	—	4	1	no	—
48	C₂×Dic₇₃	—	4	1	no	—
49	Dic₁₄₆	—	4	1	no	—
50	Dic₁₄₆	—	4	1	no	—
51	Dic₁₄₆	—	8	1	no	—
52	C₈×C₇₃	—	2	1	no	—
53	C₈×C₇₃	—	4	1	no	—
54	C₈×C₇₃	Q₁₆	1	2	yes	complemented
55	#10596831	—	4	1	no	—
56	#10596831	—	4	1	no	—
57	C₂²×C₇₃	#121	1	1	yes	characteristic
58	C₄×C₇₃	—	2	1	no	—
59	C₄×C₇₃	—	4	1	no	—
60	C₄×C₇₃	—	4	1	no	—
61	C₄×C₇₃	C₂×Q₁₆	1	1	yes	characteristic
62	C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
63	C₄×C₇₃	#137	1	1	yes	characteristic
64	C₄×C₇₃	#137	1	1	yes	characteristic
65	Dic₇₃	—	8	1	no	—
66	Dic₇₃	—	8	1	no	—
67	C₂×C₇₃	#462	1	1	yes	characteristic
68	C₂×C₇₃	#468	1	1	yes	characteristic
69	C₂×C₇₃	#471	1	1	yes	characteristic
70	#1692	—	73	1	no	maximal, Sylow
71	C₇₃	#1692	1	1	yes	characteristic, complemented, Sylow
72	#498	—	73	1	no	—
73	#477	—	73	1	no	—
74	#462	—	73	1	no	—
75	#446	D₇₃	1	1	yes	characteristic
76	#335	—	73	1	no	—
77	#333	—	73	1	no	—
78	#332	—	73	1	no	—
79	C₂×Q₁₆	—	146	1	no	—
80	C₄⋊Q₈	—	73	1	no	—
81	C₄⋊Q₈	—	73	1	no	—
82	C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic
83	#107	—	146	1	no	—
84	#106	—	146	1	no	—
85	#106	—	146	1	no	—
86	C₄⋊C₈	—	2	1	no	—
87	C₄⋊C₈	—	73	1	no	—
88	C₄⋊C₈	—	73	1	no	—
89	C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
90	#103	—	146	1	no	—
91	#103	—	146	1	no	—
92	#97	—	2	1	no	—
93	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
94	C₂×Q₈	—	146	1	no	—
95	C₂×Q₈	—	146	1	no	—
96	C₂×Q₈	D₂₉₂	1	1	yes	characteristic
97	Q₁₆	—	292	2	no	—
98	C₂×C₈	—	2	1	no	—
99	C₂×C₈	—	146	1	no	—
100	C₂×C₈	—	146	1	no	—
101	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
102	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
103	C₄⋊C₄	—	2	1	no	—
104	C₄⋊C₄	—	146	1	no	—
105	C₄⋊C₄	—	146	1	no	—
106	C₄⋊C₄	—	146	1	no	—
107	C₄⋊C₄	—	146	1	no	—
108	C₄⋊C₄	D₂₉₂	1	1	yes	characteristic
109	C₄²	—	2	1	no	—
110	C₄²	C₂²×D₇₃	1	1	yes	characteristic
111	Q₈	—	2	1	no	—
112	Q₈	—	2	1	no	—
113	Q₈	—	292	1	no	—
114	Q₈	—	292	1	no	—
115	Q₈	—	584	1	no	—
116	C₂×C₄	—	2	1	no	—
117	C₂×C₄	—	2	1	no	—
118	C₂×C₄	—	292	1	no	—
119	C₂×C₄	—	292	1	no	—
120	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
121	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
122	C₂×C₄	#11924028	1	1	yes	characteristic
123	C₈	—	2	1	no	—
124	C₈	—	4	1	no	—
125	C₈	—	292	1	no	—
126	C₈	—	292	1	no	—
127	C₈	#11924018	1	2	yes	complemented
128	C₂²	#14556565	1	1	yes	characteristic
129	C₄	—	2	1	no	—
130	C₄	—	4	1	no	—
131	C₄	—	4	1	no	—
132	C₄	—	584	1	no	—
133	C₄	—	584	1	no	—
134	C₄	C₂×#11924018	1	1	yes	characteristic
135	C₄	#14556619	1	1	yes	characteristic
136	C₄	#14556621	1	1	yes	characteristic
137	C₄	#14556624	1	1	yes	characteristic
138	C₂	#17988797	1	1	yes	characteristic
139	C₂	#17988833	1	1	yes	characteristic
140	C₂	#17988850	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988985

C₂

yes

maximal, characteristic

#17988882

C₂

yes

maximal, characteristic

#17988797

C₂

yes

maximal, characteristic

#17988340

C₂

yes

maximal, characteristic

#17988335

C₂

yes

maximal, characteristic

#17988332

C₂

yes

maximal, characteristic

#446×C₇₃

C₂

yes

maximal, characteristic

C₂×#11924018

—

#14556591

C₂²

yes

characteristic

#14556591

C₂²

yes

—

—

—

C₂²

yes

characteristic

C₄⋊#10596831

C₂²

yes

characteristic

#14556515

—

#14556514

—

C₄×Q₈×C₇₃

C₂²

yes

characteristic

C₄⋊C₈×C₇₃

—

C₄⋊C₈×C₇₃

C₂²

yes

characteristic

#97×C₇₃

—

C₄×C₈×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

#11924018

—

C₂×#10596831

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂×Q₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

D₄

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

D₄

yes

characteristic

C₄²×C₇₃

—

C₄²×C₇₃

C₂³

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

#41

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

—

C₈×C₇₃

—

C₈×C₇₃

Q₁₆

yes

complemented

#10596831

—

#10596831

—

C₂²×C₇₃

#121

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₂×Q₁₆

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

—

—

—

D₇₃

yes

—

—

—

C₂×Q₁₆

—

146

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄×Q₈

C₂×D₇₃

yes

characteristic

#107

—

146

—

#106

—

146

—

#106

—

146

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₇₃

yes

characteristic

#103

—

146

—

#103

—

146

—

#97

—

C₄×C₈

C₂×D₇₃

yes

characteristic

C₂×Q₈

—

146

—

C₂×Q₈

—

146

—

C₂×Q₈

D₂₉₂

yes

characteristic

Q₁₆

—

292

—

C₂×C₈

—

C₂×C₈

—

146

—

100

C₂×C₈

—

146

—

101

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

102

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

103

C₄⋊C₄

—

104

C₄⋊C₄

—

146

—

105

C₄⋊C₄

—

146

—

106

C₄⋊C₄

—

146

—

107

C₄⋊C₄

—

146

—

108

C₄⋊C₄

D₂₉₂

yes

characteristic

109

C₄²

—

110

C₄²

C₂²×D₇₃

yes

characteristic

111

Q₈

—

112

Q₈

—

113

Q₈

—

292

—

114

Q₈

—

292

—

115

Q₈

—

584

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

292

—

119

C₂×C₄

—

292

—

120

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

121

C₂×C₄

C₂×D₂₉₂

yes

characteristic

122

C₂×C₄

#11924028

yes

characteristic

123

C₈

—

124

C₈

—

125

C₈

—

292

—

126

C₈

—

292

—

127

C₈

#11924018

yes

complemented

128

C₂²

#14556565

yes

characteristic

129

C₄

—

130

C₄

—

131

C₄

—

132

C₄

—

584

—

133

C₄

—

584

—

134

C₄

C₂×#11924018

yes

characteristic

135

C₄

#14556619

yes

characteristic

136

C₄

#14556621

yes

characteristic

137

C₄

#14556624

yes

characteristic

138

C₂

#17988797

yes

characteristic

139

C₂

#17988833

yes

characteristic

140

C₂

#17988850

yes

characteristic

	subgroup	G/H
center	C₂²	#14556565
commutator	C₄²×C₇₃	C₂³
Frattini	C₄²	C₂²×D₇₃
Fitting	#446×C₇₃	C₂
socle	C₂²×C₇₃	#121
hypercenter	#446	D₇₃
hypocenter	C₇₃	#1692
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #446

subgroup

G/H

center

C₂²

#14556565

commutator

C₄²×C₇₃

C₂³

Frattini

C₄²

C₂²×D₇₃

Fitting

#446×C₇₃

C₂

C₂²×C₇₃

D₇₃

C₇₃

G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #446

N	H ≅ G/N	type
54. C₈×C₇₃	Q₁₆	semidirect
71. C₇₃	#1692	semidirect
127. C₈	#11924018	semidirect

H ≅ G/N

type

54. C₈×C₇₃

Q₁₆

semidirect

71. C₇₃

#1692

semidirect

127. C₈

#11924018

semidirect

Subgroups — #22609437

Conjugacy classes of subgroups

Complements