Group #22609333 — subgroups

Subgroups — #22609333

Order 9344.

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

normal subgroups only

This group has 144 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	#17988990	C₂	1	1	yes	maximal, characteristic
2	#17988882	C₂	1	1	yes	maximal, characteristic
3	Q₈×#10596831	C₂	1	1	yes	maximal, characteristic
4	#17988339	C₂	1	1	yes	maximal, characteristic
5	#17988336	C₂	1	1	yes	maximal, characteristic
6	#17988335	C₂	1	1	yes	maximal, characteristic
7	#477×C₇₃	C₂	1	1	yes	maximal, characteristic
8	#14556591	C₂²	1	1	yes	characteristic
9	#14556524	—	2	1	no	—
10	#14556524	—	2	1	no	—
11	#14556524	—	2	1	no	—
12	C₄⋊#10596831	—	2	1	no	—
13	C₄⋊#10596831	C₂²	1	1	yes	characteristic
14	C₄⋊#10596831	C₂²	1	1	yes	characteristic
15	#14556515	—	2	1	no	—
16	C₄×#10596831	—	2	1	no	—
17	C₄×#10596831	C₂²	1	1	yes	characteristic
18	C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
19	C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
20	#107×C₇₃	—	2	1	no	—
21	C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
22	#103×C₇₃	—	2	1	no	—
23	C₂×Dic₁₄₆	—	2	1	no	—
24	C₂×#10596831	—	2	1	no	—
25	C₂×#10596831	—	2	1	no	—
26	C₂×#10596831	D₄	1	1	yes	characteristic
27	C₂×#10596831	D₄	1	1	yes	characteristic
28	C₄⋊Dic₇₃	—	2	1	no	—
29	C₄⋊Dic₇₃	—	2	1	no	—
30	C₂×Q₈×C₇₃	—	2	1	no	—
31	C₂×Q₈×C₇₃	D₄	1	1	yes	characteristic
32	C₂×C₈×C₇₃	—	2	1	no	—
33	C₄⋊C₄×C₇₃	—	2	1	no	—
34	C₄⋊C₄×C₇₃	—	2	1	no	—
35	C₄⋊C₄×C₇₃	—	2	1	no	—
36	C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
37	C₄²×C₇₃	—	2	1	no	—
38	C₄²×C₇₃	C₂³	1	1	yes	characteristic
39	Q₈×C₇₃	—	2	1	no	—
40	Q₈×C₇₃	—	8	1	no	—
41	Q₈×C₇₃	Q₁₆	1	2	yes	—
42	C₂×C₄×C₇₃	—	2	1	no	—
43	C₂×C₄×C₇₃	—	2	1	no	—
44	C₂×C₄×C₇₃	—	4	1	no	—
45	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
48	C₂×Dic₇₃	—	4	1	no	—
49	Dic₁₄₆	—	8	1	no	—
50	C₈×C₇₃	—	4	1	no	—
51	#10596831	—	2	1	no	—
52	#10596831	—	4	1	no	—
53	#10596831	—	4	1	no	—
54	#10596831	Q₁₆	1	2	yes	—
55	C₂²×C₇₃	#121	1	1	yes	characteristic
56	C₄×C₇₃	—	2	2	no	—
57	C₄×C₇₃	—	2	1	no	—
58	C₄×C₇₃	—	4	1	no	—
59	C₄×C₇₃	—	8	1	no	—
60	C₄×C₇₃	C₂×Q₁₆	1	1	yes	characteristic
61	C₄×C₇₃	C₂×Q₁₆	1	1	yes	characteristic
62	C₄×C₇₃	#135	1	1	yes	characteristic
63	C₄×C₇₃	#137	1	1	yes	characteristic
64	Dic₇₃	—	8	1	no	—
65	C₂×C₇₃	#462	1	1	yes	characteristic
66	C₂×C₇₃	#467	1	1	yes	characteristic
67	C₂×C₇₃	#472	1	1	yes	characteristic
68	#1676	—	73	1	no	maximal, Sylow
69	C₇₃	#1676	1	1	yes	characteristic, complemented, Sylow
70	#500	—	73	1	no	—
71	#477	—	73	1	no	—
72	#477	D₇₃	1	1	yes	characteristic
73	C₈×Q₈	—	73	1	no	—
74	#335	—	73	1	no	—
75	#333	—	73	1	no	—
76	#333	—	73	1	no	—
77	C₄⋊Q₈	—	73	1	no	—
78	C₄⋊Q₈	C₂×D₇₃	1	1	yes	characteristic
79	C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic
80	#107	—	2	1	no	—
81	#107	—	146	1	no	—
82	#107	—	146	1	no	—
83	#107	—	146	1	no	—
84	C₄⋊C₈	—	73	1	no	—
85	C₄⋊C₈	—	73	1	no	—
86	C₄⋊C₈	—	146	1	no	—
87	C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
88	#103	—	2	1	no	—
89	#103	—	146	1	no	—
90	C₄×C₈	—	73	1	no	—
91	C₄×C₈	—	146	1	no	—
92	C₂×Q₈	—	2	1	no	—
93	C₂×Q₈	—	146	1	no	—
94	C₂×Q₈	C₂²⋊D₇₃	1	1	yes	characteristic
95	C₂×C₈	—	2	1	no	—
96	C₂×C₈	—	73	1	no	—
97	C₂×C₈	—	73	1	no	—
98	C₂×C₈	—	146	1	no	—
99	C₂×C₈	—	146	1	no	—
100	C₄⋊C₄	—	2	1	no	—
101	C₄⋊C₄	—	2	1	no	—
102	C₄⋊C₄	—	2	1	no	—
103	C₄⋊C₄	—	146	1	no	—
104	C₄⋊C₄	—	146	1	no	—
105	C₄⋊C₄	C₂²⋊D₇₃	1	1	yes	characteristic
106	C₄²	—	2	1	no	—
107	C₄²	C₂²×D₇₃	1	1	yes	characteristic
108	Q₈	—	2	1	no	—
109	Q₈	—	8	1	no	—
110	Q₈	—	584	1	no	—
111	Q₈	#11924018	1	2	yes	—
112	C₂×C₄	—	2	1	no	—
113	C₂×C₄	—	2	1	no	—
114	C₂×C₄	—	4	1	no	—
115	C₂×C₄	—	292	1	no	—
116	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
117	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
118	C₂×C₄	#11924027	1	1	yes	characteristic
119	C₈	—	4	1	no	—
120	C₈	—	292	1	no	—
121	C₈	—	292	1	no	—
122	C₈	—	73	2	no	—
123	C₈	—	146	1	no	—
124	C₂²	#14556563	1	1	yes	characteristic
125	C₄	—	2	2	no	—
126	C₄	—	2	1	no	—
127	C₄	—	4	1	no	—
128	C₄	—	8	1	no	—
129	C₄	—	584	1	no	—
130	C₄	Q₁₆×D₇₃	1	1	yes	characteristic
131	C₄	C₂×#11924018	1	1	yes	characteristic
132	C₄	#14556611	1	1	yes	characteristic
133	C₄	#14556623	1	1	yes	characteristic
134	C₂	#17988795	1	1	yes	characteristic
135	C₂	#17988826	1	1	yes	characteristic
136	C₂	#17988855	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988990

C₂

yes

maximal, characteristic

#17988882

C₂

yes

maximal, characteristic

Q₈×#10596831

C₂

yes

maximal, characteristic

#17988339

C₂

yes

maximal, characteristic

#17988336

C₂

yes

maximal, characteristic

#17988335

C₂

yes

maximal, characteristic

#477×C₇₃

C₂

yes

maximal, characteristic

#14556591

C₂²

yes

—

—

—

—

C₂²

yes

characteristic

C₄⋊#10596831

C₂²

yes

—

—

C₂²

yes

characteristic

C₄⋊Q₈×C₇₃

C₂²

yes

characteristic

C₄×Q₈×C₇₃

C₂²

yes

characteristic

#107×C₇₃

—

C₄⋊C₈×C₇₃

C₂²

yes

characteristic

#103×C₇₃

—

C₂×Dic₁₄₆

—

C₂×#10596831

—

C₂×#10596831

—

C₂×#10596831

D₄

yes

characteristic

C₂×#10596831

D₄

yes

characteristic

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

D₄

yes

characteristic

C₄²×C₇₃

—

C₄²×C₇₃

C₂³

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

Q₁₆

yes

—

C₂×C₄×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

—

Dic₁₄₆

—

C₈×C₇₃

—

—

—

—

Q₁₆

yes

—

C₂²×C₇₃

#121

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₂×Q₁₆

yes

characteristic

C₄×C₇₃

C₂×Q₁₆

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#500

—

#477

—

#477

D₇₃

yes

characteristic

C₈×Q₈

—

#335

—

#333

—

#333

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₇₃

yes

characteristic

C₄×Q₈

C₂×D₇₃

yes

characteristic

#107

—

#107

—

146

—

#107

—

146

—

#107

—

146

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

146

—

C₄⋊C₈

C₂×D₇₃

yes

characteristic

#103

—

#103

—

146

—

C₄×C₈

—

C₄×C₈

—

146

—

C₂×Q₈

—

C₂×Q₈

—

146

—

C₂×Q₈

C₂²⋊D₇₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

146

—

104

C₄⋊C₄

—

146

—

105

C₄⋊C₄

C₂²⋊D₇₃

yes

characteristic

106

C₄²

—

107

C₄²

C₂²×D₇₃

yes

characteristic

108

Q₈

—

109

Q₈

—

110

Q₈

—

584

—

111

Q₈

#11924018

yes

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

292

—

116

C₂×C₄

D₄×D₇₃

yes

characteristic

117

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

118

C₂×C₄

#11924027

yes

characteristic

119

C₈

—

120

C₈

—

292

—

121

C₈

—

292

—

122

C₈

—

123

C₈

—

146

—

124

C₂²

#14556563

yes

characteristic

125

C₄

—

126

C₄

—

127

C₄

—

128

C₄

—

129

C₄

—

584

—

130

C₄

Q₁₆×D₇₃

yes

characteristic

131

C₄

C₂×#11924018

yes

characteristic

132

C₄

#14556611

yes

characteristic

133

C₄

#14556623

yes

characteristic

134

C₂

#17988795

yes

characteristic

135

C₂

#17988826

yes

characteristic

136

C₂

#17988855

yes

characteristic

	subgroup	G/H
center	C₂²	#14556563
commutator	C₄²×C₇₃	C₂³
Frattini	C₄²	C₂²×D₇₃
Fitting	#477×C₇₃	C₂
socle	C₂²×C₇₃	#121
hypercenter	#477	D₇₃
hypocenter	C₇₃	#1676
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #477

subgroup

G/H

center

C₂²

#14556563

commutator

C₄²×C₇₃

C₂³

Frattini

C₄²

C₂²×D₇₃

Fitting

#477×C₇₃

C₂

C₂²×C₇₃

D₇₃

C₇₃

G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #477

N	H ≅ G/N	type
69. C₇₃	#1676	semidirect

H ≅ G/N

type

69. C₇₃

#1676

semidirect

Subgroups — #22609333

Conjugacy classes of subgroups

Complements