Group #22609359 — subgroups

Subgroups — #22609359

Order 9344.

150 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 55 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	#17988937	C₂	1	1	yes	maximal, characteristic
2	#17988797	C₂	1	1	yes	maximal, characteristic
3	Q₈×#10596831	C₂	1	1	yes	maximal, characteristic
4	#17988337	C₂	1	1	yes	maximal, characteristic
5	#17988334	C₂	1	1	yes	maximal, characteristic
6	#17988333	C₂	1	1	yes	maximal, characteristic
7	#475×C₇₃	C₂	1	1	yes	maximal, characteristic
8	C₂×#11924018	—	2	1	no	—
9	#14556591	C₂²	1	1	yes	characteristic
10	C₄⋊#10596831	—	2	1	no	—
11	C₄⋊#10596831	C₂²	1	1	yes	characteristic
12	C₄⋊#10596831	C₂²	1	1	yes	characteristic
13	#14556515	—	2	1	no	—
14	#14556515	—	2	1	no	—
15	#14556514	—	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	#106×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	#11924018	—	4	2	no	—
25	C₂×#10596831	—	2	1	no	—
26	C₂×#10596831	—	2	1	no	—
27	C₂×#10596831	D₄	1	1	yes	characteristic
28	C₂×#10596831	D₄	1	1	yes	characteristic
29	C₄⋊Dic₇₃	—	2	1	no	—
30	C₄⋊Dic₇₃	—	2	1	no	—
31	C₂×Q₈×C₇₃	—	2	1	no	—
32	C₂×Q₈×C₇₃	D₄	1	1	yes	characteristic
33	C₂×C₈×C₇₃	—	2	1	no	—
34	C₄⋊C₄×C₇₃	—	2	1	no	—
35	C₄⋊C₄×C₇₃	—	2	1	no	—
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	—	4	1	no	—
42	Q₈×C₇₃	—	4	1	no	—
43	Q₈×C₇₃	SD₁₆	1	2	yes	—
44	C₂×C₄×C₇₃	—	2	1	no	—
45	C₂×C₄×C₇₃	—	2	1	no	—
46	C₂×C₄×C₇₃	—	4	1	no	—
47	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
50	C₂×Dic₇₃	—	4	1	no	—
51	Dic₁₄₆	—	4	1	no	—
52	Dic₁₄₆	—	4	1	no	—
53	C₈×C₇₃	—	4	1	no	—
54	#10596831	—	2	1	no	—
55	#10596831	—	2	1	no	—
56	#10596831	—	4	1	no	—
57	#10596831	—	4	1	no	—
58	C₂²×C₇₃	#121	1	1	yes	characteristic
59	C₄×C₇₃	—	2	2	no	—
60	C₄×C₇₃	—	2	1	no	—
61	C₄×C₇₃	—	4	1	no	—
62	C₄×C₇₃	—	8	1	no	—
63	C₄×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
64	C₄×C₇₃	#135	1	1	yes	characteristic
65	C₄×C₇₃	#135	1	1	yes	characteristic
66	C₄×C₇₃	#137	1	1	yes	characteristic
67	Dic₇₃	—	8	1	no	—
68	C₂×C₇₃	#464	1	1	yes	characteristic
69	C₂×C₇₃	#465	1	1	yes	characteristic
70	C₂×C₇₃	#473	1	1	yes	characteristic
71	#1680	—	73	1	no	maximal, Sylow
72	C₇₃	#1680	1	1	yes	characteristic, complemented, Sylow
73	#487	—	73	1	no	—
74	#475	D₇₃	1	1	yes	characteristic
75	#462	—	73	1	no	—
76	C₈×Q₈	—	73	1	no	—
77	#334	—	73	1	no	—
78	#332	—	73	1	no	—
79	#332	—	73	1	no	—
80	C₂×Q₁₆	—	146	1	no	—
81	C₄⋊Q₈	—	73	1	no	—
82	C₄⋊Q₈	C₂×D₇₃	1	1	yes	characteristic
83	C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic
84	#106	—	2	1	no	—
85	C₄⋊C₈	—	73	1	no	—
86	C₄⋊C₈	—	73	1	no	—
87	C₄⋊C₈	—	146	1	no	—
88	C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
89	#103	—	2	1	no	—
90	#103	—	146	1	no	—
91	#103	—	146	1	no	—
92	#103	—	146	1	no	—
93	C₄×C₈	—	73	1	no	—
94	C₄×C₈	—	146	1	no	—
95	C₂×Q₈	—	2	1	no	—
96	C₂×Q₈	—	146	1	no	—
97	C₂×Q₈	C₂²⋊D₇₃	1	1	yes	characteristic
98	Q₁₆	—	292	2	no	—
99	C₂×C₈	—	2	1	no	—
100	C₂×C₈	—	73	1	no	—
101	C₂×C₈	—	73	1	no	—
102	C₂×C₈	—	146	1	no	—
103	C₂×C₈	—	146	1	no	—
104	C₄⋊C₄	—	2	1	no	—
105	C₄⋊C₄	—	2	1	no	—
106	C₄⋊C₄	—	2	1	no	—
107	C₄⋊C₄	—	146	1	no	—
108	C₄⋊C₄	—	146	1	no	—
109	C₄⋊C₄	C₂²⋊D₇₃	1	1	yes	characteristic
110	C₄²	—	2	1	no	—
111	C₄²	C₂²×D₇₃	1	1	yes	characteristic
112	Q₈	—	2	1	no	—
113	Q₈	—	4	1	no	—
114	Q₈	—	4	1	no	—
115	Q₈	—	292	1	no	—
116	Q₈	—	292	1	no	—
117	Q₈	#11924015	1	2	yes	—
118	C₂×C₄	—	2	1	no	—
119	C₂×C₄	—	2	1	no	—
120	C₂×C₄	—	4	1	no	—
121	C₂×C₄	—	292	1	no	—
122	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
123	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
124	C₂×C₄	#11924027	1	1	yes	characteristic
125	C₈	—	4	1	no	—
126	C₈	—	292	1	no	—
127	C₈	—	292	1	no	—
128	C₈	—	146	1	no	—
129	C₈	—	146	1	no	—
130	C₂²	#14556563	1	1	yes	characteristic
131	C₄	—	2	2	no	—
132	C₄	—	2	1	no	—
133	C₄	—	4	1	no	—
134	C₄	—	8	1	no	—
135	C₄	—	584	1	no	—
136	C₄	C₂×#11924015	1	1	yes	characteristic
137	C₄	#14556611	1	1	yes	characteristic
138	C₄	#14556612	1	1	yes	characteristic
139	C₄	#14556620	1	1	yes	characteristic
140	C₂	#17988807	1	1	yes	characteristic
141	C₂	#17988818	1	1	yes	characteristic
142	C₂	#17988860	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988937

C₂

yes

maximal, characteristic

#17988797

C₂

yes

maximal, characteristic

Q₈×#10596831

C₂

yes

maximal, characteristic

#17988337

C₂

yes

maximal, characteristic

#17988334

C₂

yes

maximal, characteristic

#17988333

C₂

yes

maximal, characteristic

#475×C₇₃

C₂

yes

maximal, characteristic

C₂×#11924018

—

#14556591

C₂²

yes

characteristic

C₄⋊#10596831

—

C₄⋊#10596831

C₂²

yes

characteristic

C₄⋊#10596831

C₂²

yes

—

—

—

—

C₂²

yes

characteristic

C₄⋊Q₈×C₇₃

C₂²

yes

characteristic

C₄×Q₈×C₇₃

C₂²

yes

characteristic

#106×C₇₃

—

C₄⋊C₈×C₇₃

C₂²

yes

characteristic

#103×C₇₃

—

C₂×Dic₁₄₆

—

—

—

—

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

—

Q₈×C₇₃

SD₁₆

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

—

Dic₁₄₆

—

C₈×C₇₃

—

—

—

—

—

C₂²×C₇₃

#121

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₂×SD₁₆

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#487

—

#475

D₇₃

yes

characteristic

#462

—

C₈×Q₈

—

#334

—

#332

—

#332

—

C₂×Q₁₆

—

146

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₇₃

yes

characteristic

C₄×Q₈

C₂×D₇₃

yes

characteristic

#106

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

146

—

C₄⋊C₈

C₂×D₇₃

yes

characteristic

#103

—

#103

—

146

—

#103

—

146

—

#103

—

146

—

C₄×C₈

—

C₄×C₈

—

146

—

C₂×Q₈

—

C₂×Q₈

—

146

—

C₂×Q₈

C₂²⋊D₇₃

yes

characteristic

Q₁₆

—

292

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

146

—

103

C₂×C₈

—

146

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

146

—

108

C₄⋊C₄

—

146

—

109

C₄⋊C₄

C₂²⋊D₇₃

yes

characteristic

110

C₄²

—

111

C₄²

C₂²×D₇₃

yes

characteristic

112

Q₈

—

113

Q₈

—

114

Q₈

—

115

Q₈

—

292

—

116

Q₈

—

292

—

117

Q₈

#11924015

yes

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

292

—

122

C₂×C₄

D₄×D₇₃

yes

characteristic

123

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

124

C₂×C₄

#11924027

yes

characteristic

125

C₈

—

126

C₈

—

292

—

127

C₈

—

292

—

128

C₈

—

146

—

129

C₈

—

146

—

130

C₂²

#14556563

yes

characteristic

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

—

584

—

136

C₄

C₂×#11924015

yes

characteristic

137

C₄

#14556611

yes

characteristic

138

C₄

#14556612

yes

characteristic

139

C₄

#14556620

yes

characteristic

140

C₂

#17988807

yes

characteristic

141

C₂

#17988818

yes

characteristic

142

C₂

#17988860

yes

characteristic

	subgroup	G/H
center	C₂²	#14556563
commutator	C₄²×C₇₃	C₂³
Frattini	C₄²	C₂²×D₇₃
Fitting	#475×C₇₃	C₂
socle	C₂²×C₇₃	#121
hypercenter	#475	D₇₃
hypocenter	C₇₃	#1680
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #475

subgroup

G/H

center

C₂²

#14556563

commutator

C₄²×C₇₃

C₂³

Frattini

C₄²

C₂²×D₇₃

Fitting

#475×C₇₃

C₂

C₂²×C₇₃

D₇₃

C₇₃

G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #475

N	H ≅ G/N	type
72. C₇₃	#1680	semidirect

H ≅ G/N

type

72. C₇₃

#1680

semidirect

Subgroups — #22609359

Conjugacy classes of subgroups

Complements