Group #22609511 — subgroups

Subgroups — #22609511

Order 9344.

140 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 51 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	#17988882	C₂	1	1	yes	maximal, characteristic
3	#17988718	C₂	1	1	yes	maximal, characteristic
4	#17988337	C₂	1	1	yes	maximal, characteristic
5	#17988335	C₂	1	1	yes	maximal, characteristic
6	#17988333	C₂	1	1	yes	maximal, characteristic
7	#475×C₇₃	C₂	1	1	yes	maximal, characteristic
8	#14556591	C₂²	1	1	yes	characteristic
9	#14556524	—	2	1	no	—
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	#14556515	—	2	1	no	—
16	#14556502	—	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	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	—	2	1	no	—
41	Q₈×C₇₃	—	4	1	no	—
42	Q₈×C₇₃	—	4	1	no	—
43	C₂×C₄×C₇₃	—	2	1	no	—
44	C₂×C₄×C₇₃	—	2	1	no	—
45	C₂×C₄×C₇₃	—	4	1	no	—
46	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
49	C₂×Dic₇₃	—	4	1	no	—
50	Dic₁₄₆	—	8	1	no	—
51	C₈×C₇₃	—	4	1	no	—
52	#10596831	—	2	1	no	—
53	#10596831	—	2	1	no	—
54	#10596831	—	4	1	no	—
55	#10596831	—	4	1	no	—
56	C₂²×C₇₃	#121	1	1	yes	characteristic
57	C₄×C₇₃	—	2	1	no	—
58	C₄×C₇₃	—	4	1	no	—
59	C₄×C₇₃	—	4	1	no	—
60	C₄×C₇₃	—	8	1	no	—
61	C₄×C₇₃	#135	1	1	yes	characteristic
62	C₄×C₇₃	#137	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	C₂×C₇₃	#464	1	1	yes	characteristic
67	C₂×C₇₃	#470	1	1	yes	characteristic
68	C₂×C₇₃	#471	1	1	yes	characteristic
69	#1704	—	73	1	no	maximal, Sylow
70	C₇₃	#1704	1	1	yes	characteristic, complemented, Sylow
71	#487	—	73	1	no	—
72	#477	—	73	1	no	—
73	#475	D₇₃	1	1	yes	characteristic
74	#446	—	73	1	no	—
75	#334	—	73	1	no	—
76	#333	—	73	1	no	—
77	#332	—	73	1	no	—
78	C₄⋊Q₈	—	73	1	no	—
79	C₄⋊Q₈	C₂×D₇₃	1	1	yes	characteristic
80	C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic
81	#107	—	146	1	no	—
82	#106	—	2	1	no	—
83	C₄⋊C₈	—	73	1	no	—
84	C₄⋊C₈	—	73	1	no	—
85	C₄⋊C₈	—	146	1	no	—
86	C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
87	#103	—	2	1	no	—
88	#103	—	146	1	no	—
89	#103	—	146	1	no	—
90	#103	—	146	1	no	—
91	#97	—	146	1	no	—
92	C₄×C₈	—	73	1	no	—
93	C₂×Q₈	—	2	1	no	—
94	C₂×Q₈	—	146	1	no	—
95	C₂×Q₈	C₂²⋊D₇₃	1	1	yes	characteristic
96	C₂×C₈	—	2	1	no	—
97	C₂×C₈	—	73	1	no	—
98	C₂×C₈	—	73	1	no	—
99	C₂×C₈	—	146	1	no	—
100	C₂×C₈	—	146	1	no	—
101	C₄⋊C₄	—	2	1	no	—
102	C₄⋊C₄	—	2	1	no	—
103	C₄⋊C₄	—	2	1	no	—
104	C₄⋊C₄	—	146	1	no	—
105	C₄⋊C₄	—	146	1	no	—
106	C₄⋊C₄	C₂²⋊D₇₃	1	1	yes	characteristic
107	C₄²	—	2	1	no	—
108	C₄²	C₂²×D₇₃	1	1	yes	characteristic
109	Q₈	—	2	1	no	—
110	Q₈	—	2	1	no	—
111	Q₈	—	4	1	no	—
112	Q₈	—	4	1	no	—
113	Q₈	—	584	1	no	—
114	C₂×C₄	—	2	1	no	—
115	C₂×C₄	—	2	1	no	—
116	C₂×C₄	—	4	1	no	—
117	C₂×C₄	—	292	1	no	—
118	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
119	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
120	C₂×C₄	#11924027	1	1	yes	characteristic
121	C₈	—	4	1	no	—
122	C₈	—	292	1	no	—
123	C₈	—	292	1	no	—
124	C₈	—	146	1	no	—
125	C₈	—	146	1	no	—
126	C₂²	#14556563	1	1	yes	characteristic
127	C₄	—	2	1	no	—
128	C₄	—	4	1	no	—
129	C₄	—	4	1	no	—
130	C₄	—	8	1	no	—
131	C₄	—	584	1	no	—
132	C₄	#14556612	1	1	yes	characteristic
133	C₄	#14556620	1	1	yes	characteristic
134	C₄	#14556621	1	1	yes	characteristic
135	C₄	#14556622	1	1	yes	characteristic
136	C₂	#17988807	1	1	yes	characteristic
137	C₂	#17988843	1	1	yes	characteristic
138	C₂	#17988852	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988937

C₂

yes

maximal, characteristic

#17988882

C₂

yes

maximal, characteristic

#17988718

C₂

yes

maximal, characteristic

#17988337

C₂

yes

maximal, characteristic

#17988335

C₂

yes

maximal, characteristic

#17988333

C₂

yes

maximal, characteristic

#475×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

#106×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

—

Q₈×C₇₃

—

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

—

—

—

—

—

C₂²×C₇₃

#121

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

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

—

#477

—

#475

D₇₃

yes

—

—

—

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₇₃

yes

characteristic

C₄×Q₈

C₂×D₇₃

yes

characteristic

#107

—

146

—

#106

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

146

—

C₄⋊C₈

C₂×D₇₃

yes

characteristic

#103

—

#103

—

146

—

#103

—

146

—

#103

—

146

—

#97

—

146

—

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

146

—

C₂×Q₈

C₂²⋊D₇₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

100

C₂×C₈

—

146

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

146

—

105

C₄⋊C₄

—

146

—

106

C₄⋊C₄

C₂²⋊D₇₃

yes

characteristic

107

C₄²

—

108

C₄²

C₂²×D₇₃

yes

characteristic

109

Q₈

—

110

Q₈

—

111

Q₈

—

112

Q₈

—

113

Q₈

—

584

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

292

—

118

C₂×C₄

D₄×D₇₃

yes

characteristic

119

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

120

C₂×C₄

#11924027

yes

characteristic

121

C₈

—

122

C₈

—

292

—

123

C₈

—

292

—

124

C₈

—

146

—

125

C₈

—

146

—

126

C₂²

#14556563

yes

characteristic

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

—

584

—

132

C₄

#14556612

yes

characteristic

133

C₄

#14556620

yes

characteristic

134

C₄

#14556621

yes

characteristic

135

C₄

#14556622

yes

characteristic

136

C₂

#17988807

yes

characteristic

137

C₂

#17988843

yes

characteristic

138

C₂

#17988852

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	#1704
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
70. C₇₃	#1704	semidirect

H ≅ G/N

type

70. C₇₃

#1704

semidirect

Subgroups — #22609511

Conjugacy classes of subgroups

Complements