Group #22625576 — subgroups

Subgroups — #22625576

Order 9344.

148 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 54 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	#17989638	C₂	1	1	yes	maximal, characteristic
2	#17989637	C₂	1	1	yes	maximal, characteristic
3	#17989449	C₂	1	1	yes	maximal, characteristic
4	#17989437	C₂	1	1	yes	maximal, characteristic
5	Q₈⋊#10596833	C₂	1	1	yes	maximal, characteristic
6	#17989428	C₂	1	1	yes	maximal, characteristic
7	#17988679	C₂	1	1	yes	maximal, characteristic
8	#14556658	—	2	1	no	—
9	C₄⋊#10596833	—	2	1	no	—
10	C₄⋊#10596833	C₂²	1	1	yes	characteristic
11	C₄⋊#10596833	C₂²	1	1	yes	characteristic
12	#14556646	—	2	1	no	—
13	#14556646	—	2	1	no	—
14	C₄×#10596833	C₂²	1	1	yes	characteristic
15	C₄×#10596833	C₂²	1	1	yes	characteristic
16	C₂×#11924018	C₄	1	1	yes	characteristic
17	Q₈×Dic₇₃	C₂²	1	1	yes	characteristic
18	#14556556	C₂²	1	1	yes	characteristic
19	#14556524	C₄	1	1	yes	characteristic
20	#14556516	C₄	1	1	yes	characteristic
21	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
22	#103×C₇₃	C₄	1	1	yes	characteristic
23	C₂×#10596833	—	2	1	no	—
24	C₂×#10596833	—	2	1	no	—
25	C₂×#10596833	—	2	1	no	—
26	C₂×#10596833	D₄	1	1	yes	characteristic
27	C₂×#10596833	D₄	1	1	yes	characteristic
28	C₂×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
29	#11924018	—	2	2	no	—
30	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
31	C₄⋊Dic₇₃	—	2	1	no	—
32	C₄⋊Dic₇₃	C₂×C₄	1	1	yes	characteristic
33	#11924007	—	2	1	no	—
34	C₄×Dic₇₃	—	2	1	no	—
35	C₄×Dic₇₃	—	2	1	no	—
36	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
37	C₂×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
38	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
39	C₄⋊C₄×C₇₃	C₂×C₄	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	C₂²×C₄	1	1	yes	characteristic
45	C₂×Dic₇₃	—	2	1	no	—
46	C₂×Dic₇₃	—	2	1	no	—
47	C₂×Dic₇₃	C₂×D₄	1	1	yes	characteristic
48	C₂×Dic₇₃	#41	1	1	yes	characteristic
49	Dic₁₄₆	—	2	1	no	—
50	Dic₁₄₆	—	2	1	no	—
51	#10596833	—	2	1	no	—
52	#10596833	—	2	1	no	—
53	#10596833	—	4	1	no	—
54	#10596833	—	4	1	no	—
55	#10596833	—	4	1	no	—
56	C₈×C₇₃	—	2	1	no	—
57	#10596831	M₁₆	1	2	yes	—
58	C₂²×C₇₃	C₄×D₄	1	1	yes	characteristic
59	C₄×C₇₃	—	4	1	no	—
60	C₄×C₇₃	—	4	1	no	—
61	C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
62	C₄×C₇₃	#131	1	1	yes	characteristic
63	Dic₇₃	—	2	1	no	—
64	Dic₇₃	—	4	1	no	—
65	Dic₇₃	—	4	1	no	—
66	Dic₇₃	#137	1	1	yes	characteristic
67	Dic₇₃	#137	1	1	yes	characteristic
68	C₂×C₇₃	#436	1	1	yes	characteristic
69	C₂×C₇₃	#441	1	1	yes	characteristic
70	C₂×C₇₃	#444	1	1	yes	characteristic
71	#1593	—	73	1	no	maximal, Sylow
72	C₇₃	#1593	1	1	yes	characteristic, complemented, Sylow
73	#446	—	73	1	no	—
74	#446	—	73	1	no	—
75	C₄×Q₁₆	—	73	1	no	—
76	#334	—	73	1	no	—
77	Q₈⋊C₈	—	73	1	no	—
78	Q₈⋊C₈	—	73	1	no	—
79	#322	—	73	1	no	—
80	C₂×Q₁₆	—	73	1	no	—
81	C₄×Q₈	—	73	1	no	—
82	C₄×Q₈	—	73	1	no	—
83	#107	—	73	1	no	—
84	C₄⋊C₈	—	73	1	no	—
85	C₄⋊C₈	—	73	1	no	—
86	C₄⋊C₈	—	146	1	no	—
87	C₄⋊C₈	—	146	1	no	—
88	#103	—	73	1	no	—
89	#103	#64408	1	1	yes	characteristic
90	#97	—	146	1	no	—
91	#97	—	146	1	no	—
92	C₄×C₈	—	73	1	no	—
93	C₄×C₈	—	73	1	no	—
94	C₄×C₈	—	73	1	no	—
95	C₂×Q₈	—	73	1	no	—
96	C₂×Q₈	C₂×#64408	1	1	yes	characteristic
97	Q₁₆	—	146	2	no	—
98	C₂×C₈	—	73	1	no	—
99	C₂×C₈	—	73	1	no	—
100	C₂×C₈	—	73	1	no	—
101	C₂×C₈	—	146	1	no	—
102	C₂×C₈	—	146	1	no	—
103	C₂×C₈	—	146	1	no	—
104	C₂×C₈	C₂×#64408	1	1	yes	characteristic
105	C₄⋊C₄	—	73	1	no	—
106	C₄⋊C₄	—	146	1	no	—
107	C₄⋊C₄	—	146	1	no	—
108	C₄⋊C₄	C₂×#64408	1	1	yes	characteristic
109	C₄²	—	73	1	no	—
110	C₄²	—	146	1	no	—
111	C₄²	—	146	1	no	—
112	Q₈	—	2	1	no	—
113	Q₈	—	2	1	no	—
114	Q₈	—	146	1	no	—
115	Q₈	—	146	1	no	—
116	C₂×C₄	—	2	1	no	—
117	C₂×C₄	—	2	1	no	—
118	C₂×C₄	—	73	1	no	—
119	C₂×C₄	—	73	1	no	—
120	C₂×C₄	—	146	1	no	—
121	C₂×C₄	—	146	1	no	—
122	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
123	C₈	—	2	1	no	—
124	C₈	—	292	1	no	—
125	C₈	—	292	1	no	—
126	C₈	—	292	1	no	—
127	C₈	—	73	2	no	—
128	C₈	—	146	1	no	—
129	C₈	—	146	1	no	—
130	C₂²	D₄×#64408	1	1	yes	characteristic
131	C₄	—	4	1	no	—
132	C₄	—	4	1	no	—
133	C₄	—	292	1	no	—
134	C₄	—	292	1	no	—
135	C₄	—	73	1	no	—
136	C₄	—	73	1	no	—
137	C₄	—	146	1	no	—
138	C₄	D₇₃⋊M₁₆	1	1	yes	characteristic
139	C₄	#14556678	1	1	yes	characteristic
140	C₂	#17989620	1	1	yes	characteristic
141	C₂	#17989627	1	1	yes	characteristic
142	C₂	#17989632	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989638

C₂

yes

maximal, characteristic

#17989637

C₂

yes

maximal, characteristic

#17989449

C₂

yes

maximal, characteristic

#17989437

C₂

yes

maximal, characteristic

Q₈⋊#10596833

C₂

yes

maximal, characteristic

#17989428

C₂

yes

maximal, characteristic

#17988679

C₂

yes

maximal, characteristic

#14556658

—

C₄⋊#10596833

—

C₄⋊#10596833

C₂²

yes

characteristic

C₄⋊#10596833

C₂²

yes

—

—

C₂²

yes

characteristic

C₄×#10596833

C₂²

yes

characteristic

C₂×#11924018

C₄

yes

characteristic

Q₈×Dic₇₃

C₂²

yes

characteristic

#14556556

C₂²

yes

characteristic

#14556524

C₄

yes

characteristic

#14556516

C₄

yes

characteristic

C₈×Dic₇₃

C₂²

yes

characteristic

#103×C₇₃

C₄

yes

—

—

—

D₄

yes

characteristic

C₂×#10596833

D₄

yes

characteristic

C₂×Dic₁₄₆

C₂×C₄

yes

characteristic

#11924018

—

C₂×#10596831

C₂×C₄

yes

characteristic

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

C₂×C₄

yes

characteristic

#11924007

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

C₂³

yes

characteristic

C₂×Q₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₄⋊C₄×C₇₃

C₂×C₄

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

#41

yes

characteristic

Dic₁₄₆

—

Dic₁₄₆

—

—

—

—

—

—

C₈×C₇₃

—

#10596831

M₁₆

yes

—

C₂²×C₇₃

C₄×D₄

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₂×M₁₆

yes

characteristic

C₄×C₇₃

#131

yes

characteristic

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

yes

Dic₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#446

—

#446

—

C₄×Q₁₆

—

#334

—

Q₈⋊C₈

—

Q₈⋊C₈

—

#322

—

C₂×Q₁₆

—

C₄×Q₈

—

C₄×Q₈

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

146

—

C₄⋊C₈

—

146

—

—

yes

—

146

—

#97

—

146

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

C₂×#64408

yes

characteristic

Q₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

146

—

102

C₂×C₈

—

146

—

103

C₂×C₈

—

146

—

104

C₂×C₈

C₂×#64408

yes

characteristic

105

C₄⋊C₄

—

106

C₄⋊C₄

—

146

—

107

C₄⋊C₄

—

146

—

108

C₄⋊C₄

C₂×#64408

yes

characteristic

109

C₄²

—

110

C₄²

—

146

—

111

C₄²

—

146

—

112

Q₈

—

113

Q₈

—

114

Q₈

—

146

—

115

Q₈

—

146

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

146

—

121

C₂×C₄

—

146

—

122

C₂×C₄

C₂²×#64408

yes

characteristic

123

C₈

—

124

C₈

—

292

—

125

C₈

—

292

—

126

C₈

—

292

—

127

C₈

—

128

C₈

—

146

—

129

C₈

—

146

—

130

C₂²

D₄×#64408

yes

characteristic

131

C₄

—

132

C₄

—

133

C₄

—

292

—

134

C₄

—

292

—

135

C₄

—

136

C₄

—

137

C₄

—

146

—

138

C₄

D₇₃⋊M₁₆

yes

characteristic

139

C₄

#14556678

yes

characteristic

140

C₂

#17989620

yes

characteristic

141

C₂

#17989627

yes

characteristic

142

C₂

#17989632

yes

characteristic

	subgroup	G/H
center	C₂²	D₄×#64408
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#64408
Fitting	#103×C₇₃	C₄
socle	C₂²×C₇₃	C₄×D₄
hypercenter	#103	#64408
hypocenter	C₇₃	#1593
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

subgroup

G/H

center

C₂²

D₄×#64408

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#64408

Fitting

#103×C₇₃

C₄

socle

C₂²×C₇₃

C₄×D₄

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

N	H ≅ G/N	type
72. C₇₃	#1593	semidirect

H ≅ G/N

type

72. C₇₃

#1593

semidirect

Subgroups — #22625576

Conjugacy classes of subgroups

Complements