Group #22625740 — subgroups

Subgroups — #22625740

Order 9344.

224 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 88 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	#17989597	C₂	1	1	yes	maximal, characteristic
2	#17989553	C₂	1	2	yes	maximal
3	C₂×#14556645	C₂	1	1	yes	maximal, characteristic
4	#17989459	C₂	1	2	yes	maximal
5	#108×D₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#11924036	C₂²	1	1	yes	characteristic
7	#14556670	C₂²	1	2	yes	—
8	C₂×C₄×#64408	C₂²	1	1	yes	characteristic
9	#14556660	C₄	1	2	yes	complemented
10	#14556659	C₄	1	2	yes	complemented
11	#14556645	—	2	2	no	—
12	#14556645	C₄	1	2	yes	complemented
13	#14556645	C₄	1	2	yes	complemented
14	C₈×#64408	—	2	2	no	—
15	M₁₆×D₇₃	C₂²	1	2	yes	—
16	C₂×C₈×D₇₃	C₂²	1	1	yes	characteristic
17	#14556527	C₄	1	1	yes	characteristic, complemented
18	#14556526	C₄	1	2	yes	complemented
19	#108×C₇₃	C₄	1	1	yes	characteristic, complemented
20	C₂²×#64408	—	2	1	no	—
21	#11924036	C₂×C₄	1	2	yes	—
22	#11924036	D₄	1	2	yes	—
23	C₂×#10596833	Q₈	1	2	yes	—
24	C₄⋊#64408	C₂×C₄	1	4	yes	—
25	C₂²⋊#64408	—	2	2	no	—
26	C₄×#64408	—	2	2	no	—
27	C₄×#64408	—	2	1	no	—
28	C₄×#64408	C₂×C₄	1	2	yes	—
29	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
30	#11924012	C₂×C₄	1	2	yes	—
31	#11924011	—	2	2	no	—
32	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
33	C₈×D₇₃	—	2	2	no	—
34	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
35	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
36	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
37	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
38	M₁₆×C₇₃	C₂×C₄	1	2	yes	—
39	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×D₇₃	#41	1	1	yes	characteristic
41	C₂×#64408	—	2	2	no	—
42	C₂×#64408	—	2	4	no	—
43	C₂×#64408	—	4	2	no	—
44	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
45	C₂×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
46	C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
47	C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
48	C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
49	C₄×D₇₃	#41	1	1	yes	characteristic
50	#10596833	C₄⋊C₄	1	4	yes	—
51	C₈×C₇₃	—	2	2	no	—
52	C₈×C₇₃	C₄²	1	1	yes	characteristic
53	C₈×C₇₃	C₄²	1	1	yes	characteristic
54	#10596831	—	2	2	no	—
55	#10596831	C₄²	1	1	yes	characteristic
56	#10596831	C₄²	1	1	yes	characteristic
57	C₂²×C₇₃	C₄×Q₈	1	1	yes	characteristic
58	C₂×D₇₃	—	2	2	no	—
59	C₂×D₇₃	#117	1	1	yes	characteristic
60	C₂×D₇₃	C₄×D₄	1	1	yes	characteristic
61	#64408	—	4	2	no	—
62	#64408	—	4	4	no	—
63	C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
64	C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
65	Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
66	Dic₇₃	C₄×Q₈	1	1	yes	characteristic
67	C₂×C₇₃	—	2	1	no	—
68	C₂×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
69	D₇₃	—	2	1	no	—
70	D₇₃	#444	1	2	yes	—
71	#1773	—	73	1	no	maximal, Sylow
72	C₇₃	#1773	1	1	yes	characteristic, complemented, Sylow
73	C₂×#108	—	73	1	no	—
74	#427	—	73	1	no	—
75	#405	—	73	2	no	—
76	C₂×#97	—	73	1	no	—
77	#339	—	73	2	no	—
78	C₂×M₁₆	—	73	2	no	—
79	C₂²×C₈	—	73	1	no	—
80	C₂²×C₈	—	73	1	no	—
81	#117	—	73	2	no	—
82	C₂×C₄²	—	73	1	no	—
83	#108	—	73	2	no	—
84	#108	—	73	1	no	—
85	#108	#64408	1	1	yes	characteristic, complemented
86	#107	—	73	2	no	—
87	#106	—	73	2	no	—
88	#97	—	73	2	no	—
89	#97	—	73	2	no	—
90	#97	—	146	2	no	—
91	C₄×C₈	—	146	2	no	—
92	C₂²×C₄	—	73	1	no	—
93	C₂²×C₄	—	146	1	no	—
94	M₁₆	—	73	2	no	—
95	M₁₆	—	146	2	no	—
96	M₁₆	C₂×#64408	1	2	yes	—
97	C₂×C₈	—	73	2	no	—
98	C₂×C₈	—	73	2	no	—
99	C₂×C₈	—	73	2	no	—
100	C₂×C₈	—	73	1	no	—
101	C₂×C₈	—	73	1	no	—
102	C₂×C₈	—	73	1	no	—
103	C₂×C₈	—	73	1	no	—
104	C₂×C₈	—	73	1	no	—
105	C₂×C₈	—	146	2	no	—
106	C₂×C₈	C₂×#64408	1	1	yes	characteristic
107	C₄⋊C₄	—	73	4	no	—
108	C₂²⋊C₄	—	146	2	no	—
109	C₄²	—	73	2	no	—
110	C₄²	—	146	2	no	—
111	C₄²	—	146	1	no	—
112	C₂³	—	73	1	no	—
113	C₂×C₄	—	292	2	no	—
114	C₂×C₄	—	73	1	no	—
115	C₂×C₄	—	73	1	no	—
116	C₂×C₄	—	73	1	no	—
117	C₂×C₄	—	73	1	no	—
118	C₂×C₄	—	73	1	no	—
119	C₂×C₄	—	146	2	no	—
120	C₂×C₄	—	146	4	no	—
121	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
122	C₈	—	2	2	no	—
123	C₈	—	73	4	no	—
124	C₈	—	73	1	no	—
125	C₈	—	73	1	no	—
126	C₈	—	146	2	no	—
127	C₈	C₄×#64408	1	1	yes	characteristic
128	C₈	C₄×#64408	1	1	yes	characteristic
129	C₂²	—	73	1	no	—
130	C₂²	—	73	1	no	—
131	C₂²	—	146	2	no	—
132	C₂²	Q₈×#64408	1	1	yes	characteristic
133	C₄	—	292	4	no	—
134	C₄	—	292	2	no	—
135	C₄	—	73	1	no	—
136	C₄	—	73	1	no	—
137	C₄	C₂×C₄×#64408	1	1	yes	characteristic
138	C₄	D₄×#64408	1	1	yes	characteristic
139	C₂	—	2	1	no	—
140	C₂	—	73	2	no	—
141	C₂	—	146	1	no	—
142	C₂	C₄⋊C₄×#64408	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989597

C₂

yes

maximal, characteristic

#17989553

C₂

yes

maximal

C₂×#14556645

C₂

yes

maximal, characteristic

#17989459

C₂

yes

maximal

#108×D₇₃

C₂

yes

maximal, characteristic

C₂×#11924036

C₂²

yes

characteristic

#14556670

C₂²

yes

—

C₂×C₄×#64408

C₂²

yes

characteristic

#14556660

C₄

yes

complemented

#14556659

C₄

yes

complemented

#14556645

—

#14556645

C₄

yes

complemented

#14556645

C₄

yes

complemented

C₈×#64408

—

M₁₆×D₇₃

C₂²

yes

—

C₂×C₈×D₇₃

C₂²

yes

characteristic

#14556527

C₄

yes

characteristic, complemented

#14556526

C₄

yes

complemented

#108×C₇₃

C₄

yes

characteristic, complemented

C₂²×#64408

—

#11924036

C₂×C₄

yes

—

#11924036

D₄

yes

—

C₂×#10596833

Q₈

yes

—

C₄⋊#64408

C₂×C₄

yes

—

—

—

—

C₂×C₄

yes

—

C₂×C₄×D₇₃

C₂³

yes

characteristic

#11924012

C₂×C₄

yes

—

#11924011

—

C₂×#10596831

C₂×C₄

yes

characteristic

C₈×D₇₃

—

C₈×D₇₃

C₂×C₄

yes

characteristic

C₈×D₇₃

C₂×C₄

yes

characteristic

C₈×D₇₃

C₂×C₄

yes

characteristic

C₈×D₇₃

C₂×C₄

yes

characteristic

M₁₆×C₇₃

C₂×C₄

yes

—

C₂×C₈×C₇₃

C₂×C₄

yes

C₂²×D₇₃

yes

—

—

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

C₂×Q₈

yes

characteristic

C₄×D₇₃

C₂²×C₄

yes

characteristic

C₄×D₇₃

C₂²×C₄

yes

characteristic

C₄×D₇₃

C₂×D₄

yes

C₄×D₇₃

yes

C₄⋊C₄

yes

—

C₈×C₇₃

—

C₈×C₇₃

C₄²

yes

characteristic

C₈×C₇₃

C₄²

yes

characteristic

#10596831

—

#10596831

C₄²

yes

characteristic

#10596831

C₄²

yes

characteristic

C₂²×C₇₃

C₄×Q₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

#117

yes

characteristic

C₂×D₇₃

C₄×D₄

yes

characteristic

#64408

—

#64408

—

C₄×C₇₃

C₂×C₄²

yes

characteristic

C₄×C₇₃

C₄×D₄

yes

characteristic

Dic₇₃

C₂×C₄⋊C₄

yes

characteristic

Dic₇₃

C₄×Q₈

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

C₄×C₄⋊C₄

yes

characteristic

D₇₃

—

D₇₃

#444

yes

—

#1773

—

maximal, Sylow

C₇₃

#1773

yes

characteristic, complemented, Sylow

C₂×#108

—

#427

—

#405

—

C₂×#97

—

#339

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

#117

—

C₂×C₄²

—

—

—

yes

characteristic, complemented

—

—

—

—

—

146

—

C₄×C₈

—

146

—

C₂²×C₄

—

C₂²×C₄

—

146

—

M₁₆

—

M₁₆

—

146

—

M₁₆

C₂×#64408

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

146

—

106

C₂×C₈

C₂×#64408

yes

characteristic

107

C₄⋊C₄

—

108

C₂²⋊C₄

—

146

—

109

C₄²

—

110

C₄²

—

146

—

111

C₄²

—

146

—

112

C₂³

—

113

C₂×C₄

—

292

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

146

—

120

C₂×C₄

—

146

—

121

C₂×C₄

C₂²×#64408

yes

characteristic

122

C₈

—

123

C₈

—

124

C₈

—

125

C₈

—

126

C₈

—

146

—

127

C₈

C₄×#64408

yes

characteristic

128

C₈

C₄×#64408

yes

characteristic

129

C₂²

—

130

C₂²

—

131

C₂²

—

146

—

132

C₂²

Q₈×#64408

yes

characteristic

133

C₄

—

292

—

134

C₄

—

292

—

135

C₄

—

136

C₄

—

137

C₄

C₂×C₄×#64408

yes

characteristic

138

C₄

D₄×#64408

yes

characteristic

139

C₂

—

140

C₂

—

141

C₂

—

146

—

142

C₂

C₄⋊C₄×#64408

yes

characteristic

	subgroup	G/H
center	C₄	D₄×#64408
commutator	C₄×C₇₃	C₂×C₄²
Frattini	C₂×C₄	C₂²×#64408
Fitting	#108×C₇₃	C₄
socle	C₂×C₇₃	C₄×C₄⋊C₄
hypercenter	#108	#64408
hypocenter	C₇₃	#1773
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #108

subgroup

G/H

center

C₄

D₄×#64408

commutator

C₄×C₇₃

C₂×C₄²

Frattini

C₂×C₄

C₂²×#64408

Fitting

#108×C₇₃

C₄

socle

C₂×C₇₃

C₄×C₄⋊C₄

C₇₃

G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ #108

N	H ≅ G/N	type
9. #14556660	C₄	semidirect
10. #14556659	C₄	semidirect
12. #14556645	C₄	semidirect
13. #14556645	C₄	semidirect
17. #14556527	C₄	semidirect
18. #14556526	C₄	semidirect
19. #108×C₇₃	C₄	semidirect
72. C₇₃	#1773	semidirect
85. #108	#64408	semidirect

H ≅ G/N

type

9. #14556660

C₄

semidirect

10. #14556659

C₄

semidirect

12. #14556645

C₄

semidirect

13. #14556645

C₄

semidirect

17. #14556527

C₄

semidirect

18. #14556526

C₄

semidirect

19. #108×C₇₃

C₄

semidirect

72. C₇₃

#1773

semidirect

85. #108

#64408

semidirect

Subgroups — #22625740

Conjugacy classes of subgroups

Complements