Group #22625734 — subgroups

Subgroups — #22625734

Order 9344.

232 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 90 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	C₂×#14556661	C₂	1	1	yes	maximal, characteristic
2	#17989552	C₂	1	2	yes	maximal
3	C₂×C₈×#64408	C₂	1	1	yes	maximal, characteristic
4	#17989457	C₂	1	2	yes	maximal
5	#17988622	C₂	1	1	yes	maximal, characteristic
6	C₂×#11924038	C₂²	1	2	yes	—
7	C₂×#11924036	C₂²	1	1	yes	characteristic
8	C₂×C₄×#64408	C₂²	1	1	yes	characteristic
9	#14556661	C₄	1	4	yes	complemented
10	#14556646	—	2	2	no	—
11	C₄×#10596833	—	2	2	no	—
12	C₈×#64408	C₄	1	4	yes	complemented
13	C₂×C₈×D₇₃	C₂²	1	1	yes	characteristic
14	#14556549	C₂²	1	2	yes	—
15	#14556524	C₄	1	2	yes	complemented
16	#14556523	C₄	1	1	yes	characteristic, complemented
17	#106×C₇₃	C₄	1	1	yes	characteristic, complemented
18	C₂²×#64408	—	2	1	no	—
19	#11924038	—	2	2	no	—
20	#11924038	C₂×C₄	1	4	yes	—
21	#11924036	C₂×C₄	1	2	yes	—
22	#11924036	Q₈	1	2	yes	—
23	C₂×#10596833	—	2	2	no	—
24	C₂×#10596833	D₄	1	1	yes	characteristic
25	C₂×#10596833	D₄	1	1	yes	characteristic
26	C₄×#64408	—	2	1	no	—
27	C₄×#64408	C₂×C₄	1	2	yes	—
28	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
29	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
30	C₈×D₇₃	C₂×C₄	1	2	yes	—
31	C₈×D₇₃	C₂×C₄	1	2	yes	—
32	C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
33	#11924005	—	2	2	no	—
34	C₄×Dic₇₃	—	2	2	no	—
35	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
36	C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
37	C₂²×D₇₃	#41	1	1	yes	characteristic
38	C₂×#64408	—	2	4	no	—
39	C₂×#64408	—	2	2	no	—
40	C₂×C₄×C₇₃	—	2	2	no	—
41	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
42	C₂×Dic₇₃	—	2	2	no	—
43	C₂×Dic₇₃	C₂×D₄	1	1	yes	characteristic
44	C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
45	C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
46	C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
47	C₄×D₇₃	#41	1	1	yes	characteristic
48	#10596833	—	2	4	no	—
49	#10596833	C₄⋊C₄	1	2	yes	—
50	#10596833	C₄⋊C₄	1	2	yes	—
51	C₈×C₇₃	C₄²	1	2	yes	—
52	#10596831	C₄²	1	2	yes	—
53	C₂²×C₇₃	C₄×D₄	1	1	yes	characteristic
54	C₂×D₇₃	—	2	2	no	—
55	C₂×D₇₃	#117	1	1	yes	characteristic
56	C₂×D₇₃	C₄×Q₈	1	1	yes	characteristic
57	#64408	—	2	4	no	—
58	C₄×C₇₃	—	4	2	no	—
59	C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
60	C₄×C₇₃	C₄×Q₈	1	1	yes	characteristic
61	Dic₇₃	—	4	2	no	—
62	Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
63	Dic₇₃	C₄×D₄	1	1	yes	characteristic
64	C₂×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
65	C₂×C₇₃	#443	1	2	yes	—
66	D₇₃	—	2	1	no	—
67	D₇₃	—	2	1	no	—
68	#1772	—	73	1	no	maximal, Sylow
69	C₇₃	#1772	1	1	yes	characteristic, complemented, Sylow
70	C₂×#108	—	73	1	no	—
71	#427	—	73	1	no	—
72	#405	—	73	2	no	—
73	C₂×C₄×C₈	—	73	1	no	—
74	#339	—	73	2	no	—
75	C₂×M₁₆	—	73	2	no	—
76	C₂²×C₈	—	73	1	no	—
77	C₂²×C₈	—	73	1	no	—
78	#117	—	73	2	no	—
79	C₂×C₄²	—	73	1	no	—
80	#108	—	73	4	no	—
81	#107	—	73	2	no	—
82	#106	—	73	1	no	—
83	#106	#64408	1	1	yes	characteristic, complemented
84	#97	—	146	2	no	—
85	C₄×C₈	—	73	4	no	—
86	C₄×C₈	—	146	2	no	—
87	C₂²×C₄	—	73	1	no	—
88	C₂²×C₄	—	146	1	no	—
89	M₁₆	—	73	4	no	—
90	M₁₆	—	146	2	no	—
91	C₂×C₈	—	73	1	no	—
92	C₂×C₈	—	73	1	no	—
93	C₂×C₈	—	73	2	no	—
94	C₂×C₈	—	73	2	no	—
95	C₂×C₈	—	73	1	no	—
96	C₂×C₈	—	73	2	no	—
97	C₂×C₈	—	73	2	no	—
98	C₂×C₈	—	146	2	no	—
99	C₂×C₈	C₂×#64408	1	1	yes	characteristic
100	C₄⋊C₄	—	73	2	no	—
101	C₄⋊C₄	C₂×#64408	1	2	yes	—
102	C₂²⋊C₄	—	146	2	no	—
103	C₄²	—	73	2	no	—
104	C₄²	—	146	2	no	—
105	C₄²	—	146	1	no	—
106	C₂³	—	73	1	no	—
107	C₂×C₄	—	2	2	no	—
108	C₂×C₄	—	73	1	no	—
109	C₂×C₄	—	73	1	no	—
110	C₂×C₄	—	73	1	no	—
111	C₂×C₄	—	73	1	no	—
112	C₂×C₄	—	73	1	no	—
113	C₂×C₄	—	146	2	no	—
114	C₂×C₄	—	146	2	no	—
115	C₂×C₄	—	146	4	no	—
116	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
117	C₈	—	73	2	no	—
118	C₈	—	73	2	no	—
119	C₈	—	73	2	no	—
120	C₈	—	146	4	no	—
121	C₈	C₄×#64408	1	2	yes	—
122	C₂²	—	73	1	no	—
123	C₂²	—	73	1	no	—
124	C₂²	—	146	2	no	—
125	C₂²	D₄×#64408	1	1	yes	characteristic
126	C₄	—	4	2	no	—
127	C₄	—	292	2	no	—
128	C₄	—	73	1	no	—
129	C₄	—	73	1	no	—
130	C₄	—	146	4	no	—
131	C₄	C₂×C₄×#64408	1	1	yes	characteristic
132	C₄	Q₈×#64408	1	1	yes	characteristic
133	C₂	—	146	1	no	—
134	C₂	—	146	1	no	—
135	C₂	C₄⋊C₄×#64408	1	1	yes	characteristic
136	C₂	#17989630	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556661

C₂

yes

maximal, characteristic

#17989552

C₂

yes

maximal

C₂×C₈×#64408

C₂

yes

maximal, characteristic

#17989457

C₂

yes

maximal

#17988622

C₂

yes

maximal, characteristic

C₂×#11924038

C₂²

yes

—

C₂×#11924036

C₂²

yes

characteristic

C₂×C₄×#64408

C₂²

yes

characteristic

#14556661

C₄

yes

—

—

C₄

yes

complemented

C₂×C₈×D₇₃

C₂²

yes

characteristic

#14556549

C₂²

yes

—

#14556524

C₄

yes

complemented

#14556523

C₄

yes

characteristic, complemented

#106×C₇₃

C₄

yes

characteristic, complemented

C₂²×#64408

—

#11924038

—

#11924038

C₂×C₄

yes

—

#11924036

C₂×C₄

yes

—

#11924036

Q₈

yes

—

C₂×#10596833

—

C₂×#10596833

D₄

yes

characteristic

C₂×#10596833

D₄

yes

characteristic

C₄×#64408

—

C₄×#64408

C₂×C₄

yes

—

C₂×C₄×D₇₃

C₂³

yes

characteristic

C₂×#10596831

C₂×C₄

yes

characteristic

C₈×D₇₃

C₂×C₄

yes

—

C₈×D₇₃

C₂×C₄

yes

—

C₄⋊Dic₇₃

C₂×C₄

yes

—

#11924005

—

C₄×Dic₇₃

—

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₄⋊C₄×C₇₃

C₂×C₄

yes

—

C₂²×D₇₃

yes

—

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂×D₄

yes

characteristic

C₄×D₇₃

C₂²×C₄

yes

characteristic

C₄×D₇₃

C₂²×C₄

yes

characteristic

C₄×D₇₃

C₂×Q₈

yes

C₄×D₇₃

yes

—

C₄⋊C₄

yes

—

#10596833

C₄⋊C₄

yes

—

C₈×C₇₃

C₄²

yes

—

#10596831

C₄²

yes

—

C₂²×C₇₃

C₄×D₄

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

#117

yes

characteristic

C₂×D₇₃

C₄×Q₈

yes

characteristic

#64408

—

C₄×C₇₃

—

C₄×C₇₃

C₂×C₄²

yes

characteristic

C₄×C₇₃

C₄×Q₈

yes

characteristic

Dic₇₃

—

Dic₇₃

C₂×C₄⋊C₄

yes

characteristic

Dic₇₃

C₄×D₄

yes

characteristic

C₂×C₇₃

C₄×C₄⋊C₄

yes

characteristic

C₂×C₇₃

#443

yes

—

D₇₃

—

D₇₃

—

#1772

—

maximal, Sylow

C₇₃

#1772

yes

characteristic, complemented, Sylow

C₂×#108

—

#427

—

#405

—

C₂×C₄×C₈

—

#339

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

#117

—

C₂×C₄²

—

—

—

—

yes

characteristic, complemented

#97

—

146

—

C₄×C₈

—

C₄×C₈

—

146

—

C₂²×C₄

—

C₂²×C₄

—

146

—

M₁₆

—

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

C₂×#64408

yes

characteristic

100

C₄⋊C₄

—

101

C₄⋊C₄

C₂×#64408

yes

—

102

C₂²⋊C₄

—

146

—

103

C₄²

—

104

C₄²

—

146

—

105

C₄²

—

146

—

106

C₂³

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

146

—

114

C₂×C₄

—

146

—

115

C₂×C₄

—

146

—

116

C₂×C₄

C₂²×#64408

yes

characteristic

117

C₈

—

118

C₈

—

119

C₈

—

120

C₈

—

146

—

121

C₈

C₄×#64408

yes

—

122

C₂²

—

123

C₂²

—

124

C₂²

—

146

—

125

C₂²

D₄×#64408

yes

characteristic

126

C₄

—

127

C₄

—

292

—

128

C₄

—

129

C₄

—

130

C₄

—

146

—

131

C₄

C₂×C₄×#64408

yes

characteristic

132

C₄

Q₈×#64408

yes

characteristic

133

C₂

—

146

—

134

C₂

—

146

—

135

C₂

C₄⋊C₄×#64408

yes

characteristic

136

C₂

#17989630

yes

—

	subgroup	G/H
center	C₂²	D₄×#64408
commutator	C₄×C₇₃	C₂×C₄²
Frattini	C₂×C₄	C₂²×#64408
Fitting	#106×C₇₃	C₄
socle	C₂²×C₇₃	C₄×D₄
hypercenter	#106	#64408
hypocenter	C₇₃	#1772
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

subgroup

G/H

center

C₂²

D₄×#64408

commutator

C₄×C₇₃

C₂×C₄²

Frattini

C₂×C₄

C₂²×#64408

Fitting

#106×C₇₃

C₄

socle

C₂²×C₇₃

C₄×D₄

C₇₃

G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

N	H ≅ G/N	type
9. #14556661	C₄	semidirect
12. C₈×#64408	C₄	semidirect
15. #14556524	C₄	semidirect
16. #14556523	C₄	semidirect
17. #106×C₇₃	C₄	semidirect
69. C₇₃	#1772	semidirect
83. #106	#64408	semidirect

H ≅ G/N

type

9. #14556661

C₄

semidirect

12. C₈×#64408

C₄

semidirect

15. #14556524

C₄

semidirect

16. #14556523

C₄

semidirect

17. #106×C₇₃

C₄

semidirect

69. C₇₃

#1772

semidirect

83. #106

#64408

semidirect

Subgroups — #22625734

Conjugacy classes of subgroups

Complements