Group #22625739 — subgroups

Subgroups — #22625739

Order 9344.

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

normal subgroups only

This group has 224 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×#14556662	C₂	1	1	yes	maximal, characteristic
2	#17989552	C₂	1	2	yes	maximal
3	C₂×#14556645	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	#14556662	C₄	1	4	yes	complemented
10	#14556646	—	2	2	no	—
11	#14556645	C₄	1	4	yes	complemented
12	C₄×#10596833	—	2	2	no	—
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	2	yes	—
25	C₄×#64408	—	2	1	no	—
26	C₄×#64408	C₂×C₄	1	2	yes	—
27	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
28	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
29	C₈×D₇₃	C₂×C₄	1	2	yes	—
30	C₈×D₇₃	C₂×C₄	1	2	yes	—
31	C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
32	#11924005	—	2	2	no	—
33	C₄×Dic₇₃	—	2	2	no	—
34	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
35	C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
36	C₂²×D₇₃	#41	1	1	yes	characteristic
37	C₂×#64408	—	2	2	no	—
38	C₂×#64408	—	4	2	no	—
39	C₂×C₄×C₇₃	—	2	2	no	—
40	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
41	C₂×Dic₇₃	—	2	2	no	—
42	C₂×Dic₇₃	C₂×D₄	1	1	yes	characteristic
43	C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
44	C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
45	C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
46	C₄×D₇₃	#41	1	1	yes	characteristic
47	#10596833	—	2	4	no	—
48	#10596833	C₄⋊C₄	1	4	yes	—
49	C₈×C₇₃	C₄²	1	2	yes	—
50	#10596831	C₄²	1	2	yes	—
51	C₂²×C₇₃	C₄×D₄	1	1	yes	characteristic
52	C₂×D₇₃	—	2	2	no	—
53	C₂×D₇₃	#117	1	1	yes	characteristic
54	C₂×D₇₃	C₄×Q₈	1	1	yes	characteristic
55	#64408	—	4	2	no	—
56	C₄×C₇₃	—	4	2	no	—
57	C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
58	C₄×C₇₃	C₄×Q₈	1	1	yes	characteristic
59	Dic₇₃	—	4	2	no	—
60	Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
61	Dic₇₃	C₄×D₄	1	1	yes	characteristic
62	C₂×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
63	C₂×C₇₃	#444	1	2	yes	—
64	D₇₃	—	2	1	no	—
65	D₇₃	—	2	1	no	—
66	#1773	—	73	1	no	maximal, Sylow
67	C₇₃	#1773	1	1	yes	characteristic, complemented, Sylow
68	C₂×#108	—	73	1	no	—
69	#427	—	73	1	no	—
70	#405	—	73	2	no	—
71	C₂×#97	—	73	1	no	—
72	#339	—	73	2	no	—
73	C₂×M₁₆	—	73	2	no	—
74	C₂²×C₈	—	73	1	no	—
75	C₂²×C₈	—	73	1	no	—
76	#117	—	73	2	no	—
77	C₂×C₄²	—	73	1	no	—
78	#108	—	73	4	no	—
79	#107	—	73	2	no	—
80	#106	—	73	1	no	—
81	#106	#64408	1	1	yes	characteristic, complemented
82	#97	—	73	4	no	—
83	#97	—	146	2	no	—
84	C₄×C₈	—	146	2	no	—
85	C₂²×C₄	—	73	1	no	—
86	C₂²×C₄	—	146	1	no	—
87	M₁₆	—	73	4	no	—
88	M₁₆	—	146	2	no	—
89	C₂×C₈	—	73	2	no	—
90	C₂×C₈	—	73	2	no	—
91	C₂×C₈	—	73	2	no	—
92	C₂×C₈	—	73	1	no	—
93	C₂×C₈	—	73	2	no	—
94	C₂×C₈	—	73	2	no	—
95	C₂×C₈	—	146	2	no	—
96	C₂×C₈	C₂×#64408	1	1	yes	characteristic
97	C₄⋊C₄	—	73	2	no	—
98	C₄⋊C₄	C₂×#64408	1	2	yes	—
99	C₂²⋊C₄	—	146	2	no	—
100	C₄²	—	73	2	no	—
101	C₄²	—	146	2	no	—
102	C₄²	—	146	1	no	—
103	C₂³	—	73	1	no	—
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	—	292	2	no	—
106	C₂×C₄	—	73	1	no	—
107	C₂×C₄	—	73	1	no	—
108	C₂×C₄	—	73	1	no	—
109	C₂×C₄	—	73	1	no	—
110	C₂×C₄	—	73	1	no	—
111	C₂×C₄	—	146	2	no	—
112	C₂×C₄	—	146	2	no	—
113	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
114	C₈	—	73	4	no	—
115	C₈	—	73	2	no	—
116	C₈	—	146	4	no	—
117	C₈	C₄×#64408	1	2	yes	—
118	C₂²	—	73	1	no	—
119	C₂²	—	73	1	no	—
120	C₂²	—	146	2	no	—
121	C₂²	D₄×#64408	1	1	yes	characteristic
122	C₄	—	4	2	no	—
123	C₄	—	292	2	no	—
124	C₄	—	292	2	no	—
125	C₄	—	73	1	no	—
126	C₄	—	73	1	no	—
127	C₄	C₂×C₄×#64408	1	1	yes	characteristic
128	C₄	Q₈×#64408	1	1	yes	characteristic
129	C₂	—	146	1	no	—
130	C₂	—	146	1	no	—
131	C₂	C₄⋊C₄×#64408	1	1	yes	characteristic
132	C₂	#17989632	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556662

C₂

yes

maximal, characteristic

#17989552

C₂

yes

maximal

C₂×#14556645

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

#14556662

C₄

yes

complemented

#14556646

—

#14556645

C₄

yes

complemented

C₄×#10596833

—

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

—

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

—

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

#444

yes

—

D₇₃

—

D₇₃

—

#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

#97

—

#97

—

146

—

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

—

146

—

C₂×C₈

C₂×#64408

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

C₂×#64408

yes

—

C₂²⋊C₄

—

146

—

100

C₄²

—

101

C₄²

—

146

—

102

C₄²

—

146

—

103

C₂³

—

104

C₂×C₄

—

105

C₂×C₄

—

292

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

146

—

112

C₂×C₄

—

146

—

113

C₂×C₄

C₂²×#64408

yes

characteristic

114

C₈

—

115

C₈

—

116

C₈

—

146

—

117

C₈

C₄×#64408

yes

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

146

—

121

C₂²

D₄×#64408

yes

characteristic

122

C₄

—

123

C₄

—

292

—

124

C₄

—

292

—

125

C₄

—

126

C₄

—

127

C₄

C₂×C₄×#64408

yes

characteristic

128

C₄

Q₈×#64408

yes

characteristic

129

C₂

—

146

—

130

C₂

—

146

—

131

C₂

C₄⋊C₄×#64408

yes

characteristic

132

C₂

#17989632

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	#1773
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. #14556662	C₄	semidirect
11. #14556645	C₄	semidirect
15. #14556524	C₄	semidirect
16. #14556523	C₄	semidirect
17. #106×C₇₃	C₄	semidirect
67. C₇₃	#1773	semidirect
81. #106	#64408	semidirect

H ≅ G/N

type

9. #14556662

C₄

semidirect

11. #14556645

C₄

semidirect

15. #14556524

C₄

semidirect

16. #14556523

C₄

semidirect

17. #106×C₇₃

C₄

semidirect

67. C₇₃

#1773

semidirect

81. #106

#64408

semidirect

Subgroups — #22625739

Conjugacy classes of subgroups

Complements