Group #22625589 — subgroups

Subgroups — #22625589

Order 9344.

328 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 158 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×#14556645	C₂	1	2	yes	maximal
2	C₄×#11924036	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×#64408	C₂	1	2	yes	maximal
4	#17989523	C₂	1	1	yes	maximal, characteristic
5	#97×D₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#11924036	C₂²	1	1	yes	characteristic
7	C₂×#11924036	C₂²	1	1	yes	characteristic
8	C₂×C₄×#64408	C₂²	1	2	yes	—
9	#14556645	C₄	1	8	yes	complemented
10	C₄×#10596833	C₄	1	4	yes	complemented
11	C₈×#64408	C₄	1	8	yes	complemented
12	(C₂×#64408)⋊C₄	C₄	1	4	yes	—
13	C₂×C₈×D₇₃	C₂²	1	2	yes	—
14	C₄²×D₇₃	C₂²	1	1	yes	characteristic
15	#14556502	C₄	1	1	yes	characteristic, complemented
16	#14556501	C₄	1	2	yes	complemented
17	#97×C₇₃	C₄	1	1	yes	characteristic, complemented
18	C₂²×#64408	C₂×C₄	1	4	yes	—
19	#11924036	C₂×C₄	1	4	yes	—
20	#11924036	C₂×C₄	1	4	yes	—
21	C₂×#10596833	C₂×C₄	1	2	yes	—
22	C₂×#10596833	C₂×C₄	1	2	yes	—
23	C₄×#64408	C₂×C₄	1	4	yes	—
24	C₄×#64408	C₂×C₄	1	4	yes	—
25	C₂×C₄×D₇₃	C₂×C₄	1	2	yes	—
26	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
27	C₂×#10596831	C₂×C₄	1	2	yes	—
28	C₈×D₇₃	C₂×C₄	1	4	yes	—
29	C₈×D₇₃	C₂×C₄	1	4	yes	—
30	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
31	C₄×Dic₇₃	C₂×C₄	1	2	yes	—
32	C₂×C₈×C₇₃	C₂×C₄	1	2	yes	—
33	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
34	C₂²×D₇₃	C₂²×C₄	1	1	yes	characteristic
35	C₂×#64408	—	2	8	no	—
36	C₂×#64408	C₄²	1	8	yes	—
37	C₂×C₄×C₇₃	C₄²	1	2	yes	—
38	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
39	C₂×Dic₇₃	C₄²	1	2	yes	—
40	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
41	C₄×D₇₃	—	2	4	no	—
42	C₄×D₇₃	C₂²×C₄	1	2	yes	—
43	C₄×D₇₃	C₂²×C₄	1	2	yes	—
44	#10596833	C₄²	1	4	yes	—
45	#10596833	C₄²	1	4	yes	—
46	C₈×C₇₃	C₄²	1	4	yes	—
47	#10596831	C₄²	1	4	yes	—
48	C₂²×C₇₃	C₂×C₄²	1	1	yes	characteristic
49	C₂×D₇₃	C₂×C₄²	1	2	yes	—
50	C₂×D₇₃	#131	1	4	yes	—
51	#64408	—	2	8	no	—
52	C₄×C₇₃	—	2	2	no	—
53	C₄×C₇₃	C₂×C₄²	1	2	yes	—
54	Dic₇₃	—	2	2	no	—
55	Dic₇₃	C₂×C₄²	1	1	yes	characteristic
56	Dic₇₃	C₂×C₄²	1	1	yes	characteristic
57	C₂×C₇₃	C₄³	1	1	yes	characteristic
58	C₂×C₇₃	#405	1	2	yes	—
59	D₇₃	#405	1	4	yes	—
60	#1726	—	73	1	no	maximal, Sylow
61	C₇₃	#1726	1	1	yes	characteristic, complemented, Sylow
62	C₂×#97	—	73	2	no	—
63	C₂×#97	—	73	1	no	—
64	C₂×C₄×C₈	—	73	2	no	—
65	C₂×C₄×C₈	—	73	1	no	—
66	#376	—	73	1	no	—
67	C₂²×C₈	—	73	1	no	—
68	C₂²×C₈	—	73	1	no	—
69	C₂²×C₈	—	73	2	no	—
70	C₂×C₄²	—	73	2	no	—
71	C₂×C₄²	—	73	1	no	—
72	#97	—	73	8	no	—
73	#97	—	73	2	no	—
74	#97	—	73	1	no	—
75	#97	#64408	1	1	yes	characteristic, complemented
76	C₄×C₈	—	73	8	no	—
77	C₄×C₈	—	73	4	no	—
78	#95	—	73	4	no	—
79	C₂²×C₄	—	73	1	no	—
80	C₂²×C₄	—	73	4	no	—
81	C₂²×C₄	—	73	2	no	—
82	C₂×C₈	—	73	2	no	—
83	C₂×C₈	—	73	2	no	—
84	C₂×C₈	—	73	4	no	—
85	C₂×C₈	—	73	4	no	—
86	C₂×C₈	—	73	2	no	—
87	C₂×C₈	—	73	4	no	—
88	C₂×C₈	—	73	4	no	—
89	C₂×C₈	C₂×#64408	1	2	yes	—
90	C₄²	—	73	4	no	—
91	C₄²	—	73	4	no	—
92	C₄²	—	73	2	no	—
93	C₄²	—	73	1	no	—
94	C₄²	C₂×#64408	1	1	yes	characteristic
95	C₂³	—	73	1	no	—
96	C₂×C₄	—	73	1	no	—
97	C₂×C₄	—	73	2	no	—
98	C₂×C₄	—	73	2	no	—
99	C₂×C₄	—	73	8	no	—
100	C₂×C₄	—	73	2	no	—
101	C₂×C₄	—	146	4	no	—
102	C₂×C₄	—	146	8	no	—
103	C₂×C₄	C₄×#64408	1	2	yes	—
104	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
105	C₈	—	73	4	no	—
106	C₈	—	73	4	no	—
107	C₈	—	73	4	no	—
108	C₈	C₄×#64408	1	4	yes	—
109	C₂²	—	73	2	no	—
110	C₂²	—	73	4	no	—
111	C₂²	C₂×C₄×#64408	1	1	yes	characteristic
112	C₄	—	2	2	no	—
113	C₄	—	73	1	no	—
114	C₄	—	73	1	no	—
115	C₄	—	146	8	no	—
116	C₄	—	146	2	no	—
117	C₄	C₂×C₄×#64408	1	2	yes	—
118	C₂	—	73	4	no	—
119	C₂	C₄²×#64408	1	1	yes	characteristic
120	C₂	#17989553	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556645

C₂

yes

maximal

C₄×#11924036

C₂

yes

maximal, characteristic

C₂×C₈×#64408

C₂

yes

maximal

#17989523

C₂

yes

maximal, characteristic

#97×D₇₃

C₂

yes

maximal, characteristic

C₂×#11924036

C₂²

yes

characteristic

C₂×#11924036

C₂²

yes

characteristic

C₂×C₄×#64408

C₂²

yes

—

#14556645

C₄

yes

complemented

C₄×#10596833

C₄

yes

complemented

C₈×#64408

C₄

yes

complemented

(C₂×#64408)⋊C₄

C₄

yes

—

C₂×C₈×D₇₃

C₂²

yes

—

C₄²×D₇₃

C₂²

yes

characteristic

#14556502

C₄

yes

characteristic, complemented

#14556501

C₄

yes

complemented

#97×C₇₃

C₄

yes

characteristic, complemented

C₂²×#64408

C₂×C₄

yes

—

#11924036

C₂×C₄

yes

—

#11924036

C₂×C₄

yes

—

C₂×#10596833

C₂×C₄

yes

—

C₂×#10596833

C₂×C₄

yes

—

C₄×#64408

C₂×C₄

yes

—

C₄×#64408

C₂×C₄

yes

—

C₂×C₄×D₇₃

C₂×C₄

yes

—

C₂×C₄×D₇₃

C₂³

yes

characteristic

C₂×#10596831

C₂×C₄

yes

—

C₈×D₇₃

C₂×C₄

yes

—

C₈×D₇₃

C₂×C₄

yes

—

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

C₂×C₄

yes

—

C₂×C₈×C₇₃

C₂×C₄

yes

—

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₂²×D₇₃

C₂²×C₄

yes

characteristic

C₂×#64408

—

C₂×#64408

C₄²

yes

—

C₂×C₄×C₇₃

C₄²

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

C₄²

yes

—

C₂×Dic₇₃

C₂²×C₄

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

C₂²×C₄

yes

—

C₄×D₇₃

C₂²×C₄

yes

—

#10596833

C₄²

yes

—

#10596833

C₄²

yes

—

C₈×C₇₃

C₄²

yes

—

#10596831

C₄²

yes

—

C₂²×C₇₃

C₂×C₄²

yes

characteristic

C₂×D₇₃

C₂×C₄²

yes

—

C₂×D₇₃

#131

yes

—

#64408

—

C₄×C₇₃

—

C₄×C₇₃

C₂×C₄²

yes

—

Dic₇₃

—

Dic₇₃

C₂×C₄²

yes

characteristic

Dic₇₃

C₂×C₄²

yes

characteristic

C₂×C₇₃

C₄³

yes

characteristic

C₂×C₇₃

#405

yes

—

D₇₃

#405

yes

—

#1726

—

maximal, Sylow

C₇₃

#1726

yes

characteristic, complemented, Sylow

C₂×#97

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

#376

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

—

—

—

yes

characteristic, complemented

C₄×C₈

—

C₄×C₈

—

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#64408

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#64408

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

146

—

102

C₂×C₄

—

146

—

103

C₂×C₄

C₄×#64408

yes

—

104

C₂×C₄

C₂²×#64408

yes

characteristic

105

C₈

—

106

C₈

—

107

C₈

—

108

C₈

C₄×#64408

yes

—

109

C₂²

—

110

C₂²

—

111

C₂²

C₂×C₄×#64408

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

—

115

C₄

—

146

—

116

C₄

—

146

—

117

C₄

C₂×C₄×#64408

yes

—

118

C₂

—

119

C₂

C₄²×#64408

yes

characteristic

120

C₂

#17989553

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#64408
commutator	C₂×C₇₃	C₄³
Fitting	#97×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₄²
hypercenter	#97	#64408
hypocenter	C₇₃	#1726
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ #97

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#64408

commutator

C₂×C₇₃

C₄³

Fitting

#97×C₇₃

C₄

socle

C₂²×C₇₃

C₂×C₄²

C₇₃

G ▷ C₂×C₇₃ ▷ C₇₃

C₁ ◁ C₂×C₄ ◁ #97

N	H ≅ G/N	type
9. #14556645	C₄	semidirect
10. C₄×#10596833	C₄	semidirect
11. C₈×#64408	C₄	semidirect
15. #14556502	C₄	semidirect
16. #14556501	C₄	semidirect
17. #97×C₇₃	C₄	semidirect
61. C₇₃	#1726	semidirect
75. #97	#64408	semidirect

H ≅ G/N

type

9. #14556645

C₄

semidirect

10. C₄×#10596833

C₄

semidirect

11. C₈×#64408

C₄

semidirect

15. #14556502

C₄

semidirect

16. #14556501

C₄

semidirect

17. #97×C₇₃

C₄

semidirect

61. C₇₃

#1726

semidirect

75. #97

#64408

semidirect

Subgroups — #22625589

Conjugacy classes of subgroups

Complements