Group #22625587 — subgroups

Subgroups — #22625587

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	#17989546	C₂	1	1	yes	maximal, characteristic
2	C₂×#14556645	C₂	1	2	yes	maximal
3	C₂×C₈×#64408	C₂	1	2	yes	maximal
4	#17989523	C₂	1	1	yes	maximal, characteristic
5	C₄×C₈×D₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#11924036	C₂²	1	2	yes	—
7	C₂×C₄×#64408	C₂²	1	2	yes	—
8	#14556646	C₄	1	4	yes	complemented
9	#14556645	C₄	1	8	yes	complemented
10	C₈×#64408	C₄	1	8	yes	complemented
11	(C₂×#64408)⋊C₄	C₄	1	4	yes	—
12	C₂×C₈×D₇₃	C₂²	1	1	yes	characteristic
13	C₂×C₈×D₇₃	C₂²	1	1	yes	characteristic
14	C₄²×D₇₃	C₂²	1	1	yes	characteristic
15	C₄×#10596831	C₄	1	1	yes	characteristic, complemented
16	C₈×Dic₇₃	C₄	1	1	yes	characteristic, complemented
17	C₈×Dic₇₃	C₄	1	1	yes	characteristic, complemented
18	C₄×C₈×C₇₃	C₄	1	1	yes	characteristic, complemented
19	C₂²×#64408	C₂×C₄	1	4	yes	—
20	#11924036	C₂×C₄	1	4	yes	—
21	#11924036	C₂×C₄	1	4	yes	—
22	C₂×#10596833	C₂×C₄	1	4	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	1	yes	characteristic
28	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
29	C₈×D₇₃	C₂×C₄	1	4	yes	—
30	C₈×D₇₃	C₂×C₄	1	4	yes	—
31	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
32	C₄×Dic₇₃	C₂×C₄	1	2	yes	—
33	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
34	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
35	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
36	C₂²×D₇₃	C₂²×C₄	1	1	yes	characteristic
37	C₂×#64408	—	2	8	no	—
38	C₂×#64408	C₄²	1	8	yes	—
39	C₂×C₄×C₇₃	C₄²	1	2	yes	—
40	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
41	C₂×Dic₇₃	C₄²	1	2	yes	—
42	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
43	C₄×D₇₃	—	2	4	no	—
44	C₄×D₇₃	C₂²×C₄	1	2	yes	—
45	C₄×D₇₃	C₂²×C₄	1	2	yes	—
46	#10596833	C₄²	1	8	yes	—
47	C₈×C₇₃	C₄²	1	2	yes	—
48	C₈×C₇₃	C₄²	1	2	yes	—
49	#10596831	C₄²	1	2	yes	—
50	#10596831	C₄²	1	2	yes	—
51	C₂²×C₇₃	C₂×C₄²	1	1	yes	characteristic
52	C₂×D₇₃	C₂×C₄²	1	2	yes	—
53	C₂×D₇₃	#131	1	4	yes	—
54	#64408	—	2	8	no	—
55	C₄×C₇₃	—	2	2	no	—
56	C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
57	C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
58	Dic₇₃	—	2	2	no	—
59	Dic₇₃	C₂×C₄²	1	2	yes	—
60	C₂×C₇₃	C₄³	1	1	yes	characteristic
61	C₂×C₇₃	#405	1	2	yes	—
62	D₇₃	#405	1	4	yes	—
63	#1726	—	73	1	no	maximal, Sylow
64	C₇₃	#1726	1	1	yes	characteristic, complemented, Sylow
65	C₂×#97	—	73	2	no	—
66	C₂×#97	—	73	1	no	—
67	C₂×C₄×C₈	—	73	2	no	—
68	C₂×C₄×C₈	—	73	1	no	—
69	#376	—	73	1	no	—
70	C₂²×C₈	—	73	2	no	—
71	C₂²×C₈	—	73	1	no	—
72	C₂²×C₈	—	73	1	no	—
73	C₂×C₄²	—	73	2	no	—
74	C₂×C₄²	—	73	1	no	—
75	#97	—	73	8	no	—
76	#97	—	73	4	no	—
77	C₄×C₈	—	73	8	no	—
78	C₄×C₈	—	73	1	no	—
79	C₄×C₈	—	73	1	no	—
80	C₄×C₈	—	73	1	no	—
81	C₄×C₈	#64408	1	1	yes	characteristic, complemented
82	#95	—	73	4	no	—
83	C₂²×C₄	—	73	1	no	—
84	C₂²×C₄	—	73	4	no	—
85	C₂²×C₄	—	73	2	no	—
86	C₂×C₈	—	73	4	no	—
87	C₂×C₈	—	73	4	no	—
88	C₂×C₈	—	73	4	no	—
89	C₂×C₈	—	73	1	no	—
90	C₂×C₈	—	73	1	no	—
91	C₂×C₈	—	73	4	no	—
92	C₂×C₈	—	73	4	no	—
93	C₂×C₈	C₂×#64408	1	1	yes	characteristic
94	C₂×C₈	C₂×#64408	1	1	yes	characteristic
95	C₄²	—	73	4	no	—
96	C₄²	—	73	4	no	—
97	C₄²	—	73	2	no	—
98	C₄²	—	73	1	no	—
99	C₄²	C₂×#64408	1	1	yes	characteristic
100	C₂³	—	73	1	no	—
101	C₂×C₄	—	73	1	no	—
102	C₂×C₄	—	73	2	no	—
103	C₂×C₄	—	73	2	no	—
104	C₂×C₄	—	73	8	no	—
105	C₂×C₄	—	73	2	no	—
106	C₂×C₄	—	146	4	no	—
107	C₂×C₄	—	146	8	no	—
108	C₂×C₄	C₄×#64408	1	2	yes	—
109	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
110	C₈	—	73	8	no	—
111	C₈	—	73	2	no	—
112	C₈	—	73	2	no	—
113	C₈	C₄×#64408	1	2	yes	—
114	C₈	C₄×#64408	1	2	yes	—
115	C₂²	—	73	2	no	—
116	C₂²	—	73	4	no	—
117	C₂²	C₂×C₄×#64408	1	1	yes	characteristic
118	C₄	—	2	2	no	—
119	C₄	—	73	2	no	—
120	C₄	—	146	8	no	—
121	C₄	—	146	2	no	—
122	C₄	C₂×C₄×#64408	1	1	yes	characteristic
123	C₄	C₂×C₄×#64408	1	1	yes	characteristic
124	C₂	—	73	4	no	—
125	C₂	C₄²×#64408	1	1	yes	characteristic
126	C₂	#17989550	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#17989546

C₂

yes

maximal, characteristic

C₂×#14556645

C₂

yes

maximal

C₂×C₈×#64408

C₂

yes

maximal

#17989523

C₂

yes

maximal, characteristic

C₄×C₈×D₇₃

C₂

yes

maximal, characteristic

C₂×#11924036

C₂²

yes

—

C₂×C₄×#64408

C₂²

yes

—

#14556646

C₄

yes

complemented

#14556645

C₄

yes

complemented

C₈×#64408

C₄

yes

complemented

(C₂×#64408)⋊C₄

C₄

yes

—

C₂×C₈×D₇₃

C₂²

yes

characteristic

C₂×C₈×D₇₃

C₂²

yes

characteristic

C₄²×D₇₃

C₂²

yes

characteristic

C₄×#10596831

C₄

yes

characteristic, complemented

C₈×Dic₇₃

C₄

yes

characteristic, complemented

C₈×Dic₇₃

C₄

yes

characteristic, complemented

C₄×C₈×C₇₃

C₄

yes

characteristic, complemented

C₂²×#64408

C₂×C₄

yes

—

#11924036

C₂×C₄

yes

—

#11924036

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

characteristic

C₂×#10596831

C₂×C₄

yes

characteristic

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

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

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

—

C₈×C₇₃

C₄²

yes

—

C₈×C₇₃

C₄²

yes

—

#10596831

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

characteristic

C₄×C₇₃

C₂×C₄²

yes

characteristic

Dic₇₃

—

Dic₇₃

C₂×C₄²

yes

—

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

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#64408

yes

characteristic, complemented

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#64408

yes

characteristic

100

C₂³

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

146

—

107

C₂×C₄

—

146

—

108

C₂×C₄

C₄×#64408

yes

—

109

C₂×C₄

C₂²×#64408

yes

characteristic

110

C₈

—

111

C₈

—

112

C₈

—

113

C₈

C₄×#64408

yes

—

114

C₈

C₄×#64408

yes

—

115

C₂²

—

116

C₂²

—

117

C₂²

C₂×C₄×#64408

yes

characteristic

118

C₄

—

119

C₄

—

120

C₄

—

146

—

121

C₄

—

146

—

122

C₄

C₂×C₄×#64408

yes

characteristic

123

C₄

C₂×C₄×#64408

yes

characteristic

124

C₂

—

125

C₂

C₄²×#64408

yes

characteristic

126

C₂

#17989550

yes

—

	subgroup	G/H
center	C₂×C₈	C₂×#64408
commutator	C₂×C₇₃	C₄³
Frattini	C₂×C₄	C₂²×#64408
Fitting	C₄×C₈×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₄²
hypercenter	C₄×C₈	#64408
hypocenter	C₇₃	#1726
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈

subgroup

G/H

center

C₂×C₈

C₂×#64408

commutator

C₂×C₇₃

C₄³

Frattini

C₂×C₄

C₂²×#64408

Fitting

C₄×C₈×C₇₃

C₄

socle

C₂²×C₇₃

C₂×C₄²

C₄×C₈

C₇₃

G ▷ C₂×C₇₃ ▷ C₇₃

C₁ ◁ C₂×C₈ ◁ C₄×C₈

N	H ≅ G/N	type
8. #14556646	C₄	semidirect
9. #14556645	C₄	semidirect
10. C₈×#64408	C₄	semidirect
15. C₄×#10596831	C₄	semidirect
16. C₈×Dic₇₃	C₄	semidirect
17. C₈×Dic₇₃	C₄	semidirect
18. C₄×C₈×C₇₃	C₄	semidirect
64. C₇₃	#1726	semidirect
81. C₄×C₈	#64408	semidirect

H ≅ G/N

type

8. #14556646

C₄

semidirect

9. #14556645

C₄

semidirect

10. C₈×#64408

C₄

semidirect

15. C₄×#10596831

C₄

semidirect

16. C₈×Dic₇₃

C₄

semidirect

17. C₈×Dic₇₃

C₄

semidirect

18. C₄×C₈×C₇₃

C₄

semidirect

64. C₇₃

#1726

semidirect

81. C₄×C₈

#64408

semidirect

Subgroups — #22625587

Conjugacy classes of subgroups

Complements