Group #22627040 — subgroups

Subgroups — #22627040

Order 9344.

212 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 97 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	#17989700	C₂	1	2	yes	maximal
2	#17989671	C₂	1	2	yes	maximal, complemented
3	C₈×#10596842	C₂	1	2	yes	maximal, complemented
4	C₂×C₈×#64408	C₂	1	1	yes	maximal, characteristic
5	C₄⋊#10596842	C₄	1	4	yes	—
6	C₂²⋊#10596842	C₄	1	4	yes	—
7	C₄×#10596842	C₂²	1	4	yes	—
8	C₂×#11924036	C₄	1	1	yes	characteristic
9	C₂×C₄×#64408	C₂²	1	1	yes	characteristic
10	C₈×#64408	C₄	1	1	yes	characteristic
11	C₈×#64408	C₄	1	1	yes	characteristic
12	C₈×#64408	C₂²	1	1	yes	characteristic
13	C₈×#64408	C₂²	1	1	yes	characteristic
14	C₂×C₈×D₇₃	C₄	1	1	yes	characteristic
15	C₂×#10596842	C₂×C₄	1	8	yes	—
16	C₂²×#64408	C₂×C₄	1	2	yes	—
17	#11924036	C₈	1	2	yes	complemented
18	#11924036	C₂×C₄	1	1	yes	characteristic
19	#11924036	C₂×C₄	1	1	yes	characteristic
20	C₂×#10596833	C₈	1	2	yes	complemented
21	C₄×#64408	C₂×C₄	1	2	yes	—
22	C₄×#64408	C₂×C₄	1	1	yes	characteristic
23	C₄×#64408	C₂³	1	1	yes	characteristic
24	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
25	C₂×#10596831	C₈	1	1	yes	characteristic, complemented
26	C₈×D₇₃	C₈	1	1	yes	characteristic, complemented
27	C₈×D₇₃	C₈	1	1	yes	characteristic, complemented
28	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
29	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
30	C₂×C₈×C₇₃	C₈	1	1	yes	characteristic, complemented
31	C₂²×D₇₃	C₄²	1	1	yes	characteristic
32	C₂×#64408	—	2	4	no	—
33	C₂×#64408	C₄²	1	2	yes	—
34	C₂×#64408	C₂²×C₄	1	2	yes	—
35	#10596842	—	2	8	no	—
36	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
37	C₂×Dic₇₃	C₂×C₈	1	1	yes	characteristic
38	C₄×D₇₃	C₄²	1	1	yes	characteristic
39	C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
40	C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
41	C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
42	#10596833	C₂×C₈	1	2	yes	—
43	#10596833	C₂×C₈	1	2	yes	—
44	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
45	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
46	#10596831	C₂×C₈	1	1	yes	characteristic
47	#10596831	C₂×C₈	1	1	yes	characteristic
48	C₂²×C₇₃	C₄×C₈	1	1	yes	characteristic
49	C₂×D₇₃	—	2	2	no	—
50	C₂×D₇₃	C₄×C₈	1	1	yes	characteristic
51	C₂×D₇₃	C₂×C₄²	1	1	yes	characteristic
52	#64408	—	2	2	no	—
53	#64408	#131	1	4	yes	—
54	C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
55	C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
56	Dic₇₃	C₄×C₈	1	1	yes	characteristic
57	Dic₇₃	C₂²×C₈	1	1	yes	characteristic
58	C₂×C₇₃	—	2	1	no	—
59	C₂×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
60	D₇₃	—	2	1	no	—
61	D₇₃	#405	1	2	yes	—
62	#1450	—	73	1	no	maximal, Sylow
63	C₇₃	#1450	1	1	yes	characteristic, complemented, Sylow
64	#431	—	73	2	no	—
65	C₂×C₄×C₈	—	73	1	no	—
66	#322	—	73	2	no	—
67	C₈²	—	73	2	no	—
68	C₂²×C₈	—	73	1	no	—
69	C₂²×C₈	—	73	1	no	—
70	C₂×C₄²	—	73	1	no	—
71	C₄⋊C₈	—	73	4	no	—
72	C₂²⋊C₈	—	73	4	no	—
73	C₄×C₈	—	73	4	no	—
74	C₄×C₈	—	73	1	no	—
75	C₄×C₈	—	73	1	no	—
76	C₄×C₈	—	73	1	no	—
77	C₄×C₈	—	73	1	no	—
78	C₂²×C₄	—	73	1	no	—
79	C₂²×C₄	—	73	2	no	—
80	C₂×C₈	—	73	2	no	—
81	C₂×C₈	—	73	2	no	—
82	C₂×C₈	—	73	1	no	—
83	C₂×C₈	—	73	1	no	—
84	C₂×C₈	—	73	1	no	—
85	C₂×C₈	—	73	1	no	—
86	C₂×C₈	—	73	1	no	—
87	C₂×C₈	—	73	1	no	—
88	C₂×C₈	—	73	1	no	—
89	C₂×C₈	—	73	8	no	—
90	C₂×C₈	#10596842	1	1	yes	characteristic, complemented
91	C₄²	—	73	1	no	—
92	C₄²	—	73	2	no	—
93	C₄²	—	73	1	no	—
94	C₂³	—	73	1	no	—
95	C₂×C₄	—	73	2	no	—
96	C₂×C₄	—	73	1	no	—
97	C₂×C₄	—	73	1	no	—
98	C₂×C₄	—	73	1	no	—
99	C₂×C₄	—	73	1	no	—
100	C₂×C₄	—	73	1	no	—
101	C₂×C₄	—	73	2	no	—
102	C₂×C₄	—	146	4	no	—
103	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
104	C₈	—	73	2	no	—
105	C₈	—	73	2	no	—
106	C₈	—	73	1	no	—
107	C₈	—	73	1	no	—
108	C₈	—	146	8	no	—
109	C₈	C₂×#10596842	1	1	yes	characteristic
110	C₈	C₂×#10596842	1	1	yes	characteristic
111	C₂²	—	73	1	no	—
112	C₂²	—	73	1	no	—
113	C₂²	—	146	2	no	—
114	C₂²	C₄×#10596842	1	1	yes	characteristic
115	C₄	—	73	4	no	—
116	C₄	—	73	1	no	—
117	C₄	—	73	1	no	—
118	C₄	—	146	2	no	—
119	C₄	C₄×#10596842	1	1	yes	characteristic
120	C₄	C₂²×#10596842	1	1	yes	characteristic
121	C₂	—	2	1	no	—
122	C₂	—	73	2	no	—
123	C₂	—	146	1	no	—
124	C₂	C₂×C₄×#10596842	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989700

C₂

yes

maximal

#17989671

C₂

yes

maximal, complemented

C₈×#10596842

C₂

yes

maximal, complemented

C₂×C₈×#64408

C₂

yes

maximal, characteristic

C₄⋊#10596842

C₄

yes

—

C₂²⋊#10596842

C₄

yes

—

C₄×#10596842

C₂²

yes

—

C₂×#11924036

C₄

yes

characteristic

C₂×C₄×#64408

C₂²

yes

characteristic

C₈×#64408

C₄

yes

characteristic

C₈×#64408

C₄

yes

characteristic

C₈×#64408

C₂²

yes

characteristic

C₈×#64408

C₂²

yes

characteristic

C₂×C₈×D₇₃

C₄

yes

characteristic

C₂×#10596842

C₂×C₄

yes

—

C₂²×#64408

C₂×C₄

yes

—

#11924036

C₈

yes

complemented

#11924036

C₂×C₄

yes

characteristic

#11924036

C₂×C₄

yes

characteristic

C₂×#10596833

C₈

yes

complemented

C₄×#64408

C₂×C₄

yes

—

C₄×#64408

C₂×C₄

yes

characteristic

C₄×#64408

C₂³

yes

characteristic

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₂×#10596831

C₈

yes

characteristic, complemented

C₈×D₇₃

C₈

yes

characteristic, complemented

C₈×D₇₃

C₈

yes

characteristic, complemented

C₈×D₇₃

C₂×C₄

yes

characteristic

C₈×D₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₈

yes

characteristic, complemented

C₂²×D₇₃

C₄²

yes

characteristic

C₂×#64408

—

C₂×#64408

C₄²

yes

—

C₂×#64408

C₂²×C₄

yes

—

#10596842

—

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

C₂×C₈

yes

characteristic

C₄×D₇₃

C₄²

yes

characteristic

C₄×D₇₃

C₂×C₈

yes

characteristic

C₄×D₇₃

C₂×C₈

yes

characteristic

C₄×D₇₃

C₂²×C₄

yes

characteristic

#10596833

C₂×C₈

yes

—

#10596833

C₂×C₈

yes

—

C₈×C₇₃

C₂×C₈

yes

characteristic

C₈×C₇₃

C₂×C₈

yes

characteristic

#10596831

C₂×C₈

yes

characteristic

#10596831

C₂×C₈

yes

characteristic

C₂²×C₇₃

C₄×C₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

C₄×C₈

yes

characteristic

C₂×D₇₃

C₂×C₄²

yes

—

yes

—

C₄×C₇₃

C₄×C₈

yes

characteristic

C₄×C₇₃

C₂²×C₈

yes

characteristic

Dic₇₃

C₄×C₈

yes

characteristic

Dic₇₃

C₂²×C₈

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

C₂×C₄×C₈

yes

characteristic

D₇₃

—

D₇₃

#405

yes

—

#1450

—

maximal, Sylow

C₇₃

#1450

yes

characteristic, complemented, Sylow

#431

—

C₂×C₄×C₈

—

#322

—

C₈²

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

#10596842

yes

characteristic, complemented

C₄²

—

C₄²

—

C₄²

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

146

—

103

C₂×C₄

C₂×#10596842

yes

characteristic

104

C₈

—

105

C₈

—

106

C₈

—

107

C₈

—

108

C₈

—

146

—

109

C₈

C₂×#10596842

yes

characteristic

110

C₈

C₂×#10596842

yes

characteristic

111

C₂²

—

112

C₂²

—

113

C₂²

—

146

—

114

C₂²

C₄×#10596842

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

146

—

119

C₄

C₄×#10596842

yes

characteristic

120

C₄

C₂²×#10596842

yes

characteristic

121

C₂

—

122

C₂

—

123

C₂

—

146

—

124

C₂

C₂×C₄×#10596842

yes

characteristic

	subgroup	G/H
center	C₈	C₂×#10596842
commutator, socle	C₂×C₇₃	C₂×C₄×C₈
Frattini	C₄	C₂²×#10596842
Fitting	C₂×C₈×C₇₃	C₈
hypercenter	C₂×C₈	#10596842
hypocenter	C₇₃	#1450
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈

subgroup

G/H

center

C₈

C₂×#10596842

commutator, socle

C₂×C₇₃

C₂×C₄×C₈

Frattini

C₄

C₂²×#10596842

Fitting

C₂×C₈×C₇₃

C₈

C₂×C₈

C₇₃

G ▷ C₂×C₇₃ ▷ C₇₃

C₁ ◁ C₈ ◁ C₂×C₈

N	H ≅ G/N	type
2. #17989671	C₂	semidirect
3. C₈×#10596842	C₂	semidirect
17. #11924036	C₈	semidirect
20. C₂×#10596833	C₈	semidirect
25. C₂×#10596831	C₈	semidirect
26. C₈×D₇₃	C₈	semidirect
27. C₈×D₇₃	C₈	semidirect
30. C₂×C₈×C₇₃	C₈	semidirect
63. C₇₃	#1450	semidirect
90. C₂×C₈	#10596842	semidirect

H ≅ G/N

type

2. #17989671

C₂

semidirect

3. C₈×#10596842

C₂

semidirect

17. #11924036

C₈

semidirect

20. C₂×#10596833

C₈

semidirect

25. C₂×#10596831

C₈

semidirect

26. C₈×D₇₃

C₈

semidirect

27. C₈×D₇₃

C₈

semidirect

30. C₂×C₈×C₇₃

C₈

semidirect

63. C₇₃

#1450

semidirect

90. C₂×C₈

#10596842

semidirect

Subgroups — #22627040

Conjugacy classes of subgroups

Complements