Group #22626290 — subgroups

Subgroups — #22626290

Order 9344.

160 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 78 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	#17989508	C₂	1	2	yes	maximal, complemented
2	#17989482	C₂	1	2	yes	maximal
3	C₄×#11924031	C₂	1	2	yes	maximal, complemented
4	C₄×C₈×D₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#11924031	C₂²	1	4	yes	—
6	C₂×C₈×D₇₃	C₄	1	1	yes	characteristic
7	C₂×C₈×D₇₃	C₂²	1	1	yes	characteristic
8	C₄²×D₇₃	C₄	1	1	yes	characteristic
9	C₄×#10596831	C₂²	1	1	yes	characteristic
10	C₈×Dic₇₃	C₄	1	1	yes	characteristic
11	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₇₃	C₄	1	1	yes	characteristic
13	#11924031	—	2	4	no	—
14	C₂×C₄×D₇₃	C₈	1	1	yes	characteristic
15	C₂×C₄×D₇₃	C₈	1	1	yes	characteristic
16	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
17	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
18	C₂×#10596831	C₂³	1	1	yes	characteristic
19	C₈×D₇₃	—	2	2	no	—
20	C₈×D₇₃	—	2	2	no	—
21	C₄×Dic₇₃	C₈	1	1	yes	characteristic
22	C₄×Dic₇₃	C₈	1	1	yes	characteristic
23	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
26	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
27	C₂²×D₇₃	C₂×C₈	1	1	yes	characteristic
28	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₇₃	C₂×C₈	1	1	yes	characteristic
32	C₂×Dic₇₃	C₂×C₈	1	1	yes	characteristic
33	C₂×Dic₇₃	C₂×C₈	1	1	yes	characteristic
34	C₄×D₇₃	—	2	2	no	—
35	C₄×D₇₃	—	2	1	no	—
36	C₄×D₇₃	—	2	1	no	—
37	C₄×D₇₃	C₁₆	1	4	yes	complemented
38	C₈×C₇₃	—	2	1	no	—
39	C₈×C₇₃	—	2	1	no	—
40	#10596831	M₁₆	1	2	yes	—
41	#10596831	#41	1	2	yes	—
42	C₂²×C₇₃	C₂²×C₈	1	1	yes	characteristic
43	C₂×D₇₃	—	2	1	no	—
44	C₂×D₇₃	—	2	1	no	—
45	C₂×D₇₃	C₂×C₁₆	1	2	yes	—
46	C₄×C₇₃	C₂×C₁₆	1	2	yes	—
47	C₄×C₇₃	M₃₂	1	2	yes	—
48	C₄×C₇₃	#117	1	1	yes	characteristic
49	C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
50	Dic₇₃	—	2	1	no	—
51	Dic₇₃	—	2	1	no	—
52	Dic₇₃	C₂×C₁₆	1	2	yes	—
53	C₂×C₇₃	#431	1	1	yes	characteristic
54	C₂×C₇₃	C₂²×C₁₆	1	1	yes	characteristic
55	C₂×C₇₃	C₂×M₃₂	1	1	yes	characteristic
56	D₇₃	—	2	2	no	—
57	#2162	—	73	1	no	maximal, Sylow
58	C₇₃	#2162	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₄×C₈	—	73	1	no	—
60	C₄⋊C₁₆	—	73	2	no	—
61	C₂²⋊C₁₆	—	73	2	no	—
62	C₄×C₁₆	—	73	2	no	—
63	C₂²×C₈	—	73	1	no	—
64	C₂²×C₈	—	73	1	no	—
65	C₂×C₄²	—	73	1	no	—
66	C₂×C₁₆	—	73	4	no	—
67	C₄×C₈	—	73	1	no	—
68	C₄×C₈	—	73	1	no	—
69	C₄×C₈	—	73	1	no	—
70	C₄×C₈	#64408	1	1	yes	characteristic
71	C₂²×C₄	—	73	1	no	—
72	C₂²×C₄	—	73	1	no	—
73	C₂²×C₄	—	73	1	no	—
74	C₂×C₈	—	73	1	no	—
75	C₂×C₈	—	73	1	no	—
76	C₂×C₈	—	146	2	no	—
77	C₂×C₈	—	146	2	no	—
78	C₂×C₈	C₂×#64408	1	1	yes	characteristic
79	C₂×C₈	C₂×#64408	1	1	yes	characteristic
80	C₄²	—	73	1	no	—
81	C₄²	—	73	1	no	—
82	C₄²	—	73	1	no	—
83	C₄²	C₂×#64408	1	1	yes	characteristic
84	C₁₆	—	146	4	no	—
85	C₂³	—	73	1	no	—
86	C₂×C₄	—	73	1	no	—
87	C₂×C₄	—	73	4	no	—
88	C₂×C₄	—	73	1	no	—
89	C₂×C₄	—	73	1	no	—
90	C₂×C₄	—	146	1	no	—
91	C₂×C₄	—	146	2	no	—
92	C₂×C₄	—	146	1	no	—
93	C₂×C₄	#11924036	1	1	yes	characteristic
94	C₂×C₄	#11924036	1	1	yes	characteristic
95	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
96	C₈	—	2	1	no	—
97	C₈	—	2	1	no	—
98	C₈	—	73	2	no	—
99	C₈	—	73	2	no	—
100	C₂²	—	73	2	no	—
101	C₂²	—	146	1	no	—
102	C₂²	—	146	1	no	—
103	C₂²	C₂×#11924036	1	1	yes	characteristic
104	C₄	—	73	2	no	—
105	C₄	—	146	1	no	—
106	C₄	—	146	1	no	—
107	C₄	#14556664	1	2	yes	—
108	C₄	#14556666	1	2	yes	—
109	C₄	#14556670	1	1	yes	characteristic
110	C₄	D₇₃⋊M₁₆	1	1	yes	characteristic
111	C₂	—	146	2	no	—
112	C₂	#17989605	1	1	yes	characteristic
113	C₂	C₂×#14556664	1	1	yes	characteristic
114	C₂	C₂×#14556666	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989508

C₂

yes

maximal, complemented

#17989482

C₂

yes

maximal

C₄×#11924031

C₂

yes

maximal, complemented

C₄×C₈×D₇₃

C₂

yes

maximal, characteristic

C₂×#11924031

C₂²

yes

—

C₂×C₈×D₇₃

C₄

yes

characteristic

C₂×C₈×D₇₃

C₂²

yes

characteristic

C₄²×D₇₃

C₄

yes

characteristic

C₄×#10596831

C₂²

yes

characteristic

C₈×Dic₇₃

C₄

yes

characteristic

C₈×Dic₇₃

C₂²

yes

characteristic

C₄×C₈×C₇₃

C₄

yes

characteristic

#11924031

—

C₂×C₄×D₇₃

C₈

yes

characteristic

C₂×C₄×D₇₃

C₈

yes

characteristic

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₂×#10596831

C₂×C₄

yes

characteristic

C₂×#10596831

C₂³

yes

characteristic

C₈×D₇₃

—

C₈×D₇₃

—

C₄×Dic₇₃

C₈

yes

characteristic

C₄×Dic₇₃

C₈

yes

characteristic

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₂²×D₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

C₂×C₈

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

C₁₆

yes

complemented

C₈×C₇₃

—

C₈×C₇₃

—

#10596831

M₁₆

yes

—

#10596831

#41

yes

—

C₂²×C₇₃

C₂²×C₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

C₂×C₁₆

yes

—

C₄×C₇₃

C₂×C₁₆

yes

—

C₄×C₇₃

M₃₂

yes

—

C₄×C₇₃

#117

yes

characteristic

C₄×C₇₃

C₂×M₁₆

yes

characteristic

Dic₇₃

—

Dic₇₃

—

Dic₇₃

C₂×C₁₆

yes

—

C₂×C₇₃

#431

yes

characteristic

C₂×C₇₃

C₂²×C₁₆

yes

characteristic

C₂×C₇₃

C₂×M₃₂

yes

characteristic

D₇₃

—

#2162

—

maximal, Sylow

C₇₃

#2162

yes

characteristic, complemented, Sylow

C₂×C₄×C₈

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

C₄×C₁₆

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₁₆

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#64408

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

yes

C₂×C₈

yes

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#64408

yes

characteristic

C₁₆

—

146

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂²×#64408

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

100

C₂²

—

101

C₂²

—

146

—

102

C₂²

—

146

—

103

C₂²

C₂×#11924036

yes

characteristic

104

C₄

—

105

C₄

—

146

—

106

C₄

—

146

—

107

C₄

#14556664

yes

—

108

C₄

#14556666

yes

—

109

C₄

#14556670

yes

characteristic

110

C₄

D₇₃⋊M₁₆

yes

characteristic

111

C₂

—

146

—

112

C₂

#17989605

yes

characteristic

113

C₂

C₂×#14556664

yes

characteristic

114

C₂

C₂×#14556666

yes

characteristic

	subgroup	G/H
center	C₄²	C₂×#64408
commutator	C₂×C₇₃	C₂²×C₁₆
Frattini	C₂×C₄	C₂²×#64408
Fitting	C₄×C₈×C₇₃	C₄
socle	C₂²×C₇₃	C₂²×C₈
hypercenter	C₄×C₈	#64408
hypocenter	C₇₃	#2162
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄² ◁ C₄×C₈

subgroup

G/H

center

C₄²

C₂×#64408

commutator

C₂×C₇₃

C₂²×C₁₆

Frattini

C₂×C₄

C₂²×#64408

Fitting

C₄×C₈×C₇₃

C₄

socle

C₂²×C₇₃

C₂²×C₈

C₄×C₈

C₇₃

G ▷ C₂×C₇₃ ▷ C₇₃

C₁ ◁ C₄² ◁ C₄×C₈

N	H ≅ G/N	type
1. #17989508	C₂	semidirect
3. C₄×#11924031	C₂	semidirect
37. C₄×D₇₃	C₁₆	semidirect
58. C₇₃	#2162	semidirect

H ≅ G/N

type

1. #17989508

C₂

semidirect

3. C₄×#11924031

C₂

semidirect

37. C₄×D₇₃

C₁₆

semidirect

58. C₇₃

#2162

semidirect

Subgroups — #22626290

Conjugacy classes of subgroups

Complements