Group #22627182 — subgroups

Subgroups — #22627182

Order 9344.

368 conjugacy classes of subgroups; only the 189 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 189 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	#17989709	C₂	1	2	yes	maximal, complemented
2	#17989708	C₂	1	6	yes	maximal, complemented
3	#17989706	C₂	1	3	yes	maximal, complemented
4	C₂×#14556686	C₂	1	3	yes	maximal, complemented
5	D₇₃⋊#131	C₂	1	1	yes	maximal, characteristic
6	#14556688	C₂²	1	6	yes	complemented
7	#14556687	C₂²	1	6	yes	complemented
8	#14556686	C₂²	1	1	yes	characteristic
9	#14556686	C₂²	1	3	yes	—
10	#14556686	C₂²	1	6	yes	complemented
11	C₂×#11924040	C₂²	1	6	yes	complemented
12	#14556679	C₄	1	1	yes	characteristic
13	#14556679	C₂²	1	1	yes	characteristic
14	#14556678	C₄	1	3	yes	—
15	#14556678	C₂²	1	3	yes	—
16	D₇₃⋊M₁₆	C₄	1	3	yes	—
17	C₂×#11924036	C₂²	1	3	yes	—
18	#41×D₇₃	C₄	1	1	yes	characteristic
19	#11924040	C₂³	1	2	yes	—
20	#11924040	C₂³	1	6	yes	—
21	#11924038	C₂×C₄	1	3	yes	—
22	#11924038	C₂×C₄	1	3	yes	—
23	#11924037	C₂×C₄	1	6	yes	—
24	#11924036	C₂×C₄	1	3	yes	—
25	#11924036	C₂×C₄	1	3	yes	—
26	#11924036	C₂³	1	1	yes	characteristic
27	#11924036	C₂³	1	3	yes	—
28	C₂×#10596833	C₂×C₄	1	3	yes	—
29	C₂×#10596833	C₂³	1	3	yes	—
30	#11924029	C₂×C₄	1	1	yes	characteristic
31	#11924028	C₈	1	3	yes	—
32	#11924027	C₂×C₄	1	3	yes	—
33	Q₈×D₇₃	C₈	1	1	yes	characteristic
34	D₄×D₇₃	C₈	1	3	yes	—
35	C₂×C₄×D₇₃	C₂×C₄	1	3	yes	—
36	#41×C₇₃	C₈	1	1	yes	characteristic
37	C₂²×D₇₃	C₂×C₈	1	3	yes	—
38	Q₈×C₇₃	C₂×C₈	1	1	yes	characteristic
39	D₄×C₇₃	C₂×C₈	1	3	yes	—
40	C₂×C₄×C₇₃	C₂×C₈	1	3	yes	—
41	C₂²⋊D₇₃	C₂×C₈	1	6	yes	—
42	C₂×Dic₇₃	C₂²×C₄	1	3	yes	—
43	D₂₉₂	C₂×C₈	1	3	yes	—
44	C₄×D₇₃	C₂×C₈	1	3	yes	—
45	C₄×D₇₃	C₂×C₈	1	3	yes	—
46	C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
47	C₄×D₇₃	C₂²×C₄	1	3	yes	—
48	Dic₁₄₆	C₂×C₈	1	3	yes	—
49	#10596833	C₂²×C₄	1	1	yes	characteristic
50	#10596833	C₂²×C₄	1	3	yes	—
51	#10596833	C₂²×C₄	1	3	yes	—
52	#10596833	C₂⁴	1	1	yes	characteristic
53	C₂²×C₇₃	C₂²×C₈	1	3	yes	—
54	C₂×D₇₃	—	2	6	no	—
55	C₂×D₇₃	C₂²×C₈	1	3	yes	—
56	C₂×D₇₃	C₂²×C₈	1	1	yes	characteristic
57	C₄×C₇₃	C₂²×C₈	1	3	yes	—
58	C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
59	Dic₇₃	C₂²×C₈	1	3	yes	—
60	Dic₇₃	C₂³×C₄	1	1	yes	characteristic
61	C₂×C₇₃	—	2	3	no	—
62	C₂×C₇₃	C₂³×C₈	1	1	yes	characteristic
63	D₇₃	—	2	3	no	—
64	D₇₃	#504	1	2	yes	complemented
65	C₂×#504	—	73	1	no	maximal, Sylow
66	C₇₃	C₂×#504	1	1	yes	characteristic, complemented, Sylow
67	C₂×#131	—	73	1	no	—
68	#504	—	73	6	no	—
69	#504	—	73	2	no	—
70	C₂×M₃₂	—	73	3	no	—
71	C₂²×C₁₆	—	73	3	no	—
72	C₂×#41	—	73	1	no	—
73	#131	—	73	3	no	—
74	#131	—	73	3	no	—
75	#131	—	73	1	no	—
76	#131	—	73	1	no	—
77	C₂×M₁₆	—	73	3	no	—
78	C₂²×C₈	—	73	3	no	—
79	M₃₂	—	73	6	no	—
80	M₃₂	—	73	6	no	—
81	C₂×C₁₆	—	73	6	no	—
82	C₂×C₁₆	—	73	1	no	—
83	C₂×C₁₆	—	73	3	no	—
84	C₂×C₁₆	—	73	6	no	—
85	#41	—	73	1	no	—
86	#41	—	73	3	no	—
87	#41	—	73	3	no	—
88	#41	#10596842	1	1	yes	characteristic
89	C₂×Q₈	—	73	1	no	—
90	C₂×D₄	—	73	3	no	—
91	C₂²×C₄	—	73	3	no	—
92	M₁₆	—	73	6	no	—
93	M₁₆	—	73	3	no	—
94	M₁₆	—	73	3	no	—
95	C₂×C₈	—	73	3	no	—
96	C₂×C₈	—	73	3	no	—
97	C₂×C₈	—	73	3	no	—
98	C₂×C₈	—	73	3	no	—
99	C₂×C₈	—	73	1	no	—
100	C₂×C₈	—	73	3	no	—
101	C₁₆	—	73	2	no	—
102	C₁₆	—	73	6	no	—
103	C₂³	—	73	3	no	—
104	Q₈	—	73	3	no	—
105	Q₈	C₂×#10596842	1	1	yes	characteristic
106	D₄	—	73	6	no	—
107	D₄	—	73	3	no	—
108	D₄	C₂×#10596842	1	3	yes	—
109	C₂×C₄	—	73	3	no	—
110	C₂×C₄	—	73	3	no	—
111	C₂×C₄	—	73	3	no	—
112	C₂×C₄	—	73	1	no	—
113	C₂×C₄	—	73	3	no	—
114	C₂×C₄	C₂×#10596842	1	3	yes	—
115	C₈	—	73	1	no	—
116	C₈	—	73	1	no	—
117	C₈	—	73	3	no	—
118	C₈	—	73	3	no	—
119	C₂²	—	73	1	no	—
120	C₂²	—	73	3	no	—
121	C₂²	—	146	6	no	—
122	C₂²	C₂²×#10596842	1	3	yes	—
123	C₄	—	73	1	no	—
124	C₄	—	73	3	no	—
125	C₄	C₂²×#10596842	1	3	yes	—
126	C₄	C₂²×#10596842	1	1	yes	characteristic
127	C₂	—	2	3	no	—
128	C₂	—	73	2	no	—
129	C₂	—	146	3	no	—
130	C₂	C₂³×#10596842	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989709

C₂

yes

maximal, complemented

#17989708

C₂

yes

maximal, complemented

#17989706

C₂

yes

maximal, complemented

C₂×#14556686

C₂

yes

maximal, complemented

D₇₃⋊#131

C₂

yes

maximal, characteristic

#14556688

C₂²

yes

complemented

#14556687

C₂²

yes

complemented

#14556686

C₂²

yes

characteristic

#14556686

C₂²

yes

—

#14556686

C₂²

yes

complemented

C₂×#11924040

C₂²

yes

complemented

#14556679

C₄

yes

characteristic

#14556679

C₂²

yes

characteristic

#14556678

C₄

yes

—

#14556678

C₂²

yes

—

D₇₃⋊M₁₆

C₄

yes

—

C₂×#11924036

C₂²

yes

—

#41×D₇₃

C₄

yes

characteristic

#11924040

C₂³

yes

—

#11924040

C₂³

yes

—

#11924038

C₂×C₄

yes

—

#11924038

C₂×C₄

yes

—

#11924037

C₂×C₄

yes

—

#11924036

C₂×C₄

yes

—

#11924036

C₂×C₄

yes

—

#11924036

C₂³

yes

characteristic

#11924036

C₂³

yes

—

C₂×#10596833

C₂×C₄

yes

—

C₂×#10596833

C₂³

yes

—

#11924029

C₂×C₄

yes

characteristic

#11924028

C₈

yes

—

#11924027

C₂×C₄

yes

—

Q₈×D₇₃

C₈

yes

characteristic

D₄×D₇₃

C₈

yes

—

C₂×C₄×D₇₃

C₂×C₄

yes

—

#41×C₇₃

C₈

yes

characteristic

C₂²×D₇₃

C₂×C₈

yes

—

Q₈×C₇₃

C₂×C₈

yes

characteristic

D₄×C₇₃

C₂×C₈

yes

—

C₂×C₄×C₇₃

C₂×C₈

yes

—

C₂²⋊D₇₃

C₂×C₈

yes

—

C₂×Dic₇₃

C₂²×C₄

yes

—

D₂₉₂

C₂×C₈

yes

—

C₄×D₇₃

C₂×C₈

yes

—

C₄×D₇₃

C₂×C₈

yes

—

C₄×D₇₃

C₂²×C₄

yes

characteristic

C₄×D₇₃

C₂²×C₄

yes

—

Dic₁₄₆

C₂×C₈

yes

—

#10596833

C₂²×C₄

yes

characteristic

#10596833

C₂²×C₄

yes

—

#10596833

C₂²×C₄

yes

—

#10596833

C₂⁴

yes

characteristic

C₂²×C₇₃

C₂²×C₈

yes

—

C₂×D₇₃

—

C₂×D₇₃

C₂²×C₈

yes

—

C₂×D₇₃

C₂²×C₈

yes

characteristic

C₄×C₇₃

C₂²×C₈

yes

—

C₄×C₇₃

C₂²×C₈

yes

characteristic

Dic₇₃

C₂²×C₈

yes

—

Dic₇₃

C₂³×C₄

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

C₂³×C₈

yes

characteristic

D₇₃

—

D₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂×#131

—

#504

—

#504

—

C₂×M₃₂

—

C₂²×C₁₆

—

C₂×#41

—

—

—

—

—

C₂×M₁₆

—

C₂²×C₈

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

—

—

—

yes

C₂×Q₈

—

C₂×D₄

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₁₆

—

102

C₁₆

—

103

C₂³

—

104

Q₈

—

105

Q₈

C₂×#10596842

yes

characteristic

106

D₄

—

107

D₄

—

108

D₄

C₂×#10596842

yes

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

C₂×#10596842

yes

—

115

C₈

—

116

C₈

—

117

C₈

—

118

C₈

—

119

C₂²

—

120

C₂²

—

121

C₂²

—

146

—

122

C₂²

C₂²×#10596842

yes

—

123

C₄

—

124

C₄

—

125

C₄

C₂²×#10596842

yes

—

126

C₄

C₂²×#10596842

yes

characteristic

127

C₂

—

128

C₂

—

129

C₂

—

146

—

130

C₂

C₂³×#10596842

yes

characteristic

	subgroup	G/H
center	C₄	C₂²×#10596842
commutator, socle	C₂×C₇₃	C₂³×C₈
Frattini	C₂	C₂³×#10596842
Fitting	#41×C₇₃	C₈
hypercenter	#41	#10596842
hypocenter	C₇₃	C₂×#504
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ #41

subgroup

G/H

center

C₄

C₂²×#10596842

commutator, socle

C₂×C₇₃

C₂³×C₈

Frattini

C₂

C₂³×#10596842

Fitting

#41×C₇₃

C₈

C₇₃

G ▷ C₂×C₇₃ ▷ C₇₃

C₁ ◁ C₄ ◁ #41

N	H ≅ G/N	type
1. #17989709	C₂	semidirect
2. #17989708	C₂	semidirect
3. #17989706	C₂	semidirect
4. C₂×#14556686	C₂	semidirect
6. #14556688	C₂²	semidirect
7. #14556687	C₂²	semidirect
10. #14556686	C₂²	semidirect
11. C₂×#11924040	C₂²	semidirect
64. D₇₃	#504	semidirect
66. C₇₃	C₂×#504	semidirect

H ≅ G/N

type

1. #17989709

C₂

semidirect

2. #17989708

C₂

semidirect

3. #17989706

C₂

semidirect

4. C₂×#14556686

C₂

semidirect

6. #14556688

C₂²

semidirect

7. #14556687

C₂²

semidirect

10. #14556686

C₂²

semidirect

11. C₂×#11924040

C₂²

semidirect

64. D₇₃

#504

semidirect

66. C₇₃

C₂×#504

semidirect

Subgroups — #22627182

Conjugacy classes of subgroups

Complements