Group #22626151 — subgroups

Subgroups — #22626151

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	C₂×#14556666	C₂	1	1	yes	maximal, characteristic
2	#17989550	C₂	1	1	yes	maximal, characteristic
3	#17989478	C₂	1	2	yes	maximal, complemented
4	#17989477	C₂	1	2	yes	maximal, complemented
5	M₃₂×D₇₃	C₂	1	1	yes	maximal, characteristic
6	D₇₃⋊M₁₆	C₄	1	1	yes	characteristic
7	#14556670	C₄	1	1	yes	characteristic
8	#14556666	C₄	1	2	yes	complemented
9	#14556666	C₂²	1	1	yes	characteristic
10	#14556666	C₂²	1	1	yes	characteristic
11	C₂×#11924031	C₄	1	2	yes	complemented
12	#14556645	C₂²	1	2	yes	—
13	C₈×#64408	C₄	1	2	yes	—
14	C₂×C₈×D₇₃	C₂²	1	1	yes	characteristic
15	#14556531	C₄	1	1	yes	characteristic, complemented
16	#14556530	C₂²	1	2	yes	—
17	C₁₆×D₇₃	C₄	1	2	yes	complemented
18	M₃₂×C₇₃	C₄	1	1	yes	characteristic, complemented
19	#11924038	—	2	1	no	—
20	#11924037	—	2	1	no	—
21	#11924036	C₂×C₄	1	2	yes	—
22	C₄⋊#64408	—	2	1	no	—
23	C₂²⋊#64408	—	2	1	no	—
24	C₄×#64408	C₂×C₄	1	2	yes	—
25	#11924031	C₂×C₄	1	2	yes	—
26	#11924031	C₂×C₄	1	2	yes	—
27	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
28	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
29	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
30	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
31	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
32	C₈×D₇₃	C₂³	1	1	yes	characteristic
33	#11924003	C₂×C₄	1	2	yes	—
34	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
35	C₁₆×C₇₃	C₂×C₄	1	2	yes	—
36	C₂²×D₇₃	M₁₆	1	1	yes	characteristic
37	C₂×#64408	—	2	2	no	—
38	C₂×C₄×C₇₃	C₄²	1	1	yes	characteristic
39	C₂×Dic₇₃	M₁₆	1	1	yes	characteristic
40	C₄×D₇₃	C₄²	1	1	yes	characteristic
41	C₄×D₇₃	M₁₆	1	1	yes	characteristic
42	C₄×D₇₃	M₁₆	1	1	yes	characteristic
43	C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
44	#10596833	—	2	2	no	—
45	C₈×C₇₃	C₄²	1	1	yes	characteristic
46	C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
47	#10596831	C₄²	1	1	yes	characteristic
48	#10596831	C₂²×C₄	1	1	yes	characteristic
49	C₂²×C₇₃	#97	1	1	yes	characteristic
50	C₂×D₇₃	—	4	1	no	—
51	C₂×D₇₃	#97	1	1	yes	characteristic
52	C₂×D₇₃	C₂×M₁₆	1	1	yes	characteristic
53	#64408	—	4	2	no	—
54	C₄×C₇₃	#97	1	1	yes	characteristic
55	C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
56	Dic₇₃	#97	1	1	yes	characteristic
57	Dic₇₃	C₂×M₁₆	1	1	yes	characteristic
58	C₂×C₇₃	—	2	1	no	—
59	C₂×C₇₃	C₂×#97	1	1	yes	characteristic
60	D₇₃	—	2	1	no	—
61	D₇₃	—	2	1	no	—
62	#2110	—	73	1	no	maximal, Sylow
63	C₇₃	#2110	1	1	yes	characteristic, complemented, Sylow
64	C₂×M₃₂	—	73	1	no	—
65	C₂×M₃₂	—	73	1	no	—
66	#405	—	73	1	no	—
67	#347	—	73	2	no	—
68	#347	—	73	2	no	—
69	C₂×M₁₆	—	73	1	no	—
70	C₂²×C₈	—	73	1	no	—
71	#117	—	73	1	no	—
72	M₃₂	—	73	1	no	—
73	M₃₂	—	73	1	no	—
74	M₃₂	—	73	2	no	—
75	M₃₂	—	73	1	no	—
76	M₃₂	—	73	2	no	—
77	M₃₂	#64408	1	1	yes	characteristic, complemented
78	C₂×C₁₆	—	73	2	no	—
79	C₂×C₁₆	—	73	2	no	—
80	#97	—	73	2	no	—
81	C₄×C₈	—	73	2	no	—
82	C₂²×C₄	—	73	1	no	—
83	M₁₆	—	146	1	no	—
84	M₁₆	—	146	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	1	no	—
90	C₂×C₈	—	73	2	no	—
91	C₂×C₈	C₂×#64408	1	1	yes	characteristic
92	C₄⋊C₄	—	146	1	no	—
93	C₂²⋊C₄	—	146	1	no	—
94	C₄²	—	73	2	no	—
95	C₁₆	—	73	2	no	—
96	C₁₆	—	73	2	no	—
97	C₁₆	—	73	2	no	—
98	C₁₆	C₂×#64408	1	2	yes	—
99	C₂³	—	73	1	no	—
100	C₂×C₄	—	73	1	no	—
101	C₂×C₄	—	73	1	no	—
102	C₂×C₄	—	73	1	no	—
103	C₂×C₄	—	73	1	no	—
104	C₂×C₄	—	73	1	no	—
105	C₂×C₄	—	146	2	no	—
106	C₂×C₄	C₄×#64408	1	1	yes	characteristic
107	C₈	—	73	1	no	—
108	C₈	—	73	1	no	—
109	C₈	—	146	2	no	—
110	C₈	C₄×#64408	1	1	yes	characteristic
111	C₈	C₂²×#64408	1	1	yes	characteristic
112	C₂²	—	292	1	no	—
113	C₂²	—	73	1	no	—
114	C₂²	—	73	1	no	—
115	C₂²	#14556645	1	1	yes	characteristic
116	C₄	—	292	2	no	—
117	C₄	—	73	1	no	—
118	C₄	—	73	1	no	—
119	C₄	#14556645	1	1	yes	characteristic
120	C₄	C₂×C₄×#64408	1	1	yes	characteristic
121	C₂	—	2	1	no	—
122	C₂	—	146	1	no	—
123	C₂	—	146	1	no	—
124	C₂	C₂×#14556645	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556666

C₂

yes

maximal, characteristic

#17989550

C₂

yes

maximal, characteristic

#17989478

C₂

yes

maximal, complemented

#17989477

C₂

yes

maximal, complemented

M₃₂×D₇₃

C₂

yes

maximal, characteristic

D₇₃⋊M₁₆

C₄

yes

characteristic

#14556670

C₄

yes

characteristic

#14556666

C₄

yes

complemented

#14556666

C₂²

yes

characteristic

#14556666

C₂²

yes

characteristic

C₂×#11924031

C₄

yes

complemented

#14556645

C₂²

yes

—

C₈×#64408

C₄

yes

—

C₂×C₈×D₇₃

C₂²

yes

characteristic

#14556531

C₄

yes

characteristic, complemented

#14556530

C₂²

yes

—

C₁₆×D₇₃

C₄

yes

complemented

M₃₂×C₇₃

C₄

yes

characteristic, complemented

#11924038

—

#11924037

—

#11924036

C₂×C₄

yes

—

C₄⋊#64408

—

C₂²⋊#64408

—

C₄×#64408

C₂×C₄

yes

—

#11924031

C₂×C₄

yes

—

#11924031

C₂×C₄

yes

—

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₂×#10596831

C₂×C₄

yes

characteristic

C₈×D₇₃

C₂×C₄

yes

characteristic

C₈×D₇₃

C₂×C₄

yes

characteristic

C₈×D₇₃

C₂×C₄

yes

characteristic

C₈×D₇₃

C₂³

yes

characteristic

#11924003

C₂×C₄

yes

—

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₁₆×C₇₃

C₂×C₄

yes

—

C₂²×D₇₃

M₁₆

yes

characteristic

C₂×#64408

—

C₂×C₄×C₇₃

C₄²

yes

characteristic

C₂×Dic₇₃

M₁₆

yes

characteristic

C₄×D₇₃

C₄²

yes

characteristic

C₄×D₇₃

M₁₆

yes

characteristic

C₄×D₇₃

M₁₆

yes

characteristic

C₄×D₇₃

C₂²×C₄

yes

characteristic

#10596833

—

C₈×C₇₃

C₄²

yes

characteristic

C₈×C₇₃

C₂²×C₄

yes

characteristic

#10596831

C₄²

yes

characteristic

#10596831

C₂²×C₄

yes

characteristic

C₂²×C₇₃

#97

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

#97

yes

characteristic

C₂×D₇₃

C₂×M₁₆

yes

characteristic

#64408

—

C₄×C₇₃

#97

yes

characteristic

C₄×C₇₃

C₂×C₄²

yes

characteristic

Dic₇₃

#97

yes

characteristic

Dic₇₃

C₂×M₁₆

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

C₂×#97

yes

characteristic

D₇₃

—

D₇₃

—

#2110

—

maximal, Sylow

C₇₃

#2110

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂×M₃₂

—

#405

—

#347

—

#347

—

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

M₃₂

—

M₃₂

—

M₃₂

—

M₃₂

—

M₃₂

#64408

yes

characteristic, complemented

C₂×C₁₆

—

C₂×C₁₆

—

#97

—

C₄×C₈

—

C₂²×C₄

—

M₁₆

—

146

—

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#64408

yes

characteristic

C₄⋊C₄

—

146

—

C₂²⋊C₄

—

146

—

C₄²

—

C₁₆

—

C₁₆

—

C₁₆

—

C₁₆

C₂×#64408

yes

—

C₂³

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

146

—

106

C₂×C₄

C₄×#64408

yes

characteristic

107

C₈

—

108

C₈

—

109

C₈

—

146

—

110

C₈

C₄×#64408

yes

characteristic

111

C₈

C₂²×#64408

yes

characteristic

112

C₂²

—

292

—

113

C₂²

—

114

C₂²

—

115

C₂²

#14556645

yes

characteristic

116

C₄

—

292

—

117

C₄

—

118

C₄

—

119

C₄

#14556645

yes

characteristic

120

C₄

C₂×C₄×#64408

yes

characteristic

121

C₂

—

122

C₂

—

146

—

123

C₂

—

146

—

124

C₂

C₂×#14556645

yes

characteristic

	subgroup	G/H
center	C₄	C₂×C₄×#64408
commutator	C₄×C₇₃	C₂×C₄²
Frattini	C₈	C₂²×#64408
Fitting	M₃₂×C₇₃	C₄
socle	C₂×C₇₃	C₂×#97
hypercenter	M₃₂	#64408
hypocenter	C₇₃	#2110
LCS	G ▷ C₄×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ M₃₂

subgroup

G/H

center

C₄

C₂×C₄×#64408

commutator

C₄×C₇₃

C₂×C₄²

Frattini

C₈

C₂²×#64408

Fitting

M₃₂×C₇₃

C₄

socle

C₂×C₇₃

C₂×#97

M₃₂

C₇₃

G ▷ C₄×C₇₃ ▷ C₇₃

C₁ ◁ C₄ ◁ M₃₂

N	H ≅ G/N	type
3. #17989478	C₂	semidirect
4. #17989477	C₂	semidirect
8. #14556666	C₄	semidirect
11. C₂×#11924031	C₄	semidirect
15. #14556531	C₄	semidirect
17. C₁₆×D₇₃	C₄	semidirect
18. M₃₂×C₇₃	C₄	semidirect
63. C₇₃	#2110	semidirect
77. M₃₂	#64408	semidirect

H ≅ G/N

type

3. #17989478

C₂

semidirect

4. #17989477

C₂

semidirect

8. #14556666

C₄

semidirect

11. C₂×#11924031

C₄

semidirect

15. #14556531

C₄

semidirect

17. C₁₆×D₇₃

C₄

semidirect

18. M₃₂×C₇₃

C₄

semidirect

63. C₇₃

#2110

semidirect

77. M₃₂

#64408

semidirect

Subgroups — #22626151

Conjugacy classes of subgroups

Complements