Group #22624971 — subgroups

Subgroups — #22624971

Order 9344.

140 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 56 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	C₂×#14556645	C₂	1	1	yes	maximal, characteristic
3	C₂×#14556530	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924036	C₄	1	1	yes	characteristic
5	C₂×C₄×#64408	C₄	1	1	yes	characteristic
6	#14556666	—	2	1	no	—
7	#14556666	—	2	1	no	—
8	C₂×#11924031	C₄	1	2	yes	complemented
9	#14556645	—	2	1	no	—
10	#14556645	—	2	1	no	—
11	C₂×C₈×D₇₃	C₂²	1	1	yes	characteristic
12	#14556530	—	2	1	no	—
13	#14556530	—	2	1	no	—
14	C₂×#11924003	C₄	1	1	yes	characteristic, complemented
15	C₂×C₁₆×C₇₃	C₄	1	1	yes	characteristic, complemented
16	C₂²×#64408	—	2	1	no	—
17	#11924036	—	2	1	no	—
18	#11924036	C₈	1	2	yes	—
19	C₂×#10596833	—	2	1	no	—
20	C₄×#64408	—	2	1	no	—
21	C₄×#64408	C₈	1	2	yes	—
22	#11924031	—	2	2	no	—
23	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
24	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
25	C₈×D₇₃	D₄	1	1	yes	characteristic
26	C₈×D₇₃	D₄	1	1	yes	characteristic
27	C₈×D₇₃	D₄	1	1	yes	characteristic
28	C₈×D₇₃	Q₈	1	1	yes	characteristic
29	#11924003	—	2	1	no	—
30	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
31	C₁₆×C₇₃	—	2	1	no	—
32	C₂²×D₇₃	M₁₆	1	1	yes	characteristic
33	C₂×#64408	—	2	2	no	—
34	C₂×#64408	—	4	1	no	—
35	C₂×#64408	—	4	1	no	—
36	C₂×C₄×C₇₃	C₄²	1	1	yes	characteristic
37	C₂×Dic₇₃	M₁₆	1	1	yes	characteristic
38	C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
39	C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
40	C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
41	C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
42	#10596833	—	2	2	no	—
43	C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
44	C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
45	#10596831	C₂²⋊C₄	1	1	yes	characteristic
46	#10596831	C₄⋊C₄	1	1	yes	characteristic
47	C₂²×C₇₃	#97	1	1	yes	characteristic
48	C₂×D₇₃	—	2	1	no	—
49	C₂×D₇₃	—	2	1	no	—
50	C₂×D₇₃	C₂²⋊C₈	1	1	yes	characteristic
51	C₂×D₇₃	C₄⋊C₈	1	1	yes	characteristic
52	#64408	—	4	2	no	—
53	C₄×C₇₃	#95	1	1	yes	characteristic
54	C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
55	Dic₇₃	C₂²⋊C₈	1	1	yes	characteristic
56	Dic₇₃	C₄⋊C₈	1	1	yes	characteristic
57	C₂×C₇₃	#336	1	1	yes	characteristic
58	C₂×C₇₃	#347	1	1	yes	characteristic
59	C₂×C₇₃	#347	1	1	yes	characteristic
60	D₇₃	—	2	1	no	—
61	D₇₃	—	2	1	no	—
62	#1375	—	73	1	no	maximal, Sylow
63	C₇₃	#1375	1	1	yes	characteristic, complemented, Sylow
64	C₂×M₃₂	—	73	1	no	—
65	C₂×M₃₂	—	73	1	no	—
66	C₂×#97	—	73	1	no	—
67	C₂²×C₈	—	73	1	no	—
68	C₂²×C₈	—	73	1	no	—
69	C₂×C₄²	—	73	1	no	—
70	M₃₂	—	146	1	no	—
71	M₃₂	—	146	1	no	—
72	M₃₂	—	146	1	no	—
73	M₃₂	—	146	1	no	—
74	C₂×C₁₆	—	73	2	no	—
75	C₂×C₁₆	—	73	1	no	—
76	C₂×C₁₆	#64408	1	1	yes	characteristic, complemented
77	#97	—	146	1	no	—
78	#97	—	146	1	no	—
79	C₂²×C₄	—	73	1	no	—
80	C₂²×C₄	—	146	1	no	—
81	C₂×C₈	—	73	1	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	2	no	—
87	C₂×C₈	—	146	1	no	—
88	C₂×C₈	—	146	1	no	—
89	C₂×C₈	C₂×#64408	1	1	yes	characteristic
90	C₄²	—	73	2	no	—
91	C₄²	—	146	1	no	—
92	C₁₆	—	2	1	no	—
93	C₁₆	—	146	2	no	—
94	C₁₆	—	146	1	no	—
95	C₂³	—	73	1	no	—
96	C₂×C₄	—	292	1	no	—
97	C₂×C₄	—	292	1	no	—
98	C₂×C₄	—	73	1	no	—
99	C₂×C₄	—	73	1	no	—
100	C₂×C₄	—	73	1	no	—
101	C₂×C₄	—	73	1	no	—
102	C₂×C₄	—	73	1	no	—
103	C₂×C₄	—	146	2	no	—
104	C₂×C₄	C₄×#64408	1	1	yes	characteristic
105	C₈	—	73	1	no	—
106	C₈	—	73	1	no	—
107	C₈	—	146	2	no	—
108	C₈	C₂²⋊#64408	1	1	yes	characteristic
109	C₈	C₄⋊#64408	1	1	yes	characteristic
110	C₂²	—	73	1	no	—
111	C₂²	—	73	1	no	—
112	C₂²	—	146	1	no	—
113	C₂²	—	146	1	no	—
114	C₂²	#14556645	1	1	yes	characteristic
115	C₄	—	292	2	no	—
116	C₄	—	73	1	no	—
117	C₄	—	73	1	no	—
118	C₄	(C₂×#64408)⋊C₄	1	1	yes	characteristic
119	C₄	C₈×#64408	1	1	yes	characteristic
120	C₂	—	146	1	no	—
121	C₂	—	146	1	no	—
122	C₂	#17989452	1	1	yes	characteristic
123	C₂	#17989477	1	1	yes	characteristic
124	C₂	#17989478	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556666

C₂

yes

maximal, characteristic

C₂×#14556645

C₂

yes

maximal, characteristic

C₂×#14556530

C₂

yes

maximal, characteristic

C₂×#11924036

C₄

yes

characteristic

C₂×C₄×#64408

C₄

yes

—

—

C₄

yes

complemented

#14556645

—

#14556645

—

C₂×C₈×D₇₃

C₂²

yes

—

—

C₄

yes

characteristic, complemented

C₂×C₁₆×C₇₃

C₄

yes

characteristic, complemented

C₂²×#64408

—

#11924036

—

#11924036

C₈

yes

—

C₂×#10596833

—

C₄×#64408

—

C₄×#64408

C₈

yes

—

#11924031

—

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₂×#10596831

C₂×C₄

yes

characteristic

C₈×D₇₃

D₄

yes

characteristic

C₈×D₇₃

D₄

yes

characteristic

C₈×D₇₃

D₄

yes

characteristic

C₈×D₇₃

Q₈

yes

characteristic

#11924003

—

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₁₆×C₇₃

—

C₂²×D₇₃

M₁₆

yes

—

—

—

C₂×C₄×C₇₃

C₄²

yes

characteristic

C₂×Dic₇₃

M₁₆

yes

characteristic

C₄×D₇₃

C₂²⋊C₄

yes

characteristic

C₄×D₇₃

C₄⋊C₄

yes

characteristic

C₄×D₇₃

C₂×C₈

yes

characteristic

C₄×D₇₃

C₂×C₈

yes

characteristic

#10596833

—

C₈×C₇₃

C₂²⋊C₄

yes

characteristic

C₈×C₇₃

C₄⋊C₄

yes

characteristic

#10596831

C₂²⋊C₄

yes

characteristic

#10596831

C₄⋊C₄

yes

characteristic

C₂²×C₇₃

#97

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

C₂²⋊C₈

yes

characteristic

C₂×D₇₃

C₄⋊C₈

yes

characteristic

#64408

—

C₄×C₇₃

#95

yes

characteristic

C₄×C₇₃

C₄×C₈

yes

characteristic

Dic₇₃

C₂²⋊C₈

yes

characteristic

Dic₇₃

C₄⋊C₈

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

D₇₃

—

D₇₃

—

#1375

—

maximal, Sylow

C₇₃

#1375

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂×M₃₂

—

C₂×#97

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

M₃₂

—

146

—

M₃₂

—

146

—

M₃₂

—

146

—

M₃₂

—

146

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

#64408

yes

characteristic, complemented

#97

—

146

—

#97

—

146

—

C₂²×C₄

—

C₂²×C₄

—

146

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

C₂×#64408

yes

characteristic

C₄²

—

C₄²

—

146

—

C₁₆

—

C₁₆

—

146

—

C₁₆

—

146

—

C₂³

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

146

—

104

C₂×C₄

C₄×#64408

yes

characteristic

105

C₈

—

106

C₈

—

107

C₈

—

146

—

108

C₈

C₂²⋊#64408

yes

characteristic

109

C₈

C₄⋊#64408

yes

characteristic

110

C₂²

—

111

C₂²

—

112

C₂²

—

146

—

113

C₂²

—

146

—

114

C₂²

#14556645

yes

characteristic

115

C₄

—

292

—

116

C₄

—

117

C₄

—

118

C₄

(C₂×#64408)⋊C₄

yes

characteristic

119

C₄

C₈×#64408

yes

characteristic

120

C₂

—

146

—

121

C₂

—

146

—

122

C₂

#17989452

yes

characteristic

123

C₂

#17989477

yes

characteristic

124

C₂

#17989478

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₄×#64408
commutator	C₄×C₇₃	C₄×C₈
Frattini	C₂×C₈	C₂×#64408
Fitting	C₂×C₁₆×C₇₃	C₄
socle	C₂²×C₇₃	#97
hypercenter	C₂×C₁₆	#64408
hypocenter	C₇₃	#1375
LCS	G ▷ C₄×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₁₆

subgroup

G/H

center

C₂×C₄

C₄×#64408

commutator

C₄×C₇₃

C₄×C₈

Frattini

C₂×C₈

C₂×#64408

Fitting

C₂×C₁₆×C₇₃

C₄

C₂²×C₇₃

C₂×C₁₆

C₇₃

G ▷ C₄×C₇₃ ▷ C₇₃

C₁ ◁ C₂×C₄ ◁ C₂×C₁₆

N	H ≅ G/N	type
8. C₂×#11924031	C₄	semidirect
14. C₂×#11924003	C₄	semidirect
15. C₂×C₁₆×C₇₃	C₄	semidirect
63. C₇₃	#1375	semidirect
76. C₂×C₁₆	#64408	semidirect

H ≅ G/N

type

8. C₂×#11924031

C₄

semidirect

14. C₂×#11924003

C₄

semidirect

15. C₂×C₁₆×C₇₃

C₄

semidirect

63. C₇₃

#1375

semidirect

76. C₂×C₁₆

#64408

semidirect

Subgroups — #22624971

Conjugacy classes of subgroups

Complements