Group #22624977 — subgroups

Subgroups — #22624977

Order 9344.

140 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 54 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	#17989643	C₂	1	1	yes	maximal, characteristic
2	C₂×#14556645	C₂	1	1	yes	maximal, characteristic
3	M₃₂×D₇₃	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	#14556665	C₄	1	2	yes	complemented
8	#14556664	—	2	1	no	—
9	#14556645	—	2	1	no	—
10	#14556645	—	2	1	no	—
11	C₂×C₈×D₇₃	C₂²	1	1	yes	characteristic
12	#14556531	C₄	1	1	yes	characteristic, complemented
13	#14556530	—	2	1	no	—
14	C₁₆×D₇₃	—	2	1	no	—
15	M₃₂×C₇₃	C₄	1	1	yes	characteristic, complemented
16	C₂²×#64408	C₈	1	2	yes	—
17	#11924036	—	2	1	no	—
18	#11924036	—	2	1	no	—
19	C₂×#10596833	C₈	1	2	yes	—
20	C₄×#64408	—	2	1	no	—
21	C₄×#64408	—	2	1	no	—
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	C₂×C₈	1	1	yes	characteristic
33	C₂×#64408	—	2	2	no	—
34	C₂×#64408	—	4	2	no	—
35	C₂×C₄×C₇₃	C₄²	1	1	yes	characteristic
36	C₂×Dic₇₃	C₂×C₈	1	1	yes	characteristic
37	C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
38	C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
39	C₄×D₇₃	M₁₆	1	1	yes	characteristic
40	C₄×D₇₃	M₁₆	1	1	yes	characteristic
41	#10596833	—	2	2	no	—
42	C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
43	C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
44	#10596831	C₂²⋊C₄	1	1	yes	characteristic
45	#10596831	C₄⋊C₄	1	1	yes	characteristic
46	C₂²×C₇₃	C₄×C₈	1	1	yes	characteristic
47	C₂×D₇₃	—	2	2	no	—
48	C₂×D₇₃	C₂²⋊C₈	1	1	yes	characteristic
49	C₂×D₇₃	C₄⋊C₈	1	1	yes	characteristic
50	#64408	—	4	2	no	—
51	C₄×C₇₃	#95	1	1	yes	characteristic
52	C₄×C₇₃	#97	1	1	yes	characteristic
53	Dic₇₃	C₂²⋊C₈	1	1	yes	characteristic
54	Dic₇₃	C₄⋊C₈	1	1	yes	characteristic
55	C₂×C₇₃	—	2	1	no	—
56	C₂×C₇₃	#336	1	1	yes	characteristic
57	D₇₃	—	2	1	no	—
58	D₇₃	#349	1	2	yes	—
59	#1377	—	73	1	no	maximal, Sylow
60	C₇₃	#1377	1	1	yes	characteristic, complemented, Sylow
61	C₂×M₃₂	—	73	1	no	—
62	C₂×M₃₂	—	73	1	no	—
63	C₂×#97	—	73	1	no	—
64	C₂²×C₈	—	73	1	no	—
65	C₂²×C₈	—	73	1	no	—
66	C₂×C₄²	—	73	1	no	—
67	M₃₂	—	73	2	no	—
68	M₃₂	—	73	1	no	—
69	M₃₂	—	146	1	no	—
70	M₃₂	—	146	1	no	—
71	M₃₂	#64408	1	1	yes	characteristic, complemented
72	C₂×C₁₆	—	146	1	no	—
73	C₂×C₁₆	—	146	1	no	—
74	#97	—	146	1	no	—
75	#97	—	146	1	no	—
76	C₂²×C₄	—	73	2	no	—
77	C₂²×C₄	—	73	1	no	—
78	C₂×C₈	—	73	1	no	—
79	C₂×C₈	—	73	1	no	—
80	C₂×C₈	—	73	1	no	—
81	C₂×C₈	—	73	1	no	—
82	C₂×C₈	—	73	1	no	—
83	C₂×C₈	—	73	2	no	—
84	C₂×C₈	—	146	1	no	—
85	C₂×C₈	—	146	1	no	—
86	C₂×C₈	C₂×#64408	1	1	yes	characteristic
87	C₄²	—	146	1	no	—
88	C₄²	—	146	1	no	—
89	C₁₆	—	2	1	no	—
90	C₁₆	—	146	2	no	—
91	C₁₆	—	146	1	no	—
92	C₂³	—	73	1	no	—
93	C₂×C₄	—	292	2	no	—
94	C₂×C₄	—	73	1	no	—
95	C₂×C₄	—	73	1	no	—
96	C₂×C₄	—	73	1	no	—
97	C₂×C₄	—	73	1	no	—
98	C₂×C₄	—	73	1	no	—
99	C₂×C₄	—	146	2	no	—
100	C₂×C₄	C₄×#64408	1	1	yes	characteristic
101	C₈	—	73	1	no	—
102	C₈	—	73	1	no	—
103	C₈	—	146	2	no	—
104	C₈	C₂²⋊#64408	1	1	yes	characteristic
105	C₈	C₄⋊#64408	1	1	yes	characteristic
106	C₂²	—	73	1	no	—
107	C₂²	—	73	1	no	—
108	C₂²	—	146	2	no	—
109	C₂²	C₈×#64408	1	1	yes	characteristic
110	C₄	—	292	2	no	—
111	C₄	—	73	1	no	—
112	C₄	—	73	1	no	—
113	C₄	(C₂×#64408)⋊C₄	1	1	yes	characteristic
114	C₄	#14556645	1	1	yes	characteristic
115	C₂	—	2	1	no	—
116	C₂	—	73	2	no	—
117	C₂	—	146	1	no	—
118	C₂	#17989452	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989643

C₂

yes

maximal, characteristic

C₂×#14556645

C₂

yes

maximal, characteristic

M₃₂×D₇₃

C₂

yes

maximal, characteristic

C₂×#11924036

C₄

yes

characteristic

C₂×C₄×#64408

C₄

yes

characteristic

#14556666

—

#14556665

C₄

yes

—

—

—

C₂×C₈×D₇₃

C₂²

yes

characteristic

#14556531

C₄

yes

characteristic, complemented

#14556530

—

C₁₆×D₇₃

—

M₃₂×C₇₃

C₄

yes

characteristic, complemented

C₂²×#64408

C₈

yes

—

#11924036

—

#11924036

—

C₂×#10596833

C₈

yes

—

C₄×#64408

—

C₄×#64408

—

#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

C₂×C₈

yes

characteristic

C₂×#64408

—

C₂×#64408

—

C₂×C₄×C₇₃

C₄²

yes

characteristic

C₂×Dic₇₃

C₂×C₈

yes

characteristic

C₄×D₇₃

C₂²⋊C₄

yes

characteristic

C₄×D₇₃

C₄⋊C₄

yes

characteristic

C₄×D₇₃

M₁₆

yes

characteristic

C₄×D₇₃

M₁₆

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

C₄×C₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

C₂²⋊C₈

yes

characteristic

C₂×D₇₃

C₄⋊C₈

yes

characteristic

#64408

—

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

C₂²⋊C₈

yes

characteristic

Dic₇₃

C₄⋊C₈

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

#336

yes

characteristic

D₇₃

—

D₇₃

#349

yes

—

#1377

—

maximal, Sylow

C₇₃

#1377

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂×M₃₂

—

C₂×#97

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

M₃₂

—

M₃₂

—

M₃₂

—

146

—

M₃₂

—

146

—

M₃₂

#64408

yes

characteristic, complemented

C₂×C₁₆

—

146

—

C₂×C₁₆

—

146

—

#97

—

146

—

#97

—

146

—

C₂²×C₄

—

C₂²×C₄

—

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

—

146

—

C₄²

—

146

—

C₁₆

—

C₁₆

—

146

—

C₁₆

—

146

—

C₂³

—

C₂×C₄

—

292

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

100

C₂×C₄

C₄×#64408

yes

characteristic

101

C₈

—

102

C₈

—

103

C₈

—

146

—

104

C₈

C₂²⋊#64408

yes

characteristic

105

C₈

C₄⋊#64408

yes

characteristic

106

C₂²

—

107

C₂²

—

108

C₂²

—

146

—

109

C₂²

C₈×#64408

yes

characteristic

110

C₄

—

292

—

111

C₄

—

112

C₄

—

113

C₄

(C₂×#64408)⋊C₄

yes

characteristic

114

C₄

#14556645

yes

characteristic

115

C₂

—

116

C₂

—

117

C₂

—

146

—

118

C₂

#17989452

yes

characteristic

	subgroup	G/H
center	C₄	(C₂×#64408)⋊C₄
commutator	C₂²×C₇₃	C₄×C₈
Frattini	C₂×C₈	C₂×#64408
Fitting	M₃₂×C₇₃	C₄
socle	C₂×C₇₃	#336
hypercenter	M₃₂	#64408
hypocenter	C₇₃	#1377
LCS	G ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ M₃₂

subgroup

G/H

center

C₄

(C₂×#64408)⋊C₄

commutator

C₂²×C₇₃

C₄×C₈

Frattini

C₂×C₈

C₂×#64408

Fitting

M₃₂×C₇₃

C₄

C₂×C₇₃

M₃₂

C₇₃

G ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₄ ◁ C₂×C₈ ◁ M₃₂

N	H ≅ G/N	type
7. #14556665	C₄	semidirect
12. #14556531	C₄	semidirect
15. M₃₂×C₇₃	C₄	semidirect
60. C₇₃	#1377	semidirect
71. M₃₂	#64408	semidirect

H ≅ G/N

type

7. #14556665

C₄

semidirect

12. #14556531

C₄

semidirect

15. M₃₂×C₇₃

C₄

semidirect

60. C₇₃

#1377

semidirect

71. M₃₂

#64408

semidirect

Subgroups — #22624977

Conjugacy classes of subgroups

Complements