Group #22625481 — subgroups

Subgroups — #22625481

Order 9344.

180 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 82 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	#17989606	C₂	1	2	yes	maximal
2	#17989450	C₂	1	2	yes	maximal, complemented
3	#17989449	C₂	1	2	yes	maximal, complemented
4	C₄×C₈×D₇₃	C₂	1	1	yes	maximal, characteristic
5	C₄⋊#10596833	C₂²	1	4	yes	—
6	#14556648	—	2	2	no	—
7	C₄×#10596833	—	2	2	no	—
8	C₂×C₈×D₇₃	C₄	1	1	yes	characteristic
9	C₂×C₈×D₇₃	C₄	1	1	yes	characteristic
10	C₄²×D₇₃	C₂²	1	1	yes	characteristic
11	C₄×#10596831	C₄	1	1	yes	characteristic
12	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
13	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₇₃	C₄	1	1	yes	characteristic
15	C₂×#10596833	—	2	4	no	—
16	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×D₇₃	D₄	1	1	yes	characteristic
18	C₂×C₄×D₇₃	Q₈	1	1	yes	characteristic
19	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
20	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
21	C₈×D₇₃	—	2	2	no	—
22	C₈×D₇₃	C₈	1	4	yes	complemented
23	C₄×Dic₇₃	D₄	1	1	yes	characteristic
24	C₄×Dic₇₃	Q₈	1	1	yes	characteristic
25	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
26	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
27	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
28	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
29	C₂²×D₇₃	C₄⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
33	C₂×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
34	C₂×Dic₇₃	C₂×D₄	1	1	yes	characteristic
35	C₂×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
36	C₄×D₇₃	—	2	2	no	—
37	C₄×D₇₃	—	2	2	no	—
38	C₄×D₇₃	C₂×C₈	1	2	yes	—
39	C₄×D₇₃	M₁₆	1	2	yes	—
40	#10596833	—	4	4	no	—
41	C₈×C₇₃	—	2	1	no	—
42	C₈×C₇₃	C₂×C₈	1	2	yes	—
43	#10596831	—	2	1	no	—
44	#10596831	C₂×C₈	1	2	yes	—
45	C₂²×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
46	C₂×D₇₃	—	2	1	no	—
47	C₂×D₇₃	—	2	1	no	—
48	C₂×D₇₃	C₄⋊C₈	1	2	yes	—
49	C₄×C₇₃	—	2	1	no	—
50	C₄×C₇₃	#108	1	2	yes	—
51	C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
52	C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
53	Dic₇₃	—	2	1	no	—
54	Dic₇₃	C₄⋊C₈	1	2	yes	—
55	Dic₇₃	#135	1	2	yes	—
56	C₂×C₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
57	C₂×C₇₃	#427	1	1	yes	characteristic
58	C₂×C₇₃	C₂×#108	1	1	yes	characteristic
59	D₇₃	—	2	2	no	—
60	#1564	—	73	1	no	maximal, Sylow
61	C₇₃	#1564	1	1	yes	characteristic, complemented, Sylow
62	#431	—	73	2	no	—
63	C₂×C₄×C₈	—	73	1	no	—
64	#335	—	73	2	no	—
65	#334	—	73	2	no	—
66	C₂²×C₈	—	73	1	no	—
67	C₂²×C₈	—	73	1	no	—
68	C₂×C₄²	—	73	1	no	—
69	C₄⋊C₈	—	73	4	no	—
70	C₂²⋊C₈	—	146	2	no	—
71	C₄×C₈	—	73	1	no	—
72	C₄×C₈	—	73	1	no	—
73	C₄×C₈	—	73	1	no	—
74	C₄×C₈	—	146	2	no	—
75	C₄×C₈	#64408	1	1	yes	characteristic
76	C₂²×C₄	—	73	1	no	—
77	C₂²×C₄	—	73	1	no	—
78	C₂²×C₄	—	73	1	no	—
79	C₂×C₈	—	73	1	no	—
80	C₂×C₈	—	73	4	no	—
81	C₂×C₈	—	73	1	no	—
82	C₂×C₈	—	146	2	no	—
83	C₂×C₈	—	146	4	no	—
84	C₂×C₈	C₂×#64408	1	1	yes	characteristic
85	C₂×C₈	C₂×#64408	1	1	yes	characteristic
86	C₄²	—	73	1	no	—
87	C₄²	—	73	1	no	—
88	C₄²	—	73	1	no	—
89	C₄²	C₂×#64408	1	1	yes	characteristic
90	C₂³	—	73	1	no	—
91	C₂×C₄	—	73	1	no	—
92	C₂×C₄	—	73	1	no	—
93	C₂×C₄	—	73	2	no	—
94	C₂×C₄	—	73	2	no	—
95	C₂×C₄	—	73	1	no	—
96	C₂×C₄	—	146	2	no	—
97	C₂×C₄	—	146	2	no	—
98	C₂×C₄	C₄⋊#64408	1	1	yes	characteristic
99	C₂×C₄	C₄⋊#64408	1	1	yes	characteristic
100	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
101	C₈	—	2	1	no	—
102	C₈	—	292	4	no	—
103	C₈	—	73	2	no	—
104	C₈	—	146	1	no	—
105	C₈	#11924036	1	2	yes	—
106	C₂²	—	73	2	no	—
107	C₂²	—	146	1	no	—
108	C₂²	—	146	1	no	—
109	C₂²	C₂×C₄⋊#64408	1	1	yes	characteristic
110	C₄	—	2	1	no	—
111	C₄	—	73	2	no	—
112	C₄	—	73	2	no	—
113	C₄	—	146	1	no	—
114	C₄	#14556662	1	2	yes	—
115	C₄	C₂×#11924036	1	1	yes	characteristic
116	C₄	D₇₃⋊M₁₆	1	1	yes	characteristic
117	C₂	—	146	2	no	—
118	C₂	#17989588	1	1	yes	characteristic
119	C₂	#17989597	1	1	yes	characteristic
120	C₂	C₂×#14556662	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989606

C₂

yes

maximal

#17989450

C₂

yes

maximal, complemented

#17989449

C₂

yes

maximal, complemented

C₄×C₈×D₇₃

C₂

yes

maximal, characteristic

C₄⋊#10596833

C₂²

yes

—

#14556648

—

C₄×#10596833

—

C₂×C₈×D₇₃

C₄

yes

characteristic

C₂×C₈×D₇₃

C₄

yes

characteristic

C₄²×D₇₃

C₂²

yes

characteristic

C₄×#10596831

C₄

yes

characteristic

C₈×Dic₇₃

C₂²

yes

characteristic

C₈×Dic₇₃

C₂²

yes

characteristic

C₄×C₈×C₇₃

C₄

yes

characteristic

C₂×#10596833

—

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₂×C₄×D₇₃

D₄

yes

characteristic

C₂×C₄×D₇₃

Q₈

yes

characteristic

C₂×#10596831

C₂×C₄

yes

characteristic

C₂×#10596831

C₂×C₄

yes

characteristic

C₈×D₇₃

—

C₈×D₇₃

C₈

yes

complemented

C₄×Dic₇₃

D₄

yes

characteristic

C₄×Dic₇₃

Q₈

yes

characteristic

C₄×Dic₇₃

C₂³

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₂²×D₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

C₄⋊C₄

yes

characteristic

C₂×Dic₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

C₂×Q₈

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

C₂×C₈

yes

—

C₄×D₇₃

M₁₆

yes

—

#10596833

—

C₈×C₇₃

—

C₈×C₇₃

C₂×C₈

yes

—

#10596831

—

#10596831

C₂×C₈

yes

—

C₂²×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

C₄⋊C₈

yes

—

C₄×C₇₃

—

C₄×C₇₃

#108

yes

—

C₄×C₇₃

C₂²×C₈

yes

characteristic

C₄×C₇₃

C₂×M₁₆

yes

characteristic

Dic₇₃

—

Dic₇₃

C₄⋊C₈

yes

—

Dic₇₃

#135

yes

—

C₂×C₇₃

C₂×C₄⋊C₈

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

D₇₃

—

#1564

—

maximal, Sylow

C₇₃

#1564

yes

characteristic, complemented, Sylow

#431

—

C₂×C₄×C₈

—

#335

—

#334

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₂²⋊C₈

—

146

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

146

—

C₄×C₈

#64408

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

yes

C₂×C₈

yes

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#64408

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

yes

C₂×C₄

yes

100

C₂×C₄

C₂²×#64408

yes

characteristic

101

C₈

—

102

C₈

—

292

—

103

C₈

—

104

C₈

—

146

—

105

C₈

#11924036

yes

—

106

C₂²

—

107

C₂²

—

146

—

108

C₂²

—

146

—

109

C₂²

C₂×C₄⋊#64408

yes

characteristic

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

—

146

—

114

C₄

#14556662

yes

—

115

C₄

C₂×#11924036

yes

characteristic

116

C₄

D₇₃⋊M₁₆

yes

characteristic

117

C₂

—

146

—

118

C₂

#17989588

yes

characteristic

119

C₂

#17989597

yes

characteristic

120

C₂

C₂×#14556662

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₄⋊#64408
commutator	C₄×C₇₃	C₂²×C₈
Frattini	C₂×C₄	C₂²×#64408
Fitting	C₄×C₈×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₄⋊C₄
hypercenter	C₄×C₈	#64408
hypocenter	C₇₃	#1564
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

subgroup

G/H

center

C₂×C₄

C₄⋊#64408

commutator

C₄×C₇₃

C₂²×C₈

Frattini

C₂×C₄

C₂²×#64408

Fitting

C₄×C₈×C₇₃

C₄

socle

C₂²×C₇₃

C₂×C₄⋊C₄

C₄×C₈

C₇₃

G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

N	H ≅ G/N	type
2. #17989450	C₂	semidirect
3. #17989449	C₂	semidirect
22. C₈×D₇₃	C₈	semidirect
61. C₇₃	#1564	semidirect

H ≅ G/N

type

2. #17989450

C₂

semidirect

3. #17989449

C₂

semidirect

22. C₈×D₇₃

C₈

semidirect

61. C₇₃

#1564

semidirect

Subgroups — #22625481

Conjugacy classes of subgroups

Complements