Group #22608666 — subgroups

Subgroups — #22608666

Order 9344.

254 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 85 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	#17988611	C₂	1	2	yes	maximal, complemented
2	#17988336	C₂	1	2	yes	maximal, complemented
3	#17988331	C₂	1	2	yes	maximal, complemented
4	#532×C₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#11924012	—	2	2	no	—
6	C₄⋊#10596831	—	2	2	no	—
7	C₄⋊#10596831	C₂²	1	4	yes	—
8	C₂×#41×C₇₃	C₄	1	2	yes	—
9	C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
10	#127×C₇₃	C₂²	1	1	yes	characteristic
11	#124×C₇₃	C₄	1	2	yes	—
12	#121×C₇₃	—	2	2	no	—
13	C₄×D₄×C₇₃	—	2	2	no	—
14	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
15	#11924012	—	4	4	no	—
16	C₂×#10596831	—	2	4	no	—
17	#41×C₇₃	—	4	4	no	—
18	C₂×Q₈×C₇₃	C₂×C₄	1	2	yes	—
19	C₂×D₄×C₇₃	—	2	2	no	—
20	C₂×D₄×C₇₃	—	2	2	no	—
21	C₂×D₄×C₇₃	C₂×C₄	1	2	yes	—
22	C₂²×C₄×C₇₃	—	2	2	no	—
23	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₄×C₇₃	D₄	1	2	yes	—
25	C₄⋊C₄×C₇₃	—	2	2	no	—
26	C₂²⋊C₄×C₇₃	—	2	4	no	—
27	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
28	C₄²×C₇₃	D₄	1	2	yes	—
29	C₄²×C₇₃	C₂³	1	1	yes	characteristic
30	C₂³×C₇₃	—	2	2	no	—
31	C₂³×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
32	Q₈×C₇₃	—	4	2	no	—
33	D₄×C₇₃	—	4	2	no	—
34	D₄×C₇₃	—	4	4	no	—
35	D₄×C₇₃	—	4	2	no	—
36	D₄×C₇₃	—	4	2	no	—
37	C₂×C₄×C₇₃	—	2	2	no	—
38	C₂×C₄×C₇₃	—	2	2	no	—
39	C₂×C₄×C₇₃	—	2	2	no	—
40	C₂×C₄×C₇₃	—	2	2	no	—
41	C₂×C₄×C₇₃	—	4	4	no	—
42	C₂×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
43	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
44	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
46	#10596831	—	4	4	no	—
47	C₂²×C₇₃	—	2	1	no	—
48	C₂²×C₇₃	—	2	2	no	—
49	C₂²×C₇₃	—	4	2	no	—
50	C₂²×C₇₃	—	4	4	no	—
51	C₂²×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
52	C₄×C₇₃	—	2	1	no	—
53	C₄×C₇₃	—	2	2	no	—
54	C₄×C₇₃	—	4	2	no	—
55	C₄×C₇₃	#100	1	2	yes	—
56	C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
57	C₄×C₇₃	#137	1	2	yes	—
58	C₂×C₇₃	—	4	1	no	—
59	C₂×C₇₃	—	8	2	no	—
60	C₂×C₇₃	C₂×#100	1	1	yes	characteristic
61	C₂×C₇₃	#417	1	2	yes	—
62	#1560	—	73	1	no	maximal, Sylow
63	C₇₃	#1560	1	1	yes	characteristic, complemented, Sylow
64	#532	D₇₃	1	1	yes	characteristic
65	#423	—	73	2	no	—
66	#333	—	73	2	no	—
67	#331	—	73	2	no	—
68	C₂×#41	Dic₇₃	1	2	yes	—
69	C₂×M₁₆	—	146	2	no	—
70	C₄⋊Q₈	C₂×D₇₃	1	1	yes	characteristic
71	#127	C₂×D₇₃	1	1	yes	characteristic
72	#124	Dic₇₃	1	2	yes	—
73	#121	—	2	2	no	—
74	C₄×D₄	—	2	2	no	—
75	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
76	C₄⋊C₈	—	73	4	no	—
77	C₄⋊C₈	—	146	2	no	—
78	#41	—	4	4	no	—
79	C₂×Q₈	C₂×Dic₇₃	1	2	yes	—
80	C₂×D₄	—	2	2	no	—
81	C₂×D₄	—	2	2	no	—
82	C₂×D₄	C₂×Dic₇₃	1	2	yes	—
83	C₂²×C₄	—	2	2	no	—
84	C₂²×C₄	C₂×Dic₇₃	1	1	yes	characteristic
85	C₂²×C₄	C₂²⋊D₇₃	1	2	yes	—
86	M₁₆	—	292	4	no	—
87	C₂×C₈	—	146	4	no	—
88	C₄⋊C₄	—	2	2	no	—
89	C₂²⋊C₄	—	2	4	no	—
90	C₄²	C₂×Dic₇₃	1	1	yes	characteristic
91	C₄²	C₂²⋊D₇₃	1	2	yes	—
92	C₄²	C₂²×D₇₃	1	1	yes	characteristic
93	C₂³	—	2	2	no	—
94	C₂³	C₂²⋊Dic₇₃	1	1	yes	characteristic
95	Q₈	—	4	2	no	—
96	D₄	—	4	2	no	—
97	D₄	—	4	4	no	—
98	D₄	—	4	2	no	—
99	D₄	—	4	2	no	—
100	C₂×C₄	—	2	2	no	—
101	C₂×C₄	—	2	2	no	—
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	4	4	no	—
105	C₂×C₄	C₂²⋊Dic₇₃	1	2	yes	—
106	C₂×C₄	C₂²⋊Dic₇₃	1	1	yes	characteristic
107	C₂×C₄	C₂²×Dic₇₃	1	1	yes	characteristic
108	C₂×C₄	C₂×C₂²⋊D₇₃	1	2	yes	—
109	C₈	—	292	4	no	—
110	C₂²	—	2	1	no	—
111	C₂²	—	2	2	no	—
112	C₂²	—	4	2	no	—
113	C₂²	—	4	4	no	—
114	C₂²	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
115	C₄	—	2	1	no	—
116	C₄	—	2	2	no	—
117	C₄	—	4	2	no	—
118	C₄	#14556508	1	2	yes	—
119	C₄	#14556616	1	2	yes	—
120	C₄	#14556621	1	2	yes	—
121	C₂	—	4	1	no	—
122	C₂	—	8	2	no	—
123	C₂	C₂×#14556508	1	1	yes	characteristic
124	C₂	#17988588	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#17988611

C₂

yes

maximal, complemented

#17988336

C₂

yes

maximal, complemented

#17988331

C₂

yes

maximal, complemented

#532×C₇₃

C₂

yes

maximal, characteristic

C₂×#11924012

—

C₄⋊#10596831

—

C₄⋊#10596831

C₂²

yes

—

C₂×#41×C₇₃

C₄

yes

—

C₄⋊Q₈×C₇₃

C₂²

yes

characteristic

#127×C₇₃

C₂²

yes

characteristic

#124×C₇₃

C₄

yes

—

#121×C₇₃

—

C₄×D₄×C₇₃

—

C₂×C₄²×C₇₃

C₂²

yes

characteristic

#11924012

—

C₂×#10596831

—

#41×C₇₃

—

C₂×Q₈×C₇₃

C₂×C₄

yes

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

C₂×C₄

yes

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₃

D₄

yes

—

C₄⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₄²×C₇₃

D₄

yes

—

C₄²×C₇₃

C₂³

yes

characteristic

C₂³×C₇₃

—

C₂³×C₇₃

C₂²⋊C₄

yes

characteristic

Q₈×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#100

yes

—

C₄×C₇₃

AGL(1,ℤ/8)

yes

—

C₄×C₇₃

#137

yes

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

C₂×#100

yes

characteristic

C₂×C₇₃

#417

yes

—

#1560

—

maximal, Sylow

C₇₃

#1560

yes

characteristic, complemented, Sylow

#532

D₇₃

yes

—

—

—

C₂×#41

Dic₇₃

yes

—

C₂×M₁₆

—

146

—

C₄⋊Q₈

C₂×D₇₃

yes

characteristic

#127

C₂×D₇₃

yes

characteristic

#124

Dic₇₃

yes

—

#121

—

C₄×D₄

—

C₂×C₄²

C₂×D₇₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

146

—

#41

—

C₂×Q₈

C₂×Dic₇₃

yes

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

C₂×Dic₇₃

yes

—

C₂²×C₄

—

C₂²×C₄

C₂×Dic₇₃

yes

characteristic

C₂²×C₄

C₂²⋊D₇₃

yes

—

M₁₆

—

292

—

C₂×C₈

—

146

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

C₂×Dic₇₃

yes

characteristic

C₄²

C₂²⋊D₇₃

yes

—

C₄²

C₂²×D₇₃

yes

characteristic

C₂³

—

C₂³

C₂²⋊Dic₇₃

yes

characteristic

Q₈

—

D₄

—

D₄

—

D₄

—

D₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

C₂²⋊Dic₇₃

yes

—

106

C₂×C₄

C₂²⋊Dic₇₃

yes

characteristic

107

C₂×C₄

C₂²×Dic₇₃

yes

characteristic

108

C₂×C₄

C₂×C₂²⋊D₇₃

yes

—

109

C₈

—

292

—

110

C₂²

—

111

C₂²

—

112

C₂²

—

113

C₂²

—

114

C₂²

C₂×C₂²⋊Dic₇₃

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

#14556508

yes

—

119

C₄

#14556616

yes

—

120

C₄

#14556621

yes

—

121

C₂

—

122

C₂

—

123

C₂

C₂×#14556508

yes

characteristic

124

C₂

#17988588

yes

—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊Dic₇₃
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₄²	C₂²×D₇₃
Fitting	#532×C₇₃	C₂
socle	C₂²×C₇₃	C₂×C₂²⋊C₄
hypercenter	#532	D₇₃
hypocenter	C₇₃	#1560
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #532

subgroup

G/H

center

C₂²

C₂×C₂²⋊Dic₇₃

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₄²

C₂²×D₇₃

Fitting

#532×C₇₃

C₂

socle

C₂²×C₇₃

C₂×C₂²⋊C₄

D₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #532

N	H ≅ G/N	type
1. #17988611	C₂	semidirect
2. #17988336	C₂	semidirect
3. #17988331	C₂	semidirect
63. C₇₃	#1560	semidirect

H ≅ G/N

type

1. #17988611

C₂

semidirect

2. #17988336

C₂

semidirect

3. #17988331

C₂

semidirect

63. C₇₃

#1560

semidirect

Subgroups — #22608666

Conjugacy classes of subgroups

Complements