Group #22609420 — subgroups

Subgroups — #22609420

Order 9344.

166 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 57 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	#17988967	C₂	1	1	yes	maximal, characteristic, complemented
2	#17988867	C₂	1	2	yes	maximal
3	#17988338	C₂	1	1	yes	maximal, characteristic, complemented
4	#17988334	C₂	1	2	yes	maximal, complemented
5	#436×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₂₉₂	—	2	1	no	—
7	C₂×Dic₂₉₂	—	2	1	no	—
8	#14556591	C₂²	1	2	yes	—
9	#14556524	—	2	2	no	—
10	C₄⋊#10596831	C₂²	1	2	yes	—
11	#14556512	—	2	2	no	—
12	C₂×M₁₆×C₇₃	—	2	1	no	—
13	C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
14	C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
15	C₂²⋊C₈×C₇₃	—	2	1	no	—
16	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×Dic₁₄₆	—	2	2	no	—
18	Dic₂₉₂	—	4	2	no	—
19	Dic₂₉₂	—	4	2	no	—
20	C₂×#10596831	—	2	2	no	—
21	C₄⋊Dic₇₃	—	2	2	no	—
22	C₄⋊Dic₇₃	—	2	2	no	—
23	C₂×D₄×C₇₃	D₄	1	1	yes	characteristic
24	C₂²×C₄×C₇₃	—	2	1	no	—
25	M₁₆×C₇₃	—	4	2	no	—
26	C₂×C₈×C₇₃	—	2	1	no	—
27	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
28	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
29	C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
30	C₂²⋊C₄×C₇₃	—	2	1	no	—
31	C₄²×C₇₃	C₂³	1	1	yes	characteristic
32	C₂³×C₇₃	—	2	1	no	—
33	D₄×C₇₃	—	2	2	no	—
34	C₂×C₄×C₇₃	—	2	1	no	—
35	C₂×C₄×C₇₃	—	4	1	no	—
36	C₂×C₄×C₇₃	—	4	1	no	—
37	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
40	C₂×Dic₇₃	—	4	2	no	—
41	Dic₁₄₆	—	4	2	no	—
42	Dic₁₄₆	—	4	2	no	—
43	C₈×C₇₃	—	2	1	no	—
44	C₈×C₇₃	—	4	1	no	—
45	C₈×C₇₃	D₈	1	2	yes	—
46	#10596831	—	4	2	no	—
47	C₂²×C₇₃	—	4	1	no	—
48	C₂²×C₇₃	—	4	1	no	—
49	C₂²×C₇₃	—	4	1	no	—
50	C₂²×C₇₃	#121	1	1	yes	characteristic
51	C₄×C₇₃	—	2	1	no	—
52	C₄×C₇₃	—	4	1	no	—
53	C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
54	C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
55	C₄×C₇₃	#137	1	2	yes	—
56	Dic₇₃	—	8	2	no	—
57	C₂×C₇₃	—	8	1	no	—
58	C₂×C₇₃	#459	1	1	yes	characteristic
59	C₂×C₇₃	#470	1	1	yes	characteristic
60	C₂×C₇₃	#473	1	1	yes	characteristic
61	#1689	—	73	1	no	maximal, Sylow
62	C₇₃	#1689	1	1	yes	characteristic, complemented, Sylow
63	#494	—	73	1	no	—
64	#474	—	73	2	no	—
65	#436	D₇₃	1	1	yes	characteristic
66	#334	—	73	1	no	—
67	#332	—	73	2	no	—
68	C₂×Q₁₆	—	146	1	no	—
69	C₂×Q₁₆	—	146	1	no	—
70	C₂×M₁₆	—	2	1	no	—
71	C₄⋊Q₈	—	73	2	no	—
72	C₄×D₄	C₂×D₇₃	1	1	yes	characteristic
73	#107	—	146	2	no	—
74	C₄⋊C₈	—	73	2	no	—
75	C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
76	#102	—	146	2	no	—
77	C₂²⋊C₈	—	2	1	no	—
78	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
79	C₂×Q₈	—	146	2	no	—
80	C₂×D₄	D₂₉₂	1	1	yes	characteristic
81	C₂²×C₄	—	2	1	no	—
82	Q₁₆	—	292	2	no	—
83	Q₁₆	—	292	2	no	—
84	M₁₆	—	4	2	no	—
85	C₂×C₈	—	2	1	no	—
86	C₂×C₈	—	146	2	no	—
87	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
88	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
89	C₄⋊C₄	—	146	2	no	—
90	C₄⋊C₄	—	146	2	no	—
91	C₄⋊C₄	D₂₉₂	1	1	yes	characteristic
92	C₂²⋊C₄	—	2	1	no	—
93	C₄²	C₂²×D₇₃	1	1	yes	characteristic
94	C₂³	—	2	1	no	—
95	Q₈	—	292	2	no	—
96	Q₈	—	292	2	no	—
97	D₄	—	2	2	no	—
98	C₂×C₄	—	2	1	no	—
99	C₂×C₄	—	4	1	no	—
100	C₂×C₄	—	4	1	no	—
101	C₂×C₄	—	292	2	no	—
102	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
103	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
104	C₂×C₄	#11924028	1	1	yes	characteristic
105	C₈	—	2	1	no	—
106	C₈	—	4	1	no	—
107	C₈	—	292	2	no	—
108	C₈	#11924013	1	2	yes	—
109	C₂²	—	4	1	no	—
110	C₂²	—	4	1	no	—
111	C₂²	—	4	1	no	—
112	C₂²	#14556565	1	1	yes	characteristic
113	C₄	—	2	1	no	—
114	C₄	—	4	1	no	—
115	C₄	—	584	2	no	—
116	C₄	C₂×#11924013	1	1	yes	characteristic
117	C₄	#14556616	1	1	yes	characteristic
118	C₄	#14556624	1	2	yes	—
119	C₂	—	8	1	no	—
120	C₂	#17988782	1	1	yes	characteristic
121	C₂	#17988845	1	1	yes	characteristic
122	C₂	#17988862	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988967

C₂

yes

maximal, characteristic, complemented

#17988867

C₂

yes

maximal

#17988338

C₂

yes

maximal, characteristic, complemented

#17988334

C₂

yes

maximal, complemented

#436×C₇₃

C₂

yes

maximal, characteristic

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

#14556591

C₂²

yes

—

#14556524

—

C₄⋊#10596831

C₂²

yes

—

#14556512

—

C₂×M₁₆×C₇₃

—

C₄×D₄×C₇₃

C₂²

yes

characteristic

C₄⋊C₈×C₇₃

C₂²

yes

characteristic

C₂²⋊C₈×C₇₃

—

C₄×C₈×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

—

Dic₂₉₂

—

Dic₂₉₂

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂×D₄×C₇₃

D₄

yes

characteristic

C₂²×C₄×C₇₃

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

D₄

yes

characteristic

C₄⋊C₄×C₇₃

D₄

yes

characteristic

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

C₂³

yes

characteristic

C₂³×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

#41

yes

characteristic

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

—

C₈×C₇₃

—

C₈×C₇₃

D₈

yes

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#121

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₂×D₈

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#494

—

#474

—

#436

D₇₃

yes

characteristic

#334

—

#332

—

C₂×Q₁₆

—

146

—

C₂×Q₁₆

—

146

—

C₂×M₁₆

—

C₄⋊Q₈

—

C₄×D₄

C₂×D₇₃

yes

characteristic

#107

—

146

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₇₃

yes

characteristic

#102

—

146

—

C₂²⋊C₈

—

C₄×C₈

C₂×D₇₃

yes

characteristic

C₂×Q₈

—

146

—

C₂×D₄

D₂₉₂

yes

characteristic

C₂²×C₄

—

Q₁₆

—

292

—

Q₁₆

—

292

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

D₂₉₂

yes

characteristic

C₂²⋊C₄

—

C₄²

C₂²×D₇₃

yes

characteristic

C₂³

—

Q₈

—

292

—

Q₈

—

292

—

D₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

292

—

102

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

103

C₂×C₄

C₂×D₂₉₂

yes

characteristic

104

C₂×C₄

#11924028

yes

characteristic

105

C₈

—

106

C₈

—

107

C₈

—

292

—

108

C₈

#11924013

yes

—

109

C₂²

—

110

C₂²

—

111

C₂²

—

112

C₂²

#14556565

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

584

—

116

C₄

C₂×#11924013

yes

characteristic

117

C₄

#14556616

yes

characteristic

118

C₄

#14556624

yes

—

119

C₂

—

120

C₂

#17988782

yes

characteristic

121

C₂

#17988845

yes

characteristic

122

C₂

#17988862

yes

characteristic

	subgroup	G/H
center	C₂²	#14556565
commutator	C₄²×C₇₃	C₂³
Frattini	C₄²	C₂²×D₇₃
Fitting	#436×C₇₃	C₂
socle	C₂²×C₇₃	#121
hypercenter	#436	D₇₃
hypocenter	C₇₃	#1689
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #436

subgroup

G/H

center

C₂²

#14556565

commutator

C₄²×C₇₃

C₂³

Frattini

C₄²

C₂²×D₇₃

Fitting

#436×C₇₃

C₂

C₂²×C₇₃

D₇₃

C₇₃

G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #436

N	H ≅ G/N	type
1. #17988967	C₂	semidirect
3. #17988338	C₂	semidirect
4. #17988334	C₂	semidirect
62. C₇₃	#1689	semidirect

H ≅ G/N

type

1. #17988967

C₂

semidirect

3. #17988338

C₂

semidirect

4. #17988334

C₂

semidirect

62. C₇₃

#1689

semidirect

Subgroups — #22609420

Conjugacy classes of subgroups

Complements