Group #22624945 — subgroups

Subgroups — #22624945

Order 9344.

118 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 118 conjugacy classes of subgroups — too many to draw. Only its 34 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	#17989508	C₂	1	1	yes	maximal, characteristic, complemented
2	#17989451	C₂	1	1	yes	maximal, characteristic, complemented
3	#17988962	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924031	—	2	1	no	—
5	C₄⋊#10596833	—	2	1	no	—
6	C₂×D₅₈₄	C₄	1	1	yes	characteristic
7	C₂×#11924013	—	2	1	no	—
8	#14556587	—	2	1	no	—
9	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
10	C₂×D₈×C₇₃	C₄	1	1	yes	characteristic
11	C₂×#10596833	—	4	1	no	—
12	#11924031	—	4	1	no	—
13	C₂×D₂₉₂	—	2	1	no	—
14	C₂×C₂²⋊D₇₃	—	4	1	no	—
15	C₂×C₂²⋊D₇₃	—	4	1	no	—
16	D₅₈₄	—	4	1	no	—
17	#11924013	—	4	1	no	—
18	#11924013	—	4	1	no	—
19	C₂×#10596831	D₄	1	1	yes	characteristic
20	C₄×Dic₇₃	D₄	1	1	yes	characteristic
21	C₂×D₄×C₇₃	—	2	1	no	—
22	D₈×C₇₃	—	4	1	no	—
23	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₇₃	—	4	1	no	—
25	C₂²×D₇₃	—	4	1	no	—
26	D₄×C₇₃	—	4	1	no	—
27	D₄×C₇₃	—	4	1	no	—
28	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
29	C₂²⋊D₇₃	—	8	2	no	—
30	C₂²⋊D₇₃	—	8	1	no	—
31	C₂²⋊D₇₃	—	8	1	no	—
32	C₂×Dic₇₃	D₈	1	1	yes	characteristic
33	C₂×Dic₇₃	SD₁₆	1	1	yes	characteristic
34	D₂₉₂	—	4	1	no	—
35	D₂₉₂	—	4	1	no	—
36	#10596833	—	8	1	no	—
37	C₈×C₇₃	—	2	1	no	—
38	#10596831	D₈	1	1	yes	characteristic
39	#10596831	SD₁₆	1	1	yes	characteristic
40	C₂²×C₇₃	—	8	1	no	—
41	C₂²×C₇₃	—	8	1	no	—
42	C₂²×C₇₃	—	8	1	no	—
43	C₂²×C₇₃	#102	1	1	yes	characteristic
44	C₂×D₇₃	—	8	1	no	—
45	C₂×D₇₃	—	8	1	no	—
46	C₂×D₇₃	—	8	1	no	—
47	C₄×C₇₃	#100	1	1	yes	characteristic
48	C₄×C₇₃	#102	1	1	yes	characteristic
49	Dic₇₃	—	2	1	no	—
50	Dic₇₃	D₁₆	1	1	yes	characteristic
51	Dic₇₃	SD₃₂	1	1	yes	characteristic
52	C₂×C₇₃	—	16	1	no	—
53	C₂×C₇₃	#331	1	1	yes	characteristic
54	C₂×C₇₃	#357	1	1	yes	characteristic
55	C₂×C₇₃	#361	1	1	yes	characteristic
56	D₇₃	—	16	1	no	—
57	#1361	—	73	1	no	maximal, Sylow
58	C₇₃	#1361	1	1	yes	characteristic, complemented, Sylow
59	#493	—	73	1	no	—
60	C₄⋊C₁₆	—	73	1	no	—
61	#335	—	73	1	no	—
62	C₂×D₈	—	73	1	no	—
63	C₂×D₈	—	146	1	no	—
64	C₂×D₈	#64408	1	1	yes	characteristic
65	#127	—	146	1	no	—
66	C₂×C₁₆	—	146	1	no	—
67	C₄⋊C₈	—	146	1	no	—
68	C₄×C₈	—	73	1	no	—
69	C₂×D₄	—	2	1	no	—
70	C₂×D₄	—	292	1	no	—
71	C₂×D₄	—	292	1	no	—
72	C₂×D₄	—	146	1	no	—
73	D₈	—	4	1	no	—
74	D₈	—	292	1	no	—
75	D₈	—	292	1	no	—
76	D₈	—	292	1	no	—
77	C₂×C₈	—	292	1	no	—
78	C₂×C₈	—	73	1	no	—
79	C₂×C₈	C₂×#64408	1	1	yes	characteristic
80	C₄²	—	73	1	no	—
81	C₁₆	—	292	1	no	—
82	C₂³	—	4	1	no	—
83	C₂³	—	292	1	no	—
84	D₄	—	4	1	no	—
85	D₄	—	4	1	no	—
86	D₄	—	292	1	no	—
87	D₄	—	292	1	no	—
88	D₄	—	584	1	no	—
89	D₄	—	584	1	no	—
90	D₄	—	584	2	no	—
91	C₂×C₄	—	73	1	no	—
92	C₂×C₄	—	73	1	no	—
93	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
94	C₈	—	2	1	no	—
95	C₈	—	584	1	no	—
96	C₈	—	73	1	no	—
97	C₈	—	73	1	no	—
98	C₂²	—	8	1	no	—
99	C₂²	—	8	1	no	—
100	C₂²	—	8	1	no	—
101	C₂²	—	584	1	no	—
102	C₂²	—	584	1	no	—
103	C₂²	—	584	1	no	—
104	C₂²	#14556653	1	1	yes	characteristic
105	C₄	—	73	1	no	—
106	C₄	—	73	1	no	—
107	C₄	—	146	1	no	—
108	C₄	#14556651	1	1	yes	characteristic
109	C₄	#14556653	1	1	yes	characteristic
110	C₂	—	16	1	no	—
111	C₂	—	1168	1	no	—
112	C₂	#17989445	1	1	yes	characteristic
113	C₂	#17989499	1	1	yes	characteristic
114	C₂	#17989505	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989508

C₂

yes

maximal, characteristic, complemented

#17989451

C₂

yes

maximal, characteristic, complemented

#17988962

C₂

yes

maximal, characteristic

C₂×#11924031

—

C₄⋊#10596833

—

C₂×D₅₈₄

C₄

yes

characteristic

C₂×#11924013

—

#14556587

—

C₈×Dic₇₃

C₂²

yes

characteristic

C₂×D₈×C₇₃

C₄

yes

characteristic

C₂×#10596833

—

#11924031

—

C₂×D₂₉₂

—

C₂×C₂²⋊D₇₃

—

C₂×C₂²⋊D₇₃

—

D₅₈₄

—

#11924013

—

#11924013

—

C₂×#10596831

D₄

yes

characteristic

C₄×Dic₇₃

D₄

yes

characteristic

C₂×D₄×C₇₃

—

D₈×C₇₃

—

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂³×C₇₃

—

C₂²×D₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂²⋊D₇₃

—

C₂²⋊D₇₃

—

C₂²⋊D₇₃

—

C₂×Dic₇₃

D₈

yes

characteristic

C₂×Dic₇₃

SD₁₆

yes

characteristic

D₂₉₂

—

D₂₉₂

—

#10596833

—

C₈×C₇₃

—

#10596831

D₈

yes

characteristic

#10596831

SD₁₆

yes

characteristic

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#102

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

Dic₇₃

D₁₆

yes

characteristic

Dic₇₃

SD₃₂

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

D₇₃

—

#1361

—

maximal, Sylow

C₇₃

#1361

yes

characteristic, complemented, Sylow

#493

—

C₄⋊C₁₆

—

#335

—

C₂×D₈

—

C₂×D₈

—

146

—

C₂×D₈

#64408

yes

characteristic

#127

—

146

—

C₂×C₁₆

—

146

—

C₄⋊C₈

—

146

—

C₄×C₈

—

C₂×D₄

—

C₂×D₄

—

292

—

C₂×D₄

—

292

—

C₂×D₄

—

146

—

D₈

—

D₈

—

292

—

D₈

—

292

—

D₈

—

292

—

C₂×C₈

—

292

—

C₂×C₈

—

C₂×C₈

C₂×#64408

yes

characteristic

C₄²

—

C₁₆

—

292

—

C₂³

—

C₂³

—

292

—

D₄

—

D₄

—

D₄

—

292

—

D₄

—

292

—

D₄

—

584

—

D₄

—

584

—

D₄

—

584

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊#64408

yes

characteristic

C₈

—

C₈

—

584

—

C₈

—

C₈

—

C₂²

—

C₂²

—

100

C₂²

—

101

C₂²

—

584

—

102

C₂²

—

584

—

103

C₂²

—

584

—

104

C₂²

#14556653

yes

characteristic

105

C₄

—

106

C₄

—

107

C₄

—

146

—

108

C₄

#14556651

yes

characteristic

109

C₄

#14556653

yes

characteristic

110

C₂

—

111

C₂

—

1168

—

112

C₂

#17989445

yes

characteristic

113

C₂

#17989499

yes

characteristic

114

C₂

#17989505

yes

characteristic

	subgroup	G/H
center	C₂²	#14556653
commutator	C₂×C₈×C₇₃	C₂×C₄
Frattini	C₂×C₈	C₂×#64408
Fitting	C₂×D₈×C₇₃	C₄
socle	C₂²×C₇₃	#102
hypercenter	C₂×D₈	#64408
hypocenter	C₇₃	#1361
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

subgroup

G/H

center

C₂²

#14556653

commutator

C₂×C₈×C₇₃

C₂×C₄

Frattini

C₂×C₈

C₂×#64408

Fitting

C₂×D₈×C₇₃

C₄

C₂²×C₇₃

C₂×D₈

C₇₃

G ▷ C₂×C₈×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

N	H ≅ G/N	type
1. #17989508	C₂	semidirect
2. #17989451	C₂	semidirect
58. C₇₃	#1361	semidirect

H ≅ G/N

type

1. #17989508

C₂

semidirect

2. #17989451

C₂

semidirect

58. C₇₃

#1361

semidirect

Subgroups — #22624945

Conjugacy classes of subgroups

Complements