Group #22609455 — subgroups

Subgroups — #22609455

Order 9344.

154 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 55 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	#17988992	C₂	1	1	yes	maximal, characteristic, complemented
2	#17988878	C₂	1	2	yes	maximal
3	#17988666	C₂	1	1	yes	maximal, characteristic
4	#17988335	C₂	1	2	yes	maximal, complemented
5	#334×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11924011	—	2	1	no	—
7	#14556591	C₂²	1	2	yes	—
8	C₄×D₂₉₂	C₂²	1	1	yes	characteristic
9	#14556525	—	2	1	no	—
10	#14556525	—	2	1	no	—
11	#14556523	—	2	2	no	—
12	C₄⋊#10596831	C₂²	1	1	yes	characteristic
13	#14556513	—	2	2	no	—
14	#14556503	—	2	1	no	—
15	C₄⋊C₈×C₇₃	C₂²	1	2	yes	—
16	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×Dic₁₄₆	—	2	2	no	—
18	C₂×D₂₉₂	D₄	1	1	yes	characteristic
19	C₂×C₄×D₇₃	—	2	1	no	—
20	#11924011	—	4	2	no	—
21	C₂×#10596831	—	2	1	no	—
22	C₄⋊Dic₇₃	—	2	2	no	—
23	C₄⋊Dic₇₃	—	2	2	no	—
24	C₄⋊Dic₇₃	D₄	1	1	yes	characteristic
25	#11924005	—	2	1	no	—
26	C₂×C₈×C₇₃	—	2	2	no	—
27	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
28	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
29	C₄²×C₇₃	C₂³	1	1	yes	characteristic
30	C₂²×D₇₃	—	2	1	no	—
31	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
34	C₂×Dic₇₃	—	2	1	no	—
35	C₂×Dic₇₃	—	4	2	no	—
36	D₂₉₂	—	2	2	no	—
37	C₄×D₇₃	—	4	1	no	—
38	C₄×D₇₃	—	4	1	no	—
39	Dic₁₄₆	—	8	2	no	—
40	C₈×C₇₃	—	2	1	no	—
41	C₈×C₇₃	—	4	2	no	—
42	C₈×C₇₃	SD₁₆	1	2	yes	—
43	#10596831	—	4	1	no	—
44	C₂²×C₇₃	#121	1	1	yes	characteristic
45	C₂×D₇₃	—	4	1	no	—
46	C₂×D₇₃	—	4	1	no	—
47	C₂×D₇₃	—	4	1	no	—
48	C₄×C₇₃	—	2	1	no	—
49	C₄×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
50	C₄×C₇₃	#137	1	2	yes	—
51	C₄×C₇₃	#137	1	1	yes	characteristic
52	Dic₇₃	—	4	1	no	—
53	Dic₇₃	—	8	2	no	—
54	C₂×C₇₃	#461	1	1	yes	characteristic
55	C₂×C₇₃	#470	1	1	yes	characteristic
56	C₂×C₇₃	#472	1	1	yes	characteristic
57	D₇₃	—	8	1	no	—
58	#1695	—	73	1	no	maximal, Sylow
59	C₇₃	#1695	1	1	yes	characteristic, complemented, Sylow
60	#500	—	73	1	no	—
61	#476	—	73	2	no	—
62	#436	—	73	1	no	—
63	#334	D₇₃	1	1	yes	characteristic, complemented
64	#333	—	73	2	no	—
65	C₂×M₁₆	—	146	1	no	—
66	C₄⋊Q₈	—	73	2	no	—
67	C₄×D₄	—	73	1	no	—
68	#107	—	146	1	no	—
69	#107	—	146	1	no	—
70	#106	—	146	2	no	—
71	C₄⋊C₈	—	73	1	no	—
72	C₄⋊C₈	C₂×D₇₃	1	2	yes	—
73	#102	—	146	2	no	—
74	C₂²⋊C₈	—	146	1	no	—
75	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
76	C₂×Q₈	—	146	2	no	—
77	C₂×D₄	—	73	1	no	—
78	C₂²×C₄	—	146	1	no	—
79	M₁₆	—	292	2	no	—
80	C₂×C₈	—	2	2	no	—
81	C₂×C₈	—	146	1	no	—
82	C₂×C₈	D₂₉₂	1	1	yes	characteristic
83	C₂×C₈	D₂₉₂	1	1	yes	characteristic
84	C₄⋊C₄	—	73	1	no	—
85	C₄⋊C₄	—	146	2	no	—
86	C₄⋊C₄	—	146	2	no	—
87	C₂²⋊C₄	—	146	1	no	—
88	C₄²	C₂²×D₇₃	1	1	yes	characteristic
89	C₂³	—	146	1	no	—
90	Q₈	—	584	2	no	—
91	D₄	—	146	2	no	—
92	C₂×C₄	—	292	1	no	—
93	C₂×C₄	—	292	1	no	—
94	C₂×C₄	—	292	2	no	—
95	C₂×C₄	—	146	1	no	—
96	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
97	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
98	C₂×C₄	#11924029	1	1	yes	characteristic
99	C₈	—	2	1	no	—
100	C₈	—	4	2	no	—
101	C₈	—	292	1	no	—
102	C₈	#11924017	1	2	yes	—
103	C₂²	—	292	1	no	—
104	C₂²	—	292	1	no	—
105	C₂²	—	292	1	no	—
106	C₂²	#14556566	1	1	yes	characteristic
107	C₄	—	2	1	no	—
108	C₄	—	292	1	no	—
109	C₄	—	584	2	no	—
110	C₄	C₂×#11924017	1	1	yes	characteristic
111	C₄	#14556620	1	2	yes	—
112	C₄	#14556624	1	1	yes	characteristic
113	C₂	—	584	1	no	—
114	C₂	#17988793	1	1	yes	characteristic
115	C₂	#17988846	1	1	yes	characteristic
116	C₂	#17988858	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988992

C₂

yes

maximal, characteristic, complemented

#17988878

C₂

yes

maximal

#17988666

C₂

yes

maximal, characteristic

#17988335

C₂

yes

maximal, complemented

#334×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂×#11924011

—

#14556591

C₂²

yes

—

C₄×D₂₉₂

C₂²

yes

—

—

—

C₂²

yes

characteristic

#14556513

—

#14556503

—

C₄⋊C₈×C₇₃

C₂²

yes

—

C₄×C₈×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

—

C₂×D₂₉₂

D₄

yes

characteristic

C₂×C₄×D₇₃

—

#11924011

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

D₄

yes

characteristic

#11924005

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

D₄

yes

characteristic

C₄²×C₇₃

C₂³

yes

characteristic

C₂²×D₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

#41

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

D₂₉₂

—

C₄×D₇₃

—

C₄×D₇₃

—

Dic₁₄₆

—

C₈×C₇₃

—

C₈×C₇₃

—

C₈×C₇₃

SD₁₆

yes

—

#10596831

—

C₂²×C₇₃

#121

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₂×SD₁₆

yes

characteristic

C₄×C₇₃

#137

yes

—

C₄×C₇₃

#137

yes

characteristic

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

D₇₃

—

#1695

—

maximal, Sylow

C₇₃

#1695

yes

characteristic, complemented, Sylow

—

—

—

D₇₃

yes

characteristic, complemented

#333

—

C₂×M₁₆

—

146

—

C₄⋊Q₈

—

C₄×D₄

—

#107

—

146

—

#107

—

146

—

#106

—

146

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₇₃

yes

—

#102

—

146

—

C₂²⋊C₈

—

146

—

C₄×C₈

C₂×D₇₃

yes

characteristic

C₂×Q₈

—

146

—

C₂×D₄

—

C₂²×C₄

—

146

—

M₁₆

—

292

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

D₂₉₂

yes

characteristic

C₂×C₈

D₂₉₂

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₂²⋊C₄

—

146

—

C₄²

C₂²×D₇₃

yes

characteristic

C₂³

—

146

—

Q₈

—

584

—

D₄

—

146

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

146

—

C₂×C₄

D₄×D₇₃

yes

characteristic

C₂×C₄

C₂×D₂₉₂

yes

characteristic

C₂×C₄

#11924029

yes

characteristic

C₈

—

100

C₈

—

101

C₈

—

292

—

102

C₈

#11924017

yes

—

103

C₂²

—

292

—

104

C₂²

—

292

—

105

C₂²

—

292

—

106

C₂²

#14556566

yes

characteristic

107

C₄

—

108

C₄

—

292

—

109

C₄

—

584

—

110

C₄

C₂×#11924017

yes

characteristic

111

C₄

#14556620

yes

—

112

C₄

#14556624

yes

characteristic

113

C₂

—

584

—

114

C₂

#17988793

yes

characteristic

115

C₂

#17988846

yes

characteristic

116

C₂

#17988858

yes

characteristic

	subgroup	G/H
center	C₂²	#14556566
commutator	C₄²×C₇₃	C₂³
Frattini	C₄²	C₂²×D₇₃
Fitting	#334×C₇₃	C₂
socle	C₂²×C₇₃	#121
hypercenter	#334	D₇₃
hypocenter	C₇₃	#1695
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #334

subgroup

G/H

center

C₂²

#14556566

commutator

C₄²×C₇₃

C₂³

Frattini

C₄²

C₂²×D₇₃

Fitting

#334×C₇₃

C₂

C₂²×C₇₃

D₇₃

C₇₃

G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #334

N	H ≅ G/N	type
1. #17988992	C₂	semidirect
4. #17988335	C₂	semidirect
5. #334×C₇₃	C₂	semidirect
59. C₇₃	#1695	semidirect
63. #334	D₇₃	semidirect

H ≅ G/N

type

1. #17988992

C₂

semidirect

4. #17988335

C₂

semidirect

5. #334×C₇₃

C₂

semidirect

59. C₇₃

#1695

semidirect

63. #334

D₇₃

semidirect

Subgroups — #22609455

Conjugacy classes of subgroups

Complements