Group #22612197 — subgroups

Subgroups — #22612197

Order 9344.

198 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 61 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	C₂×#14556536	C₂	1	2	yes	maximal, complemented
2	C₂×D₁₁₆₈	C₂	1	2	yes	maximal, complemented
3	#17988971	C₂	1	1	yes	maximal, characteristic, complemented
4	#17988964	C₂	1	1	yes	maximal, characteristic, complemented
5	#346×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₂₉₂	C₂²	1	1	yes	characteristic
7	C₂×#11924017	—	2	1	no	—
8	C₂×D₅₈₄	—	2	1	no	—
9	C₂×D₅₈₄	C₂²	1	2	yes	—
10	C₂×D₅₈₄	C₂²	1	1	yes	characteristic
11	#14556588	—	2	1	no	—
12	#14556579	—	2	1	no	—
13	#14556536	—	2	4	no	—
14	D₁₁₆₈	—	2	4	no	—
15	C₂×C₁₆×C₇₃	C₂²	1	2	yes	—
16	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×Dic₁₄₆	—	2	1	no	—
18	C₂×D₂₉₂	—	2	1	no	—
19	C₂×D₂₉₂	—	2	2	no	—
20	C₂×D₂₉₂	—	4	2	no	—
21	Dic₂₉₂	—	2	2	no	—
22	#11924017	—	4	2	no	—
23	D₅₈₄	—	2	2	no	—
24	D₅₈₄	—	2	2	no	—
25	D₅₈₄	—	2	2	no	—
26	D₅₈₄	—	4	2	no	—
27	#11924005	—	4	2	no	—
28	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
29	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
30	C₄²×C₇₃	D₄	1	1	yes	characteristic
31	C₁₆×C₇₃	D₄	1	4	yes	complemented
32	C₂²×D₇₃	—	4	1	no	—
33	C₂²×D₇₃	—	4	2	no	—
34	C₂×C₄×C₇₃	D₈	1	2	yes	—
35	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
36	C₂×Dic₇₃	—	4	1	no	—
37	D₂₉₂	—	4	1	no	—
38	D₂₉₂	—	4	2	no	—
39	D₂₉₂	—	4	2	no	—
40	D₂₉₂	—	4	1	no	—
41	D₂₉₂	—	8	4	no	—
42	Dic₁₄₆	—	4	1	no	—
43	Dic₁₄₆	—	4	1	no	—
44	C₈×C₇₃	D₈	1	2	yes	—
45	C₈×C₇₃	C₂×D₄	1	2	yes	—
46	C₂²×C₇₃	C₂×D₈	1	1	yes	characteristic
47	C₂×D₇₃	—	8	2	no	—
48	C₂×D₇₃	—	8	1	no	—
49	C₂×D₇₃	—	8	4	no	—
50	C₂×D₇₃	—	8	2	no	—
51	C₄×C₇₃	—	2	2	no	—
52	C₄×C₇₃	#127	1	1	yes	characteristic
53	C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
54	Dic₇₃	—	8	1	no	—
55	C₂×C₇₃	#493	1	1	yes	characteristic
56	C₂×C₇₃	#509	1	2	yes	—
57	D₇₃	—	16	2	no	—
58	D₇₃	—	16	1	no	—
59	#2250	—	73	1	no	maximal, Sylow
60	C₇₃	#2250	1	1	yes	characteristic, complemented, Sylow
61	C₂×SD₃₂	—	73	2	no	—
62	C₂×D₁₆	—	73	2	no	—
63	#495	—	73	1	no	—
64	#493	—	73	1	no	—
65	#346	D₇₃	1	1	yes	characteristic, complemented
66	C₂×Q₁₆	—	73	1	no	—
67	C₂×SD₁₆	—	146	1	no	—
68	C₂×D₈	—	73	2	no	—
69	C₂×D₈	—	73	1	no	—
70	C₂×D₈	—	146	1	no	—
71	#127	—	146	1	no	—
72	#124	—	146	1	no	—
73	SD₃₂	—	146	4	no	—
74	D₁₆	—	146	4	no	—
75	C₂×C₁₆	C₂×D₇₃	1	2	yes	—
76	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
77	C₂×Q₈	—	146	1	no	—
78	C₂×D₄	—	292	2	no	—
79	C₂×D₄	—	146	1	no	—
80	C₂×D₄	—	146	2	no	—
81	Q₁₆	—	146	2	no	—
82	SD₁₆	—	292	2	no	—
83	D₈	—	292	2	no	—
84	D₈	—	146	2	no	—
85	D₈	—	146	2	no	—
86	D₈	—	146	2	no	—
87	C₂×C₈	D₂₉₂	1	1	yes	characteristic
88	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
89	C₂²⋊C₄	—	292	2	no	—
90	C₄²	D₂₉₂	1	1	yes	characteristic
91	C₁₆	D₂₉₂	1	4	yes	complemented
92	C₂³	—	292	1	no	—
93	C₂³	—	292	2	no	—
94	Q₈	—	292	1	no	—
95	Q₈	—	292	1	no	—
96	D₄	—	292	1	no	—
97	D₄	—	292	2	no	—
98	D₄	—	292	2	no	—
99	D₄	—	292	1	no	—
100	D₄	—	584	4	no	—
101	C₂×C₄	—	292	1	no	—
102	C₂×C₄	D₅₈₄	1	2	yes	—
103	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
104	C₈	D₅₈₄	1	2	yes	—
105	C₈	C₂×D₂₉₂	1	2	yes	—
106	C₂²	—	584	2	no	—
107	C₂²	—	584	1	no	—
108	C₂²	—	584	4	no	—
109	C₂²	—	584	2	no	—
110	C₂²	C₂×D₅₈₄	1	1	yes	characteristic
111	C₄	—	2	2	no	—
112	C₄	—	584	1	no	—
113	C₄	#14556588	1	1	yes	characteristic
114	C₄	C₂×D₅₈₄	1	1	yes	characteristic
115	C₂	—	1168	2	no	—
116	C₂	—	1168	1	no	—
117	C₂	#17988964	1	1	yes	characteristic
118	C₂	#17989025	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556536

C₂

yes

maximal, complemented

C₂×D₁₁₆₈

C₂

yes

maximal, complemented

#17988971

C₂

yes

maximal, characteristic, complemented

#17988964

C₂

yes

maximal, characteristic, complemented

#346×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂×Dic₂₉₂

C₂²

yes

characteristic

C₂×#11924017

—

C₂×D₅₈₄

—

C₂×D₅₈₄

C₂²

yes

—

C₂×D₅₈₄

C₂²

yes

—

—

—

D₁₁₆₈

—

C₂×C₁₆×C₇₃

C₂²

yes

—

C₄×C₈×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

Dic₂₉₂

—

#11924017

—

D₅₈₄

—

D₅₈₄

—

D₅₈₄

—

D₅₈₄

—

#11924005

—

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₄²×C₇₃

D₄

yes

characteristic

C₁₆×C₇₃

D₄

yes

complemented

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂×C₄×C₇₃

D₈

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

—

D₂₉₂

—

D₂₉₂

—

D₂₉₂

—

D₂₉₂

—

D₂₉₂

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

D₈

yes

—

C₈×C₇₃

C₂×D₄

yes

—

C₂²×C₇₃

C₂×D₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#127

yes

characteristic

C₄×C₇₃

C₂×D₈

yes

characteristic

Dic₇₃

—

C₂×C₇₃

#493

yes

characteristic

C₂×C₇₃

#509

yes

—

D₇₃

—

D₇₃

—

#2250

—

maximal, Sylow

C₇₃

#2250

yes

characteristic, complemented, Sylow

C₂×SD₃₂

—

C₂×D₁₆

—

#495

—

#493

—

#346

D₇₃

yes

characteristic, complemented

C₂×Q₁₆

—

C₂×SD₁₆

—

146

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

146

—

#127

—

146

—

#124

—

146

—

SD₃₂

—

146

—

D₁₆

—

146

—

C₂×C₁₆

C₂×D₇₃

yes

—

C₄×C₈

C₂×D₇₃

yes

characteristic

C₂×Q₈

—

146

—

C₂×D₄

—

292

—

C₂×D₄

—

146

—

C₂×D₄

—

146

—

Q₁₆

—

146

—

SD₁₆

—

292

—

D₈

—

292

—

D₈

—

146

—

D₈

—

146

—

D₈

—

146

—

C₂×C₈

D₂₉₂

yes

characteristic

C₂×C₈

C₂²×D₇₃

yes

characteristic

C₂²⋊C₄

—

292

—

C₄²

D₂₉₂

yes

characteristic

C₁₆

D₂₉₂

yes

complemented

C₂³

—

292

—

C₂³

—

292

—

Q₈

—

292

—

Q₈

—

292

—

D₄

—

292

—

D₄

—

292

—

D₄

—

292

—

D₄

—

292

—

100

D₄

—

584

—

101

C₂×C₄

—

292

—

102

C₂×C₄

D₅₈₄

yes

—

103

C₂×C₄

C₂×D₂₉₂

yes

characteristic

104

C₈

D₅₈₄

yes

—

105

C₈

C₂×D₂₉₂

yes

—

106

C₂²

—

584

—

107

C₂²

—

584

—

108

C₂²

—

584

—

109

C₂²

—

584

—

110

C₂²

C₂×D₅₈₄

yes

characteristic

111

C₄

—

112

C₄

—

584

—

113

C₄

#14556588

yes

characteristic

114

C₄

C₂×D₅₈₄

yes

characteristic

115

C₂

—

1168

—

116

C₂

—

1168

—

117

C₂

#17988964

yes

characteristic

118

C₂

#17989025

yes

—

	subgroup	G/H
center	C₂²	C₂×D₅₈₄
commutator	C₂×C₈×C₇₃	C₂³
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	#346×C₇₃	C₂
socle	C₂²×C₇₃	C₂×D₈
hypercenter	#346	D₇₃
hypocenter	C₇₃	#2250
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

subgroup

G/H

center

C₂²

C₂×D₅₈₄

commutator

C₂×C₈×C₇₃

C₂³

Frattini

C₂×C₈

C₂²×D₇₃

Fitting

#346×C₇₃

C₂

socle

C₂²×C₇₃

C₂×D₈

D₇₃

C₇₃

G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

N	H ≅ G/N	type
1. C₂×#14556536	C₂	semidirect
2. C₂×D₁₁₆₈	C₂	semidirect
3. #17988971	C₂	semidirect
4. #17988964	C₂	semidirect
5. #346×C₇₃	C₂	semidirect
31. C₁₆×C₇₃	D₄	semidirect
60. C₇₃	#2250	semidirect
65. #346	D₇₃	semidirect
91. C₁₆	D₂₉₂	semidirect

H ≅ G/N

type

1. C₂×#14556536

C₂

semidirect

2. C₂×D₁₁₆₈

C₂

semidirect

3. #17988971

C₂

semidirect

4. #17988964

C₂

semidirect

5. #346×C₇₃

C₂

semidirect

31. C₁₆×C₇₃

D₄

semidirect

60. C₇₃

#2250

semidirect

65. #346

D₇₃

semidirect

91. C₁₆

D₂₉₂

semidirect

Subgroups — #22612197

Conjugacy classes of subgroups

Complements