Group #22612202 — subgroups

Subgroups — #22612202

Order 9344.

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

normal subgroups only

This group has 178 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×Dic₅₈₄	C₂	1	2	yes	maximal, complemented
2	C₂×#14556536	C₂	1	2	yes	maximal
3	#17988971	C₂	1	1	yes	maximal, characteristic
4	#17988967	C₂	1	1	yes	maximal, characteristic, complemented
5	#346×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₂₉₂	—	2	1	no	—
7	C₂×Dic₂₉₂	C₂²	1	2	yes	—
8	C₂×Dic₂₉₂	C₂²	1	1	yes	characteristic
9	C₂×#11924017	—	2	1	no	—
10	C₂×D₅₈₄	C₂²	1	1	yes	characteristic
11	#14556591	—	2	1	no	—
12	#14556579	—	2	1	no	—
13	Dic₅₈₄	—	2	4	no	—
14	#14556536	—	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×Dic₁₄₆	—	2	2	no	—
19	C₂×D₂₉₂	—	2	1	no	—
20	Dic₂₉₂	—	2	2	no	—
21	Dic₂₉₂	—	2	2	no	—
22	Dic₂₉₂	—	2	2	no	—
23	Dic₂₉₂	—	4	2	no	—
24	#11924017	—	4	2	no	—
25	D₅₈₄	—	2	2	no	—
26	C₄⋊Dic₇₃	—	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	—
32	C₂²×D₇₃	—	4	1	no	—
33	C₂×C₄×C₇₃	D₈	1	2	yes	—
34	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
35	C₂×Dic₇₃	—	4	1	no	—
36	C₂×Dic₇₃	—	4	2	no	—
37	D₂₉₂	—	4	1	no	—
38	D₂₉₂	—	4	1	no	—
39	Dic₁₄₆	—	4	2	no	—
40	Dic₁₄₆	—	4	1	no	—
41	Dic₁₄₆	—	4	1	no	—
42	Dic₁₄₆	—	4	2	no	—
43	C₈×C₇₃	D₈	1	2	yes	—
44	C₈×C₇₃	C₂×D₄	1	2	yes	—
45	C₂²×C₇₃	C₂×D₈	1	1	yes	characteristic
46	C₂×D₇₃	—	8	1	no	—
47	C₂×D₇₃	—	8	2	no	—
48	C₄×C₇₃	—	2	2	no	—
49	C₄×C₇₃	#127	1	1	yes	characteristic
50	C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
51	Dic₇₃	—	8	1	no	—
52	Dic₇₃	—	8	2	no	—
53	C₂×C₇₃	#493	1	1	yes	characteristic
54	C₂×C₇₃	#510	1	2	yes	—
55	D₇₃	—	16	1	no	—
56	#2251	—	73	1	no	maximal, Sylow
57	C₇₃	#2251	1	1	yes	characteristic, complemented, Sylow
58	C₂×Q₃₂	—	73	2	no	—
59	C₂×SD₃₂	—	73	2	no	—
60	#495	—	73	1	no	—
61	#494	—	73	1	no	—
62	#346	D₇₃	1	1	yes	characteristic, complemented
63	C₂×Q₁₆	—	73	2	no	—
64	C₂×Q₁₆	—	73	1	no	—
65	C₂×Q₁₆	—	146	1	no	—
66	C₂×SD₁₆	—	146	1	no	—
67	C₂×D₈	—	73	1	no	—
68	C₄⋊Q₈	—	146	1	no	—
69	#124	—	146	1	no	—
70	Q₃₂	—	146	4	no	—
71	SD₃₂	—	146	4	no	—
72	C₂×C₁₆	C₂×D₇₃	1	2	yes	—
73	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
74	C₂×Q₈	—	146	1	no	—
75	C₂×Q₈	—	146	2	no	—
76	C₂×D₄	—	146	1	no	—
77	Q₁₆	—	292	2	no	—
78	Q₁₆	—	146	2	no	—
79	Q₁₆	—	146	2	no	—
80	Q₁₆	—	146	2	no	—
81	SD₁₆	—	292	2	no	—
82	D₈	—	146	2	no	—
83	C₂×C₈	D₂₉₂	1	1	yes	characteristic
84	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
85	C₄⋊C₄	—	292	2	no	—
86	C₂²⋊C₄	—	292	2	no	—
87	C₄²	D₂₉₂	1	1	yes	characteristic
88	C₁₆	D₂₉₂	1	4	yes	—
89	C₂³	—	292	1	no	—
90	Q₈	—	292	2	no	—
91	Q₈	—	292	1	no	—
92	Q₈	—	292	1	no	—
93	Q₈	—	292	2	no	—
94	D₄	—	292	1	no	—
95	D₄	—	292	1	no	—
96	C₂×C₄	—	292	1	no	—
97	C₂×C₄	—	292	2	no	—
98	C₂×C₄	D₅₈₄	1	2	yes	—
99	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
100	C₈	D₅₈₄	1	2	yes	—
101	C₈	C₂×D₂₉₂	1	2	yes	—
102	C₂²	—	584	1	no	—
103	C₂²	—	584	2	no	—
104	C₂²	C₂×D₅₈₄	1	1	yes	characteristic
105	C₄	—	2	2	no	—
106	C₄	—	584	1	no	—
107	C₄	—	584	2	no	—
108	C₄	#14556588	1	1	yes	characteristic
109	C₄	C₂×D₅₈₄	1	1	yes	characteristic
110	C₂	—	1168	1	no	—
111	C₂	#17988964	1	1	yes	characteristic
112	C₂	#17989030	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₅₈₄

C₂

yes

maximal, complemented

C₂×#14556536

C₂

yes

maximal

#17988971

C₂

yes

maximal, characteristic

#17988967

C₂

yes

maximal, characteristic, complemented

#346×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

C₂²

yes

—

C₂×Dic₂₉₂

C₂²

yes

characteristic

C₂×#11924017

—

C₂×D₅₈₄

C₂²

yes

characteristic

#14556591

—

#14556579

—

Dic₅₈₄

—

#14556536

—

C₂×C₁₆×C₇₃

C₂²

yes

—

C₄×C₈×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×D₂₉₂

—

Dic₂₉₂

—

Dic₂₉₂

—

Dic₂₉₂

—

Dic₂₉₂

—

#11924017

—

D₅₈₄

—

C₄⋊Dic₇₃

—

#11924005

—

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₄²×C₇₃

D₄

yes

characteristic

C₁₆×C₇₃

D₄

yes

—

C₂²×D₇₃

—

C₂×C₄×C₇₃

D₈

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

D₂₉₂

—

D₂₉₂

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

D₈

yes

—

C₈×C₇₃

C₂×D₄

yes

—

C₂²×C₇₃

C₂×D₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#127

yes

characteristic

C₄×C₇₃

C₂×D₈

yes

characteristic

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

#493

yes

characteristic

C₂×C₇₃

#510

yes

—

D₇₃

—

#2251

—

maximal, Sylow

C₇₃

#2251

yes

characteristic, complemented, Sylow

C₂×Q₃₂

—

C₂×SD₃₂

—

#495

—

#494

—

#346

D₇₃

yes

characteristic, complemented

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

146

—

C₂×SD₁₆

—

146

—

C₂×D₈

—

C₄⋊Q₈

—

146

—

#124

—

146

—

Q₃₂

—

146

—

SD₃₂

—

146

—

C₂×C₁₆

C₂×D₇₃

yes

—

C₄×C₈

C₂×D₇₃

yes

characteristic

C₂×Q₈

—

146

—

C₂×Q₈

—

146

—

C₂×D₄

—

146

—

Q₁₆

—

292

—

Q₁₆

—

146

—

Q₁₆

—

146

—

Q₁₆

—

146

—

SD₁₆

—

292

—

D₈

—

146

—

C₂×C₈

D₂₉₂

yes

characteristic

C₂×C₈

C₂²×D₇₃

yes

characteristic

C₄⋊C₄

—

292

—

C₂²⋊C₄

—

292

—

C₄²

D₂₉₂

yes

characteristic

C₁₆

D₂₉₂

yes

—

C₂³

—

292

—

Q₈

—

292

—

Q₈

—

292

—

Q₈

—

292

—

Q₈

—

292

—

D₄

—

292

—

D₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

D₅₈₄

yes

—

C₂×C₄

C₂×D₂₉₂

yes

characteristic

100

C₈

D₅₈₄

yes

—

101

C₈

C₂×D₂₉₂

yes

—

102

C₂²

—

584

—

103

C₂²

—

584

—

104

C₂²

C₂×D₅₈₄

yes

characteristic

105

C₄

—

106

C₄

—

584

—

107

C₄

—

584

—

108

C₄

#14556588

yes

characteristic

109

C₄

C₂×D₅₈₄

yes

characteristic

110

C₂

—

1168

—

111

C₂

#17988964

yes

characteristic

112

C₂

#17989030

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	#2251
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×Dic₅₈₄	C₂	semidirect
4. #17988967	C₂	semidirect
5. #346×C₇₃	C₂	semidirect
57. C₇₃	#2251	semidirect
62. #346	D₇₃	semidirect

H ≅ G/N

type

1. C₂×Dic₅₈₄

C₂

semidirect

4. #17988967

C₂

semidirect

5. #346×C₇₃

C₂

semidirect

57. C₇₃

#2251

semidirect

62. #346

D₇₃

semidirect

Subgroups — #22612202

Conjugacy classes of subgroups

Complements