Group #22612192 — subgroups

Subgroups — #22612192

Order 9344.

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

normal subgroups only

This group has 184 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	1	yes	maximal, characteristic, complemented
2	C₂×#14556536	C₂	1	2	yes	maximal, complemented
3	C₂×D₁₁₆₈	C₂	1	1	yes	maximal, characteristic
4	#17988971	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₂₉₂	C₂²	1	2	yes	—
7	C₂×#11924017	—	2	2	no	—
8	C₂×D₅₈₄	C₂²	1	2	yes	—
9	#14556579	—	2	2	no	—
10	Dic₅₈₄	—	2	2	no	—
11	#14556536	—	2	4	no	—
12	D₁₁₆₈	—	2	2	no	—
13	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×Dic₁₄₆	—	2	2	no	—
17	C₂×D₂₉₂	—	2	2	no	—
18	Dic₂₉₂	—	2	2	no	—
19	Dic₂₉₂	—	2	2	no	—
20	#11924017	—	4	4	no	—
21	D₅₈₄	—	2	2	no	—
22	D₅₈₄	—	2	2	no	—
23	#11924005	—	4	4	no	—
24	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
25	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
26	C₄²×C₇₃	D₄	1	1	yes	characteristic
27	C₁₆×C₇₃	D₄	1	2	yes	—
28	C₁₆×C₇₃	D₄	1	2	yes	—
29	C₂²×D₇₃	—	4	2	no	—
30	C₂×C₄×C₇₃	D₈	1	2	yes	—
31	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
32	C₂×Dic₇₃	—	4	2	no	—
33	D₂₉₂	—	4	2	no	—
34	D₂₉₂	—	4	2	no	—
35	Dic₁₄₆	—	4	2	no	—
36	Dic₁₄₆	—	4	2	no	—
37	C₈×C₇₃	D₈	1	2	yes	—
38	C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
39	C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
40	C₂²×C₇₃	C₂×D₈	1	1	yes	characteristic
41	C₂×D₇₃	—	8	2	no	—
42	C₂×D₇₃	—	8	4	no	—
43	C₄×C₇₃	—	2	2	no	—
44	C₄×C₇₃	#127	1	1	yes	characteristic
45	C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
46	Dic₇₃	—	8	2	no	—
47	C₂×C₇₃	#493	1	1	yes	characteristic
48	C₂×C₇₃	#508	1	2	yes	—
49	D₇₃	—	16	2	no	—
50	#2249	—	73	1	no	maximal, Sylow
51	C₇₃	#2249	1	1	yes	characteristic, complemented, Sylow
52	C₂×Q₃₂	—	73	1	no	—
53	C₂×SD₃₂	—	73	2	no	—
54	C₂×D₁₆	—	73	1	no	—
55	#495	—	73	2	no	—
56	C₄×C₁₆	D₇₃	1	1	yes	characteristic, complemented
57	C₂×Q₁₆	—	73	2	no	—
58	C₂×SD₁₆	—	146	2	no	—
59	C₂×D₈	—	73	2	no	—
60	#124	—	146	2	no	—
61	Q₃₂	—	146	2	no	—
62	SD₃₂	—	146	4	no	—
63	D₁₆	—	146	2	no	—
64	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
65	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
66	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
67	C₂×Q₈	—	146	2	no	—
68	C₂×D₄	—	146	2	no	—
69	Q₁₆	—	146	2	no	—
70	Q₁₆	—	146	2	no	—
71	SD₁₆	—	292	4	no	—
72	D₈	—	146	2	no	—
73	D₈	—	146	2	no	—
74	C₂×C₈	D₂₉₂	1	1	yes	characteristic
75	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
76	C₂²⋊C₄	—	292	4	no	—
77	C₄²	D₂₉₂	1	1	yes	characteristic
78	C₁₆	D₂₉₂	1	2	yes	—
79	C₁₆	D₂₉₂	1	2	yes	—
80	C₂³	—	292	2	no	—
81	Q₈	—	292	2	no	—
82	Q₈	—	292	2	no	—
83	D₄	—	292	2	no	—
84	D₄	—	292	2	no	—
85	C₂×C₄	—	292	2	no	—
86	C₂×C₄	D₅₈₄	1	2	yes	—
87	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
88	C₈	D₅₈₄	1	2	yes	—
89	C₈	C₂×D₂₉₂	1	1	yes	characteristic
90	C₈	C₂×D₂₉₂	1	1	yes	characteristic
91	C₂²	—	584	2	no	—
92	C₂²	—	584	4	no	—
93	C₂²	C₂×D₅₈₄	1	1	yes	characteristic
94	C₄	—	2	2	no	—
95	C₄	—	584	2	no	—
96	C₄	#14556588	1	1	yes	characteristic
97	C₄	C₂×D₅₈₄	1	1	yes	characteristic
98	C₂	—	1168	2	no	—
99	C₂	#17988964	1	1	yes	characteristic
100	C₂	#17989019	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₅₈₄

C₂

yes

maximal, characteristic, complemented

C₂×#14556536

C₂

yes

maximal, complemented

C₂×D₁₁₆₈

C₂

yes

maximal, characteristic

#17988971

C₂

yes

maximal, complemented

C₄×C₁₆×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂×Dic₂₉₂

C₂²

yes

—

C₂×#11924017

—

C₂×D₅₈₄

C₂²

yes

—

#14556579

—

Dic₅₈₄

—

#14556536

—

D₁₁₆₈

—

C₂×C₁₆×C₇₃

C₂²

yes

characteristic

C₂×C₁₆×C₇₃

C₂²

yes

characteristic

C₄×C₈×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

—

C₂×D₂₉₂

—

Dic₂₉₂

—

Dic₂₉₂

—

#11924017

—

D₅₈₄

—

D₅₈₄

—

#11924005

—

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₄²×C₇₃

D₄

yes

characteristic

C₁₆×C₇₃

D₄

yes

—

C₁₆×C₇₃

D₄

yes

—

C₂²×D₇₃

—

C₂×C₄×C₇₃

D₈

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

—

D₂₉₂

—

D₂₉₂

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

D₈

yes

—

C₈×C₇₃

C₂×D₄

yes

characteristic

C₈×C₇₃

C₂×D₄

yes

characteristic

C₂²×C₇₃

C₂×D₈

yes

characteristic

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

#508

yes

—

D₇₃

—

#2249

—

maximal, Sylow

C₇₃

#2249

yes

characteristic, complemented, Sylow

C₂×Q₃₂

—

C₂×SD₃₂

—

C₂×D₁₆

—

#495

—

C₄×C₁₆

D₇₃

yes

characteristic, complemented

C₂×Q₁₆

—

C₂×SD₁₆

—

146

—

C₂×D₈

—

#124

—

146

—

Q₃₂

—

146

—

SD₃₂

—

146

—

D₁₆

—

146

—

C₂×C₁₆

C₂×D₇₃

yes

characteristic

C₂×C₁₆

C₂×D₇₃

yes

characteristic

C₄×C₈

C₂×D₇₃

yes

characteristic

C₂×Q₈

—

146

—

C₂×D₄

—

146

—

Q₁₆

—

146

—

Q₁₆

—

146

—

SD₁₆

—

292

—

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

—

C₁₆

D₂₉₂

yes

—

C₂³

—

292

—

Q₈

—

292

—

Q₈

—

292

—

D₄

—

292

—

D₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

D₅₈₄

yes

—

C₂×C₄

C₂×D₂₉₂

yes

characteristic

C₈

D₅₈₄

yes

—

C₈

C₂×D₂₉₂

yes

characteristic

C₈

C₂×D₂₉₂

yes

characteristic

C₂²

—

584

—

C₂²

—

584

—

C₂²

C₂×D₅₈₄

yes

characteristic

C₄

—

C₄

—

584

—

C₄

#14556588

yes

characteristic

C₄

C₂×D₅₈₄

yes

characteristic

C₂

—

1168

—

C₂

#17988964

yes

characteristic

100

C₂

#17989019

yes

—

	subgroup	G/H
center	C₂²	C₂×D₅₈₄
commutator	C₂×C₈×C₇₃	C₂³
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	C₄×C₁₆×C₇₃	C₂
socle	C₂²×C₇₃	C₂×D₈
hypercenter	C₄×C₁₆	D₇₃
hypocenter	C₇₃	#2249
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

subgroup

G/H

center

C₂²

C₂×D₅₈₄

commutator

C₂×C₈×C₇₃

C₂³

Frattini

C₂×C₈

C₂²×D₇₃

Fitting

C₄×C₁₆×C₇₃

C₂

socle

C₂²×C₇₃

C₂×D₈

hypercenter

C₄×C₁₆

D₇₃

hypocenter

C₇₃

#2249

LCS

G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

N	H ≅ G/N	type
1. C₂×Dic₅₈₄	C₂	semidirect
2. C₂×#14556536	C₂	semidirect
4. #17988971	C₂	semidirect
5. C₄×C₁₆×C₇₃	C₂	semidirect
51. C₇₃	#2249	semidirect
56. C₄×C₁₆	D₇₃	semidirect

H ≅ G/N

type

1. C₂×Dic₅₈₄

C₂

semidirect

2. C₂×#14556536

C₂

semidirect

4. #17988971

C₂

semidirect

5. C₄×C₁₆×C₇₃

C₂

semidirect

51. C₇₃

#2249

semidirect

56. C₄×C₁₆

D₇₃

semidirect

Subgroups — #22612192

Conjugacy classes of subgroups

Complements