Group #22612200 — subgroups

Subgroups — #22612200

Order 9344.

178 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 57 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×#14556537	C₂	1	2	yes	maximal, complemented
2	C₂×#14556534	C₂	1	2	yes	maximal
3	#17988971	C₂	1	1	yes	maximal, characteristic
4	#17988363	C₂	1	1	yes	maximal, characteristic, complemented
5	#494×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	C₂²	1	1	yes	characteristic
9	#14556579	—	2	1	no	—
10	#14556537	—	2	4	no	—
11	#14556534	—	2	4	no	—
12	C₂×#11924003	C₂²	1	2	yes	—
13	C₂×Q₁₆×C₇₃	—	2	1	no	—
14	C₂×Q₁₆×C₇₃	C₂²	1	2	yes	—
15	C₄⋊Q₈×C₇₃	—	2	1	no	—
16	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×Dic₁₄₆	—	2	1	no	—
18	C₂×D₂₉₂	—	2	1	no	—
19	Dic₂₉₂	—	2	2	no	—
20	#11924017	—	4	2	no	—
21	D₅₈₄	—	2	2	no	—
22	#11924005	—	4	2	no	—
23	#11924003	D₄	1	4	yes	—
24	C₂×Q₈×C₇₃	—	2	2	no	—
25	Q₁₆×C₇₃	—	2	2	no	—
26	Q₁₆×C₇₃	—	2	2	no	—
27	Q₁₆×C₇₃	—	4	2	no	—
28	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
29	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
30	C₄⋊C₄×C₇₃	—	4	2	no	—
31	C₄²×C₇₃	D₄	1	1	yes	characteristic
32	C₂²×D₇₃	—	4	1	no	—
33	Q₈×C₇₃	—	4	2	no	—
34	Q₈×C₇₃	—	4	2	no	—
35	C₂×C₄×C₇₃	—	4	2	no	—
36	C₂×C₄×C₇₃	D₈	1	2	yes	—
37	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
38	C₂×Dic₇₃	—	4	1	no	—
39	D₂₉₂	—	4	1	no	—
40	D₂₉₂	—	4	1	no	—
41	Dic₁₄₆	—	4	1	no	—
42	Dic₁₄₆	—	4	1	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	—	8	2	no	—
50	C₄×C₇₃	#127	1	1	yes	characteristic
51	C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
52	Dic₇₃	—	8	1	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	D₇₃	1	1	yes	characteristic, complemented
62	#346	—	73	1	no	—
63	C₂×Q₁₆	—	2	1	no	—
64	C₂×Q₁₆	—	73	1	no	—
65	C₂×Q₁₆	C₂×D₇₃	1	2	yes	—
66	C₂×SD₁₆	—	146	1	no	—
67	C₂×D₈	—	73	1	no	—
68	C₄⋊Q₈	—	2	1	no	—
69	#124	—	146	1	no	—
70	Q₃₂	—	146	4	no	—
71	SD₃₂	—	146	4	no	—
72	C₂×C₁₆	—	73	2	no	—
73	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
74	C₂×Q₈	—	2	2	no	—
75	C₂×Q₈	—	146	1	no	—
76	C₂×D₄	—	146	1	no	—
77	Q₁₆	—	2	2	no	—
78	Q₁₆	—	2	2	no	—
79	Q₁₆	—	4	2	no	—
80	Q₁₆	—	146	2	no	—
81	SD₁₆	—	292	2	no	—
82	D₈	—	146	2	no	—
83	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
84	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
85	C₄⋊C₄	—	4	2	no	—
86	C₂²⋊C₄	—	292	2	no	—
87	C₄²	C₂²⋊D₇₃	1	1	yes	characteristic
88	C₁₆	—	73	4	no	—
89	C₂³	—	292	1	no	—
90	Q₈	—	4	2	no	—
91	Q₈	—	4	2	no	—
92	Q₈	—	292	1	no	—
93	Q₈	—	292	1	no	—
94	D₄	—	292	1	no	—
95	D₄	—	292	1	no	—
96	C₂×C₄	—	4	2	no	—
97	C₂×C₄	—	292	1	no	—
98	C₂×C₄	#11924013	1	2	yes	—
99	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
100	C₈	#11924013	1	2	yes	—
101	C₈	D₄×D₇₃	1	2	yes	—
102	C₂²	—	584	1	no	—
103	C₂²	—	584	2	no	—
104	C₂²	C₂×#11924013	1	1	yes	characteristic
105	C₄	—	2	2	no	—
106	C₄	—	8	2	no	—
107	C₄	—	584	1	no	—
108	C₄	#14556587	1	1	yes	characteristic
109	C₄	C₂×#11924013	1	1	yes	characteristic
110	C₂	—	1168	1	no	—
111	C₂	#17988963	1	1	yes	characteristic
112	C₂	#17989028	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556537

C₂

yes

maximal, complemented

C₂×#14556534

C₂

yes

maximal

#17988971

C₂

yes

maximal, characteristic

#17988363

C₂

yes

maximal, characteristic, complemented

#494×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂×Dic₂₉₂

C₂²

yes

characteristic

C₂×#11924017

—

C₂×D₅₈₄

C₂²

yes

—

—

—

C₂²

yes

—

C₂×Q₁₆×C₇₃

—

C₂×Q₁₆×C₇₃

C₂²

yes

—

C₄⋊Q₈×C₇₃

—

C₄×C₈×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

—

C₂×D₂₉₂

—

Dic₂₉₂

—

#11924017

—

D₅₈₄

—

#11924005

—

#11924003

D₄

yes

—

C₂×Q₈×C₇₃

—

Q₁₆×C₇₃

—

Q₁₆×C₇₃

—

Q₁₆×C₇₃

—

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

D₄

yes

characteristic

C₂²×D₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

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

—

C₂²×C₇₃

C₂×D₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#127

yes

characteristic

C₄×C₇₃

C₂×D₈

yes

characteristic

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

D₇₃

yes

characteristic, complemented

#346

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₇₃

yes

—

C₂×SD₁₆

—

146

—

C₂×D₈

—

C₄⋊Q₈

—

#124

—

146

—

Q₃₂

—

146

—

SD₃₂

—

146

—

C₂×C₁₆

—

C₄×C₈

C₂×D₇₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

146

—

C₂×D₄

—

146

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

146

—

SD₁₆

—

292

—

D₈

—

146

—

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

C₂×C₈

C₂²×D₇₃

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

292

—

C₄²

C₂²⋊D₇₃

yes

characteristic

C₁₆

—

C₂³

—

292

—

Q₈

—

Q₈

—

Q₈

—

292

—

Q₈

—

292

—

D₄

—

292

—

D₄

—

292

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

#11924013

yes

—

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

100

C₈

#11924013

yes

—

101

C₈

D₄×D₇₃

yes

—

102

C₂²

—

584

—

103

C₂²

—

584

—

104

C₂²

C₂×#11924013

yes

characteristic

105

C₄

—

106

C₄

—

107

C₄

—

584

—

108

C₄

#14556587

yes

characteristic

109

C₄

C₂×#11924013

yes

characteristic

110

C₂

—

1168

—

111

C₂

#17988963

yes

characteristic

112

C₂

#17989028

yes

—

	subgroup	G/H
center	C₂²	C₂×#11924013
commutator	C₂×C₈×C₇₃	C₂³
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	#494×C₇₃	C₂
socle	C₂²×C₇₃	C₂×D₈
hypercenter	#494	D₇₃
hypocenter	C₇₃	#2251
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #494

subgroup

G/H

center

C₂²

C₂×#11924013

commutator

C₂×C₈×C₇₃

C₂³

Frattini

C₂×C₈

C₂²×D₇₃

Fitting

#494×C₇₃

C₂

socle

C₂²×C₇₃

C₂×D₈

D₇₃

C₇₃

G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #494

N	H ≅ G/N	type
1. C₂×#14556537	C₂	semidirect
4. #17988363	C₂	semidirect
5. #494×C₇₃	C₂	semidirect
57. C₇₃	#2251	semidirect
61. #494	D₇₃	semidirect

H ≅ G/N

type

1. C₂×#14556537

C₂

semidirect

4. #17988363

C₂

semidirect

5. #494×C₇₃

C₂

semidirect

57. C₇₃

#2251

semidirect

61. #494

D₇₃

semidirect

Subgroups — #22612200

Conjugacy classes of subgroups

Complements