Group #22609232 — subgroups

Subgroups — #22609232

Order 9344.

182 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 45 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	C₇₃⋊#564	C₂	1	1	yes	maximal, characteristic, complemented
2	#17988951	C₂	1	2	yes	maximal
3	#17988329	C₂	1	1	yes	maximal, characteristic, complemented
4	#17988328	C₂	1	2	yes	maximal, complemented
5	#490×C₇₃	C₂	1	1	yes	maximal, characteristic
6	#14556583	C₂²	1	2	yes	—
7	#14556582	—	2	2	no	—
8	#14556581	—	2	2	no	—
9	#14556581	—	2	2	no	—
10	#14556512	—	2	2	no	—
11	#14556512	—	2	2	no	—
12	#14556502	C₂²	1	2	yes	—
13	#127×C₇₃	C₂²	1	1	yes	characteristic
14	#125×C₇₃	C₂²	1	1	yes	characteristic
15	#102×C₇₃	—	2	2	no	—
16	#97×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×#10596831	—	2	2	no	—
18	C₄⋊Dic₇₃	—	2	2	no	—
19	C₄⋊Dic₇₃	D₄	1	2	yes	—
20	C₄⋊Dic₇₃	D₄	1	2	yes	—
21	#11924007	—	2	2	no	—
22	#11924007	—	2	2	no	—
23	#11924007	—	2	2	no	—
24	#11924007	—	2	2	no	—
25	C₄×Dic₇₃	—	2	2	no	—
26	C₂×D₄×C₇₃	—	2	1	no	—
27	C₂×D₄×C₇₃	—	2	2	no	—
28	C₂×C₈×C₇₃	—	2	1	no	—
29	C₄⋊C₄×C₇₃	—	2	2	no	—
30	C₄⋊C₄×C₇₃	D₄	1	2	yes	—
31	C₄²×C₇₃	C₂³	1	1	yes	characteristic
32	C₂³×C₇₃	—	4	1	no	—
33	D₄×C₇₃	—	4	4	no	—
34	D₄×C₇₃	—	4	2	no	—
35	C₂×C₄×C₇₃	—	2	2	no	—
36	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
37	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
38	C₂×Dic₇₃	—	2	2	no	—
39	C₂×Dic₇₃	—	2	2	no	—
40	C₈×C₇₃	—	4	1	no	—
41	#10596831	—	4	2	no	—
42	C₂²×C₇₃	—	8	2	no	—
43	C₂²×C₇₃	—	8	1	no	—
44	C₂²×C₇₃	#120	1	1	yes	characteristic
45	C₄×C₇₃	—	2	2	no	—
46	C₄×C₇₃	—	2	1	no	—
47	C₄×C₇₃	—	4	2	no	—
48	Dic₇₃	—	4	2	no	—
49	Dic₇₃	—	4	2	no	—
50	C₂×C₇₃	—	16	1	no	—
51	C₂×C₇₃	#454	1	2	yes	—
52	C₂×C₇₃	#454	1	1	yes	characteristic
53	#1658	—	73	1	no	maximal, Sylow
54	C₇₃	#1658	1	1	yes	characteristic, complemented, Sylow
55	#564	—	73	1	no	—
56	#490	—	73	2	no	—
57	#490	D₇₃	1	1	yes	characteristic
58	#330	—	73	1	no	—
59	#330	—	73	2	no	—
60	#127	C₂×D₇₃	1	1	yes	characteristic
61	#125	—	73	2	no	—
62	#125	—	146	2	no	—
63	#125	—	146	2	no	—
64	#125	—	146	2	no	—
65	#125	C₂×D₇₃	1	1	yes	characteristic
66	#102	—	2	2	no	—
67	#102	—	146	2	no	—
68	#102	—	146	2	no	—
69	#97	—	73	2	no	—
70	#97	C₂×D₇₃	1	1	yes	characteristic
71	C₂×D₄	—	2	2	no	—
72	C₂×D₄	—	2	1	no	—
73	C₂×C₈	—	2	1	no	—
74	C₂×C₈	—	146	2	no	—
75	C₄⋊C₄	—	2	2	no	—
76	C₄⋊C₄	—	73	2	no	—
77	C₄⋊C₄	—	73	2	no	—
78	C₄⋊C₄	—	146	2	no	—
79	C₄⋊C₄	—	146	2	no	—
80	C₄⋊C₄	—	146	2	no	—
81	C₄⋊C₄	—	146	2	no	—
82	C₄⋊C₄	—	146	2	no	—
83	C₄⋊C₄	C₂²⋊D₇₃	1	2	yes	—
84	C₄²	—	146	2	no	—
85	C₄²	C₂²×D₇₃	1	1	yes	characteristic
86	C₂³	—	4	1	no	—
87	D₄	—	4	4	no	—
88	D₄	—	4	2	no	—
89	C₂×C₄	—	2	2	no	—
90	C₂×C₄	—	146	2	no	—
91	C₂×C₄	—	146	2	no	—
92	C₂×C₄	D₄×D₇₃	1	2	yes	—
93	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
94	C₈	—	4	1	no	—
95	C₈	—	292	2	no	—
96	C₂²	—	8	2	no	—
97	C₂²	—	8	1	no	—
98	C₂²	#14556559	1	1	yes	characteristic
99	C₄	—	2	2	no	—
100	C₄	—	2	1	no	—
101	C₄	—	4	2	no	—
102	C₄	—	292	2	no	—
103	C₄	—	292	2	no	—
104	C₂	—	16	1	no	—
105	C₂	#17988758	1	2	yes	—
106	C₂	#17988759	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₇₃⋊#564

C₂

yes

maximal, characteristic, complemented

#17988951

C₂

yes

maximal

#17988329

C₂

yes

maximal, characteristic, complemented

#17988328

C₂

yes

maximal, complemented

#490×C₇₃

C₂

yes

maximal, characteristic

#14556583

C₂²

yes

—

—

—

—

—

—

C₂²

yes

—

#127×C₇₃

C₂²

yes

characteristic

#125×C₇₃

C₂²

yes

characteristic

#102×C₇₃

—

#97×C₇₃

C₂²

yes

characteristic

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

D₄

yes

—

C₄⋊Dic₇₃

D₄

yes

—

—

—

—

—

C₄×Dic₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×C₈×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

D₄

yes

—

C₄²×C₇₃

C₂³

yes

characteristic

C₂³×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#120

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#454

yes

—

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#564

—

#490

—

#490

D₇₃

yes

—

—

C₂×D₇₃

yes

characteristic

#125

—

#125

—

146

—

#125

—

146

—

#125

—

146

—

#125

C₂×D₇₃

yes

characteristic

#102

—

#102

—

146

—

#102

—

146

—

#97

—

#97

C₂×D₇₃

yes

characteristic

C₂×D₄

—

C₂×D₄

—

C₂×C₈

—

C₂×C₈

—

146

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

C₂²⋊D₇₃

yes

—

C₄²

—

146

—

C₄²

C₂²×D₇₃

yes

characteristic

C₂³

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

D₄×D₇₃

yes

—

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

C₈

—

C₈

—

292

—

C₂²

—

C₂²

—

C₂²

#14556559

yes

characteristic

C₄

—

100

C₄

—

101

C₄

—

102

C₄

—

292

—

103

C₄

—

292

—

104

C₂

—

105

C₂

#17988758

yes

—

106

C₂

#17988759

yes

characteristic

	subgroup	G/H
center	C₂²	#14556559
commutator	C₄²×C₇₃	C₂³
Frattini	C₄²	C₂²×D₇₃
Fitting	#490×C₇₃	C₂
socle	C₂²×C₇₃	#120
hypercenter	#490	D₇₃
hypocenter	C₇₃	#1658
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #490

subgroup

G/H

center

C₂²

#14556559

commutator

C₄²×C₇₃

C₂³

Frattini

C₄²

C₂²×D₇₃

Fitting

#490×C₇₃

C₂

C₂²×C₇₃

D₇₃

C₇₃

G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #490

N	H ≅ G/N	type
1. C₇₃⋊#564	C₂	semidirect
3. #17988329	C₂	semidirect
4. #17988328	C₂	semidirect
54. C₇₃	#1658	semidirect

H ≅ G/N

type

1. C₇₃⋊#564

C₂

semidirect

3. #17988329

C₂

semidirect

4. #17988328

C₂

semidirect

54. C₇₃

#1658

semidirect

Subgroups — #22609232

Conjugacy classes of subgroups

Complements