Group #22609619 — subgroups

Subgroups — #22609619

Order 9344.

328 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 205 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×#14556501	C₂	1	2	yes	maximal
2	C₂×C₄×#10596831	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×Dic₇₃	C₂	1	2	yes	maximal
4	#17988433	C₂	1	1	yes	maximal, characteristic
5	C₂×#97×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10596831	C₂²	1	1	yes	characteristic
7	C₂²×#10596831	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₇₃	C₂²	1	2	yes	—
9	#14556501	C₄	1	8	yes	complemented
10	C₄×#10596831	C₄	1	4	yes	complemented
11	C₈×Dic₇₃	C₄	1	8	yes	complemented
12	#14556498	C₄	1	4	yes	—
13	C₂²×C₈×C₇₃	C₂²	1	2	yes	—
14	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
15	#97×C₇₃	C₄	1	4	yes	complemented
16	C₂²×Dic₇₃	C₂×C₄	1	4	yes	—
17	C₂×#10596831	C₂×C₄	1	4	yes	—
18	C₂×#10596831	C₂×C₄	1	2	yes	—
19	C₂×#10596831	C₂×C₄	1	2	yes	—
20	C₂×#10596831	C₂×C₄	1	4	yes	—
21	C₄×Dic₇₃	C₂×C₄	1	4	yes	—
22	C₄×Dic₇₃	C₂×C₄	1	4	yes	—
23	C₂²×C₄×C₇₃	C₂×C₄	1	2	yes	—
24	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
25	C₂×C₈×C₇₃	C₂×C₄	1	4	yes	—
26	C₂×C₈×C₇₃	C₂×C₄	1	4	yes	—
27	C₂×C₈×C₇₃	C₂×C₄	1	4	yes	—
28	C₄²×C₇₃	C₂×C₄	1	2	yes	—
29	C₄²×C₇₃	C₂×C₄	1	2	yes	—
30	C₂³×C₇₃	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₇₃	—	2	4	no	—
32	C₂×C₄×C₇₃	C₄²	1	4	yes	—
33	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₇₃	C₂²×C₄	1	2	yes	—
35	C₂×C₄×C₇₃	C₂²×C₄	1	2	yes	—
36	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
37	C₂×Dic₇₃	—	2	8	no	—
38	C₂×Dic₇₃	C₄²	1	8	yes	—
39	C₈×C₇₃	C₄²	1	8	yes	—
40	#10596831	C₄²	1	4	yes	—
41	#10596831	C₄²	1	4	yes	—
42	C₂²×C₇₃	C₂×C₄²	1	2	yes	—
43	C₂²×C₇₃	C₂×C₄²	1	1	yes	characteristic
44	C₂²×C₇₃	#131	1	4	yes	—
45	C₄×C₇₃	—	2	4	no	—
46	C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
47	C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
48	C₄×C₇₃	C₂×C₄²	1	2	yes	—
49	Dic₇₃	—	2	8	no	—
50	C₂×C₇₃	C₄³	1	1	yes	characteristic
51	C₂×C₇₃	#405	1	4	yes	—
52	C₂×C₇₃	#405	1	2	yes	—
53	#1726	—	73	1	no	maximal, Sylow
54	C₇₃	#1726	1	1	yes	characteristic, complemented, Sylow
55	C₂×#97	—	73	2	no	—
56	C₂×#97	D₇₃	1	1	yes	characteristic
57	C₂×C₄×C₈	—	73	2	no	—
58	C₂×C₄×C₈	—	73	1	no	—
59	#376	—	73	1	no	—
60	C₂²×C₈	—	73	1	no	—
61	C₂²×C₈	—	73	1	no	—
62	C₂²×C₈	C₂×D₇₃	1	2	yes	—
63	C₂×C₄²	—	73	2	no	—
64	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
65	#97	—	73	8	no	—
66	#97	Dic₇₃	1	4	yes	complemented
67	C₄×C₈	—	73	8	no	—
68	C₄×C₈	—	73	4	no	—
69	#95	—	73	4	no	—
70	C₂²×C₄	—	73	4	no	—
71	C₂²×C₄	C₄×D₇₃	1	2	yes	—
72	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
73	C₂×C₈	—	73	2	no	—
74	C₂×C₈	—	73	2	no	—
75	C₂×C₈	—	73	4	no	—
76	C₂×C₈	—	73	4	no	—
77	C₂×C₈	C₄×D₇₃	1	4	yes	—
78	C₂×C₈	C₄×D₇₃	1	4	yes	—
79	C₂×C₈	C₂×Dic₇₃	1	4	yes	—
80	C₄²	—	73	4	no	—
81	C₄²	—	73	4	no	—
82	C₄²	C₄×D₇₃	1	2	yes	—
83	C₄²	C₂×Dic₇₃	1	2	yes	—
84	C₂³	C₂×C₄×D₇₃	1	1	yes	characteristic
85	C₂×C₄	—	2	4	no	—
86	C₂×C₄	—	73	8	no	—
87	C₂×C₄	—	146	8	no	—
88	C₂×C₄	C₄×Dic₇₃	1	4	yes	—
89	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
90	C₂×C₄	C₂×C₄×D₇₃	1	2	yes	—
91	C₂×C₄	C₂×C₄×D₇₃	1	2	yes	—
92	C₂×C₄	C₂²×Dic₇₃	1	1	yes	characteristic
93	C₈	—	73	4	no	—
94	C₈	—	73	4	no	—
95	C₈	C₄×Dic₇₃	1	8	yes	—
96	C₂²	C₄²×D₇₃	1	2	yes	—
97	C₂²	C₂×C₄×Dic₇₃	1	1	yes	characteristic
98	C₂²	#14556599	1	4	yes	—
99	C₄	—	2	4	no	—
100	C₄	—	146	8	no	—
101	C₄	C₄²×D₇₃	1	1	yes	characteristic
102	C₄	C₄²×D₇₃	1	1	yes	characteristic
103	C₄	C₂×C₄×Dic₇₃	1	2	yes	—
104	C₂	C₄²×Dic₇₃	1	1	yes	characteristic
105	C₂	#17988544	1	4	yes	—
106	C₂	#17988545	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556501

C₂

yes

maximal

C₂×C₄×#10596831

C₂

yes

maximal, characteristic

C₂×C₈×Dic₇₃

C₂

yes

maximal

#17988433

C₂

yes

maximal, characteristic

C₂×#97×C₇₃

C₂

yes

maximal, characteristic

C₂²×#10596831

C₂²

yes

characteristic

C₂²×#10596831

C₂²

yes

characteristic

C₂×C₄×Dic₇₃

C₂²

yes

—

#14556501

C₄

yes

complemented

C₄×#10596831

C₄

yes

complemented

C₈×Dic₇₃

C₄

yes

complemented

#14556498

C₄

yes

—

C₂²×C₈×C₇₃

C₂²

yes

—

C₂×C₄²×C₇₃

C₂²

yes

characteristic

#97×C₇₃

C₄

yes

complemented

C₂²×Dic₇₃

C₂×C₄

yes

—

C₂×#10596831

C₂×C₄

yes

—

C₂×#10596831

C₂×C₄

yes

—

C₂×#10596831

C₂×C₄

yes

—

C₂×#10596831

C₂×C₄

yes

—

C₄×Dic₇₃

C₂×C₄

yes

—

C₄×Dic₇₃

C₂×C₄

yes

—

C₂²×C₄×C₇₃

C₂×C₄

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

—

C₂×C₈×C₇₃

C₂×C₄

yes

—

C₂×C₈×C₇₃

C₂×C₄

yes

—

C₄²×C₇₃

C₂×C₄

yes

—

C₄²×C₇₃

C₂×C₄

yes

—

C₂³×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₄²

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

C₄²

yes

—

C₈×C₇₃

C₄²

yes

—

#10596831

C₄²

yes

—

#10596831

C₄²

yes

—

C₂²×C₇₃

C₂×C₄²

yes

—

C₂²×C₇₃

C₂×C₄²

yes

characteristic

C₂²×C₇₃

#131

yes

—

C₄×C₇₃

—

C₄×C₇₃

C₂×C₄²

yes

characteristic

C₄×C₇₃

C₂×C₄²

yes

characteristic

C₄×C₇₃

C₂×C₄²

yes

—

Dic₇₃

—

C₂×C₇₃

C₄³

yes

characteristic

C₂×C₇₃

#405

yes

—

C₂×C₇₃

#405

yes

—

#1726

—

maximal, Sylow

C₇₃

#1726

yes

characteristic, complemented, Sylow

C₂×#97

—

C₂×#97

D₇₃

yes

characteristic

C₂×C₄×C₈

—

C₂×C₄×C₈

—

#376

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×D₇₃

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×D₇₃

yes

characteristic

#97

—

#97

Dic₇₃

yes

complemented

C₄×C₈

—

C₄×C₈

—

#95

—

C₂²×C₄

—

C₂²×C₄

C₄×D₇₃

yes

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₇₃

yes

—

C₂×C₈

C₄×D₇₃

yes

—

C₂×C₈

C₂×Dic₇₃

yes

—

C₄²

—

C₄²

—

C₄²

C₄×D₇₃

yes

—

C₄²

C₂×Dic₇₃

yes

—

C₂³

C₂×C₄×D₇₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

C₄×Dic₇₃

yes

—

C₂×C₄

C₂×C₄×D₇₃

yes

characteristic

C₂×C₄

C₂×C₄×D₇₃

yes

—

C₂×C₄

C₂×C₄×D₇₃

yes

—

C₂×C₄

C₂²×Dic₇₃

yes

characteristic

C₈

—

C₈

—

C₈

C₄×Dic₇₃

yes

—

C₂²

C₄²×D₇₃

yes

—

C₂²

C₂×C₄×Dic₇₃

yes

characteristic

C₂²

#14556599

yes

—

C₄

—

100

C₄

—

146

—

101

C₄

C₄²×D₇₃

yes

characteristic

102

C₄

C₄²×D₇₃

yes

characteristic

103

C₄

C₂×C₄×Dic₇₃

yes

—

104

C₂

C₄²×Dic₇₃

yes

characteristic

105

C₂

#17988544

yes

—

106

C₂

#17988545

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₇₃
commutator	C₂×C₇₃	C₄³
Fitting	C₂×#97×C₇₃	C₂
socle	C₂³×C₇₃	C₂²×C₄
hypercenter	C₂×#97	D₇₃
hypocenter	C₇₃	#1726
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#97

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₇₃

commutator

C₂×C₇₃

C₄³

Fitting

C₂×#97×C₇₃

C₂

socle

C₂³×C₇₃

C₂²×C₄

hypercenter

C₂×#97

D₇₃

C₇₃

G ▷ C₂×C₇₃ ▷ C₇₃

C₁ ◁ C₂²×C₄ ◁ C₂×#97

N	H ≅ G/N	type
9. #14556501	C₄	semidirect
10. C₄×#10596831	C₄	semidirect
11. C₈×Dic₇₃	C₄	semidirect
15. #97×C₇₃	C₄	semidirect
54. C₇₃	#1726	semidirect
66. #97	Dic₇₃	semidirect

H ≅ G/N

type

9. #14556501

C₄

semidirect

10. C₄×#10596831

C₄

semidirect

11. C₈×Dic₇₃

C₄

semidirect

15. #97×C₇₃

C₄

semidirect

54. C₇₃

#1726

semidirect

66. #97

Dic₇₃

semidirect

Subgroups — #22609619

Conjugacy classes of subgroups

Complements