Group #22625135 — subgroups

Subgroups — #22625135

Order 9344.

212 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 106 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	#17989605	C₂	1	2	yes	maximal
2	#17989428	C₂	1	2	yes	maximal, complemented
3	C₈×#10596833	C₂	1	2	yes	maximal, complemented
4	C₄×C₈×D₇₃	C₂	1	1	yes	maximal, characteristic
5	#14556658	C₄	1	4	yes	—
6	#14556648	C₄	1	4	yes	—
7	C₄×#10596833	C₂²	1	4	yes	—
8	C₂×C₈×D₇₃	C₄	1	1	yes	characteristic
9	C₂×C₈×D₇₃	C₄	1	1	yes	characteristic
10	C₄²×D₇₃	C₂²	1	1	yes	characteristic
11	C₄×#10596831	C₄	1	1	yes	characteristic
12	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
13	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₇₃	C₄	1	1	yes	characteristic
15	C₂×#10596833	C₂×C₄	1	8	yes	—
16	C₂×C₄×D₇₃	C₂×C₄	1	2	yes	—
17	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
18	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
19	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
20	C₈×D₇₃	C₈	1	4	yes	complemented
21	C₈×D₇₃	C₈	1	4	yes	complemented
22	C₄×Dic₇₃	C₂×C₄	1	2	yes	—
23	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
24	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
26	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
27	C₂²×D₇₃	C₄²	1	1	yes	characteristic
28	C₂×C₄×C₇₃	C₄²	1	2	yes	—
29	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
30	C₂×Dic₇₃	C₄²	1	1	yes	characteristic
31	C₂×Dic₇₃	C₂²×C₄	1	2	yes	—
32	C₄×D₇₃	—	2	4	no	—
33	C₄×D₇₃	C₂×C₈	1	2	yes	—
34	C₄×D₇₃	C₂×C₈	1	2	yes	—
35	#10596833	—	2	8	no	—
36	C₈×C₇₃	C₂×C₈	1	2	yes	—
37	C₈×C₇₃	C₂×C₈	1	2	yes	—
38	#10596831	C₂×C₈	1	2	yes	—
39	#10596831	C₂×C₈	1	2	yes	—
40	C₂²×C₇₃	C₂×C₄²	1	1	yes	characteristic
41	C₂×D₇₃	—	2	2	no	—
42	C₂×D₇₃	C₄×C₈	1	2	yes	—
43	C₄×C₇₃	—	2	2	no	—
44	C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
45	C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
46	Dic₇₃	C₄×C₈	1	2	yes	—
47	Dic₇₃	#131	1	4	yes	—
48	C₂×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
49	C₂×C₇₃	#405	1	2	yes	—
50	D₇₃	—	2	2	no	—
51	#1450	—	73	1	no	maximal, Sylow
52	C₇₃	#1450	1	1	yes	characteristic, complemented, Sylow
53	#431	—	73	2	no	—
54	C₂×C₄×C₈	—	73	1	no	—
55	#322	—	73	2	no	—
56	C₈²	—	73	2	no	—
57	C₂²×C₈	—	73	1	no	—
58	C₂²×C₈	—	73	1	no	—
59	C₂×C₄²	—	73	1	no	—
60	C₄⋊C₈	—	73	4	no	—
61	C₂²⋊C₈	—	73	4	no	—
62	C₄×C₈	—	73	4	no	—
63	C₄×C₈	—	73	1	no	—
64	C₄×C₈	—	73	1	no	—
65	C₄×C₈	—	73	1	no	—
66	C₄×C₈	#64408	1	1	yes	characteristic
67	C₂²×C₄	—	73	1	no	—
68	C₂²×C₄	—	73	2	no	—
69	C₂×C₈	—	73	1	no	—
70	C₂×C₈	—	73	1	no	—
71	C₂×C₈	—	73	4	no	—
72	C₂×C₈	—	73	4	no	—
73	C₂×C₈	—	73	8	no	—
74	C₂×C₈	C₂×#64408	1	1	yes	characteristic
75	C₂×C₈	C₂×#64408	1	1	yes	characteristic
76	C₄²	—	73	2	no	—
77	C₄²	—	73	1	no	—
78	C₄²	C₂×#64408	1	1	yes	characteristic
79	C₂³	—	73	1	no	—
80	C₂×C₄	—	73	2	no	—
81	C₂×C₄	—	73	1	no	—
82	C₂×C₄	—	73	2	no	—
83	C₂×C₄	—	73	2	no	—
84	C₂×C₄	—	146	4	no	—
85	C₂×C₄	C₄×#64408	1	2	yes	—
86	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
87	C₈	—	73	2	no	—
88	C₈	—	73	2	no	—
89	C₈	—	146	8	no	—
90	C₈	#11924036	1	2	yes	—
91	C₈	#11924036	1	2	yes	—
92	C₂²	—	73	2	no	—
93	C₂²	—	146	2	no	—
94	C₂²	C₂×C₄×#64408	1	1	yes	characteristic
95	C₄	—	2	2	no	—
96	C₄	—	73	2	no	—
97	C₄	—	73	4	no	—
98	C₄	C₂×#11924036	1	1	yes	characteristic
99	C₄	C₂×#11924036	1	1	yes	characteristic
100	C₂	—	146	2	no	—
101	C₂	C₄×#11924036	1	1	yes	characteristic
102	C₂	#17989550	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#17989605

C₂

yes

maximal

#17989428

C₂

yes

maximal, complemented

C₈×#10596833

C₂

yes

maximal, complemented

C₄×C₈×D₇₃

C₂

yes

maximal, characteristic

#14556658

C₄

yes

—

#14556648

C₄

yes

—

C₄×#10596833

C₂²

yes

—

C₂×C₈×D₇₃

C₄

yes

characteristic

C₂×C₈×D₇₃

C₄

yes

characteristic

C₄²×D₇₃

C₂²

yes

characteristic

C₄×#10596831

C₄

yes

characteristic

C₈×Dic₇₃

C₂²

yes

characteristic

C₈×Dic₇₃

C₂²

yes

characteristic

C₄×C₈×C₇₃

C₄

yes

characteristic

C₂×#10596833

C₂×C₄

yes

—

C₂×C₄×D₇₃

C₂×C₄

yes

—

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₂×#10596831

C₂×C₄

yes

characteristic

C₂×#10596831

C₂×C₄

yes

characteristic

C₈×D₇₃

C₈

yes

complemented

C₈×D₇₃

C₈

yes

complemented

C₄×Dic₇₃

C₂×C₄

yes

—

C₄×Dic₇₃

C₂³

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₂²×D₇₃

C₄²

yes

characteristic

C₂×C₄×C₇₃

C₄²

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

C₄²

yes

characteristic

C₂×Dic₇₃

C₂²×C₄

yes

—

C₄×D₇₃

—

C₄×D₇₃

C₂×C₈

yes

—

C₄×D₇₃

C₂×C₈

yes

—

#10596833

—

C₈×C₇₃

C₂×C₈

yes

—

C₈×C₇₃

C₂×C₈

yes

—

#10596831

C₂×C₈

yes

—

#10596831

C₂×C₈

yes

—

C₂²×C₇₃

C₂×C₄²

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

C₄×C₈

yes

—

C₄×C₇₃

—

C₄×C₇₃

C₂²×C₈

yes

characteristic

C₄×C₇₃

C₂²×C₈

yes

characteristic

Dic₇₃

C₄×C₈

yes

—

Dic₇₃

#131

yes

—

C₂×C₇₃

C₂×C₄×C₈

yes

characteristic

C₂×C₇₃

#405

yes

—

D₇₃

—

#1450

—

maximal, Sylow

C₇₃

#1450

yes

characteristic, complemented, Sylow

#431

—

C₂×C₄×C₈

—

#322

—

C₈²

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#64408

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄²

—

C₄²

—

C₄²

C₂×#64408

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

C₄×#64408

yes

—

C₂×C₄

C₂²×#64408

yes

characteristic

C₈

—

C₈

—

C₈

—

146

—

C₈

#11924036

yes

—

C₈

#11924036

yes

—

C₂²

—

C₂²

—

146

—

C₂²

C₂×C₄×#64408

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

yes

C₄

yes

100

C₂

—

146

—

101

C₂

C₄×#11924036

yes

characteristic

102

C₂

#17989550

yes

—

	subgroup	G/H
center	C₂×C₈	C₂×#64408
commutator	C₂×C₇₃	C₂×C₄×C₈
Frattini	C₂×C₄	C₂²×#64408
Fitting	C₄×C₈×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₄²
hypercenter	C₄×C₈	#64408
hypocenter	C₇₃	#1450
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈

subgroup

G/H

center

C₂×C₈

C₂×#64408

commutator

C₂×C₇₃

C₂×C₄×C₈

Frattini

C₂×C₄

C₂²×#64408

Fitting

C₄×C₈×C₇₃

C₄

socle

C₂²×C₇₃

C₂×C₄²

C₄×C₈

C₇₃

G ▷ C₂×C₇₃ ▷ C₇₃

C₁ ◁ C₂×C₈ ◁ C₄×C₈

N	H ≅ G/N	type
2. #17989428	C₂	semidirect
3. C₈×#10596833	C₂	semidirect
20. C₈×D₇₃	C₈	semidirect
21. C₈×D₇₃	C₈	semidirect
52. C₇₃	#1450	semidirect

H ≅ G/N

type

2. #17989428

C₂

semidirect

3. C₈×#10596833

C₂

semidirect

20. C₈×D₇₃

C₈

semidirect

21. C₈×D₇₃

C₈

semidirect

52. C₇₃

#1450

semidirect

Subgroups — #22625135

Conjugacy classes of subgroups

Complements