Group #22626941 — subgroups

Subgroups — #22626941

Order 9344.

152 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 51 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	#17989700	C₂	1	2	yes	maximal
2	C₂×#14556645	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#10596842	—	2	2	no	—
4	C₂²⋊#10596842	C₄	1	4	yes	—
5	C₄×#10596842	—	2	2	no	—
6	C₂×#11924036	C₄	1	1	yes	characteristic
7	C₂×C₄×#64408	C₂²	1	1	yes	characteristic
8	#14556645	—	2	2	no	—
9	C₂×C₈×D₇₃	C₄	1	1	yes	characteristic
10	C₂×#10596842	—	2	4	no	—
11	C₂²×#64408	C₂×C₄	1	2	yes	—
12	#11924036	—	2	1	no	—
13	#11924036	—	2	1	no	—
14	C₂×#10596833	C₈	1	2	yes	complemented
15	C₄×#64408	D₄	1	2	yes	—
16	C₄×#64408	D₄	1	1	yes	characteristic
17	C₄×#64408	Q₈	1	1	yes	characteristic
18	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
19	C₂×#10596831	C₈	1	1	yes	characteristic, complemented
20	C₈×D₇₃	—	2	1	no	—
21	C₈×D₇₃	—	2	1	no	—
22	C₂×C₈×C₇₃	C₈	1	1	yes	characteristic, complemented
23	C₂²×D₇₃	C₄²	1	1	yes	characteristic
24	C₂×#64408	—	4	2	no	—
25	C₂×#64408	C₂²⋊C₄	1	2	yes	—
26	C₂×#64408	C₄⋊C₄	1	2	yes	—
27	#10596842	—	4	4	no	—
28	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
29	C₂×Dic₇₃	C₂×C₈	1	1	yes	characteristic
30	C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
31	C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
32	C₄×D₇₃	M₁₆	1	1	yes	characteristic
33	C₄×D₇₃	M₁₆	1	1	yes	characteristic
34	#10596833	—	2	2	no	—
35	C₈×C₇₃	—	2	1	no	—
36	#10596831	—	2	1	no	—
37	C₂²×C₇₃	C₄×C₈	1	1	yes	characteristic
38	C₂×D₇₃	—	2	2	no	—
39	C₂×D₇₃	#95	1	1	yes	characteristic
40	C₂×D₇₃	#97	1	1	yes	characteristic
41	#64408	—	2	2	no	—
42	#64408	—	2	2	no	—
43	C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
44	C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
45	Dic₇₃	C₂²⋊C₈	1	1	yes	characteristic
46	Dic₇₃	C₄⋊C₈	1	1	yes	characteristic
47	C₂×C₇₃	—	2	1	no	—
48	C₂×C₇₃	#336	1	1	yes	characteristic
49	D₇₃	—	2	1	no	—
50	D₇₃	#344	1	2	yes	—
51	#1281	—	73	1	no	maximal, Sylow
52	C₇₃	#1281	1	1	yes	characteristic, complemented, Sylow
53	#431	—	73	2	no	—
54	C₂×#97	—	73	1	no	—
55	C₂²×C₈	—	73	1	no	—
56	C₂²×C₈	—	73	1	no	—
57	C₂×C₄²	—	73	1	no	—
58	C₄⋊C₈	—	146	2	no	—
59	C₂²⋊C₈	—	73	4	no	—
60	#97	—	146	2	no	—
61	C₄×C₈	—	146	2	no	—
62	C₂²×C₄	—	73	2	no	—
63	C₂²×C₄	—	73	1	no	—
64	C₂×C₈	—	73	2	no	—
65	C₂×C₈	—	73	1	no	—
66	C₂×C₈	—	146	1	no	—
67	C₂×C₈	—	146	1	no	—
68	C₂×C₈	—	146	4	no	—
69	C₂×C₈	—	146	1	no	—
70	C₂×C₈	—	146	1	no	—
71	C₂×C₈	#10596842	1	1	yes	characteristic, complemented
72	C₄²	—	73	2	no	—
73	C₄²	—	73	1	no	—
74	C₄²	—	73	1	no	—
75	C₂³	—	73	1	no	—
76	C₂×C₄	—	292	2	no	—
77	C₂×C₄	—	73	1	no	—
78	C₂×C₄	—	73	1	no	—
79	C₂×C₄	—	73	1	no	—
80	C₂×C₄	—	73	1	no	—
81	C₂×C₄	—	73	1	no	—
82	C₂×C₄	—	73	2	no	—
83	C₂×C₄	—	73	2	no	—
84	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
85	C₈	—	2	1	no	—
86	C₈	—	292	4	no	—
87	C₈	—	146	2	no	—
88	C₈	—	146	1	no	—
89	C₂²	—	73	1	no	—
90	C₂²	—	73	1	no	—
91	C₂²	—	146	2	no	—
92	C₂²	C₄×#10596842	1	1	yes	characteristic
93	C₄	—	73	1	no	—
94	C₄	—	73	1	no	—
95	C₄	—	146	2	no	—
96	C₄	—	146	2	no	—
97	C₄	C₂²⋊#10596842	1	1	yes	characteristic
98	C₄	C₄⋊#10596842	1	1	yes	characteristic
99	C₂	—	2	1	no	—
100	C₂	—	73	2	no	—
101	C₂	—	146	1	no	—
102	C₂	(C₂×#10596842)⋊C₄	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989700

C₂

yes

maximal

C₂×#14556645

C₂

yes

maximal, characteristic

C₄⋊#10596842

—

C₂²⋊#10596842

C₄

yes

—

C₄×#10596842

—

C₂×#11924036

C₄

yes

characteristic

C₂×C₄×#64408

C₂²

yes

characteristic

#14556645

—

C₂×C₈×D₇₃

C₄

yes

characteristic

C₂×#10596842

—

C₂²×#64408

C₂×C₄

yes

—

#11924036

—

#11924036

—

C₂×#10596833

C₈

yes

complemented

C₄×#64408

D₄

yes

—

C₄×#64408

D₄

yes

characteristic

C₄×#64408

Q₈

yes

characteristic

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₂×#10596831

C₈

yes

characteristic, complemented

C₈×D₇₃

—

C₈×D₇₃

—

C₂×C₈×C₇₃

C₈

yes

characteristic, complemented

C₂²×D₇₃

C₄²

yes

characteristic

C₂×#64408

—

C₂×#64408

C₂²⋊C₄

yes

—

C₂×#64408

C₄⋊C₄

yes

—

#10596842

—

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

C₂×C₈

yes

characteristic

C₄×D₇₃

C₂²⋊C₄

yes

characteristic

C₄×D₇₃

C₄⋊C₄

yes

characteristic

C₄×D₇₃

M₁₆

yes

characteristic

C₄×D₇₃

M₁₆

yes

characteristic

#10596833

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

C₄×C₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

yes

C₂×D₇₃

yes

—

—

C₄×C₇₃

C₂²⋊C₈

yes

characteristic

C₄×C₇₃

C₄⋊C₈

yes

characteristic

Dic₇₃

C₂²⋊C₈

yes

characteristic

Dic₇₃

C₄⋊C₈

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

#336

yes

characteristic

D₇₃

—

D₇₃

#344

yes

—

#1281

—

maximal, Sylow

C₇₃

#1281

yes

characteristic, complemented, Sylow

#431

—

C₂×#97

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

146

—

C₂²⋊C₈

—

#97

—

146

—

C₄×C₈

—

146

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

#10596842

yes

characteristic, complemented

C₄²

—

C₄²

—

C₄²

—

C₂³

—

C₂×C₄

—

292

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×#10596842

yes

characteristic

C₈

—

C₈

—

292

—

C₈

—

146

—

C₈

—

146

—

C₂²

—

C₂²

—

C₂²

—

146

—

C₂²

C₄×#10596842

yes

characteristic

C₄

—

C₄

—

C₄

—

146

—

C₄

—

146

—

C₄

yes

C₄

yes

C₂

—

100

C₂

—

101

C₂

—

146

—

102

C₂

(C₂×#10596842)⋊C₄

yes

characteristic

	subgroup	G/H
center	C₄	C₂²⋊#10596842
commutator	C₂²×C₇₃	C₄×C₈
Frattini	C₂×C₄	C₂×#10596842
Fitting	C₂×C₈×C₇₃	C₈
socle	C₂×C₇₃	#336
hypercenter	C₂×C₈	#10596842
hypocenter	C₇₃	#1281
LCS	G ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

subgroup

G/H

center

C₄

C₂²⋊#10596842

commutator

C₂²×C₇₃

C₄×C₈

Frattini

C₂×C₄

C₂×#10596842

Fitting

C₂×C₈×C₇₃

C₈

C₂×C₇₃

C₂×C₈

C₇₃

G ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

N	H ≅ G/N	type
14. C₂×#10596833	C₈	semidirect
19. C₂×#10596831	C₈	semidirect
22. C₂×C₈×C₇₃	C₈	semidirect
52. C₇₃	#1281	semidirect
71. C₂×C₈	#10596842	semidirect

H ≅ G/N

type

14. C₂×#10596833

C₈

semidirect

19. C₂×#10596831

C₈

semidirect

22. C₂×C₈×C₇₃

C₈

semidirect

52. C₇₃

#1281

semidirect

71. C₂×C₈

#10596842

semidirect

Subgroups — #22626941

Conjugacy classes of subgroups

Complements