Group #22625486 — subgroups

Subgroups — #22625486

Order 9344.

184 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 82 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	#17989591	C₂	1	2	yes	maximal
2	#17989448	C₂	1	4	yes	maximal, complemented
3	C₄×C₈×D₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924038	—	2	2	no	—
5	C₄⋊#10596833	—	2	2	no	—
6	C₄⋊#10596833	C₂²	1	4	yes	—
7	C₂×C₈×D₇₃	C₄	1	2	yes	—
8	C₄²×D₇₃	C₂²	1	1	yes	characteristic
9	C₄×#10596831	C₄	1	1	yes	characteristic
10	C₈×Dic₇₃	C₂²	1	2	yes	—
11	C₄×C₈×C₇₃	C₄	1	1	yes	characteristic
12	#11924038	—	4	4	no	—
13	C₂×#10596833	—	2	4	no	—
14	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×D₇₃	D₄	1	1	yes	characteristic
16	C₂×C₄×D₇₃	Q₈	1	1	yes	characteristic
17	C₂×#10596831	C₂×C₄	1	2	yes	—
18	C₈×D₇₃	—	2	4	no	—
19	C₄×Dic₇₃	D₄	1	1	yes	characteristic
20	C₄×Dic₇₃	Q₈	1	1	yes	characteristic
21	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
22	C₂×C₈×C₇₃	C₂×C₄	1	2	yes	—
23	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
24	C₂²×D₇₃	C₄⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
28	C₂×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
29	C₂×Dic₇₃	C₂×D₄	1	1	yes	characteristic
30	C₂×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
31	C₄×D₇₃	—	2	2	no	—
32	C₄×D₇₃	—	2	2	no	—
33	C₄×D₇₃	SD₁₆	1	4	yes	—
34	#10596833	—	4	4	no	—
35	C₈×C₇₃	M₁₆	1	4	yes	complemented
36	#10596831	—	2	2	no	—
37	C₂²×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₂×D₇₃	—	2	1	no	—
39	C₂×D₇₃	—	2	1	no	—
40	C₂×D₇₃	#106	1	2	yes	—
41	C₄×C₇₃	#106	1	2	yes	—
42	C₄×C₇₃	#108	1	2	yes	—
43	C₄×C₇₃	C₂×M₁₆	1	2	yes	—
44	Dic₇₃	—	2	1	no	—
45	Dic₇₃	—	2	1	no	—
46	Dic₇₃	C₂×SD₁₆	1	2	yes	—
47	C₂×C₇₃	#423	1	1	yes	characteristic
48	C₂×C₇₃	C₂×#106	1	1	yes	characteristic
49	C₂×C₇₃	C₂×#108	1	1	yes	characteristic
50	D₇₃	—	2	2	no	—
51	#1566	—	73	1	no	maximal, Sylow
52	C₇₃	#1566	1	1	yes	characteristic, complemented, Sylow
53	#423	—	73	2	no	—
54	C₂×C₄×C₈	—	73	1	no	—
55	#334	—	73	4	no	—
56	C₂×M₁₆	—	146	2	no	—
57	C₂²×C₈	—	73	2	no	—
58	C₂×C₄²	—	73	1	no	—
59	C₄⋊C₈	—	73	4	no	—
60	C₄⋊C₈	—	146	2	no	—
61	C₄×C₈	—	73	2	no	—
62	C₄×C₈	—	73	1	no	—
63	C₄×C₈	#64408	1	1	yes	characteristic
64	C₂²×C₄	—	73	1	no	—
65	C₂²×C₄	—	73	1	no	—
66	C₂²×C₄	—	73	1	no	—
67	M₁₆	—	292	4	no	—
68	C₂×C₈	—	73	2	no	—
69	C₂×C₈	—	146	4	no	—
70	C₂×C₈	—	146	4	no	—
71	C₂×C₈	C₂×#64408	1	2	yes	—
72	C₄²	—	73	1	no	—
73	C₄²	—	73	1	no	—
74	C₄²	—	73	1	no	—
75	C₄²	C₂×#64408	1	1	yes	characteristic
76	C₂³	—	73	1	no	—
77	C₂×C₄	—	73	1	no	—
78	C₂×C₄	—	73	4	no	—
79	C₂×C₄	—	73	1	no	—
80	C₂×C₄	—	73	1	no	—
81	C₂×C₄	—	146	2	no	—
82	C₂×C₄	—	146	2	no	—
83	C₂×C₄	C₄⋊#64408	1	1	yes	characteristic
84	C₂×C₄	C₄⋊#64408	1	1	yes	characteristic
85	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
86	C₈	—	292	4	no	—
87	C₈	—	146	2	no	—
88	C₈	#11924038	1	4	yes	complemented
89	C₂²	—	73	2	no	—
90	C₂²	—	146	1	no	—
91	C₂²	—	146	1	no	—
92	C₂²	C₂×C₄⋊#64408	1	1	yes	characteristic
93	C₄	—	73	2	no	—
94	C₄	—	146	1	no	—
95	C₄	—	146	1	no	—
96	C₄	#14556659	1	2	yes	—
97	C₄	#14556661	1	2	yes	—
98	C₄	C₂×#11924038	1	2	yes	—
99	C₂	—	146	2	no	—
100	C₂	#17989591	1	1	yes	characteristic
101	C₂	C₂×#14556659	1	1	yes	characteristic
102	C₂	C₂×#14556661	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989591

C₂

yes

maximal

#17989448

C₂

yes

maximal, complemented

C₄×C₈×D₇₃

C₂

yes

maximal, characteristic

C₂×#11924038

—

C₄⋊#10596833

—

C₄⋊#10596833

C₂²

yes

—

C₂×C₈×D₇₃

C₄

yes

—

C₄²×D₇₃

C₂²

yes

characteristic

C₄×#10596831

C₄

yes

characteristic

C₈×Dic₇₃

C₂²

yes

—

C₄×C₈×C₇₃

C₄

yes

characteristic

#11924038

—

C₂×#10596833

—

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₂×C₄×D₇₃

D₄

yes

characteristic

C₂×C₄×D₇₃

Q₈

yes

characteristic

C₂×#10596831

C₂×C₄

yes

—

C₈×D₇₃

—

C₄×Dic₇₃

D₄

yes

characteristic

C₄×Dic₇₃

Q₈

yes

characteristic

C₄×Dic₇₃

C₂³

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

—

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₂²×D₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

C₄⋊C₄

yes

characteristic

C₂×Dic₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

C₂×Q₈

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

SD₁₆

yes

—

#10596833

—

C₈×C₇₃

M₁₆

yes

complemented

#10596831

—

C₂²×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

#106

yes

—

C₄×C₇₃

#106

yes

—

C₄×C₇₃

#108

yes

—

C₄×C₇₃

C₂×M₁₆

yes

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

C₂×SD₁₆

yes

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

D₇₃

—

#1566

—

maximal, Sylow

C₇₃

#1566

yes

characteristic, complemented, Sylow

#423

—

C₂×C₄×C₈

—

#334

—

C₂×M₁₆

—

146

—

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

146

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#64408

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

292

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

C₂×#64408

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#64408

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂²×#64408

yes

characteristic

C₈

—

292

—

C₈

—

146

—

C₈

#11924038

yes

complemented

C₂²

—

C₂²

—

146

—

C₂²

—

146

—

C₂²

C₂×C₄⋊#64408

yes

characteristic

C₄

—

C₄

—

146

—

C₄

—

146

—

C₄

#14556659

yes

—

C₄

#14556661

yes

—

C₄

C₂×#11924038

yes

—

C₂

—

146

—

100

C₂

#17989591

yes

characteristic

101

C₂

C₂×#14556659

yes

characteristic

102

C₂

C₂×#14556661

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×C₄⋊#64408
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#64408
Fitting	C₄×C₈×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₄⋊C₄
hypercenter	C₄×C₈	#64408
hypocenter	C₇₃	#1566
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

subgroup

G/H

center

C₂²

C₂×C₄⋊#64408

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#64408

Fitting

C₄×C₈×C₇₃

C₄

socle

C₂²×C₇₃

C₂×C₄⋊C₄

C₄×C₈

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

N	H ≅ G/N	type
2. #17989448	C₂	semidirect
35. C₈×C₇₃	M₁₆	semidirect
52. C₇₃	#1566	semidirect
88. C₈	#11924038	semidirect

H ≅ G/N

type

2. #17989448

C₂

semidirect

35. C₈×C₇₃

M₁₆

semidirect

52. C₇₃

#1566

semidirect

88. C₈

#11924038

semidirect

Subgroups — #22625486

Conjugacy classes of subgroups

Complements