Group #22625057 — subgroups

Subgroups — #22625057

Order 9344.

106 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 106 conjugacy classes of subgroups — too many to draw. Only its 20 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	#17989497	C₂	1	1	yes	maximal, characteristic, complemented
2	#17989447	C₂	1	1	yes	maximal, characteristic, complemented
3	#17988772	C₂	1	1	yes	maximal, characteristic
4	#14556658	—	2	1	no	—
5	#14556652	—	2	1	no	—
6	#14556639	C₄	1	1	yes	characteristic
7	#14556624	—	2	1	no	—
8	#14556589	C₂²	1	1	yes	characteristic
9	#14556517	—	2	1	no	—
10	#101×C₇₃	C₄	1	1	yes	characteristic
11	#11924037	—	4	1	no	—
12	C₂×#10596833	—	4	1	no	—
13	#11924029	—	4	1	no	—
14	#11924028	—	2	1	no	—
15	#11924028	—	4	1	no	—
16	C₂×Dic₁₄₆	D₄	1	1	yes	characteristic
17	Q₈×D₇₃	—	4	1	no	—
18	Dic₂₉₂	—	4	1	no	—
19	#11924017	—	4	1	no	—
20	#11924007	—	4	1	no	—
21	C₄×Dic₇₃	D₄	1	1	yes	characteristic
22	C₂×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
23	M₁₆×C₇₃	—	2	1	no	—
24	Q₈×C₇₃	—	4	1	no	—
25	C₂×C₄×C₇₃	—	2	1	no	—
26	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂²⋊D₇₃	—	4	1	no	—
28	C₂×Dic₇₃	—	2	1	no	—
29	C₂×Dic₇₃	—	2	1	no	—
30	D₂₉₂	—	2	1	no	—
31	D₂₉₂	—	4	1	no	—
32	C₄×D₇₃	—	4	1	no	—
33	C₄×D₇₃	—	4	2	no	—
34	Dic₁₄₆	—	2	1	no	—
35	Dic₁₄₆	—	4	1	no	—
36	Dic₁₄₆	—	4	1	no	—
37	#10596833	—	8	1	no	—
38	#10596833	—	8	1	no	—
39	C₈×C₇₃	—	4	1	no	—
40	C₂²×C₇₃	#99	1	1	yes	characteristic
41	C₂×D₇₃	—	4	1	no	—
42	C₄×C₇₃	—	2	1	no	—
43	C₄×C₇₃	—	4	1	no	—
44	Dic₇₃	—	2	1	no	—
45	Dic₇₃	—	2	1	no	—
46	Dic₇₃	—	4	1	no	—
47	Dic₇₃	—	4	1	no	—
48	C₂×C₇₃	—	2	1	no	—
49	C₂×C₇₃	AΣL(1,𝔽₁₆)	1	1	yes	characteristic
50	D₇₃	—	8	1	no	—
51	#1405	—	73	1	no	maximal, Sylow
52	C₇₃	#1405	1	1	yes	characteristic, complemented, Sylow
53	#456	—	73	1	no	—
54	#356	—	73	1	no	—
55	#333	—	73	1	no	—
56	2₋¹⁺⁴	—	73	1	no	—
57	#137	—	146	1	no	—
58	C₄⋊Q₈	—	73	1	no	—
59	C₄⋊C₈	—	146	1	no	—
60	#104	—	146	1	no	—
61	#101	—	146	1	no	—
62	#101	#64408	1	1	yes	characteristic
63	#41	—	292	1	no	—
64	#41	—	292	1	no	—
65	#41	—	146	1	no	—
66	C₂×Q₈	—	292	1	no	—
67	C₂×Q₈	—	73	1	no	—
68	C₂×Q₈	C₂×#64408	1	1	yes	characteristic
69	Q₁₆	—	292	1	no	—
70	SD₁₆	—	292	1	no	—
71	M₁₆	—	2	1	no	—
72	M₁₆	—	292	1	no	—
73	C₂×C₈	—	292	1	no	—
74	C₄⋊C₄	—	292	1	no	—
75	C₄²	—	73	1	no	—
76	Q₈	—	4	1	no	—
77	Q₈	—	292	1	no	—
78	Q₈	—	292	1	no	—
79	Q₈	—	146	1	no	—
80	D₄	—	292	1	no	—
81	D₄	—	292	1	no	—
82	D₄	—	146	1	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	292	1	no	—
85	C₂×C₄	—	292	2	no	—
86	C₂×C₄	—	146	1	no	—
87	C₂×C₄	—	146	1	no	—
88	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
89	C₈	—	4	1	no	—
90	C₈	—	584	1	no	—
91	C₈	—	584	1	no	—
92	C₂²	—	292	1	no	—
93	C₂²	#14556650	1	1	yes	characteristic
94	C₄	—	2	1	no	—
95	C₄	—	4	1	no	—
96	C₄	—	292	1	no	—
97	C₄	—	292	1	no	—
98	C₄	—	146	1	no	—
99	C₄	—	146	1	no	—
100	C₂	—	2	1	no	—
101	C₂	—	584	1	no	—
102	C₂	#17989488	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989497

C₂

yes

maximal, characteristic, complemented

#17989447

C₂

yes

maximal, characteristic, complemented

#17988772

C₂

yes

maximal, characteristic

#14556658

—

#14556652

—

#14556639

C₄

yes

characteristic

#14556624

—

#14556589

C₂²

yes

characteristic

#14556517

—

#101×C₇₃

C₄

yes

—

—

—

—

—

C₂×Dic₁₄₆

D₄

yes

characteristic

Q₈×D₇₃

—

Dic₂₉₂

—

#11924017

—

#11924007

—

C₄×Dic₇₃

D₄

yes

characteristic

C₂×Q₈×C₇₃

C₂×C₄

yes

characteristic

M₁₆×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂²⋊D₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

D₂₉₂

—

D₂₉₂

—

C₄×D₇₃

—

C₄×D₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

#10596833

—

#10596833

—

C₈×C₇₃

—

C₂²×C₇₃

#99

yes

characteristic

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

AΣL(1,𝔽₁₆)

yes

characteristic

D₇₃

—

#1405

—

maximal, Sylow

C₇₃

#1405

yes

characteristic, complemented, Sylow

#456

—

#356

—

#333

—

2₋¹⁺⁴

—

#137

—

146

—

C₄⋊Q₈

—

C₄⋊C₈

—

146

—

#104

—

146

—

#101

—

146

—

yes

—

292

—

#41

—

292

—

#41

—

146

—

C₂×Q₈

—

292

—

C₂×Q₈

—

C₂×Q₈

C₂×#64408

yes

characteristic

Q₁₆

—

292

—

SD₁₆

—

292

—

M₁₆

—

M₁₆

—

292

—

C₂×C₈

—

292

—

C₄⋊C₄

—

292

—

C₄²

—

Q₈

—

Q₈

—

292

—

Q₈

—

292

—

Q₈

—

146

—

D₄

—

292

—

D₄

—

292

—

D₄

—

146

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

C₂²⋊#64408

yes

characteristic

C₈

—

C₈

—

584

—

C₈

—

584

—

C₂²

—

292

—

C₂²

#14556650

yes

characteristic

C₄

—

C₄

—

C₄

—

292

—

C₄

—

292

—

C₄

—

146

—

C₄

—

146

—

100

C₂

—

101

C₂

—

584

—

102

C₂

#17989488

yes

characteristic

	subgroup	G/H
center	C₂	#17989488
commutator	C₂×Q₈×C₇₃	C₂×C₄
Frattini	C₂×Q₈	C₂×#64408
Fitting	#101×C₇₃	C₄
socle	C₂×C₇₃	AΣL(1,𝔽₁₆)
hypercenter	#101	#64408
hypocenter	C₇₃	#1405
LCS	G ▷ C₂×Q₈×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₈ ◁ #101

subgroup

G/H

center

C₂

#17989488

commutator

C₂×Q₈×C₇₃

C₂×C₄

Frattini

C₂×Q₈

C₂×#64408

Fitting

#101×C₇₃

C₄

socle

C₂×C₇₃

AΣL(1,𝔽₁₆)

C₇₃

G ▷ C₂×Q₈×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₈ ◁ #101

N	H ≅ G/N	type
1. #17989497	C₂	semidirect
2. #17989447	C₂	semidirect
52. C₇₃	#1405	semidirect

H ≅ G/N

type

1. #17989497

C₂

semidirect

2. #17989447

C₂

semidirect

52. C₇₃

#1405

semidirect

Subgroups — #22625057

Conjugacy classes of subgroups

Complements