Group #22608085 — subgroups

Subgroups — #22608085

Order 9344.

106 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 106 conjugacy classes of subgroups — too many to draw. Only its 25 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	#17988386	C₂	1	1	yes	maximal, characteristic, complemented
2	#17988336	C₂	1	1	yes	maximal, characteristic, complemented
3	#456×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#10596831	—	2	1	no	—
5	#14556510	—	2	1	no	—
6	2₋¹⁺⁴×C₇₃	C₄	1	1	yes	characteristic
7	#137×C₇₃	—	2	1	no	—
8	C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
9	#104×C₇₃	—	2	1	no	—
10	#101×C₇₃	C₄	1	1	yes	characteristic
11	#11924012	—	4	1	no	—
12	C₂×#10596831	—	4	1	no	—
13	#41×C₇₃	—	2	1	no	—
14	#41×C₇₃	—	4	1	no	—
15	#41×C₇₃	—	4	1	no	—
16	C₂×Q₈×C₇₃	—	4	1	no	—
17	C₂×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
18	C₂×Q₈×C₇₃	D₄	1	1	yes	characteristic
19	Q₁₆×C₇₃	—	4	1	no	—
20	SD₁₆×C₇₃	—	4	1	no	—
21	M₁₆×C₇₃	—	2	1	no	—
22	C₄⋊C₄×C₇₃	—	4	1	no	—
23	C₄²×C₇₃	D₄	1	1	yes	characteristic
24	Q₈×C₇₃	—	2	1	no	—
25	Q₈×C₇₃	—	4	1	no	—
26	Q₈×C₇₃	—	4	1	no	—
27	Q₈×C₇₃	—	4	1	no	—
28	D₄×C₇₃	—	2	1	no	—
29	D₄×C₇₃	—	4	1	no	—
30	D₄×C₇₃	—	4	1	no	—
31	C₂×C₄×C₇₃	—	2	1	no	—
32	C₂×C₄×C₇₃	—	2	1	no	—
33	C₂×C₄×C₇₃	—	2	1	no	—
34	C₂×C₄×C₇₃	—	4	1	no	—
35	C₂×C₄×C₇₃	—	4	2	no	—
36	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
37	C₈×C₇₃	—	4	1	no	—
38	#10596831	—	8	1	no	—
39	#10596831	—	8	1	no	—
40	C₂²×C₇₃	—	4	1	no	—
41	C₂²×C₇₃	#99	1	1	yes	characteristic
42	C₄×C₇₃	—	2	1	no	—
43	C₄×C₇₃	—	2	1	no	—
44	C₄×C₇₃	—	2	1	no	—
45	C₄×C₇₃	—	4	1	no	—
46	C₄×C₇₃	—	4	1	no	—
47	C₄×C₇₃	—	4	1	no	—
48	C₂×C₇₃	—	2	1	no	—
49	C₂×C₇₃	—	8	1	no	—
50	C₂×C₇₃	AΣL(1,𝔽₁₆)	1	1	yes	characteristic
51	#1405	—	73	1	no	maximal, Sylow
52	C₇₃	#1405	1	1	yes	characteristic, complemented, Sylow
53	#456	D₇₃	1	1	yes	characteristic
54	#356	—	73	1	no	—
55	#333	—	73	1	no	—
56	2₋¹⁺⁴	Dic₇₃	1	1	yes	characteristic
57	#137	—	2	1	no	—
58	C₄⋊Q₈	C₂×D₇₃	1	1	yes	characteristic
59	C₄⋊C₈	—	146	1	no	—
60	#104	—	2	1	no	—
61	#101	—	146	1	no	—
62	#101	Dic₇₃	1	1	yes	characteristic
63	#41	—	2	1	no	—
64	#41	—	4	1	no	—
65	#41	—	4	1	no	—
66	C₂×Q₈	—	4	1	no	—
67	C₂×Q₈	C₂×Dic₇₃	1	1	yes	characteristic
68	C₂×Q₈	C₂²⋊D₇₃	1	1	yes	characteristic
69	Q₁₆	—	4	1	no	—
70	SD₁₆	—	4	1	no	—
71	M₁₆	—	2	1	no	—
72	M₁₆	—	292	1	no	—
73	C₂×C₈	—	292	1	no	—
74	C₄⋊C₄	—	4	1	no	—
75	C₄²	C₂²⋊D₇₃	1	1	yes	characteristic
76	Q₈	—	2	1	no	—
77	Q₈	—	4	1	no	—
78	Q₈	—	4	1	no	—
79	Q₈	—	4	1	no	—
80	D₄	—	2	1	no	—
81	D₄	—	4	1	no	—
82	D₄	—	4	1	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	2	1	no	—
86	C₂×C₄	—	4	1	no	—
87	C₂×C₄	—	4	2	no	—
88	C₂×C₄	C₂²⋊Dic₇₃	1	1	yes	characteristic
89	C₈	—	4	1	no	—
90	C₈	—	584	1	no	—
91	C₈	—	584	1	no	—
92	C₂²	—	4	1	no	—
93	C₂²	#14556506	1	1	yes	characteristic
94	C₄	—	2	1	no	—
95	C₄	—	2	1	no	—
96	C₄	—	2	1	no	—
97	C₄	—	4	1	no	—
98	C₄	—	4	1	no	—
99	C₄	—	4	1	no	—
100	C₂	—	2	1	no	—
101	C₂	—	8	1	no	—
102	C₂	#17988374	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988386

C₂

yes

maximal, characteristic, complemented

#17988336

C₂

yes

maximal, characteristic, complemented

#456×C₇₃

C₂

yes

maximal, characteristic

C₄⋊#10596831

—

#14556510

—

2₋¹⁺⁴×C₇₃

C₄

yes

characteristic

#137×C₇₃

—

C₄⋊Q₈×C₇₃

C₂²

yes

characteristic

#104×C₇₃

—

#101×C₇₃

C₄

yes

characteristic

#11924012

—

C₂×#10596831

—

#41×C₇₃

—

#41×C₇₃

—

#41×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

C₂×C₄

yes

characteristic

C₂×Q₈×C₇₃

D₄

yes

characteristic

Q₁₆×C₇₃

—

SD₁₆×C₇₃

—

M₁₆×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

D₄

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₈×C₇₃

—

#10596831

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

#99

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

AΣL(1,𝔽₁₆)

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#456

D₇₃

yes

characteristic

#356

—

#333

—

2₋¹⁺⁴

Dic₇₃

yes

characteristic

#137

—

C₄⋊Q₈

C₂×D₇₃

yes

characteristic

C₄⋊C₈

—

146

—

#104

—

#101

—

146

—

#101

Dic₇₃

yes

—

—

—

C₂×Q₈

—

C₂×Q₈

C₂×Dic₇₃

yes

characteristic

C₂×Q₈

C₂²⋊D₇₃

yes

characteristic

Q₁₆

—

SD₁₆

—

M₁₆

—

M₁₆

—

292

—

C₂×C₈

—

292

—

C₄⋊C₄

—

C₄²

C₂²⋊D₇₃

yes

characteristic

Q₈

—

Q₈

—

Q₈

—

Q₈

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊Dic₇₃

yes

characteristic

C₈

—

C₈

—

584

—

C₈

—

584

—

C₂²

—

C₂²

#14556506

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

100

C₂

—

101

C₂

—

102

C₂

#17988374

yes

characteristic

	subgroup	G/H
center	C₂	#17988374
commutator	C₂×Q₈×C₇₃	C₂×C₄
Frattini	C₄⋊Q₈	C₂×D₇₃
Fitting	#456×C₇₃	C₂
socle	C₂×C₇₃	AΣL(1,𝔽₁₆)
hypercenter	#456	D₇₃
hypocenter	C₇₃	#1405
LCS	G ▷ C₂×Q₈×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊Q₈ ◁ #456

subgroup

G/H

center

C₂

#17988374

commutator

C₂×Q₈×C₇₃

C₂×C₄

Frattini

C₄⋊Q₈

C₂×D₇₃

Fitting

#456×C₇₃

C₂

socle

C₂×C₇₃

AΣL(1,𝔽₁₆)

D₇₃

C₇₃

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

UCS

C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊Q₈ ◁ #456

N	H ≅ G/N	type
1. #17988386	C₂	semidirect
2. #17988336	C₂	semidirect
52. C₇₃	#1405	semidirect

H ≅ G/N

type

1. #17988386

C₂

semidirect

2. #17988336

C₂

semidirect

52. C₇₃

#1405

semidirect

Subgroups — #22608085

Conjugacy classes of subgroups

Complements