Group #22609557 — subgroups

Subgroups — #22609557

Order 9344.

220 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 65 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	#17988985	C₂	1	1	yes	maximal, characteristic, complemented
2	#17988959	C₂	1	2	yes	maximal, complemented
3	#17988933	C₂	1	2	yes	maximal, complemented
4	#17988308	C₂	1	1	yes	maximal, characteristic, complemented
5	#493×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#11924016	—	2	4	no	—
7	#14556591	C₂²	1	2	yes	—
8	#14556523	—	2	2	no	—
9	#14556512	—	2	4	no	—
10	C₄×#10596831	C₂²	1	2	yes	—
11	C₂×D₈×C₇₃	—	2	2	no	—
12	#127×C₇₃	C₂²	1	1	yes	characteristic
13	#127×C₇₃	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×Dic₁₄₆	—	2	2	no	—
16	#11924016	—	4	8	no	—
17	C₂×#10596831	D₄	1	4	yes	—
18	C₄⋊Dic₇₃	—	2	2	no	—
19	C₄⋊Dic₇₃	—	2	2	no	—
20	C₂×D₄×C₇₃	—	2	1	no	—
21	C₂×D₄×C₇₃	—	2	1	no	—
22	C₂×D₄×C₇₃	—	2	2	no	—
23	C₂×D₄×C₇₃	—	2	2	no	—
24	D₈×C₇₃	—	4	4	no	—
25	C₂×C₈×C₇₃	D₄	1	2	yes	—
26	C₄²×C₇₃	C₂³	1	1	yes	characteristic
27	C₂³×C₇₃	—	4	1	no	—
28	C₂³×C₇₃	—	4	1	no	—
29	D₄×C₇₃	—	4	2	no	—
30	D₄×C₇₃	—	4	2	no	—
31	D₄×C₇₃	—	4	4	no	—
32	D₄×C₇₃	—	4	4	no	—
33	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
34	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
35	C₂×Dic₇₃	—	4	2	no	—
36	Dic₁₄₆	—	4	4	no	—
37	C₈×C₇₃	SD₁₆	1	4	yes	complemented
38	#10596831	—	2	4	no	—
39	C₂²×C₇₃	—	8	1	no	—
40	C₂²×C₇₃	—	8	1	no	—
41	C₂²×C₇₃	—	8	2	no	—
42	C₂²×C₇₃	—	8	2	no	—
43	C₂²×C₇₃	#127	1	1	yes	characteristic
44	C₄×C₇₃	C₂×SD₁₆	1	2	yes	—
45	C₄×C₇₃	AGL(1,ℤ/8)	1	4	yes	—
46	Dic₇₃	—	8	2	no	—
47	C₂×C₇₃	—	16	1	no	—
48	C₂×C₇₃	—	16	1	no	—
49	C₂×C₇₃	#492	1	1	yes	characteristic
50	C₂×C₇₃	#496	1	2	yes	—
51	#1715	—	73	1	no	maximal, Sylow
52	C₇₃	#1715	1	1	yes	characteristic, complemented, Sylow
53	#498	—	73	1	no	—
54	#493	D₇₃	1	1	yes	characteristic
55	#492	—	73	2	no	—
56	#486	—	73	2	no	—
57	#322	—	73	1	no	—
58	C₂×SD₁₆	—	146	4	no	—
59	C₂×D₈	—	2	2	no	—
60	C₄⋊Q₈	—	73	2	no	—
61	#127	C₂×D₇₃	1	1	yes	characteristic
62	#127	C₂×D₇₃	1	1	yes	characteristic
63	#106	—	146	2	no	—
64	#102	—	146	4	no	—
65	C₄×C₈	—	73	2	no	—
66	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
67	C₂×Q₈	—	146	2	no	—
68	C₂×D₄	—	2	2	no	—
69	C₂×D₄	—	2	2	no	—
70	C₂×D₄	—	2	1	no	—
71	C₂×D₄	—	2	1	no	—
72	SD₁₆	—	292	8	no	—
73	D₈	—	4	4	no	—
74	C₂×C₈	—	73	4	no	—
75	C₂×C₈	C₂²⋊D₇₃	1	2	yes	—
76	C₄⋊C₄	—	146	2	no	—
77	C₄⋊C₄	—	146	2	no	—
78	C₄²	C₂²×D₇₃	1	1	yes	characteristic
79	C₂³	—	4	1	no	—
80	C₂³	—	4	1	no	—
81	Q₈	—	292	4	no	—
82	D₄	—	4	2	no	—
83	D₄	—	4	2	no	—
84	D₄	—	4	4	no	—
85	D₄	—	4	4	no	—
86	C₂×C₄	—	292	2	no	—
87	C₂×C₄	D₄×D₇₃	1	2	yes	—
88	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
89	C₈	—	146	4	no	—
90	C₈	#11924016	1	4	yes	complemented
91	C₂²	—	8	1	no	—
92	C₂²	—	8	1	no	—
93	C₂²	—	8	2	no	—
94	C₂²	—	8	2	no	—
95	C₂²	#14556587	1	1	yes	characteristic
96	C₄	—	584	2	no	—
97	C₄	C₂×#11924016	1	2	yes	—
98	C₄	#14556615	1	4	yes	—
99	C₂	—	16	1	no	—
100	C₂	—	16	1	no	—
101	C₂	#17988959	1	1	yes	characteristic
102	C₂	#17988975	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#17988985

C₂

yes

maximal, characteristic, complemented

#17988959

C₂

yes

maximal, complemented

#17988933

C₂

yes

maximal, complemented

#17988308

C₂

yes

maximal, characteristic, complemented

#493×C₇₃

C₂

yes

maximal, characteristic

C₂×#11924016

—

#14556591

C₂²

yes

—

#14556523

—

#14556512

—

C₄×#10596831

C₂²

yes

—

C₂×D₈×C₇₃

—

#127×C₇₃

C₂²

yes

characteristic

#127×C₇₃

C₂²

yes

characteristic

C₄×C₈×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

—

#11924016

—

C₂×#10596831

D₄

yes

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

D₈×C₇₃

—

C₂×C₈×C₇₃

D₄

yes

—

C₄²×C₇₃

C₂³

yes

characteristic

C₂³×C₇₃

—

C₂³×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

—

Dic₁₄₆

—

C₈×C₇₃

SD₁₆

yes

complemented

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#127

yes

characteristic

C₄×C₇₃

C₂×SD₁₆

yes

—

C₄×C₇₃

AGL(1,ℤ/8)

yes

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#492

yes

characteristic

C₂×C₇₃

#496

yes

—

#1715

—

maximal, Sylow

C₇₃

#1715

yes

characteristic, complemented, Sylow

#498

—

#493

D₇₃

yes

—

—

—

C₂×SD₁₆

—

146

—

C₂×D₈

—

C₄⋊Q₈

—

#127

C₂×D₇₃

yes

characteristic

#127

C₂×D₇₃

yes

characteristic

#106

—

146

—

#102

—

146

—

C₄×C₈

—

C₄×C₈

C₂×D₇₃

yes

characteristic

C₂×Q₈

—

146

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

SD₁₆

—

292

—

D₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₇₃

yes

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄²

C₂²×D₇₃

yes

characteristic

C₂³

—

C₂³

—

Q₈

—

292

—

D₄

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

292

—

C₂×C₄

D₄×D₇₃

yes

—

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

C₈

—

146

—

C₈

#11924016

yes

complemented

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

#14556587

yes

characteristic

C₄

—

584

—

C₄

C₂×#11924016

yes

—

C₄

#14556615

yes

—

C₂

—

100

C₂

—

101

C₂

#17988959

yes

characteristic

102

C₂

#17988975

yes

—

	subgroup	G/H
center	C₂²	#14556587
commutator	C₄²×C₇₃	C₂³
Frattini	C₄²	C₂²×D₇₃
Fitting	#493×C₇₃	C₂
socle	C₂²×C₇₃	#127
hypercenter	#493	D₇₃
hypocenter	C₇₃	#1715
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #493

subgroup

G/H

center

C₂²

#14556587

commutator

C₄²×C₇₃

C₂³

Frattini

C₄²

C₂²×D₇₃

Fitting

#493×C₇₃

C₂

C₂²×C₇₃

D₇₃

C₇₃

G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #493

N	H ≅ G/N	type
1. #17988985	C₂	semidirect
2. #17988959	C₂	semidirect
3. #17988933	C₂	semidirect
4. #17988308	C₂	semidirect
37. C₈×C₇₃	SD₁₆	semidirect
52. C₇₃	#1715	semidirect
90. C₈	#11924016	semidirect

H ≅ G/N

type

1. #17988985

C₂

semidirect

2. #17988959

C₂

semidirect

3. #17988933

C₂

semidirect

4. #17988308

C₂

semidirect

37. C₈×C₇₃

SD₁₆

semidirect

52. C₇₃

#1715

semidirect

90. C₈

#11924016

semidirect

Subgroups — #22609557

Conjugacy classes of subgroups

Complements