Group #22609598 — subgroups

Subgroups — #22609598

Order 9344.

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

normal subgroups only

This group has 242 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	#17988963	C₂	1	2	yes	maximal, complemented
2	#17988960	C₂	1	1	yes	maximal, characteristic, 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, complemented
6	C₂×#11924017	—	2	2	no	—
7	C₂×#11924013	—	2	4	no	—
8	#14556591	C₂²	1	1	yes	characteristic
9	#14556588	C₂²	1	1	yes	characteristic
10	#14556512	—	2	4	no	—
11	C₄×#10596831	C₂²	1	2	yes	—
12	C₂×D₈×C₇₃	—	2	2	no	—
13	#127×C₇₃	C₂²	1	2	yes	—
14	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×Dic₁₄₆	—	2	1	no	—
16	C₂×D₂₉₂	—	2	2	no	—
17	C₂×D₂₉₂	—	2	1	no	—
18	#11924017	—	4	4	no	—
19	#11924013	—	4	8	no	—
20	C₂×#10596831	D₄	1	4	yes	—
21	C₄⋊Dic₇₃	—	2	2	no	—
22	C₂×D₄×C₇₃	—	2	2	no	—
23	C₂×D₄×C₇₃	—	2	2	no	—
24	C₂×D₄×C₇₃	—	2	2	no	—
25	D₈×C₇₃	—	4	4	no	—
26	C₂×C₈×C₇₃	D₄	1	2	yes	—
27	C₄²×C₇₃	C₂³	1	1	yes	characteristic
28	C₂³×C₇₃	—	4	2	no	—
29	C₂²×D₇₃	—	4	1	no	—
30	D₄×C₇₃	—	4	4	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	1	no	—
36	D₂₉₂	—	4	2	no	—
37	D₂₉₂	—	4	4	no	—
38	Dic₁₄₆	—	4	2	no	—
39	C₈×C₇₃	D₈	1	4	yes	complemented
40	#10596831	—	2	4	no	—
41	C₂²×C₇₃	—	8	2	no	—
42	C₂²×C₇₃	—	8	2	no	—
43	C₂²×C₇₃	—	8	2	no	—
44	C₂²×C₇₃	#127	1	1	yes	characteristic
45	C₂×D₇₃	—	8	1	no	—
46	C₂×D₇₃	—	8	2	no	—
47	C₄×C₇₃	C₂×D₈	1	2	yes	—
48	C₄×C₇₃	AGL(1,ℤ/8)	1	4	yes	—
49	Dic₇₃	—	8	1	no	—
50	C₂×C₇₃	—	16	2	no	—
51	C₂×C₇₃	#493	1	1	yes	characteristic
52	C₂×C₇₃	#496	1	2	yes	—
53	D₇₃	—	16	1	no	—
54	#1721	—	73	1	no	maximal, Sylow
55	C₇₃	#1721	1	1	yes	characteristic, complemented, Sylow
56	#493	—	73	2	no	—
57	#493	D₇₃	1	1	yes	characteristic, complemented
58	#492	—	73	1	no	—
59	#486	—	73	2	no	—
60	#322	—	73	1	no	—
61	C₂×SD₁₆	—	146	2	no	—
62	C₂×D₈	—	2	2	no	—
63	C₂×D₈	—	146	4	no	—
64	C₄⋊Q₈	—	73	1	no	—
65	#127	—	73	1	no	—
66	#127	C₂×D₇₃	1	2	yes	—
67	#102	—	146	4	no	—
68	C₄×C₈	—	73	2	no	—
69	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
70	C₂×Q₈	—	146	1	no	—
71	C₂×D₄	—	2	2	no	—
72	C₂×D₄	—	2	2	no	—
73	C₂×D₄	—	2	2	no	—
74	C₂×D₄	—	146	2	no	—
75	C₂×D₄	—	146	1	no	—
76	SD₁₆	—	292	4	no	—
77	D₈	—	4	4	no	—
78	D₈	—	292	8	no	—
79	C₂×C₈	—	73	4	no	—
80	C₂×C₈	C₂²⋊D₇₃	1	2	yes	—
81	C₄⋊C₄	—	146	2	no	—
82	C₄²	C₂²×D₇₃	1	1	yes	characteristic
83	C₂³	—	4	2	no	—
84	C₂³	—	292	1	no	—
85	Q₈	—	292	2	no	—
86	D₄	—	4	4	no	—
87	D₄	—	4	4	no	—
88	D₄	—	4	4	no	—
89	D₄	—	292	2	no	—
90	D₄	—	292	4	no	—
91	C₂×C₄	—	292	1	no	—
92	C₂×C₄	D₄×D₇₃	1	2	yes	—
93	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
94	C₈	—	146	4	no	—
95	C₈	#11924013	1	4	yes	complemented
96	C₂²	—	8	2	no	—
97	C₂²	—	8	2	no	—
98	C₂²	—	8	2	no	—
99	C₂²	—	584	1	no	—
100	C₂²	—	584	2	no	—
101	C₂²	#14556587	1	1	yes	characteristic
102	C₄	—	584	1	no	—
103	C₄	C₂×#11924013	1	2	yes	—
104	C₄	#14556615	1	4	yes	—
105	C₂	—	16	2	no	—
106	C₂	—	1168	1	no	—
107	C₂	#17988963	1	1	yes	characteristic
108	C₂	#17988975	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#17988963

C₂

yes

maximal, complemented

#17988960

C₂

yes

maximal, characteristic, complemented

#17988933

C₂

yes

maximal, complemented

#17988308

C₂

yes

maximal, characteristic, complemented

#493×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂×#11924017

—

C₂×#11924013

—

#14556591

C₂²

yes

characteristic

#14556588

C₂²

yes

characteristic

#14556512

—

C₄×#10596831

C₂²

yes

—

C₂×D₈×C₇₃

—

#127×C₇₃

C₂²

yes

—

C₄×C₈×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

#11924017

—

#11924013

—

C₂×#10596831

D₄

yes

—

C₄⋊Dic₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

D₈×C₇₃

—

C₂×C₈×C₇₃

D₄

yes

—

C₄²×C₇₃

C₂³

yes

characteristic

C₂³×C₇₃

—

C₂²×D₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

—

D₂₉₂

—

D₂₉₂

—

Dic₁₄₆

—

C₈×C₇₃

D₈

yes

complemented

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#127

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

C₂×D₈

yes

—

C₄×C₇₃

AGL(1,ℤ/8)

yes

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#493

yes

characteristic

C₂×C₇₃

#496

yes

—

D₇₃

—

#1721

—

maximal, Sylow

C₇₃

#1721

yes

characteristic, complemented, Sylow

#493

—

#493

D₇₃

yes

characteristic, complemented

#492

—

#486

—

#322

—

C₂×SD₁₆

—

146

—

C₂×D₈

—

C₂×D₈

—

146

—

C₄⋊Q₈

—

#127

—

#127

C₂×D₇₃

yes

—

#102

—

146

—

C₄×C₈

—

C₄×C₈

C₂×D₇₃

yes

characteristic

C₂×Q₈

—

146

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

146

—

C₂×D₄

—

146

—

SD₁₆

—

292

—

D₈

—

D₈

—

292

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₇₃

yes

—

C₄⋊C₄

—

146

—

C₄²

C₂²×D₇₃

yes

characteristic

C₂³

—

C₂³

—

292

—

Q₈

—

292

—

D₄

—

D₄

—

D₄

—

D₄

—

292

—

D₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

D₄×D₇₃

yes

—

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

C₈

—

146

—

C₈

#11924013

yes

complemented

C₂²

—

C₂²

—

C₂²

—

C₂²

—

584

—

100

C₂²

—

584

—

101

C₂²

#14556587

yes

characteristic

102

C₄

—

584

—

103

C₄

C₂×#11924013

yes

—

104

C₄

#14556615

yes

—

105

C₂

—

106

C₂

—

1168

—

107

C₂

#17988963

yes

characteristic

108

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	#1721
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. #17988963	C₂	semidirect
2. #17988960	C₂	semidirect
3. #17988933	C₂	semidirect
4. #17988308	C₂	semidirect
5. #493×C₇₃	C₂	semidirect
39. C₈×C₇₃	D₈	semidirect
55. C₇₃	#1721	semidirect
57. #493	D₇₃	semidirect
95. C₈	#11924013	semidirect

H ≅ G/N

type

1. #17988963

C₂

semidirect

2. #17988960

C₂

semidirect

3. #17988933

C₂

semidirect

4. #17988308

C₂

semidirect

5. #493×C₇₃

C₂

semidirect

39. C₈×C₇₃

D₈

semidirect

55. C₇₃

#1721

semidirect

57. #493

D₇₃

semidirect

95. C₈

#11924013

semidirect

Subgroups — #22609598

Conjugacy classes of subgroups

Complements