Group #22624901 — subgroups

Subgroups — #22624901

Order 9344.

114 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 114 conjugacy classes of subgroups — too many to draw. Only its 26 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	#17989484	C₂	1	1	yes	maximal, characteristic, complemented
2	#17989455	C₂	1	1	yes	maximal, characteristic, complemented
3	#17988837	C₂	1	1	yes	maximal, characteristic
4	#14556670	—	2	1	no	—
5	#14556665	—	2	1	no	—
6	C₂×#11924011	C₂²	1	1	yes	characteristic
7	#14556562	—	2	1	no	—
8	#14556523	C₄	1	1	yes	characteristic, complemented
9	#14556512	—	2	1	no	—
10	C₂×D₈×C₇₃	C₄	1	1	yes	characteristic, complemented
11	C₄⋊#64408	—	4	1	no	—
12	C₂²⋊#64408	—	4	1	no	—
13	C₄×#64408	—	2	2	no	—
14	#11924031	—	4	1	no	—
15	C₂×C₂²⋊D₇₃	—	4	1	no	—
16	C₂×C₄×D₇₃	D₄	1	1	yes	characteristic
17	#11924011	—	4	1	no	—
18	C₂×#10596831	D₄	1	1	yes	characteristic
19	C₄⋊Dic₇₃	—	2	1	no	—
20	C₂²⋊Dic₇₃	—	4	1	no	—
21	C₂×D₄×C₇₃	—	2	1	no	—
22	D₈×C₇₃	—	4	1	no	—
23	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₇₃	—	4	1	no	—
25	C₂²×D₇₃	D₈	1	1	yes	characteristic
26	C₂×#64408	—	4	2	no	—
27	D₄×C₇₃	—	4	1	no	—
28	D₄×C₇₃	—	4	1	no	—
29	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
30	C₂²⋊D₇₃	—	8	2	no	—
31	C₂×Dic₇₃	—	4	1	no	—
32	C₂×Dic₇₃	SD₁₆	1	1	yes	characteristic
33	C₄×D₇₃	—	2	1	no	—
34	C₄×D₇₃	—	2	1	no	—
35	C₈×C₇₃	—	2	1	no	—
36	#10596831	—	2	1	no	—
37	C₂²×C₇₃	—	8	1	no	—
38	C₂²×C₇₃	—	8	1	no	—
39	C₂²×C₇₃	—	8	1	no	—
40	C₂²×C₇₃	#102	1	1	yes	characteristic
41	C₂×D₇₃	—	2	1	no	—
42	C₂×D₇₃	—	4	1	no	—
43	#64408	—	8	2	no	—
44	C₄×C₇₃	#99	1	1	yes	characteristic
45	C₄×C₇₃	#104	1	1	yes	characteristic
46	Dic₇₃	—	2	1	no	—
47	Dic₇₃	—	8	1	no	—
48	C₂×C₇₃	—	2	1	no	—
49	C₂×C₇₃	—	16	1	no	—
50	C₂×C₇₃	#327	1	1	yes	characteristic
51	D₇₃	—	4	1	no	—
52	#1339	—	73	1	no	maximal, Sylow
53	C₇₃	#1339	1	1	yes	characteristic, complemented, Sylow
54	#469	—	73	1	no	—
55	#349	—	73	1	no	—
56	H(3,ℤ/4)	—	73	1	no	—
57	C₂×D₈	#64408	1	1	yes	characteristic, complemented
58	C₂×M₁₆	—	73	1	no	—
59	#121	—	146	1	no	—
60	#117	—	146	1	no	—
61	M₃₂	—	146	1	no	—
62	#106	—	73	1	no	—
63	#102	—	146	1	no	—
64	C₂×D₄	—	2	1	no	—
65	C₂×D₄	—	292	1	no	—
66	C₂²×C₄	—	73	1	no	—
67	D₈	—	4	1	no	—
68	M₁₆	—	292	1	no	—
69	C₂×C₈	—	73	1	no	—
70	C₂×C₈	C₂×#64408	1	1	yes	characteristic
71	C₄⋊C₄	—	292	1	no	—
72	C₄⋊C₄	—	146	1	no	—
73	C₂²⋊C₄	—	292	1	no	—
74	C₂²⋊C₄	—	292	1	no	—
75	C₄²	—	146	2	no	—
76	C₁₆	—	292	1	no	—
77	C₂³	—	4	1	no	—
78	C₂³	—	73	1	no	—
79	D₄	—	4	1	no	—
80	D₄	—	4	1	no	—
81	D₄	—	584	2	no	—
82	C₂×C₄	—	292	2	no	—
83	C₂×C₄	—	292	1	no	—
84	C₂×C₄	—	73	1	no	—
85	C₂×C₄	—	146	1	no	—
86	C₂×C₄	—	146	1	no	—
87	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
88	C₈	—	2	1	no	—
89	C₈	—	146	1	no	—
90	C₂²	—	8	1	no	—
91	C₂²	—	8	1	no	—
92	C₂²	—	8	1	no	—
93	C₂²	—	292	1	no	—
94	C₂²	—	146	1	no	—
95	C₂²	#14556653	1	1	yes	characteristic
96	C₄	—	584	1	no	—
97	C₄	—	584	2	no	—
98	C₄	—	146	1	no	—
99	C₄	#14556649	1	1	yes	characteristic
100	C₄	#14556655	1	1	yes	characteristic
101	C₂	—	2	1	no	—
102	C₂	—	16	1	no	—
103	C₂	—	292	1	no	—
104	C₂	#17989438	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989484

C₂

yes

maximal, characteristic, complemented

#17989455

C₂

yes

maximal, characteristic, complemented

#17988837

C₂

yes

maximal, characteristic

#14556670

—

#14556665

—

C₂×#11924011

C₂²

yes

characteristic

#14556562

—

#14556523

C₄

yes

characteristic, complemented

#14556512

—

C₂×D₈×C₇₃

C₄

yes

characteristic, complemented

—

—

—

—

C₂×C₂²⋊D₇₃

—

C₂×C₄×D₇₃

D₄

yes

characteristic

#11924011

—

C₂×#10596831

D₄

yes

characteristic

C₄⋊Dic₇₃

—

C₂²⋊Dic₇₃

—

C₂×D₄×C₇₃

—

D₈×C₇₃

—

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂³×C₇₃

—

C₂²×D₇₃

D₈

yes

characteristic

C₂×#64408

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂²⋊D₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

SD₁₆

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#102

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

#64408

—

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#327

yes

characteristic

D₇₃

—

#1339

—

maximal, Sylow

C₇₃

#1339

yes

characteristic, complemented, Sylow

#469

—

#349

—

H(3,ℤ/4)

—

C₂×D₈

#64408

yes

characteristic, complemented

C₂×M₁₆

—

#121

—

146

—

#117

—

146

—

M₃₂

—

146

—

#106

—

#102

—

146

—

C₂×D₄

—

C₂×D₄

—

292

—

C₂²×C₄

—

D₈

—

M₁₆

—

292

—

C₂×C₈

—

C₂×C₈

C₂×#64408

yes

characteristic

C₄⋊C₄

—

292

—

C₄⋊C₄

—

146

—

C₂²⋊C₄

—

292

—

C₂²⋊C₄

—

292

—

C₄²

—

146

—

C₁₆

—

292

—

C₂³

—

C₂³

—

D₄

—

D₄

—

D₄

—

584

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

C₂²⋊#64408

yes

characteristic

C₈

—

C₈

—

146

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

292

—

C₂²

—

146

—

C₂²

#14556653

yes

characteristic

C₄

—

584

—

C₄

—

584

—

C₄

—

146

—

C₄

#14556649

yes

characteristic

100

C₄

#14556655

yes

characteristic

101

C₂

—

102

C₂

—

103

C₂

—

292

—

104

C₂

#17989438

yes

characteristic

	subgroup	G/H
center	C₂	#17989438
commutator	C₂×C₈×C₇₃	C₂×C₄
Frattini	C₂×C₈	C₂×#64408
Fitting	C₂×D₈×C₇₃	C₄
socle	C₂×C₇₃	#327
hypercenter	C₂×D₈	#64408
hypocenter	C₇₃	#1339
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

subgroup

G/H

center

C₂

#17989438

commutator

C₂×C₈×C₇₃

C₂×C₄

Frattini

C₂×C₈

C₂×#64408

Fitting

C₂×D₈×C₇₃

C₄

C₂×C₇₃

C₂×D₈

C₇₃

G ▷ C₂×C₈×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

N	H ≅ G/N	type
1. #17989484	C₂	semidirect
2. #17989455	C₂	semidirect
8. #14556523	C₄	semidirect
10. C₂×D₈×C₇₃	C₄	semidirect
53. C₇₃	#1339	semidirect
57. C₂×D₈	#64408	semidirect

H ≅ G/N

type

1. #17989484

C₂

semidirect

2. #17989455

C₂

semidirect

8. #14556523

C₄

semidirect

10. C₂×D₈×C₇₃

C₄

semidirect

53. C₇₃

#1339

semidirect

57. C₂×D₈

#64408

semidirect

Subgroups — #22624901

Conjugacy classes of subgroups

Complements