Group #22624751 — subgroups

Subgroups — #22624751

Order 9344.

166 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 56 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	#17989453	C₂	1	2	yes	maximal
2	#17988494	C₂	1	1	yes	maximal, characteristic
3	C₂²×#10596833	—	2	2	no	—
4	C₂×C₄⋊Dic₇₃	C₄	1	1	yes	characteristic
5	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
6	#14556498	—	2	2	no	—
7	C₂²×Q₈×C₇₃	C₄	1	1	yes	characteristic
8	C₂×#10596833	—	2	4	no	—
9	C₂×#10596833	—	4	2	no	—
10	C₂×#10596833	—	4	2	no	—
11	C₂²×Dic₇₃	—	2	1	no	—
12	C₂²×Dic₇₃	D₄	1	2	yes	—
13	C₄⋊Dic₇₃	—	4	1	no	—
14	C₄×Dic₇₃	—	4	1	no	—
15	C₂×Q₈×C₇₃	—	2	1	no	—
16	C₂×Q₈×C₇₃	—	4	1	no	—
17	C₂×Q₈×C₇₃	—	4	1	no	—
18	C₂×Q₈×C₇₃	C₈	1	2	yes	complemented
19	C₂²×C₄×C₇₃	—	2	1	no	—
20	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
21	C₂³×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
22	Q₈×C₇₃	—	4	2	no	—
23	Q₈×C₇₃	—	4	2	no	—
24	C₂×C₄×C₇₃	—	2	1	no	—
25	C₂×C₄×C₇₃	—	2	1	no	—
26	C₂×C₄×C₇₃	—	2	2	no	—
27	C₂×C₄×C₇₃	—	4	1	no	—
28	C₂×C₄×C₇₃	—	4	1	no	—
29	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₇₃	M₁₆	1	1	yes	characteristic
31	C₂×Dic₇₃	—	2	2	no	—
32	C₂×Dic₇₃	—	2	2	no	—
33	C₂×Dic₇₃	—	4	1	no	—
34	C₂×Dic₇₃	—	4	2	no	—
35	C₂×Dic₇₃	SD₁₆	1	2	yes	—
36	C₂×Dic₇₃	Q₁₆	1	2	yes	—
37	#10596833	—	4	4	no	—
38	C₂²×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
39	C₂²×C₇₃	#99	1	1	yes	characteristic
40	C₂²×C₇₃	#100	1	1	yes	characteristic
41	C₂²×C₇₃	#103	1	2	yes	—
42	C₂²×C₇₃	#104	1	2	yes	—
43	C₄×C₇₃	—	2	1	no	—
44	C₄×C₇₃	—	2	1	no	—
45	C₄×C₇₃	—	4	2	no	—
46	Dic₇₃	—	2	2	no	—
47	Dic₇₃	—	2	2	no	—
48	Dic₇₃	—	8	1	no	—
49	C₂×C₇₃	#323	1	1	yes	characteristic
50	C₂×C₇₃	Q₈⋊C₈	1	2	yes	—
51	C₂×C₇₃	#328	1	2	yes	—
52	C₂×C₇₃	#329	1	1	yes	characteristic
53	C₂×C₇₃	#333	1	1	yes	characteristic
54	#1272	—	73	1	no	maximal, Sylow
55	C₇₃	#1272	1	1	yes	characteristic, complemented, Sylow
56	#391	—	73	1	no	—
57	#336	—	73	2	no	—
58	C₂²×Q₈	#64408	1	1	yes	characteristic
59	C₂²×C₈	—	146	2	no	—
60	C₂×C₄⋊C₄	—	73	1	no	—
61	C₂×C₄²	—	73	1	no	—
62	#95	—	146	2	no	—
63	C₂×Q₈	—	2	1	no	—
64	C₂×Q₈	—	4	1	no	—
65	C₂×Q₈	—	4	1	no	—
66	C₂×Q₈	#10596833	1	2	yes	complemented
67	C₂²×C₄	—	2	1	no	—
68	C₂²×C₄	—	73	2	no	—
69	C₂²×C₄	—	146	1	no	—
70	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
71	C₂×C₈	—	292	2	no	—
72	C₂×C₈	—	292	2	no	—
73	C₂×C₈	—	146	4	no	—
74	C₄⋊C₄	—	292	1	no	—
75	C₄²	—	292	1	no	—
76	C₂³	C₂²⋊#64408	1	1	yes	characteristic
77	Q₈	—	4	2	no	—
78	Q₈	—	4	2	no	—
79	C₂×C₄	—	2	1	no	—
80	C₂×C₄	—	2	1	no	—
81	C₂×C₄	—	2	2	no	—
82	C₂×C₄	—	4	1	no	—
83	C₂×C₄	—	4	1	no	—
84	C₂×C₄	—	292	1	no	—
85	C₂×C₄	—	292	2	no	—
86	C₂×C₄	—	73	2	no	—
87	C₂×C₄	—	73	2	no	—
88	C₂×C₄	—	146	2	no	—
89	C₂×C₄	—	146	2	no	—
90	C₂×C₄	C₂×#10596833	1	1	yes	characteristic
91	C₂×C₄	#11924037	1	1	yes	characteristic
92	C₈	—	292	4	no	—
93	C₂²	C₂²⋊#10596833	1	1	yes	characteristic
94	C₂²	#14556649	1	1	yes	characteristic
95	C₂²	#14556651	1	1	yes	characteristic
96	C₂²	#14556654	1	2	yes	—
97	C₂²	#14556656	1	2	yes	—
98	C₄	—	2	1	no	—
99	C₄	—	2	1	no	—
100	C₄	—	4	2	no	—
101	C₄	—	584	1	no	—
102	C₄	—	146	2	no	—
103	C₄	—	146	2	no	—
104	C₂	#17989430	1	1	yes	characteristic
105	C₂	Q₈⋊#10596833	1	2	yes	—
106	C₂	#17989441	1	2	yes	—
107	C₂	#17989443	1	1	yes	characteristic
108	C₂	#17989447	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989453

C₂

yes

maximal

#17988494

C₂

yes

maximal, characteristic

C₂²×#10596833

—

C₂×C₄⋊Dic₇₃

C₄

yes

characteristic

C₂×C₄×Dic₇₃

C₂²

yes

characteristic

#14556498

—

C₂²×Q₈×C₇₃

C₄

yes

—

—

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

D₄

yes

—

C₄⋊Dic₇₃

—

C₄×Dic₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

C₈

yes

complemented

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₂³×C₇₃

C₂²⋊C₄

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

M₁₆

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

SD₁₆

yes

—

C₂×Dic₇₃

Q₁₆

yes

—

#10596833

—

C₂²×C₇₃

C₂²⋊C₈

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

—

C₂²×C₇₃

#104

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

#323

yes

characteristic

C₂×C₇₃

Q₈⋊C₈

yes

—

C₂×C₇₃

#328

yes

—

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#391

—

#336

—

C₂²×Q₈

#64408

yes

characteristic

C₂²×C₈

—

146

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

#95

—

146

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

#10596833

yes

complemented

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

146

—

C₂²×C₄

C₂×#64408

yes

characteristic

C₂×C₈

—

292

—

C₂×C₈

—

292

—

C₂×C₈

—

146

—

C₄⋊C₄

—

292

—

C₄²

—

292

—

C₂³

C₂²⋊#64408

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

yes

C₂×C₄

yes

C₈

—

292

—

C₂²

yes

C₂²

yes

C₂²

yes

C₂²

yes

—

C₂²

#14556656

yes

—

C₄

—

C₄

—

100

C₄

—

101

C₄

—

584

—

102

C₄

—

146

—

103

C₄

—

146

—

104

C₂

#17989430

yes

characteristic

105

C₂

Q₈⋊#10596833

yes

—

106

C₂

#17989441

yes

—

107

C₂

#17989443

yes

characteristic

108

C₂

#17989447

yes

characteristic

	subgroup	G/H
center	C₂³	C₂²⋊#64408
commutator	C₂×C₄×C₇₃	C₂×C₈
Frattini	C₂²×C₄	C₂×#64408
Fitting	C₂²×Q₈×C₇₃	C₄
socle	C₂³×C₇₃	C₂²⋊C₄
hypercenter	C₂²×Q₈	#64408
hypocenter	C₇₃	#1272
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×Q₈

subgroup

G/H

center

C₂³

C₂²⋊#64408

commutator

C₂×C₄×C₇₃

C₂×C₈

Frattini

C₂²×C₄

C₂×#64408

Fitting

C₂²×Q₈×C₇₃

C₄

socle

C₂³×C₇₃

C₂²⋊C₄

C₂²×Q₈

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×Q₈

N	H ≅ G/N	type
18. C₂×Q₈×C₇₃	C₈	semidirect
55. C₇₃	#1272	semidirect
66. C₂×Q₈	#10596833	semidirect

H ≅ G/N

type

18. C₂×Q₈×C₇₃

C₈

semidirect

55. C₇₃

#1272

semidirect

66. C₂×Q₈

#10596833

semidirect

Subgroups — #22624751

Conjugacy classes of subgroups

Complements