Group #22609450 — subgroups

Subgroups — #22609450

Order 9344.

152 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 55 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	#17988992	C₂	1	1	yes	maximal, characteristic
2	#17988798	C₂	1	2	yes	maximal
3	#17988717	C₂	1	1	yes	maximal, characteristic
4	#17988334	C₂	1	2	yes	maximal
5	#334×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₂₉₂	—	2	2	no	—
7	#14556591	C₂²	1	2	yes	—
8	C₄×Dic₁₄₆	C₂²	1	1	yes	characteristic
9	#14556525	—	2	1	no	—
10	#14556525	—	2	1	no	—
11	C₄⋊#10596831	C₂²	1	1	yes	characteristic
12	#14556520	—	2	1	no	—
13	#14556516	—	2	2	no	—
14	#14556501	—	2	1	no	—
15	C₄⋊C₈×C₇₃	C₂²	1	2	yes	—
16	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×Dic₁₄₆	—	2	2	no	—
18	C₂×Dic₁₄₆	D₄	1	1	yes	characteristic
19	Dic₂₉₂	—	4	4	no	—
20	C₂×#10596831	—	2	1	no	—
21	C₄⋊Dic₇₃	—	2	2	no	—
22	C₄⋊Dic₇₃	—	2	2	no	—
23	C₄⋊Dic₇₃	D₄	1	1	yes	characteristic
24	#11924007	—	2	1	no	—
25	C₄×Dic₇₃	—	2	1	no	—
26	C₂×C₈×C₇₃	—	2	2	no	—
27	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
28	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
29	C₄²×C₇₃	C₂³	1	1	yes	characteristic
30	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
33	C₂×Dic₇₃	—	2	1	no	—
34	C₂×Dic₇₃	—	2	1	no	—
35	C₂×Dic₇₃	—	4	2	no	—
36	Dic₁₄₆	—	2	2	no	—
37	Dic₁₄₆	—	4	2	no	—
38	Dic₁₄₆	—	4	2	no	—
39	C₈×C₇₃	—	2	1	no	—
40	C₈×C₇₃	—	4	2	no	—
41	C₈×C₇₃	Q₁₆	1	2	yes	complemented
42	#10596831	—	4	1	no	—
43	C₂²×C₇₃	#121	1	1	yes	characteristic
44	C₄×C₇₃	—	2	1	no	—
45	C₄×C₇₃	C₂×Q₁₆	1	1	yes	characteristic
46	C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
47	C₄×C₇₃	#137	1	1	yes	characteristic
48	Dic₇₃	—	4	1	no	—
49	Dic₇₃	—	4	1	no	—
50	Dic₇₃	—	8	2	no	—
51	C₂×C₇₃	#462	1	1	yes	characteristic
52	C₂×C₇₃	#469	1	1	yes	characteristic
53	C₂×C₇₃	#473	1	1	yes	characteristic
54	#1694	—	73	1	no	maximal, Sylow
55	C₇₃	#1694	1	1	yes	characteristic, complemented, Sylow
56	#500	—	73	1	no	—
57	#462	—	73	2	no	—
58	#446	—	73	1	no	—
59	#334	D₇₃	1	1	yes	characteristic
60	#332	—	73	2	no	—
61	C₂×Q₁₆	—	146	2	no	—
62	C₄⋊Q₈	—	73	2	no	—
63	C₄×Q₈	—	73	1	no	—
64	#107	—	146	1	no	—
65	#107	—	146	1	no	—
66	C₄⋊C₈	—	73	1	no	—
67	C₄⋊C₈	—	146	1	no	—
68	C₄⋊C₈	C₂×D₇₃	1	2	yes	—
69	#103	—	146	2	no	—
70	#97	—	146	1	no	—
71	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
72	C₂×Q₈	—	73	1	no	—
73	C₂×Q₈	—	146	2	no	—
74	Q₁₆	—	292	4	no	—
75	C₂×C₈	—	2	2	no	—
76	C₂×C₈	—	146	1	no	—
77	C₂×C₈	D₂₉₂	1	1	yes	characteristic
78	C₂×C₈	D₂₉₂	1	1	yes	characteristic
79	C₄⋊C₄	—	73	1	no	—
80	C₄⋊C₄	—	146	2	no	—
81	C₄⋊C₄	—	146	2	no	—
82	C₄⋊C₄	—	146	1	no	—
83	C₄²	—	146	1	no	—
84	C₄²	C₂²×D₇₃	1	1	yes	characteristic
85	Q₈	—	292	2	no	—
86	Q₈	—	292	2	no	—
87	Q₈	—	146	2	no	—
88	C₂×C₄	—	292	2	no	—
89	C₂×C₄	—	146	1	no	—
90	C₂×C₄	—	146	1	no	—
91	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
92	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
93	C₂×C₄	#11924029	1	1	yes	characteristic
94	C₈	—	2	1	no	—
95	C₈	—	4	2	no	—
96	C₈	—	292	1	no	—
97	C₈	Dic₂₉₂	1	2	yes	complemented
98	C₂²	#14556566	1	1	yes	characteristic
99	C₄	—	2	1	no	—
100	C₄	—	292	1	no	—
101	C₄	—	292	1	no	—
102	C₄	—	584	2	no	—
103	C₄	C₂×Dic₂₉₂	1	1	yes	characteristic
104	C₄	#14556618	1	2	yes	—
105	C₄	#14556624	1	1	yes	characteristic
106	C₂	#17988798	1	1	yes	characteristic
107	C₂	#17988841	1	1	yes	characteristic
108	C₂	#17988863	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988992

C₂

yes

maximal, characteristic

#17988798

C₂

yes

maximal

#17988717

C₂

yes

maximal, characteristic

#17988334

C₂

yes

maximal

#334×C₇₃

C₂

yes

maximal, characteristic

C₂×Dic₂₉₂

—

#14556591

C₂²

yes

—

C₄×Dic₁₄₆

C₂²

yes

—

—

C₂²

yes

—

—

—

C₄⋊C₈×C₇₃

C₂²

yes

—

C₄×C₈×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

D₄

yes

characteristic

Dic₂₉₂

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

D₄

yes

characteristic

#11924007

—

C₄×Dic₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

D₄

yes

characteristic

C₄²×C₇₃

C₂³

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

#41

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

—

C₈×C₇₃

—

C₈×C₇₃

Q₁₆

yes

complemented

#10596831

—

C₂²×C₇₃

#121

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

C₂×Q₁₆

yes

characteristic

C₄×C₇₃

AGL(1,ℤ/8)

yes

—

C₄×C₇₃

#137

yes

characteristic

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

—

—

—

D₇₃

yes

characteristic

#332

—

C₂×Q₁₆

—

146

—

C₄⋊Q₈

—

C₄×Q₈

—

#107

—

146

—

#107

—

146

—

C₄⋊C₈

—

C₄⋊C₈

—

146

—

C₄⋊C₈

C₂×D₇₃

yes

—

#103

—

146

—

#97

—

146

—

C₄×C₈

C₂×D₇₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

146

—

Q₁₆

—

292

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

D₂₉₂

yes

characteristic

C₂×C₈

D₂₉₂

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄²

—

146

—

C₄²

C₂²×D₇₃

yes

characteristic

Q₈

—

292

—

Q₈

—

292

—

Q₈

—

146

—

C₂×C₄

—

292

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

D₄×D₇₃

yes

characteristic

C₂×C₄

C₂×D₂₉₂

yes

characteristic

C₂×C₄

#11924029

yes

characteristic

C₈

—

C₈

—

C₈

—

292

—

C₈

Dic₂₉₂

yes

complemented

C₂²

#14556566

yes

characteristic

C₄

—

100

C₄

—

292

—

101

C₄

—

292

—

102

C₄

—

584

—

103

C₄

C₂×Dic₂₉₂

yes

characteristic

104

C₄

#14556618

yes

—

105

C₄

#14556624

yes

characteristic

106

C₂

#17988798

yes

characteristic

107

C₂

#17988841

yes

characteristic

108

C₂

#17988863

yes

characteristic

	subgroup	G/H
center	C₂²	#14556566
commutator	C₄²×C₇₃	C₂³
Frattini	C₄²	C₂²×D₇₃
Fitting	#334×C₇₃	C₂
socle	C₂²×C₇₃	#121
hypercenter	#334	D₇₃
hypocenter	C₇₃	#1694
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #334

subgroup

G/H

center

C₂²

#14556566

commutator

C₄²×C₇₃

C₂³

Frattini

C₄²

C₂²×D₇₃

Fitting

#334×C₇₃

C₂

C₂²×C₇₃

D₇₃

C₇₃

G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #334

N	H ≅ G/N	type
41. C₈×C₇₃	Q₁₆	semidirect
55. C₇₃	#1694	semidirect
97. C₈	Dic₂₉₂	semidirect

H ≅ G/N

type

41. C₈×C₇₃

Q₁₆

semidirect

55. C₇₃

#1694

semidirect

97. C₈

Dic₂₉₂

semidirect

Subgroups — #22609450

Conjugacy classes of subgroups

Complements