Group #22612103 — subgroups

Subgroups — #22612103

Order 9344.

126 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 47 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	#17988705	C₂	1	1	yes	maximal, characteristic
3	#17988410	C₂	1	2	yes	maximal, complemented
4	#17988398	C₂	1	2	yes	maximal
5	#364×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#14556613	C₂²	1	1	yes	characteristic
7	#14556597	—	2	1	no	—
8	#14556591	—	2	1	no	—
9	#14556527	C₂²	1	1	yes	characteristic
10	#14556523	—	2	1	no	—
11	#14556523	C₂²	1	2	yes	—
12	#14556519	—	2	1	no	—
13	M₃₂×C₇₃	C₂²	1	2	yes	—
14	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
15	#11924028	—	2	1	no	—
16	C₂×Dic₁₄₆	—	4	1	no	—
17	Dic₂₉₂	Q₈	1	1	yes	characteristic, complemented
18	#11924017	—	2	1	no	—
19	D₅₈₄	Q₈	1	1	yes	characteristic, complemented
20	#11924012	—	2	1	no	—
21	#11924011	—	4	1	no	—
22	C₈×D₇₃	—	4	1	no	—
23	C₄⋊Dic₇₃	—	2	2	no	—
24	C₄⋊Dic₇₃	—	4	1	no	—
25	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
26	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
27	C₄²×C₇₃	D₄	1	1	yes	characteristic
28	C₁₆×C₇₃	—	2	2	no	—
29	C₂×C₄×C₇₃	—	2	1	no	—
30	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
31	C₂²⋊D₇₃	—	4	1	no	—
32	C₂×Dic₇₃	—	4	2	no	—
33	D₂₉₂	—	2	1	no	—
34	C₄×D₇₃	—	4	1	no	—
35	Dic₁₄₆	—	2	1	no	—
36	Dic₁₄₆	—	8	2	no	—
37	C₈×C₇₃	SD₁₆	1	1	yes	characteristic
38	C₈×C₇₃	SD₁₆	1	1	yes	characteristic
39	C₈×C₇₃	C₂×Q₈	1	1	yes	characteristic
40	C₈×C₇₃	#41	1	1	yes	characteristic
41	#10596831	—	4	1	no	—
42	C₂²×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
43	C₂×D₇₃	—	4	1	no	—
44	C₄×C₇₃	—	2	2	no	—
45	C₄×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
46	C₄×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
47	Dic₇₃	—	4	1	no	—
48	Dic₇₃	—	8	2	no	—
49	C₂×C₇₃	—	2	1	no	—
50	C₂×C₇₃	#476	1	1	yes	characteristic
51	D₇₃	—	8	1	no	—
52	#2230	—	73	1	no	maximal, Sylow
53	C₇₃	#2230	1	1	yes	characteristic, complemented, Sylow
54	#498	—	73	1	no	—
55	#443	—	73	1	no	—
56	#365	—	73	2	no	—
57	#364	D₇₃	1	1	yes	characteristic, complemented
58	#360	—	73	2	no	—
59	#135	—	73	1	no	—
60	#131	—	146	1	no	—
61	C₄⋊Q₈	—	146	1	no	—
62	M₃₂	C₂×D₇₃	1	2	yes	—
63	#108	—	73	1	no	—
64	#106	—	73	2	no	—
65	#106	—	146	1	no	—
66	#104	—	146	1	no	—
67	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
68	#41	—	146	1	no	—
69	C₂×Q₈	—	292	1	no	—
70	Q₁₆	—	73	1	no	—
71	SD₁₆	—	146	1	no	—
72	D₈	—	73	1	no	—
73	M₁₆	—	292	1	no	—
74	M₁₆	—	146	1	no	—
75	C₂×C₈	—	292	1	no	—
76	C₂×C₈	D₂₉₂	1	1	yes	characteristic
77	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
78	C₄⋊C₄	—	292	1	no	—
79	C₄⋊C₄	—	146	2	no	—
80	C₄²	D₂₉₂	1	1	yes	characteristic
81	C₁₆	—	2	2	no	—
82	Q₈	—	584	2	no	—
83	Q₈	—	146	1	no	—
84	D₄	—	292	1	no	—
85	D₄	—	146	1	no	—
86	C₂×C₄	—	2	1	no	—
87	C₂×C₄	—	292	1	no	—
88	C₂×C₄	—	292	2	no	—
89	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
90	C₈	—	292	1	no	—
91	C₈	#11924017	1	1	yes	characteristic
92	C₈	#11924017	1	1	yes	characteristic
93	C₈	Q₈×D₇₃	1	1	yes	characteristic
94	C₈	#11924027	1	1	yes	characteristic
95	C₂²	—	292	1	no	—
96	C₂²	#14556619	1	1	yes	characteristic
97	C₄	—	2	2	no	—
98	C₄	—	292	1	no	—
99	C₄	—	584	2	no	—
100	C₄	#14556571	1	1	yes	characteristic
101	C₄	C₂×#11924017	1	1	yes	characteristic
102	C₂	—	2	1	no	—
103	C₂	—	584	1	no	—
104	C₂	#17988878	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988985

C₂

yes

maximal, characteristic, complemented

#17988705

C₂

yes

maximal, characteristic

#17988410

C₂

yes

maximal, complemented

#17988398

C₂

yes

maximal

#364×C₇₃

C₂

yes

maximal, characteristic, complemented

#14556613

C₂²

yes

—

—

C₂²

yes

characteristic

#14556523

—

#14556523

C₂²

yes

—

#14556519

—

M₃₂×C₇₃

C₂²

yes

—

C₄×C₈×C₇₃

C₂²

yes

characteristic

#11924028

—

C₂×Dic₁₄₆

—

Dic₂₉₂

Q₈

yes

characteristic, complemented

#11924017

—

D₅₈₄

Q₈

yes

characteristic, complemented

#11924012

—

#11924011

—

C₈×D₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₄²×C₇₃

D₄

yes

characteristic

C₁₆×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂²⋊D₇₃

—

C₂×Dic₇₃

—

D₂₉₂

—

C₄×D₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

SD₁₆

yes

characteristic

C₈×C₇₃

SD₁₆

yes

characteristic

C₈×C₇₃

C₂×Q₈

yes

C₈×C₇₃

yes

—

C₂²×C₇₃

AGL(1,ℤ/8)

yes

characteristic

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₂²⋊Q₈

yes

characteristic

C₄×C₇₃

C₂×SD₁₆

yes

characteristic

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#476

yes

characteristic

D₇₃

—

#2230

—

maximal, Sylow

C₇₃

#2230

yes

characteristic, complemented, Sylow

—

—

—

D₇₃

yes

characteristic, complemented

#360

—

#135

—

#131

—

146

—

C₄⋊Q₈

—

146

—

M₃₂

C₂×D₇₃

yes

—

#108

—

#106

—

#106

—

146

—

#104

—

146

—

C₄×C₈

C₂×D₇₃

yes

characteristic

#41

—

146

—

C₂×Q₈

—

292

—

Q₁₆

—

SD₁₆

—

146

—

D₈

—

M₁₆

—

292

—

M₁₆

—

146

—

C₂×C₈

—

292

—

C₂×C₈

D₂₉₂

yes

characteristic

C₂×C₈

C₂²×D₇₃

yes

characteristic

C₄⋊C₄

—

292

—

C₄⋊C₄

—

146

—

C₄²

D₂₉₂

yes

characteristic

C₁₆

—

Q₈

—

584

—

Q₈

—

146

—

D₄

—

292

—

D₄

—

146

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

C₂×D₂₉₂

yes

characteristic

C₈

—

292

—

C₈

yes

C₈

yes

C₈

Q₈×D₇₃

yes

characteristic

C₈

#11924027

yes

characteristic

C₂²

—

292

—

C₂²

#14556619

yes

characteristic

C₄

—

C₄

—

292

—

C₄

—

584

—

100

C₄

#14556571

yes

characteristic

101

C₄

C₂×#11924017

yes

characteristic

102

C₂

—

103

C₂

—

584

—

104

C₂

#17988878

yes

characteristic

	subgroup	G/H
center	C₂	#17988878
commutator	C₂×C₈×C₇₃	C₂³
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	#364×C₇₃	C₂
socle	C₂×C₇₃	#476
hypercenter	#364	D₇₃
hypocenter	C₇₃	#2230
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

subgroup

G/H

center

C₂

#17988878

commutator

C₂×C₈×C₇₃

C₂³

Frattini

C₂×C₈

C₂²×D₇₃

Fitting

#364×C₇₃

C₂

C₂×C₇₃

D₇₃

C₇₃

G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

N	H ≅ G/N	type
1. #17988985	C₂	semidirect
3. #17988410	C₂	semidirect
5. #364×C₇₃	C₂	semidirect
17. Dic₂₉₂	Q₈	semidirect
19. D₅₈₄	Q₈	semidirect
53. C₇₃	#2230	semidirect
57. #364	D₇₃	semidirect

H ≅ G/N

type

1. #17988985

C₂

semidirect

3. #17988410

C₂

semidirect

5. #364×C₇₃

C₂

semidirect

17. Dic₂₉₂

Q₈

semidirect

19. D₅₈₄

Q₈

semidirect

53. C₇₃

#2230

semidirect

57. #364

D₇₃

semidirect

Subgroups — #22612103

Conjugacy classes of subgroups

Complements