Group #22610080 — subgroups

Subgroups — #22610080

Order 9344.

162 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 73 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	#17988358	C₂	1	2	yes	maximal
2	#17988347	C₂	1	2	yes	maximal
3	#17988345	C₂	1	1	yes	maximal, characteristic
4	#17988344	C₂	1	1	yes	maximal, characteristic
5	C₄×M₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#11924012	C₂²	1	2	yes	—
7	#14556550	C₂²	1	2	yes	—
8	C₂×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
9	C₂×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
10	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
11	#97×C₇₃	C₄	1	2	yes	complemented
12	C₄×C₈×C₇₃	C₄	1	2	yes	complemented
13	#11924012	—	2	2	no	—
14	#11924012	—	2	2	no	—
15	C₂×#10596831	—	2	2	no	—
16	C₄⋊Dic₇₃	—	2	2	no	—
17	C₂²⋊Dic₇₃	—	2	2	no	—
18	C₄×Dic₇₃	—	2	2	no	—
19	C₂²×C₄×C₇₃	—	2	1	no	—
20	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
21	M₁₆×C₇₃	—	2	2	no	—
22	M₁₆×C₇₃	—	2	2	no	—
23	C₂×C₈×C₇₃	C₂×C₄	1	2	yes	—
24	C₂×C₈×C₇₃	C₂×C₄	1	2	yes	—
25	C₄²×C₇₃	—	2	1	no	—
26	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
27	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₇₃	#41	1	1	yes	characteristic
29	C₂×C₄×C₇₃	—	2	1	no	—
30	C₂×C₄×C₇₃	—	2	1	no	—
31	C₂×C₄×C₇₃	—	4	2	no	—
32	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄×C₇₃	#41	1	2	yes	—
34	C₂×C₄×C₇₃	#41	1	2	yes	—
35	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
36	C₂×Dic₇₃	—	4	2	no	—
37	C₈×C₇₃	—	2	2	no	—
38	C₈×C₇₃	—	2	2	no	—
39	#10596831	—	4	2	no	—
40	C₂²×C₇₃	—	4	1	no	—
41	C₂²×C₇₃	#117	1	1	yes	characteristic
42	C₂²×C₇₃	#126	1	2	yes	—
43	C₄×C₇₃	—	2	2	no	—
44	C₄×C₇₃	—	4	1	no	—
45	C₄×C₇₃	#117	1	1	yes	characteristic
46	C₄×C₇₃	#117	1	1	yes	characteristic
47	C₄×C₇₃	#126	1	2	yes	—
48	Dic₇₃	—	8	2	no	—
49	C₂×C₇₃	—	2	2	no	—
50	C₂×C₇₃	—	2	1	no	—
51	C₂×C₇₃	#383	1	1	yes	characteristic
52	#1841	—	73	1	no	maximal, Sylow
53	C₇₃	#1841	1	1	yes	characteristic, complemented, Sylow
54	C₄×M₁₆	D₇₃	1	1	yes	characteristic
55	#344	—	73	2	no	—
56	#339	—	73	2	no	—
57	#338	—	73	1	no	—
58	H(3,ℤ/4)	—	73	1	no	—
59	C₂×M₁₆	—	73	2	no	—
60	C₂×M₁₆	C₂×D₇₃	1	1	yes	characteristic
61	C₂×M₁₆	C₂×D₇₃	1	1	yes	characteristic
62	#117	—	73	2	no	—
63	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
64	#97	Dic₇₃	1	2	yes	complemented
65	C₄×C₈	Dic₇₃	1	2	yes	complemented
66	C₂²×C₄	—	2	1	no	—
67	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
68	M₁₆	—	2	2	no	—
69	M₁₆	—	2	2	no	—
70	M₁₆	—	146	2	no	—
71	M₁₆	—	146	2	no	—
72	C₂×C₈	—	146	2	no	—
73	C₂×C₈	C₂×Dic₇₃	1	2	yes	—
74	C₂×C₈	C₂×Dic₇₃	1	2	yes	—
75	C₄⋊C₄	—	146	2	no	—
76	C₂²⋊C₄	—	146	2	no	—
77	C₄²	—	2	1	no	—
78	C₄²	—	146	2	no	—
79	C₄²	C₂×Dic₇₃	1	1	yes	characteristic
80	C₄²	C₂×Dic₇₃	1	1	yes	characteristic
81	C₂³	#11924028	1	1	yes	characteristic
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	4	2	no	—
85	C₂×C₄	—	292	2	no	—
86	C₂×C₄	C₂²×Dic₇₃	1	1	yes	characteristic
87	C₂×C₄	#11924028	1	2	yes	—
88	C₂×C₄	#11924028	1	2	yes	—
89	C₂×C₄	#11924028	1	1	yes	characteristic
90	C₈	—	2	2	no	—
91	C₈	—	2	2	no	—
92	C₈	—	292	2	no	—
93	C₂²	—	4	1	no	—
94	C₂²	#14556550	1	1	yes	characteristic
95	C₂²	#14556585	1	2	yes	—
96	C₄	—	2	2	no	—
97	C₄	—	4	1	no	—
98	C₄	—	584	2	no	—
99	C₄	#14556550	1	1	yes	characteristic
100	C₄	#14556550	1	1	yes	characteristic
101	C₄	#14556585	1	2	yes	—
102	C₂	—	2	1	no	—
103	C₂	—	2	2	no	—
104	C₂	#17988455	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988358

C₂

yes

maximal

#17988347

C₂

yes

maximal

#17988345

C₂

yes

maximal, characteristic

#17988344

C₂

yes

maximal, characteristic

C₄×M₁₆×C₇₃

C₂

yes

maximal, characteristic

C₂×#11924012

C₂²

yes

—

#14556550

C₂²

yes

—

C₂×M₁₆×C₇₃

C₂²

yes

characteristic

C₂×M₁₆×C₇₃

C₂²

yes

characteristic

C₂×C₄²×C₇₃

C₂²

yes

characteristic

#97×C₇₃

C₄

yes

complemented

C₄×C₈×C₇₃

C₄

yes

—

—

—

C₄⋊Dic₇₃

—

C₂²⋊Dic₇₃

—

C₄×Dic₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

M₁₆×C₇₃

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

C₂×C₄

yes

—

C₂×C₈×C₇₃

C₂×C₄

yes

—

C₄²×C₇₃

—

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₂³×C₇₃

#41

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

#41

yes

—

C₂×C₄×C₇₃

#41

yes

—

C₂×C₄×C₇₃

#41

yes

characteristic

C₂×Dic₇₃

—

C₈×C₇₃

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

#117

yes

characteristic

C₂²×C₇₃

#126

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₄×M₁₆

D₇₃

yes

—

—

—

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₃

yes

characteristic

C₂×M₁₆

C₂×D₇₃

yes

characteristic

#117

—

C₂×C₄²

C₂×D₇₃

yes

characteristic

#97

Dic₇₃

yes

complemented

C₄×C₈

Dic₇₃

yes

complemented

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

146

—

M₁₆

—

146

—

C₂×C₈

—

146

—

C₂×C₈

C₂×Dic₇₃

yes

—

C₂×C₈

C₂×Dic₇₃

yes

—

C₄⋊C₄

—

146

—

C₂²⋊C₄

—

146

—

C₄²

—

C₄²

—

146

—

C₄²

C₂×Dic₇₃

yes

characteristic

C₄²

C₂×Dic₇₃

yes

characteristic

C₂³

#11924028

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

C₂²×Dic₇₃

yes

characteristic

C₂×C₄

#11924028

yes

—

C₂×C₄

#11924028

yes

—

C₂×C₄

#11924028

yes

characteristic

C₈

—

C₈

—

C₈

—

292

—

C₂²

—

C₂²

#14556550

yes

characteristic

C₂²

#14556585

yes

—

C₄

—

C₄

—

C₄

—

584

—

C₄

#14556550

yes

characteristic

100

C₄

#14556550

yes

characteristic

101

C₄

#14556585

yes

—

102

C₂

—

103

C₂

—

104

C₂

#17988455

yes

characteristic

	subgroup	G/H
center	C₄	#14556550
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	C₄×M₁₆×C₇₃	C₂
socle	C₂×C₇₃	#383
hypercenter	C₄×M₁₆	D₇₃
hypocenter	C₇₃	#1841
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ C₄×M₁₆

subgroup

G/H

center

C₄

#14556550

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

C₄×M₁₆×C₇₃

C₂

socle

C₂×C₇₃

#383

hypercenter

C₄×M₁₆

D₇₃

hypocenter

C₇₃

#1841

LCS

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ C₄×M₁₆

N	H ≅ G/N	type
11. #97×C₇₃	C₄	semidirect
12. C₄×C₈×C₇₃	C₄	semidirect
53. C₇₃	#1841	semidirect
64. #97	Dic₇₃	semidirect
65. C₄×C₈	Dic₇₃	semidirect

H ≅ G/N

type

11. #97×C₇₃

C₄

semidirect

12. C₄×C₈×C₇₃

C₄

semidirect

53. C₇₃

#1841

semidirect

64. #97

Dic₇₃

semidirect

65. C₄×C₈

Dic₇₃

semidirect

Subgroups — #22610080

Conjugacy classes of subgroups

Complements