Group #22625570 — subgroups

Subgroups — #22625570

Order 9344.

152 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 58 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	#17989637	C₂	1	2	yes	maximal
2	#17989450	C₂	1	1	yes	maximal, characteristic
3	#17989437	C₂	1	2	yes	maximal
4	C₈×#10596833	C₂	1	1	yes	maximal, characteristic
5	#17988681	C₂	1	1	yes	maximal, characteristic
6	C₄⋊#10596833	—	2	2	no	—
7	C₄⋊#10596833	C₂²	1	2	yes	—
8	#14556646	—	2	2	no	—
9	C₄×#10596833	C₂²	1	1	yes	characteristic
10	C₄×#10596833	C₂²	1	1	yes	characteristic
11	C₂×Dic₂₉₂	C₄	1	1	yes	characteristic
12	#14556556	C₂²	1	2	yes	—
13	#14556514	C₄	1	2	yes	—
14	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
15	#107×C₇₃	C₄	1	1	yes	characteristic
16	C₂×#10596833	—	2	1	no	—
17	C₂×#10596833	—	2	2	no	—
18	C₂×#10596833	D₄	1	1	yes	characteristic
19	C₂×#10596833	D₄	1	1	yes	characteristic
20	C₂×Dic₁₄₆	C₂×C₄	1	2	yes	—
21	Dic₂₉₂	—	2	2	no	—
22	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
23	#11924007	—	2	2	no	—
24	C₄×Dic₇₃	—	2	2	no	—
25	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
26	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
27	C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
28	C₂×C₄×C₇₃	—	2	2	no	—
29	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
30	C₂×Dic₇₃	—	2	2	no	—
31	C₂×Dic₇₃	C₂×D₄	1	1	yes	characteristic
32	C₂×Dic₇₃	#41	1	1	yes	characteristic
33	Dic₁₄₆	—	2	2	no	—
34	Dic₁₄₆	—	2	2	no	—
35	#10596833	—	2	2	no	—
36	#10596833	—	2	1	no	—
37	#10596833	—	4	2	no	—
38	#10596833	Q₁₆	1	2	yes	complemented
39	C₈×C₇₃	M₁₆	1	2	yes	—
40	#10596831	—	2	1	no	—
41	C₂²×C₇₃	C₄×D₄	1	1	yes	characteristic
42	C₄×C₇₃	—	4	2	no	—
43	C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
44	C₄×C₇₃	#131	1	1	yes	characteristic
45	Dic₇₃	—	2	1	no	—
46	Dic₇₃	—	4	2	no	—
47	Dic₇₃	C₂×Q₁₆	1	1	yes	characteristic
48	Dic₇₃	#135	1	1	yes	characteristic
49	C₂×C₇₃	#436	1	1	yes	characteristic
50	C₂×C₇₃	C₄×Q₁₆	1	1	yes	characteristic
51	C₂×C₇₃	#443	1	1	yes	characteristic
52	#1591	—	73	1	no	maximal, Sylow
53	C₇₃	#1591	1	1	yes	characteristic, complemented, Sylow
54	#446	—	73	2	no	—
55	C₄×Q₁₆	—	73	1	no	—
56	#335	—	73	1	no	—
57	Q₈⋊C₈	—	73	2	no	—
58	C₈²	—	73	1	no	—
59	C₂×Q₁₆	—	73	1	no	—
60	C₄×Q₈	—	73	2	no	—
61	#107	#64408	1	1	yes	characteristic
62	C₄⋊C₈	—	73	2	no	—
63	C₄⋊C₈	—	146	2	no	—
64	#103	—	73	2	no	—
65	#97	—	146	2	no	—
66	C₄×C₈	—	73	1	no	—
67	C₄×C₈	—	73	1	no	—
68	C₄×C₈	—	73	1	no	—
69	C₂×Q₈	—	73	2	no	—
70	Q₁₆	—	146	2	no	—
71	C₂×C₈	—	73	1	no	—
72	C₂×C₈	—	73	1	no	—
73	C₂×C₈	—	73	1	no	—
74	C₂×C₈	—	146	2	no	—
75	C₂×C₈	—	146	1	no	—
76	C₂×C₈	C₂×#64408	1	1	yes	characteristic
77	C₄⋊C₄	—	146	2	no	—
78	C₄⋊C₄	C₂×#64408	1	2	yes	—
79	C₄²	—	73	1	no	—
80	C₄²	—	146	2	no	—
81	Q₈	—	146	2	no	—
82	Q₈	—	146	2	no	—
83	C₂×C₄	—	2	2	no	—
84	C₂×C₄	—	73	1	no	—
85	C₂×C₄	—	73	1	no	—
86	C₂×C₄	—	146	2	no	—
87	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
88	C₈	—	292	2	no	—
89	C₈	—	73	2	no	—
90	C₈	—	146	1	no	—
91	C₈	—	146	2	no	—
92	C₈	—	146	1	no	—
93	C₈	#11924038	1	2	yes	—
94	C₂²	D₄×#64408	1	1	yes	characteristic
95	C₄	—	4	2	no	—
96	C₄	—	292	2	no	—
97	C₄	—	73	1	no	—
98	C₄	—	73	1	no	—
99	C₄	—	146	1	no	—
100	C₄	C₂×#11924038	1	1	yes	characteristic
101	C₄	#14556679	1	1	yes	characteristic
102	C₂	#17989621	1	1	yes	characteristic
103	C₂	Q₁₆×#64408	1	1	yes	characteristic
104	C₂	#17989629	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989637

C₂

yes

maximal

#17989450

C₂

yes

maximal, characteristic

#17989437

C₂

yes

maximal

C₈×#10596833

C₂

yes

maximal, characteristic

#17988681

C₂

yes

maximal, characteristic

C₄⋊#10596833

—

C₄⋊#10596833

C₂²

yes

—

#14556646

—

C₄×#10596833

C₂²

yes

characteristic

C₄×#10596833

C₂²

yes

characteristic

C₂×Dic₂₉₂

C₄

yes

characteristic

#14556556

C₂²

yes

—

#14556514

C₄

yes

—

C₈×Dic₇₃

C₂²

yes

characteristic

#107×C₇₃

C₄

yes

—

—

D₄

yes

characteristic

C₂×#10596833

D₄

yes

characteristic

C₂×Dic₁₄₆

C₂×C₄

yes

—

Dic₂₉₂

—

C₂×#10596831

C₂×C₄

yes

characteristic

#11924007

—

C₄×Dic₇₃

—

C₄×Dic₇₃

C₂³

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₄⋊C₄×C₇₃

C₂×C₄

yes

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

#41

yes

characteristic

Dic₁₄₆

—

Dic₁₄₆

—

—

—

—

Q₁₆

yes

complemented

C₈×C₇₃

M₁₆

yes

—

#10596831

—

C₂²×C₇₃

C₄×D₄

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

C₂×M₁₆

yes

characteristic

C₄×C₇₃

#131

yes

characteristic

Dic₇₃

—

Dic₇₃

—

Dic₇₃

C₂×Q₁₆

yes

Dic₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

C₄×Q₁₆

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#446

—

C₄×Q₁₆

—

#335

—

Q₈⋊C₈

—

C₈²

—

C₂×Q₁₆

—

C₄×Q₈

—

#107

#64408

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

146

—

#103

—

#97

—

146

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂×Q₈

—

Q₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

C₂×#64408

yes

characteristic

C₄⋊C₄

—

146

—

C₄⋊C₄

C₂×#64408

yes

—

C₄²

—

C₄²

—

146

—

Q₈

—

146

—

Q₈

—

146

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

C₂²×#64408

yes

characteristic

C₈

—

292

—

C₈

—

C₈

—

146

—

C₈

—

146

—

C₈

—

146

—

C₈

#11924038

yes

—

C₂²

D₄×#64408

yes

characteristic

C₄

—

C₄

—

292

—

C₄

—

C₄

—

C₄

—

146

—

100

C₄

C₂×#11924038

yes

characteristic

101

C₄

#14556679

yes

characteristic

102

C₂

#17989621

yes

characteristic

103

C₂

Q₁₆×#64408

yes

characteristic

104

C₂

#17989629

yes

characteristic

	subgroup	G/H
center	C₂²	D₄×#64408
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#64408
Fitting	#107×C₇₃	C₄
socle	C₂²×C₇₃	C₄×D₄
hypercenter	#107	#64408
hypocenter	C₇₃	#1591
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

subgroup

G/H

center

C₂²

D₄×#64408

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#64408

Fitting

#107×C₇₃

C₄

socle

C₂²×C₇₃

C₄×D₄

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

N	H ≅ G/N	type
38. #10596833	Q₁₆	semidirect
53. C₇₃	#1591	semidirect

H ≅ G/N

type

38. #10596833

Q₁₆

semidirect

53. C₇₃

#1591

semidirect

Subgroups — #22625570

Conjugacy classes of subgroups

Complements