Group #22625577 — subgroups

Subgroups — #22625577

Order 9344.

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

normal subgroups only

This group has 148 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	#17989637	C₂	1	2	yes	maximal
2	#17989448	C₂	1	1	yes	maximal, characteristic
3	#17989437	C₂	1	2	yes	maximal
4	#17989428	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	2	no	—
17	C₂×#10596833	—	2	1	no	—
18	C₂×#10596833	D₄	1	2	yes	—
19	C₂×Dic₁₄₆	C₂×C₄	1	2	yes	—
20	Dic₂₉₂	—	2	2	no	—
21	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
22	#11924007	—	2	2	no	—
23	C₄×Dic₇₃	—	2	2	no	—
24	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
25	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
26	C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
27	C₂×C₄×C₇₃	—	2	2	no	—
28	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
29	C₂×Dic₇₃	—	2	2	no	—
30	C₂×Dic₇₃	C₂×D₄	1	1	yes	characteristic
31	C₂×Dic₇₃	#41	1	1	yes	characteristic
32	Dic₁₄₆	—	2	2	no	—
33	Dic₁₄₆	—	2	2	no	—
34	#10596833	—	2	2	no	—
35	#10596833	—	4	1	no	—
36	#10596833	—	4	2	no	—
37	C₈×C₇₃	M₁₆	1	2	yes	—
38	#10596831	—	2	1	no	—
39	C₂²×C₇₃	C₄×D₄	1	1	yes	characteristic
40	C₄×C₇₃	—	4	2	no	—
41	C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
42	C₄×C₇₃	#131	1	1	yes	characteristic
43	Dic₇₃	—	2	1	no	—
44	Dic₇₃	—	4	2	no	—
45	Dic₇₃	#137	1	2	yes	—
46	C₂×C₇₃	#436	1	1	yes	characteristic
47	C₂×C₇₃	#441	1	1	yes	characteristic
48	C₂×C₇₃	#444	1	1	yes	characteristic
49	#1593	—	73	1	no	maximal, Sylow
50	C₇₃	#1593	1	1	yes	characteristic, complemented, Sylow
51	#446	—	73	2	no	—
52	C₄×Q₁₆	—	73	1	no	—
53	#334	—	73	1	no	—
54	Q₈⋊C₈	—	73	2	no	—
55	#322	—	73	1	no	—
56	C₂×Q₁₆	—	73	1	no	—
57	C₄×Q₈	—	73	2	no	—
58	#107	#64408	1	1	yes	characteristic
59	C₄⋊C₈	—	73	2	no	—
60	C₄⋊C₈	—	146	2	no	—
61	#103	—	73	2	no	—
62	#97	—	146	2	no	—
63	C₄×C₈	—	73	1	no	—
64	C₄×C₈	—	73	1	no	—
65	C₄×C₈	—	73	1	no	—
66	C₂×Q₈	—	73	2	no	—
67	Q₁₆	—	146	2	no	—
68	C₂×C₈	—	73	2	no	—
69	C₂×C₈	—	73	1	no	—
70	C₂×C₈	—	146	1	no	—
71	C₂×C₈	—	146	2	no	—
72	C₂×C₈	C₂×#64408	1	1	yes	characteristic
73	C₄⋊C₄	—	146	2	no	—
74	C₄⋊C₄	C₂×#64408	1	2	yes	—
75	C₄²	—	73	1	no	—
76	C₄²	—	146	2	no	—
77	Q₈	—	146	2	no	—
78	Q₈	—	146	2	no	—
79	C₂×C₄	—	2	2	no	—
80	C₂×C₄	—	73	1	no	—
81	C₂×C₄	—	73	1	no	—
82	C₂×C₄	—	146	2	no	—
83	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
84	C₈	—	292	2	no	—
85	C₈	—	292	1	no	—
86	C₈	—	146	2	no	—
87	C₈	—	146	1	no	—
88	C₈	#11924038	1	2	yes	—
89	C₂²	D₄×#64408	1	1	yes	characteristic
90	C₄	—	4	2	no	—
91	C₄	—	292	2	no	—
92	C₄	—	73	2	no	—
93	C₄	—	146	1	no	—
94	C₄	C₂×#11924038	1	1	yes	characteristic
95	C₄	#14556679	1	1	yes	characteristic
96	C₂	#17989621	1	1	yes	characteristic
97	C₂	#17989627	1	1	yes	characteristic
98	C₂	#17989634	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989637

C₂

yes

maximal

#17989448

C₂

yes

maximal, characteristic

#17989437

C₂

yes

maximal

#17989428

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

—

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

—

#10596833

—

#10596833

—

#10596833

—

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

#137

yes

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#446

—

C₄×Q₁₆

—

#334

—

Q₈⋊C₈

—

#322

—

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

—

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

—

292

—

C₈

—

146

—

C₈

—

146

—

C₈

#11924038

yes

—

C₂²

D₄×#64408

yes

characteristic

C₄

—

C₄

—

292

—

C₄

—

C₄

—

146

—

C₄

yes

C₄

yes

C₂

yes

C₂

yes

C₂

yes

	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	#1593
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
50. C₇₃	#1593	semidirect

H ≅ G/N

type

50. C₇₃

#1593

semidirect

Subgroups — #22625577

Conjugacy classes of subgroups

Complements