Group #22609259 — subgroups

Subgroups — #22609259

Order 9344.

172 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 49 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	#17988997	C₂	1	2	yes	maximal
2	#17988957	C₂	1	1	yes	maximal, characteristic
3	#17988329	C₂	1	1	yes	maximal, characteristic
4	#17988329	C₂	1	2	yes	maximal
5	#564×C₇₃	C₂	1	1	yes	maximal, characteristic
6	#14556591	C₂²	1	1	yes	characteristic
7	#14556524	—	2	2	no	—
8	#14556522	—	2	2	no	—
9	#14556514	—	2	2	no	—
10	#14556502	C₂²	1	1	yes	characteristic
11	#14556502	C₂²	1	2	yes	—
12	#125×C₇₃	—	2	2	no	—
13	#125×C₇₃	—	2	2	no	—
14	#125×C₇₃	—	2	2	no	—
15	#125×C₇₃	C₂²	1	1	yes	characteristic
16	#125×C₇₃	C₂²	1	2	yes	—
17	C₂×Dic₁₄₆	—	2	1	no	—
18	C₂×#10596831	—	2	2	no	—
19	C₂×#10596831	—	2	1	no	—
20	C₄⋊Dic₇₃	—	2	2	no	—
21	C₄⋊C₄×C₇₃	—	2	2	no	—
22	C₄⋊C₄×C₇₃	—	2	2	no	—
23	C₄⋊C₄×C₇₃	—	2	2	no	—
24	C₄⋊C₄×C₇₃	—	2	2	no	—
25	C₄⋊C₄×C₇₃	—	2	2	no	—
26	C₄⋊C₄×C₇₃	—	2	2	no	—
27	C₄⋊C₄×C₇₃	D₄	1	2	yes	—
28	C₄⋊C₄×C₇₃	D₄	1	2	yes	—
29	C₄⋊C₄×C₇₃	D₄	1	2	yes	—
30	C₄²×C₇₃	—	2	2	no	—
31	C₄²×C₇₃	C₂³	1	1	yes	characteristic
32	C₂×C₄×C₇₃	—	2	2	no	—
33	C₂×C₄×C₇₃	—	2	2	no	—
34	C₂×C₄×C₇₃	—	2	2	no	—
35	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
36	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
37	C₂×Dic₇₃	—	4	1	no	—
38	Dic₁₄₆	—	4	2	no	—
39	#10596831	—	2	4	no	—
40	#10596831	—	4	1	no	—
41	C₂²×C₇₃	#120	1	1	yes	characteristic
42	C₄×C₇₃	—	2	1	no	—
43	C₄×C₇₃	—	2	2	no	—
44	C₄×C₇₃	—	4	2	no	—
45	C₄×C₇₃	—	4	2	no	—
46	C₄×C₇₃	—	4	2	no	—
47	Dic₇₃	—	8	1	no	—
48	C₂×C₇₃	#454	1	1	yes	characteristic
49	C₂×C₇₃	#456	1	2	yes	—
50	#1663	—	73	1	no	maximal, Sylow
51	C₇₃	#1663	1	1	yes	characteristic, complemented, Sylow
52	#564	D₇₃	1	1	yes	characteristic
53	#501	—	73	2	no	—
54	#491	—	73	1	no	—
55	#330	—	73	2	no	—
56	#330	—	73	1	no	—
57	C₄⋊Q₈	—	73	1	no	—
58	#125	—	2	2	no	—
59	#125	—	2	2	no	—
60	#125	—	2	2	no	—
61	#125	C₂×D₇₃	1	1	yes	characteristic
62	#125	C₂×D₇₃	1	2	yes	—
63	#107	—	146	2	no	—
64	#106	—	146	2	no	—
65	#103	—	146	2	no	—
66	#97	—	73	1	no	—
67	#97	—	73	2	no	—
68	C₂×Q₈	—	146	1	no	—
69	C₂×C₈	—	146	1	no	—
70	C₂×C₈	—	146	2	no	—
71	C₄⋊C₄	—	2	2	no	—
72	C₄⋊C₄	—	2	2	no	—
73	C₄⋊C₄	—	2	2	no	—
74	C₄⋊C₄	—	2	2	no	—
75	C₄⋊C₄	—	2	2	no	—
76	C₄⋊C₄	—	2	2	no	—
77	C₄⋊C₄	—	146	2	no	—
78	C₄⋊C₄	C₂²⋊D₇₃	1	2	yes	—
79	C₄⋊C₄	C₂²⋊D₇₃	1	2	yes	—
80	C₄⋊C₄	C₂²⋊D₇₃	1	2	yes	—
81	C₄²	—	2	2	no	—
82	C₄²	C₂²×D₇₃	1	1	yes	characteristic
83	Q₈	—	292	2	no	—
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	—	2	2	no	—
86	C₂×C₄	—	2	2	no	—
87	C₂×C₄	—	292	1	no	—
88	C₂×C₄	C₂×C₂²⋊D₇₃	1	2	yes	—
89	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
90	C₈	—	292	1	no	—
91	C₈	—	146	4	no	—
92	C₂²	#14556560	1	1	yes	characteristic
93	C₄	—	2	1	no	—
94	C₄	—	2	2	no	—
95	C₄	—	4	2	no	—
96	C₄	—	4	2	no	—
97	C₄	—	4	2	no	—
98	C₄	—	584	1	no	—
99	C₂	#17988760	1	1	yes	characteristic
100	C₂	#17988770	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#17988997

C₂

yes

maximal

#17988957

C₂

yes

maximal, characteristic

#17988329

C₂

yes

maximal, characteristic

#17988329

C₂

yes

maximal

#564×C₇₃

C₂

yes

maximal, characteristic

#14556591

C₂²

yes

—

—

—

C₂²

yes

characteristic

#14556502

C₂²

yes

—

#125×C₇₃

—

#125×C₇₃

—

#125×C₇₃

—

#125×C₇₃

C₂²

yes

characteristic

#125×C₇₃

C₂²

yes

—

C₂×Dic₁₄₆

—

C₂×#10596831

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

D₄

yes

—

C₄⋊C₄×C₇₃

D₄

yes

—

C₄⋊C₄×C₇₃

D₄

yes

—

C₄²×C₇₃

—

C₄²×C₇₃

C₂³

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

—

Dic₁₄₆

—

#10596831

—

#10596831

—

C₂²×C₇₃

#120

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

C₂×C₇₃

#454

yes

characteristic

C₂×C₇₃

#456

yes

—

#1663

—

maximal, Sylow

C₇₃

#1663

yes

characteristic, complemented, Sylow

#564

D₇₃

yes

—

—

—

—

C₄⋊Q₈

—

—

—

—

C₂×D₇₃

yes

characteristic

#125

C₂×D₇₃

yes

—

#107

—

146

—

#106

—

146

—

#103

—

146

—

#97

—

#97

—

C₂×Q₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

146

—

C₄⋊C₄

C₂²⋊D₇₃

yes

—

C₄⋊C₄

C₂²⋊D₇₃

yes

—

C₄⋊C₄

C₂²⋊D₇₃

yes

—

C₄²

—

C₄²

C₂²×D₇₃

yes

characteristic

Q₈

—

292

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

C₂×C₂²⋊D₇₃

yes

—

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

C₈

—

292

—

C₈

—

146

—

C₂²

#14556560

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

584

—

C₂

#17988760

yes

characteristic

100

C₂

#17988770

yes

—

	subgroup	G/H
center	C₂²	#14556560
commutator	C₄²×C₇₃	C₂³
Frattini	C₄²	C₂²×D₇₃
Fitting	#564×C₇₃	C₂
socle	C₂²×C₇₃	#120
hypercenter	#564	D₇₃
hypocenter	C₇₃	#1663
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #564

subgroup

G/H

center

C₂²

#14556560

commutator

C₄²×C₇₃

C₂³

Frattini

C₄²

C₂²×D₇₃

Fitting

#564×C₇₃

C₂

C₂²×C₇₃

D₇₃

C₇₃

G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #564

N	H ≅ G/N	type
51. C₇₃	#1663	semidirect

H ≅ G/N

type

51. C₇₃

#1663

semidirect

Subgroups — #22609259

Conjugacy classes of subgroups

Complements