Group #22626961 — subgroups

Subgroups — #22626961

Order 9344.

128 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 25 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	#17989685	C₂	1	2	yes	maximal, complemented
2	#17989559	C₂	1	1	yes	maximal, characteristic
3	#14556687	—	2	2	no	—
4	C₂×#11924037	C₄	1	1	yes	characteristic
5	C₂×#11924037	C₂²	1	1	yes	characteristic
6	#14556648	—	2	2	no	—
7	C₂²×C₄×D₇₃	C₄	1	1	yes	characteristic
8	#11924040	—	4	2	no	—
9	#11924037	—	4	1	no	—
10	#11924037	—	4	1	no	—
11	C₂×#10596833	—	2	1	no	—
12	C₂×#10596833	D₄	1	2	yes	—
13	C₂³×D₇₃	C₈	1	1	yes	characteristic
14	C₂²×Dic₇₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×D₇₃	—	2	1	no	—
16	C₂×C₄×D₇₃	—	2	1	no	—
17	C₂×C₄×D₇₃	—	4	1	no	—
18	C₂×C₄×D₇₃	—	4	1	no	—
19	C₂²×C₄×C₇₃	C₈	1	1	yes	characteristic
20	C₂³×C₇₃	C₂×C₈	1	1	yes	characteristic
21	C₂²×D₇₃	—	2	1	no	—
22	C₂²×D₇₃	—	4	2	no	—
23	C₂²×D₇₃	—	4	1	no	—
24	C₂×C₄×C₇₃	—	2	1	no	—
25	C₂×C₄×C₇₃	—	4	1	no	—
26	C₂×Dic₇₃	—	2	1	no	—
27	C₂×Dic₇₃	—	2	1	no	—
28	C₂×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×Dic₇₃	M₁₆	1	1	yes	characteristic
30	C₄×D₇₃	—	4	2	no	—
31	C₄×D₇₃	—	4	1	no	—
32	C₄×D₇₃	—	4	1	no	—
33	#10596833	—	2	2	no	—
34	#10596833	—	4	1	no	—
35	C₂²×C₇₃	—	2	1	no	—
36	C₂²×C₇₃	—	4	1	no	—
37	C₂²×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
38	C₂×D₇₃	—	2	2	no	—
39	C₂×D₇₃	—	4	1	no	—
40	C₂×D₇₃	—	4	2	no	—
41	C₂×D₇₃	—	4	1	no	—
42	C₂×D₇₃	—	4	2	no	—
43	C₄×C₇₃	—	4	1	no	—
44	Dic₇₃	—	2	1	no	—
45	Dic₇₃	#99	1	1	yes	characteristic
46	Dic₇₃	#100	1	1	yes	characteristic
47	C₂×C₇₃	—	2	1	no	—
48	C₂×C₇₃	—	4	1	no	—
49	C₂×C₇₃	#323	1	1	yes	characteristic
50	D₇₃	—	4	2	no	—
51	#1320	—	73	1	no	maximal, Sylow
52	C₇₃	#1320	1	1	yes	characteristic, complemented, Sylow
53	#407	—	73	1	no	—
54	#349	—	73	2	no	—
55	C₂³×C₄	—	73	1	no	—
56	C₂×M₁₆	—	73	1	no	—
57	C₂×M₁₆	—	73	1	no	—
58	M₃₂	—	146	2	no	—
59	C₂²⋊C₈	—	146	2	no	—
60	C₂⁴	—	73	1	no	—
61	C₂²×C₄	—	292	1	no	—
62	C₂²×C₄	—	292	1	no	—
63	C₂²×C₄	—	73	1	no	—
64	C₂²×C₄	—	146	1	no	—
65	C₂²×C₄	—	146	1	no	—
66	C₂²×C₄	#10596842	1	1	yes	characteristic
67	M₁₆	—	292	1	no	—
68	M₁₆	—	292	1	no	—
69	C₂×C₈	—	73	2	no	—
70	C₂×C₈	—	146	1	no	—
71	C₁₆	—	292	2	no	—
72	C₂³	—	292	1	no	—
73	C₂³	—	292	2	no	—
74	C₂³	—	146	1	no	—
75	C₂³	C₂×#10596842	1	1	yes	characteristic
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	4	1	no	—
78	C₂×C₄	—	292	1	no	—
79	C₂×C₄	—	292	1	no	—
80	C₂×C₄	—	292	2	no	—
81	C₂×C₄	—	73	1	no	—
82	C₂×C₄	—	73	1	no	—
83	C₂×C₄	—	146	1	no	—
84	C₂×C₄	—	146	1	no	—
85	C₈	—	292	1	no	—
86	C₈	—	146	2	no	—
87	C₂²	—	2	1	no	—
88	C₂²	—	4	1	no	—
89	C₂²	—	292	1	no	—
90	C₂²	—	292	2	no	—
91	C₂²	—	292	2	no	—
92	C₂²	—	292	1	no	—
93	C₂²	—	146	2	no	—
94	C₂²	C₂²⋊#10596842	1	1	yes	characteristic
95	C₄	—	4	1	no	—
96	C₄	—	73	1	no	—
97	C₄	—	73	1	no	—
98	C₄	—	146	1	no	—
99	C₂	—	2	1	no	—
100	C₂	—	4	1	no	—
101	C₂	—	292	2	no	—
102	C₂	#17989672	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989685

C₂

yes

maximal, complemented

#17989559

C₂

yes

maximal, characteristic

#14556687

—

C₂×#11924037

C₄

yes

characteristic

C₂×#11924037

C₂²

yes

characteristic

#14556648

—

C₂²×C₄×D₇₃

C₄

yes

—

—

—

—

D₄

yes

—

C₂³×D₇₃

C₈

yes

characteristic

C₂²×Dic₇₃

C₂×C₄

yes

characteristic

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂²×C₄×C₇₃

C₈

yes

characteristic

C₂³×C₇₃

C₂×C₈

yes

characteristic

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₇₃

M₁₆

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

#10596833

—

#10596833

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂²⋊C₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

yes

Dic₇₃

yes

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#323

yes

characteristic

D₇₃

—

#1320

—

maximal, Sylow

C₇₃

#1320

yes

characteristic, complemented, Sylow

#407

—

#349

—

C₂³×C₄

—

C₂×M₁₆

—

C₂×M₁₆

—

M₃₂

—

146

—

C₂²⋊C₈

—

146

—

C₂⁴

—

C₂²×C₄

—

292

—

C₂²×C₄

—

292

—

C₂²×C₄

—

C₂²×C₄

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

#10596842

yes

characteristic

M₁₆

—

292

—

M₁₆

—

292

—

C₂×C₈

—

C₂×C₈

—

146

—

C₁₆

—

292

—

C₂³

—

292

—

C₂³

—

292

—

C₂³

—

146

—

C₂³

C₂×#10596842

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₈

—

292

—

C₈

—

146

—

C₂²

—

C₂²

—

C₂²

—

292

—

C₂²

—

292

—

C₂²

—

292

—

C₂²

—

292

—

C₂²

—

146

—

C₂²

C₂²⋊#10596842

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

146

—

C₂

—

100

C₂

—

101

C₂

—

292

—

102

C₂

#17989672

yes

characteristic

	subgroup	G/H
center	C₂	#17989672
commutator	C₂³×C₇₃	C₂×C₈
Frattini	C₂³	C₂×#10596842
Fitting	C₂²×C₄×C₇₃	C₈
socle	C₂×C₇₃	#323
hypercenter	C₂²×C₄	#10596842
hypocenter	C₇₃	#1320
LCS	G ▷ C₂³×C₇₃ ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄

subgroup

G/H

center

C₂

#17989672

commutator

C₂³×C₇₃

C₂×C₈

Frattini

C₂³

C₂×#10596842

Fitting

C₂²×C₄×C₇₃

C₈

C₂×C₇₃

C₂²×C₄

C₇₃

G ▷ C₂³×C₇₃ ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄

N	H ≅ G/N	type
1. #17989685	C₂	semidirect
52. C₇₃	#1320	semidirect

H ≅ G/N

type

1. #17989685

C₂

semidirect

52. C₇₃

#1320

semidirect

Subgroups — #22626961

Conjugacy classes of subgroups

Complements