Group #22609836 — subgroups

Subgroups — #22609836

Order 9344.

220 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 105 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	C₂×#14556526	C₂	1	2	yes	maximal
2	M₁₆×Dic₇₃	C₂	1	2	yes	maximal
3	C₂×#14556501	C₂	1	1	yes	maximal, characteristic
4	#17988352	C₂	1	1	yes	maximal, characteristic
5	#341×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#11924012	C₂²	1	2	yes	—
7	C₂²×#10596831	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
9	#14556526	C₄	1	8	yes	complemented
10	#14556501	—	2	2	no	—
11	#14556501	C₄	1	4	yes	—
12	C₈×Dic₇₃	—	2	2	no	—
13	C₂×M₁₆×C₇₃	C₂²	1	2	yes	—
14	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
15	C₂²×Dic₇₃	Q₈	1	2	yes	—
16	#11924012	—	2	2	no	—
17	#11924012	C₂×C₄	1	4	yes	—
18	C₂×#10596831	—	2	2	no	—
19	C₂×#10596831	C₂×C₄	1	2	yes	—
20	C₂×#10596831	C₂×C₄	1	4	yes	—
21	C₄×Dic₇₃	C₂×C₄	1	2	yes	—
22	C₄×Dic₇₃	D₄	1	2	yes	—
23	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
24	M₁₆×C₇₃	—	2	2	no	—
25	M₁₆×C₇₃	C₂×C₄	1	4	yes	—
26	C₂×C₈×C₇₃	—	2	2	no	—
27	C₂×C₈×C₇₃	—	2	2	no	—
28	C₂×C₈×C₇₃	C₂×C₄	1	2	yes	—
29	C₂³×C₇₃	C₂×Q₈	1	1	yes	characteristic
30	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₇₃	C₂²×C₄	1	2	yes	—
32	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₇₃	#41	1	2	yes	—
34	C₂×Dic₇₃	—	4	2	no	—
35	C₂×Dic₇₃	C₄⋊C₄	1	4	yes	—
36	C₈×C₇₃	—	2	2	no	—
37	C₈×C₇₃	—	2	4	no	—
38	#10596831	—	2	4	no	—
39	#10596831	C₄²	1	4	yes	—
40	C₂²×C₇₃	—	2	2	no	—
41	C₂²×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
42	C₂²×C₇₃	C₄×Q₈	1	2	yes	—
43	C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
44	C₄×C₇₃	#117	1	1	yes	characteristic
45	C₄×C₇₃	C₄×D₄	1	2	yes	—
46	Dic₇₃	—	2	4	no	—
47	C₂×C₇₃	—	2	2	no	—
48	C₂×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
49	C₂×C₇₃	#430	1	2	yes	—
50	#1778	—	73	1	no	maximal, Sylow
51	C₇₃	#1778	1	1	yes	characteristic, complemented, Sylow
52	C₂×#108	—	73	2	no	—
53	C₄×M₁₆	—	73	2	no	—
54	C₂×#97	—	73	1	no	—
55	#341	—	73	1	no	—
56	#341	D₇₃	1	1	yes	characteristic
57	C₂×M₁₆	—	73	2	no	—
58	C₂×M₁₆	C₂×D₇₃	1	2	yes	—
59	C₂²×C₈	—	73	1	no	—
60	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
61	C₂×C₄²	—	73	1	no	—
62	#108	—	73	8	no	—
63	#97	—	73	4	no	—
64	#97	—	146	2	no	—
65	C₄×C₈	—	146	2	no	—
66	C₂²×C₄	—	73	2	no	—
67	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
68	M₁₆	—	2	2	no	—
69	M₁₆	—	73	4	no	—
70	M₁₆	—	146	2	no	—
71	M₁₆	C₄×D₇₃	1	4	yes	—
72	C₂×C₈	—	2	2	no	—
73	C₂×C₈	—	2	2	no	—
74	C₂×C₈	—	73	2	no	—
75	C₂×C₈	—	73	4	no	—
76	C₂×C₈	—	146	2	no	—
77	C₂×C₈	C₄×D₇₃	1	2	yes	—
78	C₄²	—	73	2	no	—
79	C₄²	—	73	2	no	—
80	C₂³	Q₈×D₇₃	1	1	yes	characteristic
81	C₂×C₄	—	292	2	no	—
82	C₂×C₄	—	73	4	no	—
83	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
84	C₂×C₄	C₂×C₄×D₇₃	1	2	yes	—
85	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
86	C₂×C₄	#11924027	1	2	yes	—
87	C₈	—	2	2	no	—
88	C₈	—	2	4	no	—
89	C₈	—	73	4	no	—
90	C₈	—	146	4	no	—
91	C₂²	—	2	2	no	—
92	C₂²	C₄⋊C₄×D₇₃	1	1	yes	characteristic
93	C₂²	#14556556	1	2	yes	—
94	C₄	—	146	4	no	—
95	C₄	C₄²×D₇₃	1	1	yes	characteristic
96	C₄	#14556547	1	1	yes	characteristic
97	C₄	#14556551	1	2	yes	—
98	C₂	—	2	2	no	—
99	C₂	#17988438	1	1	yes	characteristic
100	C₂	#17988634	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556526

C₂

yes

maximal

M₁₆×Dic₇₃

C₂

yes

maximal

C₂×#14556501

C₂

yes

maximal, characteristic

#17988352

C₂

yes

maximal, characteristic

#341×C₇₃

C₂

yes

maximal, characteristic

C₂×#11924012

C₂²

yes

—

C₂²×#10596831

C₂²

yes

characteristic

C₂×C₄×Dic₇₃

C₂²

yes

characteristic

#14556526

C₄

yes

complemented

#14556501

—

#14556501

C₄

yes

—

C₈×Dic₇₃

—

C₂×M₁₆×C₇₃

C₂²

yes

—

C₂²×C₈×C₇₃

C₂²

yes

characteristic

C₂²×Dic₇₃

Q₈

yes

—

#11924012

—

#11924012

C₂×C₄

yes

—

C₂×#10596831

—

C₂×#10596831

C₂×C₄

yes

—

C₂×#10596831

C₂×C₄

yes

—

C₄×Dic₇₃

C₂×C₄

yes

—

C₄×Dic₇₃

D₄

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

M₁₆×C₇₃

—

M₁₆×C₇₃

C₂×C₄

yes

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂×C₄

yes

—

C₂³×C₇₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

#41

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₄⋊C₄

yes

—

C₈×C₇₃

—

C₈×C₇₃

—

#10596831

—

#10596831

C₄²

yes

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₇₃

C₄×Q₈

yes

—

C₄×C₇₃

C₂×C₄²

yes

characteristic

C₄×C₇₃

#117

yes

characteristic

C₄×C₇₃

C₄×D₄

yes

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

C₄×C₄⋊C₄

yes

characteristic

C₂×C₇₃

#430

yes

—

#1778

—

maximal, Sylow

C₇₃

#1778

yes

characteristic, complemented, Sylow

C₂×#108

—

C₄×M₁₆

—

C₂×#97

—

#341

—

#341

D₇₃

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₃

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₇₃

yes

characteristic

C₂×C₄²

—

#108

—

#97

—

#97

—

146

—

C₄×C₈

—

146

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

146

—

M₁₆

C₄×D₇₃

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

C₄×D₇₃

yes

—

C₄²

—

C₄²

—

C₂³

Q₈×D₇₃

yes

characteristic

C₂×C₄

—

292

—

C₂×C₄

—

C₂×C₄

C₂×C₄×D₇₃

yes

characteristic

C₂×C₄

C₂×C₄×D₇₃

yes

—

C₂×C₄

D₄×D₇₃

yes

characteristic

C₂×C₄

#11924027

yes

—

C₈

—

C₈

—

C₈

—

C₈

—

146

—

C₂²

—

C₂²

C₄⋊C₄×D₇₃

yes

characteristic

C₂²

#14556556

yes

—

C₄

—

146

—

C₄

C₄²×D₇₃

yes

C₄

yes

C₄

yes

—

C₂

—

C₂

#17988438

yes

characteristic

100

C₂

#17988634

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₇₃
commutator	C₄×C₇₃	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	#341×C₇₃	C₂
socle	C₂²×C₇₃	C₂×C₄⋊C₄
hypercenter	#341	D₇₃
hypocenter	C₇₃	#1778
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #341

subgroup

G/H

center

C₂×C₄

D₄×D₇₃

commutator

C₄×C₇₃

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

#341×C₇₃

C₂

socle

C₂²×C₇₃

C₂×C₄⋊C₄

D₇₃

C₇₃

G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #341

N	H ≅ G/N	type
9. #14556526	C₄	semidirect
51. C₇₃	#1778	semidirect

H ≅ G/N

type

9. #14556526

C₄

semidirect

51. C₇₃

#1778

semidirect

Subgroups — #22609836

Conjugacy classes of subgroups

Complements