Group #22625010 — subgroups

Subgroups — #22625010

Order 9344.

124 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 48 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	#17989643	C₂	1	1	yes	maximal, characteristic
2	C₂×#14556662	C₂	1	1	yes	maximal, characteristic
3	#108×D₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924038	—	2	1	no	—
5	#14556666	C₄	1	2	yes	—
6	#14556665	—	2	1	no	—
7	#14556664	—	2	1	no	—
8	#14556662	—	2	1	no	—
9	#14556662	C₄	1	2	yes	—
10	M₁₆×D₇₃	—	2	1	no	—
11	C₂×C₈×D₇₃	C₂²	1	1	yes	characteristic
12	#14556527	C₄	1	1	yes	characteristic
13	#14556526	—	2	1	no	—
14	#108×C₇₃	C₄	1	1	yes	characteristic
15	#11924038	—	2	2	no	—
16	#11924038	—	4	1	no	—
17	C₂×#10596833	—	4	1	no	—
18	#11924031	—	2	2	no	—
19	C₂×C₄×D₇₃	D₄	1	1	yes	characteristic
20	#11924012	—	2	1	no	—
21	#11924011	—	4	1	no	—
22	C₂×#10596831	D₄	1	1	yes	characteristic
23	C₈×D₇₃	—	4	1	no	—
24	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
25	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
26	C₈×D₇₃	D₄	1	1	yes	characteristic
27	C₈×D₇₃	Q₈	1	1	yes	characteristic
28	M₁₆×C₇₃	—	2	1	no	—
29	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
30	C₂²×D₇₃	Q₁₆	1	1	yes	characteristic
31	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×Dic₇₃	SD₁₆	1	1	yes	characteristic
33	C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
34	C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
35	C₄×D₇₃	D₈	1	1	yes	characteristic
36	C₄×D₇₃	SD₁₆	1	1	yes	characteristic
37	#10596833	—	4	2	no	—
38	C₈×C₇₃	—	4	1	no	—
39	C₈×C₇₃	C₄²	1	1	yes	characteristic
40	C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
41	#10596831	—	4	1	no	—
42	#10596831	C₂²⋊C₄	1	1	yes	characteristic
43	#10596831	C₄⋊C₄	1	1	yes	characteristic
44	C₂²×C₇₃	#103	1	1	yes	characteristic
45	C₂×D₇₃	—	4	1	no	—
46	C₂×D₇₃	#103	1	1	yes	characteristic
47	C₂×D₇₃	#107	1	1	yes	characteristic
48	C₄×C₇₃	#95	1	1	yes	characteristic
49	C₄×C₇₃	#102	1	1	yes	characteristic
50	Dic₇₃	#102	1	1	yes	characteristic
51	Dic₇₃	#106	1	1	yes	characteristic
52	C₂×C₇₃	—	2	1	no	—
53	C₂×C₇₃	#340	1	1	yes	characteristic
54	D₇₃	—	2	1	no	—
55	D₇₃	—	2	1	no	—
56	#1388	—	73	1	no	maximal, Sylow
57	C₇₃	#1388	1	1	yes	characteristic, complemented, Sylow
58	C₂×M₃₂	—	73	1	no	—
59	C₂×#108	—	73	1	no	—
60	C₂×#108	—	73	1	no	—
61	C₂×M₁₆	—	146	1	no	—
62	C₂×M₁₆	—	146	1	no	—
63	C₂²×C₈	—	73	1	no	—
64	M₃₂	—	73	2	no	—
65	M₃₂	—	146	1	no	—
66	C₂×C₁₆	—	146	1	no	—
67	#108	—	73	2	no	—
68	#108	—	73	1	no	—
69	#108	—	146	1	no	—
70	#108	—	146	1	no	—
71	#108	#64408	1	1	yes	characteristic
72	C₂²×C₄	—	73	1	no	—
73	M₁₆	—	2	1	no	—
74	M₁₆	—	292	1	no	—
75	M₁₆	—	292	1	no	—
76	M₁₆	—	146	2	no	—
77	M₁₆	—	146	1	no	—
78	C₂×C₈	—	292	1	no	—
79	C₂×C₈	—	292	1	no	—
80	C₂×C₈	—	73	1	no	—
81	C₂×C₈	—	73	1	no	—
82	C₂×C₈	—	73	1	no	—
83	C₂×C₈	—	73	1	no	—
84	C₂×C₈	—	73	1	no	—
85	C₂×C₈	C₂×#64408	1	1	yes	characteristic
86	C₁₆	—	146	2	no	—
87	C₂³	—	73	1	no	—
88	C₂×C₄	—	73	1	no	—
89	C₂×C₄	—	73	1	no	—
90	C₂×C₄	—	73	1	no	—
91	C₂×C₄	—	73	1	no	—
92	C₂×C₄	—	73	1	no	—
93	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
94	C₈	—	4	1	no	—
95	C₈	—	292	2	no	—
96	C₈	—	292	1	no	—
97	C₈	—	73	1	no	—
98	C₈	—	73	1	no	—
99	C₈	C₄×#64408	1	1	yes	characteristic
100	C₈	C₄⋊#64408	1	1	yes	characteristic
101	C₂²	—	292	1	no	—
102	C₂²	—	73	1	no	—
103	C₂²	—	73	1	no	—
104	C₂²	#14556654	1	1	yes	characteristic
105	C₄	—	73	1	no	—
106	C₄	—	73	1	no	—
107	C₄	(C₂×#64408)⋊C₄	1	1	yes	characteristic
108	C₄	#14556653	1	1	yes	characteristic
109	C₂	—	2	1	no	—
110	C₂	—	146	1	no	—
111	C₂	—	146	1	no	—
112	C₂	#17989460	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989643

C₂

yes

maximal, characteristic

C₂×#14556662

C₂

yes

maximal, characteristic

#108×D₇₃

C₂

yes

maximal, characteristic

C₂×#11924038

—

#14556666

C₄

yes

—

—

—

—

C₄

yes

—

M₁₆×D₇₃

—

C₂×C₈×D₇₃

C₂²

yes

characteristic

#14556527

C₄

yes

characteristic

#14556526

—

#108×C₇₃

C₄

yes

—

—

—

—

C₂×C₄×D₇₃

D₄

yes

—

—

D₄

yes

characteristic

C₈×D₇₃

—

C₈×D₇₃

C₂×C₄

yes

characteristic

C₈×D₇₃

C₂×C₄

yes

characteristic

C₈×D₇₃

D₄

yes

characteristic

C₈×D₇₃

Q₈

yes

characteristic

M₁₆×C₇₃

—

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂²×D₇₃

Q₁₆

yes

characteristic

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₇₃

SD₁₆

yes

characteristic

C₄×D₇₃

C₂²⋊C₄

yes

characteristic

C₄×D₇₃

C₄⋊C₄

yes

characteristic

C₄×D₇₃

D₈

yes

characteristic

C₄×D₇₃

SD₁₆

yes

characteristic

#10596833

—

C₈×C₇₃

—

C₈×C₇₃

C₄²

yes

characteristic

C₈×C₇₃

C₄⋊C₄

yes

characteristic

#10596831

—

#10596831

C₂²⋊C₄

yes

characteristic

#10596831

C₄⋊C₄

yes

characteristic

C₂²×C₇₃

#103

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

yes

C₂×D₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

yes

Dic₇₃

yes

C₂×C₇₃

—

C₂×C₇₃

#340

yes

characteristic

D₇₃

—

D₇₃

—

#1388

—

maximal, Sylow

C₇₃

#1388

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂×#108

—

C₂×#108

—

C₂×M₁₆

—

146

—

C₂×M₁₆

—

146

—

C₂²×C₈

—

M₃₂

—

M₃₂

—

146

—

C₂×C₁₆

—

146

—

#108

—

#108

—

#108

—

146

—

#108

—

146

—

#108

#64408

yes

characteristic

C₂²×C₄

—

M₁₆

—

M₁₆

—

292

—

M₁₆

—

292

—

M₁₆

—

146

—

M₁₆

—

146

—

C₂×C₈

—

292

—

C₂×C₈

—

292

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#64408

yes

characteristic

C₁₆

—

146

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊#64408

yes

characteristic

C₈

—

C₈

—

292

—

C₈

—

292

—

C₈

—

C₈

—

C₈

C₄×#64408

yes

characteristic

100

C₈

C₄⋊#64408

yes

characteristic

101

C₂²

—

292

—

102

C₂²

—

103

C₂²

—

104

C₂²

#14556654

yes

characteristic

105

C₄

—

106

C₄

—

107

C₄

(C₂×#64408)⋊C₄

yes

characteristic

108

C₄

#14556653

yes

characteristic

109

C₂

—

110

C₂

—

146

—

111

C₂

—

146

—

112

C₂

#17989460

yes

characteristic

	subgroup	G/H
center	C₂	#17989460
commutator	C₈×C₇₃	C₄²
Frattini	C₂×C₈	C₂×#64408
Fitting	#108×C₇₃	C₄
socle	C₂×C₇₃	#340
hypercenter	#108	#64408
hypocenter	C₇₃	#1388
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #108

subgroup

G/H

center

C₂

#17989460

commutator

C₈×C₇₃

C₄²

Frattini

C₂×C₈

C₂×#64408

Fitting

#108×C₇₃

C₄

C₂×C₇₃

C₇₃

G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #108

N	H ≅ G/N	type
57. C₇₃	#1388	semidirect

H ≅ G/N

type

57. C₇₃

#1388

semidirect

Subgroups — #22625010

Conjugacy classes of subgroups

Complements