Group #32995021 — subgroups

Subgroups — #32995021

Order 18688.

260 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 163 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	#22611730	C₂	1	2	yes	maximal
2	#22607849	C₂	1	2	yes	maximal, complemented
3	#22607848	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×#11924003	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#1450	C₂	1	1	yes	maximal, characteristic
6	C₄⋊#11924003	C₄	1	4	yes	—
7	C₂²⋊#11924003	C₄	1	4	yes	—
8	C₄×#11924003	C₂²	1	2	yes	—
9	C₄×#11924003	C₂²	1	2	yes	—
10	#431×C₇₃	C₄	1	2	yes	—
11	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
12	#322×C₇₃	C₄	1	2	yes	—
13	C₈²×C₇₃	C₂²	1	1	yes	characteristic
14	C₈²×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×#11924003	C₂×C₄	1	4	yes	—
16	C₂×#11924003	C₂×C₄	1	4	yes	—
17	C₂²×C₈×C₇₃	C₂×C₄	1	2	yes	—
18	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
19	C₄⋊C₈×C₇₃	C₈	1	4	yes	—
20	C₂²⋊C₈×C₇₃	C₈	1	4	yes	—
21	C₄×C₈×C₇₃	C₂×C₄	1	2	yes	—
22	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
23	C₄×C₈×C₇₃	C₂×C₄	1	2	yes	—
24	C₄×C₈×C₇₃	C₂×C₄	1	2	yes	—
25	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
26	#11924003	—	2	4	no	—
27	#11924003	—	2	4	no	—
28	C₂²×C₄×C₇₃	C₄²	1	1	yes	characteristic
29	C₂²×C₄×C₇₃	C₂×C₈	1	2	yes	—
30	C₂×C₈×C₇₃	—	2	4	no	—
31	C₂×C₈×C₇₃	C₄²	1	2	yes	—
32	C₂×C₈×C₇₃	C₂×C₈	1	4	yes	—
33	C₂×C₈×C₇₃	C₂×C₈	1	4	yes	—
34	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
35	C₄²×C₇₃	C₄²	1	1	yes	characteristic
36	C₄²×C₇₃	C₂×C₈	1	2	yes	—
37	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
38	C₂³×C₇₃	C₄×C₈	1	1	yes	characteristic
39	C₂×C₄×C₇₃	—	2	2	no	—
40	C₂×C₄×C₇₃	—	2	4	no	—
41	C₂×C₄×C₇₃	C₄×C₈	1	2	yes	—
42	C₂×C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
43	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
44	C₂×C₄×C₇₃	C₂²×C₈	1	2	yes	—
45	C₈×C₇₃	—	2	2	no	—
46	C₈×C₇₃	—	2	4	no	—
47	C₈×C₇₃	—	2	4	no	—
48	C₈×C₇₃	#131	1	4	yes	—
49	C₂²×C₇₃	—	2	2	no	—
50	C₂²×C₇₃	—	2	1	no	—
51	C₂²×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
52	C₄×C₇₃	—	2	2	no	—
53	C₄×C₇₃	—	2	1	no	—
54	C₄×C₇₃	#405	1	2	yes	—
55	C₄×C₇₃	#504	1	4	yes	—
56	#11412	—	73	1	no	maximal, Sylow
57	C₂×C₇₃	—	4	1	no	—
58	C₂×C₇₃	#1450	1	1	yes	characteristic
59	C₂×C₇₃	#2108	1	2	yes	—
60	#2162	—	73	2	no	—
61	#1450	D₇₃	1	1	yes	characteristic
62	#1312	—	73	2	no	—
63	#1311	—	73	1	no	—
64	C₈×C₁₆	—	73	1	no	—
65	C₇₃	#11412	1	1	yes	characteristic, complemented, Sylow
66	#431	Dic₇₃	1	2	yes	—
67	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
68	C₄⋊C₁₆	—	73	4	no	—
69	C₂²⋊C₁₆	—	73	4	no	—
70	C₄×C₁₆	—	73	2	no	—
71	C₄×C₁₆	—	73	2	no	—
72	#322	Dic₇₃	1	2	yes	—
73	C₈²	C₂×D₇₃	1	1	yes	characteristic
74	C₈²	C₂×D₇₃	1	1	yes	characteristic
75	C₂²×C₈	C₄×D₇₃	1	2	yes	—
76	C₂×C₄²	C₂×Dic₇₃	1	1	yes	characteristic
77	C₂×C₁₆	—	73	4	no	—
78	C₂×C₁₆	—	73	4	no	—
79	C₄⋊C₈	#10596831	1	4	yes	—
80	C₂²⋊C₈	#10596831	1	4	yes	—
81	C₄×C₈	C₄×D₇₃	1	2	yes	—
82	C₄×C₈	C₂×Dic₇₃	1	1	yes	characteristic
83	C₄×C₈	C₂×Dic₇₃	1	2	yes	—
84	C₄×C₈	C₂×Dic₇₃	1	2	yes	—
85	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
86	C₂²×C₄	C₄×Dic₇₃	1	1	yes	characteristic
87	C₂²×C₄	C₂×#10596831	1	2	yes	—
88	C₂×C₈	—	2	4	no	—
89	C₂×C₈	C₄×Dic₇₃	1	2	yes	—
90	C₂×C₈	C₂×#10596831	1	4	yes	—
91	C₂×C₈	C₂×#10596831	1	4	yes	—
92	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
93	C₄²	C₄×Dic₇₃	1	1	yes	characteristic
94	C₄²	C₂×#10596831	1	2	yes	—
95	C₄²	C₂²×Dic₇₃	1	1	yes	characteristic
96	C₁₆	—	146	4	no	—
97	C₁₆	—	146	4	no	—
98	C₂³	C₄×#10596831	1	1	yes	characteristic
99	C₂×C₄	—	2	4	no	—
100	C₂×C₄	—	2	2	no	—
101	C₂×C₄	C₄×#10596831	1	2	yes	—
102	C₂×C₄	C₄×#10596831	1	1	yes	characteristic
103	C₂×C₄	C₂×C₄×Dic₇₃	1	1	yes	characteristic
104	C₂×C₄	C₂²×#10596831	1	2	yes	—
105	C₈	—	2	4	no	—
106	C₈	—	2	4	no	—
107	C₈	—	2	2	no	—
108	C₈	#14556597	1	4	yes	—
109	C₂²	—	2	2	no	—
110	C₂²	—	2	1	no	—
111	C₂²	C₂×C₄×#10596831	1	1	yes	characteristic
112	C₄	—	2	2	no	—
113	C₄	—	2	1	no	—
114	C₄	#17988542	1	2	yes	—
115	C₄	#17989004	1	4	yes	—
116	C₂	—	4	1	no	—
117	C₂	#22608214	1	1	yes	characteristic
118	C₂	#22611528	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#22611730

C₂

yes

maximal

#22607849

C₂

yes

maximal, complemented

#22607848

C₂

yes

maximal, characteristic, complemented

C₈×#11924003

C₂

yes

maximal, characteristic, complemented

C₇₃×#1450

C₂

yes

maximal, characteristic

C₄⋊#11924003

C₄

yes

—

C₂²⋊#11924003

C₄

yes

—

C₄×#11924003

C₂²

yes

—

C₄×#11924003

C₂²

yes

—

#431×C₇₃

C₄

yes

—

C₂×C₄×C₈×C₇₃

C₂²

yes

characteristic

#322×C₇₃

C₄

yes

—

C₈²×C₇₃

C₂²

yes

characteristic

C₈²×C₇₃

C₂²

yes

characteristic

C₂×#11924003

C₂×C₄

yes

—

C₂×#11924003

C₂×C₄

yes

—

C₂²×C₈×C₇₃

C₂×C₄

yes

—

C₂×C₄²×C₇₃

C₂×C₄

yes

characteristic

C₄⋊C₈×C₇₃

C₈

yes

—

C₂²⋊C₈×C₇₃

C₈

yes

—

C₄×C₈×C₇₃

C₂×C₄

yes

—

C₄×C₈×C₇₃

C₂×C₄

yes

characteristic

C₄×C₈×C₇₃

C₂×C₄

yes

—

C₄×C₈×C₇₃

C₂×C₄

yes

—

C₄×C₈×C₇₃

C₂³

yes

characteristic

#11924003

—

#11924003

—

C₂²×C₄×C₇₃

C₄²

yes

characteristic

C₂²×C₄×C₇₃

C₂×C₈

yes

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₄²

yes

—

C₂×C₈×C₇₃

C₂×C₈

yes

—

C₂×C₈×C₇₃

C₂×C₈

yes

—

C₂×C₈×C₇₃

C₂²×C₄

yes

—

C₄²×C₇₃

C₄²

yes

characteristic

C₄²×C₇₃

C₂×C₈

yes

—

C₄²×C₇₃

C₂²×C₄

yes

characteristic

C₂³×C₇₃

C₄×C₈

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₄×C₈

yes

—

C₂×C₄×C₇₃

C₄×C₈

yes

characteristic

C₂×C₄×C₇₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₈

yes

—

C₈×C₇₃

—

C₈×C₇₃

—

C₈×C₇₃

—

C₈×C₇₃

#131

yes

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂×C₄×C₈

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#405

yes

—

C₄×C₇₃

#504

yes

—

#11412

—

maximal, Sylow

C₂×C₇₃

—

C₂×C₇₃

#1450

yes

characteristic

C₂×C₇₃

#2108

yes

—

#2162

—

#1450

D₇₃

yes

characteristic

#1312

—

#1311

—

C₈×C₁₆

—

C₇₃

#11412

yes

characteristic, complemented, Sylow

#431

Dic₇₃

yes

—

C₂×C₄×C₈

C₂×D₇₃

yes

characteristic

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

C₄×C₁₆

—

C₄×C₁₆

—

#322

Dic₇₃

yes

—

C₈²

C₂×D₇₃

yes

characteristic

C₈²

C₂×D₇₃

yes

characteristic

C₂²×C₈

C₄×D₇₃

yes

—

C₂×C₄²

C₂×Dic₇₃

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₄⋊C₈

#10596831

yes

—

C₂²⋊C₈

#10596831

yes

—

C₄×C₈

C₄×D₇₃

yes

—

C₄×C₈

C₂×Dic₇₃

yes

characteristic

C₄×C₈

C₂×Dic₇₃

yes

—

C₄×C₈

C₂×Dic₇₃

yes

—

C₄×C₈

C₂²×D₇₃

yes

characteristic

C₂²×C₄

C₄×Dic₇₃

yes

characteristic

C₂²×C₄

C₂×#10596831

yes

—

C₂×C₈

—

C₂×C₈

C₄×Dic₇₃

yes

—

C₂×C₈

C₂×#10596831

yes

—

C₂×C₈

C₂×#10596831

yes

—

C₂×C₈

C₂×C₄×D₇₃

yes

—

C₄²

C₄×Dic₇₃

yes

characteristic

C₄²

C₂×#10596831

yes

—

C₄²

C₂²×Dic₇₃

yes

characteristic

C₁₆

—

146

—

C₁₆

—

146

—

C₂³

C₄×#10596831

yes

characteristic

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

C₄×#10596831

yes

—

102

C₂×C₄

C₄×#10596831

yes

characteristic

103

C₂×C₄

C₂×C₄×Dic₇₃

yes

characteristic

104

C₂×C₄

C₂²×#10596831

yes

—

105

C₈

—

106

C₈

—

107

C₈

—

108

C₈

#14556597

yes

—

109

C₂²

—

110

C₂²

—

111

C₂²

C₂×C₄×#10596831

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

#17988542

yes

—

115

C₄

#17989004

yes

—

116

C₂

—

117

C₂

#22608214

yes

characteristic

118

C₂

#22611528

yes

—

	subgroup	G/H
center, Frattini	C₄×C₈	C₂²×D₇₃
commutator, socle	C₂²×C₇₃	C₂×C₄×C₈
Fitting	C₇₃×#1450	C₂
prime radical	C₂³×C₇₃	C₄×C₈
cosocle	C₄×C₈×C₇₃	C₂³
hypercenter	#1450	D₇₃
hypocenter	C₇₃	#11412
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄×C₈ ◁ #1450

subgroup

G/H

center, Frattini

C₄×C₈

C₂²×D₇₃

commutator, socle

C₂²×C₇₃

C₂×C₄×C₈

Fitting

C₇₃×#1450

C₂

prime radical

C₂³×C₇₃

C₄×C₈

cosocle

C₄×C₈×C₇₃

C₂³

D₇₃

C₇₃

G ▷ C₂²×C₇₃ ▷ C₇₃

C₁ ◁ C₄×C₈ ◁ #1450

N	H ≅ G/N	type
2. #22607849	C₂	semidirect
3. #22607848	C₂	semidirect
4. C₈×#11924003	C₂	semidirect
65. C₇₃	#11412	semidirect

H ≅ G/N

type

2. #22607849

C₂

semidirect

3. #22607848

C₂

semidirect

4. C₈×#11924003

C₂

semidirect

65. C₇₃

#11412

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#22611730	2
#22607849	2
#22607848	2
C₈×#11924003	2
C₇₃×#1450	2
#11412	73

subgroup

index

C₇₃×#1450

Subgroups — #32995021

Conjugacy classes of subgroups

Complements

Maximal subgroups