Group #32995020 — subgroups

Subgroups — #32995020

Order 18688.

260 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 131 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	#22611728	C₂	1	2	yes	maximal
2	#22608213	C₂	1	1	yes	maximal, characteristic
3	#22607850	C₂	1	2	yes	maximal, complemented
4	#22607848	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×C₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#17988638	C₄	1	2	yes	—
7	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
8	#17988405	C₄	1	4	yes	—
9	#17988366	C₄	1	4	yes	—
10	C₄×#11924003	C₂²	1	2	yes	—
11	#17988309	C₄	1	2	yes	—
12	C₈×#10596831	C₂²	1	1	yes	characteristic
13	C₄×C₁₆×C₇₃	C₂²	1	2	yes	—
14	C₈²×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×C₈×D₇₃	C₂×C₄	1	2	yes	—
16	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
17	C₂×#11924003	C₂×C₄	1	4	yes	—
18	#14556520	C₈	1	4	yes	—
19	#14556503	C₈	1	4	yes	—
20	C₄×#10596831	C₂×C₄	1	1	yes	characteristic
21	C₄×#10596831	C₂×C₄	1	2	yes	—
22	C₈×Dic₇₃	C₂×C₄	1	2	yes	—
23	C₂×C₁₆×C₇₃	C₂×C₄	1	4	yes	—
24	C₄×C₈×C₇₃	C₂×C₄	1	2	yes	—
25	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
26	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
27	C₂×C₄×D₇₃	C₂×C₈	1	2	yes	—
28	C₂×#10596831	C₄²	1	2	yes	—
29	C₂×#10596831	C₂×C₈	1	4	yes	—
30	C₈×D₇₃	—	2	4	no	—
31	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
32	C₄×Dic₇₃	C₂×C₈	1	2	yes	—
33	#11924003	—	2	4	no	—
34	C₂×C₈×C₇₃	C₂×C₈	1	4	yes	—
35	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
36	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
37	C₁₆×C₇₃	—	2	4	no	—
38	C₂²×D₇₃	C₄×C₈	1	1	yes	characteristic
39	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
40	C₂×C₄×C₇₃	C₂²×C₈	1	2	yes	—
41	C₂×Dic₇₃	C₄×C₈	1	2	yes	—
42	C₂×Dic₇₃	C₄×C₈	1	1	yes	characteristic
43	C₄×D₇₃	—	2	2	no	—
44	C₄×D₇₃	—	2	4	no	—
45	C₈×C₇₃	—	2	4	no	—
46	C₈×C₇₃	#131	1	4	yes	—
47	#10596831	—	2	2	no	—
48	#10596831	—	2	4	no	—
49	C₂²×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
50	C₂×D₇₃	—	2	2	no	—
51	C₂×D₇₃	—	2	1	no	—
52	C₄×C₇₃	#405	1	2	yes	—
53	C₄×C₇₃	#504	1	4	yes	—
54	Dic₇₃	—	2	2	no	—
55	Dic₇₃	—	2	1	no	—
56	#11412	—	73	1	no	maximal, Sylow
57	C₂×C₇₃	#1450	1	1	yes	characteristic
58	C₂×C₇₃	#2108	1	2	yes	—
59	D₇₃	—	4	1	no	—
60	#2162	—	73	2	no	—
61	#1450	—	73	1	no	—
62	#1312	—	73	2	no	—
63	#1311	—	73	1	no	—
64	C₈×C₁₆	D₇₃	1	1	yes	characteristic, complemented
65	C₇₃	#11412	1	1	yes	characteristic, complemented, Sylow
66	#431	—	73	2	no	—
67	C₂×C₄×C₈	—	73	1	no	—
68	C₄⋊C₁₆	—	73	4	no	—
69	C₂²⋊C₁₆	—	73	4	no	—
70	C₄×C₁₆	—	73	2	no	—
71	C₄×C₁₆	C₂×D₇₃	1	2	yes	—
72	#322	—	73	2	no	—
73	C₈²	—	73	1	no	—
74	C₈²	C₂×D₇₃	1	1	yes	characteristic
75	C₂²×C₈	—	73	2	no	—
76	C₂×C₄²	—	73	1	no	—
77	C₂×C₁₆	—	73	4	no	—
78	C₂×C₁₆	C₄×D₇₃	1	4	yes	—
79	C₄⋊C₈	—	73	4	no	—
80	C₂²⋊C₈	—	73	4	no	—
81	C₄×C₈	—	73	2	no	—
82	C₄×C₈	—	73	2	no	—
83	C₄×C₈	—	73	1	no	—
84	C₄×C₈	C₄×D₇₃	1	2	yes	—
85	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
86	C₂²×C₄	—	73	1	no	—
87	C₂²×C₄	—	73	2	no	—
88	C₂×C₈	—	73	2	no	—
89	C₂×C₈	—	73	4	no	—
90	C₂×C₈	—	146	4	no	—
91	C₂×C₈	C₈×D₇₃	1	4	yes	—
92	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
93	C₄²	—	73	1	no	—
94	C₄²	—	73	2	no	—
95	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
96	C₁₆	—	2	4	no	—
97	C₁₆	—	146	4	no	—
98	C₂³	—	73	1	no	—
99	C₂×C₄	—	73	2	no	—
100	C₂×C₄	—	73	1	no	—
101	C₂×C₄	—	146	4	no	—
102	C₂×C₄	—	146	2	no	—
103	C₂×C₄	C₄²×D₇₃	1	1	yes	characteristic
104	C₂×C₄	C₂×C₈×D₇₃	1	2	yes	—
105	C₈	—	2	4	no	—
106	C₈	—	146	4	no	—
107	C₈	—	146	2	no	—
108	C₈	#14556597	1	4	yes	—
109	C₂²	—	146	2	no	—
110	C₂²	—	146	1	no	—
111	C₂²	C₄×C₈×D₇₃	1	1	yes	characteristic
112	C₄	—	146	2	no	—
113	C₄	—	146	1	no	—
114	C₄	#17988541	1	2	yes	—
115	C₄	#17989003	1	4	yes	—
116	C₂	—	292	1	no	—
117	C₂	#22608213	1	1	yes	characteristic
118	C₂	#22611526	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#22611728

C₂

yes

maximal

#22608213

C₂

yes

maximal, characteristic

#22607850

C₂

yes

maximal, complemented

#22607848

C₂

yes

maximal, characteristic, complemented

C₈×C₁₆×C₇₃

C₂

yes

maximal, characteristic, complemented

#17988638

C₄

yes

—

C₄×C₈×D₇₃

C₂²

yes

characteristic

#17988405

C₄

yes

—

#17988366

C₄

yes

—

C₄×#11924003

C₂²

yes

—

#17988309

C₄

yes

—

C₈×#10596831

C₂²

yes

characteristic

C₄×C₁₆×C₇₃

C₂²

yes

—

C₈²×C₇₃

C₂²

yes

characteristic

C₂×C₈×D₇₃

C₂×C₄

yes

—

C₄²×D₇₃

C₂×C₄

yes

characteristic

C₂×#11924003

C₂×C₄

yes

—

#14556520

C₈

yes

—

#14556503

C₈

yes

—

C₄×#10596831

C₂×C₄

yes

characteristic

C₄×#10596831

C₂×C₄

yes

—

C₈×Dic₇₃

C₂×C₄

yes

—

C₂×C₁₆×C₇₃

C₂×C₄

yes

—

C₄×C₈×C₇₃

C₂×C₄

yes

—

C₄×C₈×C₇₃

C₂³

yes

characteristic

C₂×C₄×D₇₃

C₄²

yes

characteristic

C₂×C₄×D₇₃

C₂×C₈

yes

—

C₂×#10596831

C₄²

yes

—

C₂×#10596831

C₂×C₈

yes

—

C₈×D₇₃

—

C₄×Dic₇₃

C₄²

yes

characteristic

C₄×Dic₇₃

C₂×C₈

yes

—

#11924003

—

C₂×C₈×C₇₃

C₂×C₈

yes

—

C₂×C₈×C₇₃

C₂²×C₄

yes

—

C₄²×C₇₃

C₂²×C₄

yes

characteristic

C₁₆×C₇₃

—

C₂²×D₇₃

C₄×C₈

yes

characteristic

C₂×C₄×C₇₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₈

yes

—

C₂×Dic₇₃

C₄×C₈

yes

—

C₂×Dic₇₃

C₄×C₈

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

—

C₈×C₇₃

—

C₈×C₇₃

#131

yes

—

#10596831

—

#10596831

—

C₂²×C₇₃

C₂×C₄×C₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

#405

yes

—

C₄×C₇₃

#504

yes

—

Dic₇₃

—

Dic₇₃

—

—

C₂×C₇₃

yes

C₂×C₇₃

yes

—

D₇₃

—

—

—

—

—

C₈×C₁₆

D₇₃

yes

characteristic, complemented

C₇₃

#11412

yes

characteristic, complemented, Sylow

#431

—

C₂×C₄×C₈

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

C₄×C₁₆

—

C₄×C₁₆

C₂×D₇₃

yes

—

#322

—

C₈²

—

C₈²

C₂×D₇₃

yes

characteristic

C₂²×C₈

—

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

C₄×D₇₃

yes

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₄×D₇₃

yes

—

C₄×C₈

C₂²×D₇₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

C₈×D₇₃

yes

—

C₂×C₈

C₂×C₄×D₇₃

yes

—

C₄²

—

C₄²

—

C₄²

C₂×C₄×D₇₃

yes

characteristic

C₁₆

—

C₁₆

—

146

—

C₂³

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

146

—

102

C₂×C₄

—

146

—

103

C₂×C₄

C₄²×D₇₃

yes

characteristic

104

C₂×C₄

C₂×C₈×D₇₃

yes

—

105

C₈

—

106

C₈

—

146

—

107

C₈

—

146

—

108

C₈

#14556597

yes

—

109

C₂²

—

146

—

110

C₂²

—

146

—

111

C₂²

C₄×C₈×D₇₃

yes

characteristic

112

C₄

—

146

—

113

C₄

—

146

—

114

C₄

#17988541

yes

—

115

C₄

#17989003

yes

—

116

C₂

—

292

—

117

C₂

#22608213

yes

characteristic

118

C₂

#22611526

yes

—

	subgroup	G/H
center, Frattini	C₄×C₈	C₂²×D₇₃
commutator, socle	C₂²×C₇₃	C₂×C₄×C₈
Fitting	C₈×C₁₆×C₇₃	C₂
prime radical	C₂²×D₇₃	C₄×C₈
cosocle	C₄×C₈×C₇₃	C₂³
hypercenter	C₈×C₁₆	D₇₃
hypocenter	C₇₃	#11412
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄×C₈ ◁ C₈×C₁₆

subgroup

G/H

center, Frattini

C₄×C₈

C₂²×D₇₃

commutator, socle

C₂²×C₇₃

C₂×C₄×C₈

Fitting

C₈×C₁₆×C₇₃

C₂

prime radical

C₂²×D₇₃

C₄×C₈

cosocle

C₄×C₈×C₇₃

C₂³

hypercenter

C₈×C₁₆

D₇₃

C₇₃

G ▷ C₂²×C₇₃ ▷ C₇₃

C₁ ◁ C₄×C₈ ◁ C₈×C₁₆

N	H ≅ G/N	type
3. #22607850	C₂	semidirect
4. #22607848	C₂	semidirect
5. C₈×C₁₆×C₇₃	C₂	semidirect
64. C₈×C₁₆	D₇₃	semidirect
65. C₇₃	#11412	semidirect

H ≅ G/N

type

3. #22607850

C₂

semidirect

4. #22607848

C₂

semidirect

5. C₈×C₁₆×C₇₃

C₂

semidirect

64. C₈×C₁₆

D₇₃

semidirect

65. C₇₃

#11412

semidirect

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

subgroup	index
#22611728	2
#22608213	2
#22607850	2
#22607848	2
C₈×C₁₆×C₇₃	2
#11412	73

subgroup

index

C₈×C₁₆×C₇₃

Subgroups — #32995020

Conjugacy classes of subgroups

Complements

Maximal subgroups