Group #35298132 — subgroups

Subgroups — #35298132

Order 21248.

258 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 99 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	#24905308	C₂	1	2	yes	maximal
2	#24905296	C₂	1	2	yes	maximal
3	#24905294	C₂	1	2	yes	maximal
4	C₈₃×#1745	C₂	1	1	yes	maximal, characteristic
5	#19127754	C₂²	1	4	yes	—
6	C₂×#97×C₈₃	C₂²	1	1	yes	characteristic
7	C₂×#97×C₈₃	C₂²	1	1	yes	characteristic
8	C₄³×C₈₃	C₂²	1	1	yes	characteristic
9	#336×C₈₃	C₄	1	4	yes	—
10	C₄⋊(C₈₃⋊C₈)	—	2	4	no	—
11	C₂²⋊(C₈₃⋊C₈)	—	2	4	no	—
12	C₄×C₈₃⋊C₈	—	2	4	no	—
13	C₂²×C₈×C₈₃	C₂×C₄	1	2	yes	—
14	C₂²×C₈×C₈₃	C₂×C₄	1	2	yes	—
15	C₂×C₄²×C₈₃	—	2	2	no	—
16	C₂×C₄²×C₈₃	C₂×C₄	1	2	yes	—
17	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
18	#97×C₈₃	—	2	2	no	—
19	#97×C₈₃	—	2	2	no	—
20	C₂×C₈₃⋊C₈	—	4	4	no	—
21	C₂²×C₄×C₈₃	—	2	2	no	—
22	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
23	C₂²×C₄×C₈₃	#41	1	2	yes	—
24	C₂×C₈×C₈₃	—	2	2	no	—
25	C₂×C₈×C₈₃	—	2	2	no	—
26	C₂×C₈×C₈₃	—	2	4	no	—
27	C₂×C₈×C₈₃	—	2	4	no	—
28	C₄²×C₈₃	—	2	4	no	—
29	C₄²×C₈₃	—	4	4	no	—
30	C₄²×C₈₃	#41	1	2	yes	—
31	C₄²×C₈₃	#41	1	2	yes	—
32	C₂³×C₈₃	#117	1	1	yes	characteristic
33	C₂×C₄×C₈₃	—	2	4	no	—
34	C₂×C₄×C₈₃	—	4	2	no	—
35	C₂×C₄×C₈₃	—	4	2	no	—
36	C₂×C₄×C₈₃	—	4	2	no	—
37	C₂×C₄×C₈₃	#117	1	1	yes	characteristic
38	C₂×C₄×C₈₃	#117	1	1	yes	characteristic
39	C₂×C₄×C₈₃	#126	1	4	yes	—
40	C₂×C₄×C₈₃	#131	1	4	yes	—
41	C₈×C₈₃	—	4	2	no	—
42	C₈×C₈₃	—	4	2	no	—
43	C₈₃⋊C₈	—	8	4	no	—
44	C₂²×C₈₃	—	2	2	no	—
45	C₂²×C₈₃	#383	1	1	yes	characteristic
46	C₂²×C₈₃	#433	1	2	yes	—
47	C₄×C₈₃	—	2	4	no	—
48	C₄×C₈₃	—	4	4	no	—
49	C₄×C₈₃	#433	1	2	yes	—
50	C₄×C₈₃	#433	1	2	yes	—
51	#8802	—	83	1	no	maximal, Sylow
52	C₂×C₈₃	—	2	2	no	—
53	C₂×C₈₃	#1840	1	1	yes	characteristic
54	C₂×C₈₃	#1841	1	2	yes	—
55	#1745	D₈₃	1	1	yes	characteristic
56	#1281	—	83	2	no	—
57	#1276	—	83	2	no	—
58	#1275	—	83	2	no	—
59	C₈₃	#8802	1	1	yes	characteristic, complemented, Sylow
60	#431	—	83	4	no	—
61	C₂×#97	C₂×D₈₃	1	1	yes	characteristic
62	C₂×#97	C₂×D₈₃	1	1	yes	characteristic
63	C₄³	C₂×D₈₃	1	1	yes	characteristic
64	#336	Dic₈₃	1	4	yes	—
65	C₂²×C₈	C₂×Dic₈₃	1	2	yes	—
66	C₂²×C₈	C₂×Dic₈₃	1	2	yes	—
67	C₂×C₄²	—	2	2	no	—
68	C₂×C₄²	C₂×Dic₈₃	1	2	yes	—
69	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
70	C₄⋊C₈	—	166	4	no	—
71	C₂²⋊C₈	—	166	4	no	—
72	#97	—	2	2	no	—
73	#97	—	2	2	no	—
74	C₄×C₈	—	166	4	no	—
75	C₂²×C₄	—	2	2	no	—
76	C₂²×C₄	C₂²×Dic₈₃	1	1	yes	characteristic
77	C₂²×C₄	#13050590	1	2	yes	—
78	C₂×C₈	—	2	4	no	—
79	C₂×C₈	—	2	4	no	—
80	C₂×C₈	—	2	2	no	—
81	C₂×C₈	—	2	2	no	—
82	C₂×C₈	—	332	4	no	—
83	C₄²	—	2	4	no	—
84	C₄²	—	4	4	no	—
85	C₄²	#13050590	1	2	yes	—
86	C₄²	#13050590	1	2	yes	—
87	C₂³	#14581751	1	1	yes	characteristic
88	C₂×C₄	—	2	4	no	—
89	C₂×C₄	—	4	2	no	—
90	C₂×C₄	—	4	2	no	—
91	C₂×C₄	—	4	2	no	—
92	C₂×C₄	#14581751	1	1	yes	characteristic
93	C₂×C₄	#14581751	1	1	yes	characteristic
94	C₂×C₄	#14581786	1	4	yes	—
95	C₂×C₄	#14581799	1	4	yes	—
96	C₈	—	4	2	no	—
97	C₈	—	4	2	no	—
98	C₈	—	664	4	no	—
99	C₂²	—	2	2	no	—
100	C₂²	#19127569	1	1	yes	characteristic
101	C₂²	#19127762	1	2	yes	—
102	C₄	—	2	4	no	—
103	C₄	—	4	4	no	—
104	C₄	#19127762	1	2	yes	—
105	C₄	#19127762	1	2	yes	—
106	C₂	—	2	2	no	—
107	C₂	#24907608	1	1	yes	characteristic
108	C₂	#24907612	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#24905308

C₂

yes

maximal

#24905296

C₂

yes

maximal

#24905294

C₂

yes

maximal

C₈₃×#1745

C₂

yes

maximal, characteristic

#19127754

C₂²

yes

—

C₂×#97×C₈₃

C₂²

yes

characteristic

C₂×#97×C₈₃

C₂²

yes

characteristic

C₄³×C₈₃

C₂²

yes

characteristic

#336×C₈₃

C₄

yes

—

C₄⋊(C₈₃⋊C₈)

—

C₂²⋊(C₈₃⋊C₈)

—

C₄×C₈₃⋊C₈

—

C₂²×C₈×C₈₃

C₂×C₄

yes

—

C₂²×C₈×C₈₃

C₂×C₄

yes

—

C₂×C₄²×C₈₃

—

C₂×C₄²×C₈₃

C₂×C₄

yes

—

C₂×C₄²×C₈₃

C₂³

yes

characteristic

#97×C₈₃

—

#97×C₈₃

—

C₂×C₈₃⋊C₈

—

C₂²×C₄×C₈₃

—

C₂²×C₄×C₈₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₈₃

#41

yes

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₄²×C₈₃

—

C₄²×C₈₃

—

C₄²×C₈₃

#41

yes

—

C₄²×C₈₃

#41

yes

—

C₂³×C₈₃

#117

yes

characteristic

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

yes

—

C₂×C₄×C₈₃

#131

yes

—

C₈×C₈₃

—

C₈×C₈₃

—

C₈₃⋊C₈

—

C₂²×C₈₃

—

C₂²×C₈₃

#383

yes

characteristic

C₂²×C₈₃

#433

yes

—

C₄×C₈₃

—

C₄×C₈₃

—

C₄×C₈₃

#433

yes

—

C₄×C₈₃

#433

yes

—

#8802

—

maximal, Sylow

C₂×C₈₃

—

C₂×C₈₃

#1840

yes

characteristic

C₂×C₈₃

#1841

yes

—

#1745

D₈₃

yes

—

—

—

C₈₃

#8802

yes

characteristic, complemented, Sylow

#431

—

C₂×#97

C₂×D₈₃

yes

characteristic

C₂×#97

C₂×D₈₃

yes

characteristic

C₄³

C₂×D₈₃

yes

characteristic

#336

Dic₈₃

yes

—

C₂²×C₈

C₂×Dic₈₃

yes

—

C₂²×C₈

C₂×Dic₈₃

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×Dic₈₃

yes

—

C₂×C₄²

C₂²×D₈₃

yes

characteristic

C₄⋊C₈

—

166

—

C₂²⋊C₈

—

166

—

#97

—

#97

—

C₄×C₈

—

166

—

C₂²×C₄

—

C₂²×C₄

C₂²×Dic₈₃

yes

characteristic

C₂²×C₄

#13050590

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

332

—

C₄²

—

C₄²

—

C₄²

#13050590

yes

—

C₄²

#13050590

yes

—

C₂³

#14581751

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

—

C₂×C₄

#14581799

yes

—

C₈

—

C₈

—

C₈

—

664

—

C₂²

—

100

C₂²

#19127569

yes

characteristic

101

C₂²

#19127762

yes

—

102

C₄

—

103

C₄

—

104

C₄

#19127762

yes

—

105

C₄

#19127762

yes

—

106

C₂

—

107

C₂

#24907608

yes

characteristic

108

C₂

#24907612

yes

—

	subgroup	G/H
center	C₂×C₄	#14581751
commutator	C₂²×C₄×C₈₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₃
Fitting	C₈₃×#1745	C₂
socle	C₂²×C₈₃	#383
prime radical	C₂³×C₈₃	#117
cosocle	C₂×C₄²×C₈₃	C₂³
hypercenter	#1745	D₈₃
hypocenter	C₈₃	#8802
LCS	G ▷ C₂²×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97 ◁ #1745

subgroup

G/H

center

C₂×C₄

#14581751

commutator

C₂²×C₄×C₈₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₈₃

Fitting

C₈₃×#1745

C₂

C₂²×C₈₃

C₂³×C₈₃

C₂×C₄²×C₈₃

C₂³

D₈₃

C₈₃

G ▷ C₂²×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×#97 ◁ #1745

N	H ≅ G/N	type
59. C₈₃	#8802	semidirect

H ≅ G/N

type

59. C₈₃

#8802

semidirect

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

subgroup	index
#24905308	2
#24905296	2
#24905294	2
C₈₃×#1745	2
#8802	83

subgroup

index

C₈₃×#1745

Subgroups — #35298132

Conjugacy classes of subgroups

Complements

Maximal subgroups