Group #29573741 — subgroups

Subgroups — #29573741

Order 15616.

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	#21443664	C₂	1	2	yes	maximal
2	#21443652	C₂	1	2	yes	maximal
3	#21443650	C₂	1	2	yes	maximal
4	C₆₁×#1745	C₂	1	1	yes	maximal, characteristic
5	#16839815	C₂²	1	4	yes	—
6	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
7	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
8	C₄³×C₆₁	C₂²	1	1	yes	characteristic
9	C₆₁×#336	C₄	1	4	yes	—
10	C₄⋊#92418	—	2	4	no	—
11	C₂²⋊#92418	—	2	4	no	—
12	C₄×#92418	—	2	4	no	—
13	C₂²×C₈×C₆₁	C₂×C₄	1	2	yes	—
14	C₂²×C₈×C₆₁	C₂×C₄	1	2	yes	—
15	C₂×C₄²×C₆₁	—	2	2	no	—
16	C₂×C₄²×C₆₁	C₂×C₄	1	2	yes	—
17	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
18	#97×C₆₁	—	2	2	no	—
19	#97×C₆₁	—	2	2	no	—
20	C₂²×C₄×C₆₁	—	2	2	no	—
21	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
22	C₂²×C₄×C₆₁	#41	1	2	yes	—
23	C₂×C₈×C₆₁	—	2	2	no	—
24	C₂×C₈×C₆₁	—	2	2	no	—
25	C₂×C₈×C₆₁	—	2	4	no	—
26	C₂×C₈×C₆₁	—	2	4	no	—
27	C₄²×C₆₁	—	2	4	no	—
28	C₄²×C₆₁	—	4	4	no	—
29	C₄²×C₆₁	#41	1	2	yes	—
30	C₄²×C₆₁	#41	1	2	yes	—
31	C₂×#92418	—	4	4	no	—
32	C₂³×C₆₁	#117	1	1	yes	characteristic
33	C₂×C₄×C₆₁	—	2	4	no	—
34	C₂×C₄×C₆₁	—	4	2	no	—
35	C₂×C₄×C₆₁	—	4	2	no	—
36	C₂×C₄×C₆₁	—	4	2	no	—
37	C₂×C₄×C₆₁	#117	1	1	yes	characteristic
38	C₂×C₄×C₆₁	#117	1	1	yes	characteristic
39	C₂×C₄×C₆₁	#126	1	4	yes	—
40	C₂×C₄×C₆₁	#131	1	4	yes	—
41	C₈×C₆₁	—	4	2	no	—
42	C₈×C₆₁	—	4	2	no	—
43	#92418	—	8	4	no	—
44	#8802	—	61	1	no	maximal, Sylow
45	C₂²×C₆₁	—	2	2	no	—
46	C₂²×C₆₁	#383	1	1	yes	characteristic
47	C₂²×C₆₁	#433	1	2	yes	—
48	C₄×C₆₁	—	2	4	no	—
49	C₄×C₆₁	—	4	4	no	—
50	C₄×C₆₁	#433	1	2	yes	—
51	C₄×C₆₁	#433	1	2	yes	—
52	#1745	D₆₁	1	1	yes	characteristic
53	#1281	—	61	2	no	—
54	#1276	—	61	2	no	—
55	#1275	—	61	2	no	—
56	C₂×C₆₁	—	2	2	no	—
57	C₂×C₆₁	#1840	1	1	yes	characteristic
58	C₂×C₆₁	#1841	1	2	yes	—
59	#431	—	61	4	no	—
60	C₂×#97	C₂×D₆₁	1	1	yes	characteristic
61	C₂×#97	C₂×D₆₁	1	1	yes	characteristic
62	C₄³	C₂×D₆₁	1	1	yes	characteristic
63	#336	Dic₆₁	1	4	yes	—
64	C₆₁	#8802	1	1	yes	characteristic, complemented, Sylow
65	C₂²×C₈	C₂×Dic₆₁	1	2	yes	—
66	C₂²×C₈	C₂×Dic₆₁	1	2	yes	—
67	C₂×C₄²	—	2	2	no	—
68	C₂×C₄²	C₂×Dic₆₁	1	2	yes	—
69	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
70	C₄⋊C₈	—	122	4	no	—
71	C₂²⋊C₈	—	122	4	no	—
72	#97	—	2	2	no	—
73	#97	—	2	2	no	—
74	C₄×C₈	—	122	4	no	—
75	C₂²×C₄	—	2	2	no	—
76	C₂²×C₄	#11758222	1	2	yes	—
77	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
78	C₂×C₈	—	2	2	no	—
79	C₂×C₈	—	2	2	no	—
80	C₂×C₈	—	2	4	no	—
81	C₂×C₈	—	2	4	no	—
82	C₂×C₈	—	244	4	no	—
83	C₄²	—	2	4	no	—
84	C₄²	—	4	4	no	—
85	C₄²	#11758222	1	2	yes	—
86	C₄²	#11758222	1	2	yes	—
87	C₂³	#14519736	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	#14519736	1	1	yes	characteristic
93	C₂×C₄	#14519736	1	1	yes	characteristic
94	C₂×C₄	#14519771	1	4	yes	—
95	C₂×C₄	#14519784	1	4	yes	—
96	C₈	—	4	2	no	—
97	C₈	—	4	2	no	—
98	C₈	—	488	4	no	—
99	C₂²	—	2	2	no	—
100	C₂²	#16839630	1	1	yes	characteristic
101	C₂²	#16839823	1	2	yes	—
102	C₄	—	2	4	no	—
103	C₄	—	4	4	no	—
104	C₄	#16839823	1	2	yes	—
105	C₄	#16839823	1	2	yes	—
106	C₂	—	2	2	no	—
107	C₂	#21445964	1	1	yes	characteristic
108	C₂	#21445968	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#21443664

C₂

yes

maximal

#21443652

C₂

yes

maximal

#21443650

C₂

yes

maximal

C₆₁×#1745

C₂

yes

maximal, characteristic

#16839815

C₂²

yes

—

C₂×#97×C₆₁

C₂²

yes

characteristic

C₂×#97×C₆₁

C₂²

yes

characteristic

C₄³×C₆₁

C₂²

yes

characteristic

C₆₁×#336

C₄

yes

—

C₄⋊#92418

—

C₂²⋊#92418

—

C₄×#92418

—

C₂²×C₈×C₆₁

C₂×C₄

yes

—

C₂²×C₈×C₆₁

C₂×C₄

yes

—

C₂×C₄²×C₆₁

—

C₂×C₄²×C₆₁

C₂×C₄

yes

—

C₂×C₄²×C₆₁

C₂³

yes

characteristic

#97×C₆₁

—

#97×C₆₁

—

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂²×C₄×C₆₁

#41

yes

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₄²×C₆₁

—

C₄²×C₆₁

—

C₄²×C₆₁

#41

yes

—

C₄²×C₆₁

#41

yes

—

C₂×#92418

—

C₂³×C₆₁

#117

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

yes

C₂×C₄×C₆₁

yes

C₂×C₄×C₆₁

yes

—

C₂×C₄×C₆₁

#131

yes

—

C₈×C₆₁

—

C₈×C₆₁

—

#92418

—

#8802

—

maximal, Sylow

C₂²×C₆₁

—

C₂²×C₆₁

#383

yes

characteristic

C₂²×C₆₁

#433

yes

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

#433

yes

—

C₄×C₆₁

#433

yes

—

#1745

D₆₁

yes

—

—

—

C₂×C₆₁

—

C₂×C₆₁

#1840

yes

characteristic

C₂×C₆₁

#1841

yes

—

#431

—

C₂×#97

C₂×D₆₁

yes

characteristic

C₂×#97

C₂×D₆₁

yes

characteristic

C₄³

C₂×D₆₁

yes

characteristic

#336

Dic₆₁

yes

—

C₆₁

#8802

yes

characteristic, complemented, Sylow

C₂²×C₈

C₂×Dic₆₁

yes

—

C₂²×C₈

C₂×Dic₆₁

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×Dic₆₁

yes

—

C₂×C₄²

C₂²×D₆₁

yes

characteristic

C₄⋊C₈

—

122

—

C₂²⋊C₈

—

122

—

#97

—

#97

—

C₄×C₈

—

122

—

C₂²×C₄

—

C₂²×C₄

#11758222

yes

—

C₂²×C₄

C₂²×Dic₆₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

244

—

C₄²

—

C₄²

—

C₄²

#11758222

yes

—

C₄²

#11758222

yes

—

C₂³

#14519736

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

—

C₂×C₄

#14519784

yes

—

C₈

—

C₈

—

C₈

—

488

—

C₂²

—

100

C₂²

#16839630

yes

characteristic

101

C₂²

#16839823

yes

—

102

C₄

—

103

C₄

—

104

C₄

#16839823

yes

—

105

C₄

#16839823

yes

—

106

C₂

—

107

C₂

#21445964

yes

characteristic

108

C₂

#21445968

yes

—

	subgroup	G/H
center	C₂×C₄	#14519736
commutator	C₂²×C₄×C₆₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₆₁
Fitting	C₆₁×#1745	C₂
socle	C₂²×C₆₁	#383
prime radical	C₂³×C₆₁	#117
cosocle	C₂×C₄²×C₆₁	C₂³
hypercenter	#1745	D₆₁
hypocenter	C₆₁	#8802
LCS	G ▷ C₂²×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97 ◁ #1745

subgroup

G/H

center

C₂×C₄

#14519736

commutator

C₂²×C₄×C₆₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₆₁

Fitting

C₆₁×#1745

C₂

C₂²×C₆₁

C₂³×C₆₁

C₂×C₄²×C₆₁

C₂³

D₆₁

C₆₁

G ▷ C₂²×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×#97 ◁ #1745

N	H ≅ G/N	type
64. C₆₁	#8802	semidirect

H ≅ G/N

type

64. C₆₁

#8802

semidirect

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

subgroup	index
#21443664	2
#21443652	2
#21443650	2
C₆₁×#1745	2
#8802	61

subgroup

index

C₆₁×#1745

Subgroups — #29573741

Conjugacy classes of subgroups

Complements

Maximal subgroups