Group #21447393 — subgroups

Subgroups — #21447393

Order 7808.

158 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 59 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	#16839785	C₂	1	1	yes	maximal, characteristic
2	#16839533	C₂	1	2	yes	maximal
3	#16839523	C₂	1	2	yes	maximal
4	#16839519	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#430	C₂	1	1	yes	maximal, characteristic
6	C₂×#11758194	C₂²	1	1	yes	characteristic
7	#14519736	C₂²	1	2	yes	—
8	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
9	#14519706	—	2	2	no	—
10	C₂×M₁₆×C₆₁	C₂²	1	2	yes	—
11	C₂×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
12	#108×C₆₁	—	2	2	no	—
13	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
14	C₂²×Dic₆₁	—	2	1	no	—
15	M₁₆×C₆₁	—	2	2	no	—
16	M₁₆×C₆₁	—	2	2	no	—
17	M₁₆×C₆₁	—	2	2	no	—
18	C₂×C₈×C₆₁	—	2	2	no	—
19	C₂×C₈×C₆₁	D₄	1	2	yes	—
20	C₂²⋊Dic₆₁	—	2	2	no	—
21	C₄⋊Dic₆₁	—	2	2	no	—
22	C₄×Dic₆₁	—	2	1	no	—
23	C₄×Dic₆₁	—	2	2	no	—
24	C₄×Dic₆₁	Q₈	1	1	yes	characteristic
25	C₄×Dic₆₁	Q₈	1	1	yes	characteristic
26	#11758194	—	2	2	no	—
27	C₂×#92418	—	2	1	no	—
28	C₂³×C₆₁	#41	1	1	yes	characteristic
29	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
31	C₂×C₄×C₆₁	#41	1	2	yes	—
32	C₂×C₄×C₆₁	#41	1	2	yes	—
33	C₂×Dic₆₁	—	2	1	no	—
34	C₂×Dic₆₁	—	2	1	no	—
35	C₂×Dic₆₁	—	4	2	no	—
36	C₂×Dic₆₁	—	4	2	no	—
37	C₈×C₆₁	—	2	2	no	—
38	C₈×C₆₁	—	4	2	no	—
39	#92418	—	4	1	no	—
40	C₂²×C₆₁	—	4	1	no	—
41	C₂²×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
42	C₂²×C₆₁	#126	1	2	yes	—
43	C₄×C₆₁	#123	1	1	yes	characteristic
44	C₄×C₆₁	#124	1	1	yes	characteristic
45	C₄×C₆₁	#125	1	2	yes	—
46	Dic₆₁	—	2	2	no	—
47	Dic₆₁	—	4	1	no	—
48	Dic₆₁	—	8	2	no	—
49	#2102	—	61	1	no	maximal, Sylow
50	C₂×C₆₁	—	2	1	no	—
51	C₂×C₆₁	—	2	2	no	—
52	C₂×C₆₁	#400	1	1	yes	characteristic
53	#430	D₆₁	1	1	yes	characteristic
54	#423	—	61	1	no	—
55	#344	—	61	2	no	—
56	#339	—	61	2	no	—
57	H(3,ℤ/4)	—	61	1	no	—
58	C₆₁	#2102	1	1	yes	characteristic, complemented, Sylow
59	C₂×M₁₆	—	61	1	no	—
60	C₂×M₁₆	C₂×D₆₁	1	2	yes	—
61	C₂×M₁₆	C₂×D₆₁	1	1	yes	characteristic
62	#117	—	61	2	no	—
63	C₂×C₄²	—	61	1	no	—
64	#108	—	2	2	no	—
65	C₄⋊C₈	—	122	2	no	—
66	C₂²×C₄	—	122	1	no	—
67	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
68	M₁₆	—	2	2	no	—
69	M₁₆	—	2	2	no	—
70	M₁₆	—	2	2	no	—
71	M₁₆	—	122	2	no	—
72	C₂×C₈	—	2	2	no	—
73	C₂×C₈	—	122	1	no	—
74	C₂×C₈	C₂²⋊D₆₁	1	2	yes	—
75	C₄⋊C₄	—	122	2	no	—
76	C₂²⋊C₄	—	122	2	no	—
77	C₄²	—	61	1	no	—
78	C₄²	—	61	1	no	—
79	C₄²	—	122	1	no	—
80	C₄²	—	122	2	no	—
81	C₂³	#11758226	1	1	yes	characteristic
82	C₂×C₄	—	122	1	no	—
83	C₂×C₄	—	122	1	no	—
84	C₂×C₄	—	244	2	no	—
85	C₂×C₄	—	244	2	no	—
86	C₂×C₄	#11758222	1	2	yes	—
87	C₂×C₄	#11758224	1	2	yes	—
88	C₂×C₄	Q₈×D₆₁	1	1	yes	characteristic
89	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
90	C₈	—	2	2	no	—
91	C₈	—	4	2	no	—
92	C₈	—	244	1	no	—
93	C₂²	—	4	1	no	—
94	C₂²	#14519753	1	1	yes	characteristic
95	C₂²	#14519772	1	2	yes	—
96	C₄	—	122	2	no	—
97	C₄	—	488	2	no	—
98	C₄	—	244	1	no	—
99	C₄	#14519760	1	1	yes	characteristic
100	C₄	#14519764	1	1	yes	characteristic
101	C₄	#14519767	1	2	yes	—
102	C₂	—	2	1	no	—
103	C₂	—	2	2	no	—
104	C₂	#16839700	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16839785

C₂

yes

maximal, characteristic

#16839533

C₂

yes

maximal

#16839523

C₂

yes

maximal

#16839519

C₂

yes

maximal, characteristic

C₆₁×#430

C₂

yes

maximal, characteristic

C₂×#11758194

C₂²

yes

characteristic

#14519736

C₂²

yes

—

C₂×C₄×Dic₆₁

C₂²

yes

characteristic

#14519706

—

C₂×M₁₆×C₆₁

C₂²

yes

—

C₂×M₁₆×C₆₁

C₂²

yes

characteristic

#108×C₆₁

—

C₂²×C₄×C₆₁

C₂³

yes

characteristic

C₂²×Dic₆₁

—

M₁₆×C₆₁

—

M₁₆×C₆₁

—

M₁₆×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

D₄

yes

—

C₂²⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄×Dic₆₁

—

C₄×Dic₆₁

—

C₄×Dic₆₁

Q₈

yes

characteristic

C₄×Dic₆₁

Q₈

yes

characteristic

#11758194

—

C₂×#92418

—

C₂³×C₆₁

#41

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₆₁

#41

yes

—

C₂×C₄×C₆₁

#41

yes

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₈×C₆₁

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

C₂²⋊Q₈

yes

characteristic

C₂²×C₆₁

#126

yes

—

C₄×C₆₁

yes

C₄×C₆₁

yes

C₄×C₆₁

yes

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

—

#2102

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

#400

yes

characteristic

#430

D₆₁

yes

—

—

—

—

C₆₁

#2102

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

C₂×D₆₁

yes

—

C₂×M₁₆

C₂×D₆₁

yes

characteristic

#117

—

C₂×C₄²

—

#108

—

C₄⋊C₈

—

122

—

C₂²×C₄

—

122

—

C₂²×C₄

C₂²×D₆₁

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

C₂²⋊D₆₁

yes

—

C₄⋊C₄

—

122

—

C₂²⋊C₄

—

122

—

C₄²

—

C₄²

—

C₄²

—

122

—

C₄²

—

122

—

C₂³

#11758226

yes

characteristic

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

#11758222

yes

—

C₂×C₄

#11758224

yes

—

C₂×C₄

Q₈×D₆₁

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

C₈

—

C₈

—

C₈

—

244

—

C₂²

—

C₂²

#14519753

yes

characteristic

C₂²

#14519772

yes

—

C₄

—

122

—

C₄

—

488

—

C₄

—

244

—

C₄

#14519760

yes

characteristic

100

C₄

#14519764

yes

characteristic

101

C₄

#14519767

yes

—

102

C₂

—

103

C₂

—

104

C₂

#16839700

yes

characteristic

	subgroup	G/H
center	C₄	#14519764
commutator	C₂²×C₄×C₆₁	C₂³
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₆₁×#430	C₂
socle	C₂×C₆₁	#400
hypercenter	#430	D₆₁
hypocenter	C₆₁	#2102
LCS	G ▷ C₂²×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #430

subgroup

G/H

center

C₄

#14519764

commutator

C₂²×C₄×C₆₁

C₂³

Frattini

C₂²×C₄

C₂²×D₆₁

Fitting

C₆₁×#430

C₂

C₂×C₆₁

D₆₁

C₆₁

G ▷ C₂²×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #430

N	H ≅ G/N	type
58. C₆₁	#2102	semidirect

H ≅ G/N

type

58. C₆₁

#2102

semidirect

Subgroups — #21447393

Conjugacy classes of subgroups

Complements