Group #21445724 — subgroups

Subgroups — #21445724

Order 7808.

220 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 105 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	C₂×#14519712	C₂	1	2	yes	maximal
2	M₁₆×Dic₆₁	C₂	1	2	yes	maximal
3	C₂×#14519687	C₂	1	1	yes	maximal, characteristic
4	#16839527	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#341	C₂	1	1	yes	maximal, characteristic
6	C₂×#11758194	C₂²	1	2	yes	—
7	C₂²×#92418	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
9	#14519712	C₄	1	8	yes	complemented
10	#14519687	—	2	2	no	—
11	#14519687	C₄	1	4	yes	—
12	C₈×Dic₆₁	—	2	2	no	—
13	C₂×M₁₆×C₆₁	C₂²	1	2	yes	—
14	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
16	C₂²×Dic₆₁	Q₈	1	2	yes	—
17	M₁₆×C₆₁	—	2	2	no	—
18	M₁₆×C₆₁	C₂×C₄	1	4	yes	—
19	C₂×C₈×C₆₁	—	2	2	no	—
20	C₂×C₈×C₆₁	—	2	2	no	—
21	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
22	C₄×Dic₆₁	C₂×C₄	1	2	yes	—
23	C₄×Dic₆₁	D₄	1	2	yes	—
24	#11758194	—	2	2	no	—
25	#11758194	C₂×C₄	1	4	yes	—
26	C₂×#92418	—	2	2	no	—
27	C₂×#92418	C₂×C₄	1	2	yes	—
28	C₂×#92418	C₂×C₄	1	4	yes	—
29	C₂³×C₆₁	C₂×Q₈	1	1	yes	characteristic
30	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₆₁	C₂²×C₄	1	2	yes	—
32	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₆₁	#41	1	2	yes	—
34	C₂×Dic₆₁	—	4	2	no	—
35	C₂×Dic₆₁	C₄⋊C₄	1	4	yes	—
36	C₈×C₆₁	—	2	2	no	—
37	C₈×C₆₁	—	2	4	no	—
38	#92418	—	2	4	no	—
39	#92418	C₄²	1	4	yes	—
40	C₂²×C₆₁	—	2	2	no	—
41	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
42	C₂²×C₆₁	C₄×Q₈	1	2	yes	—
43	C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
44	C₄×C₆₁	#117	1	1	yes	characteristic
45	C₄×C₆₁	C₄×D₄	1	2	yes	—
46	Dic₆₁	—	2	4	no	—
47	#1778	—	61	1	no	maximal, Sylow
48	C₂×C₆₁	—	2	2	no	—
49	C₂×C₆₁	C₄×C₄⋊C₄	1	1	yes	characteristic
50	C₂×C₆₁	#430	1	2	yes	—
51	C₂×#108	—	61	2	no	—
52	C₄×M₁₆	—	61	2	no	—
53	C₂×#97	—	61	1	no	—
54	#341	—	61	1	no	—
55	#341	D₆₁	1	1	yes	characteristic
56	C₆₁	#1778	1	1	yes	characteristic, complemented, Sylow
57	C₂×M₁₆	—	61	2	no	—
58	C₂×M₁₆	C₂×D₆₁	1	2	yes	—
59	C₂²×C₈	—	61	1	no	—
60	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
61	C₂×C₄²	—	61	1	no	—
62	#108	—	61	8	no	—
63	#97	—	61	4	no	—
64	#97	—	122	2	no	—
65	C₄×C₈	—	122	2	no	—
66	C₂²×C₄	—	61	2	no	—
67	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
68	M₁₆	—	2	2	no	—
69	M₁₆	—	61	4	no	—
70	M₁₆	—	122	2	no	—
71	M₁₆	C₄×D₆₁	1	4	yes	—
72	C₂×C₈	—	2	2	no	—
73	C₂×C₈	—	2	2	no	—
74	C₂×C₈	—	61	2	no	—
75	C₂×C₈	—	61	4	no	—
76	C₂×C₈	—	122	2	no	—
77	C₂×C₈	C₄×D₆₁	1	2	yes	—
78	C₄²	—	61	2	no	—
79	C₄²	—	61	2	no	—
80	C₂³	Q₈×D₆₁	1	1	yes	characteristic
81	C₂×C₄	—	61	4	no	—
82	C₂×C₄	—	244	2	no	—
83	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
84	C₂×C₄	C₂×C₄×D₆₁	1	2	yes	—
85	C₂×C₄	D₄×D₆₁	1	1	yes	characteristic
86	C₂×C₄	#11758224	1	2	yes	—
87	C₈	—	2	2	no	—
88	C₈	—	2	4	no	—
89	C₈	—	61	4	no	—
90	C₈	—	122	4	no	—
91	C₂²	—	2	2	no	—
92	C₂²	C₄⋊C₄×D₆₁	1	1	yes	characteristic
93	C₂²	#14519742	1	2	yes	—
94	C₄	—	122	4	no	—
95	C₄	C₄²×D₆₁	1	1	yes	characteristic
96	C₄	#14519733	1	1	yes	characteristic
97	C₄	#14519737	1	2	yes	—
98	C₂	—	2	2	no	—
99	C₂	#16839613	1	1	yes	characteristic
100	C₂	#16839809	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519712

C₂

yes

maximal

M₁₆×Dic₆₁

C₂

yes

maximal

C₂×#14519687

C₂

yes

maximal, characteristic

#16839527

C₂

yes

maximal, characteristic

C₆₁×#341

C₂

yes

maximal, characteristic

C₂×#11758194

C₂²

yes

—

C₂²×#92418

C₂²

yes

characteristic

C₂×C₄×Dic₆₁

C₂²

yes

characteristic

#14519712

C₄

yes

complemented

#14519687

—

#14519687

C₄

yes

—

C₈×Dic₆₁

—

C₂×M₁₆×C₆₁

C₂²

yes

—

C₂²×C₈×C₆₁

C₂²

yes

characteristic

C₂²×C₄×C₆₁

C₂³

yes

characteristic

C₂²×Dic₆₁

Q₈

yes

—

M₁₆×C₆₁

—

M₁₆×C₆₁

C₂×C₄

yes

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₄×Dic₆₁

C₂×C₄

yes

—

C₄×Dic₆₁

D₄

yes

—

#11758194

—

#11758194

C₂×C₄

yes

—

C₂×#92418

—

C₂×#92418

C₂×C₄

yes

—

C₂×#92418

C₂×C₄

yes

—

C₂³×C₆₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

#41

yes

—

C₂×Dic₆₁

—

C₂×Dic₆₁

C₄⋊C₄

yes

—

C₈×C₆₁

—

C₈×C₆₁

—

#92418

—

#92418

C₄²

yes

—

C₂²×C₆₁

—

C₂²×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₆₁

C₄×Q₈

yes

—

C₄×C₆₁

C₂×C₄²

yes

characteristic

C₄×C₆₁

#117

yes

characteristic

C₄×C₆₁

C₄×D₄

yes

—

Dic₆₁

—

#1778

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

C₄×C₄⋊C₄

yes

characteristic

C₂×C₆₁

#430

yes

—

C₂×#108

—

C₄×M₁₆

—

C₂×#97

—

#341

—

#341

D₆₁

yes

characteristic

C₆₁

#1778

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

C₂×D₆₁

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₆₁

yes

characteristic

C₂×C₄²

—

#108

—

#97

—

#97

—

122

—

C₄×C₈

—

122

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₆₁

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

122

—

M₁₆

C₄×D₆₁

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

C₄×D₆₁

yes

—

C₄²

—

C₄²

—

C₂³

Q₈×D₆₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

244

—

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

C₂×C₄

C₂×C₄×D₆₁

yes

—

C₂×C₄

D₄×D₆₁

yes

characteristic

C₂×C₄

#11758224

yes

—

C₈

—

C₈

—

C₈

—

C₈

—

122

—

C₂²

—

C₂²

C₄⋊C₄×D₆₁

yes

characteristic

C₂²

#14519742

yes

—

C₄

—

122

—

C₄

C₄²×D₆₁

yes

C₄

yes

C₄

yes

—

C₂

—

C₂

#16839613

yes

characteristic

100

C₂

#16839809

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₆₁
commutator	C₄×C₆₁	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₆₁×#341	C₂
socle	C₂²×C₆₁	C₂×C₄⋊C₄
hypercenter	#341	D₆₁
hypocenter	C₆₁	#1778
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #341

subgroup

G/H

center

C₂×C₄

D₄×D₆₁

commutator

C₄×C₆₁

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₆₁

Fitting

C₆₁×#341

C₂

socle

C₂²×C₆₁

C₂×C₄⋊C₄

D₆₁

C₆₁

G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #341

N	H ≅ G/N	type
9. #14519712	C₄	semidirect
56. C₆₁	#1778	semidirect

H ≅ G/N

type

9. #14519712

C₄

semidirect

56. C₆₁

#1778

semidirect

Subgroups — #21445724

Conjugacy classes of subgroups

Complements