Group #21443775 — subgroups

Subgroups — #21443775

Order 7808.

110 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 47 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	C₈×D₂₄₄	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#11758185	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₈×D₆₁	—	2	1	no	—
5	C₄×D₂₄₄	C₄	1	1	yes	characteristic
6	C₂×#11758185	—	2	1	no	—
7	C₄⋊#92418	C₄	1	1	yes	characteristic
8	#14519689	—	2	1	no	—
9	C₂×C₁₆×C₆₁	—	2	1	no	—
10	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
11	C₂×D₂₄₄	C₈	1	1	yes	characteristic
12	C₂×C₄×D₆₁	—	2	1	no	—
13	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
14	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
15	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
16	#11758198	—	2	1	no	—
17	C₄⋊Dic₆₁	C₈	1	1	yes	characteristic
18	C₂×#92418	—	2	1	no	—
19	C₈×D₆₁	—	4	1	no	—
20	C₈×D₆₁	—	4	1	no	—
21	C₁₆×C₆₁	—	2	2	no	—
22	#11758185	—	4	1	no	—
23	C₂²×D₆₁	—	2	1	no	—
24	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
26	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
27	C₂×Dic₆₁	—	2	1	no	—
28	D₂₄₄	—	2	1	no	—
29	D₂₄₄	C₁₆	1	2	yes	complemented
30	C₄×D₆₁	—	4	1	no	—
31	C₄×D₆₁	—	4	1	no	—
32	C₈×C₆₁	—	2	1	no	—
33	C₈×C₆₁	D₈	1	1	yes	characteristic
34	C₈×C₆₁	SD₁₆	1	1	yes	characteristic
35	#92418	—	4	1	no	—
36	C₂²×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
37	C₂×D₆₁	—	2	2	no	—
38	C₂×D₆₁	—	4	1	no	—
39	C₂×D₆₁	—	4	1	no	—
40	C₄×C₆₁	—	2	1	no	—
41	C₄×C₆₁	#102	1	1	yes	characteristic
42	C₄×C₆₁	#104	1	1	yes	characteristic
43	C₄×C₆₁	C₂×C₁₆	1	1	yes	characteristic
44	C₄×C₆₁	M₃₂	1	1	yes	characteristic
45	Dic₆₁	—	4	1	no	—
46	D₄⋊C₁₆	—	61	1	no	maximal, Sylow
47	C₂×C₆₁	D₄⋊C₈	1	1	yes	characteristic
48	C₂×C₆₁	C₂²⋊C₁₆	1	1	yes	characteristic
49	C₂×C₆₁	#350	1	1	yes	characteristic
50	D₆₁	—	4	2	no	—
51	C₈×D₄	—	61	1	no	—
52	C₄⋊C₁₆	—	61	1	no	—
53	C₄×C₁₆	D₆₁	1	1	yes	characteristic, complemented
54	C₆₁	D₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₈	—	122	1	no	—
56	C₄×D₄	—	61	1	no	—
57	C₂×C₁₆	—	2	1	no	—
58	C₂×C₁₆	—	122	1	no	—
59	C₄⋊C₈	—	61	1	no	—
60	C₂²⋊C₈	—	122	1	no	—
61	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
62	C₂×D₄	—	61	1	no	—
63	C₂²×C₄	—	122	1	no	—
64	C₂×C₈	—	122	1	no	—
65	C₂×C₈	—	244	1	no	—
66	C₂×C₈	—	244	1	no	—
67	C₂×C₈	D₂₄₄	1	1	yes	characteristic
68	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
69	C₄⋊C₄	—	61	1	no	—
70	C₂²⋊C₄	—	122	1	no	—
71	C₄²	C₄×D₆₁	1	1	yes	characteristic
72	C₁₆	—	2	2	no	—
73	C₁₆	—	244	1	no	—
74	C₂³	—	122	1	no	—
75	D₄	—	61	2	no	—
76	D₄	—	122	1	no	—
77	C₂×C₄	—	122	1	no	—
78	C₂×C₄	—	244	1	no	—
79	C₂×C₄	—	244	1	no	—
80	C₂×C₄	C₈×D₆₁	1	1	yes	characteristic
81	C₂×C₄	#11758189	1	1	yes	characteristic
82	C₂×C₄	#11758198	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	244	1	no	—
85	C₈	#11758190	1	1	yes	characteristic
86	C₈	D₄₈₈	1	1	yes	characteristic
87	C₂²	—	122	2	no	—
88	C₂²	—	244	1	no	—
89	C₂²	—	244	1	no	—
90	C₂²	#14519689	1	1	yes	characteristic
91	C₄	—	2	1	no	—
92	C₄	—	244	1	no	—
93	C₄	#14519699	1	1	yes	characteristic
94	C₄	#14519705	1	1	yes	characteristic
95	C₄	C₁₆×D₆₁	1	1	yes	characteristic
96	C₄	#14519716	1	1	yes	characteristic
97	C₂	—	244	2	no	—
98	C₂	#16839491	1	1	yes	characteristic
99	C₂	#16839541	1	1	yes	characteristic
100	C₂	#16839545	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₈×D₂₄₄

C₂

yes

maximal, characteristic

C₄⋊#11758185

C₂

yes

maximal, characteristic, complemented

C₄×C₁₆×C₆₁

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₆₁

—

C₄×D₂₄₄

C₄

yes

characteristic

C₂×#11758185

—

C₄⋊#92418

C₄

yes

characteristic

#14519689

—

C₂×C₁₆×C₆₁

—

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₂×D₂₄₄

C₈

yes

characteristic

C₂×C₄×D₆₁

—

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

D₄

yes

characteristic

C₄²×C₆₁

C₂×C₄

yes

characteristic

#11758198

—

C₄⋊Dic₆₁

C₈

yes

characteristic

C₂×#92418

—

C₈×D₆₁

—

C₈×D₆₁

—

C₁₆×C₆₁

—

#11758185

—

C₂²×D₆₁

—

C₂×C₄×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

M₁₆

yes

characteristic

C₂×Dic₆₁

—

D₂₄₄

—

D₂₄₄

C₁₆

yes

complemented

C₄×D₆₁

—

C₄×D₆₁

—

C₈×C₆₁

—

C₈×C₆₁

D₈

yes

characteristic

C₈×C₆₁

SD₁₆

yes

characteristic

#92418

—

C₂²×C₆₁

C₂²⋊C₈

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

—

C₄×C₆₁

yes

C₄×C₆₁

yes

C₄×C₆₁

C₂×C₁₆

yes

characteristic

C₄×C₆₁

M₃₂

yes

characteristic

Dic₆₁

—

D₄⋊C₁₆

—

maximal, Sylow

C₂×C₆₁

D₄⋊C₈

yes

characteristic

C₂×C₆₁

C₂²⋊C₁₆

yes

characteristic

C₂×C₆₁

#350

yes

characteristic

D₆₁

—

C₈×D₄

—

C₄⋊C₁₆

—

C₄×C₁₆

D₆₁

yes

characteristic, complemented

C₆₁

D₄⋊C₁₆

yes

characteristic, complemented, Sylow

C₂²×C₈

—

122

—

C₄×D₄

—

C₂×C₁₆

—

C₂×C₁₆

—

122

—

C₄⋊C₈

—

C₂²⋊C₈

—

122

—

C₄×C₈

C₂×D₆₁

yes

characteristic

C₂×D₄

—

C₂²×C₄

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

244

—

C₂×C₈

—

244

—

C₂×C₈

D₂₄₄

yes

characteristic

C₂×C₈

C₂²⋊D₆₁

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

122

—

C₄²

C₄×D₆₁

yes

characteristic

C₁₆

—

C₁₆

—

244

—

C₂³

—

122

—

D₄

—

D₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

C₈×D₆₁

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

C₈

—

244

—

C₈

#11758190

yes

characteristic

C₈

D₄₈₈

yes

characteristic

C₂²

—

122

—

C₂²

—

244

—

C₂²

—

244

—

C₂²

#14519689

yes

characteristic

C₄

—

C₄

—

244

—

C₄

yes

C₄

yes

C₄

C₁₆×D₆₁

yes

characteristic

C₄

#14519716

yes

characteristic

C₂

—

244

—

C₂

yes

C₂

yes

100

C₂

#16839545

yes

characteristic

	subgroup	G/H
center	C₂×C₈	D₂₄₄
commutator	C₄×C₆₁	C₂×C₁₆
Frattini	C₄×C₈	C₂×D₆₁
Fitting	C₄×C₁₆×C₆₁	C₂
socle	C₂²×C₆₁	C₂²⋊C₈
hypercenter	C₄×C₁₆	D₆₁
hypocenter	C₆₁	D₄⋊C₁₆
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆

subgroup

G/H

center

C₂×C₈

D₂₄₄

commutator

C₄×C₆₁

C₂×C₁₆

Frattini

C₄×C₈

C₂×D₆₁

Fitting

C₄×C₁₆×C₆₁

C₂

socle

C₂²×C₆₁

C₂²⋊C₈

hypercenter

C₄×C₁₆

D₆₁

hypocenter

C₆₁

D₄⋊C₁₆

LCS

G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆

N	H ≅ G/N	type
2. C₄⋊#11758185	C₂	semidirect
3. C₄×C₁₆×C₆₁	C₂	semidirect
29. D₂₄₄	C₁₆	semidirect
53. C₄×C₁₆	D₆₁	semidirect
54. C₆₁	D₄⋊C₁₆	semidirect

H ≅ G/N

type

2. C₄⋊#11758185

C₂

semidirect

3. C₄×C₁₆×C₆₁

C₂

semidirect

29. D₂₄₄

C₁₆

semidirect

53. C₄×C₁₆

D₆₁

semidirect

54. C₆₁

D₄⋊C₁₆

semidirect

Subgroups — #21443775

Conjugacy classes of subgroups

Complements