Group #21448080 — subgroups

Subgroups — #21448080

Order 7808.

184 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 61 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×Dic₄₈₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14519722	C₂	1	2	yes	maximal, complemented
3	C₂×D₉₇₆	C₂	1	1	yes	maximal, characteristic
4	#16840146	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₂₄₄	C₂²	1	2	yes	—
7	C₂×#11758190	—	2	2	no	—
8	C₂×D₄₈₈	C₂²	1	2	yes	—
9	#14519765	—	2	2	no	—
10	Dic₄₈₈	—	2	2	no	—
11	#14519722	—	2	4	no	—
12	D₉₇₆	—	2	2	no	—
13	C₂×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×D₂₄₄	—	2	2	no	—
17	C₂×Dic₁₂₂	—	2	2	no	—
18	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
19	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
20	C₄²×C₆₁	D₄	1	1	yes	characteristic
21	#11758198	—	4	4	no	—
22	Dic₂₄₄	—	2	2	no	—
23	Dic₂₄₄	—	2	2	no	—
24	D₄₈₈	—	2	2	no	—
25	D₄₈₈	—	2	2	no	—
26	#11758190	—	4	4	no	—
27	C₁₆×C₆₁	D₄	1	2	yes	—
28	C₁₆×C₆₁	D₄	1	2	yes	—
29	C₂²×D₆₁	—	4	2	no	—
30	C₂×C₄×C₆₁	D₈	1	2	yes	—
31	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
32	C₂×Dic₆₁	—	4	2	no	—
33	D₂₄₄	—	4	2	no	—
34	D₂₄₄	—	4	2	no	—
35	Dic₁₂₂	—	4	2	no	—
36	Dic₁₂₂	—	4	2	no	—
37	C₈×C₆₁	D₈	1	2	yes	—
38	C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
39	C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
40	C₂²×C₆₁	C₂×D₈	1	1	yes	characteristic
41	C₂×D₆₁	—	8	2	no	—
42	C₂×D₆₁	—	8	4	no	—
43	C₄×C₆₁	—	2	2	no	—
44	C₄×C₆₁	#127	1	1	yes	characteristic
45	C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
46	Dic₆₁	—	8	2	no	—
47	#2249	—	61	1	no	maximal, Sylow
48	C₂×C₆₁	#493	1	1	yes	characteristic
49	C₂×C₆₁	#508	1	2	yes	—
50	D₆₁	—	16	2	no	—
51	C₂×Q₃₂	—	61	1	no	—
52	C₂×SD₃₂	—	61	2	no	—
53	C₂×D₁₆	—	61	1	no	—
54	#495	—	61	2	no	—
55	C₄×C₁₆	D₆₁	1	1	yes	characteristic, complemented
56	C₆₁	#2249	1	1	yes	characteristic, complemented, Sylow
57	C₂×Q₁₆	—	61	2	no	—
58	C₂×SD₁₆	—	122	2	no	—
59	C₂×D₈	—	61	2	no	—
60	#124	—	122	2	no	—
61	Q₃₂	—	122	2	no	—
62	SD₃₂	—	122	4	no	—
63	D₁₆	—	122	2	no	—
64	C₂×C₁₆	C₂×D₆₁	1	1	yes	characteristic
65	C₂×C₁₆	C₂×D₆₁	1	1	yes	characteristic
66	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
67	C₂×Q₈	—	122	2	no	—
68	C₂×D₄	—	122	2	no	—
69	Q₁₆	—	122	2	no	—
70	Q₁₆	—	122	2	no	—
71	SD₁₆	—	244	4	no	—
72	D₈	—	122	2	no	—
73	D₈	—	122	2	no	—
74	C₂×C₈	D₂₄₄	1	1	yes	characteristic
75	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
76	C₂²⋊C₄	—	244	4	no	—
77	C₄²	D₂₄₄	1	1	yes	characteristic
78	C₁₆	D₂₄₄	1	2	yes	—
79	C₁₆	D₂₄₄	1	2	yes	—
80	C₂³	—	244	2	no	—
81	Q₈	—	244	2	no	—
82	Q₈	—	244	2	no	—
83	D₄	—	244	2	no	—
84	D₄	—	244	2	no	—
85	C₂×C₄	—	244	2	no	—
86	C₂×C₄	D₄₈₈	1	2	yes	—
87	C₂×C₄	C₂×D₂₄₄	1	1	yes	characteristic
88	C₈	D₄₈₈	1	2	yes	—
89	C₈	C₂×D₂₄₄	1	1	yes	characteristic
90	C₈	C₂×D₂₄₄	1	1	yes	characteristic
91	C₂²	—	488	4	no	—
92	C₂²	—	488	2	no	—
93	C₂²	C₂×D₄₈₈	1	1	yes	characteristic
94	C₄	—	2	2	no	—
95	C₄	—	488	2	no	—
96	C₄	#14519774	1	1	yes	characteristic
97	C₄	C₂×D₄₈₈	1	1	yes	characteristic
98	C₂	—	976	2	no	—
99	C₂	#16840139	1	1	yes	characteristic
100	C₂	#16840194	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₄₈₈

C₂

yes

maximal, characteristic, complemented

C₂×#14519722

C₂

yes

maximal, complemented

C₂×D₉₇₆

C₂

yes

maximal, characteristic

#16840146

C₂

yes

maximal, complemented

C₄×C₁₆×C₆₁

C₂

yes

maximal, characteristic, complemented

C₂×Dic₂₄₄

C₂²

yes

—

C₂×#11758190

—

C₂×D₄₈₈

C₂²

yes

—

#14519765

—

Dic₄₈₈

—

#14519722

—

D₉₇₆

—

C₂×C₁₆×C₆₁

C₂²

yes

characteristic

C₂×C₁₆×C₆₁

C₂²

yes

characteristic

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₂×D₂₄₄

—

C₂×Dic₁₂₂

—

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

C₂³

yes

characteristic

C₄²×C₆₁

D₄

yes

characteristic

#11758198

—

Dic₂₄₄

—

Dic₂₄₄

—

D₄₈₈

—

D₄₈₈

—

#11758190

—

C₁₆×C₆₁

D₄

yes

—

C₁₆×C₆₁

D₄

yes

—

C₂²×D₆₁

—

C₂×C₄×C₆₁

D₈

yes

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×Dic₆₁

—

D₂₄₄

—

D₂₄₄

—

Dic₁₂₂

—

Dic₁₂₂

—

C₈×C₆₁

D₈

yes

—

C₈×C₆₁

C₂×D₄

yes

characteristic

C₈×C₆₁

C₂×D₄

yes

characteristic

C₂²×C₆₁

C₂×D₈

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

—

C₄×C₆₁

#127

yes

characteristic

C₄×C₆₁

C₂×D₈

yes

characteristic

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

—

D₆₁

—

C₂×Q₃₂

—

C₂×SD₃₂

—

C₂×D₁₆

—

#495

—

C₄×C₁₆

D₆₁

yes

characteristic, complemented

C₆₁

#2249

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×SD₁₆

—

122

—

C₂×D₈

—

#124

—

122

—

Q₃₂

—

122

—

SD₃₂

—

122

—

D₁₆

—

122

—

C₂×C₁₆

C₂×D₆₁

yes

characteristic

C₂×C₁₆

C₂×D₆₁

yes

characteristic

C₄×C₈

C₂×D₆₁

yes

characteristic

C₂×Q₈

—

122

—

C₂×D₄

—

122

—

Q₁₆

—

122

—

Q₁₆

—

122

—

SD₁₆

—

244

—

D₈

—

122

—

D₈

—

122

—

C₂×C₈

D₂₄₄

yes

characteristic

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₂²⋊C₄

—

244

—

C₄²

D₂₄₄

yes

characteristic

C₁₆

D₂₄₄

yes

—

C₁₆

D₂₄₄

yes

—

C₂³

—

244

—

Q₈

—

244

—

Q₈

—

244

—

D₄

—

244

—

D₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

D₄₈₈

yes

—

C₂×C₄

C₂×D₂₄₄

yes

characteristic

C₈

D₄₈₈

yes

—

C₈

C₂×D₂₄₄

yes

characteristic

C₈

C₂×D₂₄₄

yes

characteristic

C₂²

—

488

—

C₂²

—

488

—

C₂²

C₂×D₄₈₈

yes

characteristic

C₄

—

C₄

—

488

—

C₄

#14519774

yes

characteristic

C₄

C₂×D₄₈₈

yes

characteristic

C₂

—

976

—

C₂

#16840139

yes

characteristic

100

C₂

#16840194

yes

—

	subgroup	G/H
center	C₂²	C₂×D₄₈₈
commutator	C₂×C₈×C₆₁	C₂³
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₄×C₁₆×C₆₁	C₂
socle	C₂²×C₆₁	C₂×D₈
hypercenter	C₄×C₁₆	D₆₁
hypocenter	C₆₁	#2249
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

subgroup

G/H

center

C₂²

C₂×D₄₈₈

commutator

C₂×C₈×C₆₁

C₂³

Frattini

C₂×C₈

C₂²×D₆₁

Fitting

C₄×C₁₆×C₆₁

C₂

socle

C₂²×C₆₁

C₂×D₈

hypercenter

C₄×C₁₆

D₆₁

hypocenter

C₆₁

#2249

LCS

G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

N	H ≅ G/N	type
1. C₂×Dic₄₈₈	C₂	semidirect
2. C₂×#14519722	C₂	semidirect
4. #16840146	C₂	semidirect
5. C₄×C₁₆×C₆₁	C₂	semidirect
55. C₄×C₁₆	D₆₁	semidirect
56. C₆₁	#2249	semidirect

H ≅ G/N

type

1. C₂×Dic₄₈₈

C₂

semidirect

2. C₂×#14519722

C₂

semidirect

4. #16840146

C₂

semidirect

5. C₄×C₁₆×C₆₁

C₂

semidirect

55. C₄×C₁₆

D₆₁

semidirect

56. C₆₁

#2249

semidirect

Subgroups — #21448080

Conjugacy classes of subgroups

Complements