Group #21448081 — subgroups

Subgroups — #21448081

Order 7808.

184 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 53 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×#14519720	C₂	1	2	yes	maximal, complemented
2	C₂×D₉₇₆	C₂	1	1	yes	maximal, characteristic
3	#16840147	C₂	1	2	yes	maximal, complemented
4	C₁₆×Dic₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₃₂×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11758201	—	2	2	no	—
7	C₂×D₄₈₈	C₂²	1	2	yes	—
8	#14519766	—	2	2	no	—
9	#14519720	—	2	4	no	—
10	D₉₇₆	—	2	2	no	—
11	C₂×#11758185	C₂²	1	1	yes	characteristic
12	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
13	C₂×Q₁₆×C₆₁	C₂²	1	2	yes	—
14	Q₃₂×C₆₁	—	2	2	no	—
15	C₂×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×Q₈×C₆₁	—	2	2	no	—
17	C₂×D₂₄₄	—	2	2	no	—
18	Q₁₆×C₆₁	—	2	2	no	—
19	Q₁₆×C₆₁	—	2	2	no	—
20	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
21	#11758201	—	4	4	no	—
22	#11758198	—	4	4	no	—
23	C₄×Dic₆₁	D₄	1	1	yes	characteristic
24	C₂×#92418	D₄	1	1	yes	characteristic
25	D₄₈₈	—	2	2	no	—
26	D₄₈₈	—	2	2	no	—
27	C₁₆×C₆₁	D₄	1	2	yes	—
28	#11758185	D₄	1	2	yes	—
29	C₂²×D₆₁	—	4	2	no	—
30	Q₈×C₆₁	—	4	2	no	—
31	Q₈×C₆₁	—	4	2	no	—
32	C₂×C₄×C₆₁	—	4	2	no	—
33	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
34	C₂×Dic₆₁	D₈	1	2	yes	—
35	D₂₄₄	—	4	2	no	—
36	D₂₄₄	—	4	2	no	—
37	C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
38	C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
39	#92418	D₈	1	2	yes	—
40	C₂²×C₆₁	C₂×D₈	1	1	yes	characteristic
41	C₂×D₆₁	—	8	2	no	—
42	C₂×D₆₁	—	8	4	no	—
43	C₄×C₆₁	—	8	2	no	—
44	C₄×C₆₁	#127	1	1	yes	characteristic
45	C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
46	Dic₆₁	—	2	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	D₆₁	1	1	yes	characteristic, complemented
52	C₂×SD₃₂	—	61	2	no	—
53	C₂×D₁₆	—	61	1	no	—
54	#495	—	61	2	no	—
55	C₄×C₁₆	—	61	1	no	—
56	C₆₁	#2249	1	1	yes	characteristic, complemented, Sylow
57	C₂×Q₁₆	C₂×D₆₁	1	2	yes	—
58	C₂×SD₁₆	—	122	2	no	—
59	C₂×D₈	—	61	2	no	—
60	#124	—	122	2	no	—
61	Q₃₂	—	2	2	no	—
62	SD₃₂	—	122	4	no	—
63	D₁₆	—	122	2	no	—
64	C₂×C₁₆	—	61	1	no	—
65	C₂×C₁₆	C₂×D₆₁	1	1	yes	characteristic
66	C₄×C₈	—	61	1	no	—
67	C₂×Q₈	—	2	2	no	—
68	C₂×D₄	—	122	2	no	—
69	Q₁₆	—	2	2	no	—
70	Q₁₆	—	2	2	no	—
71	SD₁₆	—	244	4	no	—
72	D₈	—	122	2	no	—
73	D₈	—	122	2	no	—
74	C₂×C₈	—	61	1	no	—
75	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
76	C₂²⋊C₄	—	244	4	no	—
77	C₄²	—	61	1	no	—
78	C₁₆	—	61	2	no	—
79	C₁₆	C₂²⋊D₆₁	1	2	yes	—
80	C₂³	—	244	2	no	—
81	Q₈	—	4	2	no	—
82	Q₈	—	4	2	no	—
83	D₄	—	244	2	no	—
84	D₄	—	244	2	no	—
85	C₂×C₄	—	4	2	no	—
86	C₂×C₄	—	61	2	no	—
87	C₂×C₄	D₄×D₆₁	1	1	yes	characteristic
88	C₈	—	61	2	no	—
89	C₈	D₄×D₆₁	1	1	yes	characteristic
90	C₈	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
91	C₂²	—	488	4	no	—
92	C₂²	—	488	2	no	—
93	C₂²	D₈×D₆₁	1	1	yes	characteristic
94	C₄	—	8	2	no	—
95	C₄	—	122	2	no	—
96	C₄	#14519773	1	1	yes	characteristic
97	C₄	D₈×D₆₁	1	1	yes	characteristic
98	C₂	—	976	2	no	—
99	C₂	#16840137	1	1	yes	characteristic
100	C₂	#16840195	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519720

C₂

yes

maximal, complemented

C₂×D₉₇₆

C₂

yes

maximal, characteristic

#16840147

C₂

yes

maximal, complemented

C₁₆×Dic₆₁

C₂

yes

maximal, characteristic, complemented

C₂×Q₃₂×C₆₁

C₂

yes

maximal, characteristic, complemented

C₂×#11758201

—

C₂×D₄₈₈

C₂²

yes

—

#14519766

—

#14519720

—

D₉₇₆

—

C₂×#11758185

C₂²

yes

characteristic

C₈×Dic₆₁

C₂²

yes

characteristic

C₂×Q₁₆×C₆₁

C₂²

yes

—

Q₃₂×C₆₁

—

C₂×C₁₆×C₆₁

C₂²

yes

characteristic

C₂×Q₈×C₆₁

—

C₂×D₂₄₄

—

Q₁₆×C₆₁

—

Q₁₆×C₆₁

—

C₂×C₈×C₆₁

C₂³

yes

characteristic

#11758201

—

#11758198

—

C₄×Dic₆₁

D₄

yes

characteristic

C₂×#92418

D₄

yes

characteristic

D₄₈₈

—

D₄₈₈

—

C₁₆×C₆₁

D₄

yes

—

#11758185

D₄

yes

—

C₂²×D₆₁

—

Q₈×C₆₁

—

Q₈×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×Dic₆₁

D₈

yes

—

D₂₄₄

—

D₂₄₄

—

C₈×C₆₁

C₂×D₄

yes

characteristic

C₈×C₆₁

C₂×D₄

yes

characteristic

#92418

D₈

yes

—

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

D₆₁

yes

characteristic, complemented

C₂×SD₃₂

—

C₂×D₁₆

—

#495

—

C₄×C₁₆

—

C₆₁

#2249

yes

characteristic, complemented, Sylow

C₂×Q₁₆

C₂×D₆₁

yes

—

C₂×SD₁₆

—

122

—

C₂×D₈

—

#124

—

122

—

Q₃₂

—

SD₃₂

—

122

—

D₁₆

—

122

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₆₁

yes

characteristic

C₄×C₈

—

C₂×Q₈

—

C₂×D₄

—

122

—

Q₁₆

—

Q₁₆

—

SD₁₆

—

244

—

D₈

—

122

—

D₈

—

122

—

C₂×C₈

—

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₂²⋊C₄

—

244

—

C₄²

—

C₁₆

—

C₁₆

C₂²⋊D₆₁

yes

—

C₂³

—

244

—

Q₈

—

Q₈

—

D₄

—

244

—

D₄

—

244

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₄×D₆₁

yes

characteristic

C₈

—

C₈

D₄×D₆₁

yes

characteristic

C₈

C₂×C₂²⋊D₆₁

yes

characteristic

C₂²

—

488

—

C₂²

—

488

—

C₂²

D₈×D₆₁

yes

characteristic

C₄

—

C₄

—

122

—

C₄

#14519773

yes

characteristic

C₄

D₈×D₆₁

yes

characteristic

C₂

—

976

—

C₂

#16840137

yes

characteristic

100

C₂

#16840195

yes

—

	subgroup	G/H
center	C₂²	D₈×D₆₁
commutator	C₂×C₈×C₆₁	C₂³
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₂×Q₃₂×C₆₁	C₂
socle	C₂²×C₆₁	C₂×D₈
hypercenter	C₂×Q₃₂	D₆₁
hypocenter	C₆₁	#2249
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₃₂

subgroup

G/H

center

C₂²

D₈×D₆₁

commutator

C₂×C₈×C₆₁

C₂³

Frattini

C₂×C₈

C₂²×D₆₁

Fitting

C₂×Q₃₂×C₆₁

C₂

socle

C₂²×C₆₁

C₂×D₈

hypercenter

C₂×Q₃₂

D₆₁

hypocenter

C₆₁

#2249

LCS

G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₃₂

N	H ≅ G/N	type
1. C₂×#14519720	C₂	semidirect
3. #16840147	C₂	semidirect
4. C₁₆×Dic₆₁	C₂	semidirect
5. C₂×Q₃₂×C₆₁	C₂	semidirect
51. C₂×Q₃₂	D₆₁	semidirect
56. C₆₁	#2249	semidirect

H ≅ G/N

type

1. C₂×#14519720

C₂

semidirect

3. #16840147

C₂

semidirect

4. C₁₆×Dic₆₁

C₂

semidirect

5. C₂×Q₃₂×C₆₁

C₂

semidirect

51. C₂×Q₃₂

D₆₁

semidirect

56. C₆₁

#2249

semidirect

Subgroups — #21448081

Conjugacy classes of subgroups

Complements