Group #21445947 — subgroups

Subgroups — #21445947

Order 7808.

248 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 141 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	#16839632	C₂	1	2	yes	maximal
2	#16839525	C₂	1	4	yes	maximal
3	C₂×C₄×C₈×C₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊Dic₆₁	—	2	2	no	—
5	C₂×C₄⋊Dic₆₁	—	2	2	no	—
6	C₂×C₄⋊Dic₆₁	C₂²	1	4	yes	—
7	C₂²×C₈×C₆₁	C₂²	1	2	yes	—
8	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
9	C₄×C₈×C₆₁	C₄	1	4	yes	complemented
10	C₂²×C₄×C₆₁	D₄	1	1	yes	characteristic
11	C₂²×C₄×C₆₁	D₄	1	1	yes	characteristic
12	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
13	C₂²×Dic₆₁	—	2	4	no	—
14	C₂×C₈×C₆₁	—	2	4	no	—
15	C₂×C₈×C₆₁	C₂×C₄	1	4	yes	—
16	C₄²×C₆₁	C₂×C₄	1	2	yes	—
17	C₄²×C₆₁	Q₈	1	2	yes	—
18	C₄⋊Dic₆₁	—	2	8	no	—
19	C₄⋊Dic₆₁	—	4	4	no	—
20	C₄⋊Dic₆₁	—	4	4	no	—
21	C₂³×C₆₁	C₂×D₄	1	1	yes	characteristic
22	C₂×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
23	C₂×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
24	C₂×C₄×C₆₁	D₈	1	2	yes	—
25	C₂×C₄×C₆₁	SD₁₆	1	4	yes	—
26	C₂×C₄×C₆₁	Q₁₆	1	2	yes	—
27	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
29	C₂×C₄×C₆₁	#41	1	4	yes	—
30	C₂×Dic₆₁	—	4	4	no	—
31	C₂×Dic₆₁	—	4	4	no	—
32	C₂×Dic₆₁	—	4	4	no	—
33	C₈×C₆₁	—	2	4	no	—
34	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₂²×C₆₁	#124	1	2	yes	—
36	C₂²×C₆₁	C₂×D₈	1	1	yes	characteristic
37	C₂²×C₆₁	C₂×SD₁₆	1	2	yes	—
38	C₂²×C₆₁	C₂×Q₁₆	1	1	yes	characteristic
39	C₄×C₆₁	#106	1	4	yes	—
40	C₄×C₆₁	#107	1	4	yes	—
41	C₄×C₆₁	#117	1	2	yes	—
42	C₄×C₆₁	#125	1	2	yes	—
43	Dic₆₁	—	8	4	no	—
44	#1834	—	61	1	no	maximal, Sylow
45	C₂×C₆₁	#382	1	1	yes	characteristic
46	C₂×C₆₁	C₂×#106	1	1	yes	characteristic
47	C₂×C₆₁	C₂×#107	1	1	yes	characteristic
48	C₂×C₆₁	#486	1	2	yes	—
49	C₂×C₆₁	#487	1	2	yes	—
50	C₂×C₄×C₈	D₆₁	1	1	yes	characteristic
51	#384	—	61	2	no	—
52	#340	—	61	4	no	—
53	C₆₁	#1834	1	1	yes	characteristic, complemented, Sylow
54	C₂²×C₈	C₂×D₆₁	1	2	yes	—
55	C₂×C₄⋊C₄	—	61	4	no	—
56	C₂×C₄⋊C₄	—	122	2	no	—
57	C₂×C₄⋊C₄	—	122	2	no	—
58	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
59	C₄×C₈	Dic₆₁	1	4	yes	complemented
60	C₂²×C₄	—	122	4	no	—
61	C₂²×C₄	D₂₄₄	1	1	yes	characteristic
62	C₂²×C₄	D₂₄₄	1	1	yes	characteristic
63	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
64	C₂×C₈	—	2	4	no	—
65	C₂×C₈	C₂×Dic₆₁	1	4	yes	—
66	C₄⋊C₄	—	122	8	no	—
67	C₄⋊C₄	—	244	4	no	—
68	C₄⋊C₄	—	244	4	no	—
69	C₄²	Dic₁₂₂	1	2	yes	—
70	C₄²	C₂×Dic₆₁	1	2	yes	—
71	C₂³	C₂×D₂₄₄	1	1	yes	characteristic
72	C₂×C₄	—	244	4	no	—
73	C₂×C₄	—	244	4	no	—
74	C₂×C₄	—	244	4	no	—
75	C₂×C₄	#11758190	1	4	yes	—
76	C₂×C₄	D₄₈₈	1	2	yes	—
77	C₂×C₄	Dic₂₄₄	1	2	yes	—
78	C₂×C₄	C₄⋊Dic₆₁	1	2	yes	—
79	C₂×C₄	C₄⋊Dic₆₁	1	2	yes	—
80	C₂×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
81	C₂×C₄	#11758222	1	4	yes	—
82	C₂×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
83	C₈	—	2	4	no	—
84	C₂²	C₂×C₄⋊Dic₆₁	1	1	yes	characteristic
85	C₂²	#14519765	1	2	yes	—
86	C₂²	C₂×D₄₈₈	1	1	yes	characteristic
87	C₂²	C₂×#11758190	1	2	yes	—
88	C₂²	C₂×Dic₂₄₄	1	1	yes	characteristic
89	C₄	—	488	4	no	—
90	C₄	#14519709	1	4	yes	—
91	C₄	#14519711	1	4	yes	—
92	C₄	#14519736	1	2	yes	—
93	C₄	#14519769	1	2	yes	—
94	C₂	#16839628	1	1	yes	characteristic
95	C₂	C₂×#14519709	1	1	yes	characteristic
96	C₂	C₂×#14519711	1	1	yes	characteristic
97	C₂	#16840109	1	2	yes	—
98	C₂	#16840113	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#16839632

C₂

yes

maximal

#16839525

C₂

yes

maximal

C₂×C₄×C₈×C₆₁

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₆₁

—

C₂×C₄⋊Dic₆₁

—

C₂×C₄⋊Dic₆₁

C₂²

yes

—

C₂²×C₈×C₆₁

C₂²

yes

—

C₂×C₄²×C₆₁

C₂²

yes

characteristic

C₄×C₈×C₆₁

C₄

yes

complemented

C₂²×C₄×C₆₁

D₄

yes

characteristic

C₂²×C₄×C₆₁

D₄

yes

characteristic

C₂²×C₄×C₆₁

C₂³

yes

characteristic

C₂²×Dic₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₄²×C₆₁

C₂×C₄

yes

—

C₄²×C₆₁

Q₈

yes

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₂³×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

—

C₂×C₄×C₆₁

C₄⋊C₄

yes

—

C₂×C₄×C₆₁

D₈

yes

—

C₂×C₄×C₆₁

SD₁₆

yes

—

C₂×C₄×C₆₁

Q₁₆

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₆₁

#41

yes

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₈×C₆₁

—

C₂²×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₆₁

#124

yes

—

C₂²×C₆₁

C₂×D₈

yes

characteristic

C₂²×C₆₁

C₂×SD₁₆

yes

—

C₂²×C₆₁

C₂×Q₁₆

yes

characteristic

C₄×C₆₁

#106

yes

—

C₄×C₆₁

#107

yes

—

C₄×C₆₁

#117

yes

—

C₄×C₆₁

#125

yes

—

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

—

C₂×C₆₁

#487

yes

—

C₂×C₄×C₈

D₆₁

yes

characteristic

#384

—

#340

—

C₆₁

#1834

yes

characteristic, complemented, Sylow

C₂²×C₈

C₂×D₆₁

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

122

—

C₂×C₄⋊C₄

—

122

—

C₂×C₄²

C₂×D₆₁

yes

characteristic

C₄×C₈

Dic₆₁

yes

complemented

C₂²×C₄

—

122

—

C₂²×C₄

D₂₄₄

yes

characteristic

C₂²×C₄

D₂₄₄

yes

characteristic

C₂²×C₄

C₂²×D₆₁

yes

characteristic

C₂×C₈

—

C₂×C₈

C₂×Dic₆₁

yes

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

244

—

C₄⋊C₄

—

244

—

C₄²

Dic₁₂₂

yes

—

C₄²

C₂×Dic₆₁

yes

—

C₂³

C₂×D₂₄₄

yes

characteristic

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

#11758190

yes

—

C₂×C₄

D₄₈₈

yes

—

C₂×C₄

Dic₂₄₄

yes

—

C₂×C₄

C₄⋊Dic₆₁

yes

—

C₂×C₄

C₄⋊Dic₆₁

yes

—

C₂×C₄

C₂×Dic₁₂₂

yes

characteristic

C₂×C₄

#11758222

yes

—

C₂×C₄

C₂²×Dic₆₁

yes

characteristic

C₈

—

C₂²

C₂×C₄⋊Dic₆₁

yes

characteristic

C₂²

#14519765

yes

—

C₂²

C₂×D₄₈₈

yes

characteristic

C₂²

C₂×#11758190

yes

—

C₂²

C₂×Dic₂₄₄

yes

characteristic

C₄

—

488

—

C₄

#14519709

yes

—

C₄

#14519711

yes

—

C₄

#14519736

yes

—

C₄

#14519769

yes

—

C₂

yes

C₂

yes

C₂

yes

C₂

yes

—

C₂

#16840113

yes

—

	subgroup	G/H
center	C₂³	C₂×D₂₄₄
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₂×C₄×C₈×C₆₁	C₂
socle	C₂³×C₆₁	C₂×D₄
hypercenter	C₂×C₄×C₈	D₆₁
hypocenter	C₆₁	#1834
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂³

C₂×D₂₄₄

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₆₁

Fitting

C₂×C₄×C₈×C₆₁

C₂

socle

C₂³×C₆₁

C₂×D₄

hypercenter

C₂×C₄×C₈

D₆₁

hypocenter

C₆₁

#1834

LCS

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
9. C₄×C₈×C₆₁	C₄	semidirect
53. C₆₁	#1834	semidirect
59. C₄×C₈	Dic₆₁	semidirect

H ≅ G/N

type

9. C₄×C₈×C₆₁

C₄

semidirect

53. C₆₁

#1834

semidirect

59. C₄×C₈

Dic₆₁

semidirect

Subgroups — #21445947

Conjugacy classes of subgroups

Complements