Group #21460794 — subgroups

Subgroups — #21460794

Order 7808.

110 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 26 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	#16840659	C₂	1	1	yes	maximal, characteristic, complemented
2	#16840631	C₂	1	1	yes	maximal, characteristic, complemented
3	#16840016	C₂	1	1	yes	maximal, characteristic
4	D₆₁⋊M₁₆	—	2	1	no	—
5	#14519851	—	2	1	no	—
6	C₂×D₄₈₈	C₄	1	1	yes	characteristic
7	C₂×#11758189	C₂²	1	1	yes	characteristic
8	#14519752	—	2	1	no	—
9	#14519697	—	2	1	no	—
10	#106×C₆₁	C₄	1	1	yes	characteristic
11	C₂×D₂₄₄	—	2	1	no	—
12	C₂×D₂₄₄	—	4	1	no	—
13	C₂×C₄×D₆₁	D₄	1	1	yes	characteristic
14	#11758217	—	4	1	no	—
15	#11758213	—	4	1	no	—
16	D₆₁⋊C₈	—	2	2	no	—
17	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
18	C₄⋊C₄×C₆₁	—	2	1	no	—
19	#11758198	—	4	1	no	—
20	C₂×#92418	D₄	1	1	yes	characteristic
21	D₄₈₈	—	4	1	no	—
22	#11758189	—	4	1	no	—
23	#11758187	—	4	1	no	—
24	C₂²×D₆₁	—	4	1	no	—
25	C₂²×D₆₁	SD₁₆	1	1	yes	characteristic
26	C₂×C₄×C₆₁	—	4	1	no	—
27	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×Dic₆₁	D₈	1	1	yes	characteristic
29	D₂₄₄	—	4	1	no	—
30	D₂₄₄	—	4	1	no	—
31	D₂₄₄	—	8	2	no	—
32	C₄×D₆₁	—	2	1	no	—
33	C₄×D₆₁	—	2	1	no	—
34	#92420	—	4	2	no	—
35	C₈×C₆₁	—	2	1	no	—
36	#92418	—	2	1	no	—
37	C₂²×C₆₁	#102	1	1	yes	characteristic
38	C₂×D₆₁	—	2	1	no	—
39	C₂×D₆₁	—	4	1	no	—
40	C₂×D₆₁	—	8	1	no	—
41	C₂×D₆₁	—	8	1	no	—
42	C₂×D₆₁	—	8	1	no	—
43	C₄×C₆₁	—	8	1	no	—
44	C₄×C₆₁	#99	1	1	yes	characteristic
45	C₄×C₆₁	#104	1	1	yes	characteristic
46	Dic₆₁	—	2	1	no	—
47	#1341	—	61	1	no	maximal, Sylow
48	C₂×C₆₁	—	2	1	no	—
49	C₂×C₆₁	#327	1	1	yes	characteristic
50	D₆₁	—	4	1	no	—
51	D₆₁	—	16	1	no	—
52	#469	—	61	1	no	—
53	#349	—	61	1	no	—
54	#338	—	61	1	no	—
55	C₆₁	#1341	1	1	yes	characteristic, complemented, Sylow
56	C₂×D₈	—	61	1	no	—
57	C₂×M₁₆	—	61	1	no	—
58	C₂×M₁₆	—	122	1	no	—
59	#121	—	122	1	no	—
60	M₃₂	—	122	1	no	—
61	#106	#6923	1	1	yes	characteristic
62	#102	—	122	1	no	—
63	C₂×D₄	—	122	1	no	—
64	C₂×D₄	—	244	1	no	—
65	C₂²×C₄	—	61	1	no	—
66	D₈	—	244	1	no	—
67	M₁₆	—	244	1	no	—
68	M₁₆	—	244	1	no	—
69	M₁₆	—	244	1	no	—
70	C₂×C₈	—	61	1	no	—
71	C₂×C₈	—	122	2	no	—
72	C₂×C₈	C₂×#6923	1	1	yes	characteristic
73	C₄⋊C₄	—	2	1	no	—
74	C₂²⋊C₄	—	244	1	no	—
75	C₁₆	—	244	1	no	—
76	C₂³	—	61	1	no	—
77	C₂³	—	244	1	no	—
78	D₄	—	488	2	no	—
79	D₄	—	244	1	no	—
80	D₄	—	244	1	no	—
81	C₂×C₄	—	4	1	no	—
82	C₂×C₄	—	61	1	no	—
83	C₂×C₄	—	122	1	no	—
84	C₂×C₄	—	122	1	no	—
85	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
86	C₈	—	2	1	no	—
87	C₈	—	122	1	no	—
88	C₈	—	244	2	no	—
89	C₂²	—	122	1	no	—
90	C₂²	—	488	1	no	—
91	C₂²	—	488	1	no	—
92	C₂²	—	488	1	no	—
93	C₂²	—	244	1	no	—
94	C₂²	#14519839	1	1	yes	characteristic
95	C₄	—	8	1	no	—
96	C₄	—	122	1	no	—
97	C₄	#14519836	1	1	yes	characteristic
98	C₄	#14519842	1	1	yes	characteristic
99	C₂	—	2	1	no	—
100	C₂	—	976	1	no	—
101	C₂	—	244	1	no	—
102	C₂	#16840614	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840659

C₂

yes

maximal, characteristic, complemented

#16840631

C₂

yes

maximal, characteristic, complemented

#16840016

C₂

yes

maximal, characteristic

D₆₁⋊M₁₆

—

#14519851

—

C₂×D₄₈₈

C₄

yes

characteristic

C₂×#11758189

C₂²

yes

characteristic

#14519752

—

#14519697

—

#106×C₆₁

C₄

yes

characteristic

C₂×D₂₄₄

—

C₂×D₂₄₄

—

C₂×C₄×D₆₁

D₄

yes

characteristic

#11758217

—

#11758213

—

D₆₁⋊C₈

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₄⋊C₄×C₆₁

—

#11758198

—

C₂×#92418

D₄

yes

characteristic

D₄₈₈

—

#11758189

—

#11758187

—

C₂²×D₆₁

—

C₂²×D₆₁

SD₁₆

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×Dic₆₁

D₈

yes

characteristic

D₂₄₄

—

D₂₄₄

—

D₂₄₄

—

C₄×D₆₁

—

C₄×D₆₁

—

#92420

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

#102

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

—

C₄×C₆₁

yes

C₄×C₆₁

yes

Dic₆₁

—

#1341

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

#327

yes

characteristic

D₆₁

—

D₆₁

—

#469

—

#349

—

#338

—

C₆₁

#1341

yes

characteristic, complemented, Sylow

C₂×D₈

—

C₂×M₁₆

—

C₂×M₁₆

—

122

—

#121

—

122

—

M₃₂

—

122

—

yes

—

122

—

C₂×D₄

—

122

—

C₂×D₄

—

244

—

C₂²×C₄

—

D₈

—

244

—

M₁₆

—

244

—

M₁₆

—

244

—

M₁₆

—

244

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

C₂×#6923

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

244

—

C₁₆

—

244

—

C₂³

—

C₂³

—

244

—

D₄

—

488

—

D₄

—

244

—

D₄

—

244

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

C₂²⋊#6923

yes

characteristic

C₈

—

C₈

—

122

—

C₈

—

244

—

C₂²

—

122

—

C₂²

—

488

—

C₂²

—

488

—

C₂²

—

488

—

C₂²

—

244

—

C₂²

#14519839

yes

characteristic

C₄

—

C₄

—

122

—

C₄

yes

C₄

yes

C₂

—

100

C₂

—

976

—

101

C₂

—

244

—

102

C₂

#16840614

yes

characteristic

	subgroup	G/H
center	C₂	#16840614
commutator	C₂×C₈×C₆₁	C₂×C₄
Frattini	C₂×C₈	C₂×#6923
Fitting	#106×C₆₁	C₄
socle	C₂×C₆₁	#327
hypercenter	#106	#6923
hypocenter	C₆₁	#1341
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #106

subgroup

G/H

center

C₂

#16840614

commutator

C₂×C₈×C₆₁

C₂×C₄

Frattini

C₂×C₈

C₂×#6923

Fitting

#106×C₆₁

C₄

C₂×C₆₁

C₆₁

G ▷ C₂×C₈×C₆₁ ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #106

N	H ≅ G/N	type
1. #16840659	C₂	semidirect
2. #16840631	C₂	semidirect
55. C₆₁	#1341	semidirect

H ≅ G/N

type

1. #16840659

C₂

semidirect

2. #16840631

C₂

semidirect

55. C₆₁

#1341

semidirect

Subgroups — #21460794

Conjugacy classes of subgroups

Complements