Group #21448038 — subgroups

Subgroups — #21448038

Order 7808.

124 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 45 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	#16840020	C₂	1	1	yes	maximal, characteristic
2	#16839586	C₂	1	2	yes	maximal, complemented
3	#16839577	C₂	1	2	yes	maximal, complemented
4	#16839544	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#430	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₂₄₄	C₂²	1	1	yes	characteristic
7	#14519756	—	2	1	no	—
8	#14519717	C₂²	1	2	yes	—
9	#14519709	C₂²	1	1	yes	characteristic
10	#14519702	—	2	1	no	—
11	C₂×M₁₆×C₆₁	—	2	1	no	—
12	C₂×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
13	#108×C₆₁	—	2	1	no	—
14	#108×C₆₁	C₂²	1	2	yes	—
15	C₂²×C₄×C₆₁	D₄	1	1	yes	characteristic
16	C₂×Dic₁₂₂	—	2	1	no	—
17	M₁₆×C₆₁	—	2	2	no	—
18	M₁₆×C₆₁	—	2	2	no	—
19	M₁₆×C₆₁	—	4	1	no	—
20	C₂×C₈×C₆₁	—	4	1	no	—
21	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
22	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
23	C₂²⋊Dic₆₁	—	4	1	no	—
24	C₄⋊Dic₆₁	—	2	1	no	—
25	#11758196	—	4	1	no	—
26	Dic₂₄₄	—	2	2	no	—
27	#11758185	—	2	2	no	—
28	C₂³×C₆₁	SD₁₆	1	1	yes	characteristic
29	C₂×C₄×C₆₁	—	2	1	no	—
30	C₂×C₄×C₆₁	—	2	1	no	—
31	C₂×C₄×C₆₁	SD₁₆	1	1	yes	characteristic
32	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
33	C₂×Dic₆₁	—	4	1	no	—
34	C₂×Dic₆₁	—	4	1	no	—
35	Dic₁₂₂	—	4	1	no	—
36	Dic₁₂₂	—	4	1	no	—
37	C₈×C₆₁	—	2	1	no	—
38	C₈×C₆₁	—	4	2	no	—
39	C₈×C₆₁	#41	1	2	yes	—
40	C₂²×C₆₁	—	2	1	no	—
41	C₂²×C₆₁	—	4	1	no	—
42	C₂²×C₆₁	C₂×SD₁₆	1	1	yes	characteristic
43	C₄×C₆₁	—	2	1	no	—
44	C₄×C₆₁	#123	1	1	yes	characteristic
45	C₄×C₆₁	AGL(1,ℤ/8)	1	1	yes	characteristic
46	Dic₆₁	—	8	1	no	—
47	Dic₆₁	—	8	1	no	—
48	#2239	—	61	1	no	maximal, Sylow
49	C₂×C₆₁	—	2	1	no	—
50	C₂×C₆₁	—	4	1	no	—
51	C₂×C₆₁	#481	1	1	yes	characteristic
52	#470	—	61	1	no	—
53	#430	D₆₁	1	1	yes	characteristic
54	#365	—	61	2	no	—
55	#362	—	61	2	no	—
56	#349	—	61	1	no	—
57	C₆₁	#2239	1	1	yes	characteristic, complemented, Sylow
58	C₂×Q₁₆	—	61	1	no	—
59	C₂×M₁₆	—	2	1	no	—
60	C₂×M₁₆	C₂×D₆₁	1	1	yes	characteristic
61	C₂²⋊Q₈	—	122	1	no	—
62	M₃₂	—	61	2	no	—
63	#108	—	2	1	no	—
64	#108	C₂×D₆₁	1	2	yes	—
65	#106	—	61	1	no	—
66	#103	—	122	1	no	—
67	C₂×Q₈	—	122	1	no	—
68	C₂²×C₄	C₂²⋊D₆₁	1	1	yes	characteristic
69	Q₁₆	—	122	2	no	—
70	M₁₆	—	2	2	no	—
71	M₁₆	—	2	2	no	—
72	M₁₆	—	4	1	no	—
73	C₂×C₈	—	4	1	no	—
74	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
75	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
76	C₄⋊C₄	—	122	1	no	—
77	C₄⋊C₄	—	244	1	no	—
78	C₂²⋊C₄	—	244	1	no	—
79	C₁₆	—	122	2	no	—
80	C₂³	#11758201	1	1	yes	characteristic
81	Q₈	—	244	1	no	—
82	Q₈	—	244	1	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	244	1	no	—
86	C₂×C₄	—	244	1	no	—
87	C₂×C₄	#11758201	1	1	yes	characteristic
88	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
89	C₈	—	2	1	no	—
90	C₈	—	4	2	no	—
91	C₈	#11758222	1	2	yes	—
92	C₂²	—	2	1	no	—
93	C₂²	—	4	1	no	—
94	C₂²	C₂×#11758201	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	488	1	no	—
97	C₄	—	488	1	no	—
98	C₄	#14519760	1	1	yes	characteristic
99	C₄	#14519803	1	1	yes	characteristic
100	C₂	—	2	1	no	—
101	C₂	—	4	1	no	—
102	C₂	#16840080	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840020

C₂

yes

maximal, characteristic

#16839586

C₂

yes

maximal, complemented

#16839577

C₂

yes

maximal, complemented

#16839544

C₂

yes

maximal, characteristic

C₆₁×#430

C₂

yes

maximal, characteristic

C₂×Dic₂₄₄

C₂²

yes

characteristic

#14519756

—

#14519717

C₂²

yes

—

#14519709

C₂²

yes

characteristic

#14519702

—

C₂×M₁₆×C₆₁

—

C₂×M₁₆×C₆₁

C₂²

yes

characteristic

#108×C₆₁

—

#108×C₆₁

C₂²

yes

—

C₂²×C₄×C₆₁

D₄

yes

characteristic

C₂×Dic₁₂₂

—

M₁₆×C₆₁

—

M₁₆×C₆₁

—

M₁₆×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

C₂³

yes

characteristic

C₂²⋊Dic₆₁

—

C₄⋊Dic₆₁

—

#11758196

—

Dic₂₄₄

—

#11758185

—

C₂³×C₆₁

SD₁₆

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

SD₁₆

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

Dic₁₂₂

—

Dic₁₂₂

—

C₈×C₆₁

—

C₈×C₆₁

—

C₈×C₆₁

#41

yes

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

C₂×SD₁₆

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

yes

C₄×C₆₁

yes

Dic₆₁

—

Dic₆₁

—

#2239

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

yes

—

D₆₁

yes

—

—

—

C₆₁

#2239

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₆₁

yes

characteristic

C₂²⋊Q₈

—

122

—

M₃₂

—

#108

—

#108

C₂×D₆₁

yes

—

#106

—

#103

—

122

—

C₂×Q₈

—

122

—

C₂²×C₄

C₂²⋊D₆₁

yes

characteristic

Q₁₆

—

122

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₆₁

yes

characteristic

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₄⋊C₄

—

122

—

C₄⋊C₄

—

244

—

C₂²⋊C₄

—

244

—

C₁₆

—

122

—

C₂³

#11758201

yes

characteristic

Q₈

—

244

—

Q₈

—

244

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

#11758201

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

C₈

—

C₈

—

C₈

#11758222

yes

—

C₂²

—

C₂²

—

C₂²

C₂×#11758201

yes

characteristic

C₄

—

C₄

—

488

—

C₄

—

488

—

C₄

yes

C₄

yes

100

C₂

—

101

C₂

—

102

C₂

#16840080

yes

characteristic

	subgroup	G/H
center	C₂	#16840080
commutator	C₂×C₈×C₆₁	C₂³
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₆₁×#430	C₂
socle	C₂×C₆₁	#481
hypercenter	#430	D₆₁
hypocenter	C₆₁	#2239
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #430

subgroup

G/H

center

C₂

#16840080

commutator

C₂×C₈×C₆₁

C₂³

Frattini

C₂×C₈

C₂²×D₆₁

Fitting

C₆₁×#430

C₂

C₂×C₆₁

D₆₁

C₆₁

G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #430

N	H ≅ G/N	type
2. #16839586	C₂	semidirect
3. #16839577	C₂	semidirect
57. C₆₁	#2239	semidirect

H ≅ G/N

type

2. #16839586

C₂

semidirect

3. #16839577

C₂

semidirect

57. C₆₁

#2239

semidirect

Subgroups — #21448038

Conjugacy classes of subgroups

Complements