Group #21461754 — subgroups

Subgroups — #21461754

Order 7808.

280 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 114 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×#14519845	C₂	1	4	yes	maximal
2	#16840708	C₂	1	2	yes	maximal
3	C₄×C₈×D₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊#6923	—	2	4	no	—
5	C₂×C₄⋊#6923	C₂²	1	4	yes	—
6	#14519845	—	2	8	no	—
7	C₂×C₈×D₆₁	C₂²	1	2	yes	—
8	C₄²×D₆₁	C₂²	1	1	yes	characteristic
9	C₄×#92418	C₄	1	1	yes	characteristic, complemented
10	C₈×Dic₆₁	C₄	1	2	yes	complemented
11	C₄×C₈×C₆₁	C₄	1	1	yes	characteristic, complemented
12	C₂²×#6923	—	2	4	no	—
13	C₂×C₄×D₆₁	D₄	1	2	yes	—
14	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
15	C₄⋊#6923	—	2	8	no	—
16	C₄⋊#6923	—	4	8	no	—
17	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
18	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
19	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
20	C₄×Dic₆₁	Q₈	1	2	yes	—
21	C₂×#92418	C₂×C₄	1	2	yes	—
22	C₈×D₆₁	D₄	1	4	yes	—
23	C₈×D₆₁	Q₈	1	4	yes	—
24	C₂²×D₆₁	C₂×D₄	1	1	yes	characteristic
25	C₂×#6923	—	4	4	no	—
26	C₂×#6923	—	4	8	no	—
27	C₂×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
28	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
29	C₂×Dic₆₁	C₄⋊C₄	1	2	yes	—
30	C₂×Dic₆₁	C₂×Q₈	1	1	yes	characteristic
31	C₄×D₆₁	SD₁₆	1	8	yes	—
32	C₄×D₆₁	C₂×D₄	1	2	yes	—
33	C₄×D₆₁	C₂×Q₈	1	2	yes	—
34	C₈×C₆₁	C₄⋊C₄	1	4	yes	complemented
35	#92418	C₄⋊C₄	1	4	yes	complemented
36	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
37	C₂×D₆₁	#127	1	1	yes	characteristic
38	C₂×D₆₁	C₄⋊Q₈	1	1	yes	characteristic
39	C₂×D₆₁	C₂×SD₁₆	1	4	yes	—
40	#6923	—	8	4	no	—
41	C₄×C₆₁	#106	1	4	yes	complemented
42	C₄×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
43	Dic₆₁	#106	1	4	yes	complemented
44	Dic₆₁	C₄⋊Q₈	1	2	yes	—
45	#1844	—	61	1	no	maximal, Sylow
46	C₂×C₆₁	#384	1	1	yes	characteristic
47	C₂×C₆₁	C₂×#106	1	2	yes	—
48	D₆₁	#492	1	2	yes	—
49	D₆₁	#498	1	2	yes	—
50	C₂×#106	—	61	4	no	—
51	C₂×C₄×C₈	—	61	1	no	—
52	#384	—	61	2	no	—
53	C₆₁	#1844	1	1	yes	characteristic, complemented, Sylow
54	C₂²×C₈	—	61	2	no	—
55	C₂×C₄⋊C₄	—	61	4	no	—
56	C₂×C₄⋊C₄	—	122	4	no	—
57	C₂×C₄²	—	61	1	no	—
58	#106	—	122	8	no	—
59	C₄×C₈	—	61	2	no	—
60	C₄×C₈	—	61	1	no	—
61	C₄×C₈	#6923	1	1	yes	characteristic, complemented
62	C₂²×C₄	—	61	2	no	—
63	C₂²×C₄	—	61	1	no	—
64	C₂²×C₄	—	122	4	no	—
65	C₂×C₈	—	61	2	no	—
66	C₂×C₈	—	61	4	no	—
67	C₂×C₈	—	61	4	no	—
68	C₂×C₈	C₂×#6923	1	2	yes	—
69	C₄⋊C₄	—	122	8	no	—
70	C₄⋊C₄	—	244	8	no	—
71	C₄²	—	61	2	no	—
72	C₄²	—	61	1	no	—
73	C₄²	C₂×#6923	1	1	yes	characteristic
74	C₂³	—	61	1	no	—
75	C₂×C₄	—	61	2	no	—
76	C₂×C₄	—	61	1	no	—
77	C₂×C₄	—	61	8	no	—
78	C₂×C₄	—	61	2	no	—
79	C₂×C₄	—	61	2	no	—
80	C₂×C₄	—	244	4	no	—
81	C₂×C₄	—	244	8	no	—
82	C₂×C₄	C₄⋊#6923	1	2	yes	—
83	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
84	C₈	—	61	4	no	—
85	C₈	C₄⋊#6923	1	4	yes	complemented
86	C₂²	—	61	1	no	—
87	C₂²	—	61	1	no	—
88	C₂²	—	61	4	no	—
89	C₂²	C₂×C₄⋊#6923	1	1	yes	characteristic
90	C₄	—	61	2	no	—
91	C₄	—	61	4	no	—
92	C₄	—	488	4	no	—
93	C₄	#14519845	1	4	yes	complemented
94	C₄	C₂×C₄⋊#6923	1	2	yes	—
95	C₂	—	61	2	no	—
96	C₂	—	61	2	no	—
97	C₂	#16840708	1	1	yes	characteristic
98	C₂	C₂×#14519845	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519845

C₂

yes

maximal

#16840708

C₂

yes

maximal

C₄×C₈×D₆₁

C₂

yes

maximal, characteristic

C₂×C₄⋊#6923

—

C₂×C₄⋊#6923

C₂²

yes

—

#14519845

—

C₂×C₈×D₆₁

C₂²

yes

—

C₄²×D₆₁

C₂²

yes

characteristic

C₄×#92418

C₄

yes

characteristic, complemented

C₈×Dic₆₁

C₄

yes

complemented

C₄×C₈×C₆₁

C₄

yes

characteristic, complemented

C₂²×#6923

—

C₂×C₄×D₆₁

D₄

yes

—

C₂×C₄×D₆₁

C₂³

yes

characteristic

C₄⋊#6923

—

C₄⋊#6923

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

Q₈

yes

—

C₂×#92418

C₂×C₄

yes

—

C₈×D₆₁

D₄

yes

—

C₈×D₆₁

Q₈

yes

—

C₂²×D₆₁

C₂×D₄

yes

characteristic

C₂×#6923

—

C₂×#6923

—

C₂×C₄×C₆₁

C₄⋊C₄

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

C₄⋊C₄

yes

—

C₂×Dic₆₁

C₂×Q₈

yes

characteristic

C₄×D₆₁

SD₁₆

yes

—

C₄×D₆₁

C₂×D₄

yes

—

C₄×D₆₁

C₂×Q₈

yes

—

C₈×C₆₁

C₄⋊C₄

yes

complemented

#92418

C₄⋊C₄

yes

complemented

C₂²×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₂×D₆₁

#127

yes

characteristic

C₂×D₆₁

C₄⋊Q₈

yes

characteristic

C₂×D₆₁

C₂×SD₁₆

yes

—

#6923

—

C₄×C₆₁

#106

yes

complemented

C₄×C₆₁

C₂×C₄⋊C₄

yes

—

Dic₆₁

#106

yes

complemented

Dic₆₁

C₄⋊Q₈

yes

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

—

D₆₁

#492

yes

—

D₆₁

#498

yes

—

C₂×#106

—

C₂×C₄×C₈

—

#384

—

C₆₁

#1844

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

122

—

C₂×C₄²

—

#106

—

122

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#6923

yes

characteristic, complemented

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#6923

yes

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

244

—

C₄²

—

C₄²

—

C₄²

C₂×#6923

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

C₄⋊#6923

yes

—

C₂×C₄

C₂²×#6923

yes

characteristic

C₈

—

C₈

C₄⋊#6923

yes

complemented

C₂²

—

C₂²

—

C₂²

—

C₂²

C₂×C₄⋊#6923

yes

characteristic

C₄

—

C₄

—

C₄

—

488

—

C₄

#14519845

yes

complemented

C₄

C₂×C₄⋊#6923

yes

—

C₂

—

C₂

—

C₂

#16840708

yes

characteristic

C₂

C₂×#14519845

yes

—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#6923
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×#6923
Fitting	C₄×C₈×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₄⋊C₄
hypercenter	C₄×C₈	#6923
hypocenter	C₆₁	#1844
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

subgroup

G/H

center

C₂²

C₂×C₄⋊#6923

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂×C₄

C₂²×#6923

Fitting

C₄×C₈×C₆₁

C₄

socle

C₂²×C₆₁

C₂×C₄⋊C₄

C₄×C₈

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

N	H ≅ G/N	type
9. C₄×#92418	C₄	semidirect
10. C₈×Dic₆₁	C₄	semidirect
11. C₄×C₈×C₆₁	C₄	semidirect
34. C₈×C₆₁	C₄⋊C₄	semidirect
35. #92418	C₄⋊C₄	semidirect
41. C₄×C₆₁	#106	semidirect
43. Dic₆₁	#106	semidirect
53. C₆₁	#1844	semidirect
61. C₄×C₈	#6923	semidirect
85. C₈	C₄⋊#6923	semidirect
93. C₄	#14519845	semidirect

H ≅ G/N

type

9. C₄×#92418

C₄

semidirect

10. C₈×Dic₆₁

C₄

semidirect

11. C₄×C₈×C₆₁

C₄

semidirect

34. C₈×C₆₁

C₄⋊C₄

semidirect

35. #92418

C₄⋊C₄

semidirect

41. C₄×C₆₁

#106

semidirect

43. Dic₆₁

#106

semidirect

53. C₆₁

#1844

semidirect

61. C₄×C₈

#6923

semidirect

85. C₈

C₄⋊#6923

semidirect

93. C₄

#14519845

semidirect

Subgroups — #21461754

Conjugacy classes of subgroups

Complements