Group #21461755 — subgroups

Subgroups — #21461755

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×#14519846	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	#14519846	—	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	D₈	1	4	yes	—
32	C₄×D₆₁	Q₁₆	1	4	yes	—
33	C₄×D₆₁	C₂×D₄	1	2	yes	—
34	C₄×D₆₁	C₂×Q₈	1	2	yes	—
35	C₈×C₆₁	C₄⋊C₄	1	4	yes	complemented
36	#92418	C₄⋊C₄	1	4	yes	complemented
37	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₂×D₆₁	#127	1	1	yes	characteristic
39	C₂×D₆₁	C₄⋊Q₈	1	1	yes	characteristic
40	C₂×D₆₁	C₂×D₈	1	2	yes	—
41	C₂×D₆₁	C₂×Q₁₆	1	2	yes	—
42	#6923	—	8	4	no	—
43	C₄×C₆₁	#107	1	4	yes	complemented
44	C₄×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
45	Dic₆₁	#107	1	4	yes	complemented
46	Dic₆₁	C₄⋊Q₈	1	2	yes	—
47	#1845	—	61	1	no	maximal, Sylow
48	C₂×C₆₁	#384	1	1	yes	characteristic
49	C₂×C₆₁	C₂×#107	1	2	yes	—
50	D₆₁	#493	1	1	yes	characteristic
51	D₆₁	#494	1	1	yes	characteristic
52	D₆₁	#500	1	2	yes	—
53	C₂×#107	—	61	4	no	—
54	C₂×C₄×C₈	—	61	1	no	—
55	#384	—	61	2	no	—
56	C₆₁	#1845	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₈	—	61	2	no	—
58	C₂×C₄⋊C₄	—	61	4	no	—
59	C₂×C₄⋊C₄	—	122	4	no	—
60	C₂×C₄²	—	61	1	no	—
61	#107	—	122	8	no	—
62	C₄×C₈	—	61	2	no	—
63	C₄×C₈	—	61	1	no	—
64	C₄×C₈	#6923	1	1	yes	characteristic, complemented
65	C₂²×C₄	—	61	2	no	—
66	C₂²×C₄	—	61	1	no	—
67	C₂²×C₄	—	122	4	no	—
68	C₂×C₈	—	61	2	no	—
69	C₂×C₈	—	61	4	no	—
70	C₂×C₈	—	61	4	no	—
71	C₂×C₈	C₂×#6923	1	2	yes	—
72	C₄⋊C₄	—	122	8	no	—
73	C₄⋊C₄	—	244	8	no	—
74	C₄²	—	61	2	no	—
75	C₄²	—	61	1	no	—
76	C₄²	C₂×#6923	1	1	yes	characteristic
77	C₂³	—	61	1	no	—
78	C₂×C₄	—	61	2	no	—
79	C₂×C₄	—	61	1	no	—
80	C₂×C₄	—	61	4	no	—
81	C₂×C₄	—	61	4	no	—
82	C₂×C₄	—	61	2	no	—
83	C₂×C₄	—	61	2	no	—
84	C₂×C₄	—	244	4	no	—
85	C₂×C₄	—	244	8	no	—
86	C₂×C₄	C₄⋊#6923	1	2	yes	—
87	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
88	C₈	—	61	4	no	—
89	C₈	C₄⋊#6923	1	4	yes	complemented
90	C₂²	—	61	1	no	—
91	C₂²	—	61	1	no	—
92	C₂²	—	61	2	no	—
93	C₂²	—	61	2	no	—
94	C₂²	C₂×C₄⋊#6923	1	1	yes	characteristic
95	C₄	—	61	2	no	—
96	C₄	—	61	4	no	—
97	C₄	—	488	4	no	—
98	C₄	#14519846	1	4	yes	complemented
99	C₄	C₂×C₄⋊#6923	1	2	yes	—
100	C₂	—	61	1	no	—
101	C₂	—	61	1	no	—
102	C₂	—	61	2	no	—
103	C₂	#16840708	1	1	yes	characteristic
104	C₂	C₂×#14519846	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519846

C₂

yes

maximal

#16840708

C₂

yes

maximal

C₄×C₈×D₆₁

C₂

yes

maximal, characteristic

C₂×C₄⋊#6923

—

C₂×C₄⋊#6923

C₂²

yes

—

#14519846

—

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

D₈

yes

—

C₄×D₆₁

Q₁₆

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×D₈

yes

—

C₂×D₆₁

C₂×Q₁₆

yes

—

#6923

—

C₄×C₆₁

#107

yes

complemented

C₄×C₆₁

C₂×C₄⋊C₄

yes

—

Dic₆₁

#107

yes

complemented

Dic₆₁

C₄⋊Q₈

yes

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

—

D₆₁

yes

D₆₁

yes

D₆₁

yes

—

C₂×#107

—

C₂×C₄×C₈

—

#384

—

C₆₁

#1845

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

122

—

C₂×C₄²

—

#107

—

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

—

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

—

C₂²

C₂×C₄⋊#6923

yes

characteristic

C₄

—

C₄

—

C₄

—

488

—

C₄

#14519846

yes

complemented

C₄

C₂×C₄⋊#6923

yes

—

100

C₂

—

101

C₂

—

102

C₂

—

103

C₂

#16840708

yes

characteristic

104

C₂

C₂×#14519846

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	#1845
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
35. C₈×C₆₁	C₄⋊C₄	semidirect
36. #92418	C₄⋊C₄	semidirect
43. C₄×C₆₁	#107	semidirect
45. Dic₆₁	#107	semidirect
56. C₆₁	#1845	semidirect
64. C₄×C₈	#6923	semidirect
89. C₈	C₄⋊#6923	semidirect
98. C₄	#14519846	semidirect

H ≅ G/N

type

9. C₄×#92418

C₄

semidirect

10. C₈×Dic₆₁

C₄

semidirect

11. C₄×C₈×C₆₁

C₄

semidirect

35. C₈×C₆₁

C₄⋊C₄

semidirect

36. #92418

C₄⋊C₄

semidirect

43. C₄×C₆₁

#107

semidirect

45. Dic₆₁

#107

semidirect

56. C₆₁

#1845

semidirect

64. C₄×C₈

#6923

semidirect

89. C₈

C₄⋊#6923

semidirect

98. C₄

#14519846

semidirect

Subgroups — #21461755

Conjugacy classes of subgroups

Complements