Group #21461466 — subgroups

Subgroups — #21461466

Order 7808.

148 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 56 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	#16840813	C₂	1	2	yes	maximal
2	#16840623	C₂	1	1	yes	maximal, characteristic
3	Q₈⋊#92420	C₂	1	2	yes	maximal
4	#16840603	C₂	1	1	yes	maximal, characteristic
5	Q₁₆×Dic₆₁	C₂	1	1	yes	maximal, characteristic
6	#14519844	—	2	2	no	—
7	C₄⋊#92420	C₂²	1	2	yes	—
8	#14519832	—	2	2	no	—
9	C₄×#92420	C₂²	1	1	yes	characteristic
10	C₄×#92420	C₂²	1	1	yes	characteristic
11	Q₈×Dic₆₁	C₂²	1	2	yes	—
12	#14519711	C₄	1	1	yes	characteristic
13	#14519701	C₄	1	2	yes	—
14	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
15	C₂×Q₁₆×C₆₁	C₄	1	1	yes	characteristic
16	C₂×Q₈×C₆₁	C₂×C₄	1	2	yes	—
17	C₂×#92420	—	2	2	no	—
18	C₂×#92420	—	2	1	no	—
19	C₂×#92420	D₄	1	2	yes	—
20	Q₁₆×C₆₁	—	2	2	no	—
21	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
22	C₄⋊Dic₆₁	—	2	2	no	—
23	C₄⋊Dic₆₁	C₂×C₄	1	2	yes	—
24	C₄×Dic₆₁	—	2	2	no	—
25	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
26	C₂×#92418	C₂×C₄	1	1	yes	characteristic
27	Q₈×C₆₁	—	2	2	no	—
28	Q₈×C₆₁	—	2	2	no	—
29	C₂×C₄×C₆₁	—	2	2	no	—
30	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₆₁	—	2	2	no	—
32	C₂×Dic₆₁	C₂×D₄	1	1	yes	characteristic
33	C₂×Dic₆₁	#41	1	1	yes	characteristic
34	#92420	—	2	2	no	—
35	#92420	—	4	1	no	—
36	#92420	—	4	2	no	—
37	C₈×C₆₁	M₁₆	1	2	yes	—
38	#92418	—	2	1	no	—
39	C₂²×C₆₁	C₄×D₄	1	1	yes	characteristic
40	C₄×C₆₁	—	4	2	no	—
41	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
42	C₄×C₆₁	#131	1	1	yes	characteristic
43	Dic₆₁	—	2	1	no	—
44	Dic₆₁	—	4	2	no	—
45	Dic₆₁	#137	1	2	yes	—
46	#1593	—	61	1	no	maximal, Sylow
47	C₂×C₆₁	#436	1	1	yes	characteristic
48	C₂×C₆₁	#441	1	1	yes	characteristic
49	C₂×C₆₁	#444	1	1	yes	characteristic
50	#446	—	61	2	no	—
51	C₄×Q₁₆	—	61	1	no	—
52	#334	—	61	1	no	—
53	Q₈⋊C₈	—	61	2	no	—
54	#322	—	61	1	no	—
55	C₆₁	#1593	1	1	yes	characteristic, complemented, Sylow
56	C₂×Q₁₆	#6923	1	1	yes	characteristic
57	C₄×Q₈	—	61	2	no	—
58	#107	—	61	1	no	—
59	C₄⋊C₈	—	61	2	no	—
60	C₄⋊C₈	—	122	2	no	—
61	#103	—	61	2	no	—
62	#97	—	122	2	no	—
63	C₄×C₈	—	61	1	no	—
64	C₄×C₈	—	61	1	no	—
65	C₄×C₈	—	61	1	no	—
66	C₂×Q₈	C₂×#6923	1	2	yes	—
67	Q₁₆	—	2	2	no	—
68	C₂×C₈	—	61	2	no	—
69	C₂×C₈	—	61	1	no	—
70	C₂×C₈	—	122	1	no	—
71	C₂×C₈	—	122	2	no	—
72	C₂×C₈	C₂×#6923	1	1	yes	characteristic
73	C₄⋊C₄	—	61	2	no	—
74	C₄⋊C₄	—	122	2	no	—
75	C₄²	—	61	1	no	—
76	C₄²	—	122	2	no	—
77	Q₈	—	2	2	no	—
78	Q₈	—	2	2	no	—
79	C₂×C₄	—	2	2	no	—
80	C₂×C₄	—	61	1	no	—
81	C₂×C₄	—	61	1	no	—
82	C₂×C₄	—	122	2	no	—
83	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
84	C₈	—	122	2	no	—
85	C₈	—	122	1	no	—
86	C₈	—	244	2	no	—
87	C₈	—	244	1	no	—
88	C₈	#11758217	1	2	yes	—
89	C₂²	D₄×#6923	1	1	yes	characteristic
90	C₄	—	4	2	no	—
91	C₄	—	61	2	no	—
92	C₄	—	122	1	no	—
93	C₄	—	244	2	no	—
94	C₄	C₂×#11758217	1	1	yes	characteristic
95	C₄	#14519864	1	1	yes	characteristic
96	C₂	#16840797	1	1	yes	characteristic
97	C₂	#16840802	1	1	yes	characteristic
98	C₂	#16840808	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840813

C₂

yes

maximal

#16840623

C₂

yes

maximal, characteristic

Q₈⋊#92420

C₂

yes

maximal

#16840603

C₂

yes

maximal, characteristic

Q₁₆×Dic₆₁

C₂

yes

maximal, characteristic

#14519844

—

C₄⋊#92420

C₂²

yes

—

#14519832

—

C₄×#92420

C₂²

yes

characteristic

C₄×#92420

C₂²

yes

characteristic

Q₈×Dic₆₁

C₂²

yes

—

#14519711

C₄

yes

characteristic

#14519701

C₄

yes

—

C₈×Dic₆₁

C₂²

yes

characteristic

C₂×Q₁₆×C₆₁

C₄

yes

characteristic

C₂×Q₈×C₆₁

C₂×C₄

yes

—

C₂×#92420

—

C₂×#92420

—

C₂×#92420

D₄

yes

—

Q₁₆×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

C₂×C₄

yes

—

C₄×Dic₆₁

—

C₄×Dic₆₁

C₂³

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

Q₈×C₆₁

—

Q₈×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

C₂×D₄

yes

C₂×Dic₆₁

yes

—

—

—

C₈×C₆₁

M₁₆

yes

—

#92418

—

C₂²×C₆₁

C₄×D₄

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

C₂×M₁₆

yes

characteristic

C₄×C₆₁

#131

yes

characteristic

Dic₆₁

—

Dic₆₁

—

Dic₆₁

#137

yes

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

—

C₄×Q₁₆

—

#334

—

Q₈⋊C₈

—

#322

—

C₆₁

#1593

yes

characteristic, complemented, Sylow

C₂×Q₁₆

#6923

yes

characteristic

C₄×Q₈

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

122

—

#103

—

#97

—

122

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂×Q₈

C₂×#6923

yes

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

C₂×#6923

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

122

—

C₄²

—

C₄²

—

122

—

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

C₂²×#6923

yes

characteristic

C₈

—

122

—

C₈

—

122

—

C₈

—

244

—

C₈

—

244

—

C₈

#11758217

yes

—

C₂²

D₄×#6923

yes

characteristic

C₄

—

C₄

—

C₄

—

122

—

C₄

—

244

—

C₄

yes

C₄

yes

C₂

yes

C₂

yes

C₂

yes

	subgroup	G/H
center	C₂²	D₄×#6923
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×#6923
Fitting	C₂×Q₁₆×C₆₁	C₄
socle	C₂²×C₆₁	C₄×D₄
hypercenter	C₂×Q₁₆	#6923
hypocenter	C₆₁	#1593
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

subgroup

G/H

center

C₂²

D₄×#6923

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂×C₄

C₂²×#6923

Fitting

C₂×Q₁₆×C₆₁

C₄

socle

C₂²×C₆₁

C₄×D₄

C₂×Q₁₆

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

N	H ≅ G/N	type
55. C₆₁	#1593	semidirect

H ≅ G/N

type

55. C₆₁

#1593

semidirect

Subgroups — #21461466

Conjugacy classes of subgroups

Complements