Group #21461374 — subgroups

Subgroups — #21461374

Order 7808.

184 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 82 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	#16840766	C₂	1	2	yes	maximal
2	#16840623	C₂	1	4	yes	maximal, complemented
3	C₄×C₈×D₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#11758213	—	2	2	no	—
5	C₄⋊#92420	—	2	2	no	—
6	C₄⋊#92420	C₂²	1	4	yes	—
7	C₂×C₈×D₆₁	C₄	1	2	yes	—
8	C₄²×D₆₁	C₂²	1	1	yes	characteristic
9	C₄×#92418	C₄	1	1	yes	characteristic
10	C₈×Dic₆₁	C₂²	1	2	yes	—
11	C₄×C₈×C₆₁	C₄	1	1	yes	characteristic
12	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×D₆₁	D₄	1	1	yes	characteristic
14	C₂×C₄×D₆₁	Q₈	1	1	yes	characteristic
15	C₂×#92420	—	2	4	no	—
16	#11758213	—	4	4	no	—
17	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
18	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
19	C₄×Dic₆₁	D₄	1	1	yes	characteristic
20	C₄×Dic₆₁	Q₈	1	1	yes	characteristic
21	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
22	C₂×#92418	C₂×C₄	1	2	yes	—
23	C₈×D₆₁	—	2	4	no	—
24	C₂²×D₆₁	C₄⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
28	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
29	C₂×Dic₆₁	C₂×D₄	1	1	yes	characteristic
30	C₂×Dic₆₁	C₂×Q₈	1	1	yes	characteristic
31	C₄×D₆₁	—	2	2	no	—
32	C₄×D₆₁	—	2	2	no	—
33	C₄×D₆₁	SD₁₆	1	4	yes	—
34	#92420	—	4	4	no	—
35	C₈×C₆₁	M₁₆	1	4	yes	complemented
36	#92418	—	2	2	no	—
37	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₂×D₆₁	—	2	1	no	—
39	C₂×D₆₁	—	2	1	no	—
40	C₂×D₆₁	#106	1	2	yes	—
41	C₄×C₆₁	#106	1	2	yes	—
42	C₄×C₆₁	#108	1	2	yes	—
43	C₄×C₆₁	C₂×M₁₆	1	2	yes	—
44	Dic₆₁	—	2	1	no	—
45	Dic₆₁	—	2	1	no	—
46	Dic₆₁	C₂×SD₁₆	1	2	yes	—
47	#1566	—	61	1	no	maximal, Sylow
48	C₂×C₆₁	#423	1	1	yes	characteristic
49	C₂×C₆₁	C₂×#106	1	1	yes	characteristic
50	C₂×C₆₁	C₂×#108	1	1	yes	characteristic
51	D₆₁	—	2	2	no	—
52	#423	—	61	2	no	—
53	C₂×C₄×C₈	—	61	1	no	—
54	#334	—	61	4	no	—
55	C₆₁	#1566	1	1	yes	characteristic, complemented, Sylow
56	C₂×M₁₆	—	122	2	no	—
57	C₂²×C₈	—	61	2	no	—
58	C₂×C₄²	—	61	1	no	—
59	C₄⋊C₈	—	61	4	no	—
60	C₄⋊C₈	—	122	2	no	—
61	C₄×C₈	—	61	2	no	—
62	C₄×C₈	—	61	1	no	—
63	C₄×C₈	#6923	1	1	yes	characteristic
64	C₂²×C₄	—	61	1	no	—
65	C₂²×C₄	—	61	1	no	—
66	C₂²×C₄	—	61	1	no	—
67	M₁₆	—	244	4	no	—
68	C₂×C₈	—	61	2	no	—
69	C₂×C₈	—	122	4	no	—
70	C₂×C₈	—	122	4	no	—
71	C₂×C₈	C₂×#6923	1	2	yes	—
72	C₄²	—	61	1	no	—
73	C₄²	—	61	1	no	—
74	C₄²	—	61	1	no	—
75	C₄²	C₂×#6923	1	1	yes	characteristic
76	C₂³	—	61	1	no	—
77	C₂×C₄	—	61	1	no	—
78	C₂×C₄	—	61	4	no	—
79	C₂×C₄	—	61	1	no	—
80	C₂×C₄	—	61	1	no	—
81	C₂×C₄	—	122	2	no	—
82	C₂×C₄	—	122	2	no	—
83	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
84	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
85	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
86	C₈	—	122	2	no	—
87	C₈	—	244	4	no	—
88	C₈	#11758213	1	4	yes	complemented
89	C₂²	—	61	2	no	—
90	C₂²	—	122	1	no	—
91	C₂²	—	122	1	no	—
92	C₂²	C₂×C₄⋊#6923	1	1	yes	characteristic
93	C₄	—	61	2	no	—
94	C₄	—	122	1	no	—
95	C₄	—	122	1	no	—
96	C₄	#14519845	1	2	yes	—
97	C₄	#14519847	1	2	yes	—
98	C₄	C₂×#11758213	1	2	yes	—
99	C₂	—	122	2	no	—
100	C₂	#16840766	1	1	yes	characteristic
101	C₂	C₂×#14519845	1	1	yes	characteristic
102	C₂	C₂×#14519847	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840766

C₂

yes

maximal

#16840623

C₂

yes

maximal, complemented

C₄×C₈×D₆₁

C₂

yes

maximal, characteristic

C₂×#11758213

—

C₄⋊#92420

—

C₄⋊#92420

C₂²

yes

—

C₂×C₈×D₆₁

C₄

yes

—

C₄²×D₆₁

C₂²

yes

characteristic

C₄×#92418

C₄

yes

characteristic

C₈×Dic₆₁

C₂²

yes

—

C₄×C₈×C₆₁

C₄

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₄×D₆₁

D₄

yes

characteristic

C₂×C₄×D₆₁

Q₈

yes

characteristic

C₂×#92420

—

#11758213

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

D₄

yes

characteristic

C₄×Dic₆₁

Q₈

yes

characteristic

C₄×Dic₆₁

C₂³

yes

characteristic

C₂×#92418

C₂×C₄

yes

—

C₈×D₆₁

—

C₂²×D₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

C₂×D₄

yes

characteristic

C₂×Dic₆₁

C₂×Q₈

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

SD₁₆

yes

—

#92420

—

C₈×C₆₁

M₁₆

yes

complemented

#92418

—

C₂²×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

#106

yes

—

C₄×C₆₁

#106

yes

—

C₄×C₆₁

#108

yes

—

C₄×C₆₁

C₂×M₁₆

yes

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

C₂×SD₁₆

yes

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

D₆₁

—

#423

—

C₂×C₄×C₈

—

#334

—

C₆₁

#1566

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

122

—

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

122

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#6923

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

244

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

C₂×#6923

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#6923

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂²×#6923

yes

characteristic

C₈

—

122

—

C₈

—

244

—

C₈

#11758213

yes

complemented

C₂²

—

C₂²

—

122

—

C₂²

—

122

—

C₂²

C₂×C₄⋊#6923

yes

characteristic

C₄

—

C₄

—

122

—

C₄

—

122

—

C₄

#14519845

yes

—

C₄

#14519847

yes

—

C₄

C₂×#11758213

yes

—

C₂

—

122

—

100

C₂

#16840766

yes

characteristic

101

C₂

C₂×#14519845

yes

characteristic

102

C₂

C₂×#14519847

yes

characteristic

	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	#1566
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
2. #16840623	C₂	semidirect
35. C₈×C₆₁	M₁₆	semidirect
55. C₆₁	#1566	semidirect
88. C₈	#11758213	semidirect

H ≅ G/N

type

2. #16840623

C₂

semidirect

35. C₈×C₆₁

M₁₆

semidirect

55. C₆₁

#1566

semidirect

88. C₈

#11758213

semidirect

Subgroups — #21461374

Conjugacy classes of subgroups

Complements