Group #21460643 — subgroups

Subgroups — #21460643

Order 7808.

168 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 66 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	#16840778	C₂	1	2	yes	maximal
2	#16839608	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#92420	—	2	2	no	—
4	C₂²⋊#92420	—	2	2	no	—
5	C₄×#92420	C₄	1	4	yes	complemented
6	C₂×C₄×Dic₆₁	C₄	1	1	yes	characteristic
7	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
8	#14519684	—	2	2	no	—
9	C₂×C₄²×C₆₁	C₄	1	1	yes	characteristic
10	C₂²×C₄×C₆₁	—	2	1	no	—
11	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
12	C₂²×Dic₆₁	—	2	1	no	—
13	C₂²×Dic₆₁	D₄	1	2	yes	—
14	C₂×#92420	—	2	4	no	—
15	C₄²×C₆₁	—	2	1	no	—
16	C₄²×C₆₁	C₈	1	2	yes	complemented
17	C₄×Dic₆₁	—	2	1	no	—
18	C₄×Dic₆₁	C₈	1	2	yes	complemented
19	C₄×Dic₆₁	C₂×C₄	1	2	yes	—
20	C₄×Dic₆₁	D₄	1	1	yes	characteristic
21	C₄×Dic₆₁	Q₈	1	1	yes	characteristic
22	C₂³×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₆₁	—	2	2	no	—
24	C₂×C₄×C₆₁	—	4	2	no	—
25	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
26	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
28	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
30	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
31	C₂×Dic₆₁	—	2	2	no	—
32	C₂×Dic₆₁	—	4	2	no	—
33	C₂×Dic₆₁	—	4	2	no	—
34	C₂×Dic₆₁	C₂²⋊C₄	1	2	yes	—
35	C₂×Dic₆₁	C₄⋊C₄	1	2	yes	—
36	#92420	—	4	4	no	—
37	C₂²×C₆₁	—	2	2	no	—
38	C₂²×C₆₁	#95	1	1	yes	characteristic
39	C₂²×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
40	C₂²×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
41	C₄×C₆₁	—	4	2	no	—
42	C₄×C₆₁	C₄×C₈	1	1	yes	characteristic
43	C₄×C₆₁	#97	1	1	yes	characteristic
44	C₄×C₆₁	C₄⋊C₈	1	1	yes	characteristic
45	C₄×C₆₁	C₄⋊C₈	1	1	yes	characteristic
46	Dic₆₁	—	2	2	no	—
47	Dic₆₁	—	2	2	no	—
48	Dic₆₁	—	4	2	no	—
49	#1274	—	61	1	no	maximal, Sylow
50	C₂×C₆₁	—	2	1	no	—
51	C₂×C₆₁	—	2	1	no	—
52	C₂×C₆₁	#336	1	1	yes	characteristic
53	C₂×C₆₁	H(3,ℤ/4)	1	2	yes	—
54	#431	—	61	2	no	—
55	#376	—	61	1	no	—
56	C₆₁	#1274	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₄²	—	61	1	no	—
58	C₂×C₄²	—	61	1	no	—
59	C₂×C₄²	#6923	1	1	yes	characteristic
60	C₄⋊C₈	—	122	2	no	—
61	C₂²⋊C₈	—	122	2	no	—
62	C₄×C₈	—	61	4	no	—
63	#95	—	122	2	no	—
64	C₂²×C₄	—	2	1	no	—
65	C₂²×C₄	—	61	2	no	—
66	C₂²×C₄	—	122	1	no	—
67	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
68	C₂×C₈	—	122	4	no	—
69	C₄²	—	2	1	no	—
70	C₄²	—	61	2	no	—
71	C₄²	—	61	1	no	—
72	C₄²	—	61	1	no	—
73	C₄²	—	61	2	no	—
74	C₄²	—	122	1	no	—
75	C₄²	#92420	1	2	yes	complemented
76	C₂³	C₂²⋊#6923	1	1	yes	characteristic
77	C₂×C₄	—	2	2	no	—
78	C₂×C₄	—	4	2	no	—
79	C₂×C₄	—	61	2	no	—
80	C₂×C₄	—	61	2	no	—
81	C₂×C₄	—	122	2	no	—
82	C₂×C₄	—	244	2	no	—
83	C₂×C₄	—	244	2	no	—
84	C₂×C₄	D₆₁⋊C₈	1	1	yes	characteristic
85	C₂×C₄	#11758213	1	1	yes	characteristic
86	C₂×C₄	C₄×#6923	1	1	yes	characteristic
87	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
88	C₂×C₄	C₂×#92420	1	1	yes	characteristic
89	C₂×C₄	#11758217	1	1	yes	characteristic
90	C₈	—	244	4	no	—
91	C₂²	—	2	2	no	—
92	C₂²	(C₂×#6923)⋊C₄	1	1	yes	characteristic
93	C₂²	C₂²⋊#92420	1	1	yes	characteristic
94	C₂²	#14519834	1	1	yes	characteristic
95	C₄	—	4	2	no	—
96	C₄	—	122	2	no	—
97	C₄	—	122	2	no	—
98	C₄	—	244	2	no	—
99	C₄	C₄×#92420	1	1	yes	characteristic
100	C₄	#14519832	1	1	yes	characteristic
101	C₄	C₄⋊#92420	1	1	yes	characteristic
102	C₄	#14519844	1	1	yes	characteristic
103	C₂	—	2	1	no	—
104	C₂	—	2	1	no	—
105	C₂	#16840628	1	1	yes	characteristic
106	C₂	#16840629	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#16840778

C₂

yes

maximal

#16839608

C₂

yes

maximal, characteristic

C₄⋊#92420

—

C₂²⋊#92420

—

C₄×#92420

C₄

yes

complemented

C₂×C₄×Dic₆₁

C₄

yes

characteristic

C₂×C₄×Dic₆₁

C₂²

yes

characteristic

#14519684

—

C₂×C₄²×C₆₁

C₄

yes

characteristic

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

—

C₂²×Dic₆₁

D₄

yes

—

C₂×#92420

—

C₄²×C₆₁

—

C₄²×C₆₁

C₈

yes

complemented

C₄×Dic₆₁

—

C₄×Dic₆₁

C₈

yes

complemented

C₄×Dic₆₁

C₂×C₄

yes

—

C₄×Dic₆₁

D₄

yes

characteristic

C₄×Dic₆₁

Q₈

yes

characteristic

C₂³×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

M₁₆

yes

characteristic

C₂×C₄×C₆₁

M₁₆

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

C₂²⋊C₄

yes

—

C₂×Dic₆₁

C₄⋊C₄

yes

—

#92420

—

C₂²×C₆₁

—

C₂²×C₆₁

#95

yes

characteristic

C₂²×C₆₁

C₂²⋊C₈

yes

characteristic

C₂²×C₆₁

C₂²⋊C₈

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

C₄×C₈

yes

characteristic

C₄×C₆₁

#97

yes

characteristic

C₄×C₆₁

C₄⋊C₈

yes

characteristic

C₄×C₆₁

C₄⋊C₈

yes

characteristic

Dic₆₁

—

Dic₆₁

—

Dic₆₁

—

#1274

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

#336

yes

characteristic

C₂×C₆₁

H(3,ℤ/4)

yes

—

#431

—

#376

—

C₆₁

#1274

yes

characteristic, complemented, Sylow

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

#6923

yes

characteristic

C₄⋊C₈

—

122

—

C₂²⋊C₈

—

122

—

C₄×C₈

—

#95

—

122

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

122

—

C₂²×C₄

C₂×#6923

yes

characteristic

C₂×C₈

—

122

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

122

—

C₄²

#92420

yes

complemented

C₂³

C₂²⋊#6923

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

D₆₁⋊C₈

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

244

—

C₂²

—

C₂²

yes

C₂²

yes

C₂²

yes

C₄

—

C₄

—

122

—

C₄

—

122

—

C₄

—

244

—

C₄

C₄×#92420

yes

characteristic

100

C₄

#14519832

yes

characteristic

101

C₄

C₄⋊#92420

yes

characteristic

102

C₄

#14519844

yes

characteristic

103

C₂

—

104

C₂

—

105

C₂

#16840628

yes

characteristic

106

C₂

#16840629

yes

—

	subgroup	G/H
center	C₂×C₄	C₄×#6923
commutator	C₄×C₆₁	C₄×C₈
Frattini	C₂²×C₄	C₂×#6923
Fitting	C₂×C₄²×C₆₁	C₄
socle	C₂²×C₆₁	#95
hypercenter	C₂×C₄²	#6923
hypocenter	C₆₁	#1274
LCS	G ▷ C₄×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄²

subgroup

G/H

center

C₂×C₄

C₄×#6923

commutator

C₄×C₆₁

C₄×C₈

Frattini

C₂²×C₄

C₂×#6923

Fitting

C₂×C₄²×C₆₁

C₄

C₂²×C₆₁

C₂×C₄²

C₆₁

G ▷ C₄×C₆₁ ▷ C₆₁

C₁ ◁ C₂×C₄ ◁ C₂×C₄²

N	H ≅ G/N	type
5. C₄×#92420	C₄	semidirect
16. C₄²×C₆₁	C₈	semidirect
18. C₄×Dic₆₁	C₈	semidirect
56. C₆₁	#1274	semidirect
75. C₄²	#92420	semidirect

H ≅ G/N

type

5. C₄×#92420

C₄

semidirect

16. C₄²×C₆₁

C₈

semidirect

18. C₄×Dic₆₁

C₈

semidirect

56. C₆₁

#1274

semidirect

75. C₄²

#92420

semidirect

Subgroups — #21460643

Conjugacy classes of subgroups

Complements