Group #21454010 — subgroups

Subgroups — #21454010

Order 7808.

380 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 117 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	#16839704	C₂	1	6	yes	maximal, complemented
2	#16839687	C₂	1	3	yes	maximal
3	#16839681	C₂	1	2	yes	maximal, complemented
4	#16839634	C₂	1	3	yes	maximal
5	C₆₁×#393	C₂	1	1	yes	maximal, characteristic
6	C₂³×Dic₆₁	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₆₁	C₂²	1	3	yes	—
8	C₂×#11758196	C₂²	1	6	yes	—
9	C₂×C₂²⋊Dic₆₁	C₂²	1	3	yes	—
10	#14519684	C₂²	1	6	yes	—
11	#14519684	C₂²	1	3	yes	—
12	#14519684	C₂²	1	6	yes	—
13	C₂²×Q₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊C₄×C₆₁	C₂²	1	3	yes	—
15	#95×C₆₁	C₂²	1	3	yes	—
16	C₂⁴×C₆₁	C₂³	1	1	yes	characteristic
17	C₂×Q₈×C₆₁	—	4	3	no	—
18	C₂²×C₄×C₆₁	C₂³	1	3	yes	—
19	C₂²×C₄×C₆₁	C₂³	1	3	yes	—
20	C₂²×Dic₆₁	—	4	3	no	—
21	C₂²×Dic₆₁	C₂³	1	2	yes	—
22	C₂²×Dic₆₁	C₂³	1	6	yes	—
23	C₂²⋊C₄×C₆₁	—	4	3	no	—
24	C₂²⋊Dic₆₁	—	2	6	no	—
25	C₄⋊Dic₆₁	—	4	3	no	—
26	#11758196	—	4	6	no	—
27	C₂³×C₆₁	—	2	3	no	—
28	C₂³×C₆₁	—	2	3	no	—
29	C₂³×C₆₁	#41	1	2	yes	—
30	C₂³×C₆₁	C₂⁴	1	1	yes	characteristic
31	Q₈×C₆₁	—	4	4	no	—
32	C₂×C₄×C₆₁	—	2	6	no	—
33	C₂×C₄×C₆₁	—	2	3	no	—
34	C₂×C₄×C₆₁	—	2	3	no	—
35	C₂×C₄×C₆₁	—	2	6	no	—
36	C₂×Dic₆₁	—	2	6	no	—
37	C₂×Dic₆₁	—	2	6	no	—
38	C₂×Dic₆₁	—	2	6	no	—
39	C₂×Dic₆₁	—	2	6	no	—
40	C₂×Dic₆₁	—	4	4	no	—
41	C₂²×C₆₁	—	2	6	no	—
42	C₂²×C₆₁	—	4	1	no	—
43	C₂²×C₆₁	—	4	3	no	—
44	C₂²×C₆₁	C₂×#41	1	1	yes	characteristic
45	C₂²×C₆₁	H(5,𝔽₂)	1	3	yes	—
46	C₂²×C₆₁	2₋¹⁺⁴	1	3	yes	—
47	C₄×C₆₁	—	4	3	no	—
48	C₄×C₆₁	—	4	3	no	—
49	Dic₆₁	—	4	6	no	—
50	Dic₆₁	—	4	2	no	—
51	#2835	—	61	1	no	maximal, Sylow
52	C₂×C₆₁	—	4	2	no	—
53	C₂×C₆₁	#539	1	3	yes	—
54	C₂×C₆₁	H(3,𝔽₄)	1	1	yes	characteristic
55	C₂×C₆₁	#563	1	3	yes	—
56	#400	—	61	6	no	—
57	#397	—	61	3	no	—
58	#395	—	61	2	no	—
59	#393	D₆₁	1	1	yes	characteristic
60	#385	—	61	3	no	—
61	C₆₁	#2835	1	1	yes	characteristic, complemented, Sylow
62	C₂²×Q₈	C₂×D₆₁	1	1	yes	characteristic
63	C₂³×C₄	—	61	1	no	—
64	C₂×C₄⋊C₄	—	61	6	no	—
65	C₂×C₄⋊C₄	—	61	3	no	—
66	C₂×C₂²⋊C₄	—	61	3	no	—
67	C₂×C₂²⋊C₄	C₂×D₆₁	1	3	yes	—
68	#95	—	61	6	no	—
69	#95	—	61	6	no	—
70	#95	—	61	3	no	—
71	#95	C₂×D₆₁	1	3	yes	—
72	C₂⁴	C₂²×D₆₁	1	1	yes	characteristic
73	C₂×Q₈	—	4	3	no	—
74	C₂²×C₄	—	61	6	no	—
75	C₂²×C₄	—	61	2	no	—
76	C₂²×C₄	—	244	3	no	—
77	C₂²×C₄	C₂²×D₆₁	1	3	yes	—
78	C₂²×C₄	C₂²×D₆₁	1	3	yes	—
79	C₄⋊C₄	—	244	6	no	—
80	C₄⋊C₄	—	244	3	no	—
81	C₂²⋊C₄	—	4	3	no	—
82	C₂²⋊C₄	—	122	6	no	—
83	C₂³	—	2	3	no	—
84	C₂³	—	2	3	no	—
85	C₂³	#11758226	1	2	yes	—
86	C₂³	C₂³×D₆₁	1	1	yes	characteristic
87	Q₈	—	4	4	no	—
88	C₂×C₄	—	2	3	no	—
89	C₂×C₄	—	2	3	no	—
90	C₂×C₄	—	2	6	no	—
91	C₂×C₄	—	2	6	no	—
92	C₂×C₄	—	122	6	no	—
93	C₂×C₄	—	122	6	no	—
94	C₂×C₄	—	122	6	no	—
95	C₂×C₄	—	122	6	no	—
96	C₂×C₄	—	244	4	no	—
97	C₂²	—	2	6	no	—
98	C₂²	—	4	1	no	—
99	C₂²	—	4	3	no	—
100	C₂²	C₂×#11758226	1	1	yes	characteristic
101	C₂²	#14519822	1	3	yes	—
102	C₂²	#14519824	1	3	yes	—
103	C₄	—	4	3	no	—
104	C₄	—	4	3	no	—
105	C₄	—	244	2	no	—
106	C₄	—	244	6	no	—
107	C₂	—	4	2	no	—
108	C₂	#16840361	1	3	yes	—
109	C₂	#16840505	1	1	yes	characteristic
110	C₂	#16840512	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#16839704

C₂

yes

maximal, complemented

#16839687

C₂

yes

maximal

#16839681

C₂

yes

maximal, complemented

#16839634

C₂

yes

maximal

C₆₁×#393

C₂

yes

maximal, characteristic

C₂³×Dic₆₁

C₂²

yes

characteristic

C₂×C₄⋊Dic₆₁

C₂²

yes

—

C₂×#11758196

C₂²

yes

—

C₂×C₂²⋊Dic₆₁

C₂²

yes

—

#14519684

C₂²

yes

—

#14519684

C₂²

yes

—

#14519684

C₂²

yes

—

C₂²×Q₈×C₆₁

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₆₁

C₂²

yes

—

#95×C₆₁

C₂²

yes

—

C₂⁴×C₆₁

C₂³

yes

characteristic

C₂×Q₈×C₆₁

—

C₂²×C₄×C₆₁

C₂³

yes

—

C₂²×C₄×C₆₁

C₂³

yes

—

C₂²×Dic₆₁

—

C₂²×Dic₆₁

C₂³

yes

—

C₂²×Dic₆₁

C₂³

yes

—

C₂²⋊C₄×C₆₁

—

C₂²⋊Dic₆₁

—

C₄⋊Dic₆₁

—

#11758196

—

C₂³×C₆₁

—

C₂³×C₆₁

—

C₂³×C₆₁

#41

yes

—

C₂³×C₆₁

C₂⁴

yes

characteristic

Q₈×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

C₂×#41

yes

characteristic

C₂²×C₆₁

H(5,𝔽₂)

yes

—

C₂²×C₆₁

2₋¹⁺⁴

yes

—

C₄×C₆₁

—

C₄×C₆₁

—

Dic₆₁

—

Dic₆₁

—

#2835

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

#539

yes

—

C₂×C₆₁

H(3,𝔽₄)

yes

characteristic

C₂×C₆₁

#563

yes

—

—

—

—

D₆₁

yes

characteristic

#385

—

C₆₁

#2835

yes

characteristic, complemented, Sylow

C₂²×Q₈

C₂×D₆₁

yes

characteristic

C₂³×C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₆₁

yes

—

—

—

—

C₂×D₆₁

yes

—

C₂⁴

C₂²×D₆₁

yes

characteristic

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

244

—

C₂²×C₄

C₂²×D₆₁

yes

—

C₂²×C₄

C₂²×D₆₁

yes

—

C₄⋊C₄

—

244

—

C₄⋊C₄

—

244

—

C₂²⋊C₄

—

C₂²⋊C₄

—

122

—

C₂³

—

C₂³

—

C₂³

#11758226

yes

—

C₂³

C₂³×D₆₁

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

244

—

C₂²

—

C₂²

—

C₂²

—

100

C₂²

C₂×#11758226

yes

characteristic

101

C₂²

#14519822

yes

—

102

C₂²

#14519824

yes

—

103

C₄

—

104

C₄

—

105

C₄

—

244

—

106

C₄

—

244

—

107

C₂

—

108

C₂

#16840361

yes

—

109

C₂

#16840505

yes

characteristic

110

C₂

#16840512

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₆₁
commutator, socle	C₂³×C₆₁	C₂⁴
Fitting	C₆₁×#393	C₂
hypercenter	#393	D₆₁
hypocenter	C₆₁	#2835
LCS	G ▷ C₂³×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ #393

subgroup

G/H

center, Frattini

C₂³

C₂³×D₆₁

commutator, socle

C₂³×C₆₁

C₂⁴

Fitting

C₆₁×#393

C₂

D₆₁

C₆₁

G ▷ C₂³×C₆₁ ▷ C₆₁

C₁ ◁ C₂³ ◁ #393

N	H ≅ G/N	type
1. #16839704	C₂	semidirect
3. #16839681	C₂	semidirect
61. C₆₁	#2835	semidirect

H ≅ G/N

type

1. #16839704

C₂

semidirect

3. #16839681

C₂

semidirect

61. C₆₁

#2835

semidirect

Subgroups — #21454010

Conjugacy classes of subgroups

Complements