Group #21454182 — subgroups

Subgroups — #21454182

Order 7808.

472 conjugacy classes of subgroups; only the 213 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 213 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×#14519769	C₂	1	2	yes	maximal
2	#16839660	C₂	1	8	yes	maximal
3	#16839632	C₂	1	2	yes	maximal
4	#16839628	C₂	1	2	yes	maximal
5	C₄³×C₆₁	C₂	1	1	yes	maximal, characteristic
6	#14519769	—	2	8	no	—
7	C₂×C₄⋊Dic₆₁	C₂²	1	4	yes	—
8	C₂×C₄⋊Dic₆₁	C₂²	1	8	yes	—
9	C₂×#11758196	C₂²	1	8	yes	—
10	#14519684	C₂²	1	8	yes	—
11	C₂×C₄²×C₆₁	C₂²	1	4	yes	—
12	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₆₁	C₂³	1	2	yes	—
16	C₂²×C₄×C₆₁	C₂³	1	2	yes	—
17	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
18	C₂²×C₄×C₆₁	C₂³	1	2	yes	—
19	C₂²×Dic₆₁	C₂³	1	8	yes	—
20	C₄²×C₆₁	—	2	8	no	—
21	C₄²×C₆₁	D₄	1	4	yes	—
22	C₄²×C₆₁	Q₈	1	4	yes	—
23	C₄²×C₆₁	Q₈	1	4	yes	—
24	C₄⋊Dic₆₁	—	2	8	no	—
25	C₄⋊Dic₆₁	—	2	16	no	—
26	#11758196	—	2	16	no	—
27	C₂³×C₆₁	C₂⁴	1	1	yes	characteristic
28	C₂×C₄×C₆₁	—	2	4	no	—
29	C₂×C₄×C₆₁	—	2	4	no	—
30	C₂×C₄×C₆₁	C₂×D₄	1	4	yes	—
31	C₂×C₄×C₆₁	C₂×D₄	1	2	yes	—
32	C₂×C₄×C₆₁	C₂×Q₈	1	4	yes	—
33	C₂×C₄×C₆₁	C₂×Q₈	1	4	yes	—
34	C₂×C₄×C₆₁	C₂×Q₈	1	2	yes	—
35	C₂×C₄×C₆₁	C₂×Q₈	1	2	yes	—
36	C₂×C₄×C₆₁	#41	1	8	yes	—
37	C₂×Dic₆₁	—	2	8	no	—
38	C₂×Dic₆₁	—	2	16	no	—
39	C₂²×C₆₁	C₂²×D₄	1	1	yes	characteristic
40	C₂²×C₆₁	C₂²×Q₈	1	1	yes	characteristic
41	C₂²×C₆₁	C₂²×Q₈	1	1	yes	characteristic
42	C₂²×C₆₁	C₂×#41	1	4	yes	—
43	C₄×C₆₁	—	2	4	no	—
44	C₄×C₆₁	—	2	4	no	—
45	C₄×C₆₁	#125	1	8	yes	complemented
46	C₄×C₆₁	C₄⋊Q₈	1	4	yes	—
47	Dic₆₁	—	4	8	no	—
48	#2859	—	61	1	no	maximal, Sylow
49	C₂×C₆₁	C₂×#125	1	2	yes	—
50	C₂×C₆₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
51	C₂×C₆₁	#532	1	2	yes	—
52	C₂×C₆₁	#533	1	2	yes	—
53	C₂×#125	—	61	2	no	—
54	#389	—	61	8	no	—
55	#384	—	61	2	no	—
56	#382	—	61	2	no	—
57	C₄³	D₆₁	1	1	yes	characteristic
58	C₆₁	#2859	1	1	yes	characteristic, complemented, Sylow
59	#125	—	122	8	no	—
60	C₂×C₄⋊C₄	—	61	4	no	—
61	C₂×C₄⋊C₄	—	61	8	no	—
62	C₂×C₄⋊C₄	—	61	8	no	—
63	C₂×C₄²	C₂×D₆₁	1	4	yes	—
64	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
65	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
66	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
67	#95	—	61	8	no	—
68	C₂²×C₄	—	61	8	no	—
69	C₂²×C₄	C₂²×D₆₁	1	2	yes	—
70	C₂²×C₄	C₂²×D₆₁	1	2	yes	—
71	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
72	C₂²×C₄	C₂²×D₆₁	1	2	yes	—
73	C₄⋊C₄	—	122	16	no	—
74	C₄⋊C₄	—	122	8	no	—
75	C₄⋊C₄	—	122	16	no	—
76	C₄²	—	2	8	no	—
77	C₄²	Dic₁₂₂	1	4	yes	—
78	C₄²	Dic₁₂₂	1	4	yes	—
79	C₄²	D₂₄₄	1	4	yes	—
80	C₂³	C₂³×D₆₁	1	1	yes	characteristic
81	C₂×C₄	—	2	4	no	—
82	C₂×C₄	—	2	4	no	—
83	C₂×C₄	—	122	8	no	—
84	C₂×C₄	—	122	16	no	—
85	C₂×C₄	C₂×Dic₁₂₂	1	4	yes	—
86	C₂×C₄	C₂×Dic₁₂₂	1	4	yes	—
87	C₂×C₄	C₂×Dic₁₂₂	1	2	yes	—
88	C₂×C₄	C₂×Dic₁₂₂	1	2	yes	—
89	C₂×C₄	C₂×D₂₄₄	1	4	yes	—
90	C₂×C₄	C₂×D₂₄₄	1	2	yes	—
91	C₂×C₄	#11758222	1	8	yes	—
92	C₂²	C₂²×D₂₄₄	1	1	yes	characteristic
93	C₂²	C₂²×Dic₁₂₂	1	1	yes	characteristic
94	C₂²	C₂²×Dic₁₂₂	1	1	yes	characteristic
95	C₂²	C₂×#11758222	1	4	yes	—
96	C₄	—	2	4	no	—
97	C₄	—	2	4	no	—
98	C₄	—	244	8	no	—
99	C₄	#14519769	1	8	yes	complemented
100	C₄	#14519777	1	4	yes	—
101	C₂	C₂×#14519769	1	2	yes	—
102	C₂	C₂×#14519777	1	1	yes	characteristic
103	C₂	#16840312	1	2	yes	—
104	C₂	#16840319	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519769

C₂

yes

maximal

#16839660

C₂

yes

maximal

#16839632

C₂

yes

maximal

#16839628

C₂

yes

maximal

C₄³×C₆₁

C₂

yes

maximal, characteristic

#14519769

—

C₂×C₄⋊Dic₆₁

C₂²

yes

—

C₂×C₄⋊Dic₆₁

C₂²

yes

—

C₂×#11758196

C₂²

yes

—

#14519684

C₂²

yes

—

C₂×C₄²×C₆₁

C₂²

yes

—

C₂×C₄²×C₆₁

C₂²

yes

characteristic

C₂×C₄²×C₆₁

C₂²

yes

characteristic

C₂×C₄²×C₆₁

C₂²

yes

characteristic

C₂²×C₄×C₆₁

C₂³

yes

—

C₂²×C₄×C₆₁

C₂³

yes

—

C₂²×C₄×C₆₁

C₂³

yes

characteristic

C₂²×C₄×C₆₁

C₂³

yes

—

C₂²×Dic₆₁

C₂³

yes

—

C₄²×C₆₁

—

C₄²×C₆₁

D₄

yes

—

C₄²×C₆₁

Q₈

yes

—

C₄²×C₆₁

Q₈

yes

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

#11758196

—

C₂³×C₆₁

C₂⁴

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂×D₄

yes

—

C₂×C₄×C₆₁

C₂×D₄

yes

—

C₂×C₄×C₆₁

C₂×Q₈

yes

—

C₂×C₄×C₆₁

C₂×Q₈

yes

—

C₂×C₄×C₆₁

C₂×Q₈

yes

—

C₂×C₄×C₆₁

C₂×Q₈

yes

—

C₂×C₄×C₆₁

#41

yes

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂²×C₆₁

C₂²×D₄

yes

characteristic

C₂²×C₆₁

C₂²×Q₈

yes

characteristic

C₂²×C₆₁

C₂²×Q₈

yes

characteristic

C₂²×C₆₁

C₂×#41

yes

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

#125

yes

complemented

C₄×C₆₁

C₄⋊Q₈

yes

—

Dic₆₁

—

#2859

—

maximal, Sylow

C₂×C₆₁

C₂×#125

yes

—

C₂×C₆₁

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₆₁

#532

yes

—

C₂×C₆₁

#533

yes

—

—

—

—

—

C₄³

D₆₁

yes

characteristic

C₆₁

#2859

yes

characteristic, complemented, Sylow

#125

—

122

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₆₁

yes

—

C₂×C₄²

C₂×D₆₁

yes

characteristic

C₂×C₄²

C₂×D₆₁

yes

characteristic

C₂×C₄²

C₂×D₆₁

yes

characteristic

#95

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₆₁

yes

—

C₂²×C₄

C₂²×D₆₁

yes

—

C₂²×C₄

C₂²×D₆₁

yes

characteristic

C₂²×C₄

C₂²×D₆₁

yes

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₄²

—

C₄²

Dic₁₂₂

yes

—

C₄²

Dic₁₂₂

yes

—

C₄²

D₂₄₄

yes

—

C₂³

C₂³×D₆₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

C₂×Dic₁₂₂

yes

—

C₂×C₄

C₂×Dic₁₂₂

yes

—

C₂×C₄

C₂×Dic₁₂₂

yes

—

C₂×C₄

C₂×Dic₁₂₂

yes

—

C₂×C₄

C₂×D₂₄₄

yes

—

C₂×C₄

C₂×D₂₄₄

yes

—

C₂×C₄

#11758222

yes

—

C₂²

C₂²×D₂₄₄

yes

characteristic

C₂²

C₂²×Dic₁₂₂

yes

characteristic

C₂²

C₂²×Dic₁₂₂

yes

characteristic

C₂²

C₂×#11758222

yes

—

C₄

—

C₄

—

C₄

—

244

—

C₄

#14519769

yes

complemented

100

C₄

#14519777

yes

—

101

C₂

C₂×#14519769

yes

—

102

C₂

C₂×#14519777

yes

characteristic

103

C₂

#16840312

yes

—

104

C₂

#16840319

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₆₁
commutator, socle	C₂³×C₆₁	C₂⁴
Fitting	C₄³×C₆₁	C₂
hypercenter	C₄³	D₆₁
hypocenter	C₆₁	#2859
LCS	G ▷ C₂³×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ C₄³

subgroup

G/H

center, Frattini

C₂³

C₂³×D₆₁

commutator, socle

C₂³×C₆₁

C₂⁴

Fitting

C₄³×C₆₁

C₂

hypercenter

C₄³

D₆₁

C₆₁

G ▷ C₂³×C₆₁ ▷ C₆₁

C₁ ◁ C₂³ ◁ C₄³

N	H ≅ G/N	type
45. C₄×C₆₁	#125	semidirect
58. C₆₁	#2859	semidirect
99. C₄	#14519769	semidirect

H ≅ G/N

type

45. C₄×C₆₁

#125

semidirect

58. C₆₁

#2859

semidirect

99. C₄

#14519769

semidirect

Subgroups — #21454182

Conjugacy classes of subgroups

Complements