Group #21443719 — subgroups

Subgroups — #21443719

Order 7808.

144 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 61 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	#16839819	C₂	1	1	yes	maximal, characteristic
2	C₂×#14519688	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#431	C₂	1	1	yes	maximal, characteristic
4	C₂²×#92418	—	2	1	no	—
5	C₄⋊#92418	C₄	1	2	yes	—
6	C₂²⋊#92418	—	2	1	no	—
7	#14519688	—	2	1	no	—
8	#14519688	—	2	1	no	—
9	#14519688	C₄	1	2	yes	—
10	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
11	C₄⋊C₈×C₆₁	—	2	1	no	—
12	C₂²⋊C₈×C₆₁	C₄	1	2	yes	—
13	C₄×C₈×C₆₁	—	2	1	no	—
14	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₆₁	D₄	1	1	yes	characteristic
16	C₂²×C₄×C₆₁	Q₈	1	1	yes	characteristic
17	C₂×C₈×C₆₁	—	2	2	no	—
18	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
19	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₆₁	D₄	1	1	yes	characteristic
21	C₄²×C₆₁	D₄	1	1	yes	characteristic
22	C₂×#92418	—	2	4	no	—
23	C₂×#92418	—	2	2	no	—
24	C₂×#92418	—	2	2	no	—
25	C₂³×C₆₁	C₄⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₆₁	—	2	2	no	—
27	C₂×C₄×C₆₁	—	2	2	no	—
28	C₂×C₄×C₆₁	—	4	1	no	—
29	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
30	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
35	C₈×C₆₁	—	4	2	no	—
36	#92418	—	2	4	no	—
37	#92418	—	4	2	no	—
38	C₂²×C₆₁	—	2	1	no	—
39	C₂²×C₆₁	—	2	1	no	—
40	C₂²×C₆₁	#95	1	1	yes	characteristic
41	C₂²×C₆₁	#108	1	2	yes	—
42	C₄×C₆₁	—	2	1	no	—
43	C₄×C₆₁	—	2	1	no	—
44	C₄×C₆₁	—	2	1	no	—
45	C₄×C₆₁	—	2	1	no	—
46	C₄×C₆₁	—	2	1	no	—
47	C₄×C₆₁	#104	1	2	yes	—
48	#1302	—	61	1	no	maximal, Sylow
49	C₂×C₆₁	—	2	2	no	—
50	C₂×C₆₁	#339	1	1	yes	characteristic
51	C₂×C₆₁	#341	1	1	yes	characteristic
52	C₂×C₆₁	#344	1	1	yes	characteristic
53	#432	—	61	1	no	—
54	#431	D₆₁	1	1	yes	characteristic
55	C₂×#97	—	61	1	no	—
56	C₆₁	#1302	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₈	—	122	1	no	—
58	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
59	C₄⋊C₈	—	2	1	no	—
60	C₄⋊C₈	—	61	2	no	—
61	C₂²⋊C₈	—	122	1	no	—
62	C₂²⋊C₈	Dic₆₁	1	2	yes	—
63	#97	—	61	2	no	—
64	#97	—	122	1	no	—
65	#97	—	122	1	no	—
66	C₄×C₈	—	2	1	no	—
67	C₂²×C₄	Dic₁₂₂	1	1	yes	characteristic
68	C₂²×C₄	D₂₄₄	1	1	yes	characteristic
69	C₂²×C₄	C₂×Dic₆₁	1	1	yes	characteristic
70	C₂×C₈	—	2	2	no	—
71	C₂×C₈	—	122	4	no	—
72	C₂×C₈	—	122	2	no	—
73	C₂×C₈	—	122	2	no	—
74	C₄²	C₄×D₆₁	1	1	yes	characteristic
75	C₄²	C₄×D₆₁	1	1	yes	characteristic
76	C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
77	C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
78	C₂³	C₄⋊Dic₆₁	1	1	yes	characteristic
79	C₂×C₄	—	2	2	no	—
80	C₂×C₄	—	2	2	no	—
81	C₂×C₄	—	4	1	no	—
82	C₂×C₄	C₄×Dic₆₁	1	1	yes	characteristic
83	C₂×C₄	#11758196	1	1	yes	characteristic
84	C₂×C₄	#11758196	1	1	yes	characteristic
85	C₂×C₄	#11758198	1	1	yes	characteristic
86	C₂×C₄	#11758198	1	1	yes	characteristic
87	C₂×C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
88	C₈	—	4	2	no	—
89	C₈	—	122	4	no	—
90	C₈	—	244	2	no	—
91	C₂²	—	2	1	no	—
92	C₂²	—	2	1	no	—
93	C₂²	#14519684	1	1	yes	characteristic
94	C₂²	#14519713	1	2	yes	—
95	C₄	—	2	1	no	—
96	C₄	—	2	1	no	—
97	C₄	—	2	1	no	—
98	C₄	—	2	1	no	—
99	C₄	—	2	1	no	—
100	C₄	#14519703	1	2	yes	—
101	C₂	—	2	2	no	—
102	C₂	#16839523	1	1	yes	characteristic
103	C₂	#16839527	1	1	yes	characteristic
104	C₂	#16839532	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16839819

C₂

yes

maximal, characteristic

C₂×#14519688

C₂

yes

maximal, characteristic

C₆₁×#431

C₂

yes

maximal, characteristic

C₂²×#92418

—

C₄⋊#92418

C₄

yes

—

—

—

—

C₄

yes

—

C₂×C₄²×C₆₁

C₂²

yes

characteristic

C₄⋊C₈×C₆₁

—

C₂²⋊C₈×C₆₁

C₄

yes

—

C₄×C₈×C₆₁

—

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×C₄×C₆₁

D₄

yes

characteristic

C₂²×C₄×C₆₁

Q₈

yes

characteristic

C₂×C₈×C₆₁

—

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄²×C₆₁

D₄

yes

characteristic

C₄²×C₆₁

D₄

yes

—

—

—

C₂³×C₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₈×C₆₁

—

#92418

—

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

#95

yes

characteristic

C₂²×C₆₁

#108

yes

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

#104

yes

—

#1302

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

—

D₆₁

yes

characteristic

C₂×#97

—

C₆₁

#1302

yes

characteristic, complemented, Sylow

C₂²×C₈

—

122

—

C₂×C₄²

C₂×D₆₁

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

122

—

C₂²⋊C₈

Dic₆₁

yes

—

#97

—

#97

—

122

—

#97

—

122

—

C₄×C₈

—

C₂²×C₄

Dic₁₂₂

yes

characteristic

C₂²×C₄

D₂₄₄

yes

characteristic

C₂²×C₄

C₂×Dic₆₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₄²

C₄×D₆₁

yes

characteristic

C₄²

C₄×D₆₁

yes

characteristic

C₄²

C₂²⋊D₆₁

yes

characteristic

C₄²

C₂²⋊D₆₁

yes

characteristic

C₂³

C₄⋊Dic₆₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×Dic₆₁

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂²⋊Dic₆₁

yes

characteristic

C₈

—

C₈

—

122

—

C₈

—

244

—

C₂²

—

C₂²

—

C₂²

#14519684

yes

characteristic

C₂²

#14519713

yes

—

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

100

C₄

#14519703

yes

—

101

C₂

—

102

C₂

#16839523

yes

characteristic

103

C₂

#16839527

yes

characteristic

104

C₂

#16839532

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#11758198
commutator	C₂×C₄×C₆₁	C₄²
Frattini	C₂×C₄²	C₂×D₆₁
Fitting	C₆₁×#431	C₂
socle	C₂²×C₆₁	#95
hypercenter	#431	D₆₁
hypocenter	C₆₁	#1302
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #431

subgroup

G/H

center

C₂×C₄

#11758198

commutator

C₂×C₄×C₆₁

C₄²

Frattini

C₂×C₄²

C₂×D₆₁

Fitting

C₆₁×#431

C₂

C₂²×C₆₁

D₆₁

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #431

N	H ≅ G/N	type
56. C₆₁	#1302	semidirect

H ≅ G/N

type

56. C₆₁

#1302

semidirect

Subgroups — #21443719

Conjugacy classes of subgroups

Complements