Group #21443710 — subgroups

Subgroups — #21443710

Order 7808.

150 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 65 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	#16839786	C₂	1	1	yes	maximal, characteristic
2	C₄×#11758194	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#431	C₂	1	1	yes	maximal, characteristic
4	C₂×#11758194	—	2	1	no	—
5	C₂×#11758194	C₄	1	2	yes	—
6	C₄⋊#92418	—	2	1	no	—
7	C₄⋊#92418	—	2	1	no	—
8	#14519688	C₄	1	2	yes	—
9	C₄×#92418	—	2	1	no	—
10	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
11	C₄⋊C₈×C₆₁	C₄	1	2	yes	—
12	C₂²⋊C₈×C₆₁	—	2	1	no	—
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	#11758194	—	2	4	no	—
23	#11758194	—	4	2	no	—
24	C₂×#92418	—	2	2	no	—
25	C₂×#92418	—	2	2	no	—
26	C₂³×C₆₁	C₄⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₆₁	—	2	1	no	—
28	C₂×C₄×C₆₁	—	2	1	no	—
29	C₂×C₄×C₆₁	—	2	2	no	—
30	C₂×C₄×C₆₁	—	2	2	no	—
31	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
32	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
37	C₈×C₆₁	—	4	2	no	—
38	#92418	—	2	4	no	—
39	#92418	—	4	2	no	—
40	C₂²×C₆₁	—	2	1	no	—
41	C₂²×C₆₁	—	2	1	no	—
42	C₂²×C₆₁	—	2	1	no	—
43	C₂²×C₆₁	#95	1	1	yes	characteristic
44	C₄×C₆₁	—	2	1	no	—
45	C₄×C₆₁	—	2	1	no	—
46	C₄×C₆₁	—	2	1	no	—
47	C₄×C₆₁	#100	1	1	yes	characteristic
48	C₄×C₆₁	#101	1	1	yes	characteristic
49	C₄×C₆₁	#104	1	2	yes	—
50	C₄×C₆₁	#108	1	2	yes	—
51	#1299	—	61	1	no	maximal, Sylow
52	C₂×C₆₁	—	4	1	no	—
53	C₂×C₆₁	#339	1	1	yes	characteristic
54	C₂×C₆₁	#341	1	1	yes	characteristic
55	C₂×C₆₁	#343	1	1	yes	characteristic
56	#431	D₆₁	1	1	yes	characteristic
57	#423	—	61	1	no	—
58	C₄×M₁₆	—	61	1	no	—
59	C₆₁	#1299	1	1	yes	characteristic, complemented, Sylow
60	C₂×M₁₆	—	61	2	no	—
61	C₂×M₁₆	—	122	1	no	—
62	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
63	C₄⋊C₈	—	122	1	no	—
64	C₄⋊C₈	—	122	1	no	—
65	C₄⋊C₈	Dic₆₁	1	2	yes	—
66	C₂²⋊C₈	—	2	1	no	—
67	#97	—	61	2	no	—
68	C₄×C₈	—	2	1	no	—
69	C₄×C₈	—	122	1	no	—
70	C₂²×C₄	Dic₁₂₂	1	1	yes	characteristic
71	C₂²×C₄	C₄×D₆₁	1	1	yes	characteristic
72	C₂²×C₄	C₂²⋊D₆₁	1	1	yes	characteristic
73	M₁₆	—	122	4	no	—
74	M₁₆	—	244	2	no	—
75	C₂×C₈	—	2	2	no	—
76	C₂×C₈	—	122	2	no	—
77	C₂×C₈	—	122	2	no	—
78	C₄²	C₄×D₆₁	1	1	yes	characteristic
79	C₄²	D₂₄₄	1	1	yes	characteristic
80	C₄²	C₂×Dic₆₁	1	1	yes	characteristic
81	C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
82	C₂³	#11758196	1	1	yes	characteristic
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	2	2	no	—
86	C₂×C₄	—	2	2	no	—
87	C₂×C₄	C₄×Dic₆₁	1	1	yes	characteristic
88	C₂×C₄	#11758196	1	1	yes	characteristic
89	C₂×C₄	C₄⋊Dic₆₁	1	1	yes	characteristic
90	C₂×C₄	#11758198	1	1	yes	characteristic
91	C₂×C₄	#11758198	1	1	yes	characteristic
92	C₂×C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
93	C₈	—	4	2	no	—
94	C₈	—	122	4	no	—
95	C₈	—	244	2	no	—
96	C₂²	—	2	1	no	—
97	C₂²	—	2	1	no	—
98	C₂²	—	2	1	no	—
99	C₂²	#14519684	1	1	yes	characteristic
100	C₄	—	2	1	no	—
101	C₄	—	2	1	no	—
102	C₄	—	2	1	no	—
103	C₄	#14519693	1	1	yes	characteristic
104	C₄	#14519695	1	1	yes	characteristic
105	C₄	#14519704	1	2	yes	—
106	C₄	#14519713	1	2	yes	—
107	C₂	—	4	1	no	—
108	C₂	#16839521	1	1	yes	characteristic
109	C₂	#16839527	1	1	yes	characteristic
110	C₂	#16839530	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16839786

C₂

yes

maximal, characteristic

C₄×#11758194

C₂

yes

maximal, characteristic

C₆₁×#431

C₂

yes

maximal, characteristic

C₂×#11758194

—

C₂×#11758194

C₄

yes

—

C₄⋊#92418

—

C₄⋊#92418

—

#14519688

C₄

yes

—

C₄×#92418

—

C₂×C₄²×C₆₁

C₂²

yes

characteristic

C₄⋊C₈×C₆₁

C₄

yes

—

C₂²⋊C₈×C₆₁

—

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

—

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

—

C₂²×C₆₁

#95

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

yes

C₄×C₆₁

yes

C₄×C₆₁

yes

—

C₄×C₆₁

#108

yes

—

#1299

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

D₆₁

yes

characteristic

#423

—

C₄×M₁₆

—

C₆₁

#1299

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

122

—

C₂×C₄²

C₂×D₆₁

yes

characteristic

C₄⋊C₈

—

122

—

C₄⋊C₈

—

122

—

C₄⋊C₈

Dic₆₁

yes

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₄×C₈

—

122

—

C₂²×C₄

Dic₁₂₂

yes

characteristic

C₂²×C₄

C₄×D₆₁

yes

characteristic

C₂²×C₄

C₂²⋊D₆₁

yes

characteristic

M₁₆

—

122

—

M₁₆

—

244

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₄²

C₄×D₆₁

yes

characteristic

C₄²

D₂₄₄

yes

characteristic

C₄²

C₂×Dic₆₁

yes

characteristic

C₄²

C₂²⋊D₆₁

yes

characteristic

C₂³

#11758196

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×Dic₆₁

yes

characteristic

C₂×C₄

#11758196

yes

characteristic

C₂×C₄

C₄⋊Dic₆₁

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂²⋊Dic₆₁

yes

characteristic

C₈

—

C₈

—

122

—

C₈

—

244

—

C₂²

—

C₂²

—

C₂²

—

C₂²

#14519684

yes

characteristic

100

C₄

—

101

C₄

—

102

C₄

—

103

C₄

#14519693

yes

characteristic

104

C₄

#14519695

yes

characteristic

105

C₄

#14519704

yes

—

106

C₄

#14519713

yes

—

107

C₂

—

108

C₂

#16839521

yes

characteristic

109

C₂

#16839527

yes

characteristic

110

C₂

#16839530

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	#1299
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
59. C₆₁	#1299	semidirect

H ≅ G/N

type

59. C₆₁

#1299

semidirect

Subgroups — #21443710

Conjugacy classes of subgroups

Complements