Group #21443932 — subgroups

Subgroups — #21443932

Order 7808.

124 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 69 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×#14519717	C₂	1	1	yes	maximal, characteristic
2	C₂×#14519713	C₂	1	1	yes	maximal, characteristic
3	C₂×#108×C₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#11758194	—	2	1	no	—
5	#14519717	—	2	1	no	—
6	#14519717	C₄	1	2	yes	—
7	C₂×#11758185	—	2	1	no	—
8	#14519713	—	2	1	no	—
9	#14519713	C₄	1	2	yes	—
10	C₂×M₁₆×C₆₁	—	2	1	no	—
11	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
12	#108×C₆₁	—	2	1	no	—
13	#108×C₆₁	C₄	1	2	yes	—
14	C₂²×C₄×C₆₁	D₄	1	1	yes	characteristic
15	M₁₆×C₆₁	—	2	2	no	—
16	M₁₆×C₆₁	—	4	1	no	—
17	C₂×C₈×C₆₁	—	4	1	no	—
18	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
22	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
23	C₂×C₈×C₆₁	Q₈	1	1	yes	characteristic
24	#11758194	—	2	2	no	—
25	#11758194	—	4	1	no	—
26	C₂×#92418	—	4	1	no	—
27	#11758185	—	2	2	no	—
28	C₂³×C₆₁	Q₁₆	1	1	yes	characteristic
29	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₆₁	D₈	1	1	yes	characteristic
33	C₂×C₄×C₆₁	SD₁₆	1	1	yes	characteristic
34	C₂×C₄×C₆₁	SD₁₆	1	1	yes	characteristic
35	C₈×C₆₁	—	4	2	no	—
36	C₈×C₆₁	C₄²	1	1	yes	characteristic
37	C₈×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
38	C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
39	C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
40	#92418	—	4	2	no	—
41	C₂²×C₆₁	—	4	1	no	—
42	C₂²×C₆₁	#103	1	1	yes	characteristic
43	C₂²×C₆₁	#103	1	1	yes	characteristic
44	C₂²×C₆₁	#107	1	1	yes	characteristic
45	C₄×C₆₁	#95	1	1	yes	characteristic
46	C₄×C₆₁	#102	1	1	yes	characteristic
47	C₄×C₆₁	#102	1	1	yes	characteristic
48	C₄×C₆₁	#106	1	1	yes	characteristic
49	#1388	—	61	1	no	maximal, Sylow
50	C₂×C₆₁	—	2	1	no	—
51	C₂×C₆₁	—	2	1	no	—
52	C₂×C₆₁	—	2	1	no	—
53	C₂×C₆₁	#340	1	1	yes	characteristic
54	C₂×M₃₂	—	61	1	no	—
55	C₂×#108	—	61	1	no	—
56	C₂×#108	D₆₁	1	1	yes	characteristic
57	C₆₁	#1388	1	1	yes	characteristic, complemented, Sylow
58	C₂×M₁₆	—	2	1	no	—
59	C₂×M₁₆	—	122	1	no	—
60	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
61	M₃₂	—	61	2	no	—
62	M₃₂	—	122	1	no	—
63	C₂×C₁₆	—	122	1	no	—
64	#108	—	2	1	no	—
65	#108	—	61	2	no	—
66	#108	—	122	1	no	—
67	#108	Dic₆₁	1	2	yes	—
68	C₂²×C₄	C₂²⋊D₆₁	1	1	yes	characteristic
69	M₁₆	—	2	2	no	—
70	M₁₆	—	4	1	no	—
71	M₁₆	—	122	2	no	—
72	M₁₆	—	244	1	no	—
73	C₂×C₈	—	4	1	no	—
74	C₂×C₈	—	244	1	no	—
75	C₂×C₈	Dic₁₂₂	1	1	yes	characteristic
76	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
77	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
78	C₂×C₈	D₂₄₄	1	1	yes	characteristic
79	C₂×C₈	C₂×Dic₆₁	1	1	yes	characteristic
80	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
81	C₁₆	—	122	2	no	—
82	C₂³	#11758202	1	1	yes	characteristic
83	C₂×C₄	#11758196	1	1	yes	characteristic
84	C₂×C₄	#11758198	1	1	yes	characteristic
85	C₂×C₄	#11758199	1	1	yes	characteristic
86	C₂×C₄	#11758200	1	1	yes	characteristic
87	C₂×C₄	#11758201	1	1	yes	characteristic
88	C₂×C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
89	C₈	—	4	2	no	—
90	C₈	—	244	2	no	—
91	C₈	C₄×Dic₆₁	1	1	yes	characteristic
92	C₈	#11758196	1	1	yes	characteristic
93	C₈	C₄⋊Dic₆₁	1	1	yes	characteristic
94	C₈	#11758198	1	1	yes	characteristic
95	C₂²	—	4	1	no	—
96	C₂²	#14519700	1	1	yes	characteristic
97	C₂²	#14519701	1	1	yes	characteristic
98	C₂²	#14519710	1	1	yes	characteristic
99	C₄	#14519684	1	1	yes	characteristic
100	C₄	#14519697	1	1	yes	characteristic
101	C₄	#14519698	1	1	yes	characteristic
102	C₄	#14519708	1	1	yes	characteristic
103	C₂	—	2	1	no	—
104	C₂	—	2	1	no	—
105	C₂	—	2	1	no	—
106	C₂	#16839524	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519717

C₂

yes

maximal, characteristic

C₂×#14519713

C₂

yes

maximal, characteristic

C₂×#108×C₆₁

C₂

yes

maximal, characteristic

C₂×#11758194

—

#14519717

—

#14519717

C₄

yes

—

C₂×#11758185

—

#14519713

—

#14519713

C₄

yes

—

C₂×M₁₆×C₆₁

—

C₂²×C₈×C₆₁

C₂²

yes

characteristic

#108×C₆₁

—

#108×C₆₁

C₄

yes

—

C₂²×C₄×C₆₁

D₄

yes

characteristic

M₁₆×C₆₁

—

M₁₆×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

Q₈

yes

—

—

—

—

C₂³×C₆₁

Q₁₆

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

D₈

yes

characteristic

C₂×C₄×C₆₁

SD₁₆

yes

characteristic

C₂×C₄×C₆₁

SD₁₆

yes

characteristic

C₈×C₆₁

—

C₈×C₆₁

C₄²

yes

characteristic

C₈×C₆₁

C₂²⋊C₄

yes

characteristic

C₈×C₆₁

C₄⋊C₄

yes

characteristic

C₈×C₆₁

C₄⋊C₄

yes

characteristic

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₄×C₆₁

yes

C₄×C₆₁

yes

C₄×C₆₁

yes

C₄×C₆₁

yes

—

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

#340

yes

characteristic

C₂×M₃₂

—

C₂×#108

—

C₂×#108

D₆₁

yes

characteristic

C₆₁

#1388

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

122

—

C₂²×C₈

C₂×D₆₁

yes

characteristic

M₃₂

—

M₃₂

—

122

—

C₂×C₁₆

—

122

—

#108

—

#108

—

#108

—

122

—

#108

Dic₆₁

yes

—

C₂²×C₄

C₂²⋊D₆₁

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

122

—

M₁₆

—

244

—

C₂×C₈

—

C₂×C₈

—

244

—

C₂×C₈

Dic₁₂₂

yes

characteristic

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

D₂₄₄

yes

characteristic

C₂×C₈

C₂×Dic₆₁

yes

characteristic

C₂×C₈

C₂²⋊D₆₁

yes

characteristic

C₁₆

—

122

—

C₂³

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂²⋊Dic₆₁

yes

characteristic

C₈

—

C₈

—

244

—

C₈

C₄×Dic₆₁

yes

characteristic

C₈

#11758196

yes

characteristic

C₈

C₄⋊Dic₆₁

yes

characteristic

C₈

#11758198

yes

characteristic

C₂²

—

C₂²

yes

C₂²

yes

C₂²

yes

C₄

yes

100

C₄

#14519697

yes

characteristic

101

C₄

#14519698

yes

characteristic

102

C₄

#14519708

yes

characteristic

103

C₂

—

104

C₂

—

105

C₂

—

106

C₂

#16839524

yes

characteristic

	subgroup	G/H
center	C₄	#14519697
commutator	C₈×C₆₁	C₄²
Frattini	C₂²×C₈	C₂×D₆₁
Fitting	C₂×#108×C₆₁	C₂
socle	C₂×C₆₁	#340
hypercenter	C₂×#108	D₆₁
hypocenter	C₆₁	#1388
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#108

subgroup

G/H

center

C₄

#14519697

commutator

C₈×C₆₁

C₄²

Frattini

C₂²×C₈

C₂×D₆₁

Fitting

C₂×#108×C₆₁

C₂

C₂×C₆₁

D₆₁

C₆₁

G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#108

N	H ≅ G/N	type
57. C₆₁	#1388	semidirect

H ≅ G/N

type

57. C₆₁

#1388

semidirect

Subgroups — #21443932

Conjugacy classes of subgroups

Complements