Group #21443934 — subgroups

Subgroups — #21443934

Order 7808.

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

normal subgroups only

This group has 128 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×#14519713	C₂	1	1	yes	maximal, characteristic
2	#16839800	C₂	1	1	yes	maximal, characteristic
3	C₂×M₃₂×C₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#11758194	—	2	1	no	—
5	#14519736	—	2	1	no	—
6	#14519713	—	2	1	no	—
7	#14519713	C₄	1	2	yes	complemented
8	#14519711	—	2	1	no	—
9	#14519709	C₄	1	2	yes	—
10	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
11	M₃₂×C₆₁	—	2	1	no	—
12	M₃₂×C₆₁	C₄	1	2	yes	complemented
13	C₂×C₁₆×C₆₁	—	2	1	no	—
14	C₂²×C₄×C₆₁	D₄	1	1	yes	characteristic
15	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
19	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
20	C₂×C₈×C₆₁	Q₈	1	1	yes	characteristic
21	C₂²⋊Dic₆₁	—	4	1	no	—
22	C₄⋊Dic₆₁	—	2	2	no	—
23	C₄×Dic₆₁	—	4	1	no	—
24	#11758194	—	2	2	no	—
25	#11758194	—	4	1	no	—
26	C₂×#92418	—	4	1	no	—
27	C₁₆×C₆₁	—	2	2	no	—
28	C₂³×C₆₁	SD₁₆	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	Q₁₆	1	1	yes	characteristic
35	C₂×Dic₆₁	—	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	#102	1	1	yes	characteristic
43	C₂²×C₆₁	#103	1	1	yes	characteristic
44	C₂²×C₆₁	#106	1	1	yes	characteristic
45	C₄×C₆₁	#95	1	1	yes	characteristic
46	C₄×C₆₁	#102	1	1	yes	characteristic
47	C₄×C₆₁	#103	1	1	yes	characteristic
48	C₄×C₆₁	#107	1	1	yes	characteristic
49	Dic₆₁	—	8	2	no	—
50	#1389	—	61	1	no	maximal, Sylow
51	C₂×C₆₁	—	2	1	no	—
52	C₂×C₆₁	—	2	1	no	—
53	C₂×C₆₁	—	2	1	no	—
54	C₂×C₆₁	#340	1	1	yes	characteristic
55	C₂×M₃₂	D₆₁	1	1	yes	characteristic
56	C₂×#108	—	61	1	no	—
57	#427	—	61	1	no	—
58	C₆₁	#1389	1	1	yes	characteristic, complemented, Sylow
59	C₂×M₁₆	—	122	1	no	—
60	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
61	#117	—	122	1	no	—
62	M₃₂	—	2	1	no	—
63	M₃₂	Dic₆₁	1	2	yes	complemented
64	C₂×C₁₆	—	2	1	no	—
65	#108	—	61	2	no	—
66	#108	—	122	1	no	—
67	#107	—	122	1	no	—
68	#106	—	61	2	no	—
69	C₂²×C₄	D₂₄₄	1	1	yes	characteristic
70	M₁₆	—	122	2	no	—
71	M₁₆	—	244	1	no	—
72	C₂×C₈	—	244	1	no	—
73	C₂×C₈	Dic₁₂₂	1	1	yes	characteristic
74	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
75	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
76	C₂×C₈	C₂×Dic₆₁	1	1	yes	characteristic
77	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
78	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
79	C₄⋊C₄	—	122	2	no	—
80	C₂²⋊C₄	—	244	1	no	—
81	C₄²	—	244	1	no	—
82	C₁₆	—	2	2	no	—
83	C₂³	#11758190	1	1	yes	characteristic
84	C₂×C₄	—	244	2	no	—
85	C₂×C₄	#11758190	1	1	yes	characteristic
86	C₂×C₄	D₄₈₈	1	1	yes	characteristic
87	C₂×C₄	Dic₂₄₄	1	1	yes	characteristic
88	C₂×C₄	C₄⋊Dic₆₁	1	1	yes	characteristic
89	C₂×C₄	#11758198	1	1	yes	characteristic
90	C₂×C₄	#11758198	1	1	yes	characteristic
91	C₈	—	244	2	no	—
92	C₈	C₄×Dic₆₁	1	1	yes	characteristic
93	C₈	#11758196	1	1	yes	characteristic
94	C₈	#11758196	1	1	yes	characteristic
95	C₈	C₂²⋊Dic₆₁	1	1	yes	characteristic
96	C₂²	—	4	1	no	—
97	C₂²	#14519699	1	1	yes	characteristic
98	C₂²	#14519702	1	1	yes	characteristic
99	C₂²	#14519709	1	1	yes	characteristic
100	C₄	—	488	2	no	—
101	C₄	#14519684	1	1	yes	characteristic
102	C₄	#14519699	1	1	yes	characteristic
103	C₄	#14519702	1	1	yes	characteristic
104	C₄	#14519711	1	1	yes	characteristic
105	C₂	—	2	1	no	—
106	C₂	—	2	1	no	—
107	C₂	—	2	1	no	—
108	C₂	#16839525	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519713

C₂

yes

maximal, characteristic

#16839800

C₂

yes

maximal, characteristic

C₂×M₃₂×C₆₁

C₂

yes

maximal, characteristic

—

—

—

C₄

yes

complemented

#14519711

—

#14519709

C₄

yes

—

C₂²×C₈×C₆₁

C₂²

yes

characteristic

M₃₂×C₆₁

—

M₃₂×C₆₁

C₄

yes

complemented

C₂×C₁₆×C₆₁

—

C₂²×C₄×C₆₁

D₄

yes

characteristic

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

characteristic

C₂²⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄×Dic₆₁

—

#11758194

—

#11758194

—

C₂×#92418

—

C₁₆×C₆₁

—

C₂³×C₆₁

SD₁₆

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

Q₁₆

yes

characteristic

C₂×Dic₆₁

—

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

Dic₆₁

—

#1389

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

#340

yes

characteristic

C₂×M₃₂

D₆₁

yes

characteristic

C₂×#108

—

#427

—

C₆₁

#1389

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

122

—

C₂²×C₈

C₂×D₆₁

yes

characteristic

#117

—

122

—

M₃₂

—

M₃₂

Dic₆₁

yes

complemented

C₂×C₁₆

—

#108

—

#108

—

122

—

#107

—

122

—

#106

—

C₂²×C₄

D₂₄₄

yes

characteristic

M₁₆

—

122

—

M₁₆

—

244

—

C₂×C₈

—

244

—

C₂×C₈

Dic₁₂₂

yes

characteristic

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

C₂×Dic₆₁

yes

characteristic

C₂×C₈

C₂²⋊D₆₁

yes

characteristic

C₂×C₈

C₂²⋊D₆₁

yes

characteristic

C₄⋊C₄

—

122

—

C₂²⋊C₄

—

244

—

C₄²

—

244

—

C₁₆

—

C₂³

#11758190

yes

characteristic

C₂×C₄

—

244

—

C₂×C₄

#11758190

yes

characteristic

C₂×C₄

D₄₈₈

yes

characteristic

C₂×C₄

Dic₂₄₄

yes

characteristic

C₂×C₄

C₄⋊Dic₆₁

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

244

—

C₈

C₄×Dic₆₁

yes

C₈

yes

C₈

yes

C₈

C₂²⋊Dic₆₁

yes

characteristic

C₂²

—

C₂²

yes

C₂²

yes

C₂²

yes

100

C₄

—

488

—

101

C₄

#14519684

yes

characteristic

102

C₄

#14519699

yes

characteristic

103

C₄

#14519702

yes

characteristic

104

C₄

#14519711

yes

characteristic

105

C₂

—

106

C₂

—

107

C₂

—

108

C₂

#16839525

yes

characteristic

	subgroup	G/H
center	C₄	#14519699
commutator	C₈×C₆₁	C₄²
Frattini	C₂²×C₈	C₂×D₆₁
Fitting	C₂×M₃₂×C₆₁	C₂
socle	C₂×C₆₁	#340
hypercenter	C₂×M₃₂	D₆₁
hypocenter	C₆₁	#1389
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

subgroup

G/H

center

C₄

#14519699

commutator

C₈×C₆₁

C₄²

Frattini

C₂²×C₈

C₂×D₆₁

Fitting

C₂×M₃₂×C₆₁

C₂

socle

C₂×C₆₁

#340

hypercenter

C₂×M₃₂

D₆₁

hypocenter

C₆₁

#1389

LCS

G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
7. #14519713	C₄	semidirect
12. M₃₂×C₆₁	C₄	semidirect
58. C₆₁	#1389	semidirect
63. M₃₂	Dic₆₁	semidirect

H ≅ G/N

type

7. #14519713

C₄

semidirect

12. M₃₂×C₆₁

C₄

semidirect

58. C₆₁

#1389

semidirect

63. M₃₂

Dic₆₁

semidirect

Subgroups — #21443934

Conjugacy classes of subgroups

Complements