Group #21444732 — subgroups

Subgroups — #21444732

Order 7808.

176 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 63 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	C₄×D₄₈₈	C₂	1	1	yes	maximal, characteristic
2	#16839839	C₂	1	2	yes	maximal, complemented
3	#16839489	C₂	1	2	yes	maximal, complemented
4	#16839483	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#334	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄₈₈	C₄	1	1	yes	characteristic
7	C₂×#11758189	—	2	2	no	—
8	C₄×D₂₄₄	C₂²	1	2	yes	—
9	#14519711	C₄	1	1	yes	characteristic
10	#14519699	C₄	1	2	yes	—
11	#14519689	—	2	2	no	—
12	C₄×#92418	C₂²	1	1	yes	characteristic
13	C₄×#92418	C₂²	1	1	yes	characteristic
14	C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
15	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×D₂₄₄	C₂×C₄	1	2	yes	—
17	C₂×C₄×D₆₁	—	2	2	no	—
18	C₂×C₈×C₆₁	—	2	2	no	—
19	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
21	C₄²×C₆₁	C₂³	1	1	yes	characteristic
22	#11758198	—	2	2	no	—
23	C₄⋊Dic₆₁	C₂×C₄	1	2	yes	—
24	C₂×#92418	—	2	1	no	—
25	C₂×#92418	D₄	1	2	yes	—
26	D₄₈₈	—	2	2	no	—
27	#11758189	—	4	4	no	—
28	C₂²×D₆₁	—	2	2	no	—
29	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₆₁	#41	1	1	yes	characteristic
32	C₂×Dic₆₁	—	2	2	no	—
33	D₂₄₄	—	2	2	no	—
34	D₂₄₄	—	2	2	no	—
35	C₄×D₆₁	—	4	2	no	—
36	C₄×D₆₁	—	4	2	no	—
37	C₈×C₆₁	—	2	1	no	—
38	C₈×C₆₁	—	4	2	no	—
39	C₈×C₆₁	M₁₆	1	2	yes	complemented
40	#92418	—	2	2	no	—
41	#92418	—	4	1	no	—
42	C₂²×C₆₁	C₄×D₄	1	1	yes	characteristic
43	C₂×D₆₁	—	4	2	no	—
44	C₂×D₆₁	—	4	2	no	—
45	C₂×D₆₁	—	4	2	no	—
46	C₄×C₆₁	—	2	1	no	—
47	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
48	C₄×C₆₁	#131	1	1	yes	characteristic
49	C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
50	Dic₆₁	—	4	2	no	—
51	#1594	—	61	1	no	maximal, Sylow
52	C₂×C₆₁	#436	1	1	yes	characteristic
53	C₂×C₆₁	#442	1	1	yes	characteristic
54	C₂×C₆₁	#444	1	1	yes	characteristic
55	D₆₁	—	8	2	no	—
56	C₄×D₈	—	61	1	no	—
57	#436	—	61	2	no	—
58	#334	D₆₁	1	1	yes	characteristic, complemented
59	D₄⋊C₈	—	61	2	no	—
60	#322	—	61	1	no	—
61	C₆₁	#1594	1	1	yes	characteristic, complemented, Sylow
62	C₂×D₈	—	61	1	no	—
63	C₂×M₁₆	—	122	2	no	—
64	C₄×D₄	—	61	2	no	—
65	#107	—	61	1	no	—
66	C₄⋊C₈	C₂×D₆₁	1	2	yes	—
67	#102	—	61	2	no	—
68	C₂²⋊C₈	—	122	2	no	—
69	C₄×C₈	—	61	1	no	—
70	C₄×C₈	—	61	1	no	—
71	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
72	C₂×D₄	—	61	2	no	—
73	C₂²×C₄	—	122	2	no	—
74	D₈	—	122	2	no	—
75	M₁₆	—	244	4	no	—
76	C₂×C₈	—	2	2	no	—
77	C₂×C₈	—	61	2	no	—
78	C₂×C₈	—	122	1	no	—
79	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
80	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
81	C₄⋊C₄	—	61	2	no	—
82	C₂²⋊C₄	—	122	2	no	—
83	C₄²	C₂²×D₆₁	1	1	yes	characteristic
84	C₂³	—	122	2	no	—
85	D₄	—	122	2	no	—
86	D₄	—	122	2	no	—
87	C₂×C₄	—	122	2	no	—
88	C₂×C₄	—	244	2	no	—
89	C₂×C₄	—	244	2	no	—
90	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
91	C₂×C₄	D₄×D₆₁	1	1	yes	characteristic
92	C₂×C₄	#11758226	1	1	yes	characteristic
93	C₈	—	2	1	no	—
94	C₈	—	4	2	no	—
95	C₈	—	122	2	no	—
96	C₈	—	244	1	no	—
97	C₈	#11758189	1	2	yes	complemented
98	C₂²	—	244	2	no	—
99	C₂²	—	244	2	no	—
100	C₂²	—	244	2	no	—
101	C₂²	#14519739	1	1	yes	characteristic
102	C₄	—	2	1	no	—
103	C₄	—	244	2	no	—
104	C₄	C₂×#11758189	1	1	yes	characteristic
105	C₄	#14519785	1	1	yes	characteristic
106	C₄	#14519804	1	2	yes	—
107	C₂	—	488	2	no	—
108	C₂	#16839839	1	1	yes	characteristic
109	C₂	#16839873	1	1	yes	characteristic
110	C₂	#16839883	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×D₄₈₈

C₂

yes

maximal, characteristic

#16839839

C₂

yes

maximal, complemented

#16839489

C₂

yes

maximal, complemented

#16839483

C₂

yes

maximal, characteristic, complemented

C₆₁×#334

C₂

yes

maximal, characteristic, complemented

C₂×D₄₈₈

C₄

yes

characteristic

C₂×#11758189

—

C₄×D₂₄₄

C₂²

yes

—

#14519711

C₄

yes

characteristic

#14519699

C₄

yes

—

#14519689

—

C₄×#92418

C₂²

yes

characteristic

C₄×#92418

C₂²

yes

characteristic

C₄⋊C₈×C₆₁

C₂²

yes

—

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₂×D₂₄₄

C₂×C₄

yes

—

C₂×C₄×D₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₄²×C₆₁

C₂³

yes

characteristic

#11758198

—

C₄⋊Dic₆₁

C₂×C₄

yes

—

C₂×#92418

—

C₂×#92418

D₄

yes

—

D₄₈₈

—

#11758189

—

C₂²×D₆₁

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

#41

yes

characteristic

C₂×Dic₆₁

—

D₂₄₄

—

D₂₄₄

—

C₄×D₆₁

—

C₄×D₆₁

—

C₈×C₆₁

—

C₈×C₆₁

—

C₈×C₆₁

M₁₆

yes

complemented

#92418

—

#92418

—

C₂²×C₆₁

C₄×D₄

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

—

C₄×C₆₁

C₂×M₁₆

yes

C₄×C₆₁

yes

C₄×C₆₁

yes

—

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

D₆₁

—

C₄×D₈

—

#436

—

#334

D₆₁

yes

characteristic, complemented

D₄⋊C₈

—

#322

—

C₆₁

#1594

yes

characteristic, complemented, Sylow

C₂×D₈

—

C₂×M₁₆

—

122

—

C₄×D₄

—

#107

—

C₄⋊C₈

C₂×D₆₁

yes

—

#102

—

C₂²⋊C₈

—

122

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₆₁

yes

characteristic

C₂×D₄

—

C₂²×C₄

—

122

—

D₈

—

122

—

M₁₆

—

244

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

C₄×D₆₁

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

122

—

C₄²

C₂²×D₆₁

yes

characteristic

C₂³

—

122

—

D₄

—

122

—

D₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

C₂×C₄

D₄×D₆₁

yes

characteristic

C₂×C₄

#11758226

yes

characteristic

C₈

—

C₈

—

C₈

—

122

—

C₈

—

244

—

C₈

#11758189

yes

complemented

C₂²

—

244

—

C₂²

—

244

—

100

C₂²

—

244

—

101

C₂²

#14519739

yes

characteristic

102

C₄

—

103

C₄

—

244

—

104

C₄

C₂×#11758189

yes

characteristic

105

C₄

#14519785

yes

characteristic

106

C₄

#14519804

yes

—

107

C₂

—

488

—

108

C₂

#16839839

yes

characteristic

109

C₂

#16839873

yes

characteristic

110

C₂

#16839883

yes

characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₆₁
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₄²	C₂²×D₆₁
Fitting	C₆₁×#334	C₂
socle	C₂²×C₆₁	C₄×D₄
hypercenter	#334	D₆₁
hypocenter	C₆₁	#1594
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ #334

subgroup

G/H

center

C₂×C₄

D₄×D₆₁

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₄²

C₂²×D₆₁

Fitting

C₆₁×#334

C₂

socle

C₂²×C₆₁

C₄×D₄

D₆₁

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ #334

N	H ≅ G/N	type
2. #16839839	C₂	semidirect
3. #16839489	C₂	semidirect
4. #16839483	C₂	semidirect
5. C₆₁×#334	C₂	semidirect
39. C₈×C₆₁	M₁₆	semidirect
58. #334	D₆₁	semidirect
61. C₆₁	#1594	semidirect
97. C₈	#11758189	semidirect

H ≅ G/N

type

2. #16839839

C₂

semidirect

3. #16839489

C₂

semidirect

4. #16839483

C₂

semidirect

5. C₆₁×#334

C₂

semidirect

39. C₈×C₆₁

M₁₆

semidirect

58. #334

D₆₁

semidirect

61. C₆₁

#1594

semidirect

97. C₈

#11758189

semidirect

Subgroups — #21444732

Conjugacy classes of subgroups

Complements