Group #19136377 — subgroups

Subgroups — #19136377

Order 5504.

152 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 85 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	C₂²×C₄₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#14582937	C₂	1	1	yes	maximal, characteristic
3	#14582726	C₂	1	2	yes	maximal, complemented
4	#14582724	C₂	1	2	yes	maximal, complemented
5	C₄₃×#427	C₂	1	1	yes	maximal, characteristic
6	#13063284	—	2	1	no	—
7	C₂×C₄₃⋊C₁₆	C₄	1	4	yes	complemented
8	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
9	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
10	#13063259	C₂²	1	2	yes	—
11	#13063257	—	2	1	no	—
12	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
13	#117×C₄₃	—	2	1	no	—
14	#107×C₄₃	C₂²	1	2	yes	—
15	#106×C₄₃	—	2	1	no	—
16	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
17	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
18	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
19	C₂×C₈×C₄₃	Q₈	1	2	yes	—
20	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
21	C₄⋊C₄×C₄₃	—	2	2	no	—
22	C₂²⋊C₄×C₄₃	—	4	1	no	—
23	C₄²×C₄₃	—	4	1	no	—
24	C₂²⋊Dic₄₃	—	4	1	no	—
25	C₄⋊Dic₄₃	—	2	2	no	—
26	C₄×Dic₄₃	—	4	1	no	—
27	C₄₃⋊C₁₆	C₂×C₄	1	2	yes	—
28	C₄₃⋊C₁₆	C₂×C₄	1	2	yes	—
29	C₂³×C₄₃	D₈	1	1	yes	characteristic
30	C₂×C₄×C₄₃	—	4	2	no	—
31	C₂×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
32	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
33	C₂×C₄×C₄₃	Q₁₆	1	2	yes	—
34	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
35	C₂×Dic₄₃	—	4	2	no	—
36	C₈×C₄₃	C₄⋊C₄	1	2	yes	—
37	C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
38	C₈×C₄₃	C₂×Q₈	1	1	yes	characteristic
39	C₂²×C₄₃	—	2	2	no	—
40	C₂²×C₄₃	#107	1	2	yes	—
41	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
42	C₄×C₄₃	—	8	2	no	—
43	C₄×C₄₃	#107	1	2	yes	—
44	C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
45	C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
46	Dic₄₃	—	8	2	no	—
47	#2158	—	43	1	no	maximal, Sylow
48	C₂×C₄₃	—	2	2	no	—
49	C₂×C₄₃	C₂×#107	1	1	yes	characteristic
50	C₂×C₄₃	#508	1	2	yes	—
51	C₂²×C₁₆	—	43	1	no	—
52	#427	—	43	1	no	—
53	#427	D₄₃	1	1	yes	characteristic
54	#367	—	43	2	no	—
55	#366	—	43	2	no	—
56	C₄₃	#2158	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
58	#117	—	2	1	no	—
59	#117	—	86	1	no	—
60	C₂×C₁₆	—	43	1	no	—
61	C₂×C₁₆	—	43	1	no	—
62	C₂×C₁₆	—	43	4	no	—
63	#107	—	43	2	no	—
64	#107	C₂×D₄₃	1	2	yes	—
65	#106	—	2	1	no	—
66	#106	—	86	1	no	—
67	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
68	C₂×C₈	Dic₈₆	1	2	yes	—
69	C₂×C₈	C₄×D₄₃	1	2	yes	—
70	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
71	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
72	C₄⋊C₄	—	2	2	no	—
73	C₄⋊C₄	—	86	2	no	—
74	C₂²⋊C₄	—	4	1	no	—
75	C₂²⋊C₄	—	172	1	no	—
76	C₄²	—	4	1	no	—
77	C₄²	—	172	1	no	—
78	C₁₆	—	43	2	no	—
79	C₁₆	—	43	2	no	—
80	C₂³	#10621882	1	1	yes	characteristic
81	C₂×C₄	—	4	2	no	—
82	C₂×C₄	—	172	2	no	—
83	C₂×C₄	Dic₄₃⋊C₄	1	2	yes	—
84	C₂×C₄	#10621882	1	1	yes	characteristic
85	C₂×C₄	#10621885	1	2	yes	—
86	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
87	C₈	Dic₄₃⋊C₄	1	2	yes	—
88	C₈	C₂×Dic₈₆	1	1	yes	characteristic
89	C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
90	C₂²	—	2	2	no	—
91	C₂²	#13063258	1	2	yes	—
92	C₂²	C₂×#10621882	1	1	yes	characteristic
93	C₄	—	8	2	no	—
94	C₄	—	344	2	no	—
95	C₄	#13063258	1	2	yes	—
96	C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
97	C₄	C₂×#10621885	1	1	yes	characteristic
98	C₂	—	2	2	no	—
99	C₂	C₂×#13063258	1	1	yes	characteristic
100	C₂	#14583329	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₄₃⋊C₁₆

C₂

yes

maximal, characteristic

#14582937

C₂

yes

maximal, characteristic

#14582726

C₂

yes

maximal, complemented

#14582724

C₂

yes

maximal, complemented

C₄₃×#427

C₂

yes

maximal, characteristic

#13063284

—

C₂×C₄₃⋊C₁₆

C₄

yes

complemented

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

#13063259

C₂²

yes

—

#13063257

—

C₂²×C₈×C₄₃

C₂²

yes

characteristic

#117×C₄₃

—

#107×C₄₃

C₂²

yes

—

#106×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

Q₈

yes

—

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

C₄₃⋊C₁₆

C₂×C₄

yes

—

C₄₃⋊C₁₆

C₂×C₄

yes

—

C₂³×C₄₃

D₈

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄⋊C₄

yes

—

C₂×C₄×C₄₃

D₈

yes

characteristic

C₂×C₄×C₄₃

Q₁₆

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

C₈×C₄₃

C₄⋊C₄

yes

—

C₈×C₄₃

C₂²×C₄

yes

characteristic

C₈×C₄₃

C₂×Q₈

yes

characteristic

C₂²×C₄₃

—

C₂²×C₄₃

#107

yes

—

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

#107

yes

—

C₄×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₄₃

C₂×Q₁₆

yes

characteristic

Dic₄₃

—

#2158

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₂×#107

yes

characteristic

C₂×C₄₃

#508

yes

—

C₂²×C₁₆

—

#427

—

#427

D₄₃

yes

characteristic

#367

—

#366

—

C₄₃

#2158

yes

characteristic, complemented, Sylow

C₂²×C₈

C₂×D₄₃

yes

characteristic

#117

—

#117

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

#107

—

#107

C₂×D₄₃

yes

—

#106

—

#106

—

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

C₂×C₈

Dic₈₆

yes

—

C₂×C₈

C₄×D₄₃

yes

—

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

172

—

C₄²

—

C₄²

—

172

—

C₁₆

—

C₁₆

—

C₂³

#10621882

yes

characteristic

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

Dic₄₃⋊C₄

yes

—

C₂×C₄

#10621882

yes

characteristic

C₂×C₄

#10621885

yes

—

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

C₈

Dic₄₃⋊C₄

yes

—

C₈

C₂×Dic₈₆

yes

characteristic

C₈

C₂×C₄×D₄₃

yes

characteristic

C₂²

—

C₂²

#13063258

yes

—

C₂²

C₂×#10621882

yes

characteristic

C₄

—

C₄

—

344

—

C₄

#13063258

yes

—

C₄

C₂×Dic₄₃⋊C₄

yes

characteristic

C₄

C₂×#10621885

yes

characteristic

C₂

—

C₂

C₂×#13063258

yes

characteristic

100

C₂

#14583329

yes

—

	subgroup	G/H
center	C₂×C₄	#10621882
commutator	C₈×C₄₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#427	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	#427	D₄₃
hypocenter	C₄₃	#2158
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #427

subgroup

G/H

center

C₂×C₄

#10621882

commutator

C₈×C₄₃

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#427

C₂

socle

C₂²×C₄₃

C₂×D₈

D₄₃

C₄₃

G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #427

N	H ≅ G/N	type
3. #14582726	C₂	semidirect
4. #14582724	C₂	semidirect
7. C₂×C₄₃⋊C₁₆	C₄	semidirect
56. C₄₃	#2158	semidirect

H ≅ G/N

type

3. #14582726

C₂

semidirect

4. #14582724

C₂

semidirect

7. C₂×C₄₃⋊C₁₆

C₄

semidirect

56. C₄₃

#2158

semidirect

Subgroups — #19136377

Conjugacy classes of subgroups

Complements