Group #19136409 — subgroups

Subgroups — #19136409

Order 5504.

122 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 122 conjugacy classes of subgroups — too many to draw. Only its 53 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	#14582856	C₂	1	1	yes	maximal, characteristic
2	#14582719	C₂	1	2	yes	maximal, complemented
3	#14582680	C₂	1	2	yes	maximal
4	#14582677	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#347	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10621872	C₂²	1	1	yes	characteristic
7	C₂×C₈×D₄₃	C₄	1	1	yes	characteristic
8	#13063282	C₄	1	1	yes	characteristic
9	#13063265	C₂²	1	2	yes	—
10	#13063235	C₄	1	1	yes	characteristic
11	C₄×C₄₃⋊C₈	C₄	1	1	yes	characteristic
12	C₈×Dic₄₃	C₂²	1	1	yes	characteristic
13	M₃₂×C₄₃	C₂²	1	2	yes	—
14	#97×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
18	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
19	(C₂×D₄₃)⋊C₄	—	2	1	no	—
20	Dic₄₃⋊C₄	—	2	1	no	—
21	C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
24	#10621872	—	2	2	no	—
25	C₈×D₄₃	—	2	2	no	—
26	C₁₆×C₄₃	—	2	2	no	—
27	C₄₃⋊C₁₆	—	2	2	no	—
28	C₂²×D₄₃	M₁₆	1	1	yes	characteristic
29	C₂×C₄×C₄₃	—	2	1	no	—
30	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₄₃	—	2	1	no	—
32	C₂×Dic₄₃	M₁₆	1	1	yes	characteristic
33	C₄×D₄₃	—	2	1	no	—
34	C₄×D₄₃	—	2	1	no	—
35	C₈×C₄₃	—	2	1	no	—
36	C₈×C₄₃	#41	1	2	yes	—
37	C₄₃⋊C₈	—	2	1	no	—
38	C₄₃⋊C₈	M₁₆	1	2	yes	—
39	C₂²×C₄₃	C₂×M₁₆	1	1	yes	characteristic
40	C₂×D₄₃	—	2	1	no	—
41	C₂×D₄₃	—	4	1	no	—
42	C₄×C₄₃	—	4	1	no	—
43	C₄×C₄₃	#117	1	1	yes	characteristic
44	C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
45	Dic₄₃	—	2	1	no	—
46	Dic₄₃	—	4	1	no	—
47	#2166	—	43	1	no	maximal, Sylow
48	C₂×C₄₃	—	2	1	no	—
49	C₂×C₄₃	#432	1	1	yes	characteristic
50	D₄₃	—	4	1	no	—
51	#405	—	43	1	no	—
52	#364	—	43	2	no	—
53	#349	—	43	2	no	—
54	#347	—	43	1	no	—
55	#347	D₄₃	1	1	yes	characteristic, complemented
56	C₄₃	#2166	1	1	yes	characteristic, complemented, Sylow
57	C₂×M₁₆	—	43	1	no	—
58	C₂²×C₈	—	43	1	no	—
59	#117	—	43	1	no	—
60	M₃₂	—	43	2	no	—
61	M₃₂	C₂×D₄₃	1	2	yes	—
62	#97	—	43	1	no	—
63	#97	C₂×D₄₃	1	1	yes	characteristic
64	C₄×C₈	—	43	1	no	—
65	C₄×C₈	—	43	1	no	—
66	C₂²×C₄	—	43	1	no	—
67	M₁₆	—	86	2	no	—
68	C₂×C₈	—	43	1	no	—
69	C₂×C₈	—	43	1	no	—
70	C₂×C₈	—	86	2	no	—
71	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
72	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
73	C₄⋊C₄	—	86	1	no	—
74	C₂²⋊C₄	—	86	1	no	—
75	C₄²	—	43	1	no	—
76	C₄²	C₄×D₄₃	1	1	yes	characteristic
77	C₁₆	—	2	2	no	—
78	C₁₆	—	86	2	no	—
79	C₂³	—	43	1	no	—
80	C₂×C₄	—	2	1	no	—
81	C₂×C₄	—	43	1	no	—
82	C₂×C₄	—	86	1	no	—
83	C₂×C₄	—	86	1	no	—
84	C₂×C₄	—	86	1	no	—
85	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
86	C₈	—	2	1	no	—
87	C₈	—	43	2	no	—
88	C₈	—	86	1	no	—
89	C₈	#10621898	1	2	yes	—
90	C₂²	—	86	1	no	—
91	C₂²	—	172	1	no	—
92	C₂²	M₁₆×D₄₃	1	1	yes	characteristic
93	C₄	—	4	1	no	—
94	C₄	—	86	1	no	—
95	C₄	—	172	1	no	—
96	C₄	#13063282	1	1	yes	characteristic
97	C₄	M₁₆×D₄₃	1	1	yes	characteristic
98	C₂	—	2	1	no	—
99	C₂	—	172	1	no	—
100	C₂	#14582954	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582856

C₂

yes

maximal, characteristic

#14582719

C₂

yes

maximal, complemented

#14582680

C₂

yes

maximal

#14582677

C₂

yes

maximal, characteristic, complemented

C₄₃×#347

C₂

yes

maximal, characteristic, complemented

C₂×#10621872

C₂²

yes

characteristic

C₂×C₈×D₄₃

C₄

yes

characteristic

#13063282

C₄

yes

characteristic

#13063265

C₂²

yes

—

#13063235

C₄

yes

characteristic

C₄×C₄₃⋊C₈

C₄

yes

characteristic

C₈×Dic₄₃

C₂²

yes

characteristic

M₃₂×C₄₃

C₂²

yes

—

#97×C₄₃

C₂²

yes

characteristic

C₂×C₄×D₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄²×C₄₃

C₂×C₄

yes

characteristic

(C₂×D₄₃)⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

C₂×C₄

yes

characteristic

C₂×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₂×C₄₃⋊C₈

C₂×C₄

yes

characteristic

#10621872

—

C₈×D₄₃

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂²×D₄₃

M₁₆

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

M₁₆

yes

characteristic

C₄×D₄₃

—

C₄×D₄₃

—

C₈×C₄₃

—

C₈×C₄₃

#41

yes

—

C₄₃⋊C₈

—

C₄₃⋊C₈

M₁₆

yes

—

C₂²×C₄₃

C₂×M₁₆

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#117

yes

characteristic

C₄×C₄₃

C₂×M₁₆

yes

characteristic

Dic₄₃

—

Dic₄₃

—

#2166

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#432

yes

characteristic

D₄₃

—

—

—

—

—

D₄₃

yes

characteristic, complemented

C₄₃

#2166

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

M₃₂

C₂×D₄₃

yes

—

#97

—

#97

C₂×D₄₃

yes

characteristic

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₃

yes

characteristic

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₄×D₄₃

yes

characteristic

C₁₆

—

C₁₆

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

#10621898

yes

—

C₂²

—

C₂²

—

172

—

C₂²

M₁₆×D₄₃

yes

characteristic

C₄

—

C₄

—

C₄

—

172

—

C₄

#13063282

yes

characteristic

C₄

M₁₆×D₄₃

yes

characteristic

C₂

—

C₂

—

172

—

100

C₂

#14582954

yes

characteristic

	subgroup	G/H
center	C₄	#13063282
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#347	C₂
socle	C₂×C₄₃	#432
hypercenter	#347	D₄₃
hypocenter	C₄₃	#2166
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ #97 ◁ #347

subgroup

G/H

center

C₄

#13063282

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#347

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₄ ◁ #97 ◁ #347

N	H ≅ G/N	type
2. #14582719	C₂	semidirect
4. #14582677	C₂	semidirect
5. C₄₃×#347	C₂	semidirect
55. #347	D₄₃	semidirect
56. C₄₃	#2166	semidirect

H ≅ G/N

type

2. #14582719

C₂

semidirect

4. #14582677

C₂

semidirect

5. C₄₃×#347

C₂

semidirect

55. #347

D₄₃

semidirect

56. C₄₃

#2166

semidirect

Subgroups — #19136409

Conjugacy classes of subgroups

Complements