Group #19136700 — subgroups

Subgroups — #19136700

Order 5504.

150 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 49 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×#13063264	C₂	1	1	yes	maximal, characteristic
2	#14583137	C₂	1	2	yes	maximal
3	#14582727	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582703	C₂	1	2	yes	maximal, complemented
5	C₂×Q₃₂×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₄₃	C₂²	1	1	yes	characteristic
7	#13063301	—	2	2	no	—
8	#13063264	—	2	2	no	—
9	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
10	#13063259	C₂²	1	2	yes	—
11	#13063249	—	2	2	no	—
12	C₂×Q₁₆×C₄₃	C₂²	1	2	yes	—
13	Q₃₂×C₄₃	—	2	2	no	—
14	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×Q₈×C₄₃	—	2	2	no	—
16	C₂×C₄×D₄₃	D₄	1	1	yes	characteristic
17	Q₁₆×C₄₃	—	2	2	no	—
18	Q₁₆×C₄₃	—	2	2	no	—
19	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
20	(C₂×D₄₃)⋊C₄	—	4	2	no	—
21	C₄⋊Dic₄₃	—	2	2	no	—
22	Dic₄₃⋊C₄	—	4	2	no	—
23	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
24	C₈×D₄₃	—	2	1	no	—
25	C₈×D₄₃	—	2	1	no	—
26	C₁₆×C₄₃	D₄	1	2	yes	—
27	C₄₃⋊C₁₆	—	2	1	no	—
28	C₂²×D₄₃	D₈	1	1	yes	characteristic
29	Q₈×C₄₃	—	4	2	no	—
30	Q₈×C₄₃	—	4	2	no	—
31	C₂×C₄×C₄₃	—	4	2	no	—
32	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
33	C₂×Dic₄₃	—	4	2	no	—
34	C₂×Dic₄₃	D₈	1	1	yes	characteristic
35	C₄×D₄₃	—	2	1	no	—
36	C₄×D₄₃	—	2	1	no	—
37	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
38	C₈×C₄₃	#41	1	1	yes	characteristic
39	C₄₃⋊C₈	—	2	1	no	—
40	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
41	C₂×D₄₃	—	2	1	no	—
42	C₂×D₄₃	—	2	2	no	—
43	C₄×C₄₃	—	8	2	no	—
44	C₄×C₄₃	#121	1	1	yes	characteristic
45	C₄×C₄₃	#135	1	1	yes	characteristic
46	Dic₄₃	—	2	1	no	—
47	Dic₄₃	—	8	2	no	—
48	#2219	—	43	1	no	maximal, Sylow
49	C₂×C₄₃	#466	1	1	yes	characteristic
50	C₂×C₄₃	#510	1	2	yes	—
51	D₄₃	—	4	1	no	—
52	C₂×Q₃₂	D₄₃	1	1	yes	characteristic, complemented
53	C₂×M₃₂	—	43	1	no	—
54	#467	—	43	2	no	—
55	#367	—	43	1	no	—
56	#358	—	43	2	no	—
57	C₄₃	#2219	1	1	yes	characteristic, complemented, Sylow
58	C₂×Q₁₆	C₂×D₄₃	1	2	yes	—
59	C₂²×C₈	—	43	1	no	—
60	C₂²⋊Q₈	—	86	2	no	—
61	Q₃₂	—	2	2	no	—
62	M₃₂	—	86	2	no	—
63	C₂×C₁₆	—	43	1	no	—
64	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
65	#107	—	43	2	no	—
66	#103	—	86	2	no	—
67	C₂×Q₈	—	2	2	no	—
68	C₂²×C₄	—	43	1	no	—
69	Q₁₆	—	2	2	no	—
70	Q₁₆	—	2	2	no	—
71	C₂×C₈	—	43	1	no	—
72	C₂×C₈	—	86	1	no	—
73	C₂×C₈	—	86	1	no	—
74	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
75	C₄⋊C₄	—	86	2	no	—
76	C₄⋊C₄	—	172	2	no	—
77	C₂²⋊C₄	—	172	2	no	—
78	C₁₆	—	86	1	no	—
79	C₁₆	C₂²⋊D₄₃	1	2	yes	—
80	C₂³	—	43	1	no	—
81	Q₈	—	4	2	no	—
82	Q₈	—	4	2	no	—
83	C₂×C₄	—	4	2	no	—
84	C₂×C₄	—	43	1	no	—
85	C₂×C₄	—	86	1	no	—
86	C₂×C₄	—	86	1	no	—
87	C₂×C₄	—	172	2	no	—
88	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
89	C₈	—	86	1	no	—
90	C₈	#10621900	1	1	yes	characteristic
91	C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
92	C₂²	—	86	2	no	—
93	C₂²	—	86	1	no	—
94	C₂²	D₈×D₄₃	1	1	yes	characteristic
95	C₄	—	8	2	no	—
96	C₄	—	86	1	no	—
97	C₄	—	344	2	no	—
98	C₄	#13063296	1	1	yes	characteristic
99	C₄	#13063344	1	1	yes	characteristic
100	C₂	—	172	1	no	—
101	C₂	#14583132	1	1	yes	characteristic
102	C₂	#14583341	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063264

C₂

yes

maximal, characteristic

#14583137

C₂

yes

maximal

#14582727

C₂

yes

maximal, characteristic, complemented

#14582703

C₂

yes

maximal, complemented

C₂×Q₃₂×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₄₃

C₂²

yes

characteristic

#13063301

—

#13063264

—

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

#13063259

C₂²

yes

—

#13063249

—

C₂×Q₁₆×C₄₃

C₂²

yes

—

Q₃₂×C₄₃

—

C₂×C₁₆×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×C₄×D₄₃

D₄

yes

characteristic

Q₁₆×C₄₃

—

Q₁₆×C₄₃

—

C₂×C₈×C₄₃

C₂³

yes

characteristic

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₂×C₄₃⋊C₈

D₄

yes

characteristic

C₈×D₄₃

—

C₈×D₄₃

—

C₁₆×C₄₃

D₄

yes

—

C₄₃⋊C₁₆

—

C₂²×D₄₃

D₈

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

D₈

yes

characteristic

C₄×D₄₃

—

C₄×D₄₃

—

C₈×C₄₃

C₂×D₄

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₄₃⋊C₈

—

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

—

D₄₃

—

C₂×Q₃₂

D₄₃

yes

characteristic, complemented

C₂×M₃₂

—

#467

—

#367

—

#358

—

C₄₃

#2219

yes

characteristic, complemented, Sylow

C₂×Q₁₆

C₂×D₄₃

yes

—

C₂²×C₈

—

C₂²⋊Q₈

—

Q₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₃

yes

characteristic

#107

—

#103

—

C₂×Q₈

—

C₂²×C₄

—

Q₁₆

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₂²⋊C₄

—

172

—

C₁₆

—

C₁₆

C₂²⋊D₄₃

yes

—

C₂³

—

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

D₄×D₄₃

yes

characteristic

C₈

—

C₈

#10621900

yes

characteristic

C₈

C₂×C₂²⋊D₄₃

yes

characteristic

C₂²

—

C₂²

—

C₂²

D₈×D₄₃

yes

characteristic

C₄

—

C₄

—

C₄

—

344

—

C₄

yes

C₄

yes

100

C₂

—

172

—

101

C₂

#14583132

yes

characteristic

102

C₂

#14583341

yes

—

	subgroup	G/H
center	C₂²	D₈×D₄₃
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₂×Q₃₂×C₄₃	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	C₂×Q₃₂	D₄₃
hypocenter	C₄₃	#2219
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₃₂

subgroup

G/H

center

C₂²

D₈×D₄₃

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₂×Q₃₂×C₄₃

C₂

socle

C₂²×C₄₃

C₂×D₈

hypercenter

C₂×Q₃₂

D₄₃

hypocenter

C₄₃

#2219

LCS

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₃₂

N	H ≅ G/N	type
3. #14582727	C₂	semidirect
4. #14582703	C₂	semidirect
5. C₂×Q₃₂×C₄₃	C₂	semidirect
52. C₂×Q₃₂	D₄₃	semidirect
57. C₄₃	#2219	semidirect

H ≅ G/N

type

3. #14582727

C₂

semidirect

4. #14582703

C₂

semidirect

5. C₂×Q₃₂×C₄₃

C₂

semidirect

52. C₂×Q₃₂

D₄₃

semidirect

57. C₄₃

#2219

semidirect

Subgroups — #19136700

Conjugacy classes of subgroups

Complements