Group #19132529 — subgroups

Subgroups — #19132529

Order 5504.

134 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 41 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	#14582625	C₂	1	2	yes	maximal
2	C₄₃×#391	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
4	C₂²×Q₈×C₄₃	C₄	1	1	yes	characteristic
5	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
6	C₂×C₄²×C₄₃	C₄	1	1	yes	characteristic
7	#95×C₄₃	—	2	2	no	—
8	C₂×Q₈×C₄₃	—	2	1	no	—
9	C₂×Q₈×C₄₃	—	4	1	no	—
10	C₂×Q₈×C₄₃	—	4	1	no	—
11	C₂×Q₈×C₄₃	C₈	1	2	yes	complemented
12	C₂²×C₄×C₄₃	—	2	1	no	—
13	C₂²×C₄×C₄₃	—	2	1	no	—
14	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₄₃	D₄	1	2	yes	—
16	C₄⋊C₄×C₄₃	—	4	1	no	—
17	C₄²×C₄₃	—	4	1	no	—
18	C₂×C₄₃⋊C₈	—	4	2	no	—
19	C₂³×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
20	Q₈×C₄₃	—	4	2	no	—
21	Q₈×C₄₃	—	4	2	no	—
22	C₂×C₄×C₄₃	—	2	1	no	—
23	C₂×C₄×C₄₃	—	2	1	no	—
24	C₂×C₄×C₄₃	—	2	2	no	—
25	C₂×C₄×C₄₃	—	2	2	no	—
26	C₂×C₄×C₄₃	—	2	2	no	—
27	C₂×C₄×C₄₃	—	4	1	no	—
28	C₂×C₄×C₄₃	—	4	1	no	—
29	C₂×C₄×C₄₃	—	4	1	no	—
30	C₂×C₄×C₄₃	—	4	1	no	—
31	C₂×C₄×C₄₃	—	4	2	no	—
32	C₂×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
33	C₂×C₄×C₄₃	M₁₆	1	1	yes	characteristic
34	C₄₃⋊C₈	—	8	2	no	—
35	C₂²×C₄₃	—	2	1	no	—
36	C₂²×C₄₃	—	2	1	no	—
37	C₂²×C₄₃	C₂²⋊C₈	1	1	yes	characteristic
38	C₂²×C₄₃	#99	1	1	yes	characteristic
39	C₂²×C₄₃	#100	1	1	yes	characteristic
40	C₄×C₄₃	—	2	1	no	—
41	C₄×C₄₃	—	2	1	no	—
42	C₄×C₄₃	—	4	2	no	—
43	C₄×C₄₃	—	4	2	no	—
44	C₄×C₄₃	—	4	2	no	—
45	#1319	—	43	1	no	maximal, Sylow
46	C₂×C₄₃	—	2	1	no	—
47	C₂×C₄₃	—	2	1	no	—
48	C₂×C₄₃	#323	1	1	yes	characteristic
49	C₂×C₄₃	#354	1	1	yes	characteristic
50	C₂×C₄₃	#356	1	1	yes	characteristic
51	#391	D₄₃	1	1	yes	characteristic
52	#324	—	43	2	no	—
53	C₄₃	#1319	1	1	yes	characteristic, complemented, Sylow
54	C₂²×Q₈	Dic₄₃	1	1	yes	characteristic
55	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
56	C₂×C₄²	Dic₄₃	1	1	yes	characteristic
57	C₂²⋊C₈	—	86	2	no	—
58	#95	—	2	2	no	—
59	C₂×Q₈	—	2	1	no	—
60	C₂×Q₈	—	4	1	no	—
61	C₂×Q₈	—	4	1	no	—
62	C₂×Q₈	C₄₃⋊C₈	1	2	yes	complemented
63	C₂²×C₄	—	2	1	no	—
64	C₂²×C₄	—	2	1	no	—
65	C₂²×C₄	C₂×Dic₄₃	1	1	yes	characteristic
66	C₂²×C₄	C₂²⋊D₄₃	1	2	yes	—
67	C₂×C₈	—	172	2	no	—
68	C₄⋊C₄	—	4	1	no	—
69	C₄²	—	4	1	no	—
70	C₂³	C₂²⋊Dic₄₃	1	1	yes	characteristic
71	Q₈	—	4	2	no	—
72	Q₈	—	4	2	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	2	2	no	—
76	C₂×C₄	—	2	2	no	—
77	C₂×C₄	—	2	2	no	—
78	C₂×C₄	—	4	1	no	—
79	C₂×C₄	—	4	1	no	—
80	C₂×C₄	—	4	1	no	—
81	C₂×C₄	—	4	1	no	—
82	C₂×C₄	—	4	2	no	—
83	C₂×C₄	C₂×C₄₃⋊C₈	1	1	yes	characteristic
84	C₂×C₄	#10621877	1	1	yes	characteristic
85	C₈	—	344	2	no	—
86	C₂²	—	2	1	no	—
87	C₂²	—	2	1	no	—
88	C₂²	C₂²⋊(C₄₃⋊C₈)	1	1	yes	characteristic
89	C₂²	#13063240	1	1	yes	characteristic
90	C₂²	#13063242	1	1	yes	characteristic
91	C₄	—	2	1	no	—
92	C₄	—	2	1	no	—
93	C₄	—	4	2	no	—
94	C₄	—	4	2	no	—
95	C₄	—	4	2	no	—
96	C₂	—	2	1	no	—
97	C₂	—	2	1	no	—
98	C₂	#14582623	1	1	yes	characteristic
99	C₂	#14582694	1	1	yes	characteristic
100	C₂	#14582698	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582625

C₂

yes

maximal

C₄₃×#391

C₂

yes

maximal, characteristic

C₂²⋊(C₄₃⋊C₈)

—

C₂²×Q₈×C₄₃

C₄

yes

characteristic

C₂×C₄⋊C₄×C₄₃

C₂²

yes

characteristic

C₂×C₄²×C₄₃

C₄

yes

characteristic

#95×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

C₈

yes

complemented

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂²⋊C₄

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₈

yes

characteristic

C₂×C₄×C₄₃

M₁₆

yes

characteristic

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂²⋊C₈

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

#1319

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

yes

characteristic

#324

—

C₄₃

#1319

yes

characteristic, complemented, Sylow

C₂²×Q₈

Dic₄₃

yes

characteristic

C₂×C₄⋊C₄

C₂×D₄₃

yes

characteristic

C₂×C₄²

Dic₄₃

yes

characteristic

C₂²⋊C₈

—

#95

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₄₃⋊C₈

yes

complemented

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×Dic₄₃

yes

characteristic

C₂²×C₄

C₂²⋊D₄₃

yes

—

C₂×C₈

—

172

—

C₄⋊C₄

—

C₄²

—

C₂³

C₂²⋊Dic₄₃

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄₃⋊C₈

yes

characteristic

C₂×C₄

#10621877

yes

characteristic

C₈

—

344

—

C₂²

—

C₂²

—

C₂²

C₂²⋊(C₄₃⋊C₈)

yes

C₂²

yes

C₂²

yes

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

C₂

—

C₂

—

C₂

yes

C₂

yes

100

C₂

#14582698

yes

characteristic

	subgroup	G/H
center	C₂²	#13063240
commutator	C₂×C₄×C₄₃	C₂×C₈
Frattini	C₂×C₄⋊C₄	C₂×D₄₃
Fitting	C₄₃×#391	C₂
socle	C₂²×C₄₃	#99
hypercenter	#391	D₄₃
hypocenter	C₄₃	#1319
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂×C₄⋊C₄ ◁ #391

subgroup

G/H

center

C₂²

#13063240

commutator

C₂×C₄×C₄₃

C₂×C₈

Frattini

C₂×C₄⋊C₄

C₂×D₄₃

Fitting

C₄₃×#391

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂³ ◁ C₂×C₄⋊C₄ ◁ #391

N	H ≅ G/N	type
11. C₂×Q₈×C₄₃	C₈	semidirect
53. C₄₃	#1319	semidirect
62. C₂×Q₈	C₄₃⋊C₈	semidirect

H ≅ G/N

type

11. C₂×Q₈×C₄₃

C₈

semidirect

53. C₄₃

#1319

semidirect

62. C₂×Q₈

C₄₃⋊C₈

semidirect

Subgroups — #19132529

Conjugacy classes of subgroups

Complements