Group #19136717 — subgroups

Subgroups — #19136717

Order 5504.

140 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 45 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	#14583315	C₂	1	1	yes	maximal, characteristic
2	#14583171	C₂	1	2	yes	maximal
3	#14582729	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582715	C₂	1	2	yes	maximal, complemented
5	C₂×Q₃₂×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#13063356	—	2	2	no	—
7	#13063331	C₂²	1	1	yes	characteristic
8	#13063265	C₂²	1	1	yes	characteristic
9	#13063264	—	2	1	no	—
10	C₁₆×D₄₃	—	2	1	no	—
11	#13063261	C₂²	1	2	yes	—
12	#13063244	—	2	2	no	—
13	C₂×Q₁₆×C₄₃	C₂²	1	2	yes	—
14	Q₃₂×C₄₃	—	2	1	no	—
15	Q₃₂×C₄₃	—	2	1	no	—
16	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₄₃	—	2	2	no	—
18	#10621898	D₄	1	1	yes	characteristic
19	Q₁₆×C₄₃	—	2	2	no	—
20	Q₁₆×C₄₃	—	2	2	no	—
21	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
22	#10621885	—	4	2	no	—
23	#10621884	—	4	2	no	—
24	#10621877	—	2	2	no	—
25	#10621877	D₄	1	1	yes	characteristic
26	#10621872	—	2	1	no	—
27	C₈×D₄₃	—	2	1	no	—
28	C₁₆×C₄₃	D₄	1	1	yes	characteristic
29	C₁₆×C₄₃	D₄	1	1	yes	characteristic
30	C₄₃⋊C₁₆	—	2	1	no	—
31	Q₈×C₄₃	—	4	2	no	—
32	Q₈×C₄₃	—	4	2	no	—
33	C₂×C₄×C₄₃	—	4	2	no	—
34	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
35	C₂²⋊D₄₃	—	2	1	no	—
36	D₁₇₂	D₈	1	1	yes	characteristic
37	C₄×D₄₃	—	2	1	no	—
38	Dic₈₆	D₈	1	1	yes	characteristic
39	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
40	C₈×C₄₃	#41	1	1	yes	characteristic
41	C₄₃⋊C₈	—	2	1	no	—
42	C₄₃⋊C₈	—	4	2	no	—
43	C₂²×C₄₃	#135	1	1	yes	characteristic
44	C₂×D₄₃	—	2	1	no	—
45	C₄×C₄₃	—	8	2	no	—
46	C₄×C₄₃	#121	1	1	yes	characteristic
47	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
48	Dic₄₃	—	2	1	no	—
49	#2222	—	43	1	no	maximal, Sylow
50	C₂×C₄₃	—	2	1	no	—
51	C₂×C₄₃	#466	1	1	yes	characteristic
52	D₄₃	—	4	1	no	—
53	C₂×Q₃₂	D₄₃	1	1	yes	characteristic, complemented
54	#504	—	43	1	no	—
55	#473	—	43	2	no	—
56	#368	—	43	1	no	—
57	#362	—	43	2	no	—
58	C₄₃	#2222	1	1	yes	characteristic, complemented, Sylow
59	#137	—	86	2	no	—
60	C₂×Q₁₆	C₂×D₄₃	1	2	yes	—
61	#131	—	43	1	no	—
62	Q₃₂	—	2	1	no	—
63	Q₃₂	—	2	1	no	—
64	M₃₂	—	43	1	no	—
65	M₃₂	—	86	1	no	—
66	C₂×C₁₆	—	86	1	no	—
67	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
68	#108	—	43	2	no	—
69	#101	—	86	2	no	—
70	#41	—	43	1	no	—
71	C₂×Q₈	—	2	2	no	—
72	Q₁₆	—	2	2	no	—
73	Q₁₆	—	2	2	no	—
74	Q₁₆	—	172	2	no	—
75	SD₁₆	—	172	2	no	—
76	M₁₆	—	43	1	no	—
77	M₁₆	—	86	1	no	—
78	M₁₆	—	86	2	no	—
79	C₂×C₈	—	86	1	no	—
80	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
81	C₁₆	—	86	1	no	—
82	C₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
83	C₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
84	Q₈	—	4	2	no	—
85	Q₈	—	4	2	no	—
86	Q₈	—	43	1	no	—
87	D₄	—	43	1	no	—
88	D₄	—	86	1	no	—
89	C₂×C₄	—	4	2	no	—
90	C₂×C₄	—	86	1	no	—
91	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
92	C₈	—	86	1	no	—
93	C₈	—	172	2	no	—
94	C₈	#10621900	1	1	yes	characteristic
95	C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
96	C₂²	—	86	1	no	—
97	C₂²	#13063344	1	1	yes	characteristic
98	C₄	—	8	2	no	—
99	C₄	—	86	1	no	—
100	C₄	#13063296	1	1	yes	characteristic
101	C₄	D₈×D₄₃	1	1	yes	characteristic
102	C₂	—	2	1	no	—
103	C₂	—	172	1	no	—
104	C₂	#14583132	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583315

C₂

yes

maximal, characteristic

#14583171

C₂

yes

maximal

#14582729

C₂

yes

maximal, characteristic, complemented

#14582715

C₂

yes

maximal, complemented

C₂×Q₃₂×C₄₃

C₂

yes

maximal, characteristic, complemented

#13063356

—

#13063331

C₂²

yes

characteristic

#13063265

C₂²

yes

characteristic

#13063264

—

C₁₆×D₄₃

—

#13063261

C₂²

yes

—

#13063244

—

C₂×Q₁₆×C₄₃

C₂²

yes

—

Q₃₂×C₄₃

—

Q₃₂×C₄₃

—

C₂×C₁₆×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

#10621898

D₄

yes

characteristic

Q₁₆×C₄₃

—

Q₁₆×C₄₃

—

C₂×C₈×C₄₃

C₂³

yes

—

—

—

D₄

yes

characteristic

#10621872

—

C₈×D₄₃

—

C₁₆×C₄₃

D₄

yes

characteristic

C₁₆×C₄₃

D₄

yes

characteristic

C₄₃⋊C₁₆

—

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²⋊D₄₃

—

D₁₇₂

D₈

yes

characteristic

C₄×D₄₃

—

Dic₈₆

D₈

yes

characteristic

C₈×C₄₃

C₂×D₄

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

#135

yes

characteristic

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#121

yes

characteristic

C₄×C₄₃

C₂×D₈

yes

characteristic

Dic₄₃

—

#2222

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#466

yes

characteristic

D₄₃

—

C₂×Q₃₂

D₄₃

yes

characteristic, complemented

—

—

—

—

C₄₃

#2222

yes

characteristic, complemented, Sylow

#137

—

C₂×Q₁₆

C₂×D₄₃

yes

—

#131

—

Q₃₂

—

Q₃₂

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₃

yes

—

—

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

172

—

SD₁₆

—

172

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₁₆

—

C₁₆

C₂²⋊D₄₃

yes

characteristic

C₁₆

C₂²⋊D₄₃

yes

characteristic

Q₈

—

Q₈

—

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₄×D₄₃

yes

characteristic

C₈

—

C₈

—

172

—

C₈

#10621900

yes

characteristic

C₈

C₂×C₂²⋊D₄₃

yes

characteristic

C₂²

—

C₂²

#13063344

yes

characteristic

C₄

—

C₄

—

100

C₄

#13063296

yes

characteristic

101

C₄

D₈×D₄₃

yes

characteristic

102

C₂

—

103

C₂

—

172

—

104

C₂

#14583132

yes

characteristic

	subgroup	G/H
center	C₂	#14583132
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₂×Q₃₂×C₄₃	C₂
socle	C₂×C₄₃	#466
hypercenter	C₂×Q₃₂	D₄₃
hypocenter	C₄₃	#2222
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₃₂

subgroup

G/H

center

C₂

#14583132

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₂×Q₃₂×C₄₃

C₂

socle

C₂×C₄₃

#466

hypercenter

C₂×Q₃₂

D₄₃

hypocenter

C₄₃

#2222

LCS

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₃₂

N	H ≅ G/N	type
3. #14582729	C₂	semidirect
4. #14582715	C₂	semidirect
5. C₂×Q₃₂×C₄₃	C₂	semidirect
53. C₂×Q₃₂	D₄₃	semidirect
58. C₄₃	#2222	semidirect

H ≅ G/N

type

3. #14582729

C₂

semidirect

4. #14582715

C₂

semidirect

5. C₂×Q₃₂×C₄₃

C₂

semidirect

53. C₂×Q₃₂

D₄₃

semidirect

58. C₄₃

#2222

semidirect

Subgroups — #19136717

Conjugacy classes of subgroups

Complements