Group #19136820 — subgroups

Subgroups — #19136820

Order 5504.

160 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 61 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	#14583276	C₂	1	1	yes	maximal, characteristic
2	#14582699	C₂	1	4	yes	maximal, complemented
3	C₄×C₄₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#500	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₃₄₄	—	2	1	no	—
6	C₂×D₃₄₄	C₂²	1	2	yes	—
7	#13063322	—	2	1	no	—
8	C₂×C₄₃⋊C₁₆	C₂²	1	2	yes	—
9	C₄⋊Q₈×C₄₃	—	2	1	no	—
10	#107×C₄₃	—	2	1	no	—
11	#107×C₄₃	C₂²	1	2	yes	—
12	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×Q₈×C₄₃	—	4	1	no	—
14	C₂×D₁₇₂	—	2	2	no	—
15	C₂×D₁₇₂	—	4	1	no	—
16	C₂×D₁₇₂	—	4	1	no	—
17	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
18	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
19	C₄⋊C₄×C₄₃	—	2	2	no	—
20	C₄⋊C₄×C₄₃	—	4	1	no	—
21	C₄²×C₄₃	D₄	1	1	yes	characteristic
22	D₃₄₄	—	2	4	no	—
23	D₃₄₄	—	4	2	no	—
24	C₄₃⋊C₁₆	—	2	2	no	—
25	C₂²×D₄₃	—	4	2	no	—
26	Q₈×C₄₃	—	8	2	no	—
27	C₂×C₄×C₄₃	—	4	2	no	—
28	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
29	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
30	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
31	D₁₇₂	—	4	2	no	—
32	D₁₇₂	—	4	2	no	—
33	D₁₇₂	—	8	2	no	—
34	D₁₇₂	—	8	2	no	—
35	C₈×C₄₃	SD₁₆	1	2	yes	—
36	C₈×C₄₃	#41	1	2	yes	—
37	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
38	C₂×D₄₃	—	8	2	no	—
39	C₂×D₄₃	—	8	2	no	—
40	C₂×D₄₃	—	8	2	no	—
41	C₄×C₄₃	—	8	2	no	—
42	C₄×C₄₃	D₁₆	1	2	yes	—
43	C₄×C₄₃	SD₃₂	1	2	yes	—
44	C₄×C₄₃	#124	1	1	yes	characteristic
45	C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
46	#2240	—	43	1	no	maximal, Sylow
47	C₂×C₄₃	#486	1	1	yes	characteristic
48	C₂×C₄₃	C₂×D₁₆	1	1	yes	characteristic
49	C₂×C₄₃	C₂×SD₃₂	1	1	yes	characteristic
50	D₄₃	—	16	2	no	—
51	#500	D₄₃	1	1	yes	characteristic, complemented
52	#493	—	43	1	no	—
53	#357	—	43	4	no	—
54	C₄×C₁₆	—	43	1	no	—
55	C₄₃	#2240	1	1	yes	characteristic, complemented, Sylow
56	C₂×D₈	—	43	2	no	—
57	C₂×D₈	—	86	1	no	—
58	C₄⋊Q₈	—	2	1	no	—
59	#127	—	86	1	no	—
60	C₂×C₁₆	—	43	2	no	—
61	#107	—	2	1	no	—
62	#107	C₂×D₄₃	1	2	yes	—
63	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
64	C₂×Q₈	—	4	1	no	—
65	C₂×D₄	—	86	2	no	—
66	C₂×D₄	—	172	1	no	—
67	C₂×D₄	—	172	1	no	—
68	D₈	—	86	4	no	—
69	D₈	—	172	2	no	—
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	—	4	1	no	—
74	C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
75	C₁₆	—	86	2	no	—
76	C₂³	—	172	2	no	—
77	Q₈	—	8	2	no	—
78	D₄	—	344	2	no	—
79	D₄	—	344	2	no	—
80	D₄	—	172	2	no	—
81	D₄	—	172	2	no	—
82	C₂×C₄	—	4	2	no	—
83	C₂×C₄	#10621882	1	1	yes	characteristic
84	C₂×C₄	#10621882	1	1	yes	characteristic
85	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
86	C₈	#10621884	1	2	yes	—
87	C₈	#10621902	1	2	yes	—
88	C₂²	—	344	2	no	—
89	C₂²	—	344	2	no	—
90	C₂²	—	344	2	no	—
91	C₂²	C₂×#10621882	1	1	yes	characteristic
92	C₄	—	8	2	no	—
93	C₄	#13063266	1	2	yes	—
94	C₄	#13063268	1	2	yes	—
95	C₄	#13063314	1	1	yes	characteristic
96	C₄	C₂×#10621884	1	1	yes	characteristic
97	C₂	—	688	2	no	—
98	C₂	#14583247	1	1	yes	characteristic
99	C₂	C₂×#13063266	1	1	yes	characteristic
100	C₂	C₂×#13063268	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583276

C₂

yes

maximal, characteristic

#14582699

C₂

yes

maximal, complemented

C₄×C₄₃⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₄₃×#500

C₂

yes

maximal, characteristic, complemented

C₂×D₃₄₄

—

C₂×D₃₄₄

C₂²

yes

—

#13063322

—

C₂×C₄₃⋊C₁₆

C₂²

yes

—

C₄⋊Q₈×C₄₃

—

#107×C₄₃

—

#107×C₄₃

C₂²

yes

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

D₄

yes

characteristic

D₃₄₄

—

D₃₄₄

—

C₄₃⋊C₁₆

—

C₂²×D₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

D₈

yes

characteristic

C₂×C₄×C₄₃

D₈

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

C₈×C₄₃

SD₁₆

yes

—

C₈×C₄₃

#41

yes

—

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

D₁₆

yes

—

C₄×C₄₃

SD₃₂

yes

—

C₄×C₄₃

#124

yes

characteristic

C₄×C₄₃

C₂×SD₁₆

yes

—

C₂×C₄₃

yes

C₂×C₄₃

C₂×D₁₆

yes

characteristic

C₂×C₄₃

C₂×SD₃₂

yes

characteristic

D₄₃

—

#500

D₄₃

yes

characteristic, complemented

#493

—

#357

—

C₄×C₁₆

—

C₄₃

#2240

yes

characteristic, complemented, Sylow

C₂×D₈

—

C₂×D₈

—

C₄⋊Q₈

—

#127

—

C₂×C₁₆

—

#107

—

#107

C₂×D₄₃

yes

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

172

—

C₂×D₄

—

172

—

D₈

—

D₈

—

172

—

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂²⋊D₄₃

yes

characteristic

C₁₆

—

C₂³

—

172

—

Q₈

—

D₄

—

344

—

D₄

—

344

—

D₄

—

172

—

D₄

—

172

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

C₈

#10621884

yes

—

C₈

#10621902

yes

—

C₂²

—

344

—

C₂²

—

344

—

C₂²

—

344

—

C₂²

C₂×#10621882

yes

characteristic

C₄

—

C₄

#13063266

yes

—

C₄

#13063268

yes

—

C₄

yes

C₄

yes

C₂

—

688

—

C₂

yes

C₂

yes

100

C₂

C₂×#13063268

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#10621882
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#500	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	#500	D₄₃
hypocenter	C₄₃	#2240
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #500

subgroup

G/H

center

C₂²

C₂×#10621882

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#500

C₂

socle

C₂²×C₄₃

C₂×D₈

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #500

N	H ≅ G/N	type
2. #14582699	C₂	semidirect
3. C₄×C₄₃⋊C₁₆	C₂	semidirect
4. C₄₃×#500	C₂	semidirect
51. #500	D₄₃	semidirect
55. C₄₃	#2240	semidirect

H ≅ G/N

type

2. #14582699

C₂

semidirect

3. C₄×C₄₃⋊C₁₆

C₂

semidirect

4. C₄₃×#500

C₂

semidirect

51. #500

D₄₃

semidirect

55. C₄₃

#2240

semidirect

Subgroups — #19136820

Conjugacy classes of subgroups

Complements