Group #19136856 — subgroups

Subgroups — #19136856

Order 5504.

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

normal subgroups only

This group has 184 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	C₂×Dic₃₄₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13063270	C₂	1	2	yes	maximal, complemented
3	C₂×D₆₈₈	C₂	1	1	yes	maximal, characteristic
4	#14583283	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₁₇₂	C₂²	1	2	yes	—
7	C₂×#10621873	—	2	2	no	—
8	C₂×D₃₄₄	C₂²	1	2	yes	—
9	#13063313	—	2	2	no	—
10	Dic₃₄₄	—	2	2	no	—
11	#13063270	—	2	4	no	—
12	D₆₈₈	—	2	2	no	—
13	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×D₁₇₂	—	2	2	no	—
17	C₂×Dic₈₆	—	2	2	no	—
18	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
19	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
20	C₄²×C₄₃	D₄	1	1	yes	characteristic
21	(C₂×D₄₃)⋊C₄	—	4	4	no	—
22	Dic₁₇₂	—	2	2	no	—
23	Dic₁₇₂	—	2	2	no	—
24	D₃₄₄	—	2	2	no	—
25	D₃₄₄	—	2	2	no	—
26	#10621873	—	4	4	no	—
27	C₁₆×C₄₃	D₄	1	2	yes	—
28	C₁₆×C₄₃	D₄	1	2	yes	—
29	C₂²×D₄₃	—	4	2	no	—
30	C₂×C₄×C₄₃	D₈	1	2	yes	—
31	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
32	C₂×Dic₄₃	—	4	2	no	—
33	D₁₇₂	—	4	2	no	—
34	D₁₇₂	—	4	2	no	—
35	Dic₈₆	—	4	2	no	—
36	Dic₈₆	—	4	2	no	—
37	C₈×C₄₃	D₈	1	2	yes	—
38	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
39	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
40	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
41	C₂×D₄₃	—	8	2	no	—
42	C₂×D₄₃	—	8	4	no	—
43	C₄×C₄₃	—	2	2	no	—
44	C₄×C₄₃	#127	1	1	yes	characteristic
45	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
46	Dic₄₃	—	8	2	no	—
47	#2249	—	43	1	no	maximal, Sylow
48	C₂×C₄₃	#493	1	1	yes	characteristic
49	C₂×C₄₃	#508	1	2	yes	—
50	D₄₃	—	16	2	no	—
51	C₂×Q₃₂	—	43	1	no	—
52	C₂×SD₃₂	—	43	2	no	—
53	C₂×D₁₆	—	43	1	no	—
54	#495	—	43	2	no	—
55	C₄×C₁₆	D₄₃	1	1	yes	characteristic, complemented
56	C₄₃	#2249	1	1	yes	characteristic, complemented, Sylow
57	C₂×Q₁₆	—	43	2	no	—
58	C₂×SD₁₆	—	86	2	no	—
59	C₂×D₈	—	43	2	no	—
60	#124	—	86	2	no	—
61	Q₃₂	—	86	2	no	—
62	SD₃₂	—	86	4	no	—
63	D₁₆	—	86	2	no	—
64	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
65	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
66	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
67	C₂×Q₈	—	86	2	no	—
68	C₂×D₄	—	86	2	no	—
69	Q₁₆	—	86	2	no	—
70	Q₁₆	—	86	2	no	—
71	SD₁₆	—	172	4	no	—
72	D₈	—	86	2	no	—
73	D₈	—	86	2	no	—
74	C₂×C₈	D₁₇₂	1	1	yes	characteristic
75	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
76	C₂²⋊C₄	—	172	4	no	—
77	C₄²	D₁₇₂	1	1	yes	characteristic
78	C₁₆	D₁₇₂	1	2	yes	—
79	C₁₆	D₁₇₂	1	2	yes	—
80	C₂³	—	172	2	no	—
81	Q₈	—	172	2	no	—
82	Q₈	—	172	2	no	—
83	D₄	—	172	2	no	—
84	D₄	—	172	2	no	—
85	C₂×C₄	—	172	2	no	—
86	C₂×C₄	D₃₄₄	1	2	yes	—
87	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
88	C₈	D₃₄₄	1	2	yes	—
89	C₈	C₂×D₁₇₂	1	1	yes	characteristic
90	C₈	C₂×D₁₇₂	1	1	yes	characteristic
91	C₂²	—	344	4	no	—
92	C₂²	—	344	2	no	—
93	C₂²	C₂×D₃₄₄	1	1	yes	characteristic
94	C₄	—	2	2	no	—
95	C₄	—	344	2	no	—
96	C₄	#13063322	1	1	yes	characteristic
97	C₄	C₂×D₃₄₄	1	1	yes	characteristic
98	C₂	—	688	2	no	—
99	C₂	#14583276	1	1	yes	characteristic
100	C₂	#14583331	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₃₄₄

C₂

yes

maximal, characteristic, complemented

C₂×#13063270

C₂

yes

maximal, complemented

C₂×D₆₈₈

C₂

yes

maximal, characteristic

#14583283

C₂

yes

maximal, complemented

C₄×C₁₆×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂×Dic₁₇₂

C₂²

yes

—

C₂×#10621873

—

C₂×D₃₄₄

C₂²

yes

—

#13063313

—

Dic₃₄₄

—

#13063270

—

D₆₈₈

—

C₂×C₁₆×C₄₃

C₂²

yes

characteristic

C₂×C₁₆×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×D₁₇₂

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

(C₂×D₄₃)⋊C₄

—

Dic₁₇₂

—

Dic₁₇₂

—

D₃₄₄

—

D₃₄₄

—

#10621873

—

C₁₆×C₄₃

D₄

yes

—

C₁₆×C₄₃

D₄

yes

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

D₈

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

D₈

yes

—

C₈×C₄₃

C₂×D₄

yes

characteristic

C₈×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#127

yes

characteristic

C₄×C₄₃

C₂×D₈

yes

characteristic

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

—

D₄₃

—

C₂×Q₃₂

—

C₂×SD₃₂

—

C₂×D₁₆

—

#495

—

C₄×C₁₆

D₄₃

yes

characteristic, complemented

C₄₃

#2249

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×SD₁₆

—

C₂×D₈

—

#124

—

Q₃₂

—

SD₃₂

—

D₁₆

—

C₂×C₁₆

C₂×D₄₃

yes

characteristic

C₂×C₁₆

C₂×D₄₃

yes

characteristic

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×D₄

—

Q₁₆

—

Q₁₆

—

SD₁₆

—

172

—

D₈

—

D₈

—

C₂×C₈

D₁₇₂

yes

characteristic

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₂²⋊C₄

—

172

—

C₄²

D₁₇₂

yes

characteristic

C₁₆

D₁₇₂

yes

—

C₁₆

D₁₇₂

yes

—

C₂³

—

172

—

Q₈

—

172

—

Q₈

—

172

—

D₄

—

172

—

D₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

D₃₄₄

yes

—

C₂×C₄

C₂×D₁₇₂

yes

characteristic

C₈

D₃₄₄

yes

—

C₈

C₂×D₁₇₂

yes

characteristic

C₈

C₂×D₁₇₂

yes

characteristic

C₂²

—

344

—

C₂²

—

344

—

C₂²

C₂×D₃₄₄

yes

characteristic

C₄

—

C₄

—

344

—

C₄

#13063322

yes

characteristic

C₄

C₂×D₃₄₄

yes

characteristic

C₂

—

688

—

C₂

#14583276

yes

characteristic

100

C₂

#14583331

yes

—

	subgroup	G/H
center	C₂²	C₂×D₃₄₄
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄×C₁₆×C₄₃	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	C₄×C₁₆	D₄₃
hypocenter	C₄₃	#2249
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

subgroup

G/H

center

C₂²

C₂×D₃₄₄

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄×C₁₆×C₄₃

C₂

socle

C₂²×C₄₃

C₂×D₈

hypercenter

C₄×C₁₆

D₄₃

hypocenter

C₄₃

#2249

LCS

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

N	H ≅ G/N	type
1. C₂×Dic₃₄₄	C₂	semidirect
2. C₂×#13063270	C₂	semidirect
4. #14583283	C₂	semidirect
5. C₄×C₁₆×C₄₃	C₂	semidirect
55. C₄×C₁₆	D₄₃	semidirect
56. C₄₃	#2249	semidirect

H ≅ G/N

type

1. C₂×Dic₃₄₄

C₂

semidirect

2. C₂×#13063270

C₂

semidirect

4. #14583283

C₂

semidirect

5. C₄×C₁₆×C₄₃

C₂

semidirect

55. C₄×C₁₆

D₄₃

semidirect

56. C₄₃

#2249

semidirect

Subgroups — #19136856

Conjugacy classes of subgroups

Complements