Group #19147704 — subgroups

Subgroups — C₂²×#13063269 #19147704

Order 5504.

400 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 149 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	C₂²×Dic₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13063269	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₄₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₈×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₈₆	—	2	1	no	—
6	C₂×Dic₁₇₂	—	2	3	no	—
7	C₂×Dic₁₇₂	C₂²	1	6	yes	complemented
8	#13063269	C₂²	1	16	yes	direct product factor
9	C₂×C₄₃⋊C₁₆	C₂²	1	6	yes	complemented
10	C₂²×D₄×C₄₃	—	2	1	no	—
11	C₂×D₈×C₄₃	—	2	3	no	—
12	C₂×D₈×C₄₃	C₂²	1	6	yes	—
13	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄₃	—	4	1	no	—
15	C₂×D₄×C₄₃	—	2	6	no	—
16	C₂×D₄×C₄₃	—	4	3	no	—
17	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
18	C₂²×Dic₄₃	—	4	1	no	—
19	C₂×Dic₈₆	—	2	6	no	—
20	C₂×Dic₈₆	—	4	3	no	—
21	D₈×C₄₃	—	2	6	no	—
22	D₈×C₄₃	C₂³	1	4	yes	—
23	C₂×C₈×C₄₃	D₄	1	3	yes	—
24	C₂×C₈×C₄₃	C₂³	1	3	yes	—
25	Dic₁₇₂	—	2	6	no	—
26	Dic₁₇₂	C₂³	1	4	yes	complemented
27	C₄₃⋊C₁₆	C₂³	1	4	yes	complemented
28	C₂³×C₄₃	—	4	6	no	—
29	C₂³×C₄₃	—	8	4	no	—
30	C₂³×C₄₃	D₈	1	1	yes	characteristic
31	D₄×C₄₃	—	2	4	no	—
32	D₄×C₄₃	—	4	6	no	—
33	C₂×C₄×C₄₃	D₈	1	3	yes	—
34	C₂×C₄×C₄₃	C₂×D₄	1	3	yes	—
35	C₂×Dic₄₃	—	4	6	no	—
36	Dic₈₆	—	2	4	no	—
37	Dic₈₆	—	4	6	no	—
38	C₈×C₄₃	C₂×D₄	1	3	yes	—
39	C₈×C₄₃	C₂⁴	1	1	yes	characteristic
40	C₂²×C₄₃	—	4	4	no	—
41	C₂²×C₄₃	—	8	12	no	—
42	C₂²×C₄₃	SD₃₂	1	4	yes	complemented
43	C₂²×C₄₃	C₂×D₈	1	3	yes	—
44	C₄×C₄₃	C₂×D₈	1	3	yes	—
45	C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
46	Dic₄₃	—	4	4	no	—
47	C₂²×SD₃₂	—	43	1	no	maximal, Sylow
48	C₂×C₄₃	—	8	4	no	—
49	C₂×C₄₃	C₂×SD₃₂	1	6	yes	complemented
50	C₂×C₄₃	C₂²×D₈	1	1	yes	characteristic
51	C₂²×Q₁₆	—	43	1	no	—
52	C₂²×D₈	D₄₃	1	1	yes	characteristic
53	C₂×SD₃₂	—	43	12	no	—
54	C₂²×C₁₆	—	43	1	no	—
55	C₄₃	C₂²×SD₃₂	1	1	yes	characteristic, complemented, Sylow
56	C₂²×Q₈	—	86	1	no	—
57	C₂²×D₄	—	2	1	no	—
58	C₂×Q₁₆	—	43	6	no	—
59	C₂×Q₁₆	—	86	3	no	—
60	C₂×D₈	—	2	3	no	—
61	C₂×D₈	C₂×D₄₃	1	6	yes	—
62	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
63	SD₃₂	—	43	16	no	—
64	C₂×C₁₆	—	43	6	no	—
65	C₂⁴	—	4	1	no	—
66	C₂×Q₈	—	86	6	no	—
67	C₂×Q₈	—	172	3	no	—
68	C₂×D₄	—	2	6	no	—
69	C₂×D₄	—	4	3	no	—
70	C₂²×C₄	—	172	1	no	—
71	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
72	Q₁₆	—	43	4	no	—
73	Q₁₆	—	86	6	no	—
74	D₈	—	2	6	no	—
75	D₈	C₂²×D₄₃	1	4	yes	—
76	C₂×C₈	C₂²⋊D₄₃	1	3	yes	—
77	C₂×C₈	C₂²×D₄₃	1	3	yes	—
78	C₁₆	—	43	4	no	—
79	C₂³	—	4	6	no	—
80	C₂³	—	8	4	no	—
81	C₂³	#10621882	1	1	yes	characteristic
82	Q₈	—	86	4	no	—
83	Q₈	—	172	6	no	—
84	D₄	—	2	4	no	—
85	D₄	—	4	6	no	—
86	C₂×C₄	—	172	6	no	—
87	C₂×C₄	#10621882	1	3	yes	—
88	C₂×C₄	C₂×C₂²⋊D₄₃	1	3	yes	—
89	C₈	C₂×C₂²⋊D₄₃	1	3	yes	—
90	C₈	C₂³×D₄₃	1	1	yes	characteristic
91	C₂²	—	4	4	no	—
92	C₂²	—	8	12	no	—
93	C₂²	#13063269	1	4	yes	direct product factor
94	C₂²	C₂×#10621882	1	3	yes	—
95	C₄	—	172	4	no	—
96	C₄	C₂×#10621882	1	3	yes	—
97	C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
98	C₂	—	8	4	no	—
99	C₂	C₂×#13063269	1	6	yes	direct product factor
100	C₂	C₂²×#10621882	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₁₇₂

C₂

yes

maximal, characteristic, complemented

C₂×#13063269

C₂

yes

maximal, direct product factor

C₂²×C₄₃⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₂²×D₈×C₄₃

C₂

yes

maximal, characteristic

C₂²×Dic₈₆

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

C₂²

yes

complemented

#13063269

C₂²

yes

direct product factor

C₂×C₄₃⋊C₁₆

C₂²

yes

complemented

C₂²×D₄×C₄₃

—

C₂×D₈×C₄₃

—

C₂×D₈×C₄₃

C₂²

yes

—

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂⁴×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

D₈×C₄₃

—

D₈×C₄₃

C₂³

yes

—

C₂×C₈×C₄₃

D₄

yes

—

C₂×C₈×C₄₃

C₂³

yes

—

Dic₁₇₂

—

Dic₁₇₂

C₂³

yes

complemented

C₄₃⋊C₁₆

C₂³

yes

complemented

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

D₈

yes

characteristic

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

D₈

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

C₂×D₄

yes

—

C₈×C₄₃

C₂⁴

yes

characteristic

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

SD₃₂

yes

complemented

C₂²×C₄₃

C₂×D₈

yes

—

C₄×C₄₃

C₂×D₈

yes

—

C₄×C₄₃

C₂²×D₄

yes

characteristic

Dic₄₃

—

C₂²×SD₃₂

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₂×SD₃₂

yes

complemented

C₂×C₄₃

C₂²×D₈

yes

characteristic

C₂²×Q₁₆

—

C₂²×D₈

D₄₃

yes

characteristic

C₂×SD₃₂

—

C₂²×C₁₆

—

C₄₃

C₂²×SD₃₂

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×D₄

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×D₈

—

C₂×D₈

C₂×D₄₃

yes

—

C₂²×C₈

C₂×D₄₃

yes

characteristic

SD₃₂

—

C₂×C₁₆

—

C₂⁴

—

C₂×Q₈

—

C₂×Q₈

—

172

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

172

—

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

Q₁₆

—

Q₁₆

—

D₈

—

D₈

C₂²×D₄₃

yes

—

C₂×C₈

C₂²⋊D₄₃

yes

—

C₂×C₈

C₂²×D₄₃

yes

—

C₁₆

—

C₂³

—

C₂³

—

C₂³

#10621882

yes

characteristic

Q₈

—

Q₈

—

172

—

D₄

—

D₄

—

C₂×C₄

—

172

—

C₂×C₄

#10621882

yes

—

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

C₈

C₂×C₂²⋊D₄₃

yes

—

C₈

C₂³×D₄₃

yes

characteristic

C₂²

—

C₂²

—

C₂²

#13063269

yes

direct product factor

C₂²

C₂×#10621882

yes

—

C₄

—

172

—

C₄

C₂×#10621882

yes

—

C₄

C₂²×C₂²⋊D₄₃

yes

characteristic

C₂

—

C₂

C₂×#13063269

yes

direct product factor

100

C₂

C₂²×#10621882

yes

characteristic

	subgroup	G/H
center	C₂³	#10621882
commutator	C₈×C₄₃	C₂⁴
Frattini	C₈	C₂³×D₄₃
Fitting	C₂²×D₈×C₄₃	C₂
socle	C₂³×C₄₃	D₈
hypercenter	C₂²×D₈	D₄₃
hypocenter	C₄₃	C₂²×SD₃₂
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×D₈

subgroup

G/H

center

C₂³

#10621882

commutator

C₈×C₄₃

C₂⁴

Frattini

C₈

C₂³×D₄₃

Fitting

C₂²×D₈×C₄₃

C₂

socle

C₂³×C₄₃

D₈

hypercenter

C₂²×D₈

D₄₃

hypocenter

C₄₃

C₂²×SD₃₂

LCS

G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×D₈

N	H ≅ G/N	type
1. C₂²×Dic₁₇₂	C₂	semidirect
2. C₂×#13063269	C₂	direct (N × H)
3. C₂²×C₄₃⋊C₁₆	C₂	semidirect
7. C₂×Dic₁₇₂	C₂²	semidirect
8. #13063269	C₂²	direct (N × H)
9. C₂×C₄₃⋊C₁₆	C₂²	semidirect
26. Dic₁₇₂	C₂³	semidirect
27. C₄₃⋊C₁₆	C₂³	semidirect
42. C₂²×C₄₃	SD₃₂	semidirect
49. C₂×C₄₃	C₂×SD₃₂	semidirect
55. C₄₃	C₂²×SD₃₂	semidirect
93. C₂²	#13063269	direct (N × H)
99. C₂	C₂×#13063269	direct (N × H)

H ≅ G/N

type

1. C₂²×Dic₁₇₂

C₂

semidirect

2. C₂×#13063269

C₂

direct (N × H)

3. C₂²×C₄₃⋊C₁₆

C₂

semidirect

7. C₂×Dic₁₇₂

C₂²

semidirect

8. #13063269

C₂²

direct (N × H)

9. C₂×C₄₃⋊C₁₆

C₂²

semidirect

26. Dic₁₇₂

C₂³

semidirect

27. C₄₃⋊C₁₆

C₂³

semidirect

42. C₂²×C₄₃

SD₃₂

semidirect

49. C₂×C₄₃

C₂×SD₃₂

semidirect

55. C₄₃

C₂²×SD₃₂

semidirect

93. C₂²

#13063269

direct (N × H)

99. C₂

C₂×#13063269

direct (N × H)

Subgroups — C₂²×#13063269 #19147704

Conjugacy classes of subgroups

Complements

Subgroups — C22×#13063269 #19147704

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×#13063269 #19147704