Subgroups — C₂²×Dic₈₈ #13081729

Order 1408.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₄₄	C₂	1	2	yes	maximal
2	C₂²×C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂×Dic₈₈	C₂	1	12	yes	maximal, direct product factor
4	C₂²×Dic₂₂	—	2	2	no	—
5	C₂²×C₈×C₁₁	C₂²	1	1	yes	characteristic
6	C₂×Dic₄₄	—	2	6	no	—
7	C₂×Dic₄₄	C₂²	1	12	yes	—
8	C₂×C₁₁×C₁₆	C₂²	1	6	yes	—
9	Dic₈₈	C₂²	1	16	yes	direct product factor
10	C₂²×C₄×C₁₁	D₄	1	1	yes	characteristic
11	C₂²×Dic₁₁	—	4	2	no	—
12	C₂×Dic₂₂	—	2	12	no	—
13	C₂×Dic₂₂	—	4	6	no	—
14	C₂×C₈×C₁₁	D₄	1	3	yes	—
15	C₂×C₈×C₁₁	C₂³	1	3	yes	—
16	Dic₄₄	—	2	12	no	—
17	Dic₄₄	C₂³	1	8	yes	—
18	C₁₁×C₁₆	C₂³	1	4	yes	—
19	C₂²×Q₃₂	—	11	1	no	maximal, Sylow
20	C₂³×C₁₁	D₈	1	1	yes	characteristic
21	C₂×C₄×C₁₁	D₈	1	3	yes	—
22	C₂×C₄×C₁₁	C₂×D₄	1	3	yes	—
23	C₂×Dic₁₁	—	4	12	no	—
24	Dic₂₂	—	2	8	no	—
25	Dic₂₂	—	4	12	no	—
26	C₈×C₁₁	C₂×D₄	1	3	yes	—
27	C₈×C₁₁	C₂⁴	1	1	yes	characteristic
28	C₂²×Q₁₆	—	11	2	no	—
29	C₂×Q₃₂	—	11	12	no	—
30	C₂²×C₁₆	D₁₁	1	1	yes	characteristic
31	C₂²×C₁₁	Q₃₂	1	4	yes	complemented
32	C₂²×C₁₁	C₂×D₈	1	3	yes	—
33	C₄×C₁₁	C₂×D₈	1	3	yes	—
34	C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
35	Dic₁₁	—	4	8	no	—
36	C₂²×Q₈	—	22	2	no	—
37	C₂×Q₁₆	—	11	12	no	—
38	C₂×Q₁₆	—	22	6	no	—
39	C₂²×C₈	C₂×D₁₁	1	1	yes	characteristic
40	Q₃₂	—	11	16	no	—
41	C₂×C₁₆	C₂×D₁₁	1	6	yes	—
42	C₂×C₁₁	C₂×Q₃₂	1	6	yes	complemented
43	C₂×C₁₁	C₂²×D₈	1	1	yes	characteristic
44	C₂×Q₈	—	22	12	no	—
45	C₂×Q₈	—	44	6	no	—
46	C₂²×C₄	—	44	2	no	—
47	C₂²×C₄	D₄₄	1	1	yes	characteristic
48	Q₁₆	—	11	8	no	—
49	Q₁₆	—	22	12	no	—
50	C₂×C₈	D₄₄	1	3	yes	—
51	C₂×C₈	C₂²×D₁₁	1	3	yes	—
52	C₁₆	C₂²×D₁₁	1	4	yes	—
53	C₁₁	C₂²×Q₃₂	1	1	yes	characteristic, complemented, Sylow
54	C₂³	D₈₈	1	1	yes	characteristic
55	Q₈	—	22	8	no	—
56	Q₈	—	44	12	no	—
57	C₂×C₄	—	44	12	no	—
58	C₂×C₄	D₈₈	1	3	yes	—
59	C₂×C₄	C₂×D₄₄	1	3	yes	—
60	C₈	C₂×D₄₄	1	3	yes	—
61	C₈	C₂³×D₁₁	1	1	yes	characteristic
62	C₂²	Dic₈₈	1	4	yes	direct product factor
63	C₂²	C₂×D₈₈	1	3	yes	—
64	C₄	—	44	8	no	—
65	C₄	C₂×D₈₈	1	3	yes	—
66	C₄	C₂²×D₄₄	1	1	yes	characteristic
67	C₂	C₂×Dic₈₈	1	6	yes	direct product factor
68	C₂	C₂²×D₈₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₈₈
commutator, cosocle	C₈×C₁₁	C₂⁴
Frattini	C₈	C₂³×D₁₁
Fitting	C₂²×C₁₁×C₁₆	C₂
socle, prime radical	C₂³×C₁₁	D₈
hypercenter	C₂²×C₁₆	D₁₁
hypocenter	C₁₁	C₂²×Q₃₂
LCS	G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₂×Dic₈₈	C₂	direct (N × H)
9. Dic₈₈	C₂²	direct (N × H)
31. C₂²×C₁₁	Q₃₂	semidirect
42. C₂×C₁₁	C₂×Q₃₂	semidirect
53. C₁₁	C₂²×Q₃₂	semidirect
62. C₂²	Dic₈₈	direct (N × H)
67. C₂	C₂×Dic₈₈	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×Dic₄₄	2
C₂²×C₁₁×C₁₆	2
C₂×Dic₈₈	2
C₂²×Q₃₂	11

Subgroups — C22×Dic88 #13081729

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×Dic₈₈ #13081729