Subgroups — C₂²×Dic₁₇₇₂ #43248494

Order 28352.

258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₈₈₆	C₂	1	2	yes	maximal
2	C₂×Dic₁₇₇₂	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₈×C₄₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₈₈₆	—	2	6	no	—
5	C₂×Dic₈₈₆	C₂²	1	12	yes	—
6	C₂²×Dic₄₄₃	—	2	2	no	—
7	Dic₁₇₇₂	C₂²	1	16	yes	direct product factor
8	C₂²×C₄×C₄₄₃	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₄₄₃	C₂²	1	6	yes	—
10	Dic₈₈₆	—	2	12	no	—
11	Dic₈₈₆	C₂³	1	8	yes	—
12	C₂×Dic₄₄₃	—	2	12	no	—
13	C₂³×C₄₄₃	D₄	1	1	yes	characteristic
14	C₂×C₄×C₄₄₃	D₄	1	3	yes	—
15	C₂×C₄×C₄₄₃	C₂³	1	3	yes	—
16	C₈×C₄₄₃	C₂³	1	4	yes	—
17	C₂²×C₄₄₃	Q₁₆	1	4	yes	complemented
18	C₂²×C₄₄₃	C₂×D₄	1	3	yes	—
19	C₄×C₄₄₃	C₂×D₄	1	3	yes	—
20	C₄×C₄₄₃	C₂⁴	1	1	yes	characteristic
21	Dic₄₄₃	—	2	8	no	—
22	C₂×C₄₄₃	C₂×Q₁₆	1	6	yes	complemented
23	C₂×C₄₄₃	C₂²×D₄	1	1	yes	characteristic
24	C₄₄₃	C₂²×Q₁₆	1	1	yes	characteristic, complemented, Sylow
25	C₂²×Q₁₆	—	443	1	no	maximal, Sylow
26	C₂²×Q₈	—	443	2	no	—
27	C₂×Q₁₆	—	443	12	no	—
28	C₂²×C₈	D₄₄₃	1	1	yes	characteristic
29	C₂×Q₈	—	886	6	no	—
30	C₂×Q₈	—	443	12	no	—
31	C₂²×C₄	—	886	2	no	—
32	C₂²×C₄	C₂×D₄₄₃	1	1	yes	characteristic
33	Q₁₆	—	443	16	no	—
34	C₂×C₈	C₂×D₄₄₃	1	6	yes	—
35	C₂³	D₁₇₇₂	1	1	yes	characteristic
36	Q₈	—	886	12	no	—
37	Q₈	—	443	8	no	—
38	C₂×C₄	—	886	12	no	—
39	C₂×C₄	D₁₇₇₂	1	3	yes	—
40	C₂×C₄	C₂²×D₄₄₃	1	3	yes	—
41	C₈	C₂²×D₄₄₃	1	4	yes	—
42	C₂²	Dic₁₇₇₂	1	4	yes	direct product factor
43	C₂²	C₂×D₁₇₇₂	1	3	yes	—
44	C₄	—	886	8	no	—
45	C₄	C₂×D₁₇₇₂	1	3	yes	—
46	C₄	C₂³×D₄₄₃	1	1	yes	characteristic
47	C₂	C₂×Dic₁₇₇₂	1	6	yes	direct product factor
48	C₂	C₂²×D₁₇₇₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₁₇₇₂
commutator, cosocle	C₄×C₄₄₃	C₂⁴
Frattini	C₄	C₂³×D₄₄₃
Fitting	C₂²×C₈×C₄₄₃	C₂
socle, prime radical	C₂³×C₄₄₃	D₄
hypercenter	C₂²×C₈	D₄₄₃
hypocenter	C₄₄₃	C₂²×Q₁₆
LCS	G ▷ C₄×C₄₄₃ ▷ C₂×C₄₄₃ ▷ C₄₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₁₇₇₂	C₂	direct (N × H)
7. Dic₁₇₇₂	C₂²	direct (N × H)
17. C₂²×C₄₄₃	Q₁₆	semidirect
22. C₂×C₄₄₃	C₂×Q₁₆	semidirect
24. C₄₄₃	C₂²×Q₁₆	semidirect
42. C₂²	Dic₁₇₇₂	direct (N × H)
47. C₂	C₂×Dic₁₇₇₂	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×Dic₈₈₆	2
C₂×Dic₁₇₇₂	2
C₂²×C₈×C₄₄₃	2
C₂²×Q₁₆	443

Subgroups — C22×Dic1772 #43248494

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×Dic₁₇₇₂ #43248494