Subgroups — #43247823

Order 28352.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₇₇₂	C₂	1	1	yes	maximal, characteristic
2	#28381851	C₂	1	2	yes	maximal
3	#28381809	C₂	1	2	yes	maximal
4	#28381796	C₂	1	1	yes	maximal, characteristic
5	#106×C₄₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₈₈₆	C₂²	1	2	yes	—
7	Dic₁₇₇₂	C₄	1	4	yes	complemented
8	C₂×C₄₄₃⋊C₈	C₂²	1	1	yes	characteristic
9	Dic₄₄₃⋊C₄	—	2	2	no	—
10	C₄×Dic₄₄₃	—	2	2	no	—
11	C₄×Dic₄₄₃	C₂²	1	1	yes	characteristic
12	C₂×C₈×C₄₄₃	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₄₄₃	C₂²	1	2	yes	—
14	Dic₈₈₆	—	2	2	no	—
15	Dic₈₈₆	C₂×C₄	1	4	yes	—
16	C₂×Dic₄₄₃	—	2	2	no	—
17	C₂×Dic₄₄₃	D₄	1	2	yes	—
18	C₄₄₃⋊C₈	—	2	1	no	—
19	C₂×C₄×C₄₄₃	—	2	2	no	—
20	C₂×C₄×C₄₄₃	C₂³	1	1	yes	characteristic
21	C₈×C₄₄₃	C₂×C₄	1	2	yes	—
22	C₂²×C₄₄₃	C₂×D₄	1	1	yes	characteristic
23	C₄×C₄₄₃	—	4	2	no	—
24	C₄×C₄₄₃	C₂²×C₄	1	1	yes	characteristic
25	C₄×C₄₄₃	#41	1	1	yes	characteristic
26	Dic₄₄₃	—	2	4	no	—
27	Dic₄₄₃	—	2	2	no	—
28	C₂×C₄₄₃	C₄×D₄	1	1	yes	characteristic
29	C₂×C₄₄₃	#137	1	2	yes	—
30	C₄₄₃	#441	1	1	yes	characteristic, complemented, Sylow
31	#441	—	443	1	no	maximal, Sylow
32	C₂×Q₁₆	—	443	1	no	—
33	C₄×Q₈	—	443	2	no	—
34	#106	D₄₄₃	1	1	yes	characteristic
35	#103	—	443	2	no	—
36	#97	—	443	1	no	—
37	C₂×Q₈	—	443	2	no	—
38	Q₁₆	—	443	4	no	—
39	C₂×C₈	—	443	1	no	—
40	C₂×C₈	C₂×D₄₄₃	1	1	yes	characteristic
41	C₄⋊C₄	—	886	2	no	—
42	C₄⋊C₄	C₂×D₄₄₃	1	2	yes	—
43	C₄²	—	886	2	no	—
44	C₄²	—	443	1	no	—
45	Q₈	—	886	2	no	—
46	Q₈	—	443	4	no	—
47	C₂×C₄	—	2	2	no	—
48	C₂×C₄	—	886	2	no	—
49	C₂×C₄	—	443	2	no	—
50	C₂×C₄	C₂²×D₄₄₃	1	1	yes	characteristic
51	C₈	—	886	1	no	—
52	C₈	C₄×D₄₄₃	1	2	yes	—
53	C₂²	D₄×D₄₄₃	1	1	yes	characteristic
54	C₄	—	4	2	no	—
55	C₄	—	886	4	no	—
56	C₄	—	886	2	no	—
57	C₄	C₂×C₄×D₄₄₃	1	1	yes	characteristic
58	C₄	#20296788	1	1	yes	characteristic
59	C₂	#28381848	1	1	yes	characteristic
60	C₂	#28381915	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₄₄₃
commutator	C₄×C₄₄₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₄₃
Fitting	#106×C₄₄₃	C₂
socle, prime radical	C₂²×C₄₄₃	C₂×D₄
cosocle	C₂×C₄×C₄₄₃	C₂³
hypercenter	#106	D₄₄₃
hypocenter	C₄₄₃	#441
LCS	G ▷ C₄×C₄₄₃ ▷ C₂×C₄₄₃ ▷ C₄₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
7. Dic₁₇₇₂	C₄	semidirect
30. C₄₄₃	#441	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₇₇₂	2
#28381851	2
#28381809	2
#28381796	2
#106×C₄₄₃	2
#441	443