Subgroups — #43247458

Order 28352.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28381878	C₂	1	1	yes	maximal, characteristic
2	#28381797	C₂	1	1	yes	maximal, characteristic
3	#97×C₄₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₄₃⋊C₈	—	2	1	no	—
5	C₄⋊Dic₄₄₃	C₄	1	1	yes	characteristic
6	C₄⋊Dic₄₄₃	C₄	1	1	yes	characteristic
7	Dic₄₄₃⋊C₄	—	2	1	no	—
8	Dic₄₄₃⋊C₄	—	2	1	no	—
9	C₂×C₈×C₄₄₃	—	2	1	no	—
10	C₄²×C₄₄₃	C₂²	1	1	yes	characteristic
11	C₂×Dic₄₄₃	—	2	1	no	—
12	C₂×Dic₄₄₃	—	2	1	no	—
13	C₄₄₃⋊C₈	—	2	2	no	—
14	C₂×C₄×C₄₄₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₄₄₃	D₄	1	1	yes	characteristic
16	C₂×C₄×C₄₄₃	D₄	1	1	yes	characteristic
17	C₈×C₄₄₃	—	2	2	no	—
18	C₂²×C₄₄₃	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₄₄₃	—	2	1	no	—
20	C₄×C₄₄₃	—	2	1	no	—
21	C₄×C₄₄₃	—	2	1	no	—
22	Dic₄₄₃	—	4	1	no	—
23	Dic₄₄₃	—	4	1	no	—
24	C₂×C₄₄₃	#101	1	1	yes	characteristic
25	C₂×C₄₄₃	#104	1	1	yes	characteristic
26	C₂×C₄₄₃	#104	1	1	yes	characteristic
27	C₄₄₃	#330	1	1	yes	characteristic, complemented, Sylow
28	#330	—	443	1	no	maximal, Sylow
29	#125	—	443	1	no	—
30	#97	—	443	1	no	—
31	#97	D₄₄₃	1	1	yes	characteristic
32	C₂×C₈	—	2	1	no	—
33	C₂×C₈	—	886	1	no	—
34	C₄⋊C₄	—	886	1	no	—
35	C₄⋊C₄	—	886	1	no	—
36	C₄⋊C₄	—	443	1	no	—
37	C₄⋊C₄	—	443	1	no	—
38	C₄²	C₂×D₄₄₃	1	1	yes	characteristic
39	C₂×C₄	—	886	1	no	—
40	C₂×C₄	—	886	1	no	—
41	C₂×C₄	C₄×D₄₄₃	1	1	yes	characteristic
42	C₂×C₄	C₂²⋊D₄₄₃	1	1	yes	characteristic
43	C₂×C₄	D₁₇₇₂	1	1	yes	characteristic
44	C₈	—	2	2	no	—
45	C₈	—	886	2	no	—
46	C₂²	(C₂×D₄₄₃)⋊C₄	1	1	yes	characteristic
47	C₄	—	2	1	no	—
48	C₄	—	2	1	no	—
49	C₄	—	2	1	no	—
50	C₄	—	1772	1	no	—
51	C₄	—	1772	1	no	—
52	C₂	#28381804	1	1	yes	characteristic
53	C₂	#28381812	1	1	yes	characteristic
54	C₂	#28381814	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	(C₂×D₄₄₃)⋊C₄
commutator	C₂×C₄×C₄₄₃	C₂×C₄
Frattini	C₄²	C₂×D₄₄₃
Fitting	#97×C₄₄₃	C₂
socle, prime radical	C₂²×C₄₄₃	C₂²⋊C₄
cosocle	C₄²×C₄₄₃	C₂²
hypercenter	#97	D₄₄₃
hypocenter	C₄₄₃	#330
LCS	G ▷ C₂×C₄×C₄₄₃ ▷ C₂²×C₄₄₃ ▷ C₄₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
27. C₄₄₃	#330	semidirect

Maximal subgroups

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

subgroup	index
#28381878	2
#28381797	2
#97×C₄₄₃	2
#330	443