Subgroups — #49119296

Order 36224.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31826243	C₂	1	2	yes	maximal
2	#491×C₂₈₃	C₂	1	1	yes	maximal, characteristic
3	#22583550	—	2	2	no	—
4	C₄⋊Q₈×C₂₈₃	C₄	1	1	yes	characteristic
5	#125×C₂₈₃	C₄	1	1	yes	characteristic
6	#103×C₂₈₃	—	2	2	no	—
7	#97×C₂₈₃	C₂²	1	1	yes	characteristic
8	C₂₈₃⋊C₁₆	—	2	4	no	—
9	C₂×Q₈×C₂₈₃	—	2	1	no	—
10	C₂×C₈×C₂₈₃	D₄	1	2	yes	—
11	C₄⋊C₄×C₂₈₃	—	2	1	no	—
12	C₄⋊C₄×C₂₈₃	—	4	1	no	—
13	C₄⋊C₄×C₂₈₃	—	4	1	no	—
14	C₄²×C₂₈₃	C₂×C₄	1	1	yes	characteristic
15	Q₈×C₂₈₃	—	4	2	no	—
16	C₂×C₄×C₂₈₃	—	2	1	no	—
17	C₂×C₄×C₂₈₃	—	4	1	no	—
18	C₂×C₄×C₂₈₃	—	4	1	no	—
19	C₂×C₄×C₂₈₃	C₂²⋊C₄	1	1	yes	characteristic
20	C₈×C₂₈₃	—	2	2	no	—
21	C₂²×C₂₈₃	#100	1	1	yes	characteristic
22	C₄×C₂₈₃	—	4	1	no	—
23	C₄×C₂₈₃	—	8	1	no	—
24	C₄×C₂₈₃	—	8	1	no	—
25	C₄×C₂₈₃	#104	1	2	yes	—
26	C₂×C₂₈₃	—	2	1	no	—
27	C₂×C₂₈₃	#329	1	1	yes	characteristic
28	C₂₈₃	#1356	1	1	yes	characteristic, complemented, Sylow
29	#1356	—	283	1	no	maximal, Sylow
30	#491	D₂₈₃	1	1	yes	characteristic
31	#347	—	283	2	no	—
32	C₄⋊Q₈	Dic₂₈₃	1	1	yes	characteristic
33	#125	Dic₂₈₃	1	1	yes	characteristic
34	M₃₂	—	566	2	no	—
35	#103	—	2	2	no	—
36	#97	C₂×D₂₈₃	1	1	yes	characteristic
37	C₂×Q₈	—	2	1	no	—
38	C₂×C₈	C₂²⋊D₂₈₃	1	2	yes	—
39	C₄⋊C₄	—	2	1	no	—
40	C₄⋊C₄	—	4	1	no	—
41	C₄⋊C₄	—	4	1	no	—
42	C₄²	C₂×Dic₂₈₃	1	1	yes	characteristic
43	C₁₆	—	566	4	no	—
44	Q₈	—	4	2	no	—
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	—	4	1	no	—
47	C₂×C₄	—	4	1	no	—
48	C₂×C₄	C₂²⋊Dic₂₈₃	1	1	yes	characteristic
49	C₈	—	2	2	no	—
50	C₂²	#22583527	1	1	yes	characteristic
51	C₄	—	4	1	no	—
52	C₄	—	8	1	no	—
53	C₄	—	8	1	no	—
54	C₄	#22583537	1	2	yes	—
55	C₂	—	2	1	no	—
56	C₂	#31826205	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#31826205
commutator	C₄²×C₂₈₃	C₂×C₄
Frattini	#97	C₂×D₂₈₃
Fitting	#491×C₂₈₃	C₂
socle	C₂×C₂₈₃	#329
prime radical	C₂²×C₂₈₃	#100
cosocle	#97×C₂₈₃	C₂²
hypercenter	#491	D₂₈₃
hypocenter	C₂₈₃	#1356
LCS	G ▷ C₄²×C₂₈₃ ▷ C₂×C₄×C₂₈₃ ▷ C₂×C₂₈₃ ▷ C₂₈₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #97 ◁ #491

Complements

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

N	H ≅ G/N	type
28. C₂₈₃	#1356	semidirect

Maximal subgroups

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

subgroup	index
#31826243	2
#491×C₂₈₃	2
#1356	283