Subgroups — #44505507

Order 30848.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#29508119	C₂	1	1	yes	maximal, characteristic
2	#29507538	C₂	1	1	yes	maximal, characteristic
3	#364×C₂₄₁	C₂	1	1	yes	maximal, characteristic
4	#21440634	C₄	1	2	yes	—
5	#21440582	—	2	1	no	—
6	#21440576	—	2	1	no	—
7	#21440574	—	2	1	no	—
8	M₃₂×C₂₄₁	—	2	1	no	—
9	C₄×C₈×C₂₄₁	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₂₄₁	—	2	2	no	—
11	#16838749	—	4	2	no	—
12	#16838745	—	4	1	no	—
13	C₂×C₈×C₂₄₁	D₄	1	1	yes	characteristic
14	C₂×C₈×C₂₄₁	D₄	1	1	yes	characteristic
15	C₄²×C₂₄₁	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₂₄₁	—	4	1	no	—
17	C₂×Dic₂₄₁	—	4	2	no	—
18	C₂×C₄×C₂₄₁	—	2	1	no	—
19	C₂×C₄×C₂₄₁	C₂²⋊C₄	1	1	yes	characteristic
20	C₈×C₂₄₁	SD₁₆	1	1	yes	characteristic
21	C₈×C₂₄₁	SD₁₆	1	1	yes	characteristic
22	C₈×C₂₄₁	Q₁₆	1	1	yes	characteristic
23	C₈×C₂₄₁	Q₁₆	1	1	yes	characteristic
24	C₂²×C₂₄₁	#100	1	1	yes	characteristic
25	C₄×C₂₄₁	—	4	1	no	—
26	C₄×C₂₄₁	#103	1	1	yes	characteristic
27	C₄×C₂₄₁	#103	1	1	yes	characteristic
28	Dic₂₄₁	—	8	2	no	—
29	C₂×C₂₄₁	—	2	1	no	—
30	C₂×C₂₄₁	#333	1	1	yes	characteristic
31	C₂₄₁	#1366	1	1	yes	characteristic, complemented, Sylow
32	#1366	—	241	1	no	maximal, Sylow
33	#499	—	241	1	no	—
34	#364	—	241	1	no	—
35	#364	D₂₄₁	1	1	yes	characteristic
36	#125	—	241	2	no	—
37	M₃₂	—	2	1	no	—
38	M₃₂	—	482	1	no	—
39	#107	—	482	1	no	—
40	#106	—	482	1	no	—
41	C₄×C₈	C₂×D₂₄₁	1	1	yes	characteristic
42	C₂×C₈	C₂²⋊D₂₄₁	1	1	yes	characteristic
43	C₂×C₈	D₉₆₄	1	1	yes	characteristic
44	C₄⋊C₄	—	964	2	no	—
45	C₄⋊C₄	—	482	2	no	—
46	C₄²	C₄×D₂₄₁	1	1	yes	characteristic
47	C₁₆	—	4	1	no	—
48	C₁₆	—	964	1	no	—
49	C₂×C₄	—	2	1	no	—
50	C₂×C₄	—	964	2	no	—
51	C₂×C₄	#16838747	1	1	yes	characteristic
52	C₈	#16838758	1	1	yes	characteristic
53	C₈	#16838759	1	1	yes	characteristic
54	C₈	#16838760	1	1	yes	characteristic
55	C₈	Dic₉₆₄	1	1	yes	characteristic
56	C₂²	#21440558	1	1	yes	characteristic
57	C₄	—	4	1	no	—
58	C₄	—	1928	2	no	—
59	C₄	#21440565	1	1	yes	characteristic
60	C₄	#21440567	1	1	yes	characteristic
61	C₂	—	2	1	no	—
62	C₂	#29507465	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#29507465
commutator	C₄²×C₂₄₁	C₂×C₄
Frattini	C₄×C₈	C₂×D₂₄₁
Fitting	#364×C₂₄₁	C₂
socle	C₂×C₂₄₁	#333
prime radical	C₂²×C₂₄₁	#100
cosocle	C₄×C₈×C₂₄₁	C₂²
hypercenter	#364	D₂₄₁
hypocenter	C₂₄₁	#1366
LCS	G ▷ C₄²×C₂₄₁ ▷ C₂×C₄×C₂₄₁ ▷ C₂×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
31. C₂₄₁	#1366	semidirect

Maximal subgroups

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

subgroup	index
#29508119	2
#29507538	2
#364×C₂₄₁	2
#1366	241