Subgroups — #44505510

Order 30848.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#29507493	C₂	1	1	yes	maximal, characteristic
2	#29507468	C₂	1	1	yes	maximal, characteristic
3	#334×C₂₄₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#16838745	C₄	1	1	yes	characteristic
5	C₂×#16838745	C₄	1	1	yes	characteristic
6	C₄⋊#14515349	—	2	1	no	—
7	C₄⋊C₈×C₂₄₁	—	2	1	no	—
8	C₄×C₈×C₂₄₁	C₂²	1	1	yes	characteristic
9	C₂×#14515349	—	4	1	no	—
10	#16838745	—	2	1	no	—
11	#16838745	C₈	1	2	yes	complemented
12	C₂×C₈×C₂₄₁	—	4	1	no	—
13	C₂×C₈×C₂₄₁	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₂₄₁	Q₈	1	1	yes	characteristic
15	C₄²×C₂₄₁	D₄	1	1	yes	characteristic
16	#14515349	—	8	1	no	—
17	C₂×C₄×C₂₄₁	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₄×C₂₄₁	SD₁₆	1	1	yes	characteristic
19	C₂×C₄×C₂₄₁	SD₁₆	1	1	yes	characteristic
20	C₈×C₂₄₁	—	2	1	no	—
21	C₈×C₂₄₁	—	8	1	no	—
22	C₈×C₂₄₁	C₂×C₈	1	1	yes	characteristic
23	C₈×C₂₄₁	M₁₆	1	1	yes	characteristic
24	C₂²×C₂₄₁	#106	1	1	yes	characteristic
25	C₄×C₂₄₁	—	2	1	no	—
26	C₄×C₂₄₁	—	2	1	no	—
27	C₄×C₂₄₁	C₄⋊C₈	1	1	yes	characteristic
28	C₄×C₂₄₁	#108	1	1	yes	characteristic
29	C₂×C₂₄₁	#334	1	1	yes	characteristic
30	C₂×C₂₄₁	#365	1	1	yes	characteristic
31	C₂×C₂₄₁	#365	1	1	yes	characteristic
32	C₂₄₁	#1368	1	1	yes	characteristic, complemented, Sylow
33	#1368	—	241	1	no	maximal, Sylow
34	#346	—	241	1	no	—
35	#334	—	241	1	no	—
36	#334	D₂₄₁	1	1	yes	characteristic
37	C₂×C₁₆	—	241	1	no	—
38	C₂×C₁₆	—	241	1	no	—
39	C₄⋊C₈	—	2	1	no	—
40	C₄⋊C₈	—	482	1	no	—
41	C₄×C₈	C₂×D₂₄₁	1	1	yes	characteristic
42	C₂×C₈	—	4	1	no	—
43	C₂×C₈	—	964	1	no	—
44	C₂×C₈	C₄×D₂₄₁	1	1	yes	characteristic
45	C₂×C₈	Dic₄₈₂	1	1	yes	characteristic
46	C₄²	C₂²⋊D₂₄₁	1	1	yes	characteristic
47	C₁₆	—	482	1	no	—
48	C₁₆	—	241	2	no	—
49	C₂×C₄	#16838749	1	1	yes	characteristic
50	C₂×C₄	#16838757	1	1	yes	characteristic
51	C₂×C₄	#16838758	1	1	yes	characteristic
52	C₈	—	2	1	no	—
53	C₈	—	8	1	no	—
54	C₈	—	1928	1	no	—
55	C₈	C₈×D₂₄₁	1	1	yes	characteristic
56	C₈	#16838753	1	1	yes	characteristic
57	C₂²	#21440573	1	1	yes	characteristic
58	C₄	—	2	1	no	—
59	C₄	—	2	1	no	—
60	C₄	#21440571	1	1	yes	characteristic
61	C₄	#21440577	1	1	yes	characteristic
62	C₂	#29507467	1	1	yes	characteristic
63	C₂	#29507539	1	1	yes	characteristic
64	C₂	#29507541	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#21440573
commutator	C₈×C₂₄₁	C₂×C₈
Frattini	C₄×C₈	C₂×D₂₄₁
Fitting	#334×C₂₄₁	C₂
socle, prime radical	C₂²×C₂₄₁	#106
cosocle	C₄×C₈×C₂₄₁	C₂²
hypercenter	#334	D₂₄₁
hypocenter	C₂₄₁	#1368
LCS	G ▷ C₈×C₂₄₁ ▷ C₄×C₂₄₁ ▷ C₂×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #334

Complements

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

N	H ≅ G/N	type
11. #16838745	C₈	semidirect
32. C₂₄₁	#1368	semidirect

Maximal subgroups

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

subgroup	index
#29507493	2
#29507468	2
#334×C₂₄₁	2
#1368	241