Subgroups — #46825913

Order 34432.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771527	C₂	1	2	yes	maximal
2	#31770380	C₂	1	1	yes	maximal, characteristic
3	#22575527	—	2	2	no	—
4	C₂×#16864377	C₄	1	1	yes	characteristic
5	C₈×Dic₂₆₉	C₂²	1	1	yes	characteristic
6	C₂×C₁₆×C₂₆₉	C₄	1	1	yes	characteristic
7	#16864405	—	4	2	no	—
8	C₂×#14524130	D₄	1	1	yes	characteristic
9	C₄×Dic₂₆₉	Q₈	1	1	yes	characteristic
10	#16864377	C₈	1	2	yes	—
11	C₂×C₈×C₂₆₉	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₂₆₉	—	2	1	no	—
13	C₂×Dic₂₆₉	—	2	1	no	—
14	#14524130	SD₁₆	1	2	yes	—
15	C₂×C₄×C₂₆₉	C₄⋊C₄	1	1	yes	characteristic
16	C₈×C₂₆₉	C₂×C₈	1	1	yes	characteristic
17	C₈×C₂₆₉	M₁₆	1	1	yes	characteristic
18	C₂²×C₂₆₉	#108	1	1	yes	characteristic
19	C₄×C₂₆₉	C₄⋊C₈	1	1	yes	characteristic
20	C₄×C₂₆₉	#106	1	1	yes	characteristic
21	Dic₂₆₉	—	4	1	no	—
22	C₂×C₂₆₉	—	2	1	no	—
23	C₂×C₂₆₉	#334	1	1	yes	characteristic
24	C₂₆₉	#1369	1	1	yes	characteristic, complemented, Sylow
25	#1369	—	269	1	no	maximal, Sylow
26	#364	—	269	2	no	—
27	#346	—	269	1	no	—
28	M₃₂	—	538	2	no	—
29	C₂×C₁₆	—	269	1	no	—
30	C₂×C₁₆	#11761640	1	1	yes	characteristic
31	C₄×C₈	—	269	1	no	—
32	C₂×C₈	—	269	1	no	—
33	C₂×C₈	C₂×#11761640	1	1	yes	characteristic
34	C₄²	—	269	1	no	—
35	C₁₆	—	2	1	no	—
36	C₁₆	—	269	2	no	—
37	C₁₆	—	1076	2	no	—
38	C₂×C₄	—	538	1	no	—
39	C₂×C₄	C₄⋊#11761640	1	1	yes	characteristic
40	C₈	—	269	2	no	—
41	C₈	D₂₆₉⋊C₈	1	1	yes	characteristic
42	C₈	#16864411	1	1	yes	characteristic
43	C₂²	#22575524	1	1	yes	characteristic
44	C₄	—	1076	1	no	—
45	C₄	#22575520	1	1	yes	characteristic
46	C₄	#22575521	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	#31771467	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#22575521
commutator	C₈×C₂₆₉	C₂×C₈
Frattini	C₂×C₈	C₂×#11761640
Fitting	C₂×C₁₆×C₂₆₉	C₄
socle	C₂×C₂₆₉	#334
prime radical	C₂²×C₂₆₉	#108
cosocle	C₈×Dic₂₆₉	C₂²
hypercenter	C₂×C₁₆	#11761640
hypocenter	C₂₆₉	#1369
LCS	G ▷ C₈×C₂₆₉ ▷ C₄×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
24. C₂₆₉	#1369	semidirect

Maximal subgroups

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

subgroup	index
#31771527	2
#31770380	2
#1369	269