Subgroups — #46809088

Order 34432.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22575359	C₂	1	1	yes	maximal, characteristic
2	#31770435	C₂	1	1	yes	maximal, characteristic
3	#368×C₂₆₉	C₂	1	1	yes	maximal, characteristic
4	#22575389	—	2	1	no	—
5	#22575359	C₄	1	2	yes	—
6	C₂×C₁₆×C₂₆₉	C₂²	1	1	yes	characteristic
7	#108×C₂₆₉	—	2	1	no	—
8	#16864386	—	4	1	no	—
9	M₁₆×C₂₆₉	—	4	1	no	—
10	C₂×C₈×C₂₆₉	D₄	1	1	yes	characteristic
11	C₁₆×C₂₆₉	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₂₆₉	Q₈	1	1	yes	characteristic
13	#14524130	—	8	1	no	—
14	C₂×C₄×C₂₆₉	D₈	1	1	yes	characteristic
15	C₈×C₂₆₉	—	8	1	no	—
16	C₈×C₂₆₉	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₂₆₉	Q₁₆	1	1	yes	characteristic
18	C₂²×C₂₆₉	Q₃₂	1	1	yes	characteristic
19	C₄×C₂₆₉	#107	1	1	yes	characteristic
20	C₄×C₂₆₉	D₁₆	1	1	yes	characteristic
21	C₂×C₂₆₉	—	2	1	no	—
22	C₂×C₂₆₉	#366	1	1	yes	characteristic
23	C₂₆₉	#1425	1	1	yes	characteristic, complemented, Sylow
24	#1425	—	269	1	no	maximal, Sylow
25	C₂×C₃₂	—	269	1	no	—
26	#368	—	269	1	no	—
27	#368	D₂₆₉	1	1	yes	characteristic
28	C₂×C₁₆	C₂×D₂₆₉	1	1	yes	characteristic
29	#108	—	2	1	no	—
30	#108	—	538	1	no	—
31	C₃₂	—	269	2	no	—
32	M₁₆	—	4	1	no	—
33	M₁₆	—	1076	1	no	—
34	C₂×C₈	C₂²⋊D₂₆₉	1	1	yes	characteristic
35	C₁₆	C₄×D₂₆₉	1	1	yes	characteristic
36	C₁₆	Dic₅₃₈	1	1	yes	characteristic
37	C₂×C₄	#16864387	1	1	yes	characteristic
38	C₈	—	8	1	no	—
39	C₈	—	2152	1	no	—
40	C₈	#16864381	1	1	yes	characteristic
41	C₈	#16864392	1	1	yes	characteristic
42	C₂²	#22575399	1	1	yes	characteristic
43	C₄	#22575386	1	1	yes	characteristic
44	C₄	#22575394	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#31770430	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#22575394
commutator	C₁₆×C₂₆₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₆₉
Fitting	#368×C₂₆₉	C₂
socle	C₂×C₂₆₉	#366
prime radical	C₂²×C₂₆₉	Q₃₂
cosocle	C₂×C₁₆×C₂₆₉	C₂²
hypercenter	#368	D₂₆₉
hypocenter	C₂₆₉	#1425
LCS	G ▷ C₁₆×C₂₆₉ ▷ C₈×C₂₆₉ ▷ C₄×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #368

Complements

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

N	H ≅ G/N	type
23. C₂₆₉	#1425	semidirect

Maximal subgroups

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

subgroup	index
C₂×#22575359	2
#31770435	2
#368×C₂₆₉	2
#1425	269