Subgroups — #46826050

Order 34432.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771534	C₂	1	1	yes	maximal, characteristic
2	#31771532	C₂	1	1	yes	maximal, characteristic
3	#31770438	C₂	1	1	yes	maximal, characteristic
4	#22575524	—	2	1	no	—
5	#22575522	—	2	1	no	—
6	C₁₆×D₂₆₉	C₂²	1	1	yes	characteristic
7	#22575359	C₄	1	1	yes	characteristic, complemented
8	C₃₂×C₂₆₉	C₄	1	1	yes	characteristic, complemented
9	#16864412	—	4	1	no	—
10	C₄⋊#11761640	—	4	1	no	—
11	C₈×D₂₆₉	D₄	1	1	yes	characteristic
12	#16864377	Q₈	1	1	yes	characteristic
13	C₁₆×C₂₆₉	C₂×C₄	1	1	yes	characteristic
14	C₂×#11761640	—	8	1	no	—
15	#14524137	—	8	1	no	—
16	C₄×D₂₆₉	D₈	1	1	yes	characteristic
17	#14524130	Q₁₆	1	1	yes	characteristic
18	C₈×C₂₆₉	C₄⋊C₄	1	1	yes	characteristic
19	C₂×D₂₆₉	SD₃₂	1	1	yes	characteristic
20	#11761640	—	16	1	no	—
21	C₄×C₂₆₉	#107	1	1	yes	characteristic
22	Dic₂₆₉	SD₃₂	1	1	yes	characteristic
23	C₂×C₂₆₉	#367	1	1	yes	characteristic
24	D₂₆₉	—	2	1	no	—
25	C₂₆₉	#1426	1	1	yes	characteristic, complemented, Sylow
26	#1426	—	269	1	no	maximal, Sylow
27	M₆₄	—	269	1	no	—
28	#368	—	269	1	no	—
29	#367	—	269	1	no	—
30	C₂×C₁₆	—	269	1	no	—
31	#108	—	538	1	no	—
32	#107	—	538	1	no	—
33	C₃₂	—	269	1	no	—
34	C₃₂	#11761640	1	1	yes	characteristic, complemented
35	M₁₆	—	1076	1	no	—
36	C₂×C₈	—	269	1	no	—
37	C₄⋊C₄	—	1076	1	no	—
38	C₁₆	—	269	1	no	—
39	C₁₆	C₂×#11761640	1	1	yes	characteristic
40	C₂×C₄	—	269	1	no	—
41	C₂×C₄	—	2152	1	no	—
42	C₈	—	269	1	no	—
43	C₈	—	2152	1	no	—
44	C₈	C₄⋊#11761640	1	1	yes	characteristic
45	C₂²	—	269	1	no	—
46	C₄	—	269	1	no	—
47	C₄	—	4304	1	no	—
48	C₄	#22575522	1	1	yes	characteristic
49	C₂	—	538	1	no	—
50	C₂	#31771532	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#31771532
commutator	C₁₆×C₂₆₉	C₂×C₄
Frattini	C₁₆	C₂×#11761640
Fitting	C₃₂×C₂₆₉	C₄
socle	C₂×C₂₆₉	#367
prime radical	C₂×D₂₆₉	SD₃₂
cosocle	C₁₆×D₂₆₉	C₂²
hypercenter	C₃₂	#11761640
hypocenter	C₂₆₉	#1426
LCS	G ▷ C₁₆×C₂₆₉ ▷ C₈×C₂₆₉ ▷ C₄×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂

Complements

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

N	H ≅ G/N	type
7. #22575359	C₄	semidirect
8. C₃₂×C₂₆₉	C₄	semidirect
25. C₂₆₉	#1426	semidirect
34. C₃₂	#11761640	semidirect

Maximal subgroups

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

subgroup	index
#31771534	2
#31771532	2
#31770438	2
#1426	269