Subgroups — #46826043

Order 34432.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22575503	C₂	1	2	yes	maximal
2	C₁₆×Dic₂₆₉	C₂	1	1	yes	maximal, characteristic
3	#22575503	—	2	2	no	—
4	C₂×#16864377	C₂²	1	1	yes	characteristic
5	C₈×Dic₂₆₉	C₄	1	1	yes	characteristic
6	C₂×C₁₆×C₂₆₉	C₄	1	1	yes	characteristic
7	C₂×#14524130	C₈	1	1	yes	characteristic
8	C₄×Dic₂₆₉	C₈	1	1	yes	characteristic
9	#16864377	D₄	1	1	yes	characteristic
10	#16864377	Q₈	1	1	yes	characteristic
11	C₂×C₈×C₂₆₉	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₂₆₉	—	2	1	no	—
13	C₂×Dic₂₆₉	C₁₆	1	1	yes	characteristic
14	C₂×Dic₂₆₉	C₁₆	1	1	yes	characteristic
15	#14524130	—	2	1	no	—
16	C₂×C₄×C₂₆₉	C₂×C₈	1	1	yes	characteristic
17	C₈×C₂₆₉	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₂₆₉	M₁₆	1	1	yes	characteristic
19	C₂²×C₂₆₉	C₂×C₁₆	1	1	yes	characteristic
20	C₄×C₂₆₉	C₄⋊C₈	1	1	yes	characteristic
21	C₄×C₂₆₉	M₃₂	1	1	yes	characteristic
22	Dic₂₆₉	—	2	1	no	—
23	Dic₂₆₉	C₃₂	1	2	yes	complemented
24	C₂×C₂₆₉	C₄⋊C₁₆	1	1	yes	characteristic
25	C₂×C₂₆₉	C₂×C₃₂	1	1	yes	characteristic
26	C₂×C₂₆₉	M₆₄	1	1	yes	characteristic
27	C₂₆₉	C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
28	C₄⋊C₃₂	—	269	1	no	maximal, Sylow
29	C₂×C₃₂	—	269	2	no	—
30	C₄×C₁₆	—	269	1	no	—
31	C₂×C₁₆	—	269	1	no	—
32	C₂×C₁₆	#11761640	1	1	yes	characteristic
33	C₄×C₈	—	269	1	no	—
34	C₃₂	—	538	2	no	—
35	C₂×C₈	—	269	1	no	—
36	C₂×C₈	C₂×#11761640	1	1	yes	characteristic
37	C₄²	—	269	1	no	—
38	C₁₆	—	2	1	no	—
39	C₁₆	—	269	1	no	—
40	C₁₆	—	269	1	no	—
41	C₂×C₄	—	269	1	no	—
42	C₂×C₄	—	269	1	no	—
43	C₂×C₄	D₂₆₉⋊C₈	1	1	yes	characteristic
44	C₈	—	538	1	no	—
45	C₈	C₄⋊#11761640	1	1	yes	characteristic
46	C₈	#16864411	1	1	yes	characteristic
47	C₂²	D₂₆₉⋊C₁₆	1	1	yes	characteristic
48	C₄	—	269	2	no	—
49	C₄	—	538	1	no	—
50	C₄	#22575520	1	1	yes	characteristic
51	C₄	#22575528	1	1	yes	characteristic
52	C₂	#31771526	1	1	yes	characteristic
53	C₂	D₂₆₉⋊C₃₂	1	1	yes	characteristic
54	C₂	#31771538	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×#11761640
commutator	C₂×C₂₆₉	C₂×C₃₂
Fitting	C₂×C₁₆×C₂₆₉	C₄
socle, prime radical	C₂²×C₂₆₉	C₂×C₁₆
cosocle	C₂×#16864377	C₂²
hypercenter	C₂×C₁₆	#11761640
hypocenter	C₂₆₉	C₄⋊C₃₂
LCS	G ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
23. Dic₂₆₉	C₃₂	semidirect
27. C₂₆₉	C₄⋊C₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×#22575503	2
C₁₆×Dic₂₆₉	2
C₄⋊C₃₂	269