Subgroups — #46809086

Order 34432.

56 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	#31770431	C₂	1	1	yes	maximal, characteristic
3	#366×C₂₆₉	C₂	1	1	yes	maximal, characteristic
4	#22575387	—	2	1	no	—
5	#22575359	C₄	1	2	yes	complemented
6	C₂×C₁₆×C₂₆₉	C₂²	1	1	yes	characteristic
7	#107×C₂₆₉	—	2	1	no	—
8	C₄⋊Dic₂₆₉	—	4	1	no	—
9	C₂×C₈×C₂₆₉	D₄	1	1	yes	characteristic
10	C₄⋊C₄×C₂₆₉	—	4	1	no	—
11	C₁₆×C₂₆₉	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₂₆₉	Q₈	1	1	yes	characteristic
13	C₂×Dic₂₆₉	—	8	1	no	—
14	C₂×C₄×C₂₆₉	—	8	1	no	—
15	C₂×C₄×C₂₆₉	D₈	1	1	yes	characteristic
16	C₈×C₂₆₉	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₂₆₉	Q₁₆	1	1	yes	characteristic
18	C₂²×C₂₆₉	D₁₆	1	1	yes	characteristic
19	C₄×C₂₆₉	—	16	1	no	—
20	C₄×C₂₆₉	#107	1	1	yes	characteristic
21	C₄×C₂₆₉	Q₃₂	1	1	yes	characteristic
22	Dic₂₆₉	—	16	1	no	—
23	C₂×C₂₆₉	#366	1	1	yes	characteristic
24	C₂×C₂₆₉	SD₆₄	1	1	yes	characteristic
25	C₂×C₂₆₉	SD₆₄	1	1	yes	characteristic
26	C₂₆₉	#1424	1	1	yes	characteristic, complemented, Sylow
27	#1424	—	269	1	no	maximal, Sylow
28	C₂×C₃₂	—	269	1	no	—
29	#366	—	269	1	no	—
30	#366	D₂₆₉	1	1	yes	characteristic
31	C₂×C₁₆	C₂×D₂₆₉	1	1	yes	characteristic
32	#107	—	2	1	no	—
33	#107	—	538	1	no	—
34	C₃₂	—	269	2	no	—
35	C₂×C₈	C₂²⋊D₂₆₉	1	1	yes	characteristic
36	C₄⋊C₄	—	4	1	no	—
37	C₄⋊C₄	—	1076	1	no	—
38	C₁₆	C₄×D₂₆₉	1	1	yes	characteristic
39	C₁₆	Dic₅₃₈	1	1	yes	characteristic
40	C₂×C₄	—	8	1	no	—
41	C₂×C₄	—	2152	1	no	—
42	C₂×C₄	#16864387	1	1	yes	characteristic
43	C₈	#16864381	1	1	yes	characteristic
44	C₈	#16864392	1	1	yes	characteristic
45	C₂²	#22575394	1	1	yes	characteristic
46	C₄	—	16	1	no	—
47	C₄	—	4304	1	no	—
48	C₄	#22575386	1	1	yes	characteristic
49	C₄	#22575399	1	1	yes	characteristic
50	C₂	#31770430	1	1	yes	characteristic
51	C₂	#31770442	1	1	yes	characteristic
52	C₂	#31770443	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#22575394
commutator	C₁₆×C₂₆₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₆₉
Fitting	#366×C₂₆₉	C₂
socle, prime radical	C₂²×C₂₆₉	D₁₆
cosocle	C₂×C₁₆×C₂₆₉	C₂²
hypercenter	#366	D₂₆₉
hypocenter	C₂₆₉	#1424
LCS	G ▷ C₁₆×C₂₆₉ ▷ C₈×C₂₆₉ ▷ C₄×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #366

Complements

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

N	H ≅ G/N	type
5. #22575359	C₄	semidirect
26. C₂₆₉	#1424	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
#31770431	2
#366×C₂₆₉	2
#1424	269