Subgroups — #46825919

Order 34432.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771468	C₂	1	2	yes	maximal
2	C₁₆×Dic₂₆₉	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#14524137	—	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	C₂×#14524137	—	4	2	no	—
8	C₂×#14524130	Q₈	1	1	yes	characteristic
9	C₄×Dic₂₆₉	D₄	1	1	yes	characteristic
10	#16864377	C₈	1	2	yes	complemented
11	C₂×C₈×C₂₆₉	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₂₆₉	—	2	1	no	—
13	#14524137	—	8	2	no	—
14	C₂×Dic₂₆₉	D₈	1	1	yes	characteristic
15	C₂×Dic₂₆₉	Q₁₆	1	1	yes	characteristic
16	#14524130	—	2	1	no	—
17	C₂×C₄×C₂₆₉	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₂₆₉	C₂×C₈	1	1	yes	characteristic
19	C₈×C₂₆₉	M₁₆	1	1	yes	characteristic
20	C₂²×C₂₆₉	#107	1	1	yes	characteristic
21	C₄×C₂₆₉	C₄⋊C₈	1	1	yes	characteristic
22	C₄×C₂₆₉	#108	1	1	yes	characteristic
23	Dic₂₆₉	—	2	1	no	—
24	Dic₂₆₉	SD₃₂	1	2	yes	—
25	C₂×C₂₆₉	#335	1	1	yes	characteristic
26	C₂×C₂₆₉	#367	1	1	yes	characteristic
27	C₂×C₂₆₉	#368	1	1	yes	characteristic
28	C₂₆₉	#1372	1	1	yes	characteristic, complemented, Sylow
29	#1372	—	269	1	no	maximal, Sylow
30	C₄×C₁₆	—	269	1	no	—
31	#335	—	269	2	no	—
32	C₂×C₁₆	—	269	1	no	—
33	C₂×C₁₆	#11761640	1	1	yes	characteristic
34	C₄⋊C₈	—	538	2	no	—
35	C₄×C₈	—	269	1	no	—
36	C₂×C₈	—	269	1	no	—
37	C₂×C₈	—	1076	2	no	—
38	C₂×C₈	C₂×#11761640	1	1	yes	characteristic
39	C₄²	—	269	1	no	—
40	C₁₆	—	2	1	no	—
41	C₁₆	—	269	2	no	—
42	C₂×C₄	—	269	1	no	—
43	C₂×C₄	—	269	1	no	—
44	C₂×C₄	C₄⋊#11761640	1	1	yes	characteristic
45	C₈	—	538	1	no	—
46	C₈	—	2152	2	no	—
47	C₈	D₂₆₉⋊C₈	1	1	yes	characteristic
48	C₈	#16864411	1	1	yes	characteristic
49	C₂²	#22575522	1	1	yes	characteristic
50	C₄	—	269	2	no	—
51	C₄	—	538	1	no	—
52	C₄	#22575520	1	1	yes	characteristic
53	C₄	#22575523	1	1	yes	characteristic
54	C₂	#31771469	1	1	yes	characteristic
55	C₂	#31771532	1	1	yes	characteristic
56	C₂	#31771533	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#22575522
commutator	C₈×C₂₆₉	C₂×C₈
Frattini	C₂×C₈	C₂×#11761640
Fitting	C₂×C₁₆×C₂₆₉	C₄
socle, prime radical	C₂²×C₂₆₉	#107
cosocle	C₈×Dic₂₆₉	C₂²
hypercenter	C₂×C₁₆	#11761640
hypocenter	C₂₆₉	#1372
LCS	G ▷ C₈×C₂₆₉ ▷ C₄×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
10. #16864377	C₈	semidirect
28. C₂₆₉	#1372	semidirect

Maximal subgroups

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

subgroup	index
#31771468	2
C₁₆×Dic₂₆₉	2
#1372	269