Subgroups — #46809090

Order 34432.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31770439	C₂	1	1	yes	maximal, characteristic
2	#31770435	C₂	1	1	yes	maximal, characteristic
3	#367×C₂₆₉	C₂	1	1	yes	maximal, characteristic
4	#22575389	—	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	#16864386	—	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	#14524130	—	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	SD₃₂	1	1	yes	characteristic
19	C₄×C₂₆₉	—	16	1	no	—
20	C₄×C₂₆₉	#107	1	1	yes	characteristic
21	C₄×C₂₆₉	SD₃₂	1	1	yes	characteristic
22	C₂×C₂₆₉	—	2	1	no	—
23	C₂×C₂₆₉	#367	1	1	yes	characteristic
24	C₂₆₉	#1426	1	1	yes	characteristic, complemented, Sylow
25	#1426	—	269	1	no	maximal, Sylow
26	M₆₄	—	269	1	no	—
27	#368	—	269	1	no	—
28	#367	D₂₆₉	1	1	yes	characteristic
29	C₂×C₁₆	C₂×D₂₆₉	1	1	yes	characteristic
30	#108	—	538	1	no	—
31	#107	—	2	1	no	—
32	C₃₂	—	269	2	no	—
33	M₁₆	—	1076	1	no	—
34	C₂×C₈	C₂²⋊D₂₆₉	1	1	yes	characteristic
35	C₄⋊C₄	—	4	1	no	—
36	C₁₆	C₄×D₂₆₉	1	1	yes	characteristic
37	C₁₆	Dic₅₃₈	1	1	yes	characteristic
38	C₂×C₄	—	8	1	no	—
39	C₂×C₄	#16864387	1	1	yes	characteristic
40	C₈	—	2152	1	no	—
41	C₈	#16864381	1	1	yes	characteristic
42	C₈	#16864392	1	1	yes	characteristic
43	C₂²	#22575397	1	1	yes	characteristic
44	C₄	—	16	1	no	—
45	C₄	#22575386	1	1	yes	characteristic
46	C₄	#22575396	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	#31770432	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#31770432
commutator	C₁₆×C₂₆₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₆₉
Fitting	#367×C₂₆₉	C₂
socle	C₂×C₂₆₉	#367
prime radical	C₂²×C₂₆₉	SD₃₂
cosocle	C₂×C₁₆×C₂₆₉	C₂²
hypercenter	#367	D₂₆₉
hypocenter	C₂₆₉	#1426
LCS	G ▷ C₁₆×C₂₆₉ ▷ C₈×C₂₆₉ ▷ C₄×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #367

Complements

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

N	H ≅ G/N	type
5. #22575359	C₄	semidirect
24. C₂₆₉	#1426	semidirect

Maximal subgroups

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

subgroup	index
#31770439	2
#31770435	2
#367×C₂₆₉	2
#1426	269