Subgroups — #20301055

Order 7328.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14270087	C₂	1	2	yes	maximal
2	C₄×Dic₂₂₉	C₂	1	1	yes	maximal, characteristic
3	#14270087	—	2	2	no	—
4	C₂×Dic₂₂₉	C₄	1	1	yes	characteristic
5	C₂×Dic₂₂₉	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₂₂₉	C₄	1	1	yes	characteristic
7	C₂²×C₂₂₉	C₂×C₄	1	1	yes	characteristic
8	C₄×C₂₂₉	—	2	1	no	—
9	Dic₂₂₉	C₈	1	2	yes	complemented
10	Dic₂₂₉	D₄	1	1	yes	characteristic
11	Dic₂₂₉	Q₈	1	1	yes	characteristic
12	C₂×C₂₂₉	C₄⋊C₄	1	1	yes	characteristic
13	C₂×C₂₂₉	C₂×C₈	1	1	yes	characteristic
14	C₂×C₂₂₉	M₁₆	1	1	yes	characteristic
15	C₂₂₉	C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
16	C₄⋊C₈	—	229	1	no	maximal, Sylow
17	C₂×C₈	—	229	2	no	—
18	C₄²	—	229	1	no	—
19	C₂×C₄	—	229	1	no	—
20	C₂×C₄	—	229	1	no	—
21	C₂×C₄	#11745021	1	1	yes	characteristic
22	C₈	—	458	2	no	—
23	C₂²	C₂×#11745021	1	1	yes	characteristic
24	C₄	—	2	1	no	—
25	C₄	—	229	1	no	—
26	C₄	—	229	1	no	—
27	C₄	—	229	2	no	—
28	C₂	C₄⋊#11745021	1	1	yes	characteristic
29	C₂	D₂₂₉⋊C₈	1	1	yes	characteristic
30	C₂	#16814675	1	1	yes	characteristic

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

N	H ≅ G/N	type
9. Dic₂₂₉	C₈	semidirect
15. C₂₂₉	C₄⋊C₈	semidirect