Subgroups — #28412407

Order 14656.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20301057	C₂	1	2	yes	maximal
2	C₁₆×D₂₂₉	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#11745021	—	2	2	no	—
4	C₈×D₂₂₉	C₂²	1	1	yes	characteristic
5	#16814641	C₄	1	1	yes	characteristic, complemented
6	C₁₆×C₂₂₉	C₄	1	1	yes	characteristic, complemented
7	C₂×#11745021	—	4	2	no	—
8	C₄×D₂₂₉	D₄	1	1	yes	characteristic
9	#14270080	Q₈	1	1	yes	characteristic
10	C₈×C₂₂₉	C₂×C₄	1	1	yes	characteristic
11	C₂×D₂₂₉	D₈	1	1	yes	characteristic
12	#11745021	—	8	2	no	—
13	C₄×C₂₂₉	C₄⋊C₄	1	1	yes	characteristic
14	Dic₂₂₉	Q₁₆	1	1	yes	characteristic
15	C₂×C₂₂₉	#107	1	1	yes	characteristic
16	D₂₂₉	D₁₆	1	1	yes	characteristic
17	D₂₂₉	Q₃₂	1	1	yes	characteristic
18	C₂₂₉	#366	1	1	yes	characteristic, complemented, Sylow
19	#366	—	229	1	no	maximal, Sylow
20	C₂×C₁₆	—	229	1	no	—
21	#107	—	229	2	no	—
22	C₂×C₈	—	229	1	no	—
23	C₄⋊C₄	—	458	2	no	—
24	C₁₆	—	229	1	no	—
25	C₁₆	#11745021	1	1	yes	characteristic, complemented
26	C₂×C₄	—	916	2	no	—
27	C₂×C₄	—	229	1	no	—
28	C₈	—	229	1	no	—
29	C₈	C₂×#11745021	1	1	yes	characteristic
30	C₂²	—	229	1	no	—
31	C₄	—	1832	2	no	—
32	C₄	—	229	1	no	—
33	C₄	C₄⋊#11745021	1	1	yes	characteristic
34	C₂	—	229	1	no	—
35	C₂	—	229	1	no	—
36	C₂	#20301057	1	1	yes	characteristic

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

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