Subgroups — #16810458

Order 3392.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₄₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#13133123	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₈×C₅₃	—	2	1	no	—
5	D₄₂₄	—	2	1	no	—
6	C₁₆×C₅₃	C₂²	1	1	yes	characteristic
7	D₄×C₅₃	—	4	1	no	—
8	D₂₁₂	—	4	1	no	—
9	C₈×C₅₃	D₄	1	1	yes	characteristic
10	C₂²×C₅₃	—	8	1	no	—
11	C₂×D₅₃	—	8	1	no	—
12	C₄×C₅₃	D₈	1	1	yes	characteristic
13	C₂×C₅₃	—	16	1	no	—
14	C₂×C₅₃	D₁₆	1	1	yes	characteristic
15	D₅₃	—	16	1	no	—
16	D₃₂	—	53	1	no	maximal, Sylow
17	C₅₃	D₃₂	1	1	yes	characteristic, complemented, Sylow
18	D₁₆	—	53	1	no	—
19	D₁₆	D₅₃	1	1	yes	characteristic, complemented
20	C₃₂	—	53	1	no	—
21	D₈	—	2	1	no	—
22	D₈	—	106	1	no	—
23	C₁₆	C₂×D₅₃	1	1	yes	characteristic
24	D₄	—	4	1	no	—
25	D₄	—	212	1	no	—
26	C₈	C₂²⋊D₅₃	1	1	yes	characteristic
27	C₂²	—	8	1	no	—
28	C₂²	—	424	1	no	—
29	C₄	#11719922	1	1	yes	characteristic
30	C₂	—	16	1	no	—
31	C₂	—	848	1	no	—
32	C₂	#13133158	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.