Subgroups — #16845326

Order 3968.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521426	C₂	1	6	yes	maximal, complemented
2	C₈²×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₄₈	—	2	12	no	—
4	#11758451	C₂²	1	4	yes	—
5	C₄×C₈×C₃₁	C₂²	1	3	yes	—
6	C₂×D₁₂₄	—	2	12	no	—
7	C₂×C₈×C₃₁	D₄	1	6	yes	—
8	C₄²×C₃₁	C₂³	1	1	yes	characteristic
9	D₂₄₈	—	4	24	no	—
10	C₂²×D₃₁	—	4	4	no	—
11	C₂×C₄×C₃₁	C₂×D₄	1	3	yes	—
12	D₁₂₄	—	4	24	no	—
13	C₈×C₃₁	D₈	1	12	yes	complemented
14	#1712	—	31	1	no	maximal, Sylow
15	C₂²×C₃₁	#127	1	1	yes	characteristic
16	C₂×D₃₁	—	8	12	no	—
17	C₄×C₃₁	C₂×D₈	1	6	yes	—
18	#493	—	31	6	no	—
19	C₈²	D₃₁	1	1	yes	characteristic, complemented
20	C₂×C₃₁	#493	1	3	yes	—
21	D₃₁	—	16	4	no	—
22	C₂×D₈	—	62	12	no	—
23	#127	—	31	4	no	—
24	C₄×C₈	C₂×D₃₁	1	3	yes	—
25	C₃₁	#1712	1	1	yes	characteristic, complemented, Sylow
26	C₂×D₄	—	62	12	no	—
27	D₈	—	124	24	no	—
28	C₂×C₈	D₁₂₄	1	6	yes	—
29	C₄²	C₂²×D₃₁	1	1	yes	characteristic
30	C₂³	—	124	4	no	—
31	D₄	—	124	24	no	—
32	C₂×C₄	C₂×D₁₂₄	1	3	yes	—
33	C₈	D₂₄₈	1	12	yes	complemented
34	C₂²	—	248	12	no	—
35	C₂²	#11758451	1	1	yes	characteristic
36	C₄	C₂×D₂₄₈	1	6	yes	—
37	C₂	—	496	4	no	—
38	C₂	#14521426	1	3	yes	—

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.