Subgroups — #28388784

Order 14464.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₂×D₁₁₃	C₂	1	1	yes	maximal, characteristic
2	#20298317	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₄×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₆×D₁₁₃	C₄	1	1	yes	characteristic
5	#16813528	C₄	1	1	yes	characteristic
6	C₃₂×C₁₁₃	C₂²	1	1	yes	characteristic
7	C₈×D₁₁₃	C₈	1	1	yes	characteristic
8	#14268622	C₈	1	1	yes	characteristic
9	C₁₆×C₁₁₃	C₂×C₄	1	1	yes	characteristic
10	C₄×D₁₁₃	C₁₆	1	1	yes	characteristic
11	C₈×C₁₁₃	C₂×C₈	1	1	yes	characteristic
12	#11744751	C₁₆	1	1	yes	characteristic
13	C₂×D₁₁₃	C₃₂	1	1	yes	characteristic
14	C₄×C₁₁₃	C₂×C₁₆	1	1	yes	characteristic
15	Dic₁₁₃	C₃₂	1	1	yes	characteristic
16	C₂×C₁₁₃	C₂×C₃₂	1	1	yes	characteristic
17	D₁₁₃	—	2	1	no	—
18	M₁₂₈	—	113	1	no	maximal, Sylow
19	C₁₁₃	M₁₂₈	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃₂	—	113	1	no	—
21	C₆₄	—	113	1	no	—
22	C₆₄	D₁₁₃	1	1	yes	characteristic, complemented
23	C₂×C₁₆	—	113	1	no	—
24	C₃₂	—	113	1	no	—
25	C₃₂	C₂×D₁₁₃	1	1	yes	characteristic
26	C₂×C₈	—	113	1	no	—
27	C₁₆	—	113	1	no	—
28	C₁₆	C₄×D₁₁₃	1	1	yes	characteristic
29	C₂×C₄	—	113	1	no	—
30	C₈	—	113	1	no	—
31	C₈	C₈×D₁₁₃	1	1	yes	characteristic
32	C₂²	—	113	1	no	—
33	C₄	—	113	1	no	—
34	C₄	C₁₆×D₁₁₃	1	1	yes	characteristic
35	C₂	—	226	1	no	—
36	C₂	C₃₂×D₁₁₃	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.