Subgroups — #106×C₃₈₃ #27133708

Order 12256.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×C₃₈₃	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₄×C₃₈₃	C₂	1	2	yes	maximal
3	C₂×C₄×C₃₈₃	—	2	2	no	—
4	C₂×C₄×C₃₈₃	C₂²	1	1	yes	characteristic
5	C₈×C₃₈₃	C₄	1	2	yes	complemented
6	C₂²×C₃₈₃	D₄	1	1	yes	characteristic
7	C₄×C₃₈₃	—	4	2	no	—
8	C₄×C₃₈₃	C₂×C₄	1	1	yes	characteristic
9	C₄×C₃₈₃	Q₈	1	1	yes	characteristic
10	C₂×C₃₈₃	C₄⋊C₄	1	1	yes	characteristic
11	C₂×C₃₈₃	SD₁₆	1	2	yes	—
12	C₃₈₃	#106	1	1	yes	characteristic, direct product factor, Sylow
13	#106	C₃₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₂×C₈	C₂×C₃₈₃	1	1	yes	characteristic
15	C₄⋊C₄	C₂×C₃₈₃	1	2	yes	—
16	C₂×C₄	—	2	2	no	—
17	C₂×C₄	C₂²×C₃₈₃	1	1	yes	characteristic
18	C₈	C₄×C₃₈₃	1	2	yes	complemented
19	C₂²	D₄×C₃₈₃	1	1	yes	characteristic
20	C₄	—	4	2	no	—
21	C₄	C₂×C₄×C₃₈₃	1	1	yes	characteristic
22	C₄	Q₈×C₃₈₃	1	1	yes	characteristic
23	C₂	C₄⋊C₄×C₃₈₃	1	1	yes	characteristic
24	C₂	SD₁₆×C₃₈₃	1	2	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.