Subgroups — #108×C₁₁₂₃ #49090455

Order 35936.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	M₁₆×C₁₁₂₃	C₂	1	2	yes	maximal
2	C₂×C₈×C₁₁₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₁₁₂₃	C₂²	1	1	yes	characteristic
4	C₈×C₁₁₂₃	—	2	2	no	—
5	C₈×C₁₁₂₃	C₄	1	2	yes	—
6	C₂²×C₁₁₂₃	Q₈	1	1	yes	characteristic
7	C₄×C₁₁₂₃	C₂×C₄	1	1	yes	characteristic
8	C₄×C₁₁₂₃	D₄	1	1	yes	characteristic
9	C₂×C₁₁₂₃	—	2	1	no	—
10	C₂×C₁₁₂₃	C₄⋊C₄	1	1	yes	characteristic
11	C₁₁₂₃	#108	1	1	yes	characteristic, direct product factor, Sylow
12	#108	C₁₁₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	M₁₆	C₂×C₁₁₂₃	1	2	yes	—
14	C₂×C₈	C₂×C₁₁₂₃	1	1	yes	characteristic
15	C₂×C₄	C₂²×C₁₁₂₃	1	1	yes	characteristic
16	C₈	—	2	2	no	—
17	C₈	C₄×C₁₁₂₃	1	2	yes	—
18	C₂²	Q₈×C₁₁₂₃	1	1	yes	characteristic
19	C₄	C₂×C₄×C₁₁₂₃	1	1	yes	characteristic
20	C₄	D₄×C₁₁₂₃	1	1	yes	characteristic
21	C₂	—	2	1	no	—
22	C₂	C₄⋊C₄×C₁₁₂₃	1	1	yes	characteristic

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

N	H ≅ G/N	type
11. C₁₁₂₃	#108	direct (N × H)
12. #108	C₁₁₂₃	direct (N × H)

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