Subgroups — C₃₂×D₃₅₃ #36377618

Order 22592.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₆×D₃₅₃	C₂	1	1	yes	maximal, characteristic
2	#26014898	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₂×C₃₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×D₃₅₃	C₄	1	1	yes	characteristic
5	#19150712	C₄	1	1	yes	characteristic
6	C₁₆×C₃₅₃	C₂²	1	1	yes	characteristic
7	C₄×D₃₅₃	C₈	1	1	yes	characteristic
8	#15667725	C₈	1	1	yes	characteristic
9	C₈×C₃₅₃	C₂×C₄	1	1	yes	characteristic
10	C₂×D₃₅₃	C₁₆	1	1	yes	characteristic
11	C₄×C₃₅₃	C₂×C₈	1	1	yes	characteristic
12	Dic₃₅₃	C₁₆	1	1	yes	characteristic
13	C₂×C₃₅₃	C₂×C₁₆	1	1	yes	characteristic
14	D₃₅₃	C₃₂	1	2	yes	direct product factor
15	C₃₅₃	C₂×C₃₂	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃₂	—	353	1	no	maximal, Sylow
17	C₂×C₁₆	—	353	1	no	—
18	C₃₂	—	353	1	no	—
19	C₃₂	D₃₅₃	1	1	yes	characteristic, direct product factor
20	C₂×C₈	—	353	1	no	—
21	C₁₆	—	353	1	no	—
22	C₁₆	C₂×D₃₅₃	1	1	yes	characteristic
23	C₂×C₄	—	353	1	no	—
24	C₈	—	353	1	no	—
25	C₈	C₄×D₃₅₃	1	1	yes	characteristic
26	C₂²	—	353	1	no	—
27	C₄	—	353	1	no	—
28	C₄	C₈×D₃₅₃	1	1	yes	characteristic
29	C₂	—	353	2	no	—
30	C₂	C₁₆×D₃₅₃	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.