Subgroups — C₂⁴×#13083443 #36378868

Order 22592.

1362 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#13083443	C₂	1	30	yes	maximal, direct product factor
2	C₂⁴×D₃₅₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×#13083443	C₂²	1	140	yes	direct product factor
4	C₂³×D₃₅₃	C₄	1	15	yes	complemented
5	C₂³×D₃₅₃	C₂²	1	15	yes	—
6	C₂⁴×C₃₅₃	C₄	1	1	yes	characteristic, complemented
7	C₂×#13083443	C₂³	1	120	yes	direct product factor
8	C₂²×D₃₅₃	C₂×C₄	1	105	yes	complemented
9	C₂²×D₃₅₃	C₂³	1	35	yes	—
10	C₂³×C₃₅₃	C₂×C₄	1	15	yes	complemented
11	C₂²×C₃₅₃	C₂²×C₄	1	35	yes	complemented
12	C₂×D₃₅₃	C₂²×C₄	1	105	yes	complemented
13	C₂×D₃₅₃	C₂⁴	1	15	yes	—
14	#13083443	C₂⁴	1	16	yes	direct product factor
15	C₂×C₃₅₃	C₂³×C₄	1	15	yes	complemented
16	D₃₅₃	C₂³×C₄	1	15	yes	complemented
17	D₃₅₃	C₂⁵	1	1	yes	characteristic
18	C₃₅₃	C₂⁴×C₄	1	1	yes	characteristic, complemented, Sylow
19	C₂⁴×C₄	—	353	1	no	maximal, Sylow
20	C₂⁵	—	353	1	no	—
21	C₂³×C₄	—	353	30	no	—
22	C₂⁴	—	353	15	no	—
23	C₂⁴	—	353	15	no	—
24	C₂⁴	#13083443	1	1	yes	characteristic, direct product factor
25	C₂²×C₄	—	353	140	no	—
26	C₂³	—	353	105	no	—
27	C₂³	—	353	35	no	—
28	C₂³	C₂×#13083443	1	15	yes	direct product factor
29	C₂×C₄	—	353	120	no	—
30	C₂²	—	353	15	no	—
31	C₂²	—	353	105	no	—
32	C₂²	C₂²×#13083443	1	35	yes	direct product factor
33	C₄	—	353	16	no	—
34	C₂	—	353	1	no	—
35	C₂	—	353	15	no	—
36	C₂	C₂³×#13083443	1	15	yes	direct product factor

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.