Subgroups — C₂⁴×#1181 #14272244

Order 1856.

1362 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂³×#1181	C₂	1	30	yes	maximal, direct product factor
3	C₂⁴×C₂₉	C₄	1	1	yes	characteristic, complemented
4	C₂³×D₂₉	C₄	1	15	yes	complemented
5	C₂³×D₂₉	C₂²	1	15	yes	—
6	C₂²×#1181	C₂²	1	140	yes	direct product factor
7	C₂³×C₂₉	C₂×C₄	1	15	yes	complemented
8	C₂²×D₂₉	C₂×C₄	1	105	yes	complemented
9	C₂²×D₂₉	C₂³	1	35	yes	—
10	C₂×#1181	C₂³	1	120	yes	direct product factor
11	C₂²×C₂₉	C₂²×C₄	1	35	yes	complemented
12	C₂×D₂₉	C₂²×C₄	1	105	yes	complemented
13	C₂×D₂₉	C₂⁴	1	15	yes	—
14	#1181	C₂⁴	1	16	yes	direct product factor
15	C₂⁴×C₄	—	29	1	no	maximal, Sylow
16	C₂×C₂₉	C₂³×C₄	1	15	yes	complemented
17	D₂₉	C₂³×C₄	1	15	yes	complemented
18	D₂₉	C₂⁵	1	1	yes	characteristic
19	C₂⁵	—	29	1	no	—
20	C₂³×C₄	—	29	30	no	—
21	C₂₉	C₂⁴×C₄	1	1	yes	characteristic, complemented, Sylow
22	C₂⁴	—	29	15	no	—
23	C₂⁴	—	29	15	no	—
24	C₂⁴	#1181	1	1	yes	characteristic, direct product factor
25	C₂²×C₄	—	29	140	no	—
26	C₂³	—	29	35	no	—
27	C₂³	—	29	105	no	—
28	C₂³	C₂×#1181	1	15	yes	direct product factor
29	C₂×C₄	—	29	120	no	—
30	C₂²	—	29	15	no	—
31	C₂²	—	29	105	no	—
32	C₂²	C₂²×#1181	1	35	yes	direct product factor
33	C₄	—	29	16	no	—
34	C₂	—	29	1	no	—
35	C₂	—	29	15	no	—
36	C₂	C₂³×#1181	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.