Subgroups — C₂⁴×#11715871 #27136340

Order 12352.

1362 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#11715871	C₂	1	30	yes	maximal, direct product factor
2	C₂⁴×D₁₉₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×#11715871	C₂²	1	140	yes	direct product factor
4	C₂³×D₁₉₃	C₄	1	15	yes	complemented
5	C₂³×D₁₉₃	C₂²	1	15	yes	—
6	C₂⁴×C₁₉₃	C₄	1	1	yes	characteristic, complemented
7	C₂×#11715871	C₂³	1	120	yes	direct product factor
8	C₂²×D₁₉₃	C₂×C₄	1	105	yes	complemented
9	C₂²×D₁₉₃	C₂³	1	35	yes	—
10	C₂³×C₁₉₃	C₂×C₄	1	15	yes	complemented
11	C₂²×C₁₉₃	C₂²×C₄	1	35	yes	complemented
12	C₂×D₁₉₃	C₂²×C₄	1	105	yes	complemented
13	C₂×D₁₉₃	C₂⁴	1	15	yes	—
14	#11715871	C₂⁴	1	16	yes	direct product factor
15	C₂×C₁₉₃	C₂³×C₄	1	15	yes	complemented
16	D₁₉₃	C₂³×C₄	1	15	yes	complemented
17	D₁₉₃	C₂⁵	1	1	yes	characteristic
18	C₁₉₃	C₂⁴×C₄	1	1	yes	characteristic, complemented, Sylow
19	C₂⁴×C₄	—	193	1	no	maximal, Sylow
20	C₂⁵	—	193	1	no	—
21	C₂³×C₄	—	193	30	no	—
22	C₂⁴	—	193	15	no	—
23	C₂⁴	—	193	15	no	—
24	C₂⁴	#11715871	1	1	yes	characteristic, direct product factor
25	C₂²×C₄	—	193	140	no	—
26	C₂³	—	193	35	no	—
27	C₂³	—	193	105	no	—
28	C₂³	C₂×#11715871	1	15	yes	direct product factor
29	C₂×C₄	—	193	120	no	—
30	C₂²	—	193	15	no	—
31	C₂²	—	193	105	no	—
32	C₂²	C₂²×#11715871	1	35	yes	direct product factor
33	C₄	—	193	16	no	—
34	C₂	—	193	1	no	—
35	C₂	—	193	15	no	—
36	C₂	C₂³×#11715871	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.