Subgroups — #27135094

Order 12352.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₀₈₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#20259805	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₆×C₁₉₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₅₄₄	—	2	1	no	—
5	D₈×C₁₉₃	—	2	1	no	—
6	C₁₆×C₁₉₃	C₂²	1	1	yes	characteristic
7	D₇₇₂	—	4	1	no	—
8	D₄×C₁₉₃	—	4	1	no	—
9	C₈×C₁₉₃	D₄	1	1	yes	characteristic
10	C₂²×C₁₉₃	—	8	1	no	—
11	C₂×D₁₉₃	—	8	1	no	—
12	C₄×C₁₉₃	D₈	1	1	yes	characteristic
13	C₂×C₁₉₃	—	16	1	no	—
14	C₂×C₁₉₃	D₁₆	1	1	yes	characteristic
15	D₁₉₃	—	16	1	no	—
16	C₁₉₃	D₃₂	1	1	yes	characteristic, complemented, Sylow
17	D₃₂	—	193	1	no	maximal, Sylow
18	D₁₆	—	193	1	no	—
19	D₁₆	D₁₉₃	1	1	yes	characteristic, complemented
20	C₃₂	—	193	1	no	—
21	D₈	—	2	1	no	—
22	D₈	—	386	1	no	—
23	C₁₆	C₂×D₁₉₃	1	1	yes	characteristic
24	D₄	—	4	1	no	—
25	D₄	—	772	1	no	—
26	C₈	C₂²⋊D₁₉₃	1	1	yes	characteristic
27	C₂²	—	8	1	no	—
28	C₂²	—	1544	1	no	—
29	C₄	#15690540	1	1	yes	characteristic
30	C₂	—	16	1	no	—
31	C₂	—	3088	1	no	—
32	C₂	#20259840	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.