Subgroups — #27135087

Order 12352.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20259833	C₂	1	2	yes	maximal
2	C₂×C₁₆×C₁₉₃	C₂	1	1	yes	maximal, characteristic
3	C₄⋊Dic₁₉₃	—	2	2	no	—
4	C₂×C₈×C₁₉₃	C₂²	1	1	yes	characteristic
5	C₁₆×C₁₉₃	C₄	1	2	yes	complemented
6	C₂×Dic₁₉₃	—	4	2	no	—
7	C₂×C₄×C₁₉₃	D₄	1	1	yes	characteristic
8	C₈×C₁₉₃	C₂×C₄	1	1	yes	characteristic
9	C₈×C₁₉₃	Q₈	1	1	yes	characteristic
10	C₂²×C₁₉₃	D₈	1	1	yes	characteristic
11	C₄×C₁₉₃	C₄⋊C₄	1	1	yes	characteristic
12	C₄×C₁₉₃	Q₁₆	1	1	yes	characteristic
13	Dic₁₉₃	—	8	2	no	—
14	C₂×C₁₉₃	#107	1	1	yes	characteristic
15	C₂×C₁₉₃	SD₃₂	1	2	yes	—
16	C₁₉₃	#367	1	1	yes	characteristic, complemented, Sylow
17	#367	—	193	1	no	maximal, Sylow
18	C₂×C₁₆	D₁₉₃	1	1	yes	characteristic
19	#107	—	193	2	no	—
20	C₂×C₈	C₂×D₁₉₃	1	1	yes	characteristic
21	C₄⋊C₄	—	386	2	no	—
22	C₁₆	Dic₁₉₃	1	2	yes	complemented
23	C₂×C₄	—	772	2	no	—
24	C₂×C₄	D₇₇₂	1	1	yes	characteristic
25	C₈	C₂×Dic₁₉₃	1	1	yes	characteristic
26	C₈	Dic₃₈₆	1	1	yes	characteristic
27	C₂²	D₁₅₄₄	1	1	yes	characteristic
28	C₄	—	1544	2	no	—
29	C₄	C₄⋊Dic₁₉₃	1	1	yes	characteristic
30	C₄	Dic₇₇₂	1	1	yes	characteristic
31	C₂	#20259833	1	1	yes	characteristic
32	C₂	#20259844	1	2	yes	—

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.