Subgroups — #28357285

Order 13856.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20294107	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#13181884	C₂	1	1	yes	maximal, characteristic, complemented
3	#20294098	C₂	1	1	yes	maximal, characteristic
4	C₂×#13181884	—	2	1	no	—
5	#16812365	—	2	1	no	—
6	D₁₇₃₂	—	2	1	no	—
7	D₁₇₃₂	C₄	1	1	yes	characteristic, complemented
8	C₄×D₄₃₃	—	2	1	no	—
9	C₄×D₄₃₃	C₂²	1	1	yes	characteristic
10	Q₈×C₄₃₃	C₄	1	1	yes	characteristic, complemented
11	C₂×D₄₃₃	—	2	1	no	—
12	C₂×D₄₃₃	D₄	1	1	yes	characteristic
13	#13181884	—	2	2	no	—
14	C₄×C₄₃₃	—	2	1	no	—
15	C₄×C₄₃₃	C₂×C₄	1	1	yes	characteristic
16	Dic₄₃₃	D₄	1	1	yes	characteristic
17	C₂×C₄₃₃	C₂²⋊C₄	1	1	yes	characteristic
18	D₄₃₃	—	2	1	no	—
19	D₄₃₃	—	4	1	no	—
20	C₄₃₃	#104	1	1	yes	characteristic, complemented, Sylow
21	#104	—	433	1	no	maximal, Sylow
22	#41	—	433	1	no	—
23	M₁₆	—	433	1	no	—
24	C₄²	—	433	1	no	—
25	Q₈	#13181884	1	1	yes	characteristic, complemented
26	D₄	—	866	1	no	—
27	D₄	—	433	1	no	—
28	C₂×C₄	—	866	1	no	—
29	C₂×C₄	—	866	1	no	—
30	C₂×C₄	—	433	1	no	—
31	C₈	—	866	1	no	—
32	C₂²	—	866	1	no	—
33	C₂²	—	433	1	no	—
34	C₄	—	2	1	no	—
35	C₄	—	866	2	no	—
36	C₄	—	433	1	no	—
37	C₄	C₂×#13181884	1	1	yes	characteristic
38	C₂	—	866	1	no	—
39	C₂	—	1732	1	no	—
40	C₂	C₂²⋊#13181884	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.