Subgroups — #28417524

Order 14912.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#14272347	C₂	1	2	yes	maximal
2	C₈×#11745400	C₂	1	1	yes	maximal, characteristic
3	C₂×#14272347	—	2	2	no	—
4	#16836602	C₄	1	1	yes	characteristic
5	C₄×#11745400	C₂²	1	1	yes	characteristic
6	C₈×D₂₃₃	C₄	1	1	yes	characteristic
7	#14272347	—	4	2	no	—
8	C₂×#11745400	D₄	1	1	yes	characteristic
9	C₂×#11745400	Q₈	1	1	yes	characteristic
10	#14272345	—	2	1	no	—
11	C₄×D₂₃₃	C₂×C₄	1	1	yes	characteristic
12	#14272338	C₈	1	1	yes	characteristic, complemented
13	C₈×C₂₃₃	C₈	1	1	yes	characteristic, complemented
14	C₂×D₂₃₃	C₄⋊C₄	1	1	yes	characteristic
15	#11745400	—	2	1	no	—
16	#11745400	SD₁₆	1	2	yes	—
17	C₄×C₂₃₃	C₂×C₈	1	1	yes	characteristic
18	Dic₂₃₃	M₁₆	1	1	yes	characteristic
19	C₂×C₂₃₃	C₄⋊C₈	1	1	yes	characteristic
20	D₂₃₃	#106	1	1	yes	characteristic
21	D₂₃₃	#108	1	1	yes	characteristic
22	C₂₃₃	#334	1	1	yes	characteristic, complemented, Sylow
23	#334	—	233	1	no	maximal, Sylow
24	C₄⋊C₈	—	233	2	no	—
25	C₄×C₈	—	233	1	no	—
26	C₂×C₈	—	466	2	no	—
27	C₂×C₈	—	233	1	no	—
28	C₂×C₈	—	233	1	no	—
29	C₄²	—	233	1	no	—
30	C₂×C₄	—	233	1	no	—
31	C₂×C₄	—	233	1	no	—
32	C₂×C₄	—	233	1	no	—
33	C₈	—	932	2	no	—
34	C₈	—	466	1	no	—
35	C₈	—	233	1	no	—
36	C₈	#14272347	1	1	yes	characteristic, complemented
37	C₂²	—	233	1	no	—
38	C₄	—	466	1	no	—
39	C₄	—	233	2	no	—
40	C₄	—	233	1	no	—
41	C₄	C₂×#14272347	1	1	yes	characteristic
42	C₂	—	233	1	no	—
43	C₂	—	233	1	no	—
44	C₂	C₄⋊#14272347	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.