Subgroups — #28383408

Order 14272.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20297238	C₂	1	2	yes	maximal
2	C₂×C₁₆×C₂₂₃	C₂	1	1	yes	maximal, characteristic
3	C₄⋊Dic₂₂₃	—	2	2	no	—
4	C₂×C₈×C₂₂₃	C₂²	1	1	yes	characteristic
5	C₁₆×C₂₂₃	C₄	1	2	yes	complemented
6	C₂×Dic₂₂₃	—	4	2	no	—
7	C₂×C₄×C₂₂₃	D₄	1	1	yes	characteristic
8	C₈×C₂₂₃	C₂×C₄	1	1	yes	characteristic
9	C₈×C₂₂₃	Q₈	1	1	yes	characteristic
10	C₂²×C₂₂₃	D₈	1	1	yes	characteristic
11	C₄×C₂₂₃	C₄⋊C₄	1	1	yes	characteristic
12	C₄×C₂₂₃	Q₁₆	1	1	yes	characteristic
13	Dic₂₂₃	—	8	2	no	—
14	C₂×C₂₂₃	#107	1	1	yes	characteristic
15	C₂×C₂₂₃	SD₃₂	1	2	yes	—
16	C₂₂₃	#367	1	1	yes	characteristic, complemented, Sylow
17	#367	—	223	1	no	maximal, Sylow
18	C₂×C₁₆	D₂₂₃	1	1	yes	characteristic
19	#107	—	223	2	no	—
20	C₂×C₈	C₂×D₂₂₃	1	1	yes	characteristic
21	C₄⋊C₄	—	446	2	no	—
22	C₁₆	Dic₂₂₃	1	2	yes	complemented
23	C₂×C₄	—	892	2	no	—
24	C₂×C₄	D₈₉₂	1	1	yes	characteristic
25	C₈	C₂×Dic₂₂₃	1	1	yes	characteristic
26	C₈	Dic₄₄₆	1	1	yes	characteristic
27	C₂²	D₁₇₈₄	1	1	yes	characteristic
28	C₄	—	1784	2	no	—
29	C₄	C₄⋊Dic₂₂₃	1	1	yes	characteristic
30	C₄	Dic₈₉₂	1	1	yes	characteristic
31	C₂	#20297238	1	1	yes	characteristic
32	C₂	#20297249	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.