Subgroups — #43243426

Order 28096.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28380683	C₂	1	1	yes	maximal, characteristic
2	#28380679	C₂	1	1	yes	maximal, characteristic
3	#106×C₄₃₉	C₂	1	1	yes	maximal, characteristic
4	#20296313	—	2	1	no	—
5	C₄₃₉⋊C₁₆	C₄	1	2	yes	complemented
6	C₂×C₈×C₄₃₉	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₄₃₉	—	2	1	no	—
8	C₄₃₉⋊C₈	—	4	1	no	—
9	C₂×C₄×C₄₃₉	—	4	1	no	—
10	C₂×C₄×C₄₃₉	D₄	1	1	yes	characteristic
11	C₈×C₄₃₉	C₂×C₄	1	1	yes	characteristic
12	C₈×C₄₃₉	Q₈	1	1	yes	characteristic
13	C₂²×C₄₃₉	SD₁₆	1	1	yes	characteristic
14	C₄×C₄₃₉	—	8	1	no	—
15	C₄×C₄₃₉	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₄₃₉	SD₁₆	1	1	yes	characteristic
17	C₂×C₄₃₉	—	2	1	no	—
18	C₂×C₄₃₉	#106	1	1	yes	characteristic
19	C₄₃₉	#365	1	1	yes	characteristic, complemented, Sylow
20	#365	—	439	1	no	maximal, Sylow
21	M₃₂	—	439	1	no	—
22	#108	—	439	1	no	—
23	#106	D₄₃₉	1	1	yes	characteristic
24	M₁₆	—	878	1	no	—
25	C₂×C₈	C₂×D₄₃₉	1	1	yes	characteristic
26	C₄⋊C₄	—	2	1	no	—
27	C₁₆	—	439	2	no	—
28	C₂×C₄	—	4	1	no	—
29	C₂×C₄	C₂²⋊D₄₃₉	1	1	yes	characteristic
30	C₈	—	1756	1	no	—
31	C₈	C₄×D₄₃₉	1	1	yes	characteristic
32	C₈	Dic₈₇₈	1	1	yes	characteristic
33	C₂²	#20296317	1	1	yes	characteristic
34	C₄	—	8	1	no	—
35	C₄	Dic₄₃₉⋊C₄	1	1	yes	characteristic
36	C₄	#20296316	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#28380674	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
5. C₄₃₉⋊C₁₆	C₄	semidirect
19. C₄₃₉	#365	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.