Subgroups — #28411310

Order 14656.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16814641	C₂	1	1	yes	maximal, characteristic
2	#20300924	C₂	1	1	yes	maximal, characteristic
3	#108×C₂₂₉	C₂	1	1	yes	maximal, characteristic
4	#16814650	—	2	1	no	—
5	#16814641	C₄	1	2	yes	—
6	M₁₆×C₂₂₉	—	2	1	no	—
7	C₂×C₈×C₂₂₉	C₂²	1	1	yes	characteristic
8	#14270080	—	4	1	no	—
9	C₂×C₄×C₂₂₉	D₄	1	1	yes	characteristic
10	C₈×C₂₂₉	—	4	1	no	—
11	C₈×C₂₂₉	C₂×C₄	1	1	yes	characteristic
12	C₈×C₂₂₉	Q₈	1	1	yes	characteristic
13	C₂²×C₂₂₉	Q₁₆	1	1	yes	characteristic
14	C₄×C₂₂₉	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₂₂₉	D₈	1	1	yes	characteristic
16	C₂×C₂₂₉	—	2	1	no	—
17	C₂×C₂₂₉	#107	1	1	yes	characteristic
18	C₂₂₉	#368	1	1	yes	characteristic, complemented, Sylow
19	#368	—	229	1	no	maximal, Sylow
20	C₂×C₁₆	—	229	1	no	—
21	#108	—	229	1	no	—
22	#108	D₂₂₉	1	1	yes	characteristic
23	M₁₆	—	2	1	no	—
24	M₁₆	—	458	1	no	—
25	C₂×C₈	C₂×D₂₂₉	1	1	yes	characteristic
26	C₁₆	—	229	2	no	—
27	C₂×C₄	C₂²⋊D₂₂₉	1	1	yes	characteristic
28	C₈	—	4	1	no	—
29	C₈	—	916	1	no	—
30	C₈	C₄×D₂₂₉	1	1	yes	characteristic
31	C₈	Dic₄₅₈	1	1	yes	characteristic
32	C₂²	#16814656	1	1	yes	characteristic
33	C₄	#16814645	1	1	yes	characteristic
34	C₄	#16814651	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	#20300921	1	1	yes	characteristic

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

N	H ≅ G/N	type
18. C₂₂₉	#368	semidirect

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