Subgroups — #368×C₄₉₉ #44542598

Order 31936.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×C₄₉₉	C₂	1	1	yes	maximal, characteristic
2	#108×C₄₉₉	C₂	1	2	yes	maximal
3	M₁₆×C₄₉₉	—	2	2	no	—
4	C₂×C₈×C₄₉₉	C₂²	1	1	yes	characteristic
5	C₁₆×C₄₉₉	C₄	1	2	yes	—
6	C₂×C₄×C₄₉₉	D₄	1	1	yes	characteristic
7	C₈×C₄₉₉	—	4	2	no	—
8	C₈×C₄₉₉	C₂×C₄	1	1	yes	characteristic
9	C₈×C₄₉₉	Q₈	1	1	yes	characteristic
10	C₂²×C₄₉₉	Q₁₆	1	1	yes	characteristic
11	C₄×C₄₉₉	C₄⋊C₄	1	1	yes	characteristic
12	C₄×C₄₉₉	D₈	1	1	yes	characteristic
13	C₂×C₄₉₉	—	2	1	no	—
14	C₂×C₄₉₉	#107	1	1	yes	characteristic
15	C₄₉₉	#368	1	1	yes	characteristic, direct product factor, Sylow
16	#368	C₄₉₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂×C₁₆	C₂×C₄₉₉	1	1	yes	characteristic
18	#108	C₂×C₄₉₉	1	2	yes	—
19	M₁₆	—	2	2	no	—
20	C₂×C₈	C₂²×C₄₉₉	1	1	yes	characteristic
21	C₁₆	C₄×C₄₉₉	1	2	yes	—
22	C₂×C₄	D₄×C₄₉₉	1	1	yes	characteristic
23	C₈	—	4	2	no	—
24	C₈	C₂×C₄×C₄₉₉	1	1	yes	characteristic
25	C₈	Q₈×C₄₉₉	1	1	yes	characteristic
26	C₂²	Q₁₆×C₄₉₉	1	1	yes	characteristic
27	C₄	C₄⋊C₄×C₄₉₉	1	1	yes	characteristic
28	C₄	D₈×C₄₉₉	1	1	yes	characteristic
29	C₂	—	2	1	no	—
30	C₂	#107×C₄₉₉	1	1	yes	characteristic

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

N	H ≅ G/N	type
15. C₄₉₉	#368	direct (N × H)
16. #368	C₄₉₉	direct (N × H)

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