Subgroups — #27163847

Order 12736.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#20263891	C₂	1	1	yes	maximal, characteristic
3	#108×C₁₉₉	C₂	1	1	yes	maximal, characteristic
4	#15691870	—	2	1	no	—
5	C₁₉₉⋊C₁₆	C₄	1	2	yes	—
6	M₁₆×C₁₉₉	—	2	1	no	—
7	C₂×C₈×C₁₉₉	C₂²	1	1	yes	characteristic
8	C₁₉₉⋊C₈	—	4	1	no	—
9	C₂×C₄×C₁₉₉	D₄	1	1	yes	characteristic
10	C₈×C₁₉₉	—	4	1	no	—
11	C₈×C₁₉₉	C₂×C₄	1	1	yes	characteristic
12	C₈×C₁₉₉	Q₈	1	1	yes	characteristic
13	C₂²×C₁₉₉	Q₁₆	1	1	yes	characteristic
14	C₄×C₁₉₉	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₁₉₉	D₈	1	1	yes	characteristic
16	C₂×C₁₉₉	—	2	1	no	—
17	C₂×C₁₉₉	#107	1	1	yes	characteristic
18	C₁₉₉	#368	1	1	yes	characteristic, complemented, Sylow
19	#368	—	199	1	no	maximal, Sylow
20	C₂×C₁₆	—	199	1	no	—
21	#108	—	199	1	no	—
22	#108	D₁₉₉	1	1	yes	characteristic
23	M₁₆	—	2	1	no	—
24	M₁₆	—	398	1	no	—
25	C₂×C₈	C₂×D₁₉₉	1	1	yes	characteristic
26	C₁₆	—	199	2	no	—
27	C₂×C₄	C₂²⋊D₁₉₉	1	1	yes	characteristic
28	C₈	—	4	1	no	—
29	C₈	—	796	1	no	—
30	C₈	C₄×D₁₉₉	1	1	yes	characteristic
31	C₈	Dic₃₉₈	1	1	yes	characteristic
32	C₂²	#15691876	1	1	yes	characteristic
33	C₄	Dic₁₉₉⋊C₄	1	1	yes	characteristic
34	C₄	#15691871	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	#20263888	1	1	yes	characteristic

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

N	H ≅ G/N	type
18. C₁₉₉	#368	semidirect

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