Subgroups — #27163848

Order 12736.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20263891	C₂	1	2	yes	maximal
2	C₂×C₁₆×C₁₉₉	C₂	1	1	yes	maximal, characteristic
3	#15691870	—	2	2	no	—
4	C₂×C₈×C₁₉₉	C₂²	1	1	yes	characteristic
5	C₁₆×C₁₉₉	C₄	1	2	yes	—
6	C₁₉₉⋊C₈	—	4	2	no	—
7	C₂×C₄×C₁₉₉	D₄	1	1	yes	characteristic
8	C₈×C₁₉₉	C₂×C₄	1	1	yes	characteristic
9	C₈×C₁₉₉	Q₈	1	1	yes	characteristic
10	C₂²×C₁₉₉	Q₁₆	1	1	yes	characteristic
11	C₄×C₁₉₉	C₄⋊C₄	1	1	yes	characteristic
12	C₄×C₁₉₉	D₈	1	1	yes	characteristic
13	C₂×C₁₉₉	—	2	1	no	—
14	C₂×C₁₉₉	#107	1	1	yes	characteristic
15	C₁₉₉	#368	1	1	yes	characteristic, complemented, Sylow
16	#368	—	199	1	no	maximal, Sylow
17	C₂×C₁₆	D₁₉₉	1	1	yes	characteristic
18	#108	—	199	2	no	—
19	M₁₆	—	398	2	no	—
20	C₂×C₈	C₂×D₁₉₉	1	1	yes	characteristic
21	C₁₆	Dic₁₉₉	1	2	yes	—
22	C₂×C₄	D₇₉₆	1	1	yes	characteristic
23	C₈	—	796	2	no	—
24	C₈	C₂×Dic₁₉₉	1	1	yes	characteristic
25	C₈	Dic₃₉₈	1	1	yes	characteristic
26	C₂²	Dic₇₉₆	1	1	yes	characteristic
27	C₄	C₄⋊Dic₁₉₉	1	1	yes	characteristic
28	C₄	D₁₅₉₂	1	1	yes	characteristic
29	C₂	—	2	1	no	—
30	C₂	#20263889	1	1	yes	characteristic

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

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

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