Subgroups — #27163839

Order 12736.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20263895	C₂	1	2	yes	maximal
2	C₄×C₈×C₁₉₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉₉⋊C₁₆	—	2	2	no	—
4	C₂×C₈×C₁₉₉	C₄	1	1	yes	characteristic
5	C₂×C₈×C₁₉₉	C₂²	1	1	yes	characteristic
6	C₄²×C₁₉₉	C₄	1	1	yes	characteristic
7	C₂×C₄×C₁₉₉	—	2	1	no	—
8	C₂×C₄×C₁₉₉	C₂×C₄	1	1	yes	characteristic
9	C₈×C₁₉₉	C₈	1	2	yes	—
10	C₈×C₁₉₉	D₄	1	1	yes	characteristic
11	C₈×C₁₉₉	Q₈	1	1	yes	characteristic
12	C₂²×C₁₉₉	M₁₆	1	1	yes	characteristic
13	C₄×C₁₉₉	—	2	2	no	—
14	C₄×C₁₉₉	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₁₉₉	C₂×C₈	1	1	yes	characteristic
16	C₂×C₁₉₉	—	2	1	no	—
17	C₂×C₁₉₉	C₄⋊C₈	1	1	yes	characteristic
18	C₁₉₉	#364	1	1	yes	characteristic, complemented, Sylow
19	#364	—	199	1	no	maximal, Sylow
20	M₃₂	—	199	2	no	—
21	C₄×C₈	D₁₉₉	1	1	yes	characteristic
22	C₂×C₈	Dic₁₉₉	1	1	yes	characteristic
23	C₂×C₈	C₂×D₁₉₉	1	1	yes	characteristic
24	C₄²	Dic₁₉₉	1	1	yes	characteristic
25	C₁₆	—	398	2	no	—
26	C₂×C₄	—	2	1	no	—
27	C₂×C₄	C₂×Dic₁₉₉	1	1	yes	characteristic
28	C₈	C₁₉₉⋊C₈	1	2	yes	—
29	C₈	D₇₉₆	1	1	yes	characteristic
30	C₈	Dic₃₉₈	1	1	yes	characteristic
31	C₂²	#15691870	1	1	yes	characteristic
32	C₄	—	2	2	no	—
33	C₄	C₄⋊Dic₁₉₉	1	1	yes	characteristic
34	C₄	C₂×C₁₉₉⋊C₈	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	C₄⋊(C₁₉₉⋊C₈)	1	1	yes	characteristic

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

N	H ≅ G/N	type
18. C₁₉₉	#364	semidirect

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