Subgroups — #27163846

Order 12736.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20263889	C₂	1	2	yes	maximal
2	C₂×C₁₆×C₁₉₉	C₂	1	1	yes	maximal, characteristic
3	C₄⋊Dic₁₉₉	—	2	2	no	—
4	C₂×C₈×C₁₉₉	C₂²	1	1	yes	characteristic
5	C₁₆×C₁₉₉	C₄	1	2	yes	complemented
6	C₂×Dic₁₉₉	—	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	D₈	1	1	yes	characteristic
11	C₄×C₁₉₉	C₄⋊C₄	1	1	yes	characteristic
12	C₄×C₁₉₉	Q₁₆	1	1	yes	characteristic
13	Dic₁₉₉	—	8	2	no	—
14	C₂×C₁₉₉	#107	1	1	yes	characteristic
15	C₂×C₁₉₉	SD₃₂	1	2	yes	—
16	C₁₉₉	#367	1	1	yes	characteristic, complemented, Sylow
17	#367	—	199	1	no	maximal, Sylow
18	C₂×C₁₆	D₁₉₉	1	1	yes	characteristic
19	#107	—	199	2	no	—
20	C₂×C₈	C₂×D₁₉₉	1	1	yes	characteristic
21	C₄⋊C₄	—	398	2	no	—
22	C₁₆	Dic₁₉₉	1	2	yes	complemented
23	C₂×C₄	—	796	2	no	—
24	C₂×C₄	D₇₉₆	1	1	yes	characteristic
25	C₈	C₂×Dic₁₉₉	1	1	yes	characteristic
26	C₈	Dic₃₉₈	1	1	yes	characteristic
27	C₂²	D₁₅₉₂	1	1	yes	characteristic
28	C₄	—	1592	2	no	—
29	C₄	C₄⋊Dic₁₉₉	1	1	yes	characteristic
30	C₄	Dic₇₉₆	1	1	yes	characteristic
31	C₂	#20263889	1	1	yes	characteristic
32	C₂	#20263900	1	2	yes	—

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

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