Subgroups — #27163841

Order 12736.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20263891	C₂	1	1	yes	maximal, characteristic
2	#20263887	C₂	1	1	yes	maximal, characteristic
3	M₃₂×C₁₉₉	C₂	1	1	yes	maximal, characteristic
4	#15691870	—	2	1	no	—
5	C₄⋊Dic₁₉₉	—	2	1	no	—
6	C₂×C₈×C₁₉₉	C₂²	1	1	yes	characteristic
7	C₁₆×C₁₉₉	C₄	1	2	yes	complemented
8	C₂×Dic₁₉₉	—	4	1	no	—
9	C₁₉₉⋊C₈	—	4	1	no	—
10	C₂×C₄×C₁₉₉	D₄	1	1	yes	characteristic
11	C₈×C₁₉₉	C₂×C₄	1	1	yes	characteristic
12	C₈×C₁₉₉	Q₈	1	1	yes	characteristic
13	C₂²×C₁₉₉	SD₁₆	1	1	yes	characteristic
14	C₄×C₁₉₉	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₁₉₉	SD₁₆	1	1	yes	characteristic
16	Dic₁₉₉	—	8	1	no	—
17	C₂×C₁₉₉	—	2	1	no	—
18	C₂×C₁₉₉	#106	1	1	yes	characteristic
19	C₁₉₉	#365	1	1	yes	characteristic, complemented, Sylow
20	#365	—	199	1	no	maximal, Sylow
21	M₃₂	D₁₉₉	1	1	yes	characteristic
22	#108	—	199	1	no	—
23	#106	—	199	1	no	—
24	M₁₆	—	398	1	no	—
25	C₂×C₈	C₂×D₁₉₉	1	1	yes	characteristic
26	C₄⋊C₄	—	398	1	no	—
27	C₁₆	Dic₁₉₉	1	2	yes	complemented
28	C₂×C₄	—	796	1	no	—
29	C₂×C₄	D₇₉₆	1	1	yes	characteristic
30	C₈	—	796	1	no	—
31	C₈	C₂×Dic₁₉₉	1	1	yes	characteristic
32	C₈	Dic₃₉₈	1	1	yes	characteristic
33	C₂²	#15691875	1	1	yes	characteristic
34	C₄	—	1592	1	no	—
35	C₄	C₄⋊Dic₁₉₉	1	1	yes	characteristic
36	C₄	#15691875	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#20263887	1	1	yes	characteristic

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.