Subgroups — #27163103

Order 12704.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20263715	C₂	1	3	yes	maximal, complemented
2	C₂×#15691787	C₂	1	3	yes	maximal, complemented
3	#41×C₃₉₇	C₂	1	1	yes	maximal, characteristic
4	#15691787	C₂²	1	1	yes	characteristic
5	#15691787	C₂²	1	3	yes	—
6	Q₈×C₃₉₇	C₄	1	1	yes	characteristic
7	D₄×C₃₉₇	C₄	1	3	yes	—
8	C₂×C₄×C₃₉₇	C₂²	1	3	yes	—
9	C₂²×C₃₉₇	C₂×C₄	1	3	yes	—
10	C₄×C₃₉₇	C₂×C₄	1	3	yes	—
11	C₄×C₃₉₇	C₂³	1	1	yes	characteristic
12	C₂×C₃₉₇	—	2	3	no	—
13	C₂×C₃₉₇	C₂²×C₄	1	1	yes	characteristic
14	C₃₉₇	#131	1	1	yes	characteristic, complemented, Sylow
15	#131	—	397	1	no	maximal, Sylow
16	#41	D₃₉₇	1	1	yes	characteristic
17	M₁₆	—	397	3	no	—
18	C₂×C₈	—	397	3	no	—
19	Q₈	Dic₃₉₇	1	1	yes	characteristic
20	D₄	Dic₃₉₇	1	3	yes	—
21	C₂×C₄	C₂×D₃₉₇	1	3	yes	—
22	C₈	—	397	1	no	—
23	C₈	—	397	3	no	—
24	C₂²	C₂×Dic₃₉₇	1	3	yes	—
25	C₄	C₂×Dic₃₉₇	1	3	yes	—
26	C₄	C₂²×D₃₉₇	1	1	yes	characteristic
27	C₂	—	2	3	no	—
28	C₂	C₂²×Dic₃₉₇	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.