Subgroups — #38763580

Order 25408.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27163170	C₂	1	3	yes	maximal, complemented
2	C₂×#20263734	C₂	1	3	yes	maximal, complemented
3	#27163103	C₂	1	1	yes	maximal, characteristic
4	#20263734	C₂²	1	1	yes	characteristic
5	#20263734	C₂²	1	3	yes	—
6	#20263715	C₄	1	3	yes	—
7	C₂×#15691787	C₂²	1	3	yes	—
8	#41×C₃₉₇	C₄	1	1	yes	characteristic
9	#15691787	C₂×C₄	1	3	yes	—
10	#15691787	C₂³	1	1	yes	characteristic
11	Q₈×C₃₉₇	C₈	1	1	yes	characteristic
12	D₄×C₃₉₇	C₈	1	3	yes	—
13	C₂×C₄×C₃₉₇	C₂×C₄	1	3	yes	—
14	C₂²×C₃₉₇	C₂×C₈	1	3	yes	—
15	C₄×C₃₉₇	C₂×C₈	1	3	yes	—
16	C₄×C₃₉₇	C₂²×C₄	1	1	yes	characteristic
17	C₂×C₃₉₇	—	2	3	no	—
18	C₂×C₃₉₇	C₂²×C₈	1	1	yes	characteristic
19	C₃₉₇	#504	1	1	yes	characteristic, complemented, Sylow
20	#504	—	397	1	no	maximal, Sylow
21	#131	—	397	1	no	—
22	M₃₂	—	397	3	no	—
23	C₂×C₁₆	—	397	3	no	—
24	#41	#13097544	1	1	yes	characteristic
25	M₁₆	—	397	3	no	—
26	C₂×C₈	—	397	3	no	—
27	C₁₆	—	397	1	no	—
28	C₁₆	—	397	3	no	—
29	Q₈	#15691794	1	1	yes	characteristic
30	D₄	#15691794	1	3	yes	—
31	C₂×C₄	C₂×#13097544	1	3	yes	—
32	C₈	—	397	3	no	—
33	C₈	—	397	1	no	—
34	C₂²	C₂×#15691794	1	3	yes	—
35	C₄	C₂×#15691794	1	3	yes	—
36	C₄	C₂²×#13097544	1	1	yes	characteristic
37	C₂	—	2	3	no	—
38	C₂	C₂²×#15691794	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.