Subgroups — #38763410

Order 25408.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20263734	C₂	1	2	yes	maximal
2	C₄×#15691787	C₂	1	1	yes	maximal, characteristic
3	#20263734	C₄	1	4	yes	complemented
4	C₂×#15691787	C₄	1	1	yes	characteristic
5	C₂×#15691787	C₂²	1	1	yes	characteristic
6	C₄²×C₃₉₇	C₄	1	1	yes	characteristic
7	#15691787	C₈	1	2	yes	—
8	#15691787	C₂×C₄	1	2	yes	—
9	C₂×C₄×C₃₉₇	C₈	1	2	yes	—
10	C₂×C₄×C₃₉₇	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₃₉₇	C₂×C₈	1	1	yes	characteristic
12	C₄×C₃₉₇	—	2	2	no	—
13	C₄×C₃₉₇	C₄²	1	1	yes	characteristic
14	C₄×C₃₉₇	C₂×C₈	1	1	yes	characteristic
15	C₂×C₃₉₇	C₄×C₈	1	1	yes	characteristic
16	C₂×C₃₉₇	M₃₂	1	2	yes	—
17	C₃₉₇	#346	1	1	yes	characteristic, complemented, Sylow
18	#346	—	397	1	no	maximal, Sylow
19	C₂×C₁₆	—	397	2	no	—
20	C₄×C₈	—	397	1	no	—
21	C₂×C₈	—	397	1	no	—
22	C₂×C₈	—	397	1	no	—
23	C₄²	#13097544	1	1	yes	characteristic
24	C₁₆	—	397	4	no	—
25	C₂×C₄	#15691794	1	2	yes	—
26	C₂×C₄	C₂×#13097544	1	1	yes	characteristic
27	C₈	—	397	2	no	—
28	C₈	—	397	2	no	—
29	C₂²	C₂×#15691794	1	1	yes	characteristic
30	C₄	—	2	2	no	—
31	C₄	C₄×#13097544	1	1	yes	characteristic
32	C₄	D₃₉₇⋊C₈	1	1	yes	characteristic
33	C₂	C₄×#15691794	1	1	yes	characteristic
34	C₂	#27163170	1	2	yes	—

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

N	H ≅ G/N	type
3. #20263734	C₄	semidirect
17. C₃₉₇	#346	semidirect

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