Subgroups — #38763447

Order 25408.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27163166	C₂	1	1	yes	maximal, characteristic
2	#27163164	C₂	1	1	yes	maximal, characteristic
3	#27163035	C₂	1	1	yes	maximal, characteristic
4	#20263741	—	2	1	no	—
5	C₄⋊#13097544	—	2	1	no	—
6	C₈×D₃₉₇	C₂²	1	1	yes	characteristic
7	#20263706	C₄	1	1	yes	characteristic, complemented
8	C₁₆×C₃₉₇	C₄	1	1	yes	characteristic, complemented
9	C₂×#13097544	—	4	1	no	—
10	#15691794	—	4	1	no	—
11	C₄×D₃₉₇	D₄	1	1	yes	characteristic
12	#15691787	Q₈	1	1	yes	characteristic
13	C₈×C₃₉₇	C₂×C₄	1	1	yes	characteristic
14	C₂×D₃₉₇	SD₁₆	1	1	yes	characteristic
15	#13097544	—	8	1	no	—
16	C₄×C₃₉₇	C₄⋊C₄	1	1	yes	characteristic
17	Dic₃₉₇	SD₁₆	1	1	yes	characteristic
18	C₂×C₃₉₇	#106	1	1	yes	characteristic
19	D₃₉₇	—	2	1	no	—
20	C₃₉₇	#365	1	1	yes	characteristic, complemented, Sylow
21	#365	—	397	1	no	maximal, Sylow
22	M₃₂	—	397	1	no	—
23	#108	—	397	1	no	—
24	#106	—	397	1	no	—
25	M₁₆	—	794	1	no	—
26	C₂×C₈	—	397	1	no	—
27	C₄⋊C₄	—	794	1	no	—
28	C₁₆	—	397	1	no	—
29	C₁₆	#13097544	1	1	yes	characteristic, complemented
30	C₂×C₄	—	1588	1	no	—
31	C₂×C₄	—	397	1	no	—
32	C₈	—	1588	1	no	—
33	C₈	—	397	1	no	—
34	C₈	C₂×#13097544	1	1	yes	characteristic
35	C₂²	—	397	1	no	—
36	C₄	—	3176	1	no	—
37	C₄	—	397	1	no	—
38	C₄	C₄⋊#13097544	1	1	yes	characteristic
39	C₂	—	794	1	no	—
40	C₂	#27163164	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.