Subgroups — #27156905

Order 12416.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20261574	C₂	1	2	yes	maximal, complemented
2	C₂×#15690716	C₂	1	1	yes	maximal, characteristic
3	#15690716	C₄	1	1	yes	characteristic
4	#15690716	C₂²	1	1	yes	characteristic
5	C₂×C₁₆×C₉₇	C₄	1	1	yes	characteristic
6	C₂×C₈×C₉₇	C₈	1	1	yes	characteristic
7	C₁₆×C₉₇	C₈	1	1	yes	characteristic
8	C₁₆×C₉₇	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄×C₉₇	C₁₆	1	1	yes	characteristic
10	C₈×C₉₇	C₁₆	1	1	yes	characteristic
11	C₈×C₉₇	C₂×C₈	1	1	yes	characteristic
12	C₂²×C₉₇	C₃₂	1	1	yes	characteristic
13	C₄×C₉₇	C₃₂	1	1	yes	characteristic
14	C₄×C₉₇	C₂×C₁₆	1	1	yes	characteristic
15	C₂×C₉₇	—	2	1	no	—
16	C₂×C₉₇	C₂×C₃₂	1	1	yes	characteristic
17	M₁₂₈	—	97	1	no	maximal, Sylow
18	C₉₇	M₁₂₈	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃₂	—	97	1	no	—
20	C₆₄	—	97	2	no	—
21	C₂×C₁₆	#87604	1	1	yes	characteristic
22	C₃₂	—	97	1	no	—
23	C₃₂	—	97	1	no	—
24	C₂×C₈	#11715897	1	1	yes	characteristic
25	C₁₆	#11715897	1	1	yes	characteristic
26	C₁₆	C₂×#87604	1	1	yes	characteristic
27	C₂×C₄	#13095514	1	1	yes	characteristic
28	C₈	#13095514	1	1	yes	characteristic
29	C₈	C₂×#11715897	1	1	yes	characteristic
30	C₂²	#15690860	1	1	yes	characteristic
31	C₄	#15690860	1	1	yes	characteristic
32	C₄	C₂×#13095514	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	C₂×#15690860	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #20261574	C₂	semidirect
18. C₉₇	M₁₂₈	semidirect

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