Subgroups — #27158841

Order 12416.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20261817	C₂	1	2	yes	maximal, complemented
2	#20261666	C₂	1	1	yes	maximal, characteristic
3	#15690860	C₄	1	1	yes	characteristic
4	#15690860	C₂²	1	1	yes	characteristic
5	C₁₆×D₉₇	C₄	1	1	yes	characteristic
6	C₈×D₉₇	C₈	1	1	yes	characteristic
7	#13095486	C₂×C₄	1	1	yes	characteristic
8	C₁₆×C₉₇	C₈	1	1	yes	characteristic
9	C₄×D₉₇	C₁₆	1	1	yes	characteristic
10	C₈×C₉₇	C₂×C₈	1	1	yes	characteristic
11	#11715895	C₁₆	1	1	yes	characteristic
12	C₂×D₉₇	C₃₂	1	1	yes	characteristic
13	C₄×C₉₇	C₂×C₁₆	1	1	yes	characteristic
14	Dic₉₇	C₃₂	1	1	yes	characteristic
15	C₂×C₉₇	C₂×C₃₂	1	1	yes	characteristic
16	D₉₇	—	2	1	no	—
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	—	97	1	no	—
22	C₃₂	—	97	1	no	—
23	C₃₂	—	97	1	no	—
24	C₂×C₈	—	97	1	no	—
25	C₁₆	—	97	1	no	—
26	C₁₆	#11715906	1	1	yes	characteristic
27	C₂×C₄	—	97	1	no	—
28	C₈	—	97	1	no	—
29	C₈	C₂×#11715906	1	1	yes	characteristic
30	C₂²	—	97	1	no	—
31	C₄	—	97	1	no	—
32	C₄	#15690905	1	1	yes	characteristic
33	C₂	—	194	1	no	—
34	C₂	#20261842	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #20261817	C₂	semidirect
18. C₉₇	M₁₂₈	semidirect

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