Subgroups — #27139953

Order 12416.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₅₅₂	C₂	1	1	yes	maximal, characteristic
2	#20260454	C₂	1	1	yes	maximal, characteristic
3	Q₆₄×C₉₇	C₂	1	1	yes	maximal, characteristic
4	Dic₇₇₆	—	2	1	no	—
5	Q₃₂×C₉₇	—	2	1	no	—
6	C₃₂×C₉₇	C₂²	1	1	yes	characteristic
7	Dic₃₈₈	—	4	1	no	—
8	Q₁₆×C₉₇	—	4	1	no	—
9	C₁₆×C₉₇	D₄	1	1	yes	characteristic
10	Q₈×C₉₇	—	8	1	no	—
11	Dic₁₉₄	—	8	1	no	—
12	C₈×C₉₇	D₈	1	1	yes	characteristic
13	C₄×C₉₇	—	16	1	no	—
14	C₄×C₉₇	D₁₆	1	1	yes	characteristic
15	Dic₉₇	—	16	1	no	—
16	C₂×C₉₇	D₃₂	1	1	yes	characteristic
17	Q₁₂₈	—	97	1	no	maximal, Sylow
18	C₉₇	Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
19	Q₆₄	—	97	1	no	—
20	Q₆₄	D₉₇	1	1	yes	characteristic
21	C₆₄	—	97	1	no	—
22	Q₃₂	—	2	1	no	—
23	Q₃₂	—	194	1	no	—
24	C₃₂	C₂×D₉₇	1	1	yes	characteristic
25	Q₁₆	—	4	1	no	—
26	Q₁₆	—	388	1	no	—
27	C₁₆	C₂²⋊D₉₇	1	1	yes	characteristic
28	Q₈	—	8	1	no	—
29	Q₈	—	776	1	no	—
30	C₈	#13095496	1	1	yes	characteristic
31	C₄	—	16	1	no	—
32	C₄	—	1552	1	no	—
33	C₄	#15690751	1	1	yes	characteristic
34	C₂	#20260570	1	1	yes	characteristic

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

N	H ≅ G/N	type
18. C₉₇	Q₁₂₈	semidirect

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