Subgroups — #20261664

Order 6208.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15690881	C₂	1	2	yes	maximal
2	C₁₆×D₉₇	C₂	1	1	yes	maximal, characteristic
3	#13095521	—	2	2	no	—
4	C₈×D₉₇	C₂²	1	1	yes	characteristic
5	#13095486	C₄	1	1	yes	characteristic
6	C₁₆×C₉₇	C₄	1	1	yes	characteristic
7	C₄×D₉₇	D₄	1	1	yes	characteristic
8	#11715897	—	4	2	no	—
9	C₈×C₉₇	C₂×C₄	1	1	yes	characteristic
10	#11715895	Q₈	1	1	yes	characteristic
11	C₂×D₉₇	Q₁₆	1	1	yes	characteristic
12	C₄×C₉₇	C₄⋊C₄	1	1	yes	characteristic
13	Dic₉₇	D₈	1	1	yes	characteristic
14	C₂×C₉₇	#107	1	1	yes	characteristic
15	D₉₇	—	2	1	no	—
16	C₉₇	#368	1	1	yes	characteristic, complemented, Sylow
17	#368	—	97	1	no	maximal, Sylow
18	C₂×C₁₆	—	97	1	no	—
19	#108	—	97	2	no	—
20	M₁₆	—	194	2	no	—
21	C₂×C₈	—	97	1	no	—
22	C₁₆	—	97	1	no	—
23	C₁₆	#87604	1	1	yes	characteristic
24	C₂×C₄	—	97	1	no	—
25	C₈	—	97	1	no	—
26	C₈	—	388	2	no	—
27	C₈	C₂×#87604	1	1	yes	characteristic
28	C₂²	—	97	1	no	—
29	C₄	—	97	1	no	—
30	C₄	C₄⋊#87604	1	1	yes	characteristic
31	C₂	—	194	1	no	—
32	C₂	#15690879	1	1	yes	characteristic

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

N	H ≅ G/N	type
16. C₉₇	#368	semidirect