Subgroups — #20261662

Order 6208.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15690879	C₂	1	2	yes	maximal
2	C₁₆×D₉₇	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#87604	—	2	2	no	—
4	C₈×D₉₇	C₂²	1	1	yes	characteristic
5	#13095486	C₄	1	1	yes	characteristic, complemented
6	C₁₆×C₉₇	C₄	1	1	yes	characteristic, complemented
7	C₂×#87604	—	4	2	no	—
8	C₄×D₉₇	D₄	1	1	yes	characteristic
9	C₈×C₉₇	C₂×C₄	1	1	yes	characteristic
10	#11715895	Q₈	1	1	yes	characteristic
11	C₂×D₉₇	D₈	1	1	yes	characteristic
12	#87604	—	8	2	no	—
13	C₄×C₉₇	C₄⋊C₄	1	1	yes	characteristic
14	Dic₉₇	Q₁₆	1	1	yes	characteristic
15	C₂×C₉₇	#107	1	1	yes	characteristic
16	D₉₇	SD₃₂	1	2	yes	—
17	C₉₇	#367	1	1	yes	characteristic, complemented, Sylow
18	#367	—	97	1	no	maximal, Sylow
19	C₂×C₁₆	—	97	1	no	—
20	#107	—	97	2	no	—
21	C₂×C₈	—	97	1	no	—
22	C₄⋊C₄	—	194	2	no	—
23	C₁₆	—	97	1	no	—
24	C₁₆	#87604	1	1	yes	characteristic, complemented
25	C₂×C₄	—	97	1	no	—
26	C₂×C₄	—	388	2	no	—
27	C₈	—	97	1	no	—
28	C₈	C₂×#87604	1	1	yes	characteristic
29	C₂²	—	97	1	no	—
30	C₄	—	776	2	no	—
31	C₄	—	97	1	no	—
32	C₄	C₄⋊#87604	1	1	yes	characteristic
33	C₂	—	97	2	no	—
34	C₂	#15690879	1	1	yes	characteristic

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