Subgroups — #20260558

Order 6208.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15690746	C₂	1	1	yes	maximal, characteristic
2	#15690742	C₂	1	1	yes	maximal, characteristic
3	M₃₂×C₉₇	C₂	1	1	yes	maximal, characteristic
4	#13095495	—	2	1	no	—
5	C₄⋊Dic₉₇	—	2	1	no	—
6	C₂×C₈×C₉₇	C₂²	1	1	yes	characteristic
7	C₁₆×C₉₇	C₄	1	2	yes	complemented
8	C₂×C₄×C₉₇	D₄	1	1	yes	characteristic
9	C₂×Dic₉₇	—	4	1	no	—
10	C₈×C₉₇	C₂×C₄	1	1	yes	characteristic
11	C₈×C₉₇	Q₈	1	1	yes	characteristic
12	#11715895	—	4	1	no	—
13	C₂²×C₉₇	SD₁₆	1	1	yes	characteristic
14	C₄×C₉₇	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₉₇	SD₁₆	1	1	yes	characteristic
16	Dic₉₇	—	8	1	no	—
17	C₂×C₉₇	—	2	1	no	—
18	C₂×C₉₇	#106	1	1	yes	characteristic
19	C₉₇	#365	1	1	yes	characteristic, complemented, Sylow
20	#365	—	97	1	no	maximal, Sylow
21	M₃₂	D₉₇	1	1	yes	characteristic
22	#108	—	97	1	no	—
23	#106	—	97	1	no	—
24	M₁₆	—	194	1	no	—
25	C₂×C₈	C₂×D₉₇	1	1	yes	characteristic
26	C₄⋊C₄	—	194	1	no	—
27	C₁₆	Dic₉₇	1	2	yes	complemented
28	C₂×C₄	—	388	1	no	—
29	C₂×C₄	D₃₈₈	1	1	yes	characteristic
30	C₈	—	388	1	no	—
31	C₈	Dic₁₉₄	1	1	yes	characteristic
32	C₈	C₂×Dic₉₇	1	1	yes	characteristic
33	C₂²	#13095500	1	1	yes	characteristic
34	C₄	—	776	1	no	—
35	C₄	C₄⋊Dic₉₇	1	1	yes	characteristic
36	C₄	#13095500	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#15690742	1	1	yes	characteristic

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