Subgroups — #20261659

Order 6208.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15690880	C₂	1	1	yes	maximal, characteristic
2	#15690878	C₂	1	1	yes	maximal, characteristic
3	#15690749	C₂	1	1	yes	maximal, characteristic
4	#13095521	—	2	1	no	—
5	C₄⋊#87604	—	2	1	no	—
6	C₈×D₉₇	C₂²	1	1	yes	characteristic
7	#13095486	C₄	1	1	yes	characteristic, complemented
8	C₁₆×C₉₇	C₄	1	1	yes	characteristic, complemented
9	C₂×#87604	—	4	1	no	—
10	C₄×D₉₇	D₄	1	1	yes	characteristic
11	#11715897	—	4	1	no	—
12	C₈×C₉₇	C₂×C₄	1	1	yes	characteristic
13	#11715895	Q₈	1	1	yes	characteristic
14	C₂×D₉₇	SD₁₆	1	1	yes	characteristic
15	#87604	—	8	1	no	—
16	C₄×C₉₇	C₄⋊C₄	1	1	yes	characteristic
17	Dic₉₇	SD₁₆	1	1	yes	characteristic
18	C₂×C₉₇	#106	1	1	yes	characteristic
19	D₉₇	—	2	1	no	—
20	C₉₇	#365	1	1	yes	characteristic, complemented, Sylow
21	#365	—	97	1	no	maximal, Sylow
22	M₃₂	—	97	1	no	—
23	#108	—	97	1	no	—
24	#106	—	97	1	no	—
25	M₁₆	—	194	1	no	—
26	C₂×C₈	—	97	1	no	—
27	C₄⋊C₄	—	194	1	no	—
28	C₁₆	—	97	1	no	—
29	C₁₆	#87604	1	1	yes	characteristic, complemented
30	C₂×C₄	—	97	1	no	—
31	C₂×C₄	—	388	1	no	—
32	C₈	—	97	1	no	—
33	C₈	—	388	1	no	—
34	C₈	C₂×#87604	1	1	yes	characteristic
35	C₂²	—	97	1	no	—
36	C₄	—	776	1	no	—
37	C₄	—	97	1	no	—
38	C₄	C₄⋊#87604	1	1	yes	characteristic
39	C₂	—	194	1	no	—
40	C₂	#15690878	1	1	yes	characteristic

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