Subgroups — #20261622

Order 6208.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15690883	C₂	1	1	yes	maximal, characteristic
2	C₈×#87604	C₂	1	1	yes	maximal, characteristic
3	C₁₆×D₉₇	C₂	1	1	yes	maximal, characteristic
4	#13095519	C₄	1	1	yes	characteristic
5	C₄×#87604	C₄	1	1	yes	characteristic
6	#13095514	C₄	1	2	yes	complemented
7	C₈×D₉₇	C₂²	1	1	yes	characteristic
8	#13095486	C₄	1	1	yes	characteristic, complemented
9	C₁₆×C₉₇	C₄	1	1	yes	characteristic, complemented
10	C₂×#87604	C₈	1	2	yes	—
11	C₄×D₉₇	C₂×C₄	1	1	yes	characteristic
12	#11715897	C₈	1	2	yes	—
13	C₈×C₉₇	C₂×C₄	1	1	yes	characteristic
14	#11715895	C₂×C₄	1	1	yes	characteristic
15	C₂×D₉₇	C₂×C₈	1	1	yes	characteristic
16	#87604	—	2	2	no	—
17	C₄×C₉₇	C₄²	1	1	yes	characteristic
18	Dic₉₇	C₂×C₈	1	1	yes	characteristic
19	C₂×C₉₇	C₄×C₈	1	1	yes	characteristic
20	D₉₇	M₃₂	1	2	yes	—
21	C₉₇	#346	1	1	yes	characteristic, complemented, Sylow
22	#346	—	97	1	no	maximal, Sylow
23	C₂×C₁₆	—	97	1	no	—
24	C₂×C₁₆	—	97	1	no	—
25	C₄×C₈	—	97	1	no	—
26	C₂×C₈	—	97	1	no	—
27	C₂×C₈	—	97	1	no	—
28	C₄²	—	97	1	no	—
29	C₁₆	—	97	2	no	—
30	C₁₆	—	97	1	no	—
31	C₁₆	#87604	1	1	yes	characteristic, complemented
32	C₂×C₄	—	97	1	no	—
33	C₂×C₄	—	97	2	no	—
34	C₈	—	97	2	no	—
35	C₈	—	97	1	no	—
36	C₈	C₂×#87604	1	1	yes	characteristic
37	C₂²	—	97	1	no	—
38	C₄	—	97	1	no	—
39	C₄	—	194	2	no	—
40	C₄	C₄×#87604	1	1	yes	characteristic
41	C₂	—	97	2	no	—
42	C₂	C₈×#87604	1	1	yes	characteristic

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