Subgroups — #20261623

Order 6208.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13095514	C₂	1	2	yes	maximal
2	C₄×#11715895	C₂	1	1	yes	maximal, characteristic
3	#13095514	C₄	1	4	yes	complemented
4	C₂×#11715895	C₄	1	1	yes	characteristic
5	C₂×#11715895	C₂²	1	1	yes	characteristic
6	C₄²×C₉₇	C₄	1	1	yes	characteristic
7	C₂×C₄×C₉₇	C₈	1	2	yes	—
8	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
9	#11715895	C₈	1	2	yes	—
10	#11715895	C₂×C₄	1	2	yes	—
11	C₂²×C₉₇	C₂×C₈	1	1	yes	characteristic
12	C₄×C₉₇	—	2	2	no	—
13	C₄×C₉₇	C₄²	1	1	yes	characteristic
14	C₄×C₉₇	C₂×C₈	1	1	yes	characteristic
15	C₂×C₉₇	C₄×C₈	1	1	yes	characteristic
16	C₂×C₉₇	M₃₂	1	2	yes	—
17	C₉₇	#346	1	1	yes	characteristic, complemented, Sylow
18	#346	—	97	1	no	maximal, Sylow
19	C₂×C₁₆	—	97	2	no	—
20	C₄×C₈	—	97	1	no	—
21	C₂×C₈	—	97	1	no	—
22	C₂×C₈	—	97	1	no	—
23	C₄²	#87604	1	1	yes	characteristic
24	C₁₆	—	97	4	no	—
25	C₂×C₄	#11715897	1	2	yes	—
26	C₂×C₄	C₂×#87604	1	1	yes	characteristic
27	C₈	—	97	2	no	—
28	C₈	—	97	2	no	—
29	C₂²	C₂×#11715897	1	1	yes	characteristic
30	C₄	—	2	2	no	—
31	C₄	C₄×#87604	1	1	yes	characteristic
32	C₄	#13095519	1	1	yes	characteristic
33	C₂	C₄×#11715897	1	1	yes	characteristic
34	C₂	#15690884	1	2	yes	—

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

N	H ≅ G/N	type
3. #13095514	C₄	semidirect
17. C₉₇	#346	semidirect