Subgroups — #20261830

Order 6208.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15690905	C₂	1	2	yes	maximal
2	C₈×#87604	C₂	1	1	yes	maximal, characteristic
3	#13095523	C₄	1	4	yes	complemented
4	#13095519	C₂²	1	1	yes	characteristic
5	C₄×#87604	C₄	1	1	yes	characteristic
6	C₈×D₉₇	C₄	1	1	yes	characteristic
7	C₂×#87604	C₈	1	2	yes	—
8	C₄×D₉₇	C₂×C₄	1	1	yes	characteristic
9	#11715897	C₂×C₄	1	2	yes	—
10	C₈×C₉₇	C₈	1	1	yes	characteristic
11	#11715895	C₈	1	1	yes	characteristic
12	C₂×D₉₇	C₂×C₈	1	1	yes	characteristic
13	#87604	—	2	2	no	—
14	C₄×C₉₇	C₂×C₈	1	1	yes	characteristic
15	Dic₉₇	C₄²	1	1	yes	characteristic
16	C₂×C₉₇	C₄×C₈	1	1	yes	characteristic
17	D₉₇	M₃₂	1	2	yes	—
18	C₉₇	#346	1	1	yes	characteristic, complemented, Sylow
19	#346	—	97	1	no	maximal, Sylow
20	C₂×C₁₆	—	97	2	no	—
21	C₄×C₈	—	97	1	no	—
22	C₂×C₈	—	97	1	no	—
23	C₂×C₈	—	97	1	no	—
24	C₄²	—	97	1	no	—
25	C₁₆	—	97	4	no	—
26	C₂×C₄	—	97	1	no	—
27	C₂×C₄	—	97	2	no	—
28	C₈	—	97	2	no	—
29	C₈	—	97	1	no	—
30	C₈	#11715906	1	1	yes	characteristic
31	C₂²	—	97	1	no	—
32	C₄	—	97	1	no	—
33	C₄	—	194	2	no	—
34	C₄	C₂×#11715906	1	1	yes	characteristic
35	C₂	—	97	2	no	—
36	C₂	C₄×#11715906	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. #13095523	C₄	semidirect
18. C₉₇	#346	semidirect