Subgroups — C₄×#13095486 #20260509

Order 6208.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13095486	C₂	1	2	yes	maximal
2	C₄×C₈×C₉₇	C₂	1	1	yes	maximal, characteristic
3	#13095486	C₄	1	4	yes	direct product factor
4	C₂×C₈×C₉₇	C₄	1	1	yes	characteristic
5	C₂×C₈×C₉₇	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	C₈×C₉₇	C₈	1	2	yes	—
10	C₈×C₉₇	C₂×C₄	1	2	yes	—
11	C₂²×C₉₇	C₂×C₈	1	1	yes	characteristic
12	C₄×C₉₇	C₁₆	1	4	yes	complemented
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	C₂×C₁₆	1	2	yes	—
17	C₉₇	C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
18	C₄×C₁₆	—	97	1	no	maximal, Sylow
19	C₂×C₁₆	—	97	2	no	—
20	C₄×C₈	D₉₇	1	1	yes	characteristic
21	C₂×C₈	Dic₉₇	1	1	yes	characteristic
22	C₂×C₈	C₂×D₉₇	1	1	yes	characteristic
23	C₄²	Dic₉₇	1	1	yes	characteristic
24	C₁₆	—	97	4	no	—
25	C₂×C₄	#11715895	1	2	yes	—
26	C₂×C₄	C₂×Dic₉₇	1	1	yes	characteristic
27	C₈	#11715895	1	2	yes	—
28	C₈	C₄×D₉₇	1	2	yes	—
29	C₂²	C₂×#11715895	1	1	yes	characteristic
30	C₄	#13095486	1	4	yes	direct product factor
31	C₄	C₄×Dic₉₇	1	1	yes	characteristic
32	C₄	C₂×#11715895	1	1	yes	characteristic
33	C₂	C₄×#11715895	1	1	yes	characteristic
34	C₂	C₂×#13095486	1	2	yes	—

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