Subgroups — #20260550

Order 6208.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₃₈₈	C₂	1	1	yes	maximal, characteristic
2	#15690750	C₂	1	1	yes	maximal, characteristic
3	#108×C₉₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₉₄	—	2	1	no	—
5	Dic₃₈₈	—	2	1	no	—
6	Dic₃₈₈	C₄	1	2	yes	—
7	#13095486	—	2	1	no	—
8	M₁₆×C₉₇	—	2	1	no	—
9	C₂×C₈×C₉₇	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₉₇	D₄	1	1	yes	characteristic
11	C₂×Dic₉₇	—	4	1	no	—
12	Dic₁₉₄	—	2	2	no	—
13	Dic₁₉₄	—	4	1	no	—
14	C₈×C₉₇	—	4	1	no	—
15	C₈×C₉₇	C₂×C₄	1	1	yes	characteristic
16	C₈×C₉₇	D₄	1	1	yes	characteristic
17	C₂²×C₉₇	SD₁₆	1	1	yes	characteristic
18	C₄×C₉₇	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₉₇	D₈	1	1	yes	characteristic
20	Dic₉₇	—	4	2	no	—
21	C₂×C₉₇	—	2	1	no	—
22	C₂×C₉₇	#102	1	1	yes	characteristic
23	C₉₇	#362	1	1	yes	characteristic, complemented, Sylow
24	#362	—	97	1	no	maximal, Sylow
25	C₂×Q₁₆	—	97	1	no	—
26	M₃₂	—	97	1	no	—
27	#108	D₉₇	1	1	yes	characteristic
28	C₂×Q₈	—	194	1	no	—
29	Q₁₆	—	97	2	no	—
30	Q₁₆	—	194	1	no	—
31	M₁₆	—	2	1	no	—
32	C₂×C₈	C₂×D₉₇	1	1	yes	characteristic
33	C₁₆	—	194	1	no	—
34	Q₈	—	388	1	no	—
35	Q₈	—	194	2	no	—
36	C₂×C₄	—	388	1	no	—
37	C₂×C₄	C₂²⋊D₉₇	1	1	yes	characteristic
38	C₈	—	4	1	no	—
39	C₈	C₄×D₉₇	1	1	yes	characteristic
40	C₈	D₃₈₈	1	1	yes	characteristic
41	C₂²	#13095498	1	1	yes	characteristic
42	C₄	—	388	2	no	—
43	C₄	#13095488	1	1	yes	characteristic
44	C₄	#13095496	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#15690730	1	1	yes	characteristic

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

N	H ≅ G/N	type
23. C₉₇	#362	semidirect