Subgroups — #20260551

Order 6208.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15690750	C₂	1	1	yes	maximal, characteristic
2	#15690746	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₁₆×C₉₇	C₂	1	1	yes	maximal, characteristic
4	#13095495	—	2	1	no	—
5	#13095486	—	2	1	no	—
6	C₂×Q₈×C₉₇	—	2	1	no	—
7	Q₁₆×C₉₇	—	2	1	no	—
8	Q₁₆×C₉₇	C₄	1	2	yes	—
9	C₂×C₈×C₉₇	C₂²	1	1	yes	characteristic
10	Q₈×C₉₇	—	2	2	no	—
11	Q₈×C₉₇	—	4	1	no	—
12	C₂×C₄×C₉₇	—	4	1	no	—
13	C₂×C₄×C₉₇	D₄	1	1	yes	characteristic
14	C₈×C₉₇	C₂×C₄	1	1	yes	characteristic
15	C₈×C₉₇	D₄	1	1	yes	characteristic
16	#11715895	—	4	1	no	—
17	C₂²×C₉₇	SD₁₆	1	1	yes	characteristic
18	C₄×C₉₇	—	4	2	no	—
19	C₄×C₉₇	C₂²⋊C₄	1	1	yes	characteristic
20	C₄×C₉₇	D₈	1	1	yes	characteristic
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	D₉₇	1	1	yes	characteristic
26	M₃₂	—	97	1	no	—
27	#108	—	97	1	no	—
28	C₂×Q₈	—	2	1	no	—
29	Q₁₆	—	2	1	no	—
30	Q₁₆	Dic₉₇	1	2	yes	—
31	M₁₆	—	194	1	no	—
32	C₂×C₈	C₂×D₉₇	1	1	yes	characteristic
33	C₁₆	—	194	1	no	—
34	Q₈	—	2	2	no	—
35	Q₈	—	4	1	no	—
36	C₂×C₄	—	4	1	no	—
37	C₂×C₄	C₂²⋊D₉₇	1	1	yes	characteristic
38	C₈	—	388	1	no	—
39	C₈	C₂×Dic₉₇	1	1	yes	characteristic
40	C₈	C₂²⋊D₉₇	1	1	yes	characteristic
41	C₂²	#13095499	1	1	yes	characteristic
42	C₄	—	4	2	no	—
43	C₄	C₂²⋊Dic₉₇	1	1	yes	characteristic
44	C₄	#13095496	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#15690731	1	1	yes	characteristic

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

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