Subgroups — #20261654

Order 6208.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15690885	C₂	1	1	yes	maximal, characteristic
2	#15690880	C₂	1	1	yes	maximal, characteristic
3	Q₁₆×D₉₇	C₂	1	1	yes	maximal, characteristic
4	#13095521	—	2	1	no	—
5	#13095514	—	2	1	no	—
6	Q₈×D₉₇	—	2	1	no	—
7	Dic₃₈₈	C₄	1	1	yes	characteristic
8	#13095501	—	2	1	no	—
9	C₈×D₉₇	C₂²	1	1	yes	characteristic
10	Q₁₆×C₉₇	C₄	1	1	yes	characteristic
11	Q₈×C₉₇	—	2	1	no	—
12	C₄×D₉₇	—	4	1	no	—
13	C₄×D₉₇	D₄	1	1	yes	characteristic
14	Dic₁₉₄	—	2	1	no	—
15	Dic₁₉₄	—	4	1	no	—
16	#11715897	—	4	1	no	—
17	C₈×C₉₇	C₂×C₄	1	1	yes	characteristic
18	#11715895	D₄	1	1	yes	characteristic
19	C₂×D₉₇	SD₁₆	1	1	yes	characteristic
20	C₄×C₉₇	—	4	1	no	—
21	C₄×C₉₇	C₂²⋊C₄	1	1	yes	characteristic
22	Dic₉₇	—	4	1	no	—
23	Dic₉₇	D₈	1	1	yes	characteristic
24	C₂×C₉₇	#102	1	1	yes	characteristic
25	D₉₇	—	2	1	no	—
26	C₉₇	#362	1	1	yes	characteristic, complemented, Sylow
27	#362	—	97	1	no	maximal, Sylow
28	C₂×Q₁₆	—	97	1	no	—
29	M₃₂	—	97	1	no	—
30	#108	—	97	1	no	—
31	C₂×Q₈	—	194	1	no	—
32	Q₁₆	—	97	1	no	—
33	Q₁₆	—	194	1	no	—
34	Q₁₆	#87604	1	1	yes	characteristic
35	M₁₆	—	194	1	no	—
36	C₂×C₈	—	97	1	no	—
37	C₁₆	—	194	1	no	—
38	Q₈	—	2	1	no	—
39	Q₈	—	388	1	no	—
40	Q₈	—	194	1	no	—
41	C₂×C₄	—	97	1	no	—
42	C₂×C₄	—	388	1	no	—
43	C₈	—	97	1	no	—
44	C₈	—	388	1	no	—
45	C₈	C₂×#87604	1	1	yes	characteristic
46	C₂²	—	97	1	no	—
47	C₄	—	4	1	no	—
48	C₄	—	97	1	no	—
49	C₄	—	388	1	no	—
50	C₄	C₂²⋊#87604	1	1	yes	characteristic
51	C₂	—	194	1	no	—
52	C₂	#15690872	1	1	yes	characteristic

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

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