Subgroups — #20261825

Order 6208.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11715906	C₂	1	2	yes	maximal
2	C₈×#87604	C₂	1	1	yes	maximal, characteristic
3	C₂×#11715906	—	2	2	no	—
4	#13095519	C₄	1	1	yes	characteristic
5	C₄×#87604	C₂²	1	1	yes	characteristic
6	C₈×D₉₇	C₄	1	1	yes	characteristic
7	C₂×#87604	D₄	1	1	yes	characteristic
8	C₂×#87604	Q₈	1	1	yes	characteristic
9	#11715906	—	4	2	no	—
10	C₄×D₉₇	C₂×C₄	1	1	yes	characteristic
11	#11715897	—	2	1	no	—
12	C₈×C₉₇	C₈	1	1	yes	characteristic, complemented
13	#11715895	C₈	1	1	yes	characteristic, complemented
14	C₂×D₉₇	C₄⋊C₄	1	1	yes	characteristic
15	#87604	—	2	1	no	—
16	#87604	D₈	1	1	yes	characteristic
17	#87604	Q₁₆	1	1	yes	characteristic
18	C₄×C₉₇	C₂×C₈	1	1	yes	characteristic
19	Dic₉₇	M₁₆	1	1	yes	characteristic
20	C₂×C₉₇	C₄⋊C₈	1	1	yes	characteristic
21	D₉₇	#107	1	1	yes	characteristic
22	D₉₇	#108	1	1	yes	characteristic
23	C₉₇	#335	1	1	yes	characteristic, complemented, Sylow
24	#335	—	97	1	no	maximal, Sylow
25	C₄⋊C₈	—	97	2	no	—
26	C₄×C₈	—	97	1	no	—
27	C₂×C₈	—	97	1	no	—
28	C₂×C₈	—	97	1	no	—
29	C₂×C₈	—	194	2	no	—
30	C₄²	—	97	1	no	—
31	C₂×C₄	—	97	1	no	—
32	C₂×C₄	—	97	1	no	—
33	C₂×C₄	—	97	1	no	—
34	C₈	—	97	1	no	—
35	C₈	—	388	2	no	—
36	C₈	—	194	1	no	—
37	C₈	#11715906	1	1	yes	characteristic, complemented
38	C₂²	—	97	1	no	—
39	C₄	—	97	1	no	—
40	C₄	—	97	1	no	—
41	C₄	—	97	1	no	—
42	C₄	—	194	1	no	—
43	C₄	C₂×#11715906	1	1	yes	characteristic
44	C₂	—	97	1	no	—
45	C₂	—	97	1	no	—
46	C₂	C₄⋊#11715906	1	1	yes	characteristic

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