Subgroups — #20261576

Order 6208.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#11715897	C₂	1	2	yes	maximal
2	C₈×Dic₉₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#11715897	C₄	1	4	yes	—
4	C₂×#11715895	C₄	1	1	yes	characteristic
5	C₄×Dic₉₇	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₉₇	C₄	1	1	yes	characteristic
7	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
8	C₂×Dic₉₇	C₂×C₄	1	2	yes	—
9	#11715897	—	2	4	no	—
10	C₈×C₉₇	C₈	1	2	yes	complemented
11	#11715895	C₈	1	2	yes	complemented
12	C₂²×C₉₇	C₄²	1	1	yes	characteristic
13	C₄×C₉₇	C₂×C₈	1	1	yes	characteristic
14	C₄×C₉₇	C₂×C₈	1	1	yes	characteristic
15	Dic₉₇	M₁₆	1	4	yes	—
16	C₂×C₉₇	C₄×C₈	1	1	yes	characteristic
17	C₂×C₉₇	#97	1	2	yes	—
18	C₉₇	#322	1	1	yes	characteristic, complemented, Sylow
19	#322	—	97	1	no	maximal, Sylow
20	C₄×C₈	—	97	2	no	—
21	C₄×C₈	—	97	1	no	—
22	C₂×C₈	—	97	1	no	—
23	C₂×C₈	—	97	4	no	—
24	C₂×C₈	#87604	1	1	yes	characteristic
25	C₄²	—	97	1	no	—
26	C₂×C₄	—	97	2	no	—
27	C₂×C₄	C₂×#87604	1	1	yes	characteristic
28	C₈	—	97	2	no	—
29	C₈	—	194	4	no	—
30	C₈	#11715897	1	2	yes	complemented
31	C₂²	C₄×#87604	1	1	yes	characteristic
32	C₄	—	97	4	no	—
33	C₄	C₂×#11715897	1	1	yes	characteristic
34	C₄	#13095519	1	1	yes	characteristic
35	C₂	C₄×#11715897	1	1	yes	characteristic
36	C₂	#15690864	1	2	yes	—

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