Subgroups — #15690864

Order 3104.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13095519	C₂	1	1	yes	maximal, characteristic
2	C₄×#87604	C₂	1	1	yes	maximal, characteristic
3	C₈×D₉₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#87604	C₄	1	2	yes	—
5	C₄×D₉₇	C₂²	1	1	yes	characteristic
6	#11715897	C₄	1	2	yes	complemented
7	C₈×C₉₇	C₄	1	1	yes	characteristic, complemented
8	#11715895	C₄	1	1	yes	characteristic, complemented
9	C₂×D₉₇	C₂×C₄	1	1	yes	characteristic
10	#87604	—	2	2	no	—
11	C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
12	Dic₉₇	C₂×C₄	1	1	yes	characteristic
13	C₂×C₉₇	C₄²	1	1	yes	characteristic
14	D₉₇	M₁₆	1	2	yes	—
15	C₉₇	#97	1	1	yes	characteristic, complemented, Sylow
16	#97	—	97	1	no	maximal, Sylow
17	C₂×C₈	—	97	1	no	—
18	C₂×C₈	—	97	1	no	—
19	C₄²	—	97	1	no	—
20	C₂×C₄	—	97	1	no	—
21	C₂×C₄	—	97	2	no	—
22	C₈	—	97	2	no	—
23	C₈	—	97	1	no	—
24	C₈	#87604	1	1	yes	characteristic, complemented
25	C₂²	—	97	1	no	—
26	C₄	—	97	1	no	—
27	C₄	—	194	2	no	—
28	C₄	C₂×#87604	1	1	yes	characteristic
29	C₂	—	97	2	no	—
30	C₂	C₄×#87604	1	1	yes	characteristic

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

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.