Subgroups — D₉₁⋊D₉₇ #47977205

Order 35308.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉₇×D₉₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×D₆₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×D₁₂₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×C₁₃×C₉₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₃×D₉₇	—	7	1	no	maximal, Hall
6	D₇×D₉₇	—	13	1	no	maximal, Hall
7	D₁₂₆₁	D₇	1	1	yes	characteristic, complemented
8	C₁₃×D₉₇	—	7	1	no	—
9	D₁₃×C₉₇	—	7	1	no	—
10	D₆₇₉	D₁₃	1	1	yes	characteristic, complemented
11	C₇×D₉₇	—	13	1	no	—
12	D₇×C₉₇	—	13	1	no	—
13	C₁₃×C₉₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
14	C₇×C₉₇	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
15	C₂×D₉₇	—	91	1	no	Hall
16	D₇×D₁₃	—	97	1	no	maximal, Hall
17	C₂×C₉₇	—	91	1	no	—
18	D₉₇	—	7	1	no	—
19	D₉₇	—	13	1	no	—
20	D₉₁	D₉₇	1	1	yes	characteristic, complemented
21	C₇×D₁₃	—	97	1	no	—
22	C₁₃×D₇	—	97	1	no	—
23	C₉₇	D₇×D₁₃	1	1	yes	characteristic, complemented, Sylow
24	C₇×C₁₃	C₂×D₉₇	1	1	yes	characteristic, complemented, Hall
25	C₂×D₁₃	—	679	1	no	Hall
26	C₂×D₇	—	1261	1	no	Hall
27	C₂×C₁₃	—	679	1	no	—
28	D₁₃	—	7	1	no	—
29	D₁₃	—	97	1	no	—
30	C₂×C₇	—	1261	1	no	—
31	D₇	—	13	1	no	—
32	D₇	—	97	1	no	—
33	C₁₃	D₇×D₉₇	1	1	yes	characteristic, complemented, Sylow
34	C₇	D₁₃×D₉₇	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	8827	1	no	Sylow
36	C₂	—	91	1	no	—
37	C₂	—	679	1	no	—
38	C₂	—	1261	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₃×C₉₇	C₂²
LCS	G ▷ C₇×C₁₃×C₉₇
UCS	C₁

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.