Subgroups — SD₃₂×C₉₉₇ #44542174

Order 31904.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₁₆×C₉₉₇	C₂	1	1	yes	maximal, characteristic, complemented
2	D₈×C₉₉₇	C₂	1	1	yes	maximal, characteristic
3	C₁₆×C₉₉₇	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×C₉₉₇	—	2	1	no	—
5	D₄×C₉₉₇	—	2	1	no	—
6	C₈×C₉₉₇	C₂²	1	1	yes	characteristic
7	C₂²×C₉₉₇	—	4	1	no	—
8	C₄×C₉₉₇	—	4	1	no	—
9	C₄×C₉₉₇	D₄	1	1	yes	characteristic
10	C₂×C₉₉₇	—	8	1	no	—
11	C₂×C₉₉₇	D₈	1	1	yes	characteristic
12	C₉₉₇	SD₃₂	1	1	yes	characteristic, direct product factor, Sylow
13	SD₃₂	C₉₉₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	Q₁₆	C₂×C₉₉₇	1	1	yes	characteristic, complemented
15	D₈	C₂×C₉₉₇	1	1	yes	characteristic
16	C₁₆	C₂×C₉₉₇	1	1	yes	characteristic, complemented
17	Q₈	—	2	1	no	—
18	D₄	—	2	1	no	—
19	C₈	C₂²×C₉₉₇	1	1	yes	characteristic
20	C₂²	—	4	1	no	—
21	C₄	—	4	1	no	—
22	C₄	D₄×C₉₉₇	1	1	yes	characteristic
23	C₂	—	8	1	no	—
24	C₂	D₈×C₉₉₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₉₉₇	D₈
commutator, Frattini, cosocle	C₈	C₂²×C₉₉₇
prime radical	D₈×C₉₉₇	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₉₉₇ ◁ C₄×C₉₉₇ ◁ C₈×C₉₉₇ ◁ G

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.