Subgroups — C₂×SD₁₆×C₉₉₁ #44540344

Order 31712.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₉₉₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×C₉₉₁	C₂	1	1	yes	maximal, characteristic
3	SD₁₆×C₉₉₁	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₈×C₉₉₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×C₉₉₁	—	2	1	no	—
6	Q₈×C₉₉₁	—	2	1	no	—
7	Q₈×C₉₉₁	C₂²	1	2	yes	complemented
8	D₄×C₉₉₁	—	2	1	no	—
9	D₄×C₉₉₁	C₂²	1	2	yes	—
10	C₂×C₄×C₉₉₁	—	2	1	no	—
11	C₂×C₄×C₉₉₁	C₂²	1	1	yes	characteristic
12	C₈×C₉₉₁	C₂²	1	2	yes	complemented
13	C₂²×C₉₉₁	—	2	2	no	—
14	C₂²×C₉₉₁	—	4	2	no	—
15	C₂²×C₉₉₁	D₄	1	1	yes	characteristic
16	C₄×C₉₉₁	—	2	2	no	—
17	C₄×C₉₉₁	D₄	1	1	yes	characteristic
18	C₄×C₉₉₁	C₂³	1	1	yes	characteristic
19	C₂×C₉₉₁	—	4	2	no	—
20	C₂×C₉₉₁	SD₁₆	1	2	yes	direct product factor
21	C₂×C₉₉₁	C₂×D₄	1	1	yes	characteristic
22	C₉₉₁	C₂×SD₁₆	1	1	yes	characteristic, direct product factor, Sylow
23	C₂×SD₁₆	C₉₉₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₂×Q₈	C₂×C₉₉₁	1	1	yes	characteristic, complemented
25	C₂×D₄	C₂×C₉₉₁	1	1	yes	characteristic
26	SD₁₆	C₂×C₉₉₁	1	4	yes	direct product factor
27	C₂×C₈	C₂×C₉₉₁	1	1	yes	characteristic, complemented
28	C₂³	—	2	1	no	—
29	Q₈	—	2	1	no	—
30	Q₈	C₂²×C₉₉₁	1	2	yes	complemented
31	D₄	—	2	1	no	—
32	D₄	C₂²×C₉₉₁	1	2	yes	—
33	C₂×C₄	—	2	1	no	—
34	C₂×C₄	C₂²×C₉₉₁	1	1	yes	characteristic
35	C₈	C₂²×C₉₉₁	1	2	yes	complemented
36	C₂²	—	2	2	no	—
37	C₂²	—	4	2	no	—
38	C₂²	D₄×C₉₉₁	1	1	yes	characteristic
39	C₄	—	2	2	no	—
40	C₄	D₄×C₉₉₁	1	1	yes	characteristic
41	C₄	C₂³×C₉₉₁	1	1	yes	characteristic
42	C₂	—	4	2	no	—
43	C₂	SD₁₆×C₉₉₁	1	2	yes	direct product factor
44	C₂	C₂×D₄×C₉₉₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₉₉₁	D₄
commutator, Frattini, cosocle	C₄	C₂³×C₉₉₁
prime radical	C₂×D₄×C₉₉₁	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉₉₁ ◁ C₂×C₄×C₉₉₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈×C₉₉₁	C₂	semidirect
3. SD₁₆×C₉₉₁	C₂	direct (N × H)
4. C₂×C₈×C₉₉₁	C₂	semidirect
7. Q₈×C₉₉₁	C₂²	semidirect
12. C₈×C₉₉₁	C₂²	semidirect
20. C₂×C₉₉₁	SD₁₆	direct (N × H)
22. C₉₉₁	C₂×SD₁₆	direct (N × H)
23. C₂×SD₁₆	C₉₉₁	direct (N × H)
24. C₂×Q₈	C₂×C₉₉₁	semidirect
26. SD₁₆	C₂×C₉₉₁	direct (N × H)
27. C₂×C₈	C₂×C₉₉₁	semidirect
30. Q₈	C₂²×C₉₉₁	semidirect
35. C₈	C₂²×C₉₉₁	semidirect
43. C₂	SD₁₆×C₉₉₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Q₈×C₉₉₁	2
C₂×D₄×C₉₉₁	2
SD₁₆×C₉₉₁	2
C₂×C₈×C₉₉₁	2
C₂×SD₁₆	991

Subgroups — C2×SD16×C991 #44540344

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×SD₁₆×C₉₉₁ #44540344