Subgroups — #44540481

Order 31712.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30629392	C₂	1	1	yes	maximal, characteristic
2	#30629382	C₂	1	2	yes	maximal, complemented
3	#30629379	C₂	1	2	yes	maximal, complemented
4	#30629376	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₈×C₉₉₁	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₁₉₈₂	C₂²	1	1	yes	characteristic
7	D₃₉₆₄	C₂²	1	1	yes	characteristic
8	C₂²⋊D₉₉₁	—	2	1	no	—
9	C₄×D₉₉₁	—	2	1	no	—
10	C₉₉₁⋊C₈	C₂²	1	2	yes	—
11	Q₈×C₉₉₁	—	2	1	no	—
12	Q₈×C₉₉₁	C₂²	1	2	yes	—
13	C₂×C₄×C₉₉₁	—	2	1	no	—
14	C₂×C₄×C₉₉₁	C₂²	1	1	yes	characteristic
15	C₂²×C₉₉₁	D₄	1	1	yes	characteristic
16	C₂×D₉₉₁	—	2	1	no	—
17	C₄×C₉₉₁	—	2	2	no	—
18	C₄×C₉₉₁	D₄	1	1	yes	characteristic
19	C₄×C₉₉₁	C₂³	1	1	yes	characteristic
20	Dic₉₉₁	—	2	1	no	—
21	C₂×C₉₉₁	—	2	1	no	—
22	C₂×C₉₉₁	C₂×D₄	1	1	yes	characteristic
23	D₉₉₁	—	4	1	no	—
24	C₉₉₁	#137	1	1	yes	characteristic, complemented, Sylow
25	#137	—	991	1	no	maximal, Sylow
26	#41	—	991	1	no	—
27	C₂×Q₈	D₉₉₁	1	1	yes	characteristic, complemented
28	Q₁₆	—	991	2	no	—
29	SD₁₆	—	991	2	no	—
30	M₁₆	—	991	1	no	—
31	Q₈	—	2	1	no	—
32	Q₈	—	991	1	no	—
33	Q₈	C₂×D₉₉₁	1	2	yes	—
34	D₄	—	1982	1	no	—
35	D₄	—	991	1	no	—
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	1982	1	no	—
38	C₂×C₄	C₂×D₉₉₁	1	1	yes	characteristic
39	C₈	—	991	2	no	—
40	C₂²	—	1982	1	no	—
41	C₂²	C₂²⋊D₉₉₁	1	1	yes	characteristic
42	C₄	—	2	2	no	—
43	C₄	—	1982	1	no	—
44	C₄	C₂²⋊D₉₉₁	1	1	yes	characteristic
45	C₄	C₂²×D₉₉₁	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	3964	1	no	—
48	C₂	C₂×C₂²⋊D₉₉₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₂²⋊D₉₉₁
commutator, cosocle	C₄×C₉₉₁	C₂³
Frattini	C₄	C₂²×D₉₉₁
Fitting	C₂×Q₈×C₉₉₁	C₂
socle	C₂×C₉₉₁	C₂×D₄
prime radical	#30629392	C₂
hypercenter	C₂×Q₈	D₉₉₁
hypocenter	C₉₉₁	#137
LCS	G ▷ C₄×C₉₉₁ ▷ C₂×C₉₉₁ ▷ C₉₉₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
2. #30629382	C₂	semidirect
3. #30629379	C₂	semidirect
4. #30629376	C₂	semidirect
5. C₂×Q₈×C₉₉₁	C₂	semidirect
24. C₉₉₁	#137	semidirect
27. C₂×Q₈	D₉₉₁	semidirect

Maximal subgroups

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

subgroup	index
#30629392	2
#30629382	2
#30629379	2
#30629376	2
C₂×Q₈×C₉₉₁	2
#137	991