Subgroups — #44569681

Order 32416.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30633813	C₂	1	1	yes	maximal, characteristic
2	Q₈×D₁₀₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₄₀₅₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#30633804	C₂	1	1	yes	maximal, characteristic, complemented
5	#30633802	C₂	1	1	yes	maximal, characteristic, complemented
6	#30633797	C₂	1	1	yes	maximal, characteristic, complemented
7	SD₁₆×C₁₀₁₃	C₂	1	1	yes	maximal, characteristic, complemented
8	Dic₂₀₂₆	—	2	1	no	—
9	Dic₂₀₂₆	C₂²	1	1	yes	characteristic
10	Dic₂₀₂₆	C₂²	1	1	yes	characteristic
11	C₂²⋊D₁₀₁₃	—	2	1	no	—
12	C₂×Dic₁₀₁₃	—	2	1	no	—
13	C₄×D₁₀₁₃	—	2	1	no	—
14	C₄×D₁₀₁₃	C₂²	1	1	yes	characteristic
15	#22549201	C₂²	1	1	yes	characteristic
16	Q₈×C₁₀₁₃	C₂²	1	1	yes	characteristic
17	D₄×C₁₀₁₃	C₂²	1	1	yes	characteristic
18	C₈×C₁₀₁₃	C₂²	1	1	yes	characteristic
19	C₂²×C₁₀₁₃	—	2	1	no	—
20	C₂×D₁₀₁₃	D₄	1	1	yes	characteristic
21	C₄×C₁₀₁₃	—	2	1	no	—
22	C₄×C₁₀₁₃	C₂³	1	1	yes	characteristic
23	Dic₁₀₁₃	—	2	1	no	—
24	Dic₁₀₁₃	—	2	1	no	—
25	Dic₁₀₁₃	D₄	1	1	yes	characteristic
26	C₂×C₁₀₁₃	—	4	1	no	—
27	C₂×C₁₀₁₃	C₂×D₄	1	1	yes	characteristic
28	D₁₀₁₃	—	2	1	no	—
29	C₁₀₁₃	#137	1	1	yes	characteristic, complemented, Sylow
30	#137	—	1013	1	no	maximal, Sylow
31	#41	—	1013	1	no	—
32	C₂×Q₈	—	1013	1	no	—
33	Q₁₆	—	1013	1	no	—
34	Q₁₆	—	1013	1	no	—
35	SD₁₆	—	1013	1	no	—
36	SD₁₆	D₁₀₁₃	1	1	yes	characteristic, complemented
37	M₁₆	—	1013	1	no	—
38	Q₈	—	2026	1	no	—
39	Q₈	—	1013	1	no	—
40	Q₈	—	1013	1	no	—
41	Q₈	C₂×D₁₀₁₃	1	1	yes	characteristic
42	D₄	—	2026	1	no	—
43	D₄	C₂×D₁₀₁₃	1	1	yes	characteristic
44	C₂×C₄	—	2026	1	no	—
45	C₂×C₄	—	2026	1	no	—
46	C₂×C₄	—	1013	1	no	—
47	C₈	—	1013	1	no	—
48	C₈	C₂×D₁₀₁₃	1	1	yes	characteristic
49	C₂²	—	2	1	no	—
50	C₂²	—	1013	1	no	—
51	C₄	—	2	1	no	—
52	C₄	—	2026	1	no	—
53	C₄	—	2026	1	no	—
54	C₄	—	1013	1	no	—
55	C₄	C₂²×D₁₀₁₃	1	1	yes	characteristic
56	C₂	—	4	1	no	—
57	C₂	—	2026	1	no	—
58	C₂	D₄×D₁₀₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₁₀₁₃
commutator, cosocle	C₄×C₁₀₁₃	C₂³
Frattini	C₄	C₂²×D₁₀₁₃
Fitting	SD₁₆×C₁₀₁₃	C₂
socle	C₂×C₁₀₁₃	C₂×D₄
prime radical	#30633813	C₂
hypercenter	SD₁₆	D₁₀₁₃
hypocenter	C₁₀₁₃	#137
LCS	G ▷ C₄×C₁₀₁₃ ▷ C₂×C₁₀₁₃ ▷ C₁₀₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

Complements

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

N	H ≅ G/N	type
2. Q₈×D₁₀₁₃	C₂	semidirect
3. Dic₄₀₅₂	C₂	semidirect
4. #30633804	C₂	semidirect
5. #30633802	C₂	semidirect
6. #30633797	C₂	semidirect
7. SD₁₆×C₁₀₁₃	C₂	semidirect
29. C₁₀₁₃	#137	semidirect
36. SD₁₆	D₁₀₁₃	semidirect

Maximal subgroups

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

subgroup	index
#30633813	2
Q₈×D₁₀₁₃	2
Dic₄₀₅₂	2
#30633804	2
#30633802	2
#30633797	2
SD₁₆×C₁₀₁₃	2
#137	1013