Subgroups — #13063355

Order 1376.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₈₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#10621885	C₂	1	2	yes	maximal, complemented
4	#10621883	C₂	1	2	yes	maximal, complemented
5	#10621877	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₈×C₄₃	C₂²	1	1	yes	characteristic
7	D₄×C₄₃	—	2	1	no	—
8	D₄×C₄₃	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₄₃	—	2	1	no	—
10	C₂×C₄×C₄₃	C₂²	1	1	yes	characteristic
11	C₂×Dic₄₃	—	2	1	no	—
12	Dic₈₆	—	2	1	no	—
13	Dic₈₆	C₂²	1	2	yes	—
14	C₄₃⋊C₈	C₂²	1	2	yes	—
15	C₂²×C₄₃	—	2	1	no	—
16	C₂²×C₄₃	D₄	1	1	yes	characteristic
17	C₄×C₄₃	—	2	1	no	—
18	C₄×C₄₃	D₄	1	1	yes	characteristic
19	C₄×C₄₃	C₂³	1	1	yes	characteristic
20	Dic₄₃	—	2	2	no	—
21	C₂×C₄₃	—	2	1	no	—
22	C₂×C₄₃	—	4	1	no	—
23	C₂×C₄₃	C₂×D₄	1	1	yes	characteristic
24	C₄₃	#137	1	1	yes	characteristic, complemented, Sylow
25	#137	—	43	1	no	maximal, Sylow
26	#41	D₄₃	1	1	yes	characteristic
27	C₂×Q₈	—	43	1	no	—
28	Q₁₆	—	43	2	no	—
29	SD₁₆	—	43	2	no	—
30	M₁₆	—	43	1	no	—
31	Q₈	—	43	2	no	—
32	Q₈	—	86	1	no	—
33	Q₈	C₂×D₄₃	1	1	yes	characteristic
34	D₄	—	2	1	no	—
35	D₄	C₂×D₄₃	1	1	yes	characteristic
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	86	1	no	—
38	C₂×C₄	C₂×D₄₃	1	1	yes	characteristic
39	C₈	—	43	2	no	—
40	C₂²	—	2	1	no	—
41	C₂²	C₂²⋊D₄₃	1	1	yes	characteristic
42	C₄	—	2	1	no	—
43	C₄	—	86	2	no	—
44	C₄	C₂²⋊D₄₃	1	1	yes	characteristic
45	C₄	C₂²×D₄₃	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	4	1	no	—
48	C₂	C₂×C₂²⋊D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₂²⋊D₄₃
commutator, cosocle	C₄×C₄₃	C₂³
Frattini	C₄	C₂²×D₄₃
Fitting, prime radical	#41×C₄₃	C₂
socle	C₂×C₄₃	C₂×D₄
hypercenter	#41	D₄₃
hypocenter	C₄₃	#137
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #41

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₈₆	C₂	semidirect
3. #10621885	C₂	semidirect
4. #10621883	C₂	semidirect
5. #10621877	C₂	semidirect
24. C₄₃	#137	semidirect

Maximal subgroups

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

subgroup	index
#41×C₄₃	2
C₂×Dic₈₆	2
#10621885	2
#10621883	2
#10621877	2
#137	43