Subgroups — #14582993

Order 2752.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₇₂	C₂	1	1	yes	maximal, characteristic
2	#13063290	C₂	1	2	yes	maximal
3	#13063248	C₂	1	2	yes	maximal
4	C₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic
5	#107×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₈₆	C₂²	1	2	yes	—
7	C₂×C₈×C₄₃	C₂²	1	1	yes	characteristic
8	C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
9	Dic₄₃⋊C₄	—	2	2	no	—
10	C₄×Dic₄₃	—	2	2	no	—
11	C₄×Dic₄₃	C₂²	1	1	yes	characteristic
12	C₂×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
13	Dic₁₇₂	C₄	1	4	yes	complemented
14	C₂×C₄×C₄₃	—	2	2	no	—
15	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
16	C₂×Dic₄₃	—	2	2	no	—
17	C₂×Dic₄₃	D₄	1	1	yes	characteristic
18	C₂×Dic₄₃	D₄	1	1	yes	characteristic
19	Dic₈₆	—	2	2	no	—
20	Dic₈₆	C₂×C₄	1	4	yes	—
21	C₈×C₄₃	C₂×C₄	1	2	yes	—
22	C₄₃⋊C₈	—	2	1	no	—
23	C₂²×C₄₃	C₂×D₄	1	1	yes	characteristic
24	C₄×C₄₃	—	4	2	no	—
25	C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
26	C₄×C₄₃	#41	1	1	yes	characteristic
27	Dic₄₃	—	2	4	no	—
28	Dic₄₃	—	2	1	no	—
29	Dic₄₃	Q₁₆	1	2	yes	complemented
30	C₂×C₄₃	C₄×D₄	1	1	yes	characteristic
31	C₂×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
32	C₂×C₄₃	#135	1	1	yes	characteristic
33	C₄×Q₁₆	—	43	1	no	maximal, Sylow
34	C₄₃	C₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
35	C₂×Q₁₆	—	43	1	no	—
36	C₄×Q₈	—	43	2	no	—
37	#107	D₄₃	1	1	yes	characteristic
38	#103	—	43	2	no	—
39	C₄×C₈	—	43	1	no	—
40	C₂×Q₈	—	43	2	no	—
41	Q₁₆	—	43	4	no	—
42	C₂×C₈	—	43	1	no	—
43	C₂×C₈	C₂×D₄₃	1	1	yes	characteristic
44	C₄⋊C₄	—	86	2	no	—
45	C₄⋊C₄	C₂×D₄₃	1	2	yes	—
46	C₄²	—	43	1	no	—
47	C₄²	—	86	2	no	—
48	Q₈	—	43	4	no	—
49	Q₈	—	86	2	no	—
50	C₂×C₄	—	2	2	no	—
51	C₂×C₄	—	43	1	no	—
52	C₂×C₄	—	43	1	no	—
53	C₂×C₄	—	86	2	no	—
54	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
55	C₈	—	86	1	no	—
56	C₈	C₄×D₄₃	1	2	yes	—
57	C₂²	D₄×D₄₃	1	1	yes	characteristic
58	C₄	—	4	2	no	—
59	C₄	—	43	2	no	—
60	C₄	—	86	4	no	—
61	C₄	—	86	1	no	—
62	C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
63	C₄	#10621902	1	1	yes	characteristic
64	C₂	#13063287	1	1	yes	characteristic
65	C₂	Q₁₆×D₄₃	1	1	yes	characteristic
66	C₂	#13063344	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₄₃
commutator	C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₃
Fitting	#107×C₄₃	C₂
socle, prime radical	C₂²×C₄₃	C₂×D₄
cosocle	C₂×C₄×C₄₃	C₂³
hypercenter	#107	D₄₃
hypocenter	C₄₃	C₄×Q₁₆
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
13. Dic₁₇₂	C₄	semidirect
29. Dic₄₃	Q₁₆	semidirect
34. C₄₃	C₄×Q₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₇₂	2
#13063290	2
#13063248	2
C₈×Dic₄₃	2
#107×C₄₃	2
C₄×Q₁₆	43