Subgroups — #14583230

Order 2752.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13063304	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic
3	#13063257	C₂	1	2	yes	maximal, complemented
4	#13063250	C₂	1	2	yes	maximal, complemented
5	C₂²⋊C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄×C₄₃	C₂²	1	1	yes	characteristic
7	C₂²×Dic₄₃	—	2	1	no	—
8	C₂×Dic₈₆	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₄₃	C₂²	1	2	yes	—
10	C₂²⋊Dic₄₃	—	2	1	no	—
11	C₄⋊Dic₄₃	—	2	1	no	—
12	C₄⋊Dic₄₃	C₂²	1	2	yes	—
13	C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
14	Dic₄₃⋊C₄	—	2	1	no	—
15	C₂³×C₄₃	D₄	1	1	yes	characteristic
16	C₂×C₄×C₄₃	—	2	2	no	—
17	C₂×C₄×C₄₃	D₄	1	1	yes	characteristic
18	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
19	C₂×Dic₄₃	—	2	1	no	—
20	C₂×Dic₄₃	—	2	1	no	—
21	C₂×Dic₄₃	—	2	2	no	—
22	C₂×Dic₄₃	—	4	2	no	—
23	Dic₈₆	—	2	2	no	—
24	C₈×C₄₃	—	2	2	no	—
25	C₂²×C₄₃	—	2	1	no	—
26	C₂²×C₄₃	—	2	1	no	—
27	C₂²×C₄₃	SD₁₆	1	2	yes	—
28	C₂²×C₄₃	C₂×D₄	1	1	yes	characteristic
29	C₄×C₄₃	—	2	1	no	—
30	C₄×C₄₃	#41	1	2	yes	—
31	Dic₄₃	—	4	1	no	—
32	Dic₄₃	—	4	2	no	—
33	Dic₄₃	—	4	1	no	—
34	C₂×C₄₃	—	2	2	no	—
35	C₂×C₄₃	#123	1	1	yes	characteristic
36	C₂×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
37	C₂×C₄₃	#137	1	1	yes	characteristic
38	#483	—	43	1	no	maximal, Sylow
39	C₄₃	#483	1	1	yes	characteristic, complemented, Sylow
40	C₂²⋊Q₈	—	43	1	no	—
41	C₂×C₄⋊C₄	—	43	1	no	—
42	#106	—	43	2	no	—
43	#103	—	43	2	no	—
44	C₂²⋊C₈	D₄₃	1	1	yes	characteristic
45	C₂×Q₈	—	43	1	no	—
46	C₂²×C₄	—	86	1	no	—
47	C₂²×C₄	C₂×D₄₃	1	1	yes	characteristic
48	C₂×C₈	C₂×D₄₃	1	2	yes	—
49	C₄⋊C₄	—	43	2	no	—
50	C₄⋊C₄	—	43	1	no	—
51	C₄⋊C₄	—	86	1	no	—
52	C₄⋊C₄	—	86	1	no	—
53	C₂²⋊C₄	—	86	1	no	—
54	C₂³	D₁₇₂	1	1	yes	characteristic
55	Q₈	—	86	2	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	—	86	1	no	—
58	C₂×C₄	—	86	1	no	—
59	C₂×C₄	—	86	2	no	—
60	C₂×C₄	—	172	2	no	—
61	C₂×C₄	D₁₇₂	1	1	yes	characteristic
62	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
63	C₈	—	2	2	no	—
64	C₂²	—	2	1	no	—
65	C₂²	—	2	1	no	—
66	C₂²	#10621873	1	2	yes	—
67	C₂²	C₂×D₁₇₂	1	1	yes	characteristic
68	C₄	—	2	1	no	—
69	C₄	—	172	1	no	—
70	C₄	—	172	2	no	—
71	C₄	—	172	1	no	—
72	C₄	#10621900	1	2	yes	—
73	C₂	—	2	2	no	—
74	C₂	#13063309	1	1	yes	characteristic
75	C₂	C₂×#10621873	1	1	yes	characteristic
76	C₂	#13063358	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₇₂
commutator, cosocle	C₂×C₄×C₄₃	C₂³
Frattini	C₂×C₄	C₂²×D₄₃
Fitting	C₂²⋊C₈×C₄₃	C₂
socle	C₂²×C₄₃	C₂×D₄
prime radical	C₂³×C₄₃	D₄
hypercenter	C₂²⋊C₈	D₄₃
hypocenter	C₄₃	#483
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
3. #13063257	C₂	semidirect
4. #13063250	C₂	semidirect
39. C₄₃	#483	semidirect

Maximal subgroups

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

subgroup	index
#13063304	2
C₂×C₄⋊Dic₄₃	2
#13063257	2
#13063250	2
C₂²⋊C₈×C₄₃	2
#483	43