Subgroups — #14583106

Order 2752.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10621885	C₂	1	2	yes	maximal
2	C₄×Dic₈₆	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
4	#13063249	C₂	1	2	yes	maximal
5	C₄⋊Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×C₄₃	C₂²	1	2	yes	—
7	C₂×Dic₈₆	C₂²	1	1	yes	characteristic
8	C₄⋊C₄×C₄₃	—	2	1	no	—
9	C₄⋊C₄×C₄₃	—	2	1	no	—
10	C₄²×C₄₃	C₂²	1	1	yes	characteristic
11	#10621885	—	2	4	no	—
12	C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
13	Dic₄₃⋊C₄	—	2	1	no	—
14	C₄×Dic₄₃	—	2	1	no	—
15	C₂×C₄₃⋊C₈	C₂²	1	2	yes	—
16	Q₈×C₄₃	—	2	2	no	—
17	Q₈×C₄₃	—	2	2	no	—
18	C₂×C₄×C₄₃	—	2	2	no	—
19	C₂×C₄×C₄₃	D₄	1	1	yes	characteristic
20	C₂×C₄×C₄₃	D₄	1	1	yes	characteristic
21	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
22	C₂×Dic₄₃	—	2	1	no	—
23	C₂×Dic₄₃	—	2	1	no	—
24	Dic₈₆	—	2	1	no	—
25	Dic₈₆	D₄	1	2	yes	—
26	C₄₃⋊C₈	—	2	2	no	—
27	C₂²×C₄₃	C₂×D₄	1	1	yes	characteristic
28	C₄×C₄₃	—	2	1	no	—
29	C₄×C₄₃	—	4	2	no	—
30	C₄×C₄₃	Q₁₆	1	2	yes	complemented
31	C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
32	C₄×C₄₃	#41	1	1	yes	characteristic
33	Dic₄₃	—	2	2	no	—
34	Dic₄₃	—	4	1	no	—
35	C₂×C₄₃	#121	1	1	yes	characteristic
36	C₂×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
37	C₂×C₄₃	#137	1	1	yes	characteristic
38	#462	—	43	1	no	maximal, Sylow
39	C₄₃	#462	1	1	yes	characteristic, complemented, Sylow
40	C₂×Q₁₆	—	43	2	no	—
41	C₄⋊Q₈	D₄₃	1	1	yes	characteristic
42	C₄×Q₈	—	43	1	no	—
43	C₄⋊C₈	—	43	1	no	—
44	#103	—	43	2	no	—
45	C₂×Q₈	—	43	1	no	—
46	C₂×Q₈	C₂×D₄₃	1	2	yes	—
47	Q₁₆	—	86	4	no	—
48	C₂×C₈	—	43	2	no	—
49	C₄⋊C₄	—	2	1	no	—
50	C₄⋊C₄	—	2	1	no	—
51	C₄⋊C₄	—	43	1	no	—
52	C₄⋊C₄	—	86	1	no	—
53	C₄²	—	86	1	no	—
54	C₄²	C₂×D₄₃	1	1	yes	characteristic
55	Q₈	—	2	2	no	—
56	Q₈	—	2	2	no	—
57	Q₈	—	43	2	no	—
58	Q₈	—	86	1	no	—
59	C₂×C₄	—	2	2	no	—
60	C₂×C₄	—	86	1	no	—
61	C₂×C₄	—	86	1	no	—
62	C₂×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
63	C₂×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
64	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
65	C₈	—	86	2	no	—
66	C₂²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
67	C₄	—	2	1	no	—
68	C₄	—	4	2	no	—
69	C₄	—	86	2	no	—
70	C₄	—	172	1	no	—
71	C₄	#10621885	1	2	yes	complemented
72	C₄	D₄×D₄₃	1	1	yes	characteristic
73	C₄	#10621900	1	1	yes	characteristic
74	C₂	#13063296	1	1	yes	characteristic
75	C₂	C₂×#10621885	1	1	yes	characteristic
76	C₂	#13063356	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂³
Frattini	C₂×C₄	C₂²×D₄₃
Fitting	C₄⋊Q₈×C₄₃	C₂
socle, prime radical	C₂²×C₄₃	C₂×D₄
hypercenter	C₄⋊Q₈	D₄₃
hypocenter	C₄₃	#462
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
30. C₄×C₄₃	Q₁₆	semidirect
39. C₄₃	#462	semidirect
71. C₄	#10621885	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10621885	2
C₄×Dic₈₆	2
C₄⋊(C₄₃⋊C₈)	2
#13063249	2
C₄⋊Q₈×C₄₃	2
#462	43