Subgroups — #14583187

Order 2752.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13063324	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×Dic₄₃	C₂	1	1	yes	maximal, characteristic
3	#13063257	C₂	1	1	yes	maximal, characteristic, complemented
4	#13063256	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#13063246	C₂	1	1	yes	maximal, characteristic
7	#102×C₄₃	C₂	1	1	yes	maximal, characteristic
8	C₂×D₄×C₄₃	C₂²	1	1	yes	characteristic
9	C₂²×Dic₄₃	—	2	1	no	—
10	C₂×Dic₈₆	—	2	1	no	—
11	C₂×C₈×C₄₃	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²⋊Dic₄₃	—	2	1	no	—
14	C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
15	C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
16	Dic₄₃⋊C₄	—	2	1	no	—
17	C₄×Dic₄₃	C₂²	1	1	yes	characteristic
18	C₂×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂³×C₄₃	—	2	1	no	—
20	D₄×C₄₃	—	2	1	no	—
21	D₄×C₄₃	Q₈	1	2	yes	complemented
22	C₂×C₄×C₄₃	—	2	1	no	—
23	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
24	C₂×Dic₄₃	—	2	1	no	—
25	C₂×Dic₄₃	—	2	1	no	—
26	C₂×Dic₄₃	—	4	2	no	—
27	C₂×Dic₄₃	D₄	1	1	yes	characteristic
28	C₂×Dic₄₃	D₄	1	1	yes	characteristic
29	Dic₈₆	—	4	2	no	—
30	C₈×C₄₃	—	2	1	no	—
31	C₄₃⋊C₈	—	2	1	no	—
32	C₂²×C₄₃	—	2	2	no	—
33	C₂²×C₄₃	—	4	1	no	—
34	C₂²×C₄₃	—	4	1	no	—
35	C₂²×C₄₃	C₂×D₄	1	1	yes	characteristic
36	C₄×C₄₃	—	4	1	no	—
37	C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
38	C₄×C₄₃	#41	1	1	yes	characteristic
39	Dic₄₃	—	2	1	no	—
40	Dic₄₃	—	4	1	no	—
41	Dic₄₃	—	4	1	no	—
42	Dic₄₃	SD₁₆	1	2	yes	—
43	C₂×C₄₃	—	4	2	no	—
44	C₂×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
45	C₂×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
46	C₂×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
47	#476	—	43	1	no	maximal, Sylow
48	C₄₃	#476	1	1	yes	characteristic, complemented, Sylow
49	C₄⋊Q₈	—	43	1	no	—
50	C₄×D₄	—	43	1	no	—
51	#106	—	43	1	no	—
52	#106	—	43	1	no	—
53	C₄⋊C₈	—	43	1	no	—
54	#102	—	43	1	no	—
55	#102	D₄₃	1	1	yes	characteristic
56	C₂×Q₈	—	86	1	no	—
57	C₂×D₄	C₂×D₄₃	1	1	yes	characteristic
58	C₂²×C₄	—	86	1	no	—
59	C₂×C₈	—	43	1	no	—
60	C₂×C₈	C₂×D₄₃	1	1	yes	characteristic
61	C₄⋊C₄	—	43	1	no	—
62	C₄⋊C₄	—	43	1	no	—
63	C₄⋊C₄	—	86	1	no	—
64	C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
65	C₂²⋊C₄	—	86	1	no	—
66	C₄²	—	43	1	no	—
67	C₂³	—	2	1	no	—
68	Q₈	—	172	2	no	—
69	D₄	—	2	1	no	—
70	D₄	Dic₈₆	1	2	yes	complemented
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	43	1	no	—
73	C₂×C₄	—	43	1	no	—
74	C₂×C₄	—	86	1	no	—
75	C₂×C₄	—	86	1	no	—
76	C₂×C₄	—	172	2	no	—
77	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	86	1	no	—
80	C₂²	—	2	2	no	—
81	C₂²	—	4	1	no	—
82	C₂²	—	4	1	no	—
83	C₂²	D₄×D₄₃	1	1	yes	characteristic
84	C₄	—	4	1	no	—
85	C₄	—	43	2	no	—
86	C₄	—	86	1	no	—
87	C₄	—	172	1	no	—
88	C₄	—	172	1	no	—
89	C₄	C₂×Dic₈₆	1	1	yes	characteristic
90	C₄	#10621900	1	1	yes	characteristic
91	C₂	—	4	2	no	—
92	C₂	#13063302	1	1	yes	characteristic
93	C₂	SD₁₆×D₄₃	1	1	yes	characteristic
94	C₂	#13063349	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂³
Frattini	C₂×C₄	C₂²×D₄₃
Fitting	#102×C₄₃	C₂
socle	C₂²×C₄₃	C₂×D₄
prime radical	C₂×D₄×C₄₃	C₂²
hypercenter	#102	D₄₃
hypocenter	C₄₃	#476
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #102

Complements

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

N	H ≅ G/N	type
1. #13063324	C₂	semidirect
3. #13063257	C₂	semidirect
4. #13063256	C₂	semidirect
5. Dic₄₃⋊C₈	C₂	semidirect
21. D₄×C₄₃	Q₈	semidirect
48. C₄₃	#476	semidirect
70. D₄	Dic₈₆	semidirect

Maximal subgroups

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

subgroup	index
#13063324	2
D₄×Dic₄₃	2
#13063257	2
#13063256	2
Dic₄₃⋊C₈	2
#13063246	2
#102×C₄₃	2
#476	43