Subgroups — #14583240

Order 2752.

96 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	#13063258	C₂	1	1	yes	maximal, characteristic, complemented
3	#13063256	C₂	1	1	yes	maximal, characteristic, complemented
4	#13063248	C₂	1	1	yes	maximal, characteristic, complemented
5	#13063248	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
7	#117×C₄₃	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₄×C₄₃	C₂²	1	1	yes	characteristic
9	C₂×Dic₈₆	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
11	C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
12	C₂²⋊C₄×C₄₃	—	2	1	no	—
13	C₄²×C₄₃	—	2	1	no	—
14	C₂²⋊Dic₄₃	—	2	1	no	—
15	C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
16	Dic₄₃⋊C₄	—	2	1	no	—
17	C₂×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂³×C₄₃	D₄	1	1	yes	characteristic
20	C₂×C₄×C₄₃	—	2	1	no	—
21	C₂×C₄×C₄₃	—	2	1	no	—
22	C₂×C₄×C₄₃	—	2	1	no	—
23	C₂×C₄×C₄₃	—	2	1	no	—
24	C₂×C₄×C₄₃	D₄	1	1	yes	characteristic
25	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
26	C₂×Dic₄₃	—	2	1	no	—
27	C₂×Dic₄₃	—	2	1	no	—
28	Dic₈₆	—	2	1	no	—
29	Dic₈₆	—	2	1	no	—
30	C₄₃⋊C₈	—	2	1	no	—
31	C₄₃⋊C₈	—	2	1	no	—
32	C₂²×C₄₃	—	2	1	no	—
33	C₂²×C₄₃	—	2	1	no	—
34	C₂²×C₄₃	—	2	1	no	—
35	C₂²×C₄₃	C₂×D₄	1	1	yes	characteristic
36	C₄×C₄₃	—	2	1	no	—
37	C₄×C₄₃	—	4	1	no	—
38	C₄×C₄₃	—	4	1	no	—
39	C₄×C₄₃	#41	1	1	yes	characteristic
40	C₄×C₄₃	#41	1	1	yes	characteristic
41	Dic₄₃	—	4	1	no	—
42	Dic₄₃	—	4	1	no	—
43	C₂×C₄₃	—	4	1	no	—
44	C₂×C₄₃	#123	1	1	yes	characteristic
45	C₂×C₄₃	#135	1	1	yes	characteristic
46	C₂×C₄₃	#137	1	1	yes	characteristic
47	#485	—	43	1	no	maximal, Sylow
48	C₄₃	#485	1	1	yes	characteristic, complemented, Sylow
49	C₂²⋊Q₈	—	43	1	no	—
50	#117	D₄₃	1	1	yes	characteristic
51	#107	—	43	1	no	—
52	#106	—	43	1	no	—
53	#103	—	43	1	no	—
54	#103	—	43	1	no	—
55	C₂²⋊C₈	—	43	1	no	—
56	C₂×Q₈	—	43	1	no	—
57	C₂²×C₄	C₂×D₄₃	1	1	yes	characteristic
58	C₂×C₈	—	43	1	no	—
59	C₂×C₈	—	43	1	no	—
60	C₄⋊C₄	—	43	1	no	—
61	C₄⋊C₄	—	86	1	no	—
62	C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
63	C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
64	C₂²⋊C₄	—	2	1	no	—
65	C₂²⋊C₄	—	86	1	no	—
66	C₄²	—	2	1	no	—
67	C₂³	C₂²⋊D₄₃	1	1	yes	characteristic
68	Q₈	—	86	1	no	—
69	Q₈	—	86	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	2	1	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	86	1	no	—
75	C₂×C₄	—	86	1	no	—
76	C₂×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
77	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
78	C₈	—	86	1	no	—
79	C₈	—	86	1	no	—
80	C₂²	—	2	1	no	—
81	C₂²	—	2	1	no	—
82	C₂²	—	2	1	no	—
83	C₂²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
84	C₄	—	2	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	4	1	no	—
87	C₄	—	172	1	no	—
88	C₄	—	172	1	no	—
89	C₄	#10621898	1	1	yes	characteristic
90	C₄	#10621898	1	1	yes	characteristic
91	C₂	—	4	1	no	—
92	C₂	#13063308	1	1	yes	characteristic
93	C₂	#13063345	1	1	yes	characteristic
94	C₂	#13063355	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂³
Frattini	C₂×C₄	C₂²×D₄₃
Fitting	#117×C₄₃	C₂
socle	C₂²×C₄₃	C₂×D₄
prime radical	C₂³×C₄₃	D₄
hypercenter	#117	D₄₃
hypocenter	C₄₃	#485
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
2. #13063258	C₂	semidirect
3. #13063256	C₂	semidirect
4. #13063248	C₂	semidirect
5. #13063248	C₂	semidirect
48. C₄₃	#485	semidirect

Maximal subgroups

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

subgroup	index
#13063304	2
#13063258	2
#13063256	2
#13063248	2
C₂²⋊(C₄₃⋊C₈)	2
#117×C₄₃	2
#485	43