Subgroups — #14583003

Order 2752.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10621885	C₂	1	1	yes	maximal, characteristic
2	Q₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic
3	#13063290	C₂	1	1	yes	maximal, characteristic
4	#13063256	C₂	1	1	yes	maximal, characteristic
5	#13063250	C₂	1	1	yes	maximal, characteristic
6	#13063235	C₂	1	1	yes	maximal, characteristic
7	#103×C₄₃	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₈×C₄₃	C₂²	1	1	yes	characteristic
9	C₂×Dic₈₆	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₄₃	C₂²	1	1	yes	characteristic
11	C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
12	#10621885	C₄	1	4	yes	complemented
13	C₄⋊Dic₄₃	—	2	1	no	—
14	C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
15	Dic₄₃⋊C₄	—	2	1	no	—
16	C₄×Dic₄₃	—	2	1	no	—
17	C₄×Dic₄₃	—	2	1	no	—
18	C₄×Dic₄₃	C₂²	1	1	yes	characteristic
19	C₂×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
20	Q₈×C₄₃	—	2	1	no	—
21	Q₈×C₄₃	C₂×C₄	1	2	yes	—
22	C₂×C₄×C₄₃	—	2	1	no	—
23	C₂×C₄×C₄₃	—	2	1	no	—
24	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
25	C₂×Dic₄₃	—	2	1	no	—
26	C₂×Dic₄₃	—	2	1	no	—
27	C₂×Dic₄₃	D₄	1	1	yes	characteristic
28	C₂×Dic₄₃	D₄	1	1	yes	characteristic
29	Dic₈₆	—	2	1	no	—
30	Dic₈₆	C₂×C₄	1	2	yes	—
31	C₈×C₄₃	—	2	1	no	—
32	C₄₃⋊C₈	C₂×C₄	1	2	yes	—
33	C₂²×C₄₃	C₂×D₄	1	1	yes	characteristic
34	C₄×C₄₃	—	2	2	no	—
35	C₄×C₄₃	—	4	1	no	—
36	C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
37	C₄×C₄₃	#41	1	1	yes	characteristic
38	Dic₄₃	—	2	2	no	—
39	Dic₄₃	—	2	1	no	—
40	Dic₄₃	—	2	1	no	—
41	Dic₄₃	—	4	1	no	—
42	C₂×C₄₃	C₄×D₄	1	1	yes	characteristic
43	C₂×C₄₃	#137	1	1	yes	characteristic
44	C₂×C₄₃	#137	1	1	yes	characteristic
45	#441	—	43	1	no	maximal, Sylow
46	C₄₃	#441	1	1	yes	characteristic, complemented, Sylow
47	C₂×Q₁₆	—	43	1	no	—
48	C₄×Q₈	—	43	1	no	—
49	C₄×Q₈	—	43	1	no	—
50	#106	—	43	1	no	—
51	#103	—	43	1	no	—
52	#103	D₄₃	1	1	yes	characteristic
53	#97	—	43	1	no	—
54	C₂×Q₈	—	43	1	no	—
55	C₂×Q₈	C₂×D₄₃	1	1	yes	characteristic
56	Q₁₆	—	43	4	no	—
57	C₂×C₈	—	43	1	no	—
58	C₂×C₈	C₂×D₄₃	1	1	yes	characteristic
59	C₄⋊C₄	—	43	1	no	—
60	C₄⋊C₄	—	86	1	no	—
61	C₄⋊C₄	—	86	1	no	—
62	C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
63	C₄²	—	43	1	no	—
64	C₄²	—	86	1	no	—
65	C₄²	—	86	1	no	—
66	Q₈	—	2	1	no	—
67	Q₈	—	43	2	no	—
68	Q₈	—	86	1	no	—
69	Q₈	C₄×D₄₃	1	2	yes	—
70	C₂×C₄	—	2	1	no	—
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	C₂²×D₄₃	1	1	yes	characteristic
77	C₈	—	2	1	no	—
78	C₈	—	43	2	no	—
79	C₂²	D₄×D₄₃	1	1	yes	characteristic
80	C₄	—	2	2	no	—
81	C₄	—	4	1	no	—
82	C₄	—	86	2	no	—
83	C₄	—	86	1	no	—
84	C₄	—	86	1	no	—
85	C₄	—	172	1	no	—
86	C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
87	C₄	#10621900	1	1	yes	characteristic
88	C₂	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
89	C₂	#13063354	1	1	yes	characteristic
90	C₂	#13063357	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₄₃
commutator	C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₃
Fitting	#103×C₄₃	C₂
socle, prime radical	C₂²×C₄₃	C₂×D₄
cosocle	C₂×C₄×C₄₃	C₂³
hypercenter	#103	D₄₃
hypocenter	C₄₃	#441
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
12. #10621885	C₄	semidirect
46. C₄₃	#441	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
Q₈×Dic₄₃	2
#13063290	2
#13063256	2
#13063250	2
#13063235	2
#103×C₄₃	2
#441	43