Subgroups — #14583266

Order 2752.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13063323	C₂	1	1	yes	maximal, characteristic
2	#13063316	C₂	1	1	yes	maximal, characteristic
3	#13063250	C₂	1	1	yes	maximal, characteristic
4	#13063249	C₂	1	1	yes	maximal, characteristic
5	#13063248	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	C₄⋊Dic₄₃	—	2	1	no	—
13	C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
14	Dic₄₃⋊C₄	—	2	1	no	—
15	Dic₄₃⋊C₄	—	2	1	no	—
16	Dic₄₃⋊C₄	—	2	1	no	—
17	C₄×Dic₄₃	C₂²	1	1	yes	characteristic
18	C₂×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
19	Q₈×C₄₃	—	2	1	no	—
20	Q₈×C₄₃	—	2	1	no	—
21	C₂×C₄×C₄₃	—	2	1	no	—
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	D₄	1	1	yes	characteristic
27	C₂×Dic₄₃	D₄	1	1	yes	characteristic
28	Dic₈₆	—	2	1	no	—
29	Dic₈₆	—	2	1	no	—
30	C₈×C₄₃	—	2	1	no	—
31	C₄₃⋊C₈	—	2	1	no	—
32	C₂²×C₄₃	C₂×D₄	1	1	yes	characteristic
33	C₄×C₄₃	—	4	1	no	—
34	C₄×C₄₃	—	4	1	no	—
35	C₄×C₄₃	#41	1	1	yes	characteristic
36	C₄×C₄₃	#41	1	1	yes	characteristic
37	Dic₄₃	—	2	1	no	—
38	Dic₄₃	—	2	1	no	—
39	Dic₄₃	—	4	1	no	—
40	Dic₄₃	—	4	1	no	—
41	C₂×C₄₃	#124	1	1	yes	characteristic
42	C₂×C₄₃	#137	1	1	yes	characteristic
43	C₂×C₄₃	#137	1	1	yes	characteristic
44	#491	—	43	1	no	maximal, Sylow
45	C₄₃	#491	1	1	yes	characteristic, complemented, Sylow
46	C₄⋊Q₈	—	43	1	no	—
47	#125	—	43	1	no	—
48	#103	—	43	1	no	—
49	#103	—	43	1	no	—
50	#103	—	43	1	no	—
51	#103	D₄₃	1	1	yes	characteristic
52	#97	—	43	1	no	—
53	C₂×Q₈	—	43	1	no	—
54	C₂×Q₈	C₂×D₄₃	1	1	yes	characteristic
55	C₂×C₈	—	43	1	no	—
56	C₂×C₈	C₂×D₄₃	1	1	yes	characteristic
57	C₄⋊C₄	—	43	1	no	—
58	C₄⋊C₄	—	86	1	no	—
59	C₄⋊C₄	—	86	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	Q₈	—	2	1	no	—
65	Q₈	—	2	1	no	—
66	Q₈	—	86	1	no	—
67	Q₈	—	86	1	no	—
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	43	1	no	—
71	C₂×C₄	—	43	1	no	—
72	C₂×C₄	—	86	1	no	—
73	C₂×C₄	—	86	1	no	—
74	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
75	C₈	—	2	1	no	—
76	C₈	—	86	1	no	—
77	C₂²	D₄×D₄₃	1	1	yes	characteristic
78	C₄	—	4	1	no	—
79	C₄	—	4	1	no	—
80	C₄	—	86	1	no	—
81	C₄	—	86	1	no	—
82	C₄	—	172	1	no	—
83	C₄	—	172	1	no	—
84	C₄	#10621898	1	1	yes	characteristic
85	C₄	#10621900	1	1	yes	characteristic
86	C₂	#13063311	1	1	yes	characteristic
87	C₂	#13063354	1	1	yes	characteristic
88	C₂	#13063357	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂³
Frattini	C₂×C₄	C₂²×D₄₃
Fitting	#103×C₄₃	C₂
socle, prime radical	C₂²×C₄₃	C₂×D₄
hypercenter	#103	D₄₃
hypocenter	C₄₃	#491
LCS	G ▷ C₂×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
45. C₄₃	#491	semidirect

Maximal subgroups

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

subgroup	index
#13063323	2
#13063316	2
#13063250	2
#13063249	2
#13063248	2
#13063235	2
#103×C₄₃	2
#491	43