Subgroups — #25013019

Order 11008.

278 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19136361	C₂	1	3	yes	maximal
2	#19136354	C₂	1	3	yes	maximal
3	C₄₃×#1747	C₂	1	1	yes	maximal, characteristic
4	C₂×#13063265	C₂²	1	3	yes	—
5	C₂²×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
6	#14582720	—	2	6	no	—
7	C₄⋊(C₄₃⋊C₁₆)	—	2	6	no	—
8	C₄₃×#405	C₂²	1	3	yes	—
9	C₄₃×#338	C₄	1	1	yes	characteristic
10	C₄₃×H(3,ℤ/4)	C₄	1	3	yes	—
11	#13063265	—	2	6	no	—
12	C₂×C₄₃⋊C₁₆	—	2	3	no	—
13	C₂×C₄₃⋊C₁₆	—	2	3	no	—
14	C₂×M₁₆×C₄₃	C₂×C₄	1	3	yes	—
15	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
16	#117×C₄₃	C₂×C₄	1	3	yes	—
17	#97×C₄₃	Q₈	1	6	yes	—
18	C₄×C₈×C₄₃	D₄	1	6	yes	—
19	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
20	M₁₆×C₄₃	—	2	6	no	—
21	C₂×C₈×C₄₃	C₄⋊C₄	1	6	yes	—
22	C₂×C₈×C₄₃	C₂×D₄	1	3	yes	—
23	C₂×C₈×C₄₃	C₂×Q₈	1	3	yes	—
24	C₄⋊C₄×C₄₃	—	2	3	no	—
25	C₂²⋊C₄×C₄₃	—	2	3	no	—
26	C₄²×C₄₃	C₄⋊C₄	1	6	yes	—
27	C₄₃⋊C₁₆	—	4	1	no	—
28	C₄₃⋊C₁₆	—	4	3	no	—
29	C₂³×C₄₃	#131	1	1	yes	characteristic
30	C₂×C₄×C₄₃	—	2	6	no	—
31	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	3	yes	—
32	C₂×C₄×C₄₃	#131	1	3	yes	—
33	C₈×C₄₃	—	2	6	no	—
34	C₈×C₄₃	#127	1	1	yes	characteristic
35	C₈×C₄₃	C₄⋊Q₈	1	3	yes	—
36	#12902	—	43	1	no	maximal, Sylow
37	C₂²×C₄₃	—	4	1	no	—
38	C₂²×C₄₃	#424	1	3	yes	—
39	C₄×C₄₃	—	4	6	no	—
40	C₄×C₄₃	#384	1	1	yes	characteristic
41	C₄×C₄₃	#424	1	3	yes	—
42	#2153	—	43	3	no	—
43	#2151	—	43	3	no	—
44	#1747	D₄₃	1	1	yes	characteristic
45	C₂×C₄₃	—	2	3	no	—
46	C₂×C₄₃	#1843	1	1	yes	characteristic
47	C₂×M₃₂	—	43	3	no	—
48	C₂²×C₁₆	—	43	1	no	—
49	#405	C₂×D₄₃	1	3	yes	—
50	#364	—	86	6	no	—
51	C₄⋊C₁₆	—	86	6	no	—
52	#338	Dic₄₃	1	1	yes	characteristic
53	H(3,ℤ/4)	Dic₄₃	1	3	yes	—
54	C₄₃	#12902	1	1	yes	characteristic, complemented, Sylow
55	C₂×M₁₆	C₂×Dic₄₃	1	3	yes	—
56	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
57	#117	C₂×Dic₄₃	1	3	yes	—
58	M₃₂	—	86	6	no	—
59	C₂×C₁₆	—	86	3	no	—
60	C₂×C₁₆	—	86	3	no	—
61	#97	Dic₈₆	1	6	yes	—
62	C₄×C₈	D₁₇₂	1	6	yes	—
63	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
64	M₁₆	—	2	6	no	—
65	C₂×C₈	C₄⋊Dic₄₃	1	6	yes	—
66	C₂×C₈	C₂×Dic₈₆	1	3	yes	—
67	C₂×C₈	C₂×D₁₇₂	1	3	yes	—
68	C₄⋊C₄	—	2	3	no	—
69	C₂²⋊C₄	—	2	3	no	—
70	C₄²	C₄⋊Dic₄₃	1	6	yes	—
71	C₁₆	—	172	1	no	—
72	C₁₆	—	172	3	no	—
73	C₂³	#13063332	1	1	yes	characteristic
74	C₂×C₄	—	2	6	no	—
75	C₂×C₄	C₂×C₄⋊Dic₄₃	1	3	yes	—
76	C₂×C₄	#13063332	1	3	yes	—
77	C₈	—	2	6	no	—
78	C₈	#13063322	1	1	yes	characteristic
79	C₈	#13063325	1	3	yes	—
80	C₂²	—	4	1	no	—
81	C₂²	#14582926	1	3	yes	—
82	C₄	—	4	6	no	—
83	C₄	#14582769	1	1	yes	characteristic
84	C₄	#14582926	1	3	yes	—
85	C₂	—	2	3	no	—
86	C₂	#19134749	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#13063322
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₄₃×#1747	C₂
socle	C₂×C₄₃	#1843
prime radical	C₂³×C₄₃	#131
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	#1747	D₄₃
hypocenter	C₄₃	#12902
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #1747

Complements

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

N	H ≅ G/N	type
54. C₄₃	#12902	semidirect

Maximal subgroups

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

subgroup	index
#19136361	2
#19136354	2
C₄₃×#1747	2
#12902	43