Subgroups — #24984310

Order 11008.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582729	C₂	1	2	yes	maximal
2	C₂×C₄₃×M₆₄	C₂	1	1	yes	maximal, characteristic
3	C₂×#13063261	—	2	2	no	—
4	#14582729	—	2	2	no	—
5	#14582729	C₄	1	4	yes	—
6	C₂²×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
7	C₄₃×M₆₄	—	2	2	no	—
8	C₂×C₃₂×C₄₃	C₄	1	2	yes	—
9	C₂×#10621877	—	4	2	no	—
10	#13063261	—	2	4	no	—
11	#13063261	—	4	2	no	—
12	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
13	C₂×C₁₆×C₄₃	C₂×C₄	1	2	yes	—
14	C₂×C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₁₆×C₄₃	D₄	1	2	yes	—
16	C₂×C₁₆×C₄₃	Q₈	1	1	yes	characteristic
17	C₃₂×C₄₃	—	2	2	no	—
18	C₂²×C₄×C₄₃	D₈	1	1	yes	characteristic
19	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
20	C₂×C₈×C₄₃	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₈×C₄₃	SD₁₆	1	2	yes	—
22	C₂×C₈×C₄₃	Q₁₆	1	1	yes	characteristic
23	#10621877	—	4	4	no	—
24	#10621877	—	8	2	no	—
25	C₂×C₄₃⋊C₈	—	8	2	no	—
26	C₁₆×C₄₃	C₄²	1	1	yes	characteristic
27	C₁₆×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₁₆×C₄₃	C₄⋊C₄	1	2	yes	—
29	C₂³×C₄₃	Q₃₂	1	1	yes	characteristic
30	C₂×C₄×C₄₃	#102	1	2	yes	—
31	C₂×C₄×C₄₃	#107	1	1	yes	characteristic
32	C₂×C₄×C₄₃	D₁₆	1	1	yes	characteristic
33	C₂×C₄×C₄₃	SD₃₂	1	2	yes	—
34	C₈×C₄₃	#95	1	1	yes	characteristic
35	C₈×C₄₃	#103	1	2	yes	—
36	C₈×C₄₃	#106	1	1	yes	characteristic
37	C₄₃⋊C₈	—	8	4	no	—
38	#7476	—	43	1	no	maximal, Sylow
39	C₂²×C₄₃	—	4	1	no	—
40	C₂²×C₄₃	#358	1	2	yes	—
41	C₂²×C₄₃	#366	1	1	yes	characteristic
42	C₄×C₄₃	#340	1	1	yes	characteristic
43	C₄×C₄₃	#357	1	2	yes	—
44	C₄×C₄₃	#367	1	1	yes	characteristic
45	C₂×M₆₄	D₄₃	1	1	yes	characteristic
46	C₂×#368	—	43	2	no	—
47	C₂×C₄₃	—	2	2	no	—
48	C₂×C₄₃	—	2	1	no	—
49	C₂×C₄₃	#1380	1	1	yes	characteristic
50	C₂²×C₁₆	C₂×D₄₃	1	1	yes	characteristic
51	C₂×#108	—	86	2	no	—
52	M₆₄	—	2	2	no	—
53	C₂×C₃₂	Dic₄₃	1	2	yes	—
54	#368	—	43	4	no	—
55	#368	—	86	2	no	—
56	C₄₃	#7476	1	1	yes	characteristic, complemented, Sylow
57	C₂×M₁₆	—	172	2	no	—
58	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
59	C₂×C₁₆	Dic₈₆	1	1	yes	characteristic
60	C₂×C₁₆	C₄×D₄₃	1	2	yes	—
61	C₂×C₁₆	C₂×Dic₄₃	1	1	yes	characteristic
62	C₂×C₁₆	C₂²⋊D₄₃	1	2	yes	—
63	#108	—	86	4	no	—
64	#108	—	172	2	no	—
65	C₃₂	—	2	2	no	—
66	C₂²×C₄	D₃₄₄	1	1	yes	characteristic
67	M₁₆	—	344	2	no	—
68	M₁₆	—	172	4	no	—
69	C₂×C₈	—	344	2	no	—
70	C₂×C₈	#10621873	1	2	yes	—
71	C₂×C₈	Dic₁₇₂	1	1	yes	characteristic
72	C₂×C₈	C₄⋊Dic₄₃	1	1	yes	characteristic
73	C₂×C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
74	C₁₆	C₄×Dic₄₃	1	1	yes	characteristic
75	C₁₆	Dic₄₃⋊C₄	1	2	yes	—
76	C₁₆	C₂²⋊Dic₄₃	1	1	yes	characteristic
77	C₂³	Dic₃₄₄	1	1	yes	characteristic
78	C₂×C₄	#13063247	1	2	yes	—
79	C₂×C₄	#13063259	1	1	yes	characteristic
80	C₂×C₄	D₆₈₈	1	1	yes	characteristic
81	C₂×C₄	#13063270	1	2	yes	—
82	C₈	—	344	4	no	—
83	C₈	C₄₃⋊#95	1	1	yes	characteristic
84	C₈	#13063250	1	2	yes	—
85	C₈	#13063257	1	1	yes	characteristic
86	C₂²	—	4	1	no	—
87	C₂²	#14582704	1	2	yes	—
88	C₂²	#14582725	1	1	yes	characteristic
89	C₄	#14582662	1	1	yes	characteristic
90	C₄	#14582701	1	2	yes	—
91	C₄	#14582727	1	1	yes	characteristic
92	C₂	—	2	2	no	—
93	C₂	—	2	1	no	—
94	C₂	#19132687	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14582727
commutator	C₁₆×C₄₃	C₄²
Frattini	C₂²×C₁₆	C₂×D₄₃
Fitting	C₂×C₄₃×M₆₄	C₂
socle	C₂×C₄₃	#1380
prime radical	C₂³×C₄₃	Q₃₂
cosocle	C₂²×C₁₆×C₄₃	C₂²
hypercenter	C₂×M₆₄	D₄₃
hypocenter	C₄₃	#7476
LCS	G ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ C₂×M₆₄

Complements

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

N	H ≅ G/N	type
56. C₄₃	#7476	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582729	2
C₂×C₄₃×M₆₄	2
#7476	43