Subgroups — #24984482

Order 11008.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19136904	C₂	1	1	yes	maximal, characteristic
2	#19132799	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583331	—	2	1	no	—
5	Dic₆₈₈	C₄	1	1	yes	characteristic
6	#14582738	—	2	1	no	—
7	D₁₃₇₆	C₄	1	1	yes	characteristic
8	#14582729	—	2	1	no	—
9	C₂×C₃₂×C₄₃	C₂²	1	1	yes	characteristic
10	C₄₃×C₆₄	—	2	1	no	—
11	#13063347	—	4	1	no	—
12	Dic₃₄₄	—	2	1	no	—
13	#13063270	—	4	1	no	—
14	D₆₈₈	—	2	1	no	—
15	#13063261	—	4	1	no	—
16	C₂×C₁₆×C₄₃	D₄	1	1	yes	characteristic
17	C₃₂×C₄₃	C₂×C₄	1	1	yes	characteristic
18	C₃₂×C₄₃	D₄	1	1	yes	characteristic
19	#10621898	—	8	1	no	—
20	C₂×C₈×C₄₃	D₈	1	1	yes	characteristic
21	#10621877	—	8	1	no	—
22	Dic₁₇₂	—	4	1	no	—
23	D₃₄₄	—	4	1	no	—
24	#10621873	—	8	1	no	—
25	C₁₆×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₁₆×C₄₃	SD₁₆	1	1	yes	characteristic
27	C₂×C₄×C₄₃	D₁₆	1	1	yes	characteristic
28	C₂²⋊D₄₃	—	16	1	no	—
29	D₁₇₂	—	8	1	no	—
30	C₄×D₄₃	—	16	1	no	—
31	Dic₈₆	—	8	1	no	—
32	C₈×C₄₃	#102	1	1	yes	characteristic
33	C₈×C₄₃	SD₃₂	1	1	yes	characteristic
34	C₄₃⋊C₈	—	16	1	no	—
35	#7539	—	43	1	no	maximal, Sylow
36	C₂²×C₄₃	SD₆₄	1	1	yes	characteristic
37	C₂×D₄₃	—	16	1	no	—
38	C₄×C₄₃	#357	1	1	yes	characteristic
39	C₄×C₄₃	D₃₂	1	1	yes	characteristic
40	Dic₄₃	—	16	1	no	—
41	#2262	—	43	1	no	—
42	C₂×C₆₄	D₄₃	1	1	yes	characteristic, complemented
43	#1425	—	43	1	no	—
44	C₂×C₄₃	—	2	1	no	—
45	C₂×C₄₃	#1415	1	1	yes	characteristic
46	D₄₃	—	32	1	no	—
47	#508	—	86	1	no	—
48	Q₆₄	—	43	1	no	—
49	SD₆₄	—	86	1	no	—
50	D₃₂	—	43	1	no	—
51	C₂×C₃₂	C₂×D₄₃	1	1	yes	characteristic
52	#368	—	86	1	no	—
53	C₆₄	—	2	1	no	—
54	C₄₃	#7539	1	1	yes	characteristic, complemented, Sylow
55	#135	—	172	1	no	—
56	Q₃₂	—	86	1	no	—
57	SD₃₂	—	172	1	no	—
58	D₁₆	—	86	1	no	—
59	C₂×C₁₆	D₁₇₂	1	1	yes	characteristic
60	#108	—	172	1	no	—
61	C₃₂	C₄×D₄₃	1	1	yes	characteristic
62	C₃₂	C₂²⋊D₄₃	1	1	yes	characteristic
63	#41	—	344	1	no	—
64	Q₁₆	—	172	1	no	—
65	SD₁₆	—	344	1	no	—
66	D₈	—	172	1	no	—
67	M₁₆	—	344	1	no	—
68	C₂×C₈	D₃₄₄	1	1	yes	characteristic
69	C₁₆	#10621873	1	1	yes	characteristic
70	C₁₆	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
71	Q₈	—	344	1	no	—
72	D₄	—	344	1	no	—
73	D₄	—	688	1	no	—
74	C₂×C₄	—	688	1	no	—
75	C₂×C₄	D₆₈₈	1	1	yes	characteristic
76	C₈	—	688	1	no	—
77	C₈	#13063247	1	1	yes	characteristic
78	C₈	#13063270	1	1	yes	characteristic
79	C₂²	—	688	1	no	—
80	C₂²	#14582738	1	1	yes	characteristic
81	C₄	—	688	1	no	—
82	C₄	#14582701	1	1	yes	characteristic
83	C₄	D₁₃₇₆	1	1	yes	characteristic
84	C₂	—	2	1	no	—
85	C₂	—	1376	1	no	—
86	C₂	#19132774	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₁₃₇₆
commutator	C₃₂×C₄₃	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₄₃
Fitting	C₂×C₄₃×C₆₄	C₂
socle	C₂×C₄₃	#1415
prime radical	#19136904	C₂
cosocle	C₂×C₃₂×C₄₃	C₂²
hypercenter	C₂×C₆₄	D₄₃
hypocenter	C₄₃	#7539
LCS	G ▷ C₃₂×C₄₃ ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
2. #19132799	C₂	semidirect
3. C₂×C₄₃×C₆₄	C₂	semidirect
42. C₂×C₆₄	D₄₃	semidirect
54. C₄₃	#7539	semidirect

Maximal subgroups

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

subgroup	index
#19136904	2
#19132799	2
C₂×C₄₃×C₆₄	2
#7539	43