Subgroups — #24984485

Order 11008.

90 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	#19132797	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×M₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583331	—	2	1	no	—
5	Dic₆₈₈	C₄	1	1	yes	characteristic, complemented
6	#14582738	—	2	1	no	—
7	D₁₃₇₆	C₄	1	1	yes	characteristic, complemented
8	#14582725	—	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	#13063259	—	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	C₄⋊Dic₄₃	—	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	C₂×Dic₄₃	—	16	1	no	—
30	D₁₇₂	—	8	1	no	—
31	C₄×D₄₃	—	16	1	no	—
32	Dic₈₆	—	8	1	no	—
33	C₈×C₄₃	#102	1	1	yes	characteristic
34	C₈×C₄₃	SD₃₂	1	1	yes	characteristic
35	#7540	—	43	1	no	maximal, Sylow
36	C₂²×C₄₃	D₃₂	1	1	yes	characteristic
37	C₂×D₄₃	—	16	1	no	—
38	C₄×C₄₃	#357	1	1	yes	characteristic
39	C₄×C₄₃	SD₆₄	1	1	yes	characteristic
40	Dic₄₃	—	16	1	no	—
41	Dic₄₃	—	32	1	no	—
42	#2262	—	43	1	no	—
43	M₁₂₈	D₄₃	1	1	yes	characteristic, complemented
44	#1424	—	43	1	no	—
45	C₂×C₄₃	—	2	1	no	—
46	C₂×C₄₃	#1415	1	1	yes	characteristic
47	D₄₃	—	32	1	no	—
48	#508	—	86	1	no	—
49	Q₆₄	—	43	1	no	—
50	SD₆₄	—	86	1	no	—
51	D₃₂	—	43	1	no	—
52	C₂×C₃₂	C₂×D₄₃	1	1	yes	characteristic
53	#366	—	86	1	no	—
54	C₆₄	—	2	1	no	—
55	C₄₃	#7540	1	1	yes	characteristic, complemented, Sylow
56	#135	—	172	1	no	—
57	Q₃₂	—	86	1	no	—
58	SD₃₂	—	172	1	no	—
59	D₁₆	—	86	1	no	—
60	C₂×C₁₆	D₁₇₂	1	1	yes	characteristic
61	#107	—	172	1	no	—
62	C₃₂	C₄×D₄₃	1	1	yes	characteristic
63	C₃₂	C₂²⋊D₄₃	1	1	yes	characteristic
64	#41	—	344	1	no	—
65	Q₁₆	—	172	1	no	—
66	SD₁₆	—	344	1	no	—
67	D₈	—	172	1	no	—
68	C₂×C₈	D₃₄₄	1	1	yes	characteristic
69	C₄⋊C₄	—	344	1	no	—
70	C₁₆	#10621873	1	1	yes	characteristic
71	C₁₆	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
72	Q₈	—	344	1	no	—
73	D₄	—	344	1	no	—
74	D₄	—	688	1	no	—
75	C₂×C₄	—	688	1	no	—
76	C₂×C₄	—	688	1	no	—
77	C₂×C₄	D₆₈₈	1	1	yes	characteristic
78	C₈	#13063247	1	1	yes	characteristic
79	C₈	#13063270	1	1	yes	characteristic
80	C₂²	—	688	1	no	—
81	C₂²	D₁₃₇₆	1	1	yes	characteristic
82	C₄	—	1376	1	no	—
83	C₄	—	688	1	no	—
84	C₄	#14582701	1	1	yes	characteristic
85	C₄	#14582738	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	1376	1	no	—
88	C₂	#19132774	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19132774
commutator	C₃₂×C₄₃	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₄₃
Fitting	C₄₃×M₁₂₈	C₂
socle	C₂×C₄₃	#1415
prime radical	#19136904	C₂
cosocle	C₂×C₃₂×C₄₃	C₂²
hypercenter	M₁₂₈	D₄₃
hypocenter	C₄₃	#7540
LCS	G ▷ C₃₂×C₄₃ ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ M₁₂₈

Complements

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

N	H ≅ G/N	type
2. #19132797	C₂	semidirect
3. C₄₃×M₁₂₈	C₂	semidirect
5. Dic₆₈₈	C₄	semidirect
7. D₁₃₇₆	C₄	semidirect
43. M₁₂₈	D₄₃	semidirect
55. C₄₃	#7540	semidirect

Maximal subgroups

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

subgroup	index
#19136904	2
#19132797	2
C₄₃×M₁₂₈	2
#7540	43