Subgroups — #24984486

Order 11008.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃₇₆	C₂	1	1	yes	maximal, characteristic
2	#19132806	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#1425	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₆₈₈	—	2	1	no	—
5	D₁₃₇₆	—	2	1	no	—
6	D₁₃₇₆	C₄	1	2	yes	—
7	C₄₃⋊C₆₄	—	2	1	no	—
8	C₂×C₃₂×C₄₃	C₂²	1	1	yes	characteristic
9	C₄₃×#368	—	2	1	no	—
10	C₂×D₃₄₄	—	4	1	no	—
11	D₆₈₈	—	2	2	no	—
12	D₆₈₈	—	4	1	no	—
13	C₂×C₁₆×C₄₃	D₄	1	1	yes	characteristic
14	#108×C₄₃	—	4	1	no	—
15	C₃₂×C₄₃	C₂×C₄	1	1	yes	characteristic
16	C₃₂×C₄₃	D₄	1	1	yes	characteristic
17	C₂×D₁₇₂	—	8	1	no	—
18	M₁₆×C₄₃	—	8	1	no	—
19	C₂×C₈×C₄₃	D₈	1	1	yes	characteristic
20	D₃₄₄	—	4	2	no	—
21	D₃₄₄	—	8	1	no	—
22	C₁₆×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₁₆×C₄₃	SD₁₆	1	1	yes	characteristic
24	C₂²×D₄₃	—	16	1	no	—
25	C₂×C₄×C₄₃	D₁₆	1	1	yes	characteristic
26	D₁₇₂	—	8	2	no	—
27	D₁₇₂	—	16	1	no	—
28	C₈×C₄₃	—	16	1	no	—
29	C₈×C₄₃	#102	1	1	yes	characteristic
30	C₈×C₄₃	SD₃₂	1	1	yes	characteristic
31	#7541	—	43	1	no	maximal, Sylow
32	C₂²×C₄₃	SD₆₄	1	1	yes	characteristic
33	C₂×D₄₃	—	16	2	no	—
34	C₂×D₄₃	—	32	2	no	—
35	C₄×C₄₃	#357	1	1	yes	characteristic
36	C₄×C₄₃	D₃₂	1	1	yes	characteristic
37	C₂×D₃₂	—	43	1	no	—
38	M₁₂₈	—	43	1	no	—
39	#1425	D₄₃	1	1	yes	characteristic, complemented
40	C₂×C₄₃	—	2	1	no	—
41	C₂×C₄₃	#1415	1	1	yes	characteristic
42	D₄₃	—	32	2	no	—
43	C₂×D₁₆	—	86	1	no	—
44	D₃₂	—	43	2	no	—
45	D₃₂	—	86	1	no	—
46	C₂×C₃₂	C₂×D₄₃	1	1	yes	characteristic
47	#368	—	2	1	no	—
48	C₆₄	—	86	1	no	—
49	C₄₃	#7541	1	1	yes	characteristic, complemented, Sylow
50	C₂×D₈	—	172	1	no	—
51	D₁₆	—	86	2	no	—
52	D₁₆	—	172	1	no	—
53	C₂×C₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
54	#108	—	4	1	no	—
55	C₃₂	C₄×D₄₃	1	1	yes	characteristic
56	C₃₂	D₁₇₂	1	1	yes	characteristic
57	C₂×D₄	—	344	1	no	—
58	D₈	—	344	1	no	—
59	D₈	—	172	2	no	—
60	M₁₆	—	8	1	no	—
61	C₂×C₈	#10621882	1	1	yes	characteristic
62	C₁₆	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
63	C₁₆	#10621884	1	1	yes	characteristic
64	C₂³	—	688	1	no	—
65	D₄	—	344	2	no	—
66	D₄	—	688	1	no	—
67	C₂×C₄	#13063266	1	1	yes	characteristic
68	C₈	—	16	1	no	—
69	C₈	#13063245	1	1	yes	characteristic
70	C₈	#13063268	1	1	yes	characteristic
71	C₂²	—	1376	2	no	—
72	C₂²	—	688	2	no	—
73	C₂²	#14582736	1	1	yes	characteristic
74	C₄	#14582699	1	1	yes	characteristic
75	C₄	#14582734	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	1376	2	no	—
78	C₂	#19132772	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19132772
commutator	C₃₂×C₄₃	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₄₃
Fitting	C₄₃×#1425	C₂
socle	C₂×C₄₃	#1415
prime radical	C₂×D₁₃₇₆	C₂
cosocle	C₂×C₃₂×C₄₃	C₂²
hypercenter	#1425	D₄₃
hypocenter	C₄₃	#7541
LCS	G ▷ C₃₂×C₄₃ ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ #1425

Complements

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

N	H ≅ G/N	type
2. #19132806	C₂	semidirect
3. C₄₃×#1425	C₂	semidirect
39. #1425	D₄₃	semidirect
49. C₄₃	#7541	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₃₇₆	2
#19132806	2
C₄₃×#1425	2
#7541	43