Subgroups — #24984249

Order 11008.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19136870	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₄₃⋊C₃₂)	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#1371	C₂	1	1	yes	maximal, characteristic
4	#14583304	—	2	1	no	—
5	C₂×C₄₃⋊C₃₂	—	2	1	no	—
6	#14582725	—	2	1	no	—
7	#14582725	C₄	1	2	yes	—
8	C₄×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
9	C₄₃×#335	—	2	1	no	—
10	#13063325	—	4	1	no	—
11	#13063259	—	2	2	no	—
12	#13063259	—	4	1	no	—
13	C₄₃⋊C₃₂	—	4	1	no	—
14	C₂×C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₁₆×C₄₃	D₄	1	1	yes	characteristic
16	C₄⋊C₈×C₄₃	—	4	1	no	—
17	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
18	C₂×Dic₈₆	—	8	1	no	—
19	C₂×C₈×C₄₃	—	8	1	no	—
20	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×C₈×C₄₃	SD₁₆	1	1	yes	characteristic
22	C₄²×C₄₃	D₈	1	1	yes	characteristic
23	C₄⋊Dic₄₃	—	4	2	no	—
24	C₄⋊Dic₄₃	—	8	1	no	—
25	C₁₆×C₄₃	—	2	1	no	—
26	C₁₆×C₄₃	SD₁₆	1	1	yes	characteristic
27	C₁₆×C₄₃	Q₁₆	1	1	yes	characteristic
28	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
29	C₂×C₄×C₄₃	D₁₆	1	1	yes	characteristic
30	C₂×C₄×C₄₃	SD₃₂	1	1	yes	characteristic
31	C₂×Dic₄₃	—	8	2	no	—
32	Dic₈₆	—	16	1	no	—
33	Dic₈₆	—	16	1	no	—
34	C₈×C₄₃	—	2	1	no	—
35	C₈×C₄₃	—	16	1	no	—
36	C₈×C₄₃	#101	1	1	yes	characteristic
37	C₈×C₄₃	#103	1	1	yes	characteristic
38	#7450	—	43	1	no	maximal, Sylow
39	C₂²×C₄₃	#357	1	1	yes	characteristic
40	C₄×C₄₃	—	2	1	no	—
41	C₄×C₄₃	#332	1	1	yes	characteristic
42	C₄×C₄₃	#362	1	1	yes	characteristic
43	C₄×C₄₃	D₃₂	1	1	yes	characteristic
44	C₄×C₄₃	SD₆₄	1	1	yes	characteristic
45	Dic₄₃	—	16	2	no	—
46	#2252	—	43	1	no	—
47	C₄⋊C₃₂	—	43	1	no	—
48	#1371	D₄₃	1	1	yes	characteristic
49	C₂×C₄₃	#1364	1	1	yes	characteristic
50	C₂×C₄₃	#1415	1	1	yes	characteristic
51	C₂×C₄₃	#1420	1	1	yes	characteristic
52	#500	—	86	1	no	—
53	C₂×C₃₂	—	86	1	no	—
54	#366	—	43	2	no	—
55	#366	—	86	1	no	—
56	C₄×C₁₆	C₂×D₄₃	1	1	yes	characteristic
57	#335	—	2	1	no	—
58	C₄₃	#7450	1	1	yes	characteristic, complemented, Sylow
59	C₄⋊Q₈	—	172	1	no	—
60	C₂×C₁₆	C₄×D₄₃	1	1	yes	characteristic
61	C₂×C₁₆	D₁₇₂	1	1	yes	characteristic
62	#107	—	86	2	no	—
63	#107	—	172	1	no	—
64	C₄⋊C₈	—	4	1	no	—
65	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
66	C₃₂	—	172	1	no	—
67	C₂×Q₈	—	344	1	no	—
68	C₂×C₈	—	8	1	no	—
69	C₂×C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
70	C₂×C₈	#10621884	1	1	yes	characteristic
71	C₄⋊C₄	—	344	1	no	—
72	C₄⋊C₄	—	172	2	no	—
73	C₄²	#10621882	1	1	yes	characteristic
74	C₁₆	—	2	1	no	—
75	C₁₆	#10621873	1	1	yes	characteristic
76	C₁₆	Dic₁₇₂	1	1	yes	characteristic
77	Q₈	—	688	1	no	—
78	Q₈	—	688	1	no	—
79	C₂×C₄	—	344	2	no	—
80	C₂×C₄	#13063245	1	1	yes	characteristic
81	C₂×C₄	#13063266	1	1	yes	characteristic
82	C₂×C₄	#13063268	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	16	1	no	—
85	C₈	#13063243	1	1	yes	characteristic
86	C₈	#13063250	1	1	yes	characteristic
87	C₂²	#14582699	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	688	2	no	—
90	C₄	#14582646	1	1	yes	characteristic
91	C₄	#14582714	1	1	yes	characteristic
92	C₄	#14582734	1	1	yes	characteristic
93	C₄	#14582736	1	1	yes	characteristic
94	C₂	#19132651	1	1	yes	characteristic
95	C₂	#19132772	1	1	yes	characteristic
96	C₂	#19132787	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14582699
commutator	C₂×C₁₆×C₄₃	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₄₃
Fitting	C₄₃×#1371	C₂
socle, prime radical	C₂²×C₄₃	#357
cosocle	C₄×C₁₆×C₄₃	C₂²
hypercenter	#1371	D₄₃
hypocenter	C₄₃	#7450
LCS	G ▷ C₂×C₁₆×C₄₃ ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1371

Complements

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

N	H ≅ G/N	type
58. C₄₃	#7450	semidirect

Maximal subgroups

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

subgroup	index
#19136870	2
C₄⋊(C₄₃⋊C₃₂)	2
C₄₃×#1371	2
#7450	43