Finite Group Databasebeta

← #19145836

Subgroups — #19145836

Order 5504.

328 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583454C211yesmaximal, characteristic, complemented
2#14583434C211yesmaximal, characteristic
3#14583309C211yesmaximal, characteristic, complemented
4#14583261C211yesmaximal, characteristic, complemented
5#14583259C211yesmaximal, characteristic, complemented
6#14583242C212yesmaximal, complemented
7#14583225C212yesmaximal
8#14583209C212yesmaximal, complemented
9#14583202C212yesmaximal, complemented
10#14582954C211yesmaximal, characteristic, complemented
11C43×#501C211yesmaximal, characteristic, complemented
12#13063325C2211yescharacteristic
13#13063320—21no—
14#13063316C2212yes—
15#13063313C2211yescharacteristic
16#13063310—21no—
17#13063305—21no—
18#13063305C2211yescharacteristic
19#13063301—21no—
20#13063300C2211yescharacteristic
21Q8×Dic43—21no—
22#13063290—21no—
23#13063290C2211yescharacteristic
24#13063287—21no—
25#13063287C2211yescharacteristic
26#13063283—21no—
27#13063283C2212yes—
28C42×D43C2211yescharacteristic
29#13063258C2212yes—
30#13063256C2212yes—
31Dic43⋊C8C2212yes—
32#13063250C2212yes—
33#13063248C2212yes—
34#13063247C2212yes—
35#13063245C2212yes—
36(C2×D43)⋊C8C2212yes—
37#13063236C2211yescharacteristic
38C4⋊Q8×C43C2211yescharacteristic
39#125×C43C2211yescharacteristic
40#107×C43C2212yes—
41#106×C43C2212yes—
42#97×C43C2211yescharacteristic
43C2×Q8×C43—21no—
44C2×D172—21no—
45C2×D172C2311yescharacteristic
46C2×C4×D43—21no—
47C2×C4×D43D411yescharacteristic
48C2×C4×D43D411yescharacteristic
49C2×C4×D43C2311yescharacteristic
50C2×Dic86—21no—
51C2×Dic86C2311yescharacteristic
52C2×C8×C43C2312yes—
53C4⋊C4×C43—21no—
54C4⋊C4×C43—21no—
55C4⋊C4×C43—21no—
56C4⋊C4×C43C2311yescharacteristic
57C4⋊C4×C43C2312yes—
58C4⋊C4×C43C2311yescharacteristic
59C42×C43C2311yescharacteristic
60(C2×D43)⋊C4—21no—
61(C2×D43)⋊C4—21no—
62(C2×D43)⋊C4—21no—
63(C2×D43)⋊C4—21no—
64(C2×D43)⋊C4—22no—
65(C2×D43)⋊C4—21no—
66C4⋊Dic43—21no—
67C4⋊Dic43—21no—
68C4⋊Dic43—22no—
69C4⋊Dic43C2312yes—
70Dic43⋊C4—22no—
71Dic43⋊C4—21no—
72C4×Dic43—21no—
73C4×Dic43—22no—
74C4×Dic43D411yescharacteristic
75C4×Dic43D411yescharacteristic
76C4×Dic43C2311yescharacteristic
77C2×C43⋊C8C2312yes—
78C22×D43—21no—
79C22×D43C2×D411yescharacteristic
80Q8×C43—42no—
81C2×C4×C43—22no—
82C2×C4×C43—21no—
83C2×C4×C43—21no—
84C2×C4×C43C2×D411yescharacteristic
85C2×C4×C43C2×D411yescharacteristic
86C2×C4×C43C2411yescharacteristic
87C2×Dic43—22no—
88C2×Dic43—21no—
89C2×Dic43C2×D411yescharacteristic
90C2×Dic43C2×D411yescharacteristic
91C2×Dic43C2×D411yescharacteristic
92D172—22no—
93D172—42no—
94C4×D43—22no—
95C4×D43—41no—
96C4×D43—41no—
97C4×D43—42no—
98Dic86—22no—
99Dic86—42no—
100C8×C43—22no—
101C43⋊C8—22no—
102C22×C43C22×D411yescharacteristic
103C2×D43—21no—
104C2×D43—21no—
105C2×D43—21no—
106C2×D43—41no—
107C2×D43—41no—
108C2×D43—41no—
109C4×C43—21no—
110C4×C43—21no—
111C4×C43—41no—
112C4×C43—41no—
113C4×C43—42no—
114C4×C432−1+412yes—
115Dic43—21no—
116Dic43—21no—
117Dic43—21no—
118Dic43—41no—
119Dic43—42no—
120#3240—431nomaximal, Sylow
121C2×C43#53611yescharacteristic
122C2×C43#57511yescharacteristic
123C2×C43#57511yescharacteristic
124D43—41no—
125D43—81no—
126#533—431no—
127#529—431no—
128#501—431no—
129#501D4311yescharacteristic, complemented
130#489—431no—
131#489—431no—
132#485—432no—
133#482—432no—
134#479—432no—
135#478—432no—
136#432—431no—
137C43#324011yescharacteristic, complemented, Sylow
138C4⋊Q8—431no—
139C4⋊Q8C2×D4311yescharacteristic
140#126—861no—
141#125—432no—
142#125C2×D4311yescharacteristic
143#124—431no—
144#123—861no—
145C22⋊Q8—431no—
146C22⋊Q8—861no—
147C22⋊Q8—861no—
148#121—431no—
149C4×Q8—431no—
150C4×Q8—861no—
151C4×Q8—861no—
152C4×D4—431no—
153C4×D4—861no—
154#117—432no—
155#117—861no—
156C2×C42—431no—
157#107—432no—
158#107C2×D4312yes—
159#106—432no—
160#106C2×D4312yes—
161C4⋊C8—432no—
162#103—432no—
163#103—432no—
164#102—432no—
165#102—432no—
166C22⋊C8—432no—
167#97—431no—
168#97C2×D4311yescharacteristic
169C2×Q8—21no—
170C2×Q8—431no—
171C2×Q8—861no—
172C2×D4—431no—
173C2×D4—861no—
174C22×C4—431no—
175C22×C4—431no—
176C22×C4—431no—
177C22×C4—861no—
178C2×C8—432no—
179C2×C8C22×D4312yes—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—432no—
184C4⋊C4—861no—
185C4⋊C4—861no—
186C4⋊C4—862no—
187C4⋊C4—862no—
188C4⋊C4—861no—
189C4⋊C4C22×D4312yes—
190C4⋊C4C22×D4311yescharacteristic
191C4⋊C4C22×D4311yescharacteristic
192C22⋊C4—861no—
193C22⋊C4—861no—
194C22⋊C4—862no—
195C22⋊C4—861no—
196C22⋊C4—861no—
197C22⋊C4—861no—
198C42—431no—
199C42—431no—
200C42—431no—
201C42—862no—
202C42—861no—
203C42C22×D4311yescharacteristic
204C23—431no—
205C23—861no—
206Q8—42no—
207Q8—862no—
208Q8—1722no—
209D4—862no—
210D4—1722no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—431no—
215C2×C4—431no—
216C2×C4—431no—
217C2×C4—862no—
218C2×C4—861no—
219C2×C4—862no—
220C2×C4—1721no—
221C2×C4—1721no—
222C2×C4—1722no—
223C2×C4D4×D4311yescharacteristic
224C2×C4D4×D4311yescharacteristic
225C2×C4C23×D4311yescharacteristic
226C8—22no—
227C8—862no—
228C22—861no—
229C22—861no—
230C22—861no—
231C22—1721no—
232C22—1721no—
233C22—1721no—
234C22C2×D4×D4311yescharacteristic
235C4—21no—
236C4—21no—
237C4—41no—
238C4—42no—
239C4—41no—
240C4—861no—
241C4—861no—
242C4—861no—
243C4—1722no—
244C4—1721no—
245C4#1306337312yes—
246C2—3441no—
247C2—1721no—
248C2#1458347411yescharacteristic
249C2#1458369511yescharacteristic
250C2#1458369811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#501C2
socleC22×C43C22×D4
hypercenter#501D43
hypocenterC43#3240
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #14583454C2semidirect
3. #14583309C2semidirect
4. #14583261C2semidirect
5. #14583259C2semidirect
6. #14583242C2semidirect
8. #14583209C2semidirect
9. #14583202C2semidirect
10. #14582954C2semidirect
11. C43×#501C2semidirect
129. #501D43semidirect
137. C43#3240semidirect