Finite Group Databasebeta

← #19145830

Subgroups — #19145830

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#14583428C211yesmaximal, characteristic
3#14583308C211yesmaximal, characteristic, complemented
4#14583305C211yesmaximal, characteristic, complemented
5#14583258C211yesmaximal, characteristic, complemented
6#14583238C212yesmaximal, complemented
7#14583221C212yesmaximal
8#14583208C212yesmaximal, complemented
9#14583201C212yesmaximal, complemented
10#14582954C211yesmaximal, characteristic, complemented
11C43×#489C211yesmaximal, characteristic, complemented
12#13063325C2211yescharacteristic
13#13063318—21no—
14#13063317C2211yescharacteristic
15#13063316C2212yes—
16#13063307—21no—
17#13063305—21no—
18#13063301—21no—
19#13063301C2211yescharacteristic
20#13063296C2211yescharacteristic
21Q8×Dic43—21no—
22Q8×Dic43C2211yescharacteristic
23#13063290—21no—
24D4×Dic43C2211yescharacteristic
25(C22⋊D43)⋊C4—21no—
26#13063283C2212yes—
27#13063281—21no—
28C42×D43C2211yescharacteristic
29#13063259C2212yes—
30#13063258C2212yes—
31#13063257C2212yes—
32#13063256C2212yes—
33Dic43⋊C8C2212yes—
34#13063249C2212yes—
35#13063246C2212yes—
36(C2×D43)⋊C8C2212yes—
37#13063236C2211yescharacteristic
38C4⋊Q8×C43C2211yescharacteristic
39#124×C43C2211yescharacteristic
40#103×C43C2212yes—
41#102×C43C2212yes—
42#97×C43C2211yescharacteristic
43C2×Q8×C43—21no—
44C2×Q8×C43C2311yescharacteristic
45C2×D4×C43C2311yescharacteristic
46C2×C22⋊D43—21no—
47C22×Dic43—21no—
48C2×C4×D43D411yescharacteristic
49C2×C4×D43D411yescharacteristic
50C2×C4×D43C2311yescharacteristic
51C2×Dic86—21no—
52C2×C8×C43C2312yes—
53C4⋊C4×C43—21no—
54C4⋊C4×C43C2312yes—
55C22⋊C4×C43—21no—
56C22⋊C4×C43—21no—
57C42×C43C2311yescharacteristic
58C22⋊Dic43—21no—
59C22⋊Dic43—21no—
60(C2×D43)⋊C4—22no—
61(C2×D43)⋊C4—21no—
62C4⋊Dic43—21no—
63C4⋊Dic43—22no—
64C4⋊Dic43—21no—
65C4⋊Dic43C2312yes—
66C4⋊Dic43C2311yescharacteristic
67C4⋊Dic43C2311yescharacteristic
68Dic43⋊C4—21no—
69Dic43⋊C4—21no—
70Dic43⋊C4—21no—
71Dic43⋊C4—22no—
72C4×Dic43—21no—
73C4×Dic43—22no—
74C4×Dic43D411yescharacteristic
75C4×Dic43D411yescharacteristic
76C4×Dic43C2311yescharacteristic
77C2×C43⋊C8C2312yes—
78C23×C43—21no—
79C22×D43C2×D411yescharacteristic
80Q8×C43—22no—
81Q8×C43—42no—
82D4×C43—22no—
83C2×C4×C43—21no—
84C2×C4×C43—22no—
85C2×C4×C43C2×D411yescharacteristic
86C2×C4×C43C2×D411yescharacteristic
87C2×C4×C43C2411yescharacteristic
88C22⋊D43—42no—
89C2×Dic43—21no—
90C2×Dic43—22no—
91C2×Dic43—21no—
92C2×Dic43—42no—
93C2×Dic43C2×D411yescharacteristic
94C2×Dic43C2×D411yescharacteristic
95C2×Dic43C2×D411yescharacteristic
96C4×D43—22no—
97C4×D43—41no—
98C4×D43—41no—
99Dic86—42no—
100C8×C43—22no—
101C43⋊C8—22no—
102C22×C43—41no—
103C22×C43—41no—
104C22×C43—41no—
105C22×C43C22×D411yescharacteristic
106C2×D43—21no—
107C2×D43—21no—
108C2×D43—21no—
109C4×C43—21no—
110C4×C43—21no—
111C4×C43—41no—
112C4×C43—42no—
113C4×C432−1+412yes—
114Dic43—21no—
115Dic43—21no—
116Dic43—21no—
117Dic43—42no—
118Dic43—41no—
119Dic43—41no—
120#3240—431nomaximal, Sylow
121C2×C43—81no—
122C2×C43#53611yescharacteristic
123C2×C43#57511yescharacteristic
124C2×C43#57511yescharacteristic
125D43—41no—
126#533—431no—
127#529—431no—
128#501—431no—
129#501—431no—
130#489—431no—
131#489D4311yescharacteristic, complemented
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#125—431no—
143#124C2×D4311yescharacteristic
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#107—432no—
159#106—432no—
160#106—432no—
161C4⋊C8—432no—
162#103—432no—
163#103C2×D4312yes—
164#102—432no—
165#102C2×D4312yes—
166C22⋊C8—432no—
167#97—431no—
168#97C2×D4311yescharacteristic
169C2×Q8—21no—
170C2×Q8—861no—
171C2×Q8C22×D4311yescharacteristic
172C2×D4—861no—
173C2×D4C22×D4311yescharacteristic
174C22×C4—431no—
175C22×C4—431no—
176C22×C4—431no—
177C22×C4—861no—
178C2×C8—432no—
179C2×C8C22×D4312yes—
180C4⋊C4—21no—
181C4⋊C4—432no—
182C4⋊C4—431no—
183C4⋊C4—431no—
184C4⋊C4—861no—
185C4⋊C4—861no—
186C4⋊C4—862no—
187C4⋊C4—862no—
188C4⋊C4—861no—
189C4⋊C4—861no—
190C4⋊C4—861no—
191C4⋊C4C22×D4312yes—
192C22⋊C4—21no—
193C22⋊C4—21no—
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—21no—
205C23—431no—
206Q8—22no—
207Q8—42no—
208Q8—1722no—
209D4—22no—
210D4—1722no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—431no—
214C2×C4—431no—
215C2×C4—431no—
216C2×C4—862no—
217C2×C4—861no—
218C2×C4—862no—
219C2×C4—861no—
220C2×C4—1721no—
221C2×C4—1721no—
222C2×C4—1722no—
223C2×C4D4×D4311yescharacteristic
224C2×C4D4×D4311yescharacteristic
225C2×C4C23×D4311yescharacteristic
226C8—22no—
227C8—862no—
228C22—41no—
229C22—41no—
230C22—41no—
231C22—861no—
232C22—861no—
233C22—861no—
234C22C2×D4×D4311yescharacteristic
235C4—21no—
236C4—21no—
237C4—42no—
238C4—41no—
239C4—861no—
240C4—861no—
241C4—861no—
242C4—1721no—
243C4—1721no—
244C4—1722no—
245C4#1306337212yes—
246C2—81no—
247C2—1721no—
248C2#1458346911yescharacteristic
249C2#1458369511yescharacteristic
250C2#1458369811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#489C2
socleC22×C43C22×D4
hypercenter#489D43
hypocenterC43#3240
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #14583454C2semidirect
3. #14583308C2semidirect
4. #14583305C2semidirect
5. #14583258C2semidirect
6. #14583238C2semidirect
8. #14583208C2semidirect
9. #14583201C2semidirect
10. #14582954C2semidirect
11. C43×#489C2semidirect
131. #489D43semidirect
137. C43#3240semidirect