Finite Group Databasebeta

← #19145802

Subgroups — #19145802

Order 5504.

324 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 111 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
2#125×D43C211yesmaximal, characteristic
3#14583305C211yesmaximal, characteristic, complemented
4#14583269C211yesmaximal, characteristic, complemented
5#14583268C211yesmaximal, characteristic, complemented
6#14583236C212yesmaximal
7#14583231C212yesmaximal
8#14583209C212yesmaximal, complemented
9#14583205C212yesmaximal, complemented
10#14582954C211yesmaximal, characteristic
11C43×#501C211yesmaximal, characteristic, complemented
12#13063325C2211yescharacteristic
13#13063317C2211yescharacteristic
14#13063316—21no—
15#13063316C2211yescharacteristic
16#13063316C2211yescharacteristic
17#13063315—21no—
18#13063315—21no—
19#13063305C2212yes—
20#13063301—21no—
21Q8×Dic43—21no—
22#13063290C2212yes—
23#13063283—21no—
24C4⋊C4×D43—21no—
25C4⋊C4×D43—21no—
26C4⋊C4×D43C2211yescharacteristic
27C4⋊C4×D43C2211yescharacteristic
28C42×D43C2211yescharacteristic
29#13063258C2212yes—
30#13063256C2212yes—
31Dic43⋊C8C2212yes—
32#13063250C2212yes—
33#13063250C2212yes—
34#13063248C2212yes—
35#13063248C2212yes—
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×C4×D43—21no—
45C2×C4×D43—21no—
46C2×C4×D43D411yescharacteristic
47C2×C4×D43D411yescharacteristic
48C2×C4×D43C2311yescharacteristic
49C2×Dic86C2312yes—
50C2×C8×C43C2312yes—
51C4⋊C4×C43—21no—
52C4⋊C4×C43—21no—
53C4⋊C4×C43—21no—
54C4⋊C4×C43C2311yescharacteristic
55C4⋊C4×C43C2312yes—
56C4⋊C4×C43C2311yescharacteristic
57C42×C43C2311yescharacteristic
58(C2×D43)⋊C4—22no—
59C4⋊Dic43—21no—
60C4⋊Dic43—21no—
61C4⋊Dic43—21no—
62C4⋊Dic43—21no—
63C4⋊Dic43—22no—
64C4⋊Dic43C2311yescharacteristic
65C4⋊Dic43C2311yescharacteristic
66Dic43⋊C4—21no—
67Dic43⋊C4—21no—
68Dic43⋊C4—21no—
69Dic43⋊C4—21no—
70Dic43⋊C4—21no—
71Dic43⋊C4—21no—
72Dic43⋊C4—22no—
73C4×Dic43—22no—
74C4×Dic43D411yescharacteristic
75C4×Dic43D411yescharacteristic
76C4×Dic43C2311yescharacteristic
77C2×C43⋊C8C2312yes—
78C22×D43C2×D411yescharacteristic
79Q8×C43—42no—
80C2×C4×C43—22no—
81C2×C4×C43—21no—
82C2×C4×C43—21no—
83C2×C4×C43C2×D411yescharacteristic
84C2×C4×C43C2×D411yescharacteristic
85C2×C4×C43C2411yescharacteristic
86C2×Dic43—22no—
87C2×Dic43—21no—
88C2×Dic43—21no—
89C2×Dic43C2×D411yescharacteristic
90C2×Dic43C2×D411yescharacteristic
91C2×Dic43C2×D411yescharacteristic
92C4×D43—22no—
93C4×D43—22no—
94C4×D43—41no—
95C4×D43—42no—
96C4×D43—42no—
97Dic86—24no—
98C8×C43—22no—
99C43⋊C8—22no—
100C22×C43C22×D411yescharacteristic
101C2×D43—21no—
102C2×D43—21no—
103C2×D43#13712yes—
104C4×C43—21no—
105C4×C43—21no—
106C4×C43—41no—
107C4×C43—41no—
108C4×C43—42no—
109C4×C432−1+412yes—
110Dic43—21no—
111Dic43—21no—
112Dic43—21no—
113Dic43—42no—
114Dic43—41no—
115Dic43—41no—
116#3236—431nomaximal, Sylow
117C2×C43#53611yescharacteristic
118C2×C43C2×#13711yescharacteristic
119C2×C43#57511yescharacteristic
120D43—22no—
121#533—431no—
122C2×#125—431no—
123#501—431no—
124#501D4311yescharacteristic, complemented
125#491—431no—
126#491—431no—
127#484—432no—
128#483—432no—
129#479—432no—
130#479—432no—
131#432—431no—
132C43#323611yescharacteristic, complemented, Sylow
133C4⋊Q8—431no—
134C4⋊Q8C2×D4311yescharacteristic
135#125—431no—
136#125—431no—
137#125—431no—
138#125—861no—
139#125—861no—
140#125—861no—
141#125C2×D4311yescharacteristic
142C22⋊Q8—432no—
143C22⋊Q8—861no—
144C4×Q8—432no—
145C4×Q8—861no—
146#117—861no—
147C2×C4⋊C4—431no—
148C2×C4⋊C4—431no—
149C2×C4⋊C4—861no—
150C2×C4⋊C4—861no—
151C2×C42—431no—
152#107—432no—
153#107C2×D4312yes—
154#106—432no—
155#106C2×D4312yes—
156C4⋊C8—432no—
157#103—432no—
158#103—432no—
159#103—432no—
160#103—432no—
161C22⋊C8—432no—
162#97—431no—
163#97C2×D4311yescharacteristic
164C2×Q8—21no—
165C2×Q8—432no—
166C22×C4—431no—
167C22×C4—431no—
168C22×C4—431no—
169C22×C4—861no—
170C22×C4—861no—
171C2×C8—432no—
172C2×C8C22×D4312yes—
173C4⋊C4—21no—
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4—431no—
177C4⋊C4—431no—
178C4⋊C4—861no—
179C4⋊C4—861no—
180C4⋊C4—861no—
181C4⋊C4—861no—
182C4⋊C4—861no—
183C4⋊C4—861no—
184C4⋊C4—862no—
185C4⋊C4—862no—
186C4⋊C4—861no—
187C4⋊C4—861no—
188C4⋊C4—861no—
189C4⋊C4—861no—
190C4⋊C4C22×D4311yescharacteristic
191C4⋊C4C22×D4311yescharacteristic
192C4⋊C4C22×D4312yes—
193C22⋊C4—862no—
194C42—431no—
195C42—431no—
196C42—431no—
197C42—862no—
198C42C22×D4311yescharacteristic
199C23—431no—
200Q8—42no—
201Q8—864no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—431no—
206C2×C4—431no—
207C2×C4—431no—
208C2×C4—862no—
209C2×C4—862no—
210C2×C4—862no—
211C2×C4—861no—
212C2×C4—861no—
213C2×C4—1721no—
214C2×C4—1722no—
215C2×C4—1722no—
216C2×C4D4×D4311yescharacteristic
217C2×C4D4×D4311yescharacteristic
218C2×C4C23×D4311yescharacteristic
219C8—22no—
220C8—862no—
221C22—432no—
222C22—861no—
223C22—861no—
224C22C2×D4×D4311yescharacteristic
225C4—21no—
226C4—21no—
227C4—41no—
228C4—41no—
229C4—42no—
230C4—861no—
231C4—861no—
232C4—861no—
233C4—1721no—
234C4—1721no—
235C4—1722no—
236C4#1306337312yes—
237C2—862no—
238C2#1458347411yescharacteristic
239C2#137×D4311yescharacteristic
240C2#1458369511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#501C2
socleC22×C43C22×D4
hypercenter#501D43
hypocenterC43#3236
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
3. #14583305C2semidirect
4. #14583269C2semidirect
5. #14583268C2semidirect
8. #14583209C2semidirect
9. #14583205C2semidirect
11. C43×#501C2semidirect
124. #501D43semidirect
132. C43#3236semidirect