Finite Group Databasebeta

← #19144987

Subgroups — #19144987

Order 5504.

424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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#14583448C211yesmaximal, characteristic
2C4⋊Q8×D43C211yesmaximal, characteristic, complemented
3#14583261C211yesmaximal, characteristic, complemented
4#14583259C211yesmaximal, characteristic, complemented
5#14583258C211yesmaximal, characteristic, complemented
6#14583248C212yesmaximal, complemented
7#14583244C212yesmaximal, complemented
8#14582899C212yesmaximal, complemented
9#14582897C212yesmaximal, complemented
10#14582851C211yesmaximal, characteristic, complemented
11C43×#489C211yesmaximal, characteristic, complemented
12C2×#10621902C2211yescharacteristic
13C2×#10621900C2211yescharacteristic
14C2×Q8×D43—21no—
15C2×#10621872C2212yes—
16#13063325C2211yescharacteristic
17#13063324—21no—
18#13063324C2212yes—
19#13063323—21no—
20#13063323C2211yescharacteristic
21#13063321C2211yescharacteristic
22#13063313C2211yescharacteristic
23#13063298—21no—
24#13063298—21no—
25(C22⋊D43)⋊C4—21no—
26(C22⋊D43)⋊C4—21no—
27C4⋊C4×D43—21no—
28C4⋊C4×D43C2212yes—
29C42×D43C2211yescharacteristic
30#13063250C2212yes—
31#13063249C2212yes—
32#13063248C2212yes—
33#13063247C2212yes—
34#13063246C2212yes—
35#13063245C2212yes—
36#13063236C2211yescharacteristic
37C8×Dic43C2212yes—
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—
47C2×C22⋊D43—21no—
48C2×C22⋊D43—21no—
49C22×Dic43—21no—
50#10621902—24no—
51Q8×D43—44no—
52#10621900—24no—
53C2×D172—21no—
54C2×D172C2311yescharacteristic
55C2×C4×D43—21no—
56C2×C4×D43—22no—
57C2×C4×D43D411yescharacteristic
58C2×C4×D43D411yescharacteristic
59C2×C4×D43C2311yescharacteristic
60C2×Dic86—21no—
61C2×Dic86—22no—
62C2×Dic86C2311yescharacteristic
63C2×C8×C43C2312yes—
64C4⋊C4×C43—21no—
65C4⋊C4×C43C2312yes—
66C22⋊C4×C43—21no—
67C22⋊C4×C43—21no—
68C42×C43C2311yescharacteristic
69(C2×D43)⋊C4—21no—
70(C2×D43)⋊C4—21no—
71C4⋊Dic43—21no—
72C4⋊Dic43C2312yes—
73Dic43⋊C4—22no—
74Dic43⋊C4—22no—
75Dic43⋊C4—21no—
76Dic43⋊C4—21no—
77C4×Dic43D411yescharacteristic
78C4×Dic43D411yescharacteristic
79C4×Dic43C2311yescharacteristic
80C2×C43⋊C8C2312yes—
81#10621872—24no—
82C23×C43—21no—
83C22×D43—21no—
84C22×D43C2×D411yescharacteristic
85Q8×C43—22no—
86Q8×C43—42no—
87D4×C43—22no—
88C2×C4×C43—21no—
89C2×C4×C43—22no—
90C2×C4×C43C2×D411yescharacteristic
91C2×C4×C43C2×D411yescharacteristic
92C2×C4×C43C2411yescharacteristic
93C22⋊D43—42no—
94C22⋊D43—42no—
95C22⋊D43—42no—
96C2×Dic43—22no—
97C2×Dic43—21no—
98C2×Dic43—42no—
99C2×Dic43C2×D411yescharacteristic
100C2×Dic43C2×D411yescharacteristic
101C2×Dic43C2×D411yescharacteristic
102D172—22no—
103D172—42no—
104C4×D43—22no—
105C4×D43—22no—
106C4×D43—44no—
107C4×D43—42no—
108C4×D43#4114yes—
109Dic86—22no—
110Dic86—42no—
111Dic86—44no—
112C8×C43—22no—
113C43⋊C8—22no—
114C22×C43—41no—
115C22×C43—41no—
116C22×C43—41no—
117C22×C43C22×D411yescharacteristic
118C2×D43—21no—
119C2×D43—21no—
120C2×D43—41no—
121C2×D43—41no—
122C2×D43—41no—
123C2×D43#12412yes—
124C4×C43—21no—
125C4×C43—21no—
126C4×C43—41no—
127C4×C43—42no—
128C4×C43C2×#4112yes—
129Dic43—41no—
130Dic43—42no—
131Dic43#12412yes—
132Dic43AGL(1,ℤ/8)12yes—
133Dic43#13712yes—
134#3141—431nomaximal, Sylow
135C2×C43—81no—
136C2×C43C2×#12411yescharacteristic
137C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C43C2×#13711yescharacteristic
139D43—22no—
140D43—81no—
141#532—431no—
142C2×C4⋊Q8—431no—
143#489—431no—
144#489—431no—
145#489—431no—
146#489D4311yescharacteristic, complemented
147#487—432no—
148#486—432no—
149#417—432no—
150#417—432no—
151C4×M16—431no—
152C43#314111yescharacteristic, complemented, Sylow
153C2×#41—431no—
154C2×#41—431no—
155C22×Q8—861no—
156C2×M16—432no—
157C4⋊Q8—432no—
158C4⋊Q8—431no—
159C4⋊Q8—431no—
160C4⋊Q8—861no—
161C4⋊Q8—861no—
162C4⋊Q8C2×D4311yescharacteristic
163#127—431no—
164#124—431no—
165#124C2×D4311yescharacteristic
166#121—861no—
167#121—861no—
168C4×D4—861no—
169C4×D4—861no—
170C2×C4⋊C4—432no—
171C2×C4⋊C4—861no—
172C2×C42—431no—
173#103—432no—
174#103—432no—
175#103—432no—
176#103C2×D4312yes—
177#102—432no—
178#102—432no—
179#102—432no—
180#102C2×D4312yes—
181#97—431no—
182#97C2×D4311yescharacteristic
183C4×C8—432no—
184#41—864no—
185#41—864no—
186C2×Q8—21no—
187C2×Q8—431no—
188C2×Q8—862no—
189C2×Q8—861no—
190C2×Q8—1724no—
191C2×Q8C22×D4311yescharacteristic
192C2×D4—431no—
193C2×D4—861no—
194C2×D4—861no—
195C2×D4—861no—
196C2×D4—861no—
197C2×D4C22×D4311yescharacteristic
198C22×C4—431no—
199C22×C4—431no—
200C22×C4—431no—
201C22×C4—861no—
202C22×C4—862no—
203C22×C4—861no—
204M16—864no—
205C2×C8—432no—
206C2×C8C22×D4312yes—
207C4⋊C4—21no—
208C4⋊C4—432no—
209C4⋊C4—862no—
210C4⋊C4—862no—
211C4⋊C4—861no—
212C4⋊C4—861no—
213C4⋊C4—861no—
214C4⋊C4C22×D4312yes—
215C22⋊C4—21no—
216C22⋊C4—21no—
217C22⋊C4—861no—
218C22⋊C4—861no—
219C42—431no—
220C42—431no—
221C42—431no—
222C42C22×D4311yescharacteristic
223C23—21no—
224C23—431no—
225C23—861no—
226Q8—22no—
227Q8—42no—
228Q8—862no—
229Q8—1722no—
230Q8—1724no—
231D4—22no—
232D4—862no—
233D4—1722no—
234D4—1722no—
235D4—1722no—
236D4—1722no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—431no—
240C2×C4—431no—
241C2×C4—431no—
242C2×C4—434no—
243C2×C4—862no—
244C2×C4—862no—
245C2×C4—861no—
246C2×C4—862no—
247C2×C4—1722no—
248C2×C4—1724no—
249C2×C4—1722no—
250C2×C4D4×D4311yescharacteristic
251C2×C4D4×D4311yescharacteristic
252C2×C4C23×D4311yescharacteristic
253C8—22no—
254C8—862no—
255C22—41no—
256C22—41no—
257C22—41no—
258C22—432no—
259C22—861no—
260C22—861no—
261C22—1721no—
262C22—1721no—
263C22—1721no—
264C22C2×D4×D4311yescharacteristic
265C4—21no—
266C4—21no—
267C4—41no—
268C4—42no—
269C4—432no—
270C4—432no—
271C4—432no—
272C4—1721no—
273C4—1722no—
274C4#41×D4312yes—
275C2—81no—
276C2—862no—
277C2—3441no—
278C2#124×D4311yescharacteristic
279C2AGL(1,ℤ/8)×D4311yescharacteristic
280C2#137×D4311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#489C2
socleC22×C43C22×D4
hypercenter#489D43
hypocenterC43#3141
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
2. C4⋊Q8×D43C2semidirect
3. #14583261C2semidirect
4. #14583259C2semidirect
5. #14583258C2semidirect
6. #14583248C2semidirect
7. #14583244C2semidirect
8. #14582899C2semidirect
9. #14582897C2semidirect
10. #14582851C2semidirect
11. C43×#489C2semidirect
146. #489D43semidirect
152. C43#3141semidirect