Finite Group Databasebeta

← #19146161

Subgroups — #19146161

Order 5504.

472 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063355C211yesmaximal, characteristic, complemented
2C22×#10621885C211yesmaximal, characteristic, complemented
3D4×Dic86C211yesmaximal, characteristic, complemented
4#14583294C211yesmaximal, characteristic, complemented
5#14583155C211yesmaximal, characteristic, complemented
6#14583126C211yesmaximal, characteristic, complemented
7#14583118C211yesmaximal, characteristic, complemented
8#14583109C211yesmaximal, characteristic, complemented
9#14583061C211yesmaximal, characteristic, complemented
10#14583055C211yesmaximal, characteristic, complemented
11#14583054C211yesmaximal, characteristic, complemented
12#14583037C211yesmaximal, characteristic, complemented
13#14583004C211yesmaximal, characteristic, complemented
14#14582971C211yesmaximal, characteristic, complemented
15C43×#548C211yesmaximal, characteristic
16C22×Dic86C2211yescharacteristic
17C22×Dic86C2211yescharacteristic
18#13063355—24no—
19C2×#10621885—24no—
20C2×#10621885C2211yescharacteristic
21C2×#10621885C2211yescharacteristic
22C2×#10621885C2211yescharacteristic
23C2×#10621885C2211yescharacteristic
24C2×#10621885C2211yescharacteristic
25C2×#10621885C2211yescharacteristic
26C2×#10621883C2211yescharacteristic
27C2×#10621883C2211yescharacteristic
28C2×#10621883C2211yescharacteristic
29C2×#10621877C2211yescharacteristic
30C22×C43⋊C8C2211yescharacteristic
31#13063325C2211yescharacteristic
32#13063324—21no—
33#13063304C2211yescharacteristic
34#13063304C2211yescharacteristic
35#13063302—21no—
36#13063302—21no—
37C4×Dic86C2211yescharacteristic
38D4×Dic43—21no—
39#13063256C2211yescharacteristic
40C4⋊(C43⋊C8)C2211yescharacteristic
41#13063249C2211yescharacteristic
42#13063249C2211yescharacteristic
43#13063248C2211yescharacteristic
44#13063248C2211yescharacteristic
45#13063248C2211yescharacteristic
46#13063246C2211yescharacteristic
47C22⋊(C43⋊C8)C2211yescharacteristic
48C22⋊(C43⋊C8)C2211yescharacteristic
49#13063236C2211yescharacteristic
50C2×#41×C43C2211yescharacteristic
51C22×Q8×C43C2211yescharacteristic
52#124×C43—21no—
53#124×C43C2211yescharacteristic
54C22⋊Q8×C43—21no—
55C22⋊Q8×C43C2211yescharacteristic
56#121×C43—21no—
57#121×C43C2211yescharacteristic
58C4×Q8×C43C2211yescharacteristic
59C4×D4×C43—21no—
60C4×D4×C43C2211yescharacteristic
61#41×C43—22no—
62#41×C43—41no—
63C2×Q8×C43—21no—
64C2×Q8×C43—22no—
65C2×Q8×C43—41no—
66C2×Q8×C43C2311yescharacteristic
67C2×Q8×C43C2311yescharacteristic
68C2×D4×C43—21no—
69C2×D4×C43—21no—
70C2×D4×C43D411yescharacteristic
71C2×D4×C43C2311yescharacteristic
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43C2311yescharacteristic
75C22×C4×C43C2311yescharacteristic
76C22×Dic43—21no—
77C22×Dic43—21no—
78C2×Dic86—22no—
79C2×Dic86—22no—
80C2×Dic86—21no—
81C2×Dic86—21no—
82C2×Dic86—41no—
83C2×Dic86—41no—
84C2×Dic86C2311yescharacteristic
85C2×Dic86C2311yescharacteristic
86C2×Dic86C2311yescharacteristic
87C4⋊C4×C43—21no—
88C4⋊C4×C43—21no—
89C4⋊C4×C43D411yescharacteristic
90C4⋊C4×C43C2311yescharacteristic
91C22⋊C4×C43—21no—
92C22⋊C4×C43—21no—
93C22⋊C4×C43—21no—
94C22⋊C4×C43—21no—
95C22⋊C4×C43D411yescharacteristic
96C22⋊C4×C43D411yescharacteristic
97C42×C43—21no—
98C42×C43C2311yescharacteristic
99C22⋊Dic43—21no—
100C22⋊Dic43—21no—
101#10621885—22no—
102#10621885—22no—
103#10621885—22no—
104#10621885—22no—
105#10621885—41no—
106#10621885D414yescomplemented
107#10621883—22no—
108#10621883—22no—
109#10621883—41no—
110C4⋊Dic43—21no—
111C4⋊Dic43—21no—
112C4⋊Dic43C2311yescharacteristic
113Dic43⋊C4—21no—
114Dic43⋊C4—21no—
115Dic43⋊C4—21no—
116C4×Dic43—21no—
117#10621877—22no—
118C2×C43⋊C8—22no—
119C2×C43⋊C8C2311yescharacteristic
120C2×C43⋊C8C2311yescharacteristic
121C2×C43⋊C8C2311yescharacteristic
122C2×C43⋊C8C2311yescharacteristic
123C23×C43—21no—
124C23×C43C2×D411yescharacteristic
125C23×C43C2×D411yescharacteristic
126Q8×C43—21no—
127Q8×C43—21no—
128Q8×C43—21no—
129Q8×C43—42no—
130Q8×C43C2×D412yes—
131D4×C43—22no—
132D4×C43—21no—
133D4×C43—21no—
134D4×C43—42no—
135D4×C43—42no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—42no—
144C2×C4×C43—42no—
145C2×C4×C43C2×D411yescharacteristic
146C2×C4×C43C2×D411yescharacteristic
147C2×C4×C43C2×D411yescharacteristic
148C2×C4×C43C2×D411yescharacteristic
149C2×C4×C43C2411yescharacteristic
150C2×Dic43—21no—
151C2×Dic43—21no—
152C2×Dic43—21no—
153C2×Dic43—21no—
154C2×Dic43—42no—
155C2×Dic43—42no—
156Dic86—21no—
157Dic86—21no—
158Dic86—21no—
159Dic86—21no—
160Dic86—21no—
161Dic86—42no—
162Dic86—42no—
163Dic86C2×D412yes—
164C43⋊C8—21no—
165C43⋊C8—21no—
166C43⋊C8—21no—
167C43⋊C8C2×D412yes—
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—41no—
174C22×C43—41no—
175C22×C43—41no—
176C22×C43#13712yescomplemented
177C22×C43C22×D411yescharacteristic
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—22no—
181C4×C43—21no—
182C4×C43—21no—
183C4×C43—41no—
184C4×C43—41no—
185C4×C43C22×D411yescharacteristic
186C4×C43H(5,𝔽2)11yescharacteristic
187Dic43—22no—
188Dic43—41no—
189Dic43—41no—
190Dic43—41no—
191#3270—431nomaximal, Sylow
192C2×C43—22no—
193C2×C43—41no—
194C2×C43—81no—
195C2×C43D4211yescharacteristic
196C2×C43C2×#13711yescharacteristic
197C2×C43#57811yescharacteristic
198C2×#137—431no—
199C22×Q16—431no—
200D4×Q8—431no—
201#548D4311yescharacteristic
202#497—431no—
203#470—431no—
204#465—431no—
205#464—431no—
206#462—431no—
207#452—431no—
208#451—431no—
209#451—431no—
210#448—431no—
211#441—431no—
212#435—431no—
213C43#327011yescharacteristic, complemented, Sylow
214C2×#41C2×D4311yescharacteristic
215C22×Q8—431no—
216C22×Q8—431no—
217C22×Q8C2×D4311yescharacteristic
218#137—864no—
219C2×Q16—431no—
220C2×Q16—431no—
221C2×Q16—431no—
222C2×Q16—431no—
223C2×Q16—431no—
224C2×Q16—431no—
225C2×Q16—864no—
226C2×SD16—431no—
227C2×SD16—431no—
228C2×SD16—431no—
229C2×M16—431no—
230C22×C8—431no—
231C4⋊Q8—431no—
232C4⋊Q8—861no—
233#124—21no—
234#124C2×D4311yescharacteristic
235C22⋊Q8—21no—
236C22⋊Q8—431no—
237C22⋊Q8—431no—
238C22⋊Q8—861no—
239C22⋊Q8—861no—
240C22⋊Q8C2×D4311yescharacteristic
241#121—21no—
242#121C2×D4311yescharacteristic
243C4×Q8—431no—
244C4×Q8C2×D4311yescharacteristic
245C4×D4—21no—
246C4×D4—861no—
247C4×D4C2×D4311yescharacteristic
248#106—431no—
249C4⋊C8—431no—
250#103—431no—
251#103—431no—
252#103—431no—
253#103—431no—
254#103—431no—
255#102—431no—
256C22⋊C8—431no—
257C22⋊C8—431no—
258#97—431no—
259#41—22no—
260#41—41no—
261C2×Q8—21no—
262C2×Q8—22no—
263C2×Q8—41no—
264C2×Q8—431no—
265C2×Q8—431no—
266C2×Q8—431no—
267C2×Q8—862no—
268C2×Q8—862no—
269C2×Q8—861no—
270C2×Q8—861no—
271C2×Q8—1721no—
272C2×Q8—1721no—
273C2×Q8C22×D4311yescharacteristic
274C2×Q8C22×D4311yescharacteristic
275C2×D4—21no—
276C2×D4—21no—
277C2×D4C22⋊D4311yescharacteristic
278C2×D4C22×D4311yescharacteristic
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—861no—
282C22×C4—861no—
283C22×C4C22×D4311yescharacteristic
284C22×C4C22×D4311yescharacteristic
285Q16—434no—
286Q16—862no—
287Q16—862no—
288Q16—862no—
289Q16—862no—
290Q16—1721no—
291SD16—862no—
292SD16—862no—
293SD16—1721no—
294M16—862no—
295C2×C8—431no—
296C2×C8—431no—
297C2×C8—431no—
298C2×C8—431no—
299C2×C8—862no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—431no—
303C4⋊C4—861no—
304C4⋊C4—861no—
305C4⋊C4—861no—
306C4⋊C4—861no—
307C4⋊C4—861no—
308C4⋊C4C22⋊D4311yescharacteristic
309C4⋊C4C22×D4311yescharacteristic
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—861no—
315C22⋊C4—861no—
316C22⋊C4C22⋊D4311yescharacteristic
317C22⋊C4C22⋊D4311yescharacteristic
318C42—21no—
319C42—861no—
320C42C22×D4311yescharacteristic
321C23—21no—
322C23C2×C22⋊D4311yescharacteristic
323C23C2×C22⋊D4311yescharacteristic
324Q8—21no—
325Q8—21no—
326Q8—21no—
327Q8—42no—
328Q8—432no—
329Q8—861no—
330Q8—861no—
331Q8—861no—
332Q8—861no—
333Q8—861no—
334Q8—1722no—
335Q8—1722no—
336Q8D4×D4312yes—
337D4—22no—
338D4—21no—
339D4—21no—
340D4—42no—
341D4—42no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—861no—
352C2×C4—861no—
353C2×C4—861no—
354C2×C4—861no—
355C2×C4—1722no—
356C2×C4—1722no—
357C2×C4C2×C22⋊D4311yescharacteristic
358C2×C4C2×C22⋊D4311yescharacteristic
359C2×C4C2×C22⋊D4311yescharacteristic
360C2×C4C2×C22⋊D4311yescharacteristic
361C2×C4C23×D4311yescharacteristic
362C8—432no—
363C8—861no—
364C8—861no—
365C8—861no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22#1306335512yescomplemented
375C22C22×C22⋊D4311yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—22no—
381C4—41no—
382C4—41no—
383C4—862no—
384C4—1721no—
385C4—1721no—
386C4—1721no—
387C4C2×D4×D4311yescharacteristic
388C4#1306337011yescharacteristic
389C2—22no—
390C2—41no—
391C2—81no—
392C2D4×C22⋊D4311yescharacteristic
393C2C2×#1306335511yescharacteristic
394C2#1458371411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#548C2
socleC22×C43C22×D4
hypercenter#548D43
hypocenterC43#3270
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#13063355C2semidirect
2. C22×#10621885C2semidirect
3. D4×Dic86C2semidirect
4. #14583294C2semidirect
5. #14583155C2semidirect
6. #14583126C2semidirect
7. #14583118C2semidirect
8. #14583109C2semidirect
9. #14583061C2semidirect
10. #14583055C2semidirect
11. #14583054C2semidirect
12. #14583037C2semidirect
13. #14583004C2semidirect
14. #14582971C2semidirect
106. #10621885D4semidirect
176. C22×C43#137semidirect
213. C43#3270semidirect
374. C22#13063355semidirect