Finite Group Databasebeta

← #19146303

Subgroups — #19146303

Order 5504.

504 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063345C211yesmaximal, characteristic, complemented
2C22×#10621884C211yesmaximal, characteristic, complemented
3#14583545C211yesmaximal, characteristic, complemented
4#14583281C211yesmaximal, characteristic, complemented
5#14583130C211yesmaximal, characteristic, complemented
6#14583126C211yesmaximal, characteristic, complemented
7#14583121C211yesmaximal, characteristic, complemented
8#14583111C211yesmaximal, characteristic, complemented
9#14583059C211yesmaximal, characteristic, complemented
10#14583055C211yesmaximal, characteristic, complemented
11#14583044C211yesmaximal, characteristic, complemented
12#14583032C211yesmaximal, characteristic, complemented
13C4×#10621884C211yesmaximal, characteristic, complemented
14D4×C43⋊C8C211yesmaximal, characteristic, complemented
15C43×#548C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C22×D172C2211yescharacteristic
18#13063345—24no—
19C2×#10621885C2211yescharacteristic, complemented
20C2×#10621885C2211yescharacteristic, complemented
21C2×#10621883C2211yescharacteristic, complemented
22C2×#10621884—24no—
23C2×#10621884C2211yescharacteristic
24C2×#10621884C2211yescharacteristic
25C2×#10621884C2211yescharacteristic
26C2×#10621884C2211yescharacteristic
27C2×#10621882C2211yescharacteristic
28C2×#10621882C2211yescharacteristic
29C22×C43⋊C8C2211yescharacteristic
30C22×C43⋊C8C2211yescharacteristic, complemented
31#13063313C2211yescharacteristic
32#13063310—21no—
33#13063304C2211yescharacteristic
34#13063299C2211yescharacteristic
35#13063298—21no—
36#13063293—21no—
37C4×D172C2211yescharacteristic
38C22⋊C4×D43—21no—
39#13063256C2211yescharacteristic, complemented
40C4⋊(C43⋊C8)C2211yescharacteristic, complemented
41#13063249C2211yescharacteristic, complemented
42#13063249C2211yescharacteristic, complemented
43#13063248C2211yescharacteristic, complemented
44#13063246C2211yescharacteristic, complemented
45#13063245C2211yescharacteristic
46#13063245C2211yescharacteristic
47C22⋊(C43⋊C8)C2211yescharacteristic
48C22⋊(C43⋊C8)C2211yescharacteristic, complemented
49C4×C43⋊C8C2211yescharacteristic, complemented
50C2×#41×C43C2211yescharacteristic, complemented
51C22×Q8×C43C2211yescharacteristic
52#124×C43—21no—
53#124×C43C2211yescharacteristic, complemented
54C22⋊Q8×C43—21no—
55C22⋊Q8×C43C2211yescharacteristic, complemented
56#121×C43—21no—
57#121×C43C2211yescharacteristic
58C4×Q8×C43C2211yescharacteristic, complemented
59C4×D4×C43—21no—
60C4×D4×C43C2211yescharacteristic
61C23×D43—21no—
62#41×C43—22no—
63#41×C43—41no—
64C2×Q8×C43—21no—
65C2×Q8×C43—22no—
66C2×Q8×C43—41no—
67C2×Q8×C43C2311yescharacteristic
68C2×Q8×C43C2311yescharacteristic
69C2×D4×C43—21no—
70C2×D4×C43—21no—
71C2×D4×C43D411yescharacteristic
72C2×D4×C43C2311yescharacteristic
73C22×C4×C43—21no—
74C22×C4×C43—21no—
75C22×C4×C43C2311yescharacteristic
76C22×C4×C43C2311yescharacteristic
77C2×C22⋊D43—21no—
78C2×C22⋊D43—21no—
79#10621898—22no—
80#10621898—41no—
81C2×D172—21no—
82C2×D172—22no—
83C2×D172—41no—
84C2×D172C2311yescharacteristic
85C2×D172C2311yescharacteristic
86C2×C4×D43—21no—
87C2×C4×D43—21no—
88C2×Dic86C2311yescharacteristic
89C4⋊C4×C43—21no—
90C4⋊C4×C43—21no—
91C4⋊C4×C43D411yescharacteristic
92C4⋊C4×C43C2311yescharacteristic
93C22⋊C4×C43—21no—
94C22⋊C4×C43—21no—
95C22⋊C4×C43—21no—
96C22⋊C4×C43—21no—
97C22⋊C4×C43D411yescharacteristic
98C22⋊C4×C43D411yescharacteristic
99C42×C43—21no—
100C42×C43C2311yescharacteristic
101C22⋊Dic43—21no—
102#10621885—22no—
103#10621885—41no—
104#10621884—22no—
105#10621884—22no—
106#10621884—22no—
107#10621884D414yescomplemented
108#10621883—22no—
109#10621882—22no—
110#10621882—41no—
111(C2×D43)⋊C4—21no—
112(C2×D43)⋊C4—21no—
113(C2×D43)⋊C4—21no—
114(C2×D43)⋊C4—21no—
115C4⋊Dic43C2311yescharacteristic
116Dic43⋊C4—21no—
117C2×C43⋊C8—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
126C22×D43—21no—
127C22×D43—21no—
128C22×D43—42no—
129C22×D43—42no—
130C22×D43—81no—
131Q8×C43—21no—
132Q8×C43—21no—
133Q8×C43—21no—
134Q8×C43—42no—
135Q8×C43C2×D412yes—
136D4×C43—22no—
137D4×C43—21no—
138D4×C43—21no—
139D4×C43—42no—
140D4×C43—42no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—21no—
148C2×C4×C43—42no—
149C2×C4×C43—42no—
150C2×C4×C43C2×D411yescharacteristic
151C2×C4×C43C2×D411yescharacteristic
152C2×C4×C43C2×D411yescharacteristic
153C2×C4×C43C2×D411yescharacteristic
154C2×C4×C43C2411yescharacteristic
155C22⋊D43—42no—
156C22⋊D43—81no—
157C2×Dic43—21no—
158C2×Dic43—21no—
159D172—21no—
160D172—21no—
161D172—21no—
162D172—42no—
163D172C2×D412yes—
164C4×D43—42no—
165C4×D43—81no—
166Dic86—21no—
167Dic86—21no—
168C43⋊C8—21no—
169C43⋊C8—21no—
170C43⋊C8—21no—
171C43⋊C8C2×D412yes—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—21no—
176C22×C43—21no—
177C22×C43—41no—
178C22×C43—41no—
179C22×C43—41no—
180C22×C43#13512yescomplemented
181C22×C43C22×D411yescharacteristic
182C2×D43—22no—
183C2×D43—41no—
184C2×D43—41no—
185C2×D43—41no—
186C2×D43—41no—
187C2×D43—41no—
188C2×D43—84no—
189C4×C43—21no—
190C4×C43—21no—
191C4×C43—22no—
192C4×C43—21no—
193C4×C43—21no—
194C4×C43—41no—
195C4×C43—41no—
196C4×C43C22×D411yescharacteristic
197C4×C43H(5,𝔽2)11yescharacteristic
198Dic43—41no—
199Dic43—41no—
200#3282—431nomaximal, Sylow
201C2×C43—22no—
202C2×C43—41no—
203C2×C43—81no—
204C2×C43D4211yescharacteristic
205C2×C43C2×#13511yescharacteristic
206C2×C43#57711yescharacteristic
207D43—42no—
208D43—81no—
209C2×#135—431no—
210C22×SD16—431no—
211#548D4311yescharacteristic, complemented
212#546—431no—
213#495—431no—
214#465—431no—
215#465—431no—
216#464—431no—
217#463—431no—
218#452—431no—
219#451—431no—
220#449—431no—
221#447—431no—
222C4×SD16—431no—
223C8×D4—431no—
224C43#328211yescharacteristic, complemented, Sylow
225C2×#41—431no—
226C2×#41C2×D4311yescharacteristic, complemented
227C22×Q8C2×D4311yescharacteristic
228C22×D4—431no—
229#135—864no—
230C2×Q16—431no—
231C2×Q16—431no—
232C2×SD16—431no—
233C2×SD16—431no—
234C2×SD16—431no—
235C2×SD16—431no—
236C2×SD16—431no—
237C2×SD16—864no—
238C2×D8—431no—
239C2×D8—431no—
240C22×C8—431no—
241C22×C8—431no—
242#124—21no—
243#124—431no—
244#124C2×D4311yescharacteristic, complemented
245#123—861no—
246C22⋊Q8—21no—
247C22⋊Q8—431no—
248C22⋊Q8C2×D4311yescharacteristic, complemented
249#121—21no—
250#121—431no—
251#121—861no—
252#121C2×D4311yescharacteristic
253#120—861no—
254C4×Q8C2×D4311yescharacteristic, complemented
255C4×D4—21no—
256C4×D4—431no—
257C4×D4C2×D4311yescharacteristic
258C2×C22⋊C4—861no—
259#106—431no—
260C4⋊C8—431no—
261#103—431no—
262#103—431no—
263#103—431no—
264#102—431no—
265#102—431no—
266#102—431no—
267C22⋊C8—431no—
268C22⋊C8—431no—
269C4×C8—431no—
270C24—861no—
271#41—22no—
272#41—41no—
273#41—862no—
274#41—1721no—
275C2×Q8—21no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—431no—
279C2×Q8C22×D4311yescharacteristic
280C2×Q8C22×D4311yescharacteristic
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—431no—
284C2×D4—431no—
285C2×D4—862no—
286C2×D4—861no—
287C2×D4—861no—
288C2×D4—861no—
289C2×D4—1721no—
290C2×D4C22⋊D4311yescharacteristic
291C2×D4C22×D4311yescharacteristic
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—861no—
295C22×C4—861no—
296C22×C4C22×D4311yescharacteristic
297C22×C4C22×D4311yescharacteristic
298Q16—862no—
299Q16—1721no—
300SD16—434no—
301SD16—862no—
302SD16—862no—
303SD16—862no—
304SD16—862no—
305D8—862no—
306D8—1721no—
307C2×C8—431no—
308C2×C8—431no—
309C2×C8—431no—
310C2×C8—431no—
311C2×C8—862no—
312C2×C8—862no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—431no—
316C4⋊C4—861no—
317C4⋊C4C22⋊D4311yescharacteristic
318C4⋊C4C22×D4311yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—861no—
324C22⋊C4—861no—
325C22⋊C4—861no—
326C22⋊C4—861no—
327C22⋊C4—861no—
328C22⋊C4C22⋊D4311yescharacteristic
329C22⋊C4C22⋊D4311yescharacteristic
330C42—21no—
331C42C22×D4311yescharacteristic
332C23—21no—
333C23—861no—
334C23—861no—
335C23—3441no—
336C23—1722no—
337C23—1722no—
338C23C2×C22⋊D4311yescharacteristic
339C23C2×C22⋊D4311yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—42no—
344Q8—861no—
345Q8—861no—
346Q8D4×D4312yes—
347D4—22no—
348D4—21no—
349D4—21no—
350D4—42no—
351D4—42no—
352D4—432no—
353D4—861no—
354D4—861no—
355D4—861no—
356D4—3441no—
357D4—1722no—
358D4—1722no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—861no—
369C2×C4—861no—
370C2×C4—3441no—
371C2×C4—1722no—
372C2×C4C2×C22⋊D4311yescharacteristic
373C2×C4C2×C22⋊D4311yescharacteristic
374C2×C4C2×C22⋊D4311yescharacteristic
375C2×C4C2×C22⋊D4311yescharacteristic
376C2×C4C23×D4311yescharacteristic
377C8—432no—
378C8—861no—
379C8—861no—
380C8—861no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—862no—
390C22—3444no—
391C22—1721no—
392C22—1721no—
393C22—1721no—
394C22—1721no—
395C22—1721no—
396C22#1306334512yescomplemented
397C22C22×C22⋊D4311yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—22no—
403C4—41no—
404C4—41no—
405C4—1721no—
406C4—1721no—
407C4C2×D4×D4311yescharacteristic
408C4#1306337011yescharacteristic
409C2—22no—
410C2—41no—
411C2—81no—
412C2—3441no—
413C2—1722no—
414C2D4×C22⋊D4311yescharacteristic
415C2C2×#1306334511yescharacteristic
416C2#1458370711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#548C2
socleC22×C43C22×D4
hypercenter#548D43
hypocenterC43#3282
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×#13063345C2semidirect
2. C22×#10621884C2semidirect
3. #14583545C2semidirect
4. #14583281C2semidirect
5. #14583130C2semidirect
6. #14583126C2semidirect
7. #14583121C2semidirect
8. #14583111C2semidirect
9. #14583059C2semidirect
10. #14583055C2semidirect
11. #14583044C2semidirect
12. #14583032C2semidirect
13. C4×#10621884C2semidirect
14. D4×C43⋊C8C2semidirect
15. C43×#548C2semidirect
19. C2×#10621885C22semidirect
20. C2×#10621885C22semidirect
21. C2×#10621883C22semidirect
30. C22×C43⋊C8C22semidirect
39. #13063256C22semidirect
40. C4⋊(C43⋊C8)C22semidirect
41. #13063249C22semidirect
42. #13063249C22semidirect
43. #13063248C22semidirect
44. #13063246C22semidirect
48. C22⋊(C43⋊C8)C22semidirect
49. C4×C43⋊C8C22semidirect
50. C2×#41×C43C22semidirect
53. #124×C43C22semidirect
55. C22⋊Q8×C43C22semidirect
58. C4×Q8×C43C22semidirect
107. #10621884D4semidirect
180. C22×C43#135semidirect
211. #548D43semidirect
224. C43#3282semidirect
226. C2×#41C2×D43semidirect
244. #124C2×D43semidirect
248. C22⋊Q8C2×D43semidirect
254. C4×Q8C2×D43semidirect
396. C22#13063345semidirect