Finite Group Databasebeta

← #19146136

Subgroups — #19146136

Order 5504.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063350C211yesmaximal, characteristic, complemented
2C2×#13063345C211yesmaximal, characteristic, complemented
3#14583545C211yesmaximal, characteristic, complemented
4#14583286C211yesmaximal, characteristic, complemented
5#14583143C211yesmaximal, characteristic, complemented
6#14583133C211yesmaximal, characteristic, complemented
7#14583121C211yesmaximal, characteristic, complemented
8#14583091C211yesmaximal, characteristic, complemented
9#14583061C211yesmaximal, characteristic, complemented
10#14583044C211yesmaximal, characteristic, complemented
11#14583042C211yesmaximal, characteristic, complemented
12#14583032C211yesmaximal, characteristic, complemented
13#14582997C211yesmaximal, characteristic, complemented
14#14582971C211yesmaximal, characteristic, complemented
15C43×#550C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C22×D172C2211yescharacteristic
18#13063350—24no—
19#13063345—24no—
20C2×#10621885C2211yescharacteristic, complemented
21C2×#10621883C2211yescharacteristic, complemented
22C2×#10621883C2211yescharacteristic, complemented
23C2×#10621884C2211yescharacteristic
24C2×#10621884C2211yescharacteristic
25C2×#10621882C2211yescharacteristic
26C2×#10621882C2211yescharacteristic
27C2×#10621882C2211yescharacteristic
28C2×#10621882C2211yescharacteristic
29C2×#10621877C2211yescharacteristic
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#13063258C2211yescharacteristic, complemented
40C4⋊(C43⋊C8)C2211yescharacteristic, complemented
41#13063249C2211yescharacteristic, complemented
42#13063248C2211yescharacteristic, complemented
43#13063246C2211yescharacteristic, complemented
44#13063246C2211yescharacteristic, complemented
45#13063245C2211yescharacteristic
46#13063245C2211yescharacteristic
47C22⋊(C43⋊C8)C2211yescharacteristic
48C22⋊(C43⋊C8)C2211yescharacteristic, complemented
49#13063236C2211yescharacteristic, complemented
50C2×#41×C43C2211yescharacteristic
51C2×#41×C43C2211yescharacteristic, complemented
52#127×C43—21no—
53#127×C43C2211yescharacteristic, complemented
54#121×C43—21no—
55#121×C43—21no—
56#121×C43C2211yescharacteristic
57#121×C43C2211yescharacteristic, complemented
58C4×Q8×C43C2211yescharacteristic, complemented
59C4×D4×C43—21no—
60C4×D4×C43C2211yescharacteristic
61C23×D43—21no—
62#41×C43—22no—
63#41×C43—22no—
64#41×C43—41no—
65#41×C43—41no—
66C2×Q8×C43C2311yescharacteristic
67C2×D4×C43—21no—
68C2×D4×C43—21no—
69C2×D4×C43—21no—
70C2×D4×C43—21no—
71C2×D4×C43—21no—
72C2×D4×C43—21no—
73C2×D4×C43D411yescharacteristic
74C2×D4×C43C2311yescharacteristic
75C2×D4×C43C2311yescharacteristic
76C22×C4×C43—21no—
77C22×C4×C43—21no—
78C22×C4×C43C2311yescharacteristic
79C22×C4×C43C2311yescharacteristic
80C2×C22⋊D43—21no—
81C2×C22⋊D43—21no—
82#10621898—22no—
83#10621898—41no—
84C2×D172—21no—
85C2×D172—22no—
86C2×D172—41no—
87C2×D172C2311yescharacteristic
88C2×D172C2311yescharacteristic
89C2×C4×D43—21no—
90C2×C4×D43—21no—
91C2×Dic86C2311yescharacteristic
92C4⋊C4×C43—21no—
93C4⋊C4×C43D411yescharacteristic
94C4⋊C4×C43C2311yescharacteristic
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#10621884—22no—
104#10621884D414yescomplemented
105#10621883—22no—
106#10621883—41no—
107#10621882—22no—
108#10621882—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—
117#10621877—22no—
118C2×C43⋊C8—22no—
119C2×C43⋊C8C2311yescharacteristic
120C2×C43⋊C8C2311yescharacteristic
121C2×C43⋊C8C2311yescharacteristic
122C2×C43⋊C8C2311yescharacteristic
123C23×C43—21no—
124C23×C43—21no—
125C23×C43C2×D411yescharacteristic
126C23×C43C2×D411yescharacteristic
127C22×D43—21no—
128C22×D43—21no—
129C22×D43—42no—
130C22×D43—42no—
131C22×D43—81no—
132Q8×C43—21no—
133Q8×C43C2×D412yes—
134D4×C43—21no—
135D4×C43—21no—
136D4×C43—21no—
137D4×C43—21no—
138D4×C43—41no—
139D4×C43—42no—
140D4×C43—42no—
141D4×C43—42no—
142D4×C43—81no—
143D4×C43—81no—
144D4×C43—81no—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—42no—
152C2×C4×C43—42no—
153C2×C4×C43C2×D411yescharacteristic
154C2×C4×C43C2×D411yescharacteristic
155C2×C4×C43C2×D411yescharacteristic
156C2×C4×C43C2×D411yescharacteristic
157C2×C4×C43C2411yescharacteristic
158C22⋊D43—42no—
159C22⋊D43—81no—
160C2×Dic43—21no—
161C2×Dic43—21no—
162D172—21no—
163D172—21no—
164D172—21no—
165D172—42no—
166D172C2×D412yes—
167C4×D43—42no—
168C4×D43—81no—
169Dic86—21no—
170Dic86—21no—
171C43⋊C8—21no—
172C43⋊C8—21no—
173C43⋊C8—21no—
174C43⋊C8C2×D412yes—
175C22×C43—21no—
176C22×C43—21no—
177C22×C43—21no—
178C22×C43—21no—
179C22×C43—21no—
180C22×C43—21no—
181C22×C43—41no—
182C22×C43—41no—
183C22×C43—41no—
184C22×C43—41no—
185C22×C43—41no—
186C22×C43—41no—
187C22×C43C22×D411yescharacteristic
188C2×D43—22no—
189C2×D43—41no—
190C2×D43—41no—
191C2×D43—41no—
192C2×D43—41no—
193C2×D43—41no—
194C2×D43—84no—
195C4×C43—21no—
196C4×C43—21no—
197C4×C43—22no—
198C4×C43—21no—
199C4×C43—21no—
200C4×C43—41no—
201C4×C43C22×D411yescharacteristic
202C4×C43H(5,𝔽2)11yescharacteristic
203Dic43—41no—
204Dic43—41no—
205#3268—431nomaximal, Sylow
206C2×C43—41no—
207C2×C43—41no—
208C2×C43—81no—
209C2×C43—81no—
210C2×C43D4211yescharacteristic
211C2×C43#57511yescharacteristic
212C2×C43#57611yescharacteristic
213D43—42no—
214D43—81no—
215C2×AGL(1,ℤ/8)—431no—
216C2×#135—431no—
217#550D4311yescharacteristic, complemented
218#546—431no—
219#496—431no—
220#468—431no—
221#466—431no—
222#464—431no—
223#459—431no—
224#452—431no—
225#449—431no—
226#449—431no—
227#447—431no—
228#440—431no—
229#435—431no—
230C43#326811yescharacteristic, complemented, Sylow
231C2×#41—431no—
232C2×#41C2×D4311yescharacteristic
233C2×#41C2×D4311yescharacteristic, complemented
234C22×D4—431no—
235AGL(1,ℤ/8)—864no—
236#135—864no—
237C2×Q16—431no—
238C2×SD16—431no—
239C2×SD16—431no—
240C2×SD16—431no—
241C2×SD16—431no—
242C2×D8—431no—
243C2×D8—431no—
244C2×D8—431no—
245C2×D8—431no—
246C2×M16—431no—
247C22×C8—431no—
248#127—21no—
249#127C2×D4311yescharacteristic, complemented
250#124—431no—
251#123—861no—
252C22⋊Q8—431no—
253#121—21no—
254#121—21no—
255#121—431no—
256#121—861no—
257#121C2×D4311yescharacteristic
258#121C2×D4311yescharacteristic, complemented
259#120—861no—
260C4×Q8C2×D4311yescharacteristic, complemented
261C4×D4—21no—
262C4×D4—431no—
263C4×D4C2×D4311yescharacteristic
264C2×C22⋊C4—861no—
265#107—431no—
266C4⋊C8—431no—
267#103—431no—
268#103—431no—
269#102—431no—
270#102—431no—
271#102—431no—
272#102—431no—
273C22⋊C8—431no—
274C22⋊C8—431no—
275#97—431no—
276C24—861no—
277#41—22no—
278#41—22no—
279#41—41no—
280#41—41no—
281#41—862no—
282#41—1721no—
283C2×Q8—431no—
284C2×Q8C22×D4311yescharacteristic
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—431no—
292C2×D4—431no—
293C2×D4—862no—
294C2×D4—861no—
295C2×D4—861no—
296C2×D4—861no—
297C2×D4—1721no—
298C2×D4C22⋊D4311yescharacteristic
299C2×D4C22×D4311yescharacteristic
300C2×D4C22×D4311yescharacteristic
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—861no—
304C22×C4—861no—
305C22×C4C22×D4311yescharacteristic
306C22×C4C22×D4311yescharacteristic
307Q16—862no—
308SD16—434no—
309SD16—862no—
310SD16—862no—
311SD16—1721no—
312D8—862no—
313D8—862no—
314D8—862no—
315D8—1721no—
316M16—862no—
317C2×C8—431no—
318C2×C8—431no—
319C2×C8—431no—
320C2×C8—431no—
321C2×C8—862no—
322C4⋊C4—21no—
323C4⋊C4—431no—
324C4⋊C4—861no—
325C4⋊C4C22⋊D4311yescharacteristic
326C4⋊C4C22×D4311yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—861no—
330C22⋊C4—861no—
331C22⋊C4—861no—
332C22⋊C4—861no—
333C22⋊C4—861no—
334C22⋊C4C22⋊D4311yescharacteristic
335C22⋊C4C22⋊D4311yescharacteristic
336C42—21no—
337C42C22×D4311yescharacteristic
338C23—21no—
339C23—21no—
340C23—861no—
341C23—861no—
342C23—3441no—
343C23—1722no—
344C23—1722no—
345C23C2×C22⋊D4311yescharacteristic
346C23C2×C22⋊D4311yescharacteristic
347Q8—21no—
348Q8—861no—
349Q8—861no—
350Q8D4×D4312yes—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—41no—
356D4—42no—
357D4—42no—
358D4—42no—
359D4—81no—
360D4—81no—
361D4—81no—
362D4—432no—
363D4—861no—
364D4—861no—
365D4—861no—
366D4—3441no—
367D4—1722no—
368D4—1722no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—861no—
378C2×C4—861no—
379C2×C4—3441no—
380C2×C4—1722no—
381C2×C4C2×C22⋊D4311yescharacteristic
382C2×C4C2×C22⋊D4311yescharacteristic
383C2×C4C2×C22⋊D4311yescharacteristic
384C2×C4C2×C22⋊D4311yescharacteristic
385C2×C4C23×D4311yescharacteristic
386C8—432no—
387C8—861no—
388C8—861no—
389C8—861no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—862no—
403C22—3444no—
404C22—1721no—
405C22—1721no—
406C22—1721no—
407C22—1721no—
408C22—1721no—
409C22C22×C22⋊D4311yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—22no—
415C4—41no—
416C4—1721no—
417C4—1721no—
418C4C2×D4×D4311yescharacteristic
419C4#1306337011yescharacteristic
420C2—41no—
421C2—41no—
422C2—81no—
423C2—81no—
424C2—3441no—
425C2—1722no—
426C2D4×C22⋊D4311yescharacteristic
427C2#1458369711yescharacteristic
428C2#1458370211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#550C2
socleC22×C43C22×D4
hypercenter#550D43
hypocenterC43#3268
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C2×#13063350C2semidirect
2. C2×#13063345C2semidirect
3. #14583545C2semidirect
4. #14583286C2semidirect
5. #14583143C2semidirect
6. #14583133C2semidirect
7. #14583121C2semidirect
8. #14583091C2semidirect
9. #14583061C2semidirect
10. #14583044C2semidirect
11. #14583042C2semidirect
12. #14583032C2semidirect
13. #14582997C2semidirect
14. #14582971C2semidirect
15. C43×#550C2semidirect
20. C2×#10621885C22semidirect
21. C2×#10621883C22semidirect
22. C2×#10621883C22semidirect
30. C22×C43⋊C8C22semidirect
39. #13063258C22semidirect
40. C4⋊(C43⋊C8)C22semidirect
41. #13063249C22semidirect
42. #13063248C22semidirect
43. #13063246C22semidirect
44. #13063246C22semidirect
48. C22⋊(C43⋊C8)C22semidirect
49. #13063236C22semidirect
51. C2×#41×C43C22semidirect
53. #127×C43C22semidirect
57. #121×C43C22semidirect
58. C4×Q8×C43C22semidirect
104. #10621884D4semidirect
217. #550D43semidirect
230. C43#3268semidirect
233. C2×#41C2×D43semidirect
249. #127C2×D43semidirect
258. #121C2×D43semidirect
260. C4×Q8C2×D43semidirect