Finite Group Databasebeta

← #25303762

Subgroups — #25303762

Order 11008.

1854 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142882C212yesmaximal
2#19141790C214yesmaximal, complemented
3#19141500C214yesmaximal, complemented
4#19141253C214yesmaximal, complemented
5#19141061C214yesmaximal, complemented
6#19140709C211yesmaximal, characteristic, complemented
7#19140565C211yesmaximal, characteristic, complemented
8#19138835C214yesmaximal
9#19138730C214yesmaximal, complemented
10#19137328C212yesmaximal, complemented
11C2×C43×#380C211yesmaximal, characteristic
12C2×#13063318C2214yes—
13C2×#13063315C2214yescomplemented
14C2×#13063304C2212yes—
15C2×#13063304C2212yes—
16C2×#13063304C2212yes—
17#14582841C2214yescomplemented
18#14582837C2214yescomplemented
19#14582833C2214yescomplemented
20#14582832C2214yescomplemented
21#14582831C2214yescomplemented
22#14582830C2214yescomplemented
23#14582829C2214yescomplemented
24#14582827C2214yes—
25#14582827C2214yes—
26#14582824C2214yes—
27#14582822C2214yes—
28#14582820C2214yescomplemented
29#14582803C2214yescomplemented
30#14582796C2214yescomplemented
31#14582794C2214yescomplemented
32#14582793C2214yes—
33#14582792C2214yes—
34#14582787C2214yes—
35#14582786C2214yescomplemented
36#14582785C2214yescomplemented
37#14582782C2214yescomplemented
38#14582780C2214yescomplemented
39#14582772C2214yes—
40#14582772C2214yes—
41#14582772C2214yes—
42#14582772C2214yes—
43#14582772C2214yes—
44#14582759C2214yes—
45#14582759C2212yes—
46#14582759C2212yes—
47#14582759C2212yes—
48#14582755C2214yes—
49C4×C22⋊Dic43C2214yes—
50C24×C4×C43C2211yescharacteristic
51C22×C4⋊C4×C43C2212yes—
52C22×C22⋊C4×C43C2212yes—
53C43×#380C2214yes—
54C43×#380C2214yes—
55C2×#95×C43C2211yescharacteristic
56C2×#95×C43C2211yescharacteristic
57C22×Dic86C2312yes—
58#13063318—48no—
59#13063315—48no—
60#13063304—28no—
61#13063304—44no—
62#13063304—44no—
63C2×C4⋊Dic43C2312yes—
64C2×C4⋊Dic43C2314yes—
65C2×C4⋊Dic43C2312yes—
66C2×C4⋊Dic43C2314yes—
67C2×C4⋊Dic43C2312yes—
68C2×Dic43⋊C4C2314yes—
69C2×Dic43⋊C4C2314yes—
70C2×Dic43⋊C4C2314yes—
71C2×Dic43⋊C4C2314yes—
72C2×Dic43⋊C4C2314yes—
73C2×Dic43⋊C4C2314yes—
74C2×Dic43⋊C4C2314yes—
75C2×C22⋊Dic43C2314yes—
76C2×C22⋊Dic43C2314yes—
77C2×C22⋊Dic43C2314yes—
78C2×C22⋊Dic43C2314yes—
79C2×C22⋊Dic43C2314yes—
80C2×C22⋊Dic43C2314yes—
81C2×C4×Dic43C2314yes—
82C2×C4×Dic43C2314yes—
83C43⋊#95C2314yes—
84C43⋊#95C2314yes—
85C43⋊#95C2314yes—
86C43⋊#95C2314yes—
87C43⋊#95C2314yes—
88C43⋊#95C2314yes—
89C43⋊#95C2314yes—
90C43⋊#95C2314yes—
91C43⋊#95C2314yes—
92C43⋊#95C2314yes—
93C43⋊#95C2314yes—
94C25×C43C2311yescharacteristic
95C23×C4×C43—24no—
96C23×C4×C43—44no—
97C23×C4×C43C2311yescharacteristic
98C23×C4×C43C2312yes—
99C23×C4×C43C2312yes—
100C23×C4×C43C2312yes—
101C23×C4×C43C2312yes—
102C23×C4×C43C2311yescharacteristic
103C2×C4⋊C4×C43—44no—
104C2×C4⋊C4×C43C2314yes—
105C2×C4⋊C4×C43C2314yes—
106C2×C22⋊C4×C43—44no—
107C2×C22⋊C4×C43C2314yes—
108C2×C22⋊C4×C43C2314yes—
109#95×C43C2314yes—
110#95×C43C2314yes—
111C24×C43—22no—
112C24×C43—22no—
113C24×C43—22no—
114C24×C43—24no—
115C24×C43—42no—
116C24×C43C2411yescharacteristic
117C24×C43C2411yescharacteristic
118C24×C43C2411yescharacteristic
119C22×C4×C43—24no—
120C22×C4×C43—24no—
121C22×C4×C43—24no—
122C22×C4×C43—24no—
123C22×C4×C43—24no—
124C22×C4×C43—22no—
125C22×C4×C43—24no—
126C22×C4×C43—24no—
127C22×C4×C43—42no—
128C22×C4×C43—42no—
129C22×C4×C43—42no—
130C22×C4×C43—42no—
131C22×C4×C43—42no—
132C22×C4×C43—42no—
133C22×C4×C43—42no—
134C22×C4×C43—416no—
135C22×C4×C43#4114yes—
136C22×C4×C43C2414yes—
137C22×C4×C43C2414yes—
138C22×C4×C43C2412yes—
139C22×C4×C43C2412yes—
140C22×Dic43C2414yes—
141C22×Dic43C2414yes—
142C22×Dic43C2414yes—
143C22×Dic43C2414yes—
144C2×Dic86—24no—
145C2×Dic86—42no—
146C2×Dic86—42no—
147C4⋊C4×C43—28no—
148C4⋊C4×C43—44no—
149C22⋊C4×C43—28no—
150C22⋊C4×C43—44no—
151C22⋊Dic43—28no—
152C22⋊Dic43—28no—
153C22⋊Dic43—28no—
154C22⋊Dic43—28no—
155C22⋊Dic43—44no—
156C22⋊Dic43—44no—
157C4⋊Dic43—24no—
158C4⋊Dic43—42no—
159C4⋊Dic43—42no—
160C4⋊Dic43—44no—
161C4⋊Dic43—44no—
162Dic43⋊C4—28no—
163Dic43⋊C4—28no—
164Dic43⋊C4—28no—
165Dic43⋊C4—44no—
166Dic43⋊C4—44no—
167Dic43⋊C4—44no—
168Dic43⋊C4—44no—
169C4×Dic43—44no—
170C4×Dic43—44no—
171C23×C43—22no—
172C23×C43—21no—
173C23×C43—21no—
174C23×C43—28no—
175C23×C43—21no—
176C23×C43—21no—
177C23×C43—22no—
178C23×C43—22no—
179C23×C43—21no—
180C23×C43—22no—
181C23×C43—22no—
182C23×C43—21no—
183C23×C43—48no—
184C23×C43—48no—
185C23×C43—44no—
186C23×C43—44no—
187C23×C43C2×#4112yes—
188C23×C43H(5,𝔽2)12yes—
189C23×C432−1+414yes—
190C23×C432−1+412yes—
191C23×C43C2511yescharacteristic
192C2×C4×C43—28no—
193C2×C4×C43—22no—
194C2×C4×C43—22no—
195C2×C4×C43—22no—
196C2×C4×C43—22no—
197C2×C4×C43—24no—
198C2×C4×C43—24no—
199C2×C4×C43—24no—
200C2×C4×C43—24no—
201C2×C4×C43—24no—
202C2×C4×C43—24no—
203C2×C4×C43—44no—
204C2×C4×C43—48no—
205C2×C4×C43—48no—
206C2×C4×C43—84no—
207C2×C4×C43—84no—
208C2×C4×C43C2×#4114yes—
209C2×C4×C43H(5,𝔽2)14yes—
210C2×Dic43—24no—
211C2×Dic43—24no—
212C2×Dic43—24no—
213C2×Dic43—24no—
214C2×Dic43—24no—
215C2×Dic43—24no—
216C2×Dic43—24no—
217C2×Dic43—24no—
218C2×Dic43—24no—
219C2×Dic43—24no—
220C2×Dic43—24no—
221C2×Dic43—24no—
222Dic86—84no—
223#36728—431nomaximal, Sylow
224C22×C43—22no—
225C22×C43—22no—
226C22×C43—24no—
227C22×C43—24no—
228C22×C43—22no—
229C22×C43—22no—
230C22×C43—24no—
231C22×C43—24no—
232C22×C43—416no—
233C22×C43—41no—
234C22×C43—41no—
235C22×C43—41no—
236C22×C43—41no—
237C22×C43—42no—
238C22×C43—42no—
239C22×C43#54114yes—
240C22×C43C22×#4111yescharacteristic
241C22×C43C2×H(5,𝔽2)12yes—
242C22×C43C2×H(5,𝔽2)11yescharacteristic
243C22×C43C2×2−1+412yes—
244C22×C43C2×2−1+411yescharacteristic
245C4×C43—24no—
246C4×C43—24no—
247C4×C43—44no—
248C4×C43—44no—
249Dic43—44no—
250Dic43—44no—
251Dic43—44no—
252Dic43—44no—
253#2848—432no—
254#2747—434no—
255#2722—434no—
256#2704—434no—
257#2690—434no—
258#2659—431no—
259#2646—431no—
260#2480—434no—
261#2473—434no—
262#2329—432no—
263C2×#380D4311yescharacteristic
264C2×C43—24no—
265C2×C43—42no—
266C2×C43—42no—
267C2×C43C2×#54111yescharacteristic
268C2×C43#349011yescharacteristic
269C2×C43#349211yescharacteristic
270C2×C43#353612yes—
271C2×C43#353812yes—
272C24×C4C2×D4311yescharacteristic
273C2×#126—434no—
274C2×#125—434no—
275C2×C22⋊Q8—432no—
276C2×C22⋊Q8—432no—
277C2×C22⋊Q8—432no—
278C22×C4⋊C4C2×D4312yes—
279C22×C22⋊C4C2×D4312yes—
280#400—434no—
281#400—434no—
282#398—434no—
283#398—434no—
284#398—434no—
285#398—434no—
286#398—434no—
287#397—434no—
288#397—434no—
289#397—434no—
290#396—434no—
291#395—434no—
292#391—434no—
293#389—434no—
294#389—434no—
295#388—434no—
296#388—434no—
297#388—434no—
298#387—434no—
299#387—434no—
300#387—434no—
301#387—434no—
302#385—434no—
303#385—434no—
304#385—434no—
305#385—434no—
306#385—434no—
307#380—432no—
308#380—432no—
309#380—432no—
310#380—434no—
311#380C2×D4314yes—
312#380C2×D4314yes—
313#379—434no—
314C4×C22⋊C4—434no—
315C2×#95C2×D4311yescharacteristic
316C2×#95C2×D4311yescharacteristic
317C43#3672811yescharacteristic, complemented, Sylow
318C25C22×D4311yescharacteristic
319C22×Q8—432no—
320C23×C4—24no—
321C23×C4—44no—
322C23×C4C22×D4311yescharacteristic
323C23×C4C22×D4312yes—
324C23×C4C22×D4312yes—
325C23×C4C22×D4312yes—
326C23×C4C22×D4312yes—
327C23×C4C22×D4311yescharacteristic
328#126—1728no—
329#125—1728no—
330C22⋊Q8—868no—
331C22⋊Q8—1724no—
332C22⋊Q8—1724no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—434no—
335C2×C4⋊C4—434no—
336C2×C4⋊C4—434no—
337C2×C4⋊C4—432no—
338C2×C4⋊C4—432no—
339C2×C4⋊C4—432no—
340C2×C4⋊C4—434no—
341C2×C4⋊C4—434no—
342C2×C4⋊C4—434no—
343C2×C4⋊C4—434no—
344C2×C4⋊C4—434no—
345C2×C4⋊C4—434no—
346C2×C4⋊C4C22×D4314yes—
347C2×C4⋊C4C22×D4314yes—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—434no—
350C2×C22⋊C4—434no—
351C2×C22⋊C4—434no—
352C2×C22⋊C4—434no—
353C2×C22⋊C4—434no—
354C2×C22⋊C4—434no—
355C2×C22⋊C4C22×D4314yes—
356C2×C22⋊C4C22×D4314yes—
357C2×C42—434no—
358C2×C42—434no—
359#95—434no—
360#95—434no—
361#95—434no—
362#95—434no—
363#95—434no—
364#95—434no—
365#95—434no—
366#95—434no—
367#95—434no—
368#95—434no—
369#95—434no—
370#95C22×D4314yes—
371#95C22×D4314yes—
372C24—22no—
373C24—22no—
374C24—22no—
375C24—24no—
376C24—42no—
377C24C23×D4311yescharacteristic
378C24C23×D4311yescharacteristic
379C24C23×D4311yescharacteristic
380C2×Q8—864no—
381C2×Q8—1722no—
382C2×Q8—1722no—
383C22×C4—22no—
384C22×C4—24no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—42no—
392C22×C4—42no—
393C22×C4—42no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—42no—
397C22×C4—42no—
398C22×C4—416no—
399C22×C4—434no—
400C22×C4—434no—
401C22×C4—434no—
402C22×C4—434no—
403C22×C4#1062189814yes—
404C22×C4C23×D4314yes—
405C22×C4C23×D4314yes—
406C22×C4C23×D4312yes—
407C22×C4C23×D4312yes—
408C4⋊C4—28no—
409C4⋊C4—44no—
410C4⋊C4—868no—
411C4⋊C4—864no—
412C4⋊C4—868no—
413C4⋊C4—868no—
414C4⋊C4—1722no—
415C4⋊C4—1722no—
416C4⋊C4—1724no—
417C4⋊C4—1724no—
418C4⋊C4—1724no—
419C4⋊C4—1724no—
420C4⋊C4—1724no—
421C4⋊C4—1724no—
422C22⋊C4—28no—
423C22⋊C4—44no—
424C22⋊C4—868no—
425C22⋊C4—868no—
426C22⋊C4—868no—
427C22⋊C4—868no—
428C22⋊C4—1724no—
429C22⋊C4—1724no—
430C42—1724no—
431C42—1724no—
432C23—22no—
433C23—21no—
434C23—21no—
435C23—28no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—22no—
440C23—22no—
441C23—22no—
442C23—22no—
443C23—21no—
444C23—48no—
445C23—48no—
446C23—44no—
447C23—44no—
448C23C2×#1062189812yes—
449C23#1306337012yes—
450C23#1306337214yes—
451C23#1306337312yes—
452C23C24×D4311yescharacteristic
453Q8—3444no—
454C2×C4—28no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—44no—
466C2×C4—48no—
467C2×C4—48no—
468C2×C4—84no—
469C2×C4—84no—
470C2×C4—864no—
471C2×C4—864no—
472C2×C4—864no—
473C2×C4—864no—
474C2×C4—864no—
475C2×C4—864no—
476C2×C4—864no—
477C2×C4—864no—
478C2×C4—864no—
479C2×C4—864no—
480C2×C4—864no—
481C2×C4—864no—
482C2×C4C2×#1062189814yes—
483C2×C4#1306337014yes—
484C22—22no—
485C22—24no—
486C22—24no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—24no—
491C22—24no—
492C22—416no—
493C22—42no—
494C22—42no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22#1458351114yes—
500C22C22×#1062189811yescharacteristic
501C22C2×#1306337011yescharacteristic
502C22C2×#1306337012yes—
503C22C2×#1306337212yes—
504C22C2×#1306337311yescharacteristic
505C4—24no—
506C4—24no—
507C4—44no—
508C4—44no—
509C4—1724no—
510C4—1724no—
511C4—1724no—
512C4—1724no—
513C2—24no—
514C2—42no—
515C2—42no—
516C2C2×#1458351111yescharacteristic
517C2#1914828411yescharacteristic
518C2#1914830411yescharacteristic
519C2#1914881712yes—
520C2#1914884012yes—
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC2×C43×#380C2
prime radicalC25×C43C23
hypercenterC2×#380D43
hypocenterC43#36728
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. #19141790C2semidirect
3. #19141500C2semidirect
4. #19141253C2semidirect
5. #19141061C2semidirect
6. #19140709C2semidirect
7. #19140565C2semidirect
9. #19138730C2semidirect
10. #19137328C2semidirect
13. C2×#13063315C22semidirect
17. #14582841C22semidirect
18. #14582837C22semidirect
19. #14582833C22semidirect
20. #14582832C22semidirect
21. #14582831C22semidirect
22. #14582830C22semidirect
23. #14582829C22semidirect
28. #14582820C22semidirect
29. #14582803C22semidirect
30. #14582796C22semidirect
31. #14582794C22semidirect
35. #14582786C22semidirect
36. #14582785C22semidirect
37. #14582782C22semidirect
38. #14582780C22semidirect
317. C43#36728semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191428822
#191417902
#191415002
#191412532
#191410612
#191407092
#191405652
#191388352
#191387302
#191373282
C2×C43×#3802
#3672843