Finite Group Databasebeta

← #25080602

Subgroups — #25080602

Order 11008.

712 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145154C211yesmaximal, characteristic, complemented
2#19144392C211yesmaximal, characteristic, complemented
3#19144059C211yesmaximal, characteristic
4#19134142C212yesmaximal, complemented
5#19134128C212yesmaximal, complemented
6#19134094C212yesmaximal, complemented
7#19134060C212yesmaximal, complemented
8#19133354C211yesmaximal, characteristic, complemented
9#19133283C211yesmaximal, characteristic, complemented
10#19133270C211yesmaximal, characteristic, complemented
11C2×C43×#436C211yesmaximal, characteristic, complemented
12C2×#13063351—21no—
13#14583456C2211yescharacteristic
14#14583449C2211yescharacteristic
15#14583297C2211yescharacteristic, complemented
16#14583272C2211yescharacteristic, complemented
17#14583250C2211yescharacteristic, complemented
18#14583246C2211yescharacteristic, complemented
19#14583199—22no—
20#14583189C2212yes—
21#14583179C2212yes—
22#14583128—21no—
23#14583128—21no—
24#14583114—22no—
25#14583104C2212yes—
26#14583094C2212yes—
27C4×#10621873—21no—
28C4×#10621873—21no—
29#14582939—21no—
30#14582923C2211yescharacteristic
31#14582923C2211yescharacteristic
32#14582904—21no—
33#14582898—21no—
34#14582652C2212yescomplemented
35#14582652C2212yescomplemented
36#14582647C2212yescomplemented
37#14582646C2212yescomplemented
38#14582644C2212yescomplemented
39#14582642C2212yescomplemented
40C22×M16×C43—21no—
41C2×C4×D4×C43C2211yescharacteristic
42C43×#436—21no—
43C43×#436—21no—
44C43×#436C2212yes—
45C43×#436C2212yes—
46C2×C4⋊C8×C43C2211yescharacteristic
47C2×C22⋊C8×C43—21no—
48C2×C4×C8×C43C2211yescharacteristic
49C2×#10621898—21no—
50#13063351—44no—
51C2×#10621873—21no—
52C2×#10621873—21no—
53C2×#10621883—22no—
54C2×#10621882—22no—
55C2×#10621877—21no—
56C2×#10621877—21no—
57#13063325C2311yescharacteristic
58#13063325C2311yescharacteristic
59#13063325C2311yescharacteristic
60#13063322C2311yescharacteristic
61#13063317—21no—
62#13063313—21no—
63#13063304—21no—
64#13063304—21no—
65#13063299—21no—
66#13063299—21no—
67C4×Dic86—21no—
68C4×Dic86—21no—
69C4×D172—21no—
70C4×D172—21no—
71#13063284—21no—
72#13063258—22no—
73#13063257—21no—
74#13063257—21no—
75#13063256—22no—
76C4⋊(C43⋊C8)—21no—
77C4⋊(C43⋊C8)—21no—
78C4⋊(C43⋊C8)C2312yes—
79C4⋊(C43⋊C8)C2312yes—
80#13063250—21no—
81#13063250—21no—
82#13063248—22no—
83#13063247—21no—
84#13063247—21no—
85#13063246—22no—
86#13063246—22no—
87#13063245—22no—
88C22×D4×C43D411yescharacteristic
89C23×C4×C43—21no—
90C2×M16×C43—22no—
91C2×M16×C43—22no—
92C2×M16×C43—44no—
93C22×C8×C43—21no—
94C22×C8×C43D411yescharacteristic
95C22×C8×C43D411yescharacteristic
96C4×D4×C43—21no—
97C4×D4×C43—21no—
98C4×D4×C43D412yes—
99C4×D4×C43C2312yes—
100C2×C4⋊C4×C43D411yescharacteristic
101C2×C22⋊C4×C43—21no—
102C2×C42×C43C2311yescharacteristic
103C4⋊C8×C43—21no—
104C4⋊C8×C43C2312yes—
105C22⋊C8×C43—22no—
106C22⋊C8×C43—22no—
107C4×C8×C43D411yescharacteristic
108C4×C8×C43D411yescharacteristic
109C4×C8×C43C2311yescharacteristic
110C4×C8×C43C2311yescharacteristic
111C24×C43—21no—
112C2×D4×C43—21no—
113C2×D4×C43—22no—
114C2×D4×C43—22no—
115C2×D4×C43C2×D412yes—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—21no—
119C22×C4×C43—42no—
120C22×C4×C43—42no—
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43#4111yescharacteristic
124C2×C22⋊D43—41no—
125#10621898—42no—
126#10621898—42no—
127C2×D172—21no—
128C2×D172—21no—
129C2×D172—21no—
130C2×C4×D43—41no—
131C2×Dic86—21no—
132C2×Dic86—21no—
133C2×Dic86—21no—
134M16×C43—44no—
135M16×C43—44no—
136C2×C8×C43—22no—
137C2×C8×C43—22no—
138C2×C8×C43—41no—
139C2×C8×C43—42no—
140C2×C8×C43C2×D411yescharacteristic
141C2×C8×C43C2×D411yescharacteristic
142C2×C8×C43C2×D411yescharacteristic
143C2×C8×C43C2×D411yescharacteristic
144C4⋊C4×C43—21no—
145C4⋊C4×C43C2×D412yes—
146C22⋊C4×C43—22no—
147C22⋊C4×C43—22no—
148C42×C43C2×D411yescharacteristic
149C42×C43C2×D411yescharacteristic
150C42×C43#4111yescharacteristic
151C42×C43C2411yescharacteristic
152C22⋊Dic43—41no—
153#10621883—44no—
154#10621882—44no—
155(C2×D43)⋊C4—41no—
156(C2×D43)⋊C4—41no—
157C4⋊Dic43—21no—
158C4⋊Dic43—21no—
159C4⋊Dic43—21no—
160C4⋊Dic43—21no—
161C4⋊Dic43—21no—
162C4⋊Dic43—21no—
163Dic43⋊C4—41no—
164Dic43⋊C4—41no—
165C4×Dic43—41no—
166#10621877—42no—
167#10621877—42no—
168C2×C43⋊C8—22no—
169C2×C43⋊C8—22no—
170#10621873—42no—
171#10621873—42no—
172C23×C43—22no—
173C23×C43—42no—
174C23×C43—42no—
175C23×C43—42no—
176C23×C43#12111yescharacteristic
177C22×D43—41no—
178D4×C43—22no—
179D4×C43—22no—
180D4×C43—42no—
181C2×C4×C43—21no—
182C2×C4×C43—21no—
183C2×C4×C43—22no—
184C2×C4×C43—41no—
185C2×C4×C43—44no—
186C2×C4×C43—42no—
187C2×C4×C43—42no—
188C2×C4×C43—42no—
189C2×C4×C43#12111yescharacteristic
190C2×C4×C43#12111yescharacteristic
191C2×C4×C43#12111yescharacteristic
192C2×C4×C43AGL(1,ℤ/8)12yes—
193C2×C4×C43#13712yes—
194C2×C4×C43C22×D411yescharacteristic
195C2×C4×C43C22×D411yescharacteristic
196C2×C4×C43C2×#4111yescharacteristic
197C22⋊D43—82no—
198C2×Dic43—41no—
199C2×Dic43—41no—
200C2×Dic43—41no—
201D172—41no—
202D172—41no—
203D172—41no—
204D172—41no—
205D172—81no—
206C4×D43—82no—
207Dic86—41no—
208Dic86—41no—
209Dic86—41no—
210Dic86—41no—
211Dic86—81no—
212C8×C43—21no—
213C8×C43—21no—
214C8×C43—21no—
215C8×C43—42no—
216C8×C43AGL(1,ℤ/8)12yescomplemented
217C43⋊C8—42no—
218C43⋊C8—42no—
219#19279—431nomaximal, Sylow
220C22×C43—21no—
221C22×C43—21no—
222C22×C43—42no—
223C22×C43—42no—
224C22×C43—42no—
225C22×C43—84no—
226C22×C43#46812yes—
227C22×C43C2×#12111yescharacteristic
228C2×D43—81no—
229C2×D43—81no—
230C2×D43—81no—
231C4×C43—21no—
232C4×C43—21no—
233C4×C43—21no—
234C4×C43—42no—
235C4×C43#46812yes—
236C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
237C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
238C4×C43C2×#13711yescharacteristic
239C4×C43#57511yescharacteristic
240Dic43—81no—
241Dic43—81no—
242Dic43—81no—
243#3167—431no—
244#3077—431no—
245#3036—431no—
246C2×#436D4311yescharacteristic, complemented
247#1699—432no—
248#1697—432no—
249#1691—432no—
250#1685—432no—
251#1567—431no—
252#1550—431no—
253#1547—431no—
254C2×C43—22no—
255C2×C43—82no—
256C2×C43#303611yescharacteristic
257C2×C43C2×#46811yescharacteristic
258C2×C43#306711yescharacteristic
259D43—161no—
260C2×AGL(1,ℤ/8)—861no—
261C22×M16—21no—
262#533—431no—
263#532—431no—
264C2×C4×D4C2×D4311yescharacteristic
265#498—431no—
266#492—431no—
267#487—431no—
268#486—431no—
269#478—862no—
270#476—432no—
271#474—432no—
272#465—861no—
273#465—861no—
274#463—862no—
275#461—432no—
276#459—432no—
277C4×SD16—861no—
278C4×SD16—861no—
279#436—21no—
280#436—21no—
281#436C2×D4312yes—
282#436C2×D4312yes—
283#428—861no—
284#423—431no—
285#423—431no—
286C2×C4⋊C8C2×D4311yescharacteristic
287#418—861no—
288#417—861no—
289C2×C22⋊C8—21no—
290C2×C4×C8C2×D4311yescharacteristic
291#335—432no—
292#335—432no—
293#333—432no—
294#332—432no—
295#332—432no—
296#331—432no—
297C43#1927911yescharacteristic, complemented, Sylow
298C2×#41—861no—
299C22×D4D17211yescharacteristic
300C23×C4—21no—
301AGL(1,ℤ/8)—1724no—
302C2×SD16—862no—
303C2×SD16—861no—
304C2×SD16—861no—
305C2×D8—862no—
306C2×M16—22no—
307C2×M16—22no—
308C2×M16—44no—
309C2×M16—861no—
310C2×M16—861no—
311C22×C8—21no—
312C22×C8C22⋊D4311yescharacteristic
313C22×C8C22⋊D4311yescharacteristic
314C4⋊Q8—431no—
315C4⋊Q8—431no—
316C4⋊Q8—431no—
317#127—431no—
318#125—861no—
319#124—861no—
320C22⋊Q8—861no—
321C22⋊Q8—861no—
322#121—861no—
323#121—861no—
324C4×Q8—861no—
325C4×Q8—861no—
326C4×D4—21no—
327C4×D4—21no—
328C4×D4—861no—
329C4×D4—861no—
330C4×D4D17212yes—
331C4×D4C22×D4312yes—
332#117—861no—
333C2×C4⋊C4D17211yescharacteristic
334C2×C22⋊C4—21no—
335C2×C42C22×D4311yescharacteristic
336#107—862no—
337#106—861no—
338#106—861no—
339#106—862no—
340C4⋊C8—21no—
341C4⋊C8—432no—
342C4⋊C8—432no—
343C4⋊C8—861no—
344C4⋊C8—861no—
345C4⋊C8C22×D4312yes—
346#103—861no—
347#103—861no—
348#103—862no—
349#102—862no—
350#102—862no—
351#102—861no—
352#102—861no—
353#102—862no—
354C22⋊C8—22no—
355C22⋊C8—22no—
356C4×C8C22⋊D4311yescharacteristic
357C4×C8C22⋊D4311yescharacteristic
358C4×C8C22×D4311yescharacteristic
359C4×C8C22×D4311yescharacteristic
360C24—21no—
361#41—1722no—
362#41—1722no—
363C2×Q8—861no—
364C2×Q8—861no—
365C2×Q8—861no—
366C2×D4—21no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—861no—
370C2×D4—861no—
371C2×D4—861no—
372C2×D4—1721no—
373C2×D4C2×D17212yes—
374C22×C4—21no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—1721no—
380C22×C4C2×D17211yescharacteristic
381C22×C4#1062189811yescharacteristic
382C22×C4C2×C22⋊D4311yescharacteristic
383SD16—1722no—
384SD16—1724no—
385SD16—1722no—
386D8—1724no—
387M16—44no—
388M16—44no—
389M16—1722no—
390M16—1722no—
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—41no—
394C2×C8—42no—
395C2×C8—862no—
396C2×C8—862no—
397C2×C8C2×C22⋊D4311yescharacteristic
398C2×C8C2×C22⋊D4311yescharacteristic
399C2×C8C2×C22⋊D4311yescharacteristic
400C2×C8C2×C22⋊D4311yescharacteristic
401C4⋊C4—21no—
402C4⋊C4—861no—
403C4⋊C4—861no—
404C4⋊C4—861no—
405C4⋊C4—861no—
406C4⋊C4—861no—
407C4⋊C4—861no—
408C4⋊C4—1721no—
409C4⋊C4—1721no—
410C4⋊C4C2×D17212yes—
411C22⋊C4—22no—
412C22⋊C4—22no—
413C22⋊C4—1721no—
414C22⋊C4—1721no—
415C22⋊C4—1721no—
416C42—1721no—
417C42C2×D17211yescharacteristic
418C42#1062189811yescharacteristic
419C42C2×C22⋊D4311yescharacteristic
420C42C23×D4311yescharacteristic
421C23—22no—
422C23—42no—
423C23—42no—
424C23—42no—
425C23—1721no—
426C23#1306329911yescharacteristic
427Q8—3441no—
428Q8—1721no—
429Q8—1721no—
430Q8—1721no—
431Q8—1721no—
432D4—22no—
433D4—22no—
434D4—42no—
435D4—3441no—
436D4—3442no—
437D4—1721no—
438D4—1721no—
439D4—1721no—
440D4—1721no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—22no—
444C2×C4—41no—
445C2×C4—44no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—3442no—
450C2×C4—1721no—
451C2×C4—1721no—
452C2×C4—1721no—
453C2×C4#1306329911yescharacteristic
454C2×C4#1306329911yescharacteristic
455C2×C4#1306329911yescharacteristic
456C2×C4#1306335312yes—
457C2×C4#1306335812yes—
458C2×C4C22×C22⋊D4311yescharacteristic
459C2×C4C22×D17211yescharacteristic
460C2×C4C2×#1062189811yescharacteristic
461C8—21no—
462C8—21no—
463C8—21no—
464C8—42no—
465C8—1722no—
466C8—1722no—
467C8#1306335112yescomplemented
468C22—21no—
469C22—21no—
470C22—42no—
471C22—42no—
472C22—42no—
473C22—84no—
474C22—3441no—
475C22—3441no—
476C22—3441no—
477C22#1458314512yes—
478C22C2×#1306329911yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—42no—
483C4—3441no—
484C4—3441no—
485C4—3441no—
486C4#1458314512yes—
487C4C2×#1306335111yescharacteristic
488C4C2×#1306335311yescharacteristic
489C4C2×#1306335811yescharacteristic
490C4#1458369711yescharacteristic
491C2—22no—
492C2—82no—
493C2—6881no—
494C2#1914405911yescharacteristic
495C2C2×#1458314511yescharacteristic
496C2#1914431511yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#436C2
socleC22×C43C2×#121
prime radical#19144059C2
hypercenterC2×#436D43
hypocenterC43#19279
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
1. #19145154C2semidirect
2. #19144392C2semidirect
4. #19134142C2semidirect
5. #19134128C2semidirect
6. #19134094C2semidirect
7. #19134060C2semidirect
8. #19133354C2semidirect
9. #19133283C2semidirect
10. #19133270C2semidirect
11. C2×C43×#436C2semidirect
15. #14583297C22semidirect
16. #14583272C22semidirect
17. #14583250C22semidirect
18. #14583246C22semidirect
34. #14582652C22semidirect
35. #14582652C22semidirect
36. #14582647C22semidirect
37. #14582646C22semidirect
38. #14582644C22semidirect
39. #14582642C22semidirect
216. C8×C43AGL(1,ℤ/8)semidirect
246. C2×#436D43semidirect
297. C43#19279semidirect
467. C8#13063351semidirect

Maximal subgroups

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

subgroupindex
#191451542
#191443922
#191440592
#191341422
#191341282
#191340942
#191340602
#191333542
#191332832
#191332702
C2×C43×#4362
#1927943