Finite Group Databasebeta

← #25087340

Subgroups — #25087340

Order 11008.

556 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147331C211yesmaximal, characteristic
2#19147276C211yesmaximal, characteristic
3#19147271C211yesmaximal, characteristic, complemented
4#19134240C211yesmaximal, characteristic, complemented
5#19134147C211yesmaximal, characteristic, complemented
6#19134051C211yesmaximal, characteristic, complemented
7#19134046C211yesmaximal, characteristic
8#19133986C211yesmaximal, characteristic, complemented
9#19133871C211yesmaximal, characteristic, complemented
10#19133865C211yesmaximal, characteristic
11#19133815C211yesmaximal, characteristic, complemented
12#19133767C211yesmaximal, characteristic
13#19133446C211yesmaximal, characteristic, complemented
14#19133407C211yesmaximal, characteristic
15C43×#3342C211yesmaximal, characteristic
16Q8×Dic86C2211yescharacteristic
17#14583627C2211yescharacteristic
18#14583295C2211yescharacteristic
19#14583258—21no—
20#14583253—21no—
21#14583251C2211yescharacteristic
22#14583250C2211yescharacteristic
23#14583249C2211yescharacteristic
24#14583249C2211yescharacteristic
25#14583248—21no—
26#14583206—21no—
27#14583194C2211yescharacteristic
28#14583193—21no—
29#14583189C2211yescharacteristic
30#14583184—21no—
31#14583179C2211yescharacteristic
32#14583118—21no—
33#14583118—21no—
34#14583109C2211yescharacteristic
35#14583107—21no—
36#14583106C2211yescharacteristic
37#14583106C2211yescharacteristic
38#14583030C2211yescharacteristic
39Q8×C43⋊C8C2211yescharacteristic
40C8×Dic86C2211yescharacteristic
41#14583004—21no—
42C4×#10621885—21no—
43#14582991—21no—
44C4×#10621883C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582651C2211yescharacteristic
47#14582647C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582645C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53#14582629C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582621C2211yescharacteristic
56C43×#556C2211yescharacteristic
57C43×#556C2211yescharacteristic
58C43×#500C2211yescharacteristic
59C43×#485—21no—
60C43×#485—21no—
61C43×#475C2211yescharacteristic
62C43×#475C2211yescharacteristic
63C43×#467—21no—
64C4×Q16×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic
66C43×#427—21no—
67C2×#10621885—21no—
68C2×#10621885—21no—
69C2×#10621885—21no—
70C2×#10621883D411yescharacteristic
71#13063325—21no—
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063324—21no—
75#13063324—41no—
76#13063323—21no—
77#13063317—21no—
78#13063315—41no—
79Q8×Dic43—21no—
80C4×Dic86—21no—
81C4×Dic86—21no—
82C4×Dic86C2311yescharacteristic
83#13063290—21no—
84#13063258—21no—
85#13063258—21no—
86#13063256—21no—
87#13063256—41no—
88#13063256D411yescharacteristic
89C4⋊(C43⋊C8)—21no—
90C4⋊(C43⋊C8)—21no—
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94Dic43⋊C8—21no—
95#13063250—21no—
96#13063250—21no—
97#13063249—21no—
98#13063249—21no—
99#13063249—21no—
100#13063249—21no—
101#13063249—21no—
102#13063249—21no—
103#13063249—21no—
104#13063248—21no—
105#13063248—41no—
106#13063248D411yescharacteristic
107#13063246—21no—
108#13063246—21no—
109#13063246D411yescharacteristic
110#13063236—21no—
111C4×C43⋊C8—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C2×Q16×C43D411yescharacteristic
116C22×C8×C43—21no—
117C4⋊Q8×C43C2311yescharacteristic
118C4⋊Q8×C43C2311yescharacteristic
119#126×C43—41no—
120#126×C43—41no—
121#124×C43—21no—
122#124×C43—21no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—21no—
125C4×Q8×C43—21no—
126C4×Q8×C43—21no—
127C4×Q8×C43C2311yescharacteristic
128C4×Q8×C43C2311yescharacteristic
129C4×D4×C43C2311yescharacteristic
130#117×C43—21no—
131#117×C43—21no—
132#107×C43—21no—
133#107×C43—21no—
134#107×C43D411yescharacteristic
135#106×C43—21no—
136#106×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#103×C43D411yescharacteristic
141#103×C43D411yescharacteristic
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×Q8×C43C2×D411yescharacteristic
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—41no—
153C2×Dic86C2×D411yescharacteristic
154Q16×C43—41no—
155C2×C8×C43—21no—
156C2×C8×C43—42no—
157C2×C8×C43C2×D411yescharacteristic
158C2×C8×C43C2×D411yescharacteristic
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—41no—
166C4⋊C4×C43—41no—
167C4⋊C4×C43C2×D411yescharacteristic
168C4⋊C4×C43C2×D411yescharacteristic
169C4⋊C4×C43C2×D411yescharacteristic
170C22⋊C4×C43—21no—
171C22⋊C4×C43—41no—
172C22⋊C4×C43—41no—
173C22⋊C4×C43—41no—
174C22⋊C4×C43—41no—
175C42×C43—21no—
176C42×C43—21no—
177C42×C43—41no—
178C42×C43—41no—
179C42×C43C2411yescharacteristic
180#10621885—42no—
181#10621885—42no—
182#10621885—42no—
183#10621883—22no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—41no—
189C4⋊Dic43C2×D411yescharacteristic
190Dic43⋊C4—21no—
191Dic43⋊C4—41no—
192Dic43⋊C4—41no—
193Dic43⋊C4—41no—
194Dic43⋊C4—41no—
195C4×Dic43—21no—
196C4×Dic43—41no—
197C4×Dic43—41no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204C23×C43—21no—
205Q8×C43—21no—
206Q8×C43—21no—
207Q8×C43—21no—
208Q8×C43—21no—
209Q8×C43—41no—
210Q8×C43—41no—
211Q8×C43—41no—
212Q8×C43—41no—
213D4×C43—21no—
214D4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C22×D411yescharacteristic
226C2×C4×C43H(5,𝔽2)11yescharacteristic
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231Dic86—21no—
232Dic86—41no—
233Dic86—41no—
234Dic86—81no—
235Dic86—161no—
236Dic86#13512yes—
237C8×C43—21no—
238C8×C43—21no—
239C8×C43—41no—
240C43⋊C8—21no—
241C43⋊C8—21no—
242C43⋊C8—41no—
243C43⋊C8—41no—
244C43⋊C8—41no—
245C43⋊C8—41no—
246#19848—431nomaximal, Sylow
247C22×C43—41no—
248C22×C43—41no—
249C22×C43—41no—
250C22×C43D4211yescharacteristic
251C4×C43—21no—
252C4×C43—41no—
253C4×C43—41no—
254C4×C43—41no—
255C4×C43—41no—
256C4×C43—41no—
257C4×C43—81no—
258C4×C43—81no—
259C4×C43C2×#13511yescharacteristic
260C4×C43#57511yescharacteristic
261C4×C43#57811yescharacteristic
262C4×C43#57811yescharacteristic
263Dic43—22no—
264Dic43—41no—
265Dic43—81no—
266Dic43—81no—
267#3369—431no—
268#3364—431no—
269#3363—431no—
270#3342D4311yescharacteristic
271#1718—431no—
272#1700—431no—
273#1684—431no—
274#1683—431no—
275#1674—431no—
276#1653—431no—
277#1652—431no—
278#1645—431no—
279#1638—431no—
280#1584—431no—
281SD16⋊C8—431no—
282C2×C43—81no—
283C2×C43#326911yescharacteristic
284C2×C43#328511yescharacteristic
285C2×C43#328911yescharacteristic
286Q82—431no—
287#557—431no—
288#556C2×D4311yescharacteristic
289#556C2×D4311yescharacteristic
290#500C2×D4311yescharacteristic
291#498—431no—
292#489—861no—
293#488—861no—
294#487—431no—
295#487—431no—
296#487—431no—
297#487—431no—
298#487—861no—
299#485—21no—
300#485—21no—
301#479—861no—
302#477—431no—
303#477—861no—
304#476—431no—
305#475—861no—
306#475C2×D4311yescharacteristic
307#475C2×D4311yescharacteristic
308#474—431no—
309#467—21no—
310#464—861no—
311#464—861no—
312#462—431no—
313#462—431no—
314#462—431no—
315#462—861no—
316#446—431no—
317C8×Q8—431no—
318C8×Q8—431no—
319#441—861no—
320C4×Q16—861no—
321C4×Q16—861no—
322C4×Q16C2×D4311yescharacteristic
323C4×SD16—431no—
324C8×D4C2×D4311yescharacteristic
325#427—21no—
326#335—431no—
327#335—431no—
328#333—431no—
329#332—431no—
330#332—431no—
331#332—431no—
332Q8⋊C8—431no—
333Q8⋊C8—431no—
334Q8⋊C8—431no—
335D4⋊C8—431no—
336#322—431no—
337C43#1984811yescharacteristic, complemented, Sylow
338C2×Q16—861no—
339C2×Q16—861no—
340C2×Q16—861no—
341C2×Q16C22⋊D4311yescharacteristic
342C2×SD16—431no—
343C22×C8—21no—
344C4⋊Q8—431no—
345C4⋊Q8—431no—
346C4⋊Q8—861no—
347C4⋊Q8—861no—
348C4⋊Q8—861no—
349C4⋊Q8—1721no—
350C4⋊Q8C22×D4311yescharacteristic
351C4⋊Q8C22×D4311yescharacteristic
352#126—41no—
353#126—41no—
354#125—861no—
355#125—1721no—
356#124—21no—
357#124—21no—
358C22⋊Q8—21no—
359C22⋊Q8—21no—
360C4×Q8—21no—
361C4×Q8—21no—
362C4×Q8—431no—
363C4×Q8—861no—
364C4×Q8—861no—
365C4×Q8—861no—
366C4×Q8—861no—
367C4×Q8C22×D4311yescharacteristic
368C4×Q8C22×D4311yescharacteristic
369C4×D4C22×D4311yescharacteristic
370#117—21no—
371#117—21no—
372#107—21no—
373#107—21no—
374#107—861no—
375#107—861no—
376#107C22⋊D4311yescharacteristic
377#106—21no—
378#106—21no—
379#106—431no—
380#106—861no—
381#106—1721no—
382C4⋊C8—431no—
383C4⋊C8—431no—
384C4⋊C8—431no—
385C4⋊C8—861no—
386C4⋊C8—861no—
387C4⋊C8—861no—
388C4⋊C8C22×D4311yescharacteristic
389#103—21no—
390#103—21no—
391#103—431no—
392#103—861no—
393#103—861no—
394#103—861no—
395#103—861no—
396#103—861no—
397#103—861no—
398#103—861no—
399#103—861no—
400#103—861no—
401#103—861no—
402#103—1721no—
403#103C22⋊D4311yescharacteristic
404#103C22⋊D4311yescharacteristic
405#102—431no—
406#102—861no—
407#102—861no—
408C22⋊C8—21no—
409#97—861no—
410C4×C8—431no—
411C4×C8—431no—
412C4×C8—861no—
413C4×C8—861no—
414C4×C8C22×D4311yescharacteristic
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—431no—
418C2×Q8—861no—
419C2×Q8—861no—
420C2×Q8—1721no—
421C2×Q8C2×C22⋊D4311yescharacteristic
422C2×Q8C2×C22⋊D4311yescharacteristic
423C2×D4D4×D4311yescharacteristic
424C22×C4—21no—
425Q16—41no—
426Q16—1722no—
427Q16—1722no—
428Q16—1722no—
429SD16—862no—
430C2×C8—21no—
431C2×C8—42no—
432C2×C8—431no—
433C2×C8—431no—
434C2×C8—861no—
435C2×C8—861no—
436C2×C8—861no—
437C2×C8—861no—
438C2×C8C2×C22⋊D4311yescharacteristic
439C2×C8C2×C22⋊D4311yescharacteristic
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—41no—
447C4⋊C4—41no—
448C4⋊C4—431no—
449C4⋊C4—861no—
450C4⋊C4—861no—
451C4⋊C4—861no—
452C4⋊C4—861no—
453C4⋊C4—861no—
454C4⋊C4—1721no—
455C4⋊C4—1721no—
456C4⋊C4—1721no—
457C4⋊C4—1721no—
458C4⋊C4—1721no—
459C4⋊C4D4×D4311yescharacteristic
460C4⋊C4C2×C22⋊D4311yescharacteristic
461C4⋊C4C2×C22⋊D4311yescharacteristic
462C22⋊C4—21no—
463C22⋊C4—41no—
464C22⋊C4—41no—
465C22⋊C4—41no—
466C22⋊C4—41no—
467C42—21no—
468C42—21no—
469C42—41no—
470C42—41no—
471C42—861no—
472C42—1721no—
473C42—1721no—
474C42C23×D4311yescharacteristic
475C23—21no—
476Q8—21no—
477Q8—21no—
478Q8—21no—
479Q8—21no—
480Q8—41no—
481Q8—41no—
482Q8—41no—
483Q8—41no—
484Q8—432no—
485Q8—861no—
486Q8—3441no—
487Q8—1721no—
488Q8—1721no—
489Q8—6881no—
490D4—21no—
491D4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—861no—
502C2×C4—861no—
503C2×C4—1721no—
504C2×C4—1721no—
505C2×C4C2×D4×D4311yescharacteristic
506C2×C4C22×C22⋊D4311yescharacteristic
507C2×C4#1306337011yescharacteristic
508C8—21no—
509C8—21no—
510C8—41no—
511C8—861no—
512C8—861no—
513C8—1721no—
514C8—1721no—
515C8—1721no—
516C8—1721no—
517C22—41no—
518C22—41no—
519C22—41no—
520C22D4×C22⋊D4311yescharacteristic
521C4—21no—
522C4—41no—
523C4—41no—
524C4—41no—
525C4—41no—
526C4—41no—
527C4—81no—
528C4—81no—
529C4—862no—
530C4—3441no—
531C4—3441no—
532C4—1721no—
533C4#135×D4311yescharacteristic
534C4#1458369711yescharacteristic
535C4#1458371311yescharacteristic
536C4#1458371411yescharacteristic
537C2—81no—
538C2#1914614611yescharacteristic
539C2#1914633011yescharacteristic
540C2#1914636611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3342C2
socleC22×C43D42
prime radicalC2×D4×C43C2×D4
hypercenter#3342D43
hypocenterC43#19848
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3342

Complements

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

NH ≅ G/Ntype
3. #19147271C2semidirect
4. #19134240C2semidirect
5. #19134147C2semidirect
6. #19134051C2semidirect
8. #19133986C2semidirect
9. #19133871C2semidirect
11. #19133815C2semidirect
13. #19133446C2semidirect
337. C43#19848semidirect

Maximal subgroups

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

subgroupindex
#191473312
#191472762
#191472712
#191342402
#191341472
#191340512
#191340462
#191339862
#191338712
#191338652
#191338152
#191337672
#191334462
#191334072
C43×#33422
#1984843