Finite Group Databasebeta

← #25081729

Subgroups — #25081729

Order 11008.

594 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145957C211yesmaximal, characteristic
2#19145813C211yesmaximal, characteristic, complemented
3#19144989C211yesmaximal, characteristic, complemented
4#19134177C211yesmaximal, characteristic, complemented
5#19134170C211yesmaximal, characteristic, complemented
6#19134135C211yesmaximal, characteristic, complemented
7#19134128C211yesmaximal, characteristic, complemented
8#19134053C211yesmaximal, characteristic, complemented
9#19134046C211yesmaximal, characteristic, complemented
10#19134011C211yesmaximal, characteristic, complemented
11#19134004C211yesmaximal, characteristic, complemented
12#19133362C211yesmaximal, characteristic, complemented
13#19133298C211yesmaximal, characteristic, complemented
14#19133275C211yesmaximal, characteristic, complemented
15C43×#2969C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17C2×#13063325C2211yescharacteristic
18#14583309—21no—
19#14583259—21no—
20#14583259—21no—
21#14583258—21no—
22#14583250C2211yescharacteristic
23#14583250C2211yescharacteristic
24#14583246C2211yescharacteristic
25#14583246C2211yescharacteristic
26#14583227—21no—
27#14583210—21no—
28#14583196—21no—
29#14583194C2211yescharacteristic
30#14583194C2211yescharacteristic
31#14583189C2211yescharacteristic
32#14583189C2211yescharacteristic
33#14583184C2211yescharacteristic
34#14583179C2211yescharacteristic
35#14583150—21no—
36#14583147—21no—
37#14583111—21no—
38#14583099C2211yescharacteristic
39#14583094C2211yescharacteristic
40#14582956C2211yescharacteristic
41#14582923C2211yescharacteristic
42#14582901—21no—
43#14582901—21no—
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582647C2211yescharacteristic
51#14582647C2211yescharacteristic
52#14582646C2211yescharacteristic
53#14582646C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C43×#529C2211yescharacteristic
57C43×#446C2211yescharacteristic
58C8×Q8×C43C2211yescharacteristic
59C43×#436—21no—
60C43×#436C2211yescharacteristic
61C43×#435—21no—
62C8×D4×C43C2211yescharacteristic
63C43×#433—21no—
64C43×#431C2211yescharacteristic
65C43×#405—21no—
66C4×M16×C43C2211yescharacteristic
67C2×#10621898—21no—
68C22×Dic86—21no—
69C2×#10621884—21no—
70C2×#10621882—21no—
71C2×#10621877—21no—
72#13063325—21no—
73#13063325—21no—
74#13063325—21no—
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063322C2311yescharacteristic
79#13063313—21no—
80#13063299—21no—
81#13063299—21no—
82C4×D172—21no—
83C4×D172—21no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43—21no—
86#13063258—21no—
87#13063258—21no—
88#13063258—21no—
89#13063256—21no—
90#13063256—21no—
91#13063256—21no—
92C4⋊(C43⋊C8)—21no—
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97#13063250—21no—
98#13063250—21no—
99#13063250—21no—
100#13063250—21no—
101#13063249—21no—
102#13063249—21no—
103#13063249—21no—
104#13063247—21no—
105#13063247—21no—
106#13063247—21no—
107#13063247—21no—
108#13063246—21no—
109#13063246—21no—
110#13063246—21no—
111#13063245—21no—
112#13063245—21no—
113C22⋊(C43⋊C8)—21no—
114#13063236—21no—
115C2×M16×C43—21no—
116C2×M16×C43D411yescharacteristic
117C2×M16×C43D411yescharacteristic
118C22×C8×C43—21no—
119#126×C43—21no—
120#125×C43D411yescharacteristic
121#124×C43D411yescharacteristic
122#123×C43—21no—
123C22⋊Q8×C43D411yescharacteristic
124#121×C43D411yescharacteristic
125C4×Q8×C43C2311yescharacteristic
126C4×D4×C43—21no—
127C4×D4×C43C2311yescharacteristic
128#117×C43—21no—
129C2×C42×C43C2311yescharacteristic
130C4⋊C8×C43—21no—
131C4⋊C8×C43—21no—
132C4⋊C8×C43C2311yescharacteristic
133C4⋊C8×C43C2311yescharacteristic
134C22⋊C8×C43—21no—
135C22⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137#97×C43—21no—
138#97×C43D411yescharacteristic
139#97×C43D411yescharacteristic
140C4×C8×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C2×D411yescharacteristic
145C2×D4×C43—21no—
146C2×D4×C43C2×D411yescharacteristic
147C22×C4×C43—21no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43#4111yescharacteristic
151C2×C22⋊D43—41no—
152C22×Dic43—41no—
153#10621898—42no—
154#10621898—42no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×C4×D43—41no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—41no—
163C2×Dic86—82no—
164M16×C43—41no—
165M16×C43—41no—
166M16×C43—42no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—42no—
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43C2×D411yescharacteristic
179C4⋊C4×C43C2×D411yescharacteristic
180C22⋊C4×C43—21no—
181C22⋊C4×C43—21no—
182C22⋊C4×C43—21no—
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C42×C43—21no—
186C42×C43C2×D411yescharacteristic
187C42×C43C2×D411yescharacteristic
188C42×C43#4111yescharacteristic
189C42×C43C2411yescharacteristic
190#10621884—81no—
191#10621882—81no—
192(C2×D43)⋊C4—41no—
193(C2×D43)⋊C4—41no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—41no—
201C4⋊Dic43—41no—
202#10621877—81no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C23×C43—21no—
208C23×C43#12111yescharacteristic
209C22×D43—41no—
210Q8×C43—21no—
211Q8×C43—21no—
212D4×C43—21no—
213D4×C43—21no—
214D4×C43—81no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43#12111yescharacteristic
226C2×C4×C43#12111yescharacteristic
227C2×C4×C43#12111yescharacteristic
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C22×D411yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C22⋊D43—82no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43—82no—
236D172—41no—
237D172—41no—
238D172—41no—
239D172—41no—
240D172—81no—
241C4×D43—82no—
242Dic86—41no—
243Dic86—41no—
244Dic86—82no—
245Dic86—81no—
246Dic86—81no—
247C8×C43—21no—
248C8×C43—21no—
249C8×C43—21no—
250C8×C43—21no—
251C8×C43—41no—
252C8×C43—41no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257#19382—431nomaximal, Sylow
258C22×C43—21no—
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—41no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43C2×#12111yescharacteristic
265C2×D43—81no—
266C2×D43—81no—
267C2×D43—81no—
268C4×C43—21no—
269C4×C43—21no—
270C4×C43—21no—
271C4×C43—21no—
272C4×C43—41no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43#57511yescharacteristic
276C4×C43#57511yescharacteristic
277C4×C43#57711yescharacteristic
278C4×C43#57811yescharacteristic
279Dic43—81no—
280Dic43—81no—
281Dic43—81no—
282#3251—431no—
283#3238—431no—
284#3141—431no—
285#2969D4311yescharacteristic, complemented
286#1704—431no—
287#1703—431no—
288#1698—431no—
289#1697—431no—
290#1684—431no—
291#1683—431no—
292#1678—431no—
293#1677—431no—
294#1569—431no—
295#1553—431no—
296#1548—431no—
297C2×C43—41no—
298C2×C43—81no—
299C2×C43#304011yescharacteristic
300C2×C43#306311yescharacteristic
301C2×C43#306811yescharacteristic
302D43—161no—
303#532—431no—
304C2×C4⋊Q8—431no—
305#529C2×D4311yescharacteristic
306#501—861no—
307#489—861no—
308#489—861no—
309#489—861no—
310#487—431no—
311#487—431no—
312#486—431no—
313#486—431no—
314#483—861no—
315#480—861no—
316#478—861no—
317#477—431no—
318#477—431no—
319#476—431no—
320#476—431no—
321#475—431no—
322#474—431no—
323#469—861no—
324#468—861no—
325#463—861no—
326#460—431no—
327#459—431no—
328#446C2×D4311yescharacteristic
329C8×Q8C2×D4311yescharacteristic
330#436—21no—
331#436C2×D4311yescharacteristic
332#435—21no—
333C8×D4C2×D4311yescharacteristic
334#433—21no—
335#432—431no—
336#431C2×D4311yescharacteristic
337#423—431no—
338#417—861no—
339#417—861no—
340#405—21no—
341C4×M16C2×D4311yescharacteristic
342#335—431no—
343#335—431no—
344#334—431no—
345#334—431no—
346#333—431no—
347#333—431no—
348#333—431no—
349#333—431no—
350#332—431no—
351#332—431no—
352#331—431no—
353#331—431no—
354C43#1938211yescharacteristic, complemented, Sylow
355C2×#41—861no—
356C22×Q8—861no—
357C2×SD16—861no—
358C2×D8—861no—
359C2×M16—21no—
360C2×M16—861no—
361C2×M16C22⋊D4311yescharacteristic
362C2×M16C22⋊D4311yescharacteristic
363C22×C8—21no—
364C4⋊Q8—431no—
365C4⋊Q8—431no—
366C4⋊Q8—431no—
367C4⋊Q8—861no—
368C4⋊Q8—861no—
369C4⋊Q8—861no—
370#127—431no—
371#126—21no—
372#125D17211yescharacteristic
373#124—861no—
374#124D17211yescharacteristic
375#123—21no—
376C22⋊Q8D17211yescharacteristic
377#121—861no—
378#121—861no—
379#121D17211yescharacteristic
380C4×Q8C22×D4311yescharacteristic
381C4×D4—21no—
382C4×D4—861no—
383C4×D4—861no—
384C4×D4C22×D4311yescharacteristic
385#117—21no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4—861no—
388C2×C42C22×D4311yescharacteristic
389#107—861no—
390#107—861no—
391#107—861no—
392#106—861no—
393#106—861no—
394#106—861no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—861no—
402C4⋊C8C22×D4311yescharacteristic
403C4⋊C8C22×D4311yescharacteristic
404#103—861no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#102—861no—
412#102—861no—
413#102—861no—
414#102—861no—
415#102—861no—
416#102—861no—
417#102—861no—
418#102—861no—
419#102—861no—
420C22⋊C8—21no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8—861no—
424#97—21no—
425#97—861no—
426#97C22⋊D4311yescharacteristic
427#97C22⋊D4311yescharacteristic
428C4×C8—21no—
429C4×C8—21no—
430C4×C8C22×D4311yescharacteristic
431C4×C8C22×D4311yescharacteristic
432#41—1722no—
433#41—1722no—
434C2×Q8—861no—
435C2×Q8—861no—
436C2×Q8—861no—
437C2×Q8—3442no—
438C2×Q8—1721no—
439C2×Q8C2×D17211yescharacteristic
440C2×D4—21no—
441C2×D4—861no—
442C2×D4—861no—
443C2×D4—861no—
444C2×D4—1721no—
445C2×D4C2×D17211yescharacteristic
446C22×C4—21no—
447C22×C4—1721no—
448C22×C4—1721no—
449C22×C4C2×D17211yescharacteristic
450C22×C4#1062189811yescharacteristic
451C22×C4C2×C22⋊D4311yescharacteristic
452SD16—3441no—
453D8—3441no—
454M16—41no—
455M16—41no—
456M16—42no—
457M16—3441no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—42no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8C2×C22⋊D4311yescharacteristic
466C2×C8C2×C22⋊D4311yescharacteristic
467C2×C8C2×C22⋊D4311yescharacteristic
468C2×C8C2×C22⋊D4311yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—1721no—
480C4⋊C4—1721no—
481C4⋊C4C2×D17211yescharacteristic
482C4⋊C4C2×D17211yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—1721no—
489C22⋊C4—1721no—
490C42—21no—
491C42C2×D17211yescharacteristic
492C42#1062189811yescharacteristic
493C42C2×C22⋊D4311yescharacteristic
494C42C23×D4311yescharacteristic
495C23—21no—
496C23—1721no—
497C23#1306329911yescharacteristic
498Q8—21no—
499Q8—21no—
500Q8—3441no—
501Q8—3441no—
502Q8—3442no—
503Q8—1721no—
504Q8—1721no—
505D4—21no—
506D4—21no—
507D4—81no—
508D4—3441no—
509D4—3442no—
510D4—1721no—
511D4—1721no—
512D4—1721no—
513D4—1721no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—3442no—
525C2×C4—3442no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4#1306329911yescharacteristic
530C2×C4#1306329911yescharacteristic
531C2×C4#1306329911yescharacteristic
532C2×C4C22×C22⋊D4311yescharacteristic
533C2×C4C22×D17211yescharacteristic
534C2×C4C2×#1062189811yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—1721no—
542C8—1721no—
543C8—1721no—
544C8—1721no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—3441no—
552C22—3441no—
553C22—3441no—
554C22C2×#1306329911yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—3441no—
563C4—3441no—
564C4—3441no—
565C4#1458369711yescharacteristic
566C4#1458369711yescharacteristic
567C4#1458371111yescharacteristic
568C4#1458371611yescharacteristic
569C2—41no—
570C2—81no—
571C2—6881no—
572C2#1914408911yescharacteristic
573C2#1914428611yescharacteristic
574C2#1914432311yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#2969C2
socleC22×C43C2×#121
prime radical#19145957C2
hypercenter#2969D43
hypocenterC43#19382
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2969

Complements

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

NH ≅ G/Ntype
2. #19145813C2semidirect
3. #19144989C2semidirect
4. #19134177C2semidirect
5. #19134170C2semidirect
6. #19134135C2semidirect
7. #19134128C2semidirect
8. #19134053C2semidirect
9. #19134046C2semidirect
10. #19134011C2semidirect
11. #19134004C2semidirect
12. #19133362C2semidirect
13. #19133298C2semidirect
14. #19133275C2semidirect
15. C43×#2969C2semidirect
285. #2969D43semidirect
354. C43#19382semidirect

Maximal subgroups

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

subgroupindex
#191459572
#191458132
#191449892
#191341772
#191341702
#191341352
#191341282
#191340532
#191340462
#191340112
#191340042
#191333622
#191332982
#191332752
C43×#29692
#1938243