Finite Group Databasebeta

← #25082039

Subgroups — #25082039

Order 11008.

650 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145528C211yesmaximal, characteristic, complemented
2#19144655C211yesmaximal, characteristic, complemented
3#19143706C211yesmaximal, characteristic, complemented
4#19134051C211yesmaximal, characteristic, complemented
5#19134044C211yesmaximal, characteristic, complemented
6#19134009C211yesmaximal, characteristic, complemented
7#19134002C211yesmaximal, characteristic, complemented
8#19133953C211yesmaximal, characteristic, complemented
9#19133948C211yesmaximal, characteristic, complemented
10#19133945C211yesmaximal, characteristic, complemented
11#19133938C211yesmaximal, characteristic, complemented
12#19133376C211yesmaximal, characteristic, complemented
13#19133291C211yesmaximal, characteristic, complemented
14#19133244C211yesmaximal, characteristic, complemented
15C43×#3115C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17#14583275C2211yescharacteristic
18#14583273C2211yescharacteristic
19#14583249C2211yescharacteristic
20#14583245C2211yescharacteristic
21#14583223—21no—
22#14583194C2211yescharacteristic
23#14583189C2211yescharacteristic
24#14583111—21no—
25#14583111—21no—
26#14583099C2211yescharacteristic
27#14583094C2211yescharacteristic
28#14583044—21no—
29#14583044—21no—
30#14583044—21no—
31Q8×C43⋊C8C2211yescharacteristic
32Q8×C43⋊C8C2211yescharacteristic
33C4×#10621884—21no—
34C4×#10621882—21no—
35D4×C43⋊C8—21no—
36D4×C43⋊C8—21no—
37D4×C43⋊C8C2211yescharacteristic
38D4×C43⋊C8C2211yescharacteristic
39#14582952—21no—
40#14582952C2211yescharacteristic
41#14582952C2211yescharacteristic
42C2×C4⋊(C43⋊C8)—21no—
43C2×C4⋊(C43⋊C8)C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582649C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582645C2211yescharacteristic
51#14582645C2211yescharacteristic
52#14582643C2211yescharacteristic
53#14582643C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C43×#532C2211yescharacteristic
57C4×#41×C43C2211yescharacteristic
58C43×#482—21no—
59C43×#475C2211yescharacteristic
60C43×#474C2211yescharacteristic
61C43×#460C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C43×#449—21no—
64C43×#442—21no—
65C43×#440—21no—
66C43×#432C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621884—21no—
69C2×#10621884—21no—
70C2×#10621884—21no—
71C2×#10621882—21no—
72C2×#10621882—21no—
73C2×#10621882—21no—
74C22×C43⋊C8—21no—
75C22×C43⋊C8—21no—
76C22×C43⋊C8—21no—
77#13063325C2311yescharacteristic
78#13063322C2311yescharacteristic
79#13063313—21no—
80#13063299—21no—
81#13063299—21no—
82C4×D172—21no—
83C4×D172—21no—
84#13063258—21no—
85#13063256—21no—
86C4⋊(C43⋊C8)—21no—
87C4⋊(C43⋊C8)—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)D411yescharacteristic
90C4⋊(C43⋊C8)D411yescharacteristic
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95#13063249—21no—
96#13063249—21no—
97#13063249—21no—
98#13063246—21no—
99#13063246—21no—
100#13063246—21no—
101#13063245—21no—
102#13063245—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)—21no—
105C22⋊(C43⋊C8)—21no—
106C22⋊(C43⋊C8)D411yescharacteristic
107C22⋊(C43⋊C8)D411yescharacteristic
108C4×C43⋊C8—21no—
109C4×C43⋊C8—21no—
110C4×C43⋊C8—21no—
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C2×#41×C43—21no—
114C2×#41×C43D411yescharacteristic
115C2×SD16×C43—21no—
116C2×D8×C43—21no—
117C4⋊Q8×C43C2311yescharacteristic
118#127×C43C2311yescharacteristic
119#124×C43—21no—
120#121×C43—21no—
121#121×C43—21no—
122C4×Q8×C43D411yescharacteristic
123C4×Q8×C43C2311yescharacteristic
124C4×D4×C43—21no—
125C4×D4×C43—21no—
126C4×D4×C43—21no—
127C4×D4×C43—21no—
128C4×D4×C43D411yescharacteristic
129C4×D4×C43C2311yescharacteristic
130#117×C43—21no—
131#117×C43D411yescharacteristic
132C2×C42×C43—21no—
133C2×C42×C43C2311yescharacteristic
134#107×C43—21no—
135#106×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142C22⋊C8×C43—21no—
143#97×C43—21no—
144#41×C43—22no—
145#41×C43—22no—
146#41×C43—81no—
147#41×C43—81no—
148C2×Q8×C43—21no—
149C2×Q8×C43C2×D411yescharacteristic
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—41no—
155C2×D4×C43C2×D411yescharacteristic
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—41no—
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43#4111yescharacteristic
163C2×C22⋊D43—41no—
164#10621898—82no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×C4×D43—41no—
169C2×Dic86—21no—
170SD16×C43—42no—
171D8×C43—42no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
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—41no—
184C22⋊C4×C43—41no—
185C42×C43—21no—
186C42×C43—21no—
187C42×C43—21no—
188C42×C43C2×D411yescharacteristic
189C42×C43C2×D411yescharacteristic
190C42×C43#4111yescharacteristic
191C42×C43C2411yescharacteristic
192#10621884—42no—
193#10621884—81no—
194#10621884—81no—
195#10621882—42no—
196#10621882—81no—
197#10621882—81no—
198(C2×D43)⋊C4—41no—
199(C2×D43)⋊C4—41no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—81no—
207C2×C43⋊C8—81no—
208C2×C43⋊C8—81no—
209C2×C43⋊C8C2×D411yescharacteristic
210C2×C43⋊C8C2×D411yescharacteristic
211C2×C43⋊C8C2×D411yescharacteristic
212C2×C43⋊C8C2×D411yescharacteristic
213C23×C43—21no—
214C23×C43—41no—
215C23×C43#12111yescharacteristic
216C22×D43—41no—
217Q8×C43—21no—
218Q8×C43—41no—
219Q8×C43—41no—
220Q8×C43#13512yes—
221D4×C43—24no—
222D4×C43—21no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—81no—
228D4×C43—82no—
229D4×C43#13512yes—
230C2×C4×C43—24no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—81no—
243C2×C4×C43—82no—
244C2×C4×C43#12111yescharacteristic
245C2×C4×C43#12111yescharacteristic
246C2×C4×C43#12111yescharacteristic
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C22⋊D43—82no—
251C2×Dic43—41no—
252D172—41no—
253D172—41no—
254D172—41no—
255D172—41no—
256D172—81no—
257C4×D43—82no—
258Dic86—81no—
259C8×C43—41no—
260C8×C43—41no—
261C43⋊C8—21no—
262C43⋊C8—21no—
263C43⋊C8—21no—
264C43⋊C8—21no—
265C43⋊C8—41no—
266C43⋊C8—41no—
267C43⋊C8—41no—
268C43⋊C8—41no—
269#19412—431nomaximal, Sylow
270C22×C43—21no—
271C22×C43—22no—
272C22×C43—21no—
273C22×C43—21no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—81no—
277C22×C43—81no—
278C22×C43—81no—
279C22×C43C2×#12111yescharacteristic
280C2×D43—81no—
281C2×D43—81no—
282C2×D43—81no—
283C4×C43—21no—
284C4×C43—21no—
285C4×C43—22no—
286C4×C43—21no—
287C4×C43—21no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—81no—
291C4×C43C2×#13511yescharacteristic
292C4×C43C2×#13511yescharacteristic
293C4×C43#57611yescharacteristic
294C4×C43#57711yescharacteristic
295Dic43—81no—
296#3207—431no—
297#3115D4311yescharacteristic, complemented
298#3106—431no—
299#2988—431no—
300#1684—431no—
301#1683—431no—
302#1678—431no—
303#1677—431no—
304#1668—431no—
305#1667—431no—
306#1666—431no—
307#1665—431no—
308#1572—431no—
309#1551—431no—
310#1540—431no—
311C2×C43—41no—
312C2×C43—42no—
313C2×C43—161no—
314C2×C43#304511yescharacteristic
315C2×C43#305011yescharacteristic
316C2×C43#306811yescharacteristic
317D43—161no—
318#532—431no—
319#532C2×D4311yescharacteristic
320C4×#41C2×D4311yescharacteristic
321#493—431no—
322#492—431no—
323#487—431no—
324#486—431no—
325#482—21no—
326#482—861no—
327#477—431no—
328#476—431no—
329#475C2×D4311yescharacteristic
330#474C2×D4311yescharacteristic
331#463—861no—
332#463—861no—
333#460—431no—
334#460C2×D4311yescharacteristic
335#459—431no—
336#459C2×D4311yescharacteristic
337#449—21no—
338#449—861no—
339#449—861no—
340#449—861no—
341C8×Q8—431no—
342C8×Q8—431no—
343#442—21no—
344#440—21no—
345C4×SD16—861no—
346C4×D8—861no—
347C8×D4—431no—
348C8×D4—431no—
349C8×D4—861no—
350C8×D4—861no—
351#432C2×D4311yescharacteristic
352#431—431no—
353#431—431no—
354#431—861no—
355C2×C4⋊C8—431no—
356C2×C4⋊C8—861no—
357#335—431no—
358#335—431no—
359#334—431no—
360#334—431no—
361#333—431no—
362#333—431no—
363#332—431no—
364#332—431no—
365#331—431no—
366#331—431no—
367#331—431no—
368#331—431no—
369C43#1941211yescharacteristic, complemented, Sylow
370C2×#41—21no—
371C2×#41—861no—
372C2×#41C22⋊D4311yescharacteristic
373C2×SD16—21no—
374C2×SD16—861no—
375C2×SD16—861no—
376C2×SD16—861no—
377C2×D8—21no—
378C2×D8—861no—
379C2×D8—861no—
380C2×D8—861no—
381C22×C8—861no—
382C22×C8—861no—
383C22×C8—861no—
384C4⋊Q8—431no—
385C4⋊Q8C22×D4311yescharacteristic
386#127—431no—
387#127C22×D4311yescharacteristic
388#124—21no—
389#124—861no—
390#121—21no—
391#121—21no—
392#121—861no—
393#121—861no—
394C4×Q8C22⋊D4311yescharacteristic
395C4×Q8C22×D4311yescharacteristic
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4—21no—
400C4×D4—861no—
401C4×D4—861no—
402C4×D4C22⋊D4311yescharacteristic
403C4×D4C22×D4311yescharacteristic
404#117—21no—
405#117C22⋊D4311yescharacteristic
406C2×C42—21no—
407C2×C42C22×D4311yescharacteristic
408#107—21no—
409#107—861no—
410#106—21no—
411#106—861no—
412C4⋊C8—431no—
413C4⋊C8—431no—
414C4⋊C8—431no—
415C4⋊C8—431no—
416C4⋊C8—431no—
417C4⋊C8—431no—
418C4⋊C8—861no—
419C4⋊C8—861no—
420C4⋊C8—861no—
421C4⋊C8C22×D4311yescharacteristic
422C4⋊C8C22×D4311yescharacteristic
423#103—21no—
424#103—861no—
425#103—861no—
426#103—861no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—861no—
431#102—861no—
432#102—861no—
433#102—861no—
434#102—861no—
435C22⋊C8—21no—
436C22⋊C8—431no—
437C22⋊C8—431no—
438C22⋊C8—861no—
439C22⋊C8—861no—
440C22⋊C8—861no—
441#97—21no—
442C4×C8—431no—
443C4×C8—431no—
444C4×C8—861no—
445C4×C8—861no—
446C4×C8—861no—
447#41—22no—
448#41—22no—
449#41—81no—
450#41—81no—
451#41—3442no—
452C2×Q8—21no—
453C2×Q8—861no—
454C2×Q8C2×C22⋊D4311yescharacteristic
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—41no—
460C2×D4—861no—
461C2×D4—861no—
462C2×D4—861no—
463C2×D4—1721no—
464C2×D4C2×C22⋊D4311yescharacteristic
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—41no—
469C22×C4—1721no—
470C22×C4D4×D4311yescharacteristic
471C22×C4#1062190011yescharacteristic
472C22×C4C2×C22⋊D4311yescharacteristic
473SD16—42no—
474SD16—3441no—
475SD16—3441no—
476SD16—1722no—
477D8—42no—
478D8—3441no—
479D8—3441no—
480D8—1722no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—431no—
484C2×C8—431no—
485C2×C8—431no—
486C2×C8—431no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—3441no—
492C2×C8—3441no—
493C2×C8—3441no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4C2×C22⋊D4311yescharacteristic
501C4⋊C4C2×C22⋊D4311yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C22⋊C4—1721no—
508C22⋊C4—1721no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42D4×D4311yescharacteristic
513C42#1062190011yescharacteristic
514C42C2×C22⋊D4311yescharacteristic
515C42C23×D4311yescharacteristic
516C23—21no—
517C23—41no—
518C23—1721no—
519C23#1306329711yescharacteristic
520Q8—21no—
521Q8—41no—
522Q8—41no—
523Q8—3441no—
524Q8#1306334512yes—
525D4—24no—
526D4—21no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—81no—
532D4—82no—
533D4—3441no—
534D4—3442no—
535D4—1721no—
536D4—1721no—
537D4—1721no—
538D4—1721no—
539D4#1306334512yes—
540C2×C4—24no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—81no—
553C2×C4—82no—
554C2×C4—3442no—
555C2×C4—1721no—
556C2×C4#1306329711yescharacteristic
557C2×C4#1306329711yescharacteristic
558C2×C4#1306329711yescharacteristic
559C2×C4C2×D4×D4311yescharacteristic
560C2×C4C22×C22⋊D4311yescharacteristic
561C2×C4C2×#1062190011yescharacteristic
562C8—41no—
563C8—41no—
564C8—861no—
565C8—861no—
566C8—861no—
567C8—861no—
568C8—1721no—
569C8—1721no—
570C8—1721no—
571C8—1721no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22—3441no—
582C22—3441no—
583C22—3441no—
584C22C2×#1306329711yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—22no—
590C4—41no—
591C4—41no—
592C4—81no—
593C4—3441no—
594C4C2×#1306334511yescharacteristic
595C4C2×#1306334511yescharacteristic
596C4#1458370311yescharacteristic
597C4#1458370911yescharacteristic
598C2—41no—
599C2—42no—
600C2—161no—
601C2—6881no—
602C2#1914413811yescharacteristic
603C2#1914417311yescharacteristic
604C2#1914432511yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3115C2
socleC22×C43C2×#121
hypercenter#3115D43
hypocenterC43#19412
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3115

Complements

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

NH ≅ G/Ntype
1. #19145528C2semidirect
2. #19144655C2semidirect
3. #19143706C2semidirect
4. #19134051C2semidirect
5. #19134044C2semidirect
6. #19134009C2semidirect
7. #19134002C2semidirect
8. #19133953C2semidirect
9. #19133948C2semidirect
10. #19133945C2semidirect
11. #19133938C2semidirect
12. #19133376C2semidirect
13. #19133291C2semidirect
14. #19133244C2semidirect
15. C43×#3115C2semidirect
297. #3115D43semidirect
369. C43#19412semidirect

Maximal subgroups

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

subgroupindex
#191455282
#191446552
#191437062
#191340512
#191340442
#191340092
#191340022
#191339532
#191339482
#191339452
#191339382
#191333762
#191332912
#191332442
C43×#31152
#1941243