Finite Group Databasebeta

← #25070809

Subgroups — #25070809

Order 11008.

1078 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145416C211yesmaximal, characteristic, complemented
2#19145401C211yesmaximal, characteristic, complemented
3#19139753C211yesmaximal, characteristic, complemented
4#19133609C214yesmaximal, complemented
5#19133575C214yesmaximal, complemented
6#19133115C211yesmaximal, characteristic, complemented
7#19133111C211yesmaximal, characteristic, complemented
8#19132922C211yesmaximal, characteristic, complemented
9C2×C43×#538C211yesmaximal, characteristic
10C2×#13063304C2211yescharacteristic
11#14583234—21no—
12#14583229—21no—
13#14583227C2212yescomplemented
14#14583210C2212yescomplemented
15#14583155—22no—
16#14583143—22no—
17#14583055—21no—
18#14583054C2212yescomplemented
19#14583050—21no—
20#14583037C2212yescomplemented
21#14582863C2211yescharacteristic
22#14582863C2211yescharacteristic
23#14582824C2212yescomplemented
24#14582811C2212yescomplemented
25#14582793—22no—
26#14582762—21no—
27#14582755—21no—
28C4×C22⋊Dic43C2211yescharacteristic
29#14582636C2214yescomplemented
30#14582633C2214yescomplemented
31#14582623C2214yescomplemented
32C43×#538—22no—
33C43×#538—22no—
34C43×#538—22no—
35C43×#538C2214yes—
36C2×#126×C43—21no—
37C2×#124×C43—21no—
38C2×#123×C43—21no—
39C2×C22⋊Q8×C43C2211yescharacteristic
40C2×#121×C43—21no—
41C2×#121×C43C2211yescharacteristic
42C2×#120×C43—21no—
43C2×C4×D4×C43—21no—
44C22×C22⋊C4×C43C2211yescharacteristic
45C22×Dic86C2311yescharacteristic
46C2×#10621885—22no—
47C2×#10621883—22no—
48C2×#10621877—21no—
49C2×#10621877—21no—
50#13063304—21no—
51#13063304—21no—
52#13063304—21no—
53#13063304—21no—
54C2×C4⋊Dic43C2311yescharacteristic
55C2×Dic43⋊C4—21no—
56C2×C22⋊Dic43—22no—
57C2×C22⋊Dic43—21no—
58C2×C22⋊Dic43—21no—
59C2×C22⋊Dic43—22no—
60C2×C4×Dic43—21no—
61#13063258—22no—
62#13063256—22no—
63#13063249—22no—
64#13063248—22no—
65#13063248—22no—
66#13063246—22no—
67C22⋊(C43⋊C8)—21no—
68C22⋊(C43⋊C8)—21no—
69C22⋊(C43⋊C8)C2312yes—
70C22⋊(C43⋊C8)C2312yes—
71C43⋊#95—22no—
72C43⋊#95—22no—
73C43⋊#95C2312yes—
74C25×C43D411yescharacteristic
75C22×Q8×C43D411yescharacteristic
76C22×D4×C43—21no—
77C22×D4×C43—21no—
78C22×D4×C43—21no—
79C22×D4×C43D411yescharacteristic
80C23×C4×C43—21no—
81C23×C4×C43D411yescharacteristic
82C23×C4×C43C2311yescharacteristic
83#126×C43—24no—
84#126×C43—24no—
85#124×C43—24no—
86#124×C43—24no—
87#123×C43—24no—
88#123×C43—24no—
89C22⋊Q8×C43—21no—
90C22⋊Q8×C43—21no—
91C22⋊Q8×C43D412yes—
92C22⋊Q8×C43C2312yes—
93#121×C43—24no—
94#121×C43—24no—
95#121×C43—21no—
96#121×C43—21no—
97#121×C43D412yes—
98#121×C43C2312yes—
99#120×C43—24no—
100#120×C43—24no—
101C4×D4×C43—24no—
102C4×D4×C43—24no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43D411yescharacteristic
106C2×C4⋊C4×C43D411yescharacteristic
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43—21no—
109C2×C22⋊C4×C43—21no—
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43D412yes—
117C2×C22⋊C4×C43C2312yes—
118C2×C42×C43—21no—
119C24×C43—21no—
120C24×C43—21no—
121C24×C43—21no—
122C24×C43—42no—
123C24×C43—42no—
124C24×C43—81no—
125C24×C43C2×D411yescharacteristic
126C24×C43C2×D412yes—
127C2×Q8×C43—21no—
128C2×Q8×C43—81no—
129C2×Q8×C43C2×D412yes—
130C2×D4×C43—24no—
131C2×D4×C43—24no—
132C2×D4×C43—21no—
133C2×D4×C43—22no—
134C2×D4×C43—22no—
135C2×D4×C43—44no—
136C2×D4×C43—81no—
137C2×D4×C43—82no—
138C2×D4×C43—82no—
139C2×D4×C43C2×D412yes—
140C22×C4×C43—24no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—42no—
147C22×C4×C43—81no—
148C22×C4×C43—82no—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D412yes—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2411yescharacteristic
156C22×Dic43—22no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—81no—
162C4⋊C4×C43—24no—
163C4⋊C4×C43—22no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—22no—
167C4⋊C4×C43C2×D412yes—
168C4⋊C4×C43C2×D412yes—
169C22⋊C4×C43—24no—
170C22⋊C4×C43—24no—
171C22⋊C4×C43—24no—
172C22⋊C4×C43—22no—
173C22⋊C4×C43—22no—
174C22⋊C4×C43—22no—
175C22⋊C4×C43—22no—
176C22⋊C4×C43—22no—
177C22⋊C4×C43—22no—
178C22⋊C4×C43—22no—
179C22⋊C4×C43—22no—
180C42×C43—24no—
181C22⋊Dic43—42no—
182C22⋊Dic43—44no—
183C22⋊Dic43—41no—
184C22⋊Dic43—41no—
185C22⋊Dic43—82no—
186#10621885—82no—
187#10621883—82no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190Dic43⋊C4—41no—
191Dic43⋊C4—41no—
192C4×Dic43—81no—
193#10621877—81no—
194#10621877—81no—
195C2×C43⋊C8—22no—
196C2×C43⋊C8—22no—
197C23×C43—22no—
198C23×C43—22no—
199C23×C43—22no—
200C23×C43—22no—
201C23×C43—22no—
202C23×C43—22no—
203C23×C43—41no—
204C23×C43—42no—
205C23×C43—42no—
206C23×C43—42no—
207C23×C43—42no—
208C23×C43—42no—
209C23×C43—42no—
210C23×C43—42no—
211C23×C43—42no—
212C23×C43—42no—
213C23×C43—81no—
214C23×C43—81no—
215C23×C43—88no—
216C23×C43#12011yescharacteristic
217C23×C43#12011yescharacteristic
218C23×C43C22×D411yescharacteristic
219Q8×C43—42no—
220Q8×C43—81no—
221D4×C43—42no—
222D4×C43—44no—
223D4×C43—44no—
224D4×C43—81no—
225D4×C43—84no—
226D4×C43—84no—
227C2×C4×C43—22no—
228C2×C4×C43—22no—
229C2×C4×C43—22no—
230C2×C4×C43—22no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43—81no—
243C2×C4×C43—84no—
244C2×C4×C43#12011yescharacteristic
245C2×C4×C43#12011yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C22×D411yescharacteristic
248C2×Dic43—42no—
249C2×Dic43—42no—
250C2×Dic43—42no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—42no—
254C2×Dic43—42no—
255Dic86—42no—
256Dic86—42no—
257C43⋊C8—42no—
258C43⋊C8—42no—
259#18329—431nomaximal, Sylow
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—21no—
263C22×C43—21no—
264C22×C43—21no—
265C22×C43—21no—
266C22×C43—21no—
267C22×C43—44no—
268C22×C43—44no—
269C22×C43—42no—
270C22×C43—42no—
271C22×C43—42no—
272C22×C43—42no—
273C22×C43—42no—
274C22×C43—42no—
275C22×C43—82no—
276C22×C43—84no—
277C22×C43—84no—
278C22×C43—84no—
279C22×C43#45512yes—
280C22×C43C2×#12011yescharacteristic
281C22×C43#57512yes—
282C4×C43—21no—
283C4×C43—21no—
284C4×C43—21no—
285C4×C43—21no—
286C4×C43—42no—
287C4×C43—42no—
288C4×C43—42no—
289C4×C43—42no—
290Dic43—82no—
291Dic43—81no—
292Dic43—81no—
293C2×#538D4311yescharacteristic
294#3195—431no—
295#3193—431no—
296#2561—431no—
297#1612—434no—
298#1606—434no—
299#1508—431no—
300#1507—431no—
301#1462—431no—
302C2×C43—22no—
303C2×C43—22no—
304C2×C43—41no—
305C2×C43—82no—
306C2×C43—82no—
307C2×C43#300511yescharacteristic
308C2×C43C2×#45511yescharacteristic
309C2×C43#302611yescharacteristic
310#538—22no—
311#538—22no—
312#538—22no—
313#538C2×D4314yes—
314C2×#126—21no—
315C2×#124—21no—
316C2×#123—21no—
317C2×C22⋊Q8—431no—
318C2×C22⋊Q8C2×D4311yescharacteristic
319C2×#121—21no—
320C2×#121C2×D4311yescharacteristic
321C2×#120—21no—
322C2×C4×D4—21no—
323C22×C22⋊C4C2×D4311yescharacteristic
324#484—861no—
325#483—432no—
326#483—861no—
327#480—432no—
328#470—862no—
329#468—862no—
330#451—432no—
331#451—861no—
332#450—861no—
333#448—432no—
334#407—431no—
335#407—431no—
336#397—432no—
337#393—432no—
338#388—862no—
339#381—861no—
340#379—861no—
341C4×C22⋊C4—431no—
342#328—434no—
343#327—434no—
344#323—434no—
345C43#1832911yescharacteristic, complemented, Sylow
346C25C22⋊D4311yescharacteristic
347C22×Q8—431no—
348C22×Q8C22⋊D4311yescharacteristic
349C22×D4—21no—
350C22×D4—21no—
351C22×D4—21no—
352C22×D4C22⋊D4311yescharacteristic
353C23×C4—21no—
354C23×C4C22⋊D4311yescharacteristic
355C23×C4C22×D4311yescharacteristic
356C2×Q16—862no—
357C2×SD16—862no—
358C2×M16—861no—
359C2×M16—861no—
360#126—24no—
361#126—24no—
362#124—24no—
363#124—24no—
364#123—24no—
365#123—24no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8—861no—
369C22⋊Q8—861no—
370C22⋊Q8—861no—
371C22⋊Q8—861no—
372C22⋊Q8C22⋊D4312yes—
373C22⋊Q8C22×D4312yes—
374#121—24no—
375#121—24no—
376#121—21no—
377#121—21no—
378#121C22⋊D4312yes—
379#121C22×D4312yes—
380#120—24no—
381#120—24no—
382C4×D4—24no—
383C4×D4—24no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—431no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4C22⋊D4311yescharacteristic
389C2×C4⋊C4C22⋊D4311yescharacteristic
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—862no—
400C2×C22⋊C4—861no—
401C2×C22⋊C4—861no—
402C2×C22⋊C4—862no—
403C2×C22⋊C4C22⋊D4312yes—
404C2×C22⋊C4C22×D4312yes—
405C2×C42—21no—
406C2×C42—861no—
407#107—862no—
408#106—862no—
409#103—862no—
410#103—862no—
411#103—862no—
412#102—862no—
413C22⋊C8—432no—
414C22⋊C8—432no—
415C22⋊C8—861no—
416C22⋊C8—861no—
417#95—432no—
418#95—862no—
419#95—862no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—42no—
424C24—42no—
425C24—81no—
426C24C2×C22⋊D4311yescharacteristic
427C24C2×C22⋊D4312yes—
428C2×Q8—21no—
429C2×Q8—81no—
430C2×Q8—861no—
431C2×Q8—861no—
432C2×Q8—3441no—
433C2×Q8C2×C22⋊D4312yes—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—24no—
437C2×D4—24no—
438C2×D4—21no—
439C2×D4—44no—
440C2×D4—81no—
441C2×D4—82no—
442C2×D4—82no—
443C2×D4C2×C22⋊D4312yes—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—24no—
449C22×C4—21no—
450C22×C4—42no—
451C22×C4—81no—
452C22×C4—82no—
453C22×C4—862no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4C2×C22⋊D4312yes—
457C22×C4C2×C22⋊D4311yescharacteristic
458C22×C4C2×C22⋊D4311yescharacteristic
459C22×C4C2×C22⋊D4311yescharacteristic
460C22×C4C2×C22⋊D4311yescharacteristic
461C22×C4C2×C22⋊D4311yescharacteristic
462C22×C4C23×D4311yescharacteristic
463Q16—3442no—
464SD16—3442no—
465M16—3441no—
466M16—3441no—
467C2×C8—862no—
468C2×C8—862no—
469C4⋊C4—24no—
470C4⋊C4—22no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—22no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—1721no—
477C4⋊C4—1721no—
478C4⋊C4C2×C22⋊D4312yes—
479C4⋊C4C2×C22⋊D4312yes—
480C22⋊C4—24no—
481C22⋊C4—24no—
482C22⋊C4—24no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—3442no—
492C22⋊C4—1722no—
493C22⋊C4—1724no—
494C22⋊C4—1721no—
495C22⋊C4—1721no—
496C42—24no—
497C42—3441no—
498C23—22no—
499C23—22no—
500C23—22no—
501C23—22no—
502C23—22no—
503C23—22no—
504C23—41no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—81no—
515C23—81no—
516C23—88no—
517C23#1306329411yescharacteristic
518C23#1306329411yescharacteristic
519C23C22×C22⋊D4311yescharacteristic
520Q8—42no—
521Q8—81no—
522Q8—1722no—
523Q8—1722no—
524D4—42no—
525D4—44no—
526D4—44no—
527D4—81no—
528D4—84no—
529D4—84no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—81no—
546C2×C4—84no—
547C2×C4—1722no—
548C2×C4—1722no—
549C2×C4—1722no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1722no—
553C2×C4—1722no—
554C2×C4#1306329411yescharacteristic
555C2×C4#1306329411yescharacteristic
556C2×C4C22×C22⋊D4311yescharacteristic
557C2×C4C22×C22⋊D4311yescharacteristic
558C8—1722no—
559C8—1722no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—44no—
568C22—44no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—82no—
576C22—84no—
577C22—84no—
578C22—84no—
579C22#1458307712yes—
580C22C2×#1306329411yescharacteristic
581C22#1458369712yes—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—21no—
586C4—42no—
587C4—42no—
588C4—42no—
589C4—42no—
590C4—3442no—
591C4—3441no—
592C4—3441no—
593C2—22no—
594C2—22no—
595C2—41no—
596C2—82no—
597C2—82no—
598C2#1914383711yescharacteristic
599C2C2×#1458307711yescharacteristic
600C2#1914399211yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#538C2
socleC22×C43C2×#120
hypercenterC2×#538D43
hypocenterC43#18329
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#538

Complements

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

NH ≅ G/Ntype
1. #19145416C2semidirect
2. #19145401C2semidirect
3. #19139753C2semidirect
4. #19133609C2semidirect
5. #19133575C2semidirect
6. #19133115C2semidirect
7. #19133111C2semidirect
8. #19132922C2semidirect
13. #14583227C22semidirect
14. #14583210C22semidirect
18. #14583054C22semidirect
20. #14583037C22semidirect
23. #14582824C22semidirect
24. #14582811C22semidirect
29. #14582636C22semidirect
30. #14582633C22semidirect
31. #14582623C22semidirect
345. C43#18329semidirect

Maximal subgroups

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

subgroupindex
#191454162
#191454012
#191397532
#191336092
#191335752
#191331152
#191331112
#191329222
C2×C43×#5382
#1832943