Finite Group Databasebeta

← #25103833

Subgroups — #25103833

Order 11008.

876 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583237C211yesmaximal, characteristic
2C4×#13063284C211yesmaximal, characteristic
3#19135233C211yesmaximal, characteristic, complemented
4#19135226C211yesmaximal, characteristic, complemented
5#19135184C211yesmaximal, characteristic, complemented
6#19135177C211yesmaximal, characteristic, complemented
7#19134908C211yesmaximal, characteristic
8#19134792C211yesmaximal, characteristic
9#19134687C211yesmaximal, characteristic
10#19134493C211yesmaximal, characteristic, complemented
11#19134493C211yesmaximal, characteristic, complemented
12#19134425C211yesmaximal, characteristic, complemented
13#19134425C211yesmaximal, characteristic, complemented
14#19134357C211yesmaximal, characteristic
15C4×C22⋊Q8×C43C211yesmaximal, characteristic
16C2×#13063284C2211yescharacteristic
17C2×#13063284C2211yescharacteristic
18#14583237C418yescomplemented
19C2×#13063258C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×C22⋊(C43⋊C8)C2211yescharacteristic
28C2×C22⋊(C43⋊C8)C2211yescharacteristic
29C2×#13063236C2211yescharacteristic
30C2×#13063236C2211yescharacteristic
31C4×C4⋊Dic43C2211yescharacteristic
32C4×C4⋊Dic43C2211yescharacteristic
33C4×C4⋊Dic43C2211yescharacteristic
34C4×C4⋊Dic43C2211yescharacteristic
35C4×C22⋊Dic43—21no—
36C4×C22⋊Dic43—21no—
37#14582745—21no—
38C42×Dic43—21no—
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582654C2211yescharacteristic
48#14582654C2211yescharacteristic
49C2×C22⋊Q8×C43C2211yescharacteristic
50C2×C4×Q8×C43C2211yescharacteristic
51C22×C42×C43C2211yescharacteristic
52C43×#391C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C43×#387—21no—
55C43×#385—21no—
56C43×#380C2211yescharacteristic
57C4×C4⋊C4×C43—21no—
58C4×C4⋊C4×C43C2211yescharacteristic
59C4×C22⋊C4×C43—21no—
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64#13063284—22no—
65#13063284—22no—
66#13063284—22no—
67#13063284C2×C414yes—
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C22⋊Dic43—21no—
73C2×C22⋊Dic43—21no—
74C2×C4×Dic43—21no—
75C2×C4×Dic43—21no—
76C2×C4×Dic43—21no—
77C2×C4×Dic43—21no—
78C2×C4×Dic43—21no—
79C2×C4×Dic43—21no—
80#13063258—22no—
81#13063258C2×C414yescomplemented
82#13063256—22no—
83#13063256C2×C414yescomplemented
84#13063249—22no—
85#13063249—22no—
86#13063249C2×C414yescomplemented
87#13063249C2×C414yescomplemented
88C22⋊(C43⋊C8)—22no—
89C22⋊(C43⋊C8)C2×C414yes—
90#13063236—22no—
91#13063236—22no—
92C43⋊#95—21no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C22×Q8×C43C2311yescharacteristic
97C23×C4×C43D411yescharacteristic
98C23×C4×C43D411yescharacteristic
99C23×C4×C43C2311yescharacteristic
100C22⋊Q8×C43—22no—
101C22⋊Q8×C43C2×C414yes—
102C4×Q8×C43—22no—
103C4×Q8×C43—22no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C42×C43—22no—
113C2×C42×C43—22no—
114C2×C42×C43—21no—
115C2×C42×C43—21no—
116C2×C42×C43D411yescharacteristic
117C2×C42×C43D411yescharacteristic
118C2×C42×C43C2311yescharacteristic
119C2×C42×C43C2311yescharacteristic
120#95×C43—21no—
121#95×C43—21no—
122#95×C43—21no—
123#95×C43—21no—
124#95×C43—21no—
125C24×C43C2×D411yescharacteristic
126C2×Q8×C43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43C22×C412yes—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—41no—
144C22×C4×C43—41no—
145C22×C4×C43—41no—
146C22×C4×C43C22×C412yes—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43#4112yes—
153C22×C4×C43C2411yescharacteristic
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C4⋊C4×C43—24no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—42no—
165C4⋊C4×C43—42no—
166C4⋊C4×C43C22×C412yes—
167C22⋊C4×C43—24no—
168C22⋊C4×C43—42no—
169C42×C43—22no—
170C42×C43—22no—
171C42×C43—21no—
172C42×C43—21no—
173C42×C43—42no—
174C42×C43—42no—
175C42×C43#4112yes—
176C42×C43#4112yes—
177C22⋊Dic43—24no—
178C22⋊Dic43—24no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43C22×C412yes—
184C4⋊Dic43C22×C412yes—
185C4⋊Dic43#4112yes—
186C4⋊Dic43#4112yes—
187C4×Dic43—24no—
188C4×Dic43—24no—
189C4×Dic43—42no—
190C4×Dic43—42no—
191C4×Dic43—42no—
192C4×Dic43—42no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8C22×C412yes—
204C2×C43⋊C8C22×C412yes—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43C4×D412yes—
212C23×C43C22×D411yescharacteristic
213Q8×C43—22no—
214Q8×C43—22no—
215Q8×C43—41no—
216Q8×C43—41no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—22no—
226C2×C4×C43—22no—
227C2×C4×C43—22no—
228C2×C4×C43—22no—
229C2×C4×C43—22no—
230C2×C4×C43—22no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—44no—
235C2×C4×C43—44no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43C4×D412yes—
247C2×C4×C43#12312yes—
248C2×C4×C43#12312yes—
249C2×C4×C43#13712yes—
250C2×C4×C43C23×C411yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C43⋊C8—22no—
269C43⋊C8—22no—
270C43⋊C8—41no—
271C43⋊C8—41no—
272#21583—431nomaximal, Sylow
273C22×C43—22no—
274C22×C43—22no—
275C22×C43—22no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43C2×C4×D411yescharacteristic
281C22×C43C2×#12311yescharacteristic
282C22×C43#52511yescharacteristic
283C22×C43C2×#13711yescharacteristic
284C22×C43#57511yescharacteristic
285C22×C43#57511yescharacteristic
286C22×C43#57511yescharacteristic
287C4×C43—22no—
288C4×C43—22no—
289C4×C43—22no—
290C4×C43—22no—
291C4×C43—41no—
292C4×C43—42no—
293C4×C43—42no—
294C4×C43—81no—
295C4×C43—81no—
296C4×C43C4×#4111yescharacteristic
297C4×C43C4×#4111yescharacteristic
298C4×C43#52911yescharacteristic
299C4×C43#52911yescharacteristic
300Dic43—42no—
301Dic43—42no—
302Dic43—42no—
303Dic43—42no—
304C2×#485—431no—
305C4×C22⋊Q8D4311yescharacteristic
306C4×#117—431no—
307#1928—431no—
308#1927—431no—
309#1921—431no—
310#1920—431no—
311#1873—431no—
312#1854—431no—
313#1825—431no—
314#1776—431no—
315#1776—431no—
316#1763—431no—
317#1763—431no—
318#1749—431no—
319C2×C43—42no—
320C2×C43C4×#12311yescharacteristic
321C2×C43#294311yescharacteristic
322C2×C43C4×#13711yescharacteristic
323C2×C43#309311yescharacteristic
324C2×C43#309511yescharacteristic
325C2×C43#311111yescharacteristic
326C2×C43#311611yescharacteristic
327C2×C22⋊Q8C2×D4311yescharacteristic
328C2×C4×Q8C2×D4311yescharacteristic
329C2×#117—431no—
330C2×#117—431no—
331C22×C42C2×D4311yescharacteristic
332#485—438no—
333C2×#107—431no—
334C2×#107—431no—
335C2×#106—431no—
336C2×#106—431no—
337C2×#103—431no—
338C2×#103—431no—
339C2×#103—431no—
340C2×#103—431no—
341C2×C22⋊C8—431no—
342C2×C22⋊C8—431no—
343C2×#97—431no—
344C2×#97—431no—
345#391C2×D4311yescharacteristic
346#389C2×D4311yescharacteristic
347#387—21no—
348#385—21no—
349#380C2×D4311yescharacteristic
350C4×C4⋊C4—21no—
351C4×C4⋊C4—431no—
352C4×C4⋊C4—431no—
353C4×C4⋊C4—431no—
354C4×C4⋊C4—431no—
355C4×C4⋊C4C2×D4311yescharacteristic
356C4×C22⋊C4—21no—
357C4×C22⋊C4—861no—
358C4×C22⋊C4—861no—
359#376—861no—
360C43—861no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368#340—431no—
369#336—431no—
370#336—431no—
371C43#2158311yescharacteristic, complemented, Sylow
372C22×Q8C22×D4311yescharacteristic
373C23×C4C22⋊D4311yescharacteristic
374C23×C4C22⋊D4311yescharacteristic
375C23×C4C22×D4311yescharacteristic
376C22×C8—431no—
377C22×C8—431no—
378C22×C8—431no—
379C22×C8—431no—
380C22⋊Q8—22no—
381C22⋊Q8C4×D4314yes—
382C4×Q8—22no—
383C4×Q8—22no—
384#117—434no—
385#117—862no—
386#117—862no—
387#117—862no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4C22×D4311yescharacteristic
396C2×C4⋊C4C22×D4311yescharacteristic
397C2×C4⋊C4C22×D4311yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—861no—
401C2×C22⋊C4—861no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—861no—
407C2×C42—861no—
408C2×C42—861no—
409C2×C42—861no—
410C2×C42—861no—
411C2×C42—861no—
412C2×C42C22⋊D4311yescharacteristic
413C2×C42C22⋊D4311yescharacteristic
414C2×C42C22×D4311yescharacteristic
415C2×C42C22×D4311yescharacteristic
416#107—434no—
417#107—862no—
418#106—434no—
419#106—862no—
420#103—434no—
421#103—434no—
422#103—862no—
423#103—862no—
424C22⋊C8—434no—
425C22⋊C8—862no—
426#97—862no—
427#97—862no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437C24C2×C22⋊D4311yescharacteristic
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8C2×C4×D4312yes—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4C2×C4×D4312yes—
463C22×C4#1062189812yes—
464C22×C4C2×C22⋊D4311yescharacteristic
465C22×C4C2×C22⋊D4311yescharacteristic
466C22×C4C2×C22⋊D4311yescharacteristic
467C22×C4C2×C22⋊D4311yescharacteristic
468C22×C4C2×C22⋊D4311yescharacteristic
469C22×C4C23×D4311yescharacteristic
470C2×C8—432no—
471C2×C8—432no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—861no—
482C4⋊C4—24no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—42no—
489C4⋊C4—42no—
490C4⋊C4—432no—
491C4⋊C4—432no—
492C4⋊C4—432no—
493C4⋊C4—432no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4C2×C4×D4312yes—
499C22⋊C4—24no—
500C22⋊C4—42no—
501C22⋊C4—864no—
502C22⋊C4—864no—
503C42—22no—
504C42—22no—
505C42—21no—
506C42—21no—
507C42—42no—
508C42—42no—
509C42—864no—
510C42—864no—
511C42—1722no—
512C42—1722no—
513C42—1722no—
514C42—1722no—
515C42#1062190012yes—
516C42#1062190012yes—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23C4×C22⋊D4312yes—
524C23C22×C22⋊D4311yescharacteristic
525Q8—22no—
526Q8—22no—
527Q8—41no—
528Q8—41no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—44no—
547C2×C4—44no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—862no—
559C2×C4—862no—
560C2×C4—862no—
561C2×C4—862no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4C4×C22⋊D4312yes—
571C2×C4#1306330612yes—
572C2×C4#1306330612yes—
573C2×C4#1306335612yes—
574C2×C4C22×C4×D4311yescharacteristic
575C2×C4#41×D4311yescharacteristic
576C2×C4#41×D4311yescharacteristic
577C2×C4C2×#1062190011yescharacteristic
578C2×C4C2×#1062190011yescharacteristic
579C2×C4C2×#1062189811yescharacteristic
580C8—862no—
581C8—862no—
582C8—1721no—
583C8—1721no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22C2×C4×C22⋊D4311yescharacteristic
592C22C2×#1306330611yescharacteristic
593C22#1458340611yescharacteristic
594C22C2×#1306335611yescharacteristic
595C22#1458369711yescharacteristic
596C22#1458369711yescharacteristic
597C22#1458369711yescharacteristic
598C4—22no—
599C4—22no—
600C4—22no—
601C4—22no—
602C4—41no—
603C4—42no—
604C4—42no—
605C4—81no—
606C4—81no—
607C4—1722no—
608C4—1722no—
609C4—1722no—
610C4—1722no—
611C4C4×#1062190011yescharacteristic
612C4C4×#1062190011yescharacteristic
613C4#1458342911yescharacteristic
614C4#1458342911yescharacteristic
615C2—42no—
616C2C4×#1306330611yescharacteristic
617C2#1914339311yescharacteristic
618C2C4×#1306335611yescharacteristic
619C2#1914452411yescharacteristic
620C2#1914453911yescharacteristic
621C2#1914469811yescharacteristic
622C2#1914475111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×C22⋊Q8×C43C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenterC4×C22⋊Q8D43
hypocenterC43#21583
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #19135233C2semidirect
4. #19135226C2semidirect
5. #19135184C2semidirect
6. #19135177C2semidirect
10. #19134493C2semidirect
11. #19134493C2semidirect
12. #19134425C2semidirect
13. #19134425C2semidirect
18. #14583237C4semidirect
81. #13063258C2×C4semidirect
83. #13063256C2×C4semidirect
86. #13063249C2×C4semidirect
87. #13063249C2×C4semidirect
371. C43#21583semidirect

Maximal subgroups

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

subgroupindex
C2×#145832372
C4×#130632842
#191352332
#191352262
#191351842
#191351772
#191349082
#191347922
#191346872
#191344932
#191344252
#191343572
C4×C22⋊Q8×C432
#2158343