Finite Group Databasebeta

← #25073232

Subgroups — #25073232

Order 11008.

932 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145813C211yesmaximal, characteristic, complemented
2#19144977C211yesmaximal, characteristic, complemented
3C2×#14583189C211yesmaximal, characteristic, complemented
4#19133767C212yesmaximal, complemented
5#19133760C212yesmaximal, complemented
6#19133746C212yesmaximal, complemented
7#19133746C212yesmaximal, complemented
8#19133295C211yesmaximal, characteristic, complemented
9#19133038C211yesmaximal, characteristic, complemented
10#19133008C211yesmaximal, characteristic, complemented
11C43×#3520C211yesmaximal, characteristic
12C2×#13063325C2211yescharacteristic
13#14583309—21no—
14#14583269—22no—
15#14583258—21no—
16#14583251C2212yescomplemented
17#14583251C2212yescomplemented
18#14583227—21no—
19#14583210—21no—
20#14583194C2212yescomplemented
21#14583189—21no—
22#14583189—21no—
23#14583189C2212yes—
24#14583189C2212yes—
25#14583189C2212yescomplemented
26#14582956C2211yescharacteristic
27C2×#13063256—21no—
28C2×C4⋊(C43⋊C8)C2211yescharacteristic
29#14582907—22no—
30C2×#13063246—21no—
31C4×#10621877C2211yescharacteristic
32#14582645C2212yescomplemented
33#14582645C2212yescomplemented
34Q8⋊(C43⋊C8)C2212yescomplemented
35D4⋊(C43⋊C8)C2212yes—
36D4⋊(C43⋊C8)C2212yes—
37D4⋊(C43⋊C8)C2212yescomplemented
38C43×#556C2211yescharacteristic
39C43×#554—21no—
40C43×#552—21no—
41C43×#551—22no—
42D4×Q8×C43C2211yescharacteristic
43C43×#548—21no—
44C43×#547C2211yescharacteristic
45C43×#547C2211yescharacteristic
46C43×#546—21no—
47C43×#542—21no—
48C43×#539—22no—
49C43×#533C2211yescharacteristic
50C43×#529C2211yescharacteristic
51C43×#525—21no—
52C2×C22⋊Q8×C43—21no—
53C43×#520—21no—
54C2×C4×D4×C43C2211yescharacteristic
55C22×Dic86—21no—
56C2×#10621877—21no—
57C22×C43⋊C8—21no—
58#13063325—21no—
59#13063325—21no—
60#13063325—21no—
61#13063325C2312yes—
62C2×C4⋊Dic43—21no—
63C2×C4⋊Dic43—21no—
64#13063258—22no—
65#13063256—22no—
66#13063256—22no—
67#13063256—22no—
68C4⋊(C43⋊C8)—21no—
69C4⋊(C43⋊C8)C2312yes—
70C4⋊(C43⋊C8)C2312yes—
71#13063249—22no—
72#13063248—24no—
73#13063248—24no—
74#13063246—22no—
75#13063246—22no—
76#13063246—22no—
77C22⋊(C43⋊C8)—21no—
78#13063236—21no—
79#13063236—21no—
80C4×C43⋊C8C2312yes—
81C2×#41×C43—21no—
82C2×#41×C43—21no—
83C22×Q8×C43—21no—
84C22×D4×C43D411yescharacteristic
85C23×C4×C43—21no—
86C4⋊Q8×C43—21no—
87C4⋊Q8×C43C2311yescharacteristic
88C4⋊Q8×C43C2311yescharacteristic
89#126×C43—22no—
90#126×C43—22no—
91#126×C43—21no—
92#125×C43—22no—
93#125×C43D411yescharacteristic
94#125×C43D412yes—
95#124×C43—22no—
96#124×C43—21no—
97#124×C43D411yescharacteristic
98#123×C43—22no—
99#123×C43—22no—
100#123×C43—21no—
101#123×C43—22no—
102#123×C43—22no—
103C22⋊Q8×C43—22no—
104C22⋊Q8×C43—22no—
105C22⋊Q8×C43—22no—
106C22⋊Q8×C43—21no—
107C22⋊Q8×C43—21no—
108C22⋊Q8×C43—21no—
109C22⋊Q8×C43—21no—
110C22⋊Q8×C43—21no—
111C22⋊Q8×C43—22no—
112C22⋊Q8×C43—21no—
113C22⋊Q8×C43D411yescharacteristic
114#121×C43—22no—
115#121×C43—21no—
116#121×C43—21no—
117#121×C43D411yescharacteristic
118#120×C43—22no—
119C4×Q8×C43—21no—
120C4×Q8×C43—21no—
121C4×Q8×C43—21no—
122C4×Q8×C43C2311yescharacteristic
123C4×D4×C43—22no—
124C4×D4×C43—22no—
125C4×D4×C43—22no—
126C4×D4×C43—21no—
127C4×D4×C43—21no—
128C4×D4×C43—21no—
129C4×D4×C43—21no—
130C4×D4×C43D411yescharacteristic
131C4×D4×C43D411yescharacteristic
132C4×D4×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134C4×D4×C43C2311yescharacteristic
135#117×C43—22no—
136#117×C43—21no—
137#117×C43—21no—
138#117×C43D412yes—
139C2×C4⋊C4×C43—22no—
140C2×C4⋊C4×C43—21no—
141C2×C4⋊C4×C43—21no—
142C2×C4⋊C4×C43D411yescharacteristic
143C2×C22⋊C4×C43—22no—
144C2×C22⋊C4×C43—21no—
145C2×C42×C43C2311yescharacteristic
146C24×C43—21no—
147#41×C43—42no—
148#41×C43—42no—
149#41×C43—82no—
150C2×Q8×C43—22no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—82no—
154C2×Q8×C43C2×D411yescharacteristic
155C2×D4×C43—22no—
156C2×D4×C43—22no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—22no—
160C2×D4×C43—41no—
161C2×D4×C43C2×D411yescharacteristic
162C2×D4×C43C2×D411yescharacteristic
163C2×D4×C43C2×D411yescharacteristic
164C22×C4×C43—22no—
165C22×C4×C43—22no—
166C22×C4×C43—22no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—82no—
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177C22×Dic43—41no—
178C2×Dic86—22no—
179C2×Dic86—44no—
180C2×Dic86—41no—
181C4⋊C4×C43—22no—
182C4⋊C4×C43—22no—
183C4⋊C4×C43—22no—
184C4⋊C4×C43—22no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—22no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—22no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43C2×D411yescharacteristic
195C4⋊C4×C43C2×D411yescharacteristic
196C4⋊C4×C43C2×D411yescharacteristic
197C4⋊C4×C43C2×D411yescharacteristic
198C4⋊C4×C43C2×D412yes—
199C4⋊C4×C43C2×D412yes—
200C22⋊C4×C43—22no—
201C22⋊C4×C43—22no—
202C22⋊C4×C43—22no—
203C22⋊C4×C43—22no—
204C22⋊C4×C43—22no—
205C22⋊C4×C43—21no—
206C22⋊C4×C43—21no—
207C22⋊C4×C43—21no—
208C22⋊C4×C43—21no—
209C22⋊C4×C43—21no—
210C22⋊C4×C43—21no—
211C22⋊C4×C43—21no—
212C22⋊C4×C43—21no—
213C22⋊C4×C43—21no—
214C22⋊C4×C43—22no—
215C42×C43—22no—
216C42×C43—22no—
217C42×C43—21no—
218C42×C43C2×D411yescharacteristic
219C42×C43C2×D411yescharacteristic
220C42×C43C2×D411yescharacteristic
221C42×C43C2411yescharacteristic
222C4⋊Dic43—22no—
223C4⋊Dic43—22no—
224C4⋊Dic43—41no—
225C4⋊Dic43—41no—
226#10621877—42no—
227C2×C43⋊C8—22no—
228C2×C43⋊C8—22no—
229C2×C43⋊C8—22no—
230C2×C43⋊C8—42no—
231C23×C43—21no—
232C23×C43—21no—
233C23×C43—21no—
234C23×C43—42no—
235C23×C43—42no—
236C23×C43—81no—
237C23×C43#12011yescharacteristic
238Q8×C43—22no—
239Q8×C43—41no—
240Q8×C43—41no—
241Q8×C43—42no—
242Q8×C43—82no—
243D4×C43—21no—
244D4×C43—21no—
245D4×C43—21no—
246D4×C43—22no—
247D4×C43—42no—
248D4×C43—44no—
249D4×C43—42no—
250D4×C43—82no—
251D4×C43#13712yes—
252C2×C4×C43—22no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—22no—
256C2×C4×C43—21no—
257C2×C4×C43—22no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43—22no—
261C2×C4×C43—21no—
262C2×C4×C43—21no—
263C2×C4×C43—44no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—42no—
267C2×C4×C43—42no—
268C2×C4×C43—81no—
269C2×C4×C43—81no—
270C2×C4×C43—81no—
271C2×C4×C43—82no—
272C2×C4×C43—82no—
273C2×C4×C43#12011yescharacteristic
274C2×C4×C43#12011yescharacteristic
275C2×C4×C43#12011yescharacteristic
276C2×C4×C43C22×D411yescharacteristic
277C2×C4×C43C22×D411yescharacteristic
278C2×C4×C43C22×D411yescharacteristic
279C2×Dic43—42no—
280C2×Dic43—82no—
281Dic86—44no—
282Dic86—82no—
283C43⋊C8—42no—
284C43⋊C8—42no—
285C43⋊C8—42no—
286#18579—431nomaximal, Sylow
287C22×C43—21no—
288C22×C43—21no—
289C22×C43—22no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43—41no—
293C22×C43—41no—
294C22×C43—41no—
295C22×C43—41no—
296C22×C43—41no—
297C22×C43—41no—
298C22×C43—84no—
299C22×C43#45412yes—
300C22×C43C2×#12011yescharacteristic
301C4×C43—21no—
302C4×C43—21no—
303C4×C43—21no—
304C4×C43—21no—
305C4×C43—41no—
306C4×C43—42no—
307C4×C43—41no—
308C4×C43—41no—
309C4×C43—42no—
310C4×C43—41no—
311C4×C43—41no—
312C4×C43C2×#13711yescharacteristic
313C4×C43#57511yescharacteristic
314C4×C43#57712yes—
315Dic43—82no—
316#3520D4311yescharacteristic
317#3238—431no—
318#3139—431no—
319C2×#476—431no—
320#1638—432no—
321#1637—432no—
322#1635—432no—
323#1635—432no—
324#1552—431no—
325#1490—431no—
326#1483—431no—
327C2×C43—22no—
328C2×C43—42no—
329C2×C43—81no—
330C2×C43—81no—
331C2×C43#300711yescharacteristic
332C2×C43#300911yescharacteristic
333C2×C43C2×#45411yescharacteristic
334#556C2×D4311yescharacteristic
335#554—21no—
336#552—21no—
337#551—22no—
338D4×Q8C2×D4311yescharacteristic
339#548—21no—
340#547C2×D4311yescharacteristic
341#547C2×D4311yescharacteristic
342#546—21no—
343#542—21no—
344#539—22no—
345#533C2×D4311yescharacteristic
346C2×C4⋊Q8—431no—
347#529C2×D4311yescharacteristic
348#525—21no—
349C2×C22⋊Q8—21no—
350#520—21no—
351C2×C4×D4C2×D4311yescharacteristic
352#501—861no—
353#491—862no—
354#489—861no—
355#487—432no—
356#487—432no—
357#483—861no—
358#480—861no—
359#477—432no—
360#476—432no—
361#476—432no—
362#476—432no—
363#476—861no—
364#476—861no—
365#432—431no—
366C2×#106—861no—
367C2×C4⋊C8—431no—
368#419—862no—
369C2×#102—861no—
370C4×M16—431no—
371#332—432no—
372#332—432no—
373Q8⋊C8—432no—
374D4⋊C8—432no—
375D4⋊C8—432no—
376D4⋊C8—432no—
377C43#1857911yescharacteristic, complemented, Sylow
378C2×#41—21no—
379C2×#41—21no—
380C22×Q8—21no—
381C22×Q8—861no—
382C22×D4C22⋊D4311yescharacteristic
383C23×C4—21no—
384C2×M16—861no—
385C22×C8—861no—
386C4⋊Q8—21no—
387C4⋊Q8—432no—
388C4⋊Q8—861no—
389C4⋊Q8—861no—
390C4⋊Q8—861no—
391C4⋊Q8C22×D4311yescharacteristic
392C4⋊Q8C22×D4311yescharacteristic
393#126—22no—
394#126—22no—
395#126—21no—
396#125—22no—
397#125C22⋊D4311yescharacteristic
398#125C22⋊D4312yes—
399#124—22no—
400#124—21no—
401#124C22⋊D4311yescharacteristic
402#123—22no—
403#123—22no—
404#123—21no—
405#123—22no—
406#123—22no—
407C22⋊Q8—22no—
408C22⋊Q8—22no—
409C22⋊Q8—22no—
410C22⋊Q8—21no—
411C22⋊Q8—21no—
412C22⋊Q8—21no—
413C22⋊Q8—21no—
414C22⋊Q8—21no—
415C22⋊Q8—22no—
416C22⋊Q8—21no—
417C22⋊Q8C22⋊D4311yescharacteristic
418#121—22no—
419#121—21no—
420#121—21no—
421#121C22⋊D4311yescharacteristic
422#120—22no—
423C4×Q8—21no—
424C4×Q8—21no—
425C4×Q8—21no—
426C4×Q8C22×D4311yescharacteristic
427C4×D4—22no—
428C4×D4—22no—
429C4×D4—22no—
430C4×D4—21no—
431C4×D4—21no—
432C4×D4—21no—
433C4×D4—21no—
434C4×D4C22⋊D4311yescharacteristic
435C4×D4C22⋊D4311yescharacteristic
436C4×D4C22×D4311yescharacteristic
437C4×D4C22×D4311yescharacteristic
438C4×D4C22×D4311yescharacteristic
439#117—22no—
440#117—21no—
441#117—21no—
442#117C22⋊D4312yes—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—861no—
447C2×C4⋊C4—861no—
448C2×C4⋊C4C22⋊D4311yescharacteristic
449C2×C22⋊C4—22no—
450C2×C22⋊C4—21no—
451C2×C42C22×D4311yescharacteristic
452#107—862no—
453#106—862no—
454#106—862no—
455#106—862no—
456C4⋊C8—432no—
457C4⋊C8—432no—
458C4⋊C8—861no—
459#103—862no—
460#103—864no—
461#103—864no—
462#102—862no—
463#102—862no—
464#102—862no—
465C22⋊C8—861no—
466#97—861no—
467#97—861no—
468C4×C8—432no—
469C24—21no—
470#41—42no—
471#41—42no—
472#41—82no—
473C2×Q8—22no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—82no—
477C2×Q8—862no—
478C2×Q8—1724no—
479C2×Q8—1721no—
480C2×Q8C2×C22⋊D4311yescharacteristic
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—21no—
484C2×D4—22no—
485C2×D4—21no—
486C2×D4—41no—
487C2×D4C2×C22⋊D4311yescharacteristic
488C2×D4C2×C22⋊D4311yescharacteristic
489C2×D4C2×C22⋊D4311yescharacteristic
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—82no—
500C22×C4—1721no—
501C22×C4C2×C22⋊D4311yescharacteristic
502C22×C4C2×C22⋊D4311yescharacteristic
503C22×C4C2×C22⋊D4311yescharacteristic
504M16—1722no—
505C2×C8—862no—
506C2×C8—862no—
507C2×C8—862no—
508C2×C8—1722no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—21no—
514C4⋊C4—22no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—22no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—862no—
523C4⋊C4—862no—
524C4⋊C4—1721no—
525C4⋊C4—1721no—
526C4⋊C4C2×C22⋊D4312yes—
527C4⋊C4C2×C22⋊D4312yes—
528C4⋊C4C2×C22⋊D4311yescharacteristic
529C4⋊C4C2×C22⋊D4311yescharacteristic
530C4⋊C4C2×C22⋊D4311yescharacteristic
531C4⋊C4C2×C22⋊D4311yescharacteristic
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—21no—
538C22⋊C4—22no—
539C22⋊C4—21no—
540C22⋊C4—21no—
541C22⋊C4—21no—
542C22⋊C4—21no—
543C22⋊C4—21no—
544C22⋊C4—21no—
545C22⋊C4—21no—
546C22⋊C4—21no—
547C42—22no—
548C42—22no—
549C42—21no—
550C42C2×C22⋊D4311yescharacteristic
551C42C2×C22⋊D4311yescharacteristic
552C42C2×C22⋊D4311yescharacteristic
553C42C23×D4311yescharacteristic
554C23—21no—
555C23—21no—
556C23—21no—
557C23—42no—
558C23—42no—
559C23—81no—
560C23#1306329411yescharacteristic
561Q8—22no—
562Q8—41no—
563Q8—41no—
564Q8—42no—
565Q8—82no—
566Q8—3442no—
567Q8—1724no—
568D4—21no—
569D4—21no—
570D4—21no—
571D4—22no—
572D4—42no—
573D4—44no—
574D4—42no—
575D4—82no—
576D4#1306335512yes—
577C2×C4—22no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—44no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—81no—
594C2×C4—81no—
595C2×C4—81no—
596C2×C4—82no—
597C2×C4—82no—
598C2×C4—3442no—
599C2×C4—1722no—
600C2×C4#1306329411yescharacteristic
601C2×C4#1306329411yescharacteristic
602C2×C4#1306329411yescharacteristic
603C2×C4C22×C22⋊D4311yescharacteristic
604C2×C4C22×C22⋊D4311yescharacteristic
605C2×C4C22×C22⋊D4311yescharacteristic
606C8—1722no—
607C8—1722no—
608C8—1722no—
609C22—21no—
610C22—21no—
611C22—22no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—84no—
621C22#1458307212yes—
622C22C2×#1306329411yescharacteristic
623C4—21no—
624C4—21no—
625C4—21no—
626C4—21no—
627C4—41no—
628C4—42no—
629C4—41no—
630C4—41no—
631C4—42no—
632C4—41no—
633C4—41no—
634C4—3442no—
635C4C2×#1306335511yescharacteristic
636C4#1458369711yescharacteristic
637C4#1458371012yes—
638C2—22no—
639C2—42no—
640C2—81no—
641C2—81no—
642C2#1914385511yescharacteristic
643C2#1914387211yescharacteristic
644C2C2×#1458307211yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3520C2
socleC22×C43C2×#120
hypercenter#3520D43
hypocenterC43#18579
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3520

Complements

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

NH ≅ G/Ntype
1. #19145813C2semidirect
2. #19144977C2semidirect
3. C2×#14583189C2semidirect
4. #19133767C2semidirect
5. #19133760C2semidirect
6. #19133746C2semidirect
7. #19133746C2semidirect
8. #19133295C2semidirect
9. #19133038C2semidirect
10. #19133008C2semidirect
16. #14583251C22semidirect
17. #14583251C22semidirect
20. #14583194C22semidirect
25. #14583189C22semidirect
32. #14582645C22semidirect
33. #14582645C22semidirect
34. Q8⋊(C43⋊C8)C22semidirect
37. D4⋊(C43⋊C8)C22semidirect
377. C43#18579semidirect

Maximal subgroups

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

subgroupindex
#191458132
#191449772
C2×#145831892
#191337672
#191337602
#191337462
#191332952
#191330382
#191330082
C43×#35202
#1857943