Finite Group Databasebeta

← #25064298

Subgroups — #25064298

Order 11008.

930 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148341C211yesmaximal, characteristic
2#19143249C211yesmaximal, characteristic, complemented
3#19137490C211yesmaximal, characteristic, complemented
4#19133171C212yesmaximal, complemented
5#19133144C212yesmaximal, complemented
6#19133136C211yesmaximal, characteristic
7#19133119C212yesmaximal, complemented
8#19133115C211yesmaximal, characteristic, complemented
9#19133092C212yesmaximal, complemented
10#19133087C211yesmaximal, characteristic
11C43×#1520C211yesmaximal, characteristic, complemented
12#14583620—21no—
13#14583607—21no—
14#14583591—21no—
15#14583584—22no—
16#14583583—21no—
17#14583575—22no—
18#14583530C411yescharacteristic, complemented
19#14583522C412yescomplemented
20#14583509C412yescomplemented
21#14583473C411yescharacteristic, complemented
22#14583451C2212yes—
23#14583435C2212yes—
24#14583410C2211yescharacteristic
25#14583380C411yescharacteristic, complemented
26#14583377C411yescharacteristic, complemented
27C2×#13063284C2211yescharacteristic
28#14582957—22no—
29#14582953C2212yes—
30#14582949C2212yes—
31#14582925—21no—
32#14582863C2211yescharacteristic
33#14582854—21no—
34#14582795—21no—
35#14582787—22no—
36#14582766C2212yes—
37C4⋊C4×Dic43—21no—
38#14582750C2212yes—
39C4×C22⋊Dic43C2211yescharacteristic
40#14582637C2211yescharacteristic
41#14582637C2211yescharacteristic
42#14582636C2212yes—
43#14582636C2212yes—
44#14582635C2212yes—
45#14582634C2211yescharacteristic
46#14582634C2211yescharacteristic
47#14582632C2212yes—
48C2×C22⋊Q8×C43C2211yescharacteristic
49C2×C22⋊C8×C43C2211yescharacteristic
50C43×#380C2211yescharacteristic
51C43×#328C2212yes—
52C43×#328C2212yes—
53C2×#10621898C2×C411yescharacteristic
54C2×#10621877—21no—
55#13063324—21no—
56#13063324C2×C412yes—
57#13063323C2×C412yes—
58#13063320—22no—
59#13063320—22no—
60#13063318—22no—
61#13063318—22no—
62#13063316—21no—
63#13063316—22no—
64#13063316C2×C412yes—
65#13063315—22no—
66#13063315—22no—
67#13063314C2×C412yes—
68#13063311—22no—
69#13063309—22no—
70#13063308—21no—
71#13063308—22no—
72#13063307—22no—
73#13063305—22no—
74#13063304—22no—
75#13063304C2×C411yescharacteristic
76#13063304C2311yescharacteristic
77#13063302—22no—
78#13063301—21no—
79#13063301—21no—
80#13063299C2×C411yescharacteristic
81#13063299C2311yescharacteristic
82#13063294—21no—
83Q8×Dic43—21no—
84Q8×Dic43—21no—
85Q8×Dic43C2×C412yes—
86Q8×Dic43C2×C412yes—
87#13063290—22no—
88#13063290C2×C412yes—
89#13063287C2×C412yes—
90C4×C22⋊D43—21no—
91C4×C22⋊D43—21no—
92C4×C22⋊D43—22no—
93(C22⋊D43)⋊C4—22no—
94#13063284—22no—
95#13063284C2×C411yescharacteristic
96#13063284C2×C411yescharacteristic
97#13063284C2×C411yescharacteristic
98#13063284C2×C412yes—
99#13063284D411yescharacteristic
100#13063284D412yes—
101#13063284D411yescharacteristic
102#13063283—21no—
103#13063283—22no—
104#13063281—22no—
105C2×C4⋊Dic43D411yescharacteristic
106C2×C4⋊Dic43D411yescharacteristic
107C2×Dic43⋊C4—22no—
108C4⋊C4×D43—21no—
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43D412yes—
111C2×C4×Dic43—21no—
112C2×C4×Dic43—22no—
113C2×C4×Dic43C2312yes—
114Dic43⋊C8—22no—
115Dic43⋊C8—22no—
116C22⋊(C43⋊C8)—21no—
117C22⋊(C43⋊C8)C2312yes—
118#13063235—22no—
119C8×Dic43—22no—
120C43⋊#95—22no—
121C43⋊#95—22no—
122C43⋊#95C2311yescharacteristic
123C43⋊#95C2311yescharacteristic
124C22×Q8×C43C2×C411yescharacteristic
125C23×C4×C43C2311yescharacteristic
126C22×C8×C43—21no—
127C22⋊Q8×C43—21no—
128C22⋊Q8×C43—21no—
129C22⋊Q8×C43C2×C412yes—
130C22⋊Q8×C43C2312yes—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43C2×C411yescharacteristic
134C2×C22⋊C4×C43—21no—
135C2×C22⋊C4×C43—21no—
136C22⋊C8×C43—21no—
137C22⋊C8×C43C2311yescharacteristic
138C22⋊C8×C43C2311yescharacteristic
139#95×C43C2312yes—
140C24×C43C2×D411yescharacteristic
141C2×Q8×C43—21no—
142C2×Q8×C43—42no—
143C2×Q8×C43C22×C412yes—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—22no—
147C22×C4×C43—42no—
148C22×C4×C43C22×C411yescharacteristic
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2411yescharacteristic
154C2×C22⋊D43—21no—
155C2×C22⋊D43—21no—
156C2×C22⋊D43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43C2×D412yes—
160C22×Dic43C2×D412yes—
161#10621898—42no—
162C2×D172C22×C411yescharacteristic
163C2×C4×D43—21no—
164C2×C4×D43—22no—
165C2×Dic86—22no—
166C2×Dic86C22×C411yescharacteristic
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—42no—
170C4⋊C4×C43—22no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—22no—
173C4⋊C4×C43—42no—
174C4⋊C4×C43C22×C412yes—
175C22⋊C4×C43—22no—
176C22⋊C4×C43—22no—
177C22⋊C4×C43—81no—
178C22⋊Dic43—21no—
179C22⋊Dic43—21no—
180C22⋊Dic43—21no—
181C22⋊Dic43—42no—
182C22⋊Dic43C22⋊C412yes—
183C22⋊Dic43C22⋊C412yes—
184C22⋊Dic43C22⋊C412yes—
185C22⋊Dic43C22⋊C412yes—
186(C2×D43)⋊C4—21no—
187(C2×D43)⋊C4—21no—
188(C2×D43)⋊C4—22no—
189(C2×D43)⋊C4—22no—
190(C2×D43)⋊C4—22no—
191C4⋊Dic43—22no—
192C4⋊Dic43—22no—
193C4⋊Dic43—22no—
194C4⋊Dic43C22⋊C411yescharacteristic
195C4⋊Dic43C22⋊C411yescharacteristic
196C4⋊Dic43C22⋊C411yescharacteristic
197C4⋊Dic43C22⋊C411yescharacteristic
198C4⋊Dic43C22⋊C412yes—
199C4⋊Dic43C22⋊C412yes—
200C4⋊Dic43C22×C411yescharacteristic
201C4⋊Dic43C22×C411yescharacteristic
202Dic43⋊C4—21no—
203Dic43⋊C4—21no—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208Dic43⋊C4—22no—
209Dic43⋊C4—44no—
210C4×Dic43—21no—
211C4×Dic43—22no—
212C4×Dic43—22no—
213C4×Dic43—22no—
214C4×Dic43—42no—
215C4×Dic43—82no—
216C4×Dic43C22×C412yes—
217C4×Dic43C22×C412yes—
218C4×Dic43C2×D412yes—
219C4×Dic43C2×D412yes—
220#10621877—42no—
221C2×C43⋊C8—22no—
222C23×C43—21no—
223C23×C43—21no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43C2×C22⋊C411yescharacteristic
227C23×C43C2×C22⋊C411yescharacteristic
228C23×C43C22×D411yescharacteristic
229C22×D43—21no—
230Q8×C43—42no—
231Q8×C43—42no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—22no—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43—81no—
245C2×C4×C43C2×C22⋊C411yescharacteristic
246C2×C4×C43C2×C22⋊C411yescharacteristic
247C2×C4×C43C23×C411yescharacteristic
248C2×C4×C43C22×D411yescharacteristic
249C22⋊D43—42no—
250C22⋊D43—41no—
251C22⋊D43—41no—
252C22⋊D43—81no—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—22no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—42no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43C2×C22⋊C412yes—
266C2×Dic43C2×C22⋊C412yes—
267C2×Dic43C2×C22⋊C412yes—
268C2×Dic43C2×C22⋊C412yes—
269D172—41no—
270C4×D43—42no—
271C4×D43—82no—
272Dic86—41no—
273Dic86—82no—
274C8×C43—41no—
275C8×C43—41no—
276C43⋊C8—42no—
277#17612—431nomaximal, Sylow
278C22×C43—21no—
279C22×C43—21no—
280C22×C43—21no—
281C22×C43—21no—
282C22×C43—21no—
283C22×C43—21no—
284C22×C43—21no—
285C22×C43—21no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43C22×C22⋊C411yescharacteristic
289C22×C43#57711yescharacteristic
290C22×C43#57811yescharacteristic
291C2×D43—41no—
292C2×D43—41no—
293C2×D43—41no—
294C4×C43—21no—
295C4×C43—21no—
296C4×C43—21no—
297C4×C43—42no—
298C4×C43—42no—
299C4×C43—82no—
300C4×C43#41012yes—
301Dic43—22no—
302Dic43—22no—
303Dic43—22no—
304Dic43—22no—
305Dic43—42no—
306Dic43—41no—
307Dic43—41no—
308Dic43—41no—
309Dic43—81no—
310#3495—431no—
311#2924—431no—
312#2347—431no—
313#1521—432no—
314#1520D4311yescharacteristic, complemented
315#1515—432no—
316#1513—431no—
317#1509—432no—
318#1508—431no—
319#1503—432no—
320#1501—431no—
321C2×C43—21no—
322C2×C43—21no—
323C2×C43—41no—
324C2×C43—41no—
325C2×C43C2×#41011yescharacteristic
326C2×C43#289811yescharacteristic
327C2×C43#290111yescharacteristic
328D43—81no—
329#556—861no—
330#554—861no—
331#552—862no—
332#552—861no—
333#552—861no—
334#551—862no—
335#544—431no—
336#542—432no—
337#541—432no—
338#536—431no—
339#533—432no—
340#529—432no—
341#525—431no—
342C2×C22⋊Q8C2×D4311yescharacteristic
343#520—431no—
344#519—431no—
345C2×#117—431no—
346#433—862no—
347#432—432no—
348#431—432no—
349#424—861no—
350#407—431no—
351C2×C22⋊C8C2×D4311yescharacteristic
352#405—861no—
353#389—861no—
354#388—862no—
355#383—432no—
356#380C2×D4311yescharacteristic
357C4×C4⋊C4—432no—
358C4×C4⋊C4—861no—
359C4×C22⋊C4—431no—
360#328—432no—
361#328—432no—
362#328—431no—
363#328—431no—
364#328—432no—
365#328C2×D4312yes—
366#328C2×D4312yes—
367#327—431no—
368#327—431no—
369#327—432no—
370C43#1761211yescharacteristic, complemented, Sylow
371C2×#41—431no—
372C22×Q8C4×D4311yescharacteristic
373C23×C4C22×D4311yescharacteristic
374C2×M16—861no—
375C22×C8—21no—
376C4⋊Q8—432no—
377C4⋊Q8—432no—
378C4⋊Q8—861no—
379#126—862no—
380#126—862no—
381#126—862no—
382#126—862no—
383#125—432no—
384#125—862no—
385#125—862no—
386#125—862no—
387#125—861no—
388#124—432no—
389#124—862no—
390#123—862no—
391#123—862no—
392#123—862no—
393#123—861no—
394C22⋊Q8—21no—
395C22⋊Q8—21no—
396C22⋊Q8—431no—
397C22⋊Q8—431no—
398C22⋊Q8—862no—
399C22⋊Q8—862no—
400C22⋊Q8—862no—
401C22⋊Q8—861no—
402C22⋊Q8—861no—
403C22⋊Q8C4×D4312yes—
404C22⋊Q8C22×D4312yes—
405#121—431no—
406#121—431no—
407#120—861no—
408C4×Q8—432no—
409C4×Q8—432no—
410C4×Q8—432no—
411C4×Q8—862no—
412C4×Q8—861no—
413C4×Q8—861no—
414C4×D4—432no—
415C4×D4—862no—
416C4×D4—862no—
417C4×D4—861no—
418C4×D4—861no—
419#117—431no—
420#117—431no—
421#117—432no—
422#117—431no—
423#117—432no—
424#117—431no—
425#117—431no—
426#117—862no—
427#117—862no—
428#117—862no—
429#117—861no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—431no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4—862no—
436C2×C4⋊C4C4×D4311yescharacteristic
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—432no—
440C2×C22⋊C4—861no—
441C2×C42—432no—
442C2×C42—862no—
443C2×C42—861no—
444C4⋊C8—862no—
445C4⋊C8—862no—
446C22⋊C8—21no—
447C22⋊C8—432no—
448C22⋊C8—861no—
449C22⋊C8C22×D4311yescharacteristic
450C22⋊C8C22×D4311yescharacteristic
451#97—862no—
452C4×C8—862no—
453#95—431no—
454#95—431no—
455#95—862no—
456#95—862no—
457#95C22×D4312yes—
458C24D4×D4311yescharacteristic
459#41—1722no—
460C2×Q8—21no—
461C2×Q8—42no—
462C2×Q8—431no—
463C2×Q8—862no—
464C2×Q8C2×C4×D4312yes—
465C2×D4—431no—
466C2×D4—861no—
467C2×D4—861no—
468C2×D4—861no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—42no—
473C22×C4—432no—
474C22×C4—432no—
475C22×C4—862no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4C2×C4×D4311yescharacteristic
480C22×C4C2×C4×D4311yescharacteristic
481C22×C4D4×D4311yescharacteristic
482C22×C4D4×D4311yescharacteristic
483C22×C4D4×D4311yescharacteristic
484C22×C4C23×D4311yescharacteristic
485M16—1722no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—42no—
489C2×C8—862no—
490C4⋊C4—22no—
491C4⋊C4—21no—
492C4⋊C4—22no—
493C4⋊C4—42no—
494C4⋊C4—431no—
495C4⋊C4—431no—
496C4⋊C4—432no—
497C4⋊C4—431no—
498C4⋊C4—431no—
499C4⋊C4—432no—
500C4⋊C4—431no—
501C4⋊C4—431no—
502C4⋊C4—862no—
503C4⋊C4—862no—
504C4⋊C4—862no—
505C4⋊C4—862no—
506C4⋊C4—862no—
507C4⋊C4—862no—
508C4⋊C4—862no—
509C4⋊C4—862no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—1724no—
513C4⋊C4C2×C4×D4312yes—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—81no—
517C22⋊C4—432no—
518C22⋊C4—432no—
519C22⋊C4—432no—
520C22⋊C4—432no—
521C22⋊C4—862no—
522C22⋊C4—862no—
523C22⋊C4—862no—
524C22⋊C4—861no—
525C22⋊C4—861no—
526C22⋊C4—861no—
527C22⋊C4—861no—
528C22⋊C4—861no—
529C22⋊C4—1722no—
530C42—432no—
531C42—432no—
532C42—432no—
533C42—432no—
534C42—862no—
535C42—862no—
536C42—862no—
537C42—861no—
538C42—3442no—
539C42—1722no—
540C23—21no—
541C23—21no—
542C23—41no—
543C23—41no—
544C23—861no—
545C23C22⋊C4×D4311yescharacteristic
546C23C22⋊C4×D4311yescharacteristic
547C23C2×D4×D4311yescharacteristic
548Q8—42no—
549Q8—42no—
550Q8—3442no—
551Q8—1721no—
552D4—3441no—
553D4—1721no—
554D4—1722no—
555D4—1721no—
556D4—1721no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—81no—
570C2×C4—432no—
571C2×C4—432no—
572C2×C4—432no—
573C2×C4—432no—
574C2×C4—862no—
575C2×C4—862no—
576C2×C4—862no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—3442no—
581C2×C4—1722no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1722no—
588C2×C4C22⋊C4×D4311yescharacteristic
589C2×C4C22⋊C4×D4311yescharacteristic
590C2×C4C22×C4×D4311yescharacteristic
591C2×C4C2×D4×D4311yescharacteristic
592C8—41no—
593C8—41no—
594C8—1722no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—21no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—81no—
604C22—81no—
605C22—1721no—
606C22—1721no—
607C22—1721no—
608C22C2×C22⋊C4×D4311yescharacteristic
609C22#1458370511yescharacteristic
610C22#1458371211yescharacteristic
611C4—21no—
612C4—21no—
613C4—21no—
614C4—42no—
615C4—42no—
616C4—82no—
617C4—862no—
618C4—862no—
619C4—862no—
620C4—862no—
621C4—3441no—
622C4—1722no—
623C4—1721no—
624C4—1721no—
625C4—1721no—
626C4#1458287112yes—
627C2—21no—
628C2—21no—
629C2—41no—
630C2—41no—
631C2—3441no—
632C2C2×#1458287111yescharacteristic
633C2#1914312311yescharacteristic
634C2#1914314111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1520C2
socleC22×C43C22×C22⋊C4
prime radical#14583410C22
cosocleC22×C4×C43C24
hypercenter#1520D43
hypocenterC43#17612
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
2. #19143249C2semidirect
3. #19137490C2semidirect
4. #19133171C2semidirect
5. #19133144C2semidirect
7. #19133119C2semidirect
8. #19133115C2semidirect
9. #19133092C2semidirect
11. C43×#1520C2semidirect
18. #14583530C4semidirect
19. #14583522C4semidirect
20. #14583509C4semidirect
21. #14583473C4semidirect
25. #14583380C4semidirect
26. #14583377C4semidirect
314. #1520D43semidirect
370. C43#17612semidirect

Maximal subgroups

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

subgroupindex
#191483412
#191432492
#191374902
#191331712
#191331442
#191331362
#191331192
#191331152
#191330922
#191330872
C43×#15202
#1761243