Finite Group Databasebeta

← #25064240

Subgroups — #25064240

Order 11008.

990 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148332C211yesmaximal, characteristic
2#19143255C211yesmaximal, characteristic, complemented
3#19137490C211yesmaximal, characteristic, complemented
4#19133171C212yesmaximal, complemented
5#19133162C211yesmaximal, characteristic, complemented
6#19133140C212yesmaximal, complemented
7#19133119C212yesmaximal, complemented
8#19133112C211yesmaximal, characteristic, complemented
9#19133088C212yesmaximal, complemented
10#19133086C211yesmaximal, characteristic, complemented
11C43×#1513C211yesmaximal, characteristic, complemented
12#14583614—21no—
13#14583595—21no—
14#14583595—21no—
15#14583572—22no—
16#14583553—21no—
17#14583536—22no—
18#14583527C411yescharacteristic, complemented
19#14583522C412yescomplemented
20#14583502C412yescomplemented
21#14583463C411yescharacteristic, complemented
22#14583444C2212yes—
23#14583435C2212yes—
24C2×#13063299C2211yescharacteristic
25#14583382C411yescharacteristic, complemented
26#14583373C411yescharacteristic, complemented
27C2×#13063284C2211yescharacteristic
28#14582957—22no—
29#14582953C2212yescomplemented
30#14582949C2212yescomplemented
31#14582927—21no—
32C2×C22⋊(C43⋊C8)C2211yescharacteristic
33#14582857—21no—
34#14582795—21no—
35#14582787—22no—
36#14582766C2212yescomplemented
37C4⋊C4×Dic43—21no—
38#14582750C2212yescomplemented
39C4×C22⋊Dic43C2211yescharacteristic
40#14582636C2211yescharacteristic, complemented
41#14582636C2211yescharacteristic, complemented
42#14582634C2212yes—
43#14582634C2212yes—
44#14582633C2211yescharacteristic, complemented
45#14582633C2211yescharacteristic, complemented
46#14582632C2212yes—
47#14582632C2212yes—
48C43×#525C2211yescharacteristic
49C43×#407C2211yescharacteristic
50C43×#380C2211yescharacteristic
51C43×#328C2212yescomplemented
52C43×#327C2212yescomplemented
53C2×#10621900—22no—
54C22×D172C2×C411yescharacteristic
55C22×C22⋊D43—21no—
56C22×C43⋊C8—21no—
57#13063325—21no—
58#13063324C2×C412yes—
59#13063321C2×C412yes—
60#13063320—22no—
61#13063320—22no—
62#13063317—21no—
63#13063316C2×C412yes—
64#13063314C2×C412yes—
65#13063311—22no—
66#13063311—22no—
67#13063309—22no—
68#13063309—22no—
69#13063307—22no—
70#13063307—22no—
71#13063305—22no—
72#13063302—22no—
73#13063299—21no—
74#13063299—21no—
75#13063299—21no—
76#13063299—21no—
77#13063299C2×C412yes—
78#13063299C2312yes—
79#13063297—22no—
80#13063297—22no—
81#13063296—22no—
82#13063293—22no—
83Q8×Dic43C2×C412yes—
84C4×D172—21no—
85C4×D172—21no—
86D4×Dic43—22no—
87D4×Dic43C2×C412yes—
88#13063287C2×C412yes—
89#13063287C2×C412yes—
90(C22⋊D43)⋊C4—22no—
91(C22⋊D43)⋊C4—22no—
92#13063284—21no—
93#13063284C2×C411yescharacteristic
94#13063284C2×C411yescharacteristic
95#13063284C2×C412yes—
96#13063284D412yes—
97#13063284D411yescharacteristic
98#13063284D411yescharacteristic
99#13063283—22no—
100C2×C4⋊Dic43—21no—
101C2×C4⋊Dic43C2×C411yescharacteristic
102C2×C4⋊Dic43D411yescharacteristic
103C2×C4⋊Dic43D411yescharacteristic
104C2×Dic43⋊C4—22no—
105C2×C22⋊Dic43—21no—
106C2×C22⋊Dic43D412yes—
107C2×(C2×D43)⋊C4—21no—
108C22⋊C4×D43—22no—
109C2×C4×Dic43—21no—
110C2×C4×Dic43—22no—
111C2×C4×Dic43C2312yes—
112Dic43⋊C8—22no—
113Dic43⋊C8—22no—
114C22⋊(C43⋊C8)—21no—
115C22⋊(C43⋊C8)C2311yescharacteristic
116C22⋊(C43⋊C8)C2311yescharacteristic
117#13063235—22no—
118C8×Dic43—22no—
119C43⋊#95—22no—
120C43⋊#95—22no—
121C43⋊#95C2311yescharacteristic
122C43⋊#95C2311yescharacteristic
123C2×#41×C43C2×C411yescharacteristic
124C23×C4×C43C2311yescharacteristic
125C2×M16×C43—21no—
126#123×C43—21no—
127C22⋊Q8×C43C2×C411yescharacteristic
128C22⋊Q8×C43C2311yescharacteristic
129#121×C43C2×C411yescharacteristic
130#121×C43C2311yescharacteristic
131#120×C43—21no—
132C4×D4×C43—21no—
133C4×D4×C43—21no—
134#117×C43C2×C411yescharacteristic
135C2×C4⋊C4×C43—21no—
136C2×C22⋊C4×C43—21no—
137C22⋊C8×C43—21no—
138C22⋊C8×C43C2312yes—
139#95×C43C2312yes—
140C24×C43C2×D411yescharacteristic
141C23×D43—21no—
142#41×C43—42no—
143C2×Q8×C43C22×C411yescharacteristic
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43C22×C411yescharacteristic
148C22×C4×C43—21no—
149C22×C4×C43—22no—
150C22×C4×C43—42no—
151C22×C4×C43C22×C411yescharacteristic
152C22×C4×C43C22×C411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2411yescharacteristic
157C2×C22⋊D43—22no—
158C2×C22⋊D43—22no—
159C2×C22⋊D43—22no—
160C2×C22⋊D43—22no—
161C2×C22⋊D43—81no—
162C2×C22⋊D43—81no—
163C22×Dic43—22no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43C2×D412yes—
168C22×Dic43C2×D412yes—
169#10621900—82no—
170#10621900—82no—
171C2×D172—21no—
172C2×D172—42no—
173C2×D172C22×C412yes—
174C2×C4×D43—22no—
175C2×C4×D43—22no—
176C2×Dic86—22no—
177M16×C43—42no—
178C2×C8×C43—22no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—42no—
182C4⋊C4×C43C22×C411yescharacteristic
183C4⋊C4×C43C22×C411yescharacteristic
184C22⋊C4×C43—21no—
185C22⋊C4×C43—21no—
186C22⋊C4×C43—21no—
187C22⋊C4×C43—21no—
188C22⋊C4×C43—21no—
189C22⋊C4×C43—81no—
190C42×C43—21no—
191C22⋊Dic43—22no—
192C22⋊Dic43—42no—
193C22⋊Dic43C22⋊C412yes—
194C22⋊Dic43C22⋊C412yes—
195C22⋊Dic43C22⋊C412yes—
196C22⋊Dic43C22⋊C412yes—
197(C2×D43)⋊C4—22no—
198(C2×D43)⋊C4—22no—
199(C2×D43)⋊C4—22no—
200(C2×D43)⋊C4—22no—
201(C2×D43)⋊C4—22no—
202(C2×D43)⋊C4—22no—
203C4⋊Dic43—21no—
204C4⋊Dic43—22no—
205C4⋊Dic43—22no—
206C4⋊Dic43C22⋊C411yescharacteristic
207C4⋊Dic43C22⋊C411yescharacteristic
208C4⋊Dic43C22⋊C411yescharacteristic
209C4⋊Dic43C22⋊C411yescharacteristic
210C4⋊Dic43C22⋊C412yes—
211C4⋊Dic43C22⋊C412yes—
212C4⋊Dic43C22×C412yes—
213Dic43⋊C4—22no—
214Dic43⋊C4—22no—
215Dic43⋊C4—44no—
216C4×Dic43—22no—
217C4×Dic43—42no—
218C4×Dic43—82no—
219C4×Dic43C22×C412yes—
220C4×Dic43C22×C412yes—
221C4×Dic43C2×D412yes—
222C4×Dic43C2×D412yes—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—42no—
226C23×C43—21no—
227C23×C43—21no—
228C23×C43—21no—
229C23×C43—41no—
230C23×C43—41no—
231C23×C43C2×C22⋊C411yescharacteristic
232C23×C43C2×C22⋊C411yescharacteristic
233C23×C43C22×D411yescharacteristic
234C22×D43—22no—
235C22×D43—42no—
236C22×D43—81no—
237C22×D43—81no—
238Q8×C43—41no—
239D4×C43—41no—
240D4×C43—42no—
241D4×C43—41no—
242D4×C43—41no—
243D4×C43—81no—
244C2×C4×C43—22no—
245C2×C4×C43—22no—
246C2×C4×C43—22no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—42no—
254C2×C4×C43—42no—
255C2×C4×C43—42no—
256C2×C4×C43—42no—
257C2×C4×C43C2×C22⋊C411yescharacteristic
258C2×C4×C43C2×C22⋊C411yescharacteristic
259C2×C4×C43C23×C411yescharacteristic
260C2×C4×C43C22×D411yescharacteristic
261C22⋊D43—42no—
262C22⋊D43—42no—
263C22⋊D43—82no—
264C22⋊D43—82no—
265C22⋊D43—82no—
266C2×Dic43—22no—
267C2×Dic43—22no—
268C2×Dic43—22no—
269C2×Dic43—22no—
270C2×Dic43—42no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—82no—
277C2×Dic43—81no—
278C2×Dic43C2×C22⋊C412yes—
279C2×Dic43C2×C22⋊C412yes—
280C2×Dic43C2×C22⋊C412yes—
281C2×Dic43C2×C22⋊C412yes—
282D172—42no—
283D172—42no—
284C4×D43—82no—
285C4×D43—82no—
286Dic86—82no—
287C8×C43—42no—
288C43⋊C8—41no—
289C43⋊C8—41no—
290#17607—431nomaximal, Sylow
291C22×C43—21no—
292C22×C43—21no—
293C22×C43—21no—
294C22×C43—21no—
295C22×C43—21no—
296C22×C43—21no—
297C22×C43—21no—
298C22×C43—21no—
299C22×C43—41no—
300C22×C43—41no—
301C22×C43—41no—
302C22×C43—81no—
303C22×C43—81no—
304C22×C43C22×C22⋊C411yescharacteristic
305C22×C43#57611yescharacteristic
306C22×C43#57711yescharacteristic
307C2×D43—42no—
308C2×D43—42no—
309C2×D43—42no—
310C2×D43—162no—
311C4×C43—21no—
312C4×C43—21no—
313C4×C43—21no—
314C4×C43—41no—
315C4×C43—41no—
316C4×C43—41no—
317C4×C43—82no—
318C4×C43#41012yes—
319Dic43—22no—
320Dic43—22no—
321Dic43—22no—
322Dic43—22no—
323Dic43—42no—
324Dic43—42no—
325Dic43—81no—
326#3494—431no—
327#2924—431no—
328#2347—431no—
329#1521—432no—
330#1519—431no—
331#1514—432no—
332#1513D4311yescharacteristic, complemented
333#1509—432no—
334#1507—431no—
335#1502—432no—
336#1501—431no—
337C2×C43—21no—
338C2×C43—21no—
339C2×C43—41no—
340C2×C43—41no—
341C2×C43—81no—
342C2×C43C2×#41011yescharacteristic
343C2×C43#289711yescharacteristic
344C2×C43#290111yescharacteristic
345D43—82no—
346#555—861no—
347#553—861no—
348#553—861no—
349#551—862no—
350#547—861no—
351#546—862no—
352#544—431no—
353#542—432no—
354#540—432no—
355#535—431no—
356#532—432no—
357#529—432no—
358#525C2×D4311yescharacteristic
359C2×#121—431no—
360#520—431no—
361#518—431no—
362C2×#117—431no—
363#433—862no—
364#432—432no—
365#431—432no—
366#424—861no—
367#407C2×D4311yescharacteristic
368C2×C22⋊C8—431no—
369#405—861no—
370#389—861no—
371#388—862no—
372#383—432no—
373#380C2×D4311yescharacteristic
374C4×C4⋊C4—432no—
375C4×C4⋊C4—861no—
376C4×C22⋊C4—431no—
377#328—431no—
378#328—431no—
379#328C2×D4312yescomplemented
380#327—431no—
381#327—431no—
382#327—432no—
383#327—432no—
384#327—432no—
385#327—432no—
386#327C2×D4312yescomplemented
387C43#1760711yescharacteristic, complemented, Sylow
388C2×#41—862no—
389C2×#41C4×D4311yescharacteristic
390C22×D4—431no—
391C22×D4—861no—
392C23×C4C22×D4311yescharacteristic
393C2×M16—21no—
394C22×C8—861no—
395C4⋊Q8—432no—
396C4⋊Q8—861no—
397#127—432no—
398#126—862no—
399#126—862no—
400#125—432no—
401#125—861no—
402#124—432no—
403#124—862no—
404#124—862no—
405#123—21no—
406#123—862no—
407#123—862no—
408#123—862no—
409#123—862no—
410C22⋊Q8—862no—
411C22⋊Q8—862no—
412C22⋊Q8C4×D4311yescharacteristic
413C22⋊Q8C22×D4311yescharacteristic
414#121—432no—
415#121—432no—
416#121—862no—
417#121—862no—
418#121—861no—
419#121—861no—
420#121—862no—
421#121—861no—
422#121—861no—
423#121C4×D4311yescharacteristic
424#121C22×D4311yescharacteristic
425#120—21no—
426#120—862no—
427C4×Q8—432no—
428C4×D4—21no—
429C4×D4—21no—
430C4×D4—432no—
431C4×D4—432no—
432C4×D4—432no—
433C4×D4—861no—
434C4×D4—861no—
435C4×D4—862no—
436C4×D4—862no—
437C4×D4—862no—
438#117—431no—
439#117—431no—
440#117—432no—
441#117—432no—
442#117—431no—
443#117—431no—
444#117—862no—
445#117—861no—
446#117C4×D4311yescharacteristic
447C2×C4⋊C4—21no—
448C2×C4⋊C4—431no—
449C2×C4⋊C4—431no—
450C2×C4⋊C4—431no—
451C2×C4⋊C4—861no—
452C2×C4⋊C4—862no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—432no—
455C2×C22⋊C4—862no—
456C2×C22⋊C4—861no—
457C2×C22⋊C4—861no—
458C2×C42—432no—
459C2×C42—862no—
460C2×C42—861no—
461C4⋊C8—862no—
462C4⋊C8—862no—
463C22⋊C8—21no—
464C22⋊C8—431no—
465C22⋊C8—431no—
466C22⋊C8—861no—
467C22⋊C8C22×D4312yes—
468#97—862no—
469C4×C8—862no—
470#95—431no—
471#95—431no—
472#95—862no—
473#95—862no—
474#95C22×D4312yes—
475C24—861no—
476C24D4×D4311yescharacteristic
477#41—42no—
478#41—3442no—
479#41—3442no—
480C2×Q8—862no—
481C2×Q8C2×C4×D4311yescharacteristic
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—432no—
486C2×D4—862no—
487C2×D4—862no—
488C2×D4—862no—
489C2×D4—862no—
490C2×D4—861no—
491C2×D4—3441no—
492C2×D4—3441no—
493C2×D4—1722no—
494C2×D4C2×C4×D4311yescharacteristic
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—42no—
498C22×C4—432no—
499C22×C4—432no—
500C22×C4—862no—
501C22×C4—862no—
502C22×C4—862no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—861no—
506C22×C4C2×C4×D4311yescharacteristic
507C22×C4C2×C4×D4311yescharacteristic
508C22×C4D4×D4311yescharacteristic
509C22×C4D4×D4311yescharacteristic
510C22×C4D4×D4311yescharacteristic
511C22×C4C23×D4311yescharacteristic
512M16—42no—
513C2×C8—22no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—1722no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—42no—
520C4⋊C4—431no—
521C4⋊C4—431no—
522C4⋊C4—431no—
523C4⋊C4—431no—
524C4⋊C4—432no—
525C4⋊C4—432no—
526C4⋊C4—432no—
527C4⋊C4—862no—
528C4⋊C4—862no—
529C4⋊C4—862no—
530C4⋊C4—862no—
531C4⋊C4—861no—
532C4⋊C4—1724no—
533C4⋊C4C2×C4×D4311yescharacteristic
534C4⋊C4C2×C4×D4311yescharacteristic
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—21no—
540C22⋊C4—81no—
541C22⋊C4—432no—
542C22⋊C4—432no—
543C22⋊C4—432no—
544C22⋊C4—432no—
545C22⋊C4—862no—
546C22⋊C4—862no—
547C22⋊C4—862no—
548C22⋊C4—862no—
549C22⋊C4—862no—
550C22⋊C4—862no—
551C22⋊C4—862no—
552C22⋊C4—1722no—
553C42—21no—
554C42—432no—
555C42—432no—
556C42—432no—
557C42—432no—
558C42—862no—
559C42—3442no—
560C42—1722no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—41no—
565C23—41no—
566C23—862no—
567C23—3441no—
568C23—3441no—
569C23—1722no—
570C23C22⋊C4×D4311yescharacteristic
571C23C22⋊C4×D4311yescharacteristic
572C23C2×D4×D4311yescharacteristic
573Q8—41no—
574Q8—3442no—
575D4—41no—
576D4—42no—
577D4—41no—
578D4—41no—
579D4—81no—
580D4—3442no—
581D4—3442no—
582D4—3442no—
583D4—1722no—
584D4—1722no—
585D4—1722no—
586D4—1722no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—432no—
601C2×C4—432no—
602C2×C4—432no—
603C2×C4—432no—
604C2×C4—862no—
605C2×C4—862no—
606C2×C4—862no—
607C2×C4—862no—
608C2×C4—3442no—
609C2×C4—3442no—
610C2×C4—3442no—
611C2×C4—3441no—
612C2×C4—1722no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4C22⋊C4×D4311yescharacteristic
619C2×C4C22⋊C4×D4311yescharacteristic
620C2×C4C22×C4×D4311yescharacteristic
621C2×C4C2×D4×D4311yescharacteristic
622C8—42no—
623C8—1721no—
624C8—1721no—
625C22—21no—
626C22—21no—
627C22—21no—
628C22—21no—
629C22—21no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—81no—
637C22—81no—
638C22—1722no—
639C22—1722no—
640C22—1722no—
641C22—6882no—
642C22C2×C22⋊C4×D4311yescharacteristic
643C22#1458370311yescharacteristic
644C22#1458370811yescharacteristic
645C4—21no—
646C4—21no—
647C4—21no—
648C4—41no—
649C4—41no—
650C4—41no—
651C4—82no—
652C4—862no—
653C4—862no—
654C4—862no—
655C4—862no—
656C4—3441no—
657C4—1722no—
658C4—1722no—
659C4#1458287112yes—
660C2—21no—
661C2—21no—
662C2—41no—
663C2—41no—
664C2—81no—
665C2—3442no—
666C2C2×#1458287111yescharacteristic
667C2#1914311911yescharacteristic
668C2#1914314111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1513C2
socleC22×C43C22×C22⋊C4
prime radical#19148332C2
cosocleC22×C4×C43C24
hypercenter#1513D43
hypocenterC43#17607
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1513

Complements

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

NH ≅ G/Ntype
2. #19143255C2semidirect
3. #19137490C2semidirect
4. #19133171C2semidirect
5. #19133162C2semidirect
6. #19133140C2semidirect
7. #19133119C2semidirect
8. #19133112C2semidirect
9. #19133088C2semidirect
10. #19133086C2semidirect
11. C43×#1513C2semidirect
18. #14583527C4semidirect
19. #14583522C4semidirect
20. #14583502C4semidirect
21. #14583463C4semidirect
25. #14583382C4semidirect
26. #14583373C4semidirect
29. #14582953C22semidirect
30. #14582949C22semidirect
36. #14582766C22semidirect
38. #14582750C22semidirect
40. #14582636C22semidirect
41. #14582636C22semidirect
44. #14582633C22semidirect
45. #14582633C22semidirect
51. C43×#328C22semidirect
52. C43×#327C22semidirect
332. #1513D43semidirect
379. #328C2×D43semidirect
386. #327C2×D43semidirect
387. C43#17607semidirect

Maximal subgroups

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

subgroupindex
#191483322
#191432552
#191374902
#191331712
#191331622
#191331402
#191331192
#191331122
#191330882
#191330862
C43×#15132
#1760743