Finite Group Databasebeta

← #25064296

Subgroups — #25064296

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#19148347C211yesmaximal, characteristic
2#19137488C211yesmaximal, characteristic, complemented
3#19133173C212yesmaximal, complemented
4#19133168C211yesmaximal, characteristic, complemented
5#19133147C212yesmaximal, complemented
6#19133139C211yesmaximal, characteristic
7#19133121C212yesmaximal, complemented
8#19133116C211yesmaximal, characteristic, complemented
9#19133095C212yesmaximal, complemented
10#19133087C211yesmaximal, characteristic
11C43×#2924C211yesmaximal, characteristic, complemented
12#14583617—21no—
13#14583604—21no—
14#14583588—21no—
15#14583584—21no—
16#14583582—22no—
17#14583575—22no—
18#14583527C411yescharacteristic, complemented
19#14583520C412yescomplemented
20#14583511C412yescomplemented
21#14583475C411yescharacteristic, complemented
22#14583456C2212yes—
23#14583433C2212yes—
24#14583410C2211yescharacteristic
25C2×#13063304C2211yescharacteristic
26#14583379C411yescharacteristic, complemented
27#14583376C411yescharacteristic, complemented
28#14582798—21no—
29#14582792—22no—
30#14582767C2212yes—
31#14582759C2211yescharacteristic
32C4⋊C4×Dic43—21no—
33C4×C4⋊Dic43C2212yes—
34C4×C22⋊Dic43C2211yescharacteristic
35#14582637C2211yescharacteristic
36#14582637C2211yescharacteristic
37#14582637C2212yes—
38#14582637C2212yes—
39#14582637C2212yes—
40#14582637C2212yes—
41#14582637C2212yes—
42#14582634C2211yescharacteristic
43#14582634C2211yescharacteristic
44#14582634C2212yes—
45C2×#117×C43C2211yescharacteristic
46C43×#433—22no—
47C43×#432C2212yes—
48C43×#431C2212yes—
49C43×#424—21no—
50C43×#407C2211yescharacteristic
51C2×C22⋊C8×C43C2211yescharacteristic
52C43×#405—21no—
53C2×#10621898C2×C411yescharacteristic
54C22×Dic86C2×C411yescharacteristic
55#13063325C2×C412yes—
56#13063325C2×C412yes—
57#13063324—21no—
58#13063320—22no—
59#13063319—22no—
60#13063318—22no—
61#13063318—22no—
62#13063317—22no—
63#13063317C2×C412yes—
64#13063316—21no—
65#13063315—22no—
66#13063315—22no—
67#13063313C2×C412yes—
68#13063311—22no—
69#13063309—22no—
70#13063308—22no—
71#13063308—21no—
72#13063307—22no—
73#13063305—21no—
74#13063305—21no—
75#13063304—22no—
76#13063304—21no—
77#13063304—21no—
78#13063304C2×C412yes—
79#13063304C2×C411yescharacteristic
80#13063304C2312yes—
81#13063304C2311yescharacteristic
82#13063303—22no—
83#13063302—22no—
84#13063299C2×C411yescharacteristic
85#13063299C2311yescharacteristic
86#13063294—21no—
87C4×Dic86—22no—
88C4×Dic86C2×C412yes—
89C4×Dic86C2×C412yes—
90C4×Dic86C2×C412yes—
91#13063290—21no—
92#13063290—21no—
93C4×D172C2×C412yes—
94C4×C22⋊D43—22no—
95C4×C22⋊D43—21no—
96C4×C22⋊D43—21no—
97(C22⋊D43)⋊C4—22no—
98#13063284—22no—
99#13063284C2×C411yescharacteristic
100#13063283—21no—
101#13063282—22no—
102#13063281—22no—
103C2×C4⋊Dic43—22no—
104C2×C4⋊Dic43—21no—
105C2×C4⋊Dic43C2×C411yescharacteristic
106C2×Dic43⋊C4—21no—
107C4⋊C4×D43—21no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43—21no—
111C2×C4×Dic43—21no—
112C2×C4×Dic43—22no—
113C43⋊#95—22no—
114C43⋊#95—22no—
115C43⋊#95C2311yescharacteristic
116C43⋊#95C2311yescharacteristic
117C43⋊#95C2312yes—
118C23×C4×C43C2311yescharacteristic
119C2×M16×C43—21no—
120C22×C8×C43—21no—
121#117×C43C2×C411yescharacteristic
122#117×C43C2×C411yescharacteristic
123#117×C43C2×C412yes—
124#117×C43D412yes—
125#117×C43D411yescharacteristic
126#117×C43D411yescharacteristic
127C2×C4⋊C4×C43D411yescharacteristic
128C2×C4⋊C4×C43D411yescharacteristic
129C2×C22⋊C4×C43D412yes—
130C2×C42×C43C2312yes—
131C4⋊C8×C43—22no—
132C4⋊C8×C43—22no—
133C22⋊C8×C43—21no—
134C22⋊C8×C43—21no—
135C22⋊C8×C43C2311yescharacteristic
136C22⋊C8×C43C2311yescharacteristic
137C22⋊C8×C43C2312yes—
138#97×C43—22no—
139C4×C8×C43—22no—
140C24×C43C2×D411yescharacteristic
141C22×C4×C43—42no—
142C22×C4×C43C22×C411yescharacteristic
143C22×C4×C43C22×C411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D412yes—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D412yes—
149C22×C4×C43C2411yescharacteristic
150C2×C22⋊D43—21no—
151C2×C22⋊D43—21no—
152C2×C22⋊D43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—22no—
158#10621898—42no—
159C2×D172C22×C411yescharacteristic
160C2×C4×D43—21no—
161C2×C4×D43—22no—
162C2×Dic86—21no—
163C2×Dic86—22no—
164C2×Dic86—42no—
165C2×Dic86C22×C412yes—
166C2×Dic86C22×C411yescharacteristic
167M16×C43—42no—
168C2×C8×C43—21no—
169C2×C8×C43—22no—
170C2×C8×C43—21no—
171C2×C8×C43—42no—
172C4⋊C4×C43C22⋊C411yescharacteristic
173C4⋊C4×C43C22⋊C411yescharacteristic
174C4⋊C4×C43C22⋊C412yes—
175C4⋊C4×C43C22⋊C411yescharacteristic
176C4⋊C4×C43C22⋊C411yescharacteristic
177C4⋊C4×C43C22⋊C412yes—
178C22⋊C4×C43C22⋊C412yes—
179C22⋊C4×C43C22⋊C412yes—
180C22⋊C4×C43C22⋊C412yes—
181C22⋊C4×C43C22⋊C412yes—
182C42×C43C22×C412yes—
183C42×C43C22×C412yes—
184C42×C43C2×D412yes—
185C42×C43C2×D412yes—
186C22⋊Dic43—22no—
187C22⋊Dic43—21no—
188C22⋊Dic43—21no—
189C22⋊Dic43—22no—
190C22⋊Dic43—21no—
191C22⋊Dic43—42no—
192C22⋊Dic43—81no—
193(C2×D43)⋊C4—22no—
194(C2×D43)⋊C4—22no—
195(C2×D43)⋊C4—21no—
196(C2×D43)⋊C4—22no—
197(C2×D43)⋊C4—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—22no—
200C4⋊Dic43—22no—
201C4⋊Dic43—22no—
202C4⋊Dic43—44no—
203C4⋊Dic43—42no—
204C4⋊Dic43C22×C412yes—
205C4⋊Dic43C22×C411yescharacteristic
206C4⋊Dic43C22×C411yescharacteristic
207Dic43⋊C4—22no—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210Dic43⋊C4—22no—
211Dic43⋊C4—22no—
212Dic43⋊C4—22no—
213Dic43⋊C4—21no—
214Dic43⋊C4—22no—
215Dic43⋊C4—21no—
216C4×Dic43—22no—
217C4×Dic43—22no—
218C4×Dic43—22no—
219C4×Dic43—21no—
220C4×Dic43—42no—
221C4×Dic43—82no—
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—
230C2×C4×C43—22no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—22no—
235C2×C4×C43—42no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43C2×C22⋊C412yes—
240C2×C4×C43C2×C22⋊C412yes—
241C2×C4×C43C2×C22⋊C411yescharacteristic
242C2×C4×C43C2×C22⋊C412yes—
243C2×C4×C43C2×C22⋊C412yes—
244C2×C4×C43C2×C22⋊C411yescharacteristic
245C2×C4×C43C23×C411yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C22⋊D43—42no—
248C22⋊D43—41no—
249C22⋊D43—41no—
250C22⋊D43—81no—
251C2×Dic43—22no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—22no—
256C2×Dic43—22no—
257C2×Dic43—41no—
258C2×Dic43—42no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—42no—
262C2×Dic43—42no—
263C2×Dic43—41no—
264C2×Dic43—42no—
265C2×Dic43—41no—
266C2×Dic43—81no—
267D172—41no—
268C4×D43—42no—
269C4×D43—82no—
270Dic86—42no—
271Dic86—42no—
272Dic86—41no—
273Dic86—82no—
274C8×C43—41no—
275C8×C43—41no—
276C8×C43—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—22no—
298C4×C43—22no—
299C4×C43—22no—
300C4×C43—22no—
301C4×C43#41012yes—
302Dic43—42no—
303Dic43—42no—
304Dic43—41no—
305Dic43—41no—
306Dic43—41no—
307Dic43—42no—
308Dic43—82no—
309Dic43—81no—
310#3495—431no—
311#2924D4311yescharacteristic, complemented
312#2347—431no—
313#1521—432no—
314#1520—431no—
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⋊Q8—431no—
343#520—431no—
344#519—431no—
345C2×#117C2×D4311yescharacteristic
346#433—22no—
347#432C2×D4312yes—
348#431C2×D4312yes—
349#424—21no—
350#407C2×D4311yescharacteristic
351C2×C22⋊C8C2×D4311yescharacteristic
352#405—21no—
353#389—861no—
354#388—862no—
355#383—432no—
356#380—431no—
357C4×C4⋊C4—432no—
358C4×C4⋊C4—861no—
359C4×C22⋊C4—431no—
360#328—431no—
361#328—431no—
362#328—432no—
363#328—432no—
364#328—432no—
365#328—432no—
366#328—432no—
367#327—431no—
368#327—431no—
369#327—432no—
370C43#1761211yescharacteristic, complemented, Sylow
371C2×#41—431no—
372C22×Q8—431no—
373C23×C4C22×D4311yescharacteristic
374C2×M16—21no—
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—861no—
387#125—862no—
388#124—432no—
389#124—862no—
390#123—862no—
391#123—861no—
392#123—862no—
393#123—862no—
394C22⋊Q8—432no—
395C22⋊Q8—431no—
396C22⋊Q8—432no—
397C22⋊Q8—431no—
398C22⋊Q8—861no—
399C22⋊Q8—862no—
400C22⋊Q8—861no—
401C22⋊Q8—861no—
402C22⋊Q8—861no—
403C22⋊Q8—862no—
404C22⋊Q8—862no—
405#121—431no—
406#121—431no—
407#120—861no—
408C4×Q8—432no—
409C4×Q8—432no—
410C4×Q8—432no—
411C4×Q8—861no—
412C4×Q8—861no—
413C4×Q8—862no—
414C4×D4—432no—
415C4×D4—861no—
416C4×D4—862no—
417C4×D4—861no—
418C4×D4—862no—
419#117—431no—
420#117—862no—
421#117—861no—
422#117—862no—
423#117—862no—
424#117C4×D4311yescharacteristic
425#117C4×D4311yescharacteristic
426#117C4×D4312yes—
427#117C22⋊D4311yescharacteristic
428#117C22⋊D4312yes—
429#117C22⋊D4311yescharacteristic
430C2×C4⋊C4—431no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—862no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4D17211yescharacteristic
436C2×C4⋊C4D17211yescharacteristic
437C2×C22⋊C4—861no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4D17212yes—
441C2×C42—862no—
442C2×C42—861no—
443C2×C42C22×D4312yes—
444C4⋊C8—22no—
445C4⋊C8—22no—
446C22⋊C8—21no—
447C22⋊C8—21no—
448C22⋊C8C22×D4311yescharacteristic
449C22⋊C8C22×D4311yescharacteristic
450C22⋊C8C22×D4312yes—
451#97—22no—
452C4×C8—22no—
453#95—431no—
454#95—431no—
455#95—432no—
456#95—862no—
457#95—862no—
458C24C2×D17211yescharacteristic
459#41—1722no—
460C2×Q8—432no—
461C2×Q8—431no—
462C2×Q8—862no—
463C2×Q8—861no—
464C2×Q8—1722no—
465C2×D4—431no—
466C2×D4—861no—
467C2×D4—861no—
468C2×D4—861no—
469C22×C4—42no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—862no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—862no—
477C22×C4C2×C4×D4311yescharacteristic
478C22×C4C2×C4×D4311yescharacteristic
479C22×C4C2×D17212yes—
480C22×C4C2×D17211yescharacteristic
481C22×C4C2×D17212yes—
482C22×C4C2×C22⋊D4311yescharacteristic
483C22×C4C2×C22⋊D4311yescharacteristic
484C22×C4C23×D4311yescharacteristic
485M16—42no—
486C2×C8—21no—
487C2×C8—22no—
488C2×C8—21no—
489C2×C8—42no—
490C4⋊C4—432no—
491C4⋊C4—431no—
492C4⋊C4—431no—
493C4⋊C4—861no—
494C4⋊C4—862no—
495C4⋊C4—862no—
496C4⋊C4—862no—
497C4⋊C4—862no—
498C4⋊C4—862no—
499C4⋊C4—862no—
500C4⋊C4—862no—
501C4⋊C4—861no—
502C4⋊C4—862no—
503C4⋊C4—862no—
504C4⋊C4—862no—
505C4⋊C4—861no—
506C4⋊C4—1722no—
507C4⋊C4—1724no—
508C4⋊C4(C2×D43)⋊C411yescharacteristic
509C4⋊C4(C2×D43)⋊C411yescharacteristic
510C4⋊C4(C2×D43)⋊C412yes—
511C4⋊C4(C2×D43)⋊C411yescharacteristic
512C4⋊C4(C2×D43)⋊C411yescharacteristic
513C4⋊C4(C2×D43)⋊C412yes—
514C22⋊C4—862no—
515C22⋊C4—861no—
516C22⋊C4—861no—
517C22⋊C4—862no—
518C22⋊C4—861no—
519C22⋊C4—862no—
520C22⋊C4—862no—
521C22⋊C4—861no—
522C22⋊C4—862no—
523C22⋊C4—861no—
524C22⋊C4—3441no—
525C22⋊C4—1722no—
526C22⋊C4(C2×D43)⋊C412yes—
527C22⋊C4(C2×D43)⋊C412yes—
528C22⋊C4(C2×D43)⋊C412yes—
529C22⋊C4(C2×D43)⋊C412yes—
530C42—861no—
531C42—862no—
532C42—862no—
533C42—862no—
534C42—3442no—
535C42—1722no—
536C42C2×C4×D4312yes—
537C42C2×C4×D4312yes—
538C42C2×C22⋊D4312yes—
539C42C2×C22⋊D4312yes—
540C23—21no—
541C23—21no—
542C23—41no—
543C23—41no—
544C23—861no—
545C23C2×(C2×D43)⋊C411yescharacteristic
546C23C2×(C2×D43)⋊C411yescharacteristic
547C23C22×D17211yescharacteristic
548Q8—3442no—
549Q8—1722no—
550Q8—1721no—
551Q8—1722no—
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—42no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—862no—
567C2×C4—861no—
568C2×C4—861no—
569C2×C4—862no—
570C2×C4—861no—
571C2×C4—862no—
572C2×C4—3442no—
573C2×C4—3441no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1722no—
577C2×C4—1722no—
578C2×C4—1722no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1722no—
582C2×C4—1721no—
583C2×C4—1722no—
584C2×C4C2×(C2×D43)⋊C412yes—
585C2×C4C2×(C2×D43)⋊C412yes—
586C2×C4C2×(C2×D43)⋊C412yes—
587C2×C4C2×(C2×D43)⋊C412yes—
588C2×C4C2×(C2×D43)⋊C411yescharacteristic
589C2×C4C2×(C2×D43)⋊C411yescharacteristic
590C2×C4C22×C4×D4311yescharacteristic
591C2×C4C22×C22⋊D4311yescharacteristic
592C8—41no—
593C8—41no—
594C8—42no—
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—
608C22C22×(C2×D43)⋊C411yescharacteristic
609C22#1458371111yescharacteristic
610C22#1458371611yescharacteristic
611C4—21no—
612C4—21no—
613C4—21no—
614C4—22no—
615C4—22no—
616C4—22no—
617C4—22no—
618C4—3442no—
619C4—3441no—
620C4—1722no—
621C4—1721no—
622C4—1722no—
623C4—1721no—
624C4—1722no—
625C4—1721no—
626C4#1458287212yes—
627C2—21no—
628C2—21no—
629C2—41no—
630C2—41no—
631C2—3441no—
632C2C2×#1458287211yescharacteristic
633C2#1914312911yescharacteristic
634C2#1914314011yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2924C2
socleC22×C43C22×C22⋊C4
prime radical#14583410C22
cosocleC22×C4×C43C24
hypercenter#2924D43
hypocenterC43#17612
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2924

Complements

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

NH ≅ G/Ntype
2. #19137488C2semidirect
3. #19133173C2semidirect
4. #19133168C2semidirect
5. #19133147C2semidirect
7. #19133121C2semidirect
8. #19133116C2semidirect
9. #19133095C2semidirect
11. C43×#2924C2semidirect
18. #14583527C4semidirect
19. #14583520C4semidirect
20. #14583511C4semidirect
21. #14583475C4semidirect
26. #14583379C4semidirect
27. #14583376C4semidirect
311. #2924D43semidirect
370. C43#17612semidirect

Maximal subgroups

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

subgroupindex
#191483472
#191374882
#191331732
#191331682
#191331472
#191331392
#191331212
#191331162
#191330952
#191330872
C43×#29242
#1761243