Finite Group Databasebeta

← #25064185

Subgroups — #25064185

Order 11008.

938 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148678C211yesmaximal, characteristic
2#19143685C211yesmaximal, characteristic, complemented
3#19137241C211yesmaximal, characteristic, complemented
4#19133171C212yesmaximal, complemented
5#19133153C212yesmaximal, complemented
6#19133140C212yesmaximal, complemented
7#19133132C212yesmaximal, complemented
8#19133104C211yesmaximal, characteristic, complemented
9#19133089C211yesmaximal, characteristic, complemented
10#19133081C211yesmaximal, characteristic, complemented
11C43×#1509C211yesmaximal, characteristic, complemented
12#14583634C411yescharacteristic, complemented
13#14583631C412yescomplemented
14Q8×Dic86C411yescharacteristic, complemented
15#14583606C411yescharacteristic, complemented
16#14583605C412yescomplemented
17#14583570C411yescharacteristic, complemented
18#14583558—21no—
19#14583553—21no—
20#14583547—22no—
21#14583520—21no—
22#14583515—22no—
23#14583449C2211yescharacteristic
24#14583444C2212yes—
25#14583435C2212yes—
26#14583379—21no—
27C2×C4×Dic86C2211yescharacteristic
28#14583027—22no—
29#14583026—21no—
30#14583023—21no—
31#14582953C2212yes—
32#14582952C2211yescharacteristic
33#14582949C2212yes—
34#14582804—21no—
35#14582795—21no—
36#14582783—22no—
37#14582766C2212yes—
38#14582763C2212yes—
39#14582745C2211yescharacteristic
40#14582636C2211yescharacteristic
41#14582636C2211yescharacteristic
42#14582634C2212yes—
43#14582634C2212yes—
44#14582633C2211yescharacteristic
45#14582633C2211yescharacteristic
46#14582632C2212yes—
47#14582632C2212yes—
48C43×#529C2211yescharacteristic
49C43×#432C2211yescharacteristic
50C4×C4⋊C4×C43C2211yescharacteristic
51C43×#328C2212yes—
52C43×#327C2212yes—
53C2×#10621898—21no—
54C2×#10621898—21no—
55C2×#10621900—22no—
56C22×Dic86D411yescharacteristic
57#13063325—21no—
58#13063325C2×C411yescharacteristic
59#13063324—22no—
60#13063324C2×C412yes—
61#13063322C2×C411yescharacteristic
62#13063321C2×C412yes—
63#13063320—22no—
64#13063316C2×C412yes—
65#13063314C2×C412yes—
66#13063313—21no—
67#13063313—21no—
68#13063311—22no—
69#13063311—22no—
70#13063310—22no—
71#13063309—22no—
72#13063309—22no—
73#13063307—22no—
74#13063305—22no—
75#13063304—21no—
76#13063303—22no—
77#13063303—22no—
78#13063302—22no—
79#13063299—21no—
80#13063299—21no—
81#13063299C2312yes—
82#13063298—22no—
83#13063297—22no—
84Q8×Dic43C2×C412yes—
85C4×Dic86—21no—
86C4×Dic86C2×C411yescharacteristic
87C4×Dic86C2×C412yes—
88C4×Dic86C2×C411yescharacteristic
89C4×Dic86D411yescharacteristic
90C4×Dic86D412yes—
91C4×Dic86D411yescharacteristic
92C4×D172—21no—
93C4×D172—21no—
94C4×D172C2×C412yes—
95D4×Dic43C2×C412yes—
96#13063287C2×C412yes—
97#13063287C2×C412yes—
98(C22⋊D43)⋊C4—22no—
99(C22⋊D43)⋊C4—22no—
100(C22⋊D43)⋊C4—22no—
101#13063283—22no—
102C2×C4⋊Dic43—21no—
103C2×C4⋊Dic43D411yescharacteristic
104C2×Dic43⋊C4—22no—
105C2×Dic43⋊C4D412yes—
106C4⋊C4×D43—22no—
107C2×C4×Dic43—21no—
108C2×C4×Dic43C2312yes—
109C4⋊(C43⋊C8)—21no—
110Dic43⋊C8—22no—
111Dic43⋊C8—22no—
112C22⋊(C43⋊C8)C2311yescharacteristic
113C22⋊(C43⋊C8)C2311yescharacteristic
114#13063235—22no—
115C4×C43⋊C8—21no—
116C8×Dic43—22no—
117C43⋊#95—21no—
118C43⋊#95—22no—
119C43⋊#95—22no—
120C43⋊#95—22no—
121C43⋊#95C2311yescharacteristic
122C43⋊#95C2311yescharacteristic
123#126×C43—21no—
124#125×C43C2×C411yescharacteristic
125#124×C43C2×C411yescharacteristic
126#123×C43—21no—
127C22⋊Q8×C43C2311yescharacteristic
128#121×C43C2311yescharacteristic
129C4×Q8×C43C2×C411yescharacteristic
130C4×D4×C43—21no—
131C4×D4×C43C2×C411yescharacteristic
132#117×C43—21no—
133C2×C4⋊C4×C43—21no—
134C2×C42×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43—21no—
137C22⋊C8×C43C2312yes—
138#97×C43—21no—
139#95×C43C2312yes—
140C2×Q8×C43C22×C411yescharacteristic
141C2×D4×C43—21no—
142C2×D4×C43C22×C411yescharacteristic
143C22×C4×C43—21no—
144C22×C4×C43—22no—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2411yescharacteristic
148C2×C22⋊D43—22no—
149C2×C22⋊D43—22no—
150C2×C22⋊D43—22no—
151C22×Dic43—22no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43C2×D412yes—
155C22×Dic43C2×D412yes—
156#10621900—82no—
157#10621900—82no—
158#10621898—44no—
159#10621898—81no—
160#10621898—81no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172C22×C412yes—
164C2×C4×D43—22no—
165C2×C4×D43—22no—
166C2×C4×D43—22no—
167C2×Dic86—21no—
168C2×Dic86—22no—
169C2×Dic86—42no—
170C2×Dic86C22⋊C411yescharacteristic
171C2×Dic86C22⋊C411yescharacteristic
172C2×Dic86C22⋊C412yes—
173C2×C8×C43—22no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—42no—
179C4⋊C4×C43C22×C411yescharacteristic
180C4⋊C4×C43C22×C411yescharacteristic
181C22⋊C4×C43—21no—
182C22⋊C4×C43—21no—
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C22⋊C4×C43—21no—
186C42×C43—21no—
187C42×C43—81no—
188C42×C43C22×C411yescharacteristic
189C42×C43C22×C411yescharacteristic
190C42×C43C2×D411yescharacteristic
191C42×C43C2×D411yescharacteristic
192C22⋊Dic43—22no—
193(C2×D43)⋊C4—22no—
194(C2×D43)⋊C4—22no—
195(C2×D43)⋊C4—22no—
196(C2×D43)⋊C4—22no—
197(C2×D43)⋊C4—22no—
198(C2×D43)⋊C4—22no—
199C4⋊Dic43—21no—
200C4⋊Dic43—22no—
201C4⋊Dic43—22no—
202C4⋊Dic43C22⋊C411yescharacteristic
203C4⋊Dic43C22⋊C411yescharacteristic
204C4⋊Dic43C22⋊C412yes—
205C4⋊Dic43C22×C412yes—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208Dic43⋊C4—82no—
209Dic43⋊C4C22⋊C412yes—
210Dic43⋊C4C22⋊C412yes—
211Dic43⋊C4C22⋊C412yes—
212Dic43⋊C4C22⋊C412yes—
213C4×Dic43—22no—
214C4×Dic43—42no—
215C4×Dic43C22×C412yes—
216C4×Dic43C22×C412yes—
217C4×Dic43C2×D412yes—
218C4×Dic43C2×D412yes—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C23×C43—21no—
222C23×C43C22×D411yescharacteristic
223C22×D43—22no—
224Q8×C43—41no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—41no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—22no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—41no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43C2×C22⋊C411yescharacteristic
240C2×C4×C43C2×C22⋊C411yescharacteristic
241C2×C4×C43C2×C22⋊C411yescharacteristic
242C2×C4×C43C2×C22⋊C411yescharacteristic
243C2×C4×C43C23×C411yescharacteristic
244C2×C4×C43C22×D411yescharacteristic
245C22⋊D43—44no—
246C22⋊D43—42no—
247C22⋊D43—42no—
248C22⋊D43—82no—
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—42no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—82no—
260C2×Dic43C2×C22⋊C412yes—
261C2×Dic43C2×C22⋊C412yes—
262C2×Dic43C2×C22⋊C412yes—
263C2×Dic43C2×C22⋊C412yes—
264D172—42no—
265D172—42no—
266D172—81no—
267C4×D43—44no—
268C4×D43—82no—
269C4×D43—82no—
270Dic86—22no—
271Dic86—22no—
272Dic86—42no—
273Dic86—82no—
274Dic86—81no—
275C8×C43—42no—
276C43⋊C8—41no—
277C43⋊C8—41no—
278#17602—431nomaximal, Sylow
279C22×C43—21no—
280C22×C43—21no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43C22×C22⋊C411yescharacteristic
285C22×C43#57611yescharacteristic
286C22×C43#57711yescharacteristic
287C2×D43—42no—
288C2×D43—42no—
289C2×D43—42no—
290C4×C43—21no—
291C4×C43—21no—
292C4×C43—21no—
293C4×C43—21no—
294C4×C43—21no—
295C4×C43—41no—
296C4×C43—41no—
297C4×C43—41no—
298C4×C43—82no—
299C4×C43#42112yes—
300Dic43—22no—
301Dic43—22no—
302Dic43—22no—
303Dic43—22no—
304Dic43—42no—
305Dic43—81no—
306Dic43—81no—
307#3522—431no—
308#2984—431no—
309#2320—431no—
310#1521—432no—
311#1517—432no—
312#1514—432no—
313#1512—432no—
314#1509D4311yescharacteristic, complemented
315#1505—431no—
316#1502—431no—
317#1500—431no—
318C2×C43—21no—
319C2×C43—21no—
320C2×C43—81no—
321C2×C43#288411yescharacteristic
322C2×C43#289711yescharacteristic
323C2×C43C2×#42111yescharacteristic
324D43—82no—
325#559—432no—
326#559—431no—
327Q82—431no—
328#554—432no—
329#554—431no—
330#550—431no—
331#548—861no—
332#547—861no—
333#547—862no—
334#542—861no—
335#542—862no—
336#532—432no—
337#532—431no—
338#529—432no—
339#529C2×D4311yescharacteristic
340#520—861no—
341C2×C4×Q8—431no—
342#446—862no—
343#446—861no—
344C8×Q8—861no—
345#432—432no—
346#432C2×D4311yescharacteristic
347#431—431no—
348#431—432no—
349#391—861no—
350#389—861no—
351#387—862no—
352#383—432no—
353#382—432no—
354C4×C4⋊C4C2×D4311yescharacteristic
355#376—431no—
356#328—431no—
357#328—431no—
358#328C2×D4312yes—
359#327—431no—
360#327—431no—
361#327—432no—
362#327—432no—
363#327—432no—
364#327—432no—
365#327C2×D4312yes—
366C43#1760211yescharacteristic, complemented, Sylow
367C2×#41—861no—
368C2×#41—862no—
369C2×#41—861no—
370C22×Q8—431no—
371C4⋊Q8—432no—
372C4⋊Q8—431no—
373C4⋊Q8—861no—
374C4⋊Q8—862no—
375#127—432no—
376#127—431no—
377#126—21no—
378#126—862no—
379#125—432no—
380#125C4×D4311yescharacteristic
381#124—432no—
382#124—861no—
383#124—862no—
384#124—862no—
385#124—861no—
386#124C4×D4311yescharacteristic
387#123—21no—
388#123—862no—
389#123—862no—
390#123—862no—
391#123—862no—
392C22⋊Q8—862no—
393C22⋊Q8—862no—
394C22⋊Q8—862no—
395C22⋊Q8—862no—
396C22⋊Q8—861no—
397C22⋊Q8C22×D4311yescharacteristic
398#121—432no—
399#121—862no—
400#121—861no—
401#121—862no—
402#121—861no—
403#121C22×D4311yescharacteristic
404C4×Q8—431no—
405C4×Q8—431no—
406C4×Q8—432no—
407C4×Q8—431no—
408C4×Q8—431no—
409C4×Q8—432no—
410C4×Q8—432no—
411C4×Q8—861no—
412C4×Q8C4×D4311yescharacteristic
413C4×D4—21no—
414C4×D4—432no—
415C4×D4—432no—
416C4×D4—432no—
417C4×D4—432no—
418C4×D4—861no—
419C4×D4—862no—
420C4×D4—862no—
421C4×D4—862no—
422C4×D4—861no—
423C4×D4C4×D4311yescharacteristic
424#117—21no—
425#117—862no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—432no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—862no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—862no—
432C2×C42—21no—
433C2×C42—432no—
434C2×C42—861no—
435C2×C42C22×D4311yescharacteristic
436C4⋊C8—21no—
437C4⋊C8—862no—
438C4⋊C8—862no—
439C4⋊C8—861no—
440C22⋊C8—431no—
441C22⋊C8—431no—
442C22⋊C8C22×D4312yes—
443#97—21no—
444#97—862no—
445C4×C8—862no—
446C4×C8—861no—
447#95—431no—
448#95—431no—
449#95—862no—
450#95—862no—
451#95—862no—
452#95—861no—
453#95C22×D4312yes—
454#41—3441no—
455#41—3441no—
456#41—3442no—
457#41—3442no—
458#41—1724no—
459C2×Q8—431no—
460C2×Q8—431no—
461C2×Q8—432no—
462C2×Q8—862no—
463C2×Q8—861no—
464C2×Q8—1722no—
465C2×Q8C2×C4×D4311yescharacteristic
466C2×D4—21no—
467C2×D4—432no—
468C2×D4—862no—
469C2×D4—862no—
470C2×D4—862no—
471C2×D4—861no—
472C2×D4—861no—
473C2×D4C2×C4×D4311yescharacteristic
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—432no—
477C22×C4—432no—
478C22×C4—862no—
479C22×C4—862no—
480C22×C4—862no—
481C22×C4—862no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4D4×D4311yescharacteristic
485C22×C4D4×D4311yescharacteristic
486C22×C4C23×D4311yescharacteristic
487C2×C8—22no—
488C2×C8—861no—
489C2×C8—861no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—42no—
495C4⋊C4—432no—
496C4⋊C4—431no—
497C4⋊C4—432no—
498C4⋊C4—431no—
499C4⋊C4—432no—
500C4⋊C4—432no—
501C4⋊C4—432no—
502C4⋊C4—432no—
503C4⋊C4—862no—
504C4⋊C4—862no—
505C4⋊C4—862no—
506C4⋊C4—862no—
507C4⋊C4—861no—
508C4⋊C4—3442no—
509C4⋊C4C2×C4×D4311yescharacteristic
510C4⋊C4C2×C4×D4311yescharacteristic
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—862no—
517C22⋊C4—862no—
518C22⋊C4—862no—
519C22⋊C4—862no—
520C22⋊C4—862no—
521C22⋊C4—862no—
522C22⋊C4—862no—
523C42—21no—
524C42—81no—
525C42—432no—
526C42—432no—
527C42—432no—
528C42—432no—
529C42—862no—
530C42—1722no—
531C42C2×C4×D4311yescharacteristic
532C42C2×C4×D4311yescharacteristic
533C42D4×D4311yescharacteristic
534C42D4×D4311yescharacteristic
535C23—21no—
536C23—862no—
537C23C2×D4×D4311yescharacteristic
538Q8—41no—
539Q8—862no—
540Q8—862no—
541Q8—3441no—
542Q8—3442no—
543Q8—1722no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—3441no—
548D4—3442no—
549D4—1722no—
550D4—1724no—
551D4—1722no—
552D4—1722no—
553D4—1722no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—41no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—432no—
566C2×C4—432no—
567C2×C4—432no—
568C2×C4—432no—
569C2×C4—862no—
570C2×C4—862no—
571C2×C4—862no—
572C2×C4—3442no—
573C2×C4—3442no—
574C2×C4—3442no—
575C2×C4—1724no—
576C2×C4—1722no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4C22⋊C4×D4311yescharacteristic
584C2×C4C22⋊C4×D4311yescharacteristic
585C2×C4C22⋊C4×D4311yescharacteristic
586C2×C4C22⋊C4×D4311yescharacteristic
587C2×C4C22×C4×D4311yescharacteristic
588C2×C4C2×D4×D4311yescharacteristic
589C8—42no—
590C8—1721no—
591C8—1721no—
592C22—21no—
593C22—21no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—1722no—
598C22—1722no—
599C22—1722no—
600C22C2×C22⋊C4×D4311yescharacteristic
601C22#1458370311yescharacteristic
602C22#1458370811yescharacteristic
603C4—21no—
604C4—21no—
605C4—21no—
606C4—21no—
607C4—21no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—82no—
612C4—862no—
613C4—862no—
614C4—862no—
615C4—862no—
616C4—3441no—
617C4—3441no—
618C4—1722no—
619C4#1458291412yes—
620C2—21no—
621C2—21no—
622C2—81no—
623C2—3442no—
624C2#1914305711yescharacteristic
625C2#1914311911yescharacteristic
626C2C2×#1458291411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1509C2
socleC22×C43C22×C22⋊C4
prime radical#19148678C2
cosocleC22×C4×C43C24
hypercenter#1509D43
hypocenterC43#17602
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1509

Complements

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

NH ≅ G/Ntype
2. #19143685C2semidirect
3. #19137241C2semidirect
4. #19133171C2semidirect
5. #19133153C2semidirect
6. #19133140C2semidirect
7. #19133132C2semidirect
8. #19133104C2semidirect
9. #19133089C2semidirect
10. #19133081C2semidirect
11. C43×#1509C2semidirect
12. #14583634C4semidirect
13. #14583631C4semidirect
14. Q8×Dic86C4semidirect
15. #14583606C4semidirect
16. #14583605C4semidirect
17. #14583570C4semidirect
314. #1509D43semidirect
366. C43#17602semidirect

Maximal subgroups

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

subgroupindex
#191486782
#191436852
#191372412
#191331712
#191331532
#191331402
#191331322
#191331042
#191330892
#191330812
C43×#15092
#1760243