Finite Group Databasebeta

← #25064182

Subgroups — #25064182

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#19148672C211yesmaximal, characteristic
2#19143685C211yesmaximal, characteristic, complemented
3#19137247C211yesmaximal, characteristic, complemented
4#19133169C212yesmaximal, complemented
5#19133153C212yesmaximal, complemented
6#19133140C212yesmaximal, complemented
7#19133130C212yesmaximal, complemented
8#19133121C211yesmaximal, characteristic, complemented
9#19133090C211yesmaximal, characteristic, complemented
10#19133079C211yesmaximal, characteristic, complemented
11C43×#1505C211yesmaximal, characteristic, complemented
12#14583635C411yescharacteristic, complemented
13#14583632C412yescomplemented
14#14583629C411yescharacteristic, complemented
15#14583610C411yescharacteristic, complemented
16#14583608C412yescomplemented
17#14583569C411yescharacteristic, complemented
18#14583555—21no—
19#14583549—21no—
20#14583548—22no—
21#14583514—21no—
22#14583513—22no—
23#14583444C2212yes—
24#14583433C2211yescharacteristic
25#14583430C2212yes—
26#14583378—21no—
27C2×C4×Dic86C2211yescharacteristic
28#14583027—22no—
29#14583026—21no—
30#14583023—21no—
31#14582953C2212yes—
32#14582952C2211yescharacteristic
33#14582949C2212yes—
34#14582805—21no—
35#14582797—21no—
36#14582781—22no—
37#14582766C2212yes—
38#14582763C2212yes—
39C4×C4⋊Dic43C2211yescharacteristic
40#14582637C2212yes—
41#14582635C2211yescharacteristic
42#14582635C2211yescharacteristic
43#14582634C2212yes—
44#14582633C2212yes—
45#14582633C2212yes—
46#14582632C2211yescharacteristic
47#14582632C2211yescharacteristic
48C43×#532C2211yescharacteristic
49C43×#432C2211yescharacteristic
50C43×#376C2211yescharacteristic
51C43×#327C2212yes—
52C43×#327C2212yes—
53C2×#10621900—22no—
54C2×#10621900—21no—
55C22×Dic86D411yescharacteristic
56#13063324—21no—
57#13063324C2×C412yes—
58#13063323—22no—
59#13063321C2×C412yes—
60#13063319—21no—
61#13063318—22no—
62#13063317C2×C411yescharacteristic
63#13063316C2×C412yes—
64#13063313C2×C411yescharacteristic
65#13063312—21no—
66#13063312C2×C412yes—
67#13063311—22no—
68#13063311—22no—
69#13063308—21no—
70#13063308—22no—
71#13063307—22no—
72#13063306—22no—
73#13063306—22no—
74#13063305—21no—
75#13063304—22no—
76#13063304C2311yescharacteristic
77#13063302—22no—
78#13063302—22no—
79#13063301—22no—
80#13063299C2311yescharacteristic
81#13063297—22no—
82#13063297—22no—
83#13063296—21no—
84C4×Dic86C2×C411yescharacteristic
85C4×Dic86C2×C411yescharacteristic
86C4×Dic86C2×C412yes—
87C4×Dic86C2×C411yescharacteristic
88C4×Dic86D411yescharacteristic
89C4×Dic86D412yes—
90C4×Dic86D411yescharacteristic
91#13063290—21no—
92#13063290C2×C412yes—
93C4×D172C2×C411yescharacteristic
94D4×Dic43—22no—
95D4×Dic43—21no—
96D4×Dic43C2×C412yes—
97D4×Dic43C2×C412yes—
98#13063287C2×C412yes—
99C4×C22⋊D43—21no—
100C4×C22⋊D43—22no—
101(C22⋊D43)⋊C4—22no—
102#13063282—21no—
103#13063281—22no—
104C2×C4⋊Dic43—21no—
105C2×C4⋊Dic43D411yescharacteristic
106C2×Dic43⋊C4—22no—
107C2×Dic43⋊C4—22no—
108C2×Dic43⋊C4D412yes—
109C4⋊C4×D43—21no—
110C2×C4×Dic43—21no—
111C2×C4×Dic43C2312yes—
112C4⋊(C43⋊C8)—21no—
113Dic43⋊C8—22no—
114Dic43⋊C8—22no—
115C22⋊(C43⋊C8)C2311yescharacteristic
116C22⋊(C43⋊C8)C2311yescharacteristic
117#13063235—22no—
118C4×C43⋊C8—21no—
119C8×Dic43—22no—
120C43⋊#95—22no—
121C43⋊#95—22no—
122C43⋊#95—22no—
123C43⋊#95C2312yes—
124C2×#41×C43—21no—
125C4⋊Q8×C43C2×C411yescharacteristic
126#127×C43C2×C411yescharacteristic
127#124×C43—21no—
128#121×C43—21no—
129#121×C43C2312yes—
130C4×D4×C43—21no—
131C4×D4×C43C2×C412yes—
132C2×C42×C43—21no—
133C2×C42×C43C2311yescharacteristic
134C4⋊C8×C43—21no—
135C22⋊C8×C43C2312yes—
136#97×C43—21no—
137#95×C43—21no—
138#95×C43C2311yescharacteristic
139#95×C43C2311yescharacteristic
140#41×C43—81no—
141#41×C43—81no—
142C2×Q8×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—22no—
146C2×D4×C43C22×C412yes—
147C22×C4×C43—22no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2411yescharacteristic
153C2×C22⋊D43—22no—
154C2×C22⋊D43—22no—
155C2×C22⋊D43—21no—
156C22×Dic43—22no—
157C22×Dic43—22no—
158C22×Dic43—22no—
159C22×Dic43C2×D412yes—
160C22×Dic43C2×D412yes—
161#10621900—44no—
162#10621900—82no—
163#10621900—82no—
164C2×D172C22×C411yescharacteristic
165C2×C4×D43—21no—
166C2×C4×D43—22no—
167C2×Dic86—22no—
168C2×Dic86—42no—
169C2×Dic86C22⋊C411yescharacteristic
170C2×Dic86C22⋊C411yescharacteristic
171C2×Dic86C22⋊C412yes—
172C2×Dic86C22×C411yescharacteristic
173C2×C8×C43—22no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43C22×C412yes—
176C22⋊C4×C43—22no—
177C22⋊C4×C43—22no—
178C42×C43—42no—
179C42×C43C22×C411yescharacteristic
180C42×C43C22×C411yescharacteristic
181C42×C43C2×D411yescharacteristic
182C42×C43C2×D411yescharacteristic
183C22⋊Dic43—22no—
184C22⋊Dic43—22no—
185C22⋊Dic43—22no—
186C22⋊Dic43—22no—
187C22⋊Dic43—21no—
188(C2×D43)⋊C4—21no—
189(C2×D43)⋊C4—21no—
190(C2×D43)⋊C4—21no—
191(C2×D43)⋊C4—21no—
192(C2×D43)⋊C4—22no—
193C4⋊Dic43—22no—
194C4⋊Dic43—42no—
195C4⋊Dic43C22⋊C411yescharacteristic
196C4⋊Dic43C22⋊C411yescharacteristic
197C4⋊Dic43C22⋊C412yes—
198C4⋊Dic43C22×C411yescharacteristic
199C4⋊Dic43C22×C411yescharacteristic
200Dic43⋊C4—21no—
201Dic43⋊C4—21no—
202Dic43⋊C4—21no—
203Dic43⋊C4—21no—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207Dic43⋊C4—82no—
208Dic43⋊C4C22⋊C412yes—
209Dic43⋊C4C22⋊C412yes—
210Dic43⋊C4C22⋊C412yes—
211Dic43⋊C4C22⋊C412yes—
212C4×Dic43—21no—
213C4×Dic43—22no—
214C4×Dic43—81no—
215C4×Dic43C22×C412yes—
216C4×Dic43C22×C412yes—
217C4×Dic43C2×D412yes—
218C4×Dic43C2×D412yes—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C23×C43—22no—
222C23×C43C22×D411yescharacteristic
223C22×D43—21no—
224Q8×C43—81no—
225D4×C43—42no—
226D4×C43—42no—
227D4×C43—42no—
228D4×C43—42no—
229D4×C43—81no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—82no—
242C2×C4×C43C2×C22⋊C411yescharacteristic
243C2×C4×C43C2×C22⋊C411yescharacteristic
244C2×C4×C43C2×C22⋊C411yescharacteristic
245C2×C4×C43C2×C22⋊C411yescharacteristic
246C2×C4×C43C23×C411yescharacteristic
247C2×C4×C43C22×D411yescharacteristic
248C22⋊D43—44no—
249C22⋊D43—41no—
250C22⋊D43—41no—
251C22⋊D43—82no—
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—42no—
258C2×Dic43—44no—
259C2×Dic43—42no—
260C2×Dic43—42no—
261C2×Dic43—42no—
262C2×Dic43—82no—
263C2×Dic43C2×C22⋊C412yes—
264C2×Dic43C2×C22⋊C412yes—
265C2×Dic43C2×C22⋊C412yes—
266C2×Dic43C2×C22⋊C412yes—
267D172—41no—
268C4×D43—42no—
269C4×D43—82no—
270Dic86—22no—
271Dic86—22no—
272Dic86—42no—
273Dic86—41no—
274Dic86—82no—
275C8×C43—42no—
276C43⋊C8—41no—
277C43⋊C8—41no—
278#17602—431nomaximal, Sylow
279C22×C43—21no—
280C22×C43—21no—
281C22×C43—42no—
282C22×C43—42no—
283C22×C43—42no—
284C22×C43C22×C22⋊C411yescharacteristic
285C22×C43#57611yescharacteristic
286C22×C43#57711yescharacteristic
287C2×D43—41no—
288C2×D43—41no—
289C2×D43—41no—
290C4×C43—21no—
291C4×C43—21no—
292C4×C43—21no—
293C4×C43—21no—
294C4×C43—21no—
295C4×C43—42no—
296C4×C43—81no—
297C4×C43—81no—
298C4×C43#42112yes—
299Dic43—22no—
300Dic43—22no—
301Dic43—22no—
302Dic43—22no—
303Dic43—41no—
304Dic43—41no—
305Dic43—41no—
306Dic43—82no—
307#3522—431no—
308#2984—431no—
309#2320—431no—
310#1521—432no—
311#1517—432no—
312#1514—432no—
313#1512—432no—
314#1509—431no—
315#1505D4311yescharacteristic, complemented
316#1502—431no—
317#1500—431no—
318C2×C43—21no—
319C2×C43—21no—
320C2×C43—82no—
321C2×C43#288411yescharacteristic
322C2×C43#289711yescharacteristic
323C2×C43C2×#42111yescharacteristic
324D43—81no—
325#559—431no—
326#559—432no—
327Q82—431no—
328#554—431no—
329#554—432no—
330#550—431no—
331#548—861no—
332#547—861no—
333#547—862no—
334#542—861no—
335#542—862no—
336#532—432no—
337#532C2×D4311yescharacteristic
338#529—432no—
339#529—431no—
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⋊C4—431no—
355#376C2×D4311yescharacteristic
356#328—432no—
357#328—431no—
358#328—431no—
359#327—432no—
360#327—432no—
361#327—432no—
362#327—431no—
363#327—431no—
364#327C2×D4312yes—
365#327C2×D4312yes—
366C43#1760211yescharacteristic, complemented, Sylow
367C2×#41—21no—
368C2×#41—862no—
369C2×#41—861no—
370C22×Q8—431no—
371C4⋊Q8—432no—
372C4⋊Q8—861no—
373C4⋊Q8—862no—
374C4⋊Q8C4×D4311yescharacteristic
375#127—432no—
376#127C4×D4311yescharacteristic
377#126—862no—
378#126—861no—
379#125—432no—
380#125—431no—
381#124—21no—
382#124—432no—
383#124—431no—
384#124—862no—
385#124—862no—
386#124—861no—
387#123—862no—
388#123—862no—
389#123—862no—
390#123—862no—
391#123—861no—
392C22⋊Q8—431no—
393C22⋊Q8—862no—
394C22⋊Q8—862no—
395C22⋊Q8—861no—
396C22⋊Q8—862no—
397C22⋊Q8—862no—
398#121—21no—
399#121—431no—
400#121—861no—
401#121—862no—
402#121—862no—
403#121C22×D4312yes—
404C4×Q8—431no—
405C4×Q8—431no—
406C4×Q8—432no—
407C4×Q8—431no—
408C4×Q8—431no—
409C4×Q8—432no—
410C4×Q8—432no—
411C4×Q8—431no—
412C4×Q8—861no—
413C4×D4—21no—
414C4×D4—432no—
415C4×D4—432no—
416C4×D4—432no—
417C4×D4—431no—
418C4×D4—862no—
419C4×D4—862no—
420C4×D4—861no—
421C4×D4—862no—
422C4×D4—861no—
423C4×D4C4×D4312yes—
424#117—862no—
425#117—861no—
426C2×C4⋊C4—432no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—862no—
430C2×C4⋊C4—862no—
431C2×C4⋊C4—861no—
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—21no—
448#95—432no—
449#95—862no—
450#95—862no—
451#95—862no—
452#95C22×D4311yescharacteristic
453#95C22×D4311yescharacteristic
454#41—81no—
455#41—81no—
456#41—3442no—
457#41—3442no—
458#41—1724no—
459C2×Q8—21no—
460C2×Q8—431no—
461C2×Q8—431no—
462C2×Q8—432no—
463C2×Q8—431no—
464C2×Q8—862no—
465C2×Q8—1722no—
466C2×D4—22no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—431no—
470C2×D4—862no—
471C2×D4—862no—
472C2×D4—861no—
473C2×D4C2×C4×D4312yes—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—432no—
478C22×C4—432no—
479C22×C4—862no—
480C22×C4—862no—
481C22×C4—862no—
482C22×C4—861no—
483C22×C4—862no—
484C22×C4D4×D4311yescharacteristic
485C22×C4D4×D4311yescharacteristic
486C22×C4C23×D4311yescharacteristic
487C2×C8—22no—
488C2×C8—861no—
489C2×C8—861no—
490C4⋊C4—21no—
491C4⋊C4—432no—
492C4⋊C4—431no—
493C4⋊C4—432no—
494C4⋊C4—431no—
495C4⋊C4—432no—
496C4⋊C4—432no—
497C4⋊C4—432no—
498C4⋊C4—431no—
499C4⋊C4—431no—
500C4⋊C4—862no—
501C4⋊C4—862no—
502C4⋊C4—862no—
503C4⋊C4—862no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—3442no—
509C4⋊C4—1722no—
510C4⋊C4C2×C4×D4312yes—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—862no—
514C22⋊C4—862no—
515C22⋊C4—862no—
516C22⋊C4—862no—
517C22⋊C4—862no—
518C22⋊C4—861no—
519C22⋊C4—861no—
520C22⋊C4—861no—
521C22⋊C4—861no—
522C22⋊C4—861no—
523C42—42no—
524C42—432no—
525C42—432no—
526C42—432no—
527C42—432no—
528C42—862no—
529C42—861no—
530C42—3441no—
531C42C2×C4×D4311yescharacteristic
532C42C2×C4×D4311yescharacteristic
533C42D4×D4311yescharacteristic
534C42D4×D4311yescharacteristic
535C23—22no—
536C23—861no—
537C23C2×D4×D4311yescharacteristic
538Q8—81no—
539Q8—862no—
540Q8—862no—
541Q8—3442no—
542Q8—1722no—
543Q8—1721no—
544D4—42no—
545D4—42no—
546D4—42no—
547D4—42no—
548D4—81no—
549D4—3442no—
550D4—1721no—
551D4—1724no—
552D4—1721no—
553D4—1721no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—82no—
566C2×C4—432no—
567C2×C4—432no—
568C2×C4—432no—
569C2×C4—432no—
570C2×C4—862no—
571C2×C4—862no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—3442no—
576C2×C4—3442no—
577C2×C4—1722no—
578C2×C4—1724no—
579C2×C4—1722no—
580C2×C4—1722no—
581C2×C4—1722no—
582C2×C4—1722no—
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—42no—
595C22—42no—
596C22—42no—
597C22—1721no—
598C22—1721no—
599C22—1721no—
600C22C2×C22⋊C4×D4311yescharacteristic
601C22#1458370311yescharacteristic
602C22#1458370911yescharacteristic
603C4—21no—
604C4—21no—
605C4—21no—
606C4—21no—
607C4—21no—
608C4—42no—
609C4—81no—
610C4—81no—
611C4—862no—
612C4—862no—
613C4—862no—
614C4—862no—
615C4—3442no—
616C4—1721no—
617C4—1721no—
618C4—1721no—
619C4#1458291412yes—
620C2—21no—
621C2—21no—
622C2—82no—
623C2—3441no—
624C2#1914305711yescharacteristic
625C2#1914312011yescharacteristic
626C2C2×#1458291411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1505C2
socleC22×C43C22×C22⋊C4
prime radical#19148672C2
cosocleC22×C4×C43C24
hypercenter#1505D43
hypocenterC43#17602
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1505

Complements

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

NH ≅ G/Ntype
2. #19143685C2semidirect
3. #19137247C2semidirect
4. #19133169C2semidirect
5. #19133153C2semidirect
6. #19133140C2semidirect
7. #19133130C2semidirect
8. #19133121C2semidirect
9. #19133090C2semidirect
10. #19133079C2semidirect
11. C43×#1505C2semidirect
12. #14583635C4semidirect
13. #14583632C4semidirect
14. #14583629C4semidirect
15. #14583610C4semidirect
16. #14583608C4semidirect
17. #14583569C4semidirect
315. #1505D43semidirect
366. C43#17602semidirect

Maximal subgroups

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

subgroupindex
#191486722
#191436852
#191372472
#191331692
#191331532
#191331402
#191331302
#191331212
#191330902
#191330792
C43×#15052
#1760243