Finite Group Databasebeta

← #25063285

Subgroups — #25063285

Order 11008.

920 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148022C211yesmaximal, characteristic
2#19143713C211yesmaximal, characteristic, complemented
3#19143551C211yesmaximal, characteristic, complemented
4#19133066C212yesmaximal, complemented
5#19133057C212yesmaximal, complemented
6#19133052C212yesmaximal, complemented
7#19133048C212yesmaximal, complemented
8#19132991C211yesmaximal, characteristic, complemented
9#19132977C211yesmaximal, characteristic, complemented
10C2×#14582629C211yesmaximal, characteristic, complemented
11C43×#1477C211yesmaximal, characteristic, complemented
12#14583527C411yescharacteristic
13#14583520—21no—
14#14583514C412yes—
15#14583511—21no—
16#14583507C412yes—
17#14583491—22no—
18#14583477C411yescharacteristic
19#14583475C411yescharacteristic
20#14583470C411yescharacteristic
21#14583456—21no—
22#14583453C2212yes—
23#14583433—21no—
24#14583431C2212yes—
25#14583429—22no—
26C4×#10621898C2211yescharacteristic
27C2×C4×Dic86C2211yescharacteristic
28#14583026—21no—
29#14583023—21no—
30#14582976—21no—
31#14582970—22no—
32#14582964—21no—
33(C22⋊D43)⋊C8—22no—
34#14582955C2212yes—
35#14582952C2211yescharacteristic
36#14582950C2212yes—
37#14582921C2212yes—
38C2×C4×C43⋊C8C2211yescharacteristic
39C4×C8×D43C2212yes—
40#14582631C2212yes—
41#14582631C2212yes—
42Q8⋊(C43⋊C8)C2211yescharacteristic
43Q8⋊(C43⋊C8)C2211yescharacteristic
44#14582629C2212yes—
45#14582629C2212yes—
46D4⋊(C43⋊C8)C2211yescharacteristic
47D4⋊(C43⋊C8)C2211yescharacteristic
48C4×#41×C43C2211yescharacteristic
49C43×#431C2211yescharacteristic
50C2×C4⋊C8×C43C2211yescharacteristic
51C43×Q8⋊C8C2212yes—
52C43×D4⋊C8C2212yes—
53C2×#10621898C2×C411yescharacteristic
54C22×Dic86C2×C411yescharacteristic
55C2×#10621872—22no—
56C22×C43⋊C8—21no—
57C2×C8×D43—22no—
58#13063325—21no—
59#13063325—21no—
60#13063324C2×C412yes—
61#13063323C2×C412yes—
62#13063320—22no—
63#13063319—22no—
64#13063318—22no—
65#13063318—22no—
66#13063317—21no—
67#13063317—22no—
68#13063316C2×C412yes—
69#13063315—22no—
70#13063315—22no—
71#13063313—21no—
72#13063312C2×C412yes—
73#13063311—22no—
74#13063309—22no—
75#13063308—22no—
76#13063307—22no—
77#13063306—22no—
78#13063305C2×C412yes—
79#13063305C2×C412yes—
80#13063304—21no—
81#13063304—21no—
82#13063304—21no—
83#13063304—22no—
84#13063303—22no—
85#13063302—22no—
86#13063301C2×C412yes—
87#13063299—21no—
88#13063297—22no—
89#13063296C2×C412yes—
90C4×Dic86—21no—
91C4×Dic86—21no—
92C4×Dic86—22no—
93C4×Dic86C2×C412yes—
94C4×Dic86D411yescharacteristic
95C4×Dic86D411yescharacteristic
96C4×Dic86C2312yes—
97C4×D172D411yescharacteristic
98C4×D172D411yescharacteristic
99C4×C22⋊D43—22no—
100C4×C22⋊D43D412yes—
101C4×C22⋊D43D412yes—
102#13063284—22no—
103#13063284C2×C411yescharacteristic
104#13063282—22no—
105#13063282C2×C412yes—
106C2×C4⋊Dic43C2×C411yescharacteristic
107C2×Dic43⋊C4—21no—
108C2×C4×Dic43—21no—
109C42×D43C2312yes—
110C4⋊(C43⋊C8)C2311yescharacteristic
111C4⋊(C43⋊C8)C2311yescharacteristic
112Dic43⋊C8—22no—
113Dic43⋊C8—22no—
114C22⋊(C43⋊C8)—21no—
115(C2×D43)⋊C8—22no—
116(C2×D43)⋊C8—22no—
117#13063235—22no—
118C4×C43⋊C8—21no—
119C4×C43⋊C8—21no—
120C4×C43⋊C8C2311yescharacteristic
121C4×C43⋊C8C2311yescharacteristic
122C8×Dic43—22no—
123C2×#41×C43C2×C411yescharacteristic
124C22×C8×C43—21no—
125C4×Q8×C43C2×C411yescharacteristic
126C4×Q8×C43C2311yescharacteristic
127C4×D4×C43—21no—
128C4×D4×C43—21no—
129C4×D4×C43C2×C411yescharacteristic
130C4×D4×C43C2311yescharacteristic
131#117×C43—21no—
132#117×C43C2×C411yescharacteristic
133C2×C42×C43—21no—
134C2×C42×C43C2311yescharacteristic
135C4⋊C8×C43—21no—
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2312yes—
138C22⋊C8×C43—21no—
139C4×C8×C43C2312yes—
140#41×C43—22no—
141#41×C43—22no—
142C2×Q8×C43C22×C411yescharacteristic
143C2×D4×C43—21no—
144C2×D4×C43C22×C411yescharacteristic
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43C22×C411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C2×C22⋊D43—22no—
152C2×C22⋊D43C22⋊C412yes—
153C22×Dic43—21no—
154C22×Dic43—21no—
155#10621898—22no—
156#10621898—22no—
157C2×D172C22⋊C411yescharacteristic
158C2×C4×D43C22×C412yes—
159C2×C4×D43C2×D412yes—
160C2×C4×D43C2×D412yes—
161C2×Dic86—22no—
162C2×Dic86—22no—
163C2×Dic86—21no—
164C2×Dic86—22no—
165C2×Dic86C22⋊C411yescharacteristic
166C2×Dic86C22×C412yes—
167C2×C8×C43—22no—
168C2×C8×C43—22no—
169C2×C8×C43—81no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43C22×C411yescharacteristic
173C4⋊C4×C43C22×C411yescharacteristic
174C22⋊C4×C43—21no—
175C22⋊C4×C43—21no—
176C22⋊C4×C43—21no—
177C42×C43—21no—
178C42×C43—21no—
179C42×C43—21no—
180C42×C43C22×C411yescharacteristic
181C42×C43C2×D411yescharacteristic
182C42×C43C2×D411yescharacteristic
183C42×C43C2411yescharacteristic
184C22⋊Dic43—22no—
185C22⋊Dic43—22no—
186C22⋊Dic43—22no—
187C22⋊Dic43C22⋊C412yes—
188(C2×D43)⋊C4—22no—
189(C2×D43)⋊C4—22no—
190(C2×D43)⋊C4—22no—
191(C2×D43)⋊C4C22⋊C412yes—
192(C2×D43)⋊C4C22⋊C412yes—
193C4⋊Dic43—21no—
194C4⋊Dic43—22no—
195C4⋊Dic43—22no—
196C4⋊Dic43—22no—
197C4⋊Dic43C22⋊C411yescharacteristic
198C4⋊Dic43C22⋊C411yescharacteristic
199C4⋊Dic43C22×C412yes—
200Dic43⋊C4—22no—
201Dic43⋊C4—22no—
202Dic43⋊C4—22no—
203Dic43⋊C4—22no—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207Dic43⋊C4C22⋊C412yes—
208Dic43⋊C4C22⋊C412yes—
209C4×Dic43—22no—
210C4×Dic43—22no—
211C4×Dic43C22×C412yes—
212C4×Dic43C2×D412yes—
213C4×Dic43C2×D412yes—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—42no—
219#10621872—82no—
220C8×D43—44no—
221C23×C43—21no—
222C23×C43C2×C22⋊C411yescharacteristic
223C22×D43C2×C22⋊C412yes—
224Q8×C43—21no—
225Q8×C43—21no—
226D4×C43—21no—
227D4×C43—21no—
228D4×C43—42no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—42no—
238C2×C4×C43—81no—
239C2×C4×C43C2×C22⋊C411yescharacteristic
240C2×C4×C43C2×C22⋊C411yescharacteristic
241C2×C4×C43C2×C22⋊C411yescharacteristic
242C2×C4×C43#13112yes—
243C2×C4×C43#13112yes—
244C2×C4×C43C23×C411yescharacteristic
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C22⋊D43—24no—
248C22⋊D43—82no—
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—42no—
252C2×Dic43—81no—
253C2×Dic43C2×C22⋊C412yes—
254C2×Dic43C2×C22⋊C412yes—
255C2×Dic43C2×C22⋊C412yes—
256D172—22no—
257C4×D43—22no—
258C4×D43—22no—
259C4×D43—22no—
260C4×D43—22no—
261C4×D43—42no—
262Dic86—22no—
263Dic86—22no—
264Dic86—22no—
265Dic86—42no—
266Dic86—82no—
267C8×C43—42no—
268C8×C43—42no—
269C43⋊C8—22no—
270C43⋊C8—41no—
271C43⋊C8—41no—
272C43⋊C8—41no—
273#17484—431nomaximal, Sylow
274C22×C43—21no—
275C22×C43—21no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43#40812yes—
280C22×C43C22×C22⋊C411yescharacteristic
281C2×D43—22no—
282C2×D43—22no—
283C2×D43—22no—
284C4×C43—21no—
285C4×C43—21no—
286C4×C43—21no—
287C4×C43—41no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43#40812yes—
291C4×C43C2×#13111yescharacteristic
292C4×C43C2×#13111yescharacteristic
293C4×C43#57711yescharacteristic
294C4×C43#57811yescharacteristic
295Dic43—22no—
296Dic43—22no—
297Dic43—22no—
298Dic43—42no—
299Dic43—42no—
300#3461—431no—
301#2989—431no—
302C8×#41—431no—
303#1497—432no—
304#1495—432no—
305#1494—432no—
306#1493—432no—
307#1479—431no—
308#1477D4311yescharacteristic, complemented
309#1476—431no—
310C2×Q8⋊C8—431no—
311C2×C43—22no—
312C2×C43—81no—
313C2×C43C2×#40811yescharacteristic
314C2×C43#289811yescharacteristic
315C2×C43#290111yescharacteristic
316D43—42no—
317#544—431no—
318#542—432no—
319#542—861no—
320#541—432no—
321#541—861no—
322#539—862no—
323#537—431no—
324#536—431no—
325#536—431no—
326#533—432no—
327#533—861no—
328#529—432no—
329#529—861no—
330#529—862no—
331C4×#41—431no—
332C4×#41C2×D4311yescharacteristic
333C2×C4×Q8—431no—
334#446—861no—
335C8×Q8—861no—
336#436—861no—
337#435—862no—
338C8×D4—862no—
339C8×D4—861no—
340#432—432no—
341#431—432no—
342#431—431no—
343#431C2×D4311yescharacteristic
344#423—432no—
345C2×C4⋊C8C2×D4311yescharacteristic
346C2×C4×C8—431no—
347C2×C4×C8—432no—
348Q8⋊C8—431no—
349Q8⋊C8—431no—
350Q8⋊C8—432no—
351Q8⋊C8—432no—
352Q8⋊C8—432no—
353Q8⋊C8—432no—
354Q8⋊C8C2×D4312yes—
355D4⋊C8—431no—
356D4⋊C8—431no—
357D4⋊C8C2×D4312yes—
358C43#1748411yescharacteristic, complemented, Sylow
359C2×#41—431no—
360C2×#41C4×D4311yescharacteristic
361C22×Q8—431no—
362C2×M16—862no—
363C22×C8—21no—
364C22×C8—862no—
365C22×C8—861no—
366C4⋊Q8—432no—
367C4⋊Q8—432no—
368C4⋊Q8—861no—
369C4⋊Q8—861no—
370#126—862no—
371#126—862no—
372#126—862no—
373#126—862no—
374#125—432no—
375#125—861no—
376#125—862no—
377#125—862no—
378#125—862no—
379#124—432no—
380#124—861no—
381#124—862no—
382#123—862no—
383#123—862no—
384#123—862no—
385#123—862no—
386C22⋊Q8—432no—
387C22⋊Q8—432no—
388C22⋊Q8—432no—
389C22⋊Q8—862no—
390C22⋊Q8—862no—
391C22⋊Q8—861no—
392C22⋊Q8—861no—
393C22⋊Q8—862no—
394C22⋊Q8—861no—
395#121—432no—
396#121—861no—
397#121—862no—
398C4×Q8—431no—
399C4×Q8—431no—
400C4×Q8—432no—
401C4×Q8—432no—
402C4×Q8—862no—
403C4×Q8—861no—
404C4×Q8—861no—
405C4×Q8C4×D4311yescharacteristic
406C4×Q8C22×D4311yescharacteristic
407C4×D4—21no—
408C4×D4—21no—
409C4×D4—432no—
410C4×D4—432no—
411C4×D4—431no—
412C4×D4—431no—
413C4×D4—862no—
414C4×D4C4×D4311yescharacteristic
415C4×D4C22×D4311yescharacteristic
416#117—21no—
417#117—431no—
418#117—432no—
419#117—862no—
420#117—862no—
421#117C4×D4311yescharacteristic
422C2×C4⋊C4—431no—
423C2×C4⋊C4—861no—
424C2×C42—21no—
425C2×C42—432no—
426C2×C42—861no—
427C2×C42C22×D4311yescharacteristic
428C4⋊C8—21no—
429C4⋊C8—21no—
430C4⋊C8—431no—
431C4⋊C8—431no—
432C4⋊C8—862no—
433C4⋊C8—862no—
434C4⋊C8C22×D4312yes—
435C22⋊C8—21no—
436C22⋊C8—862no—
437C22⋊C8—862no—
438C22⋊C8—861no—
439#97—862no—
440C4×C8—431no—
441C4×C8—431no—
442C4×C8—862no—
443C4×C8—861no—
444C4×C8—861no—
445C4×C8C22×D4312yes—
446#41—22no—
447#41—22no—
448#41—862no—
449#41—862no—
450C2×Q8—431no—
451C2×Q8—432no—
452C2×Q8—862no—
453C2×Q8—861no—
454C2×Q8—862no—
455C2×Q8—862no—
456C2×Q8C2×C4×D4311yescharacteristic
457C2×D4—21no—
458C2×D4—432no—
459C2×D4—431no—
460C2×D4—862no—
461C2×D4C2×C4×D4311yescharacteristic
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—432no—
466C22×C4—432no—
467C22×C4—432no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4C2×C4×D4311yescharacteristic
471C22×C4D4×D4311yescharacteristic
472C22×C4D4×D4311yescharacteristic
473M16—3442no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—81no—
477C2×C8—861no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—1724no—
482C2×C8—1722no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—432no—
486C4⋊C4—431no—
487C4⋊C4—431no—
488C4⋊C4—432no—
489C4⋊C4—432no—
490C4⋊C4—862no—
491C4⋊C4—862no—
492C4⋊C4—862no—
493C4⋊C4—862no—
494C4⋊C4—862no—
495C4⋊C4—862no—
496C4⋊C4—862no—
497C4⋊C4—862no—
498C4⋊C4—861no—
499C4⋊C4—862no—
500C4⋊C4—862no—
501C4⋊C4C2×C4×D4311yescharacteristic
502C4⋊C4C2×C4×D4311yescharacteristic
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—432no—
507C22⋊C4—432no—
508C22⋊C4—432no—
509C22⋊C4—862no—
510C22⋊C4—862no—
511C22⋊C4—862no—
512C22⋊C4—862no—
513C22⋊C4—862no—
514C22⋊C4—862no—
515C42—21no—
516C42—21no—
517C42—21no—
518C42—432no—
519C42—432no—
520C42—432no—
521C42—862no—
522C42—862no—
523C42C2×C4×D4311yescharacteristic
524C42D4×D4311yescharacteristic
525C42D4×D4311yescharacteristic
526C42C23×D4311yescharacteristic
527C23—21no—
528C23—432no—
529C23C22⋊C4×D4311yescharacteristic
530Q8—21no—
531Q8—21no—
532Q8—862no—
533Q8—862no—
534Q8—862no—
535Q8—3442no—
536Q8—1722no—
537D4—21no—
538D4—21no—
539D4—42no—
540D4—864no—
541D4—862no—
542D4—3442no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—81no—
553C2×C4—432no—
554C2×C4—432no—
555C2×C4—432no—
556C2×C4—862no—
557C2×C4—862no—
558C2×C4—862no—
559C2×C4—862no—
560C2×C4—862no—
561C2×C4—862no—
562C2×C4—3441no—
563C2×C4—1722no—
564C2×C4—1722no—
565C2×C4C22⋊C4×D4311yescharacteristic
566C2×C4C22⋊C4×D4311yescharacteristic
567C2×C4C22⋊C4×D4311yescharacteristic
568C2×C4#1306333112yes—
569C2×C4#1306333312yes—
570C2×C4C22×C4×D4311yescharacteristic
571C2×C4C2×D4×D4311yescharacteristic
572C2×C4C2×D4×D4311yescharacteristic
573C8—42no—
574C8—42no—
575C8—862no—
576C8—1721no—
577C8—1721no—
578C8—1721no—
579C22—21no—
580C22—21no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—862no—
585C22—862no—
586C22—862no—
587C22#1458286412yes—
588C22C2×C22⋊C4×D4311yescharacteristic
589C4—21no—
590C4—21no—
591C4—21no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—862no—
596C4—862no—
597C4—862no—
598C4—1722no—
599C4—1722no—
600C4#1458286412yes—
601C4C2×#1306333111yescharacteristic
602C4C2×#1306333311yescharacteristic
603C4#1458370911yescharacteristic
604C4#1458371511yescharacteristic
605C2—22no—
606C2—81no—
607C2—1722no—
608C2C2×#1458286411yescharacteristic
609C2#1914312611yescharacteristic
610C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1477C2
socleC22×C43C22×C22⋊C4
prime radical#14583477C4
cosocleC42×C43C24
hypercenter#1477D43
hypocenterC43#17484
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1477

Complements

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

NH ≅ G/Ntype
2. #19143713C2semidirect
3. #19143551C2semidirect
4. #19133066C2semidirect
5. #19133057C2semidirect
6. #19133052C2semidirect
7. #19133048C2semidirect
8. #19132991C2semidirect
9. #19132977C2semidirect
10. C2×#14582629C2semidirect
11. C43×#1477C2semidirect
308. #1477D43semidirect
358. C43#17484semidirect

Maximal subgroups

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

subgroupindex
#191480222
#191437132
#191435512
#191330662
#191330572
#191330522
#191330482
#191329912
#191329772
C2×#145826292
C43×#14772
#1748443