Finite Group Databasebeta

← #25064146

Subgroups — #25064146

Order 11008.

1046 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148629C211yesmaximal, characteristic
2#19143629C211yesmaximal, characteristic, complemented
3#19137239C211yesmaximal, characteristic, complemented
4#19133161C212yesmaximal, complemented
5#19133150C212yesmaximal, complemented
6#19133137C212yesmaximal, complemented
7#19133122C212yesmaximal, complemented
8#19133120C211yesmaximal, characteristic, complemented
9#19133102C211yesmaximal, characteristic, complemented
10#19133091C211yesmaximal, characteristic, complemented
11C43×#1500C211yesmaximal, characteristic, complemented
12#14583614C411yescharacteristic, complemented
13#14583609C411yescharacteristic, complemented
14#14583602C412yescomplemented
15#14583595—21no—
16#14583571C411yescharacteristic, complemented
17#14583542C412yescomplemented
18#14583541—22no—
19D4×D172—21no—
20D4×D172C411yescharacteristic, complemented
21#14583504—21no—
22#14583488—22no—
23#14583449C2211yescharacteristic
24#14583412C2212yes—
25#121×D43C2212yes—
26#14583373—21no—
27C2×C4×D172C2211yescharacteristic
28#14582978—21no—
29#14582969—22no—
30C8×D172—21no—
31#14582956C2211yescharacteristic, complemented
32#14582861C2212yescomplemented
33C22⋊C8×D43C2212yescomplemented
34#14582801—21no—
35#14582797—21no—
36#14582788—22no—
37#14582761C2212yescomplemented
38#14582758C2212yescomplemented
39C4×C4⋊Dic43C2211yescharacteristic, complemented
40#14582636C2212yescomplemented
41#14582634C2212yescomplemented
42#14582634C2212yescomplemented
43#14582633C2212yes—
44#14582632C2212yescomplemented
45#14582632C2212yescomplemented
46C43×#529C2211yescharacteristic
47C43×#431C2211yescharacteristic, complemented
48C43×#376C2211yescharacteristic, complemented
49C43×#328C2211yescharacteristic, complemented
50C43×#328C2211yescharacteristic, complemented
51C43×#327C2211yescharacteristic
52C43×#327C2211yescharacteristic
53C2×#10621902C2×C412yes—
54C2×#10621898—21no—
55C22×D172—21no—
56C22×D172D411yescharacteristic
57C2×D4×D43—22no—
58C2×D4×D43C2×C412yes—
59C22×C4×D43C2312yes—
60C2×#10621872—22no—
61C2×C8×D43—22no—
62#13063325C2×C411yescharacteristic
63#13063322—21no—
64#13063322C2×C411yescharacteristic
65#13063320—22no—
66#13063317—21no—
67#13063313—21no—
68#13063311—22no—
69#13063310—22no—
70#13063310—22no—
71#13063307—22no—
72#13063303—22no—
73#13063301C2×C412yes—
74#13063300—22no—
75#13063300—22no—
76#13063300C2×C412yes—
77#13063300C2×C412yes—
78#13063299—21no—
79#13063299—21no—
80#13063299—21no—
81#13063299C2312yes—
82#13063298—22no—
83#13063298—22no—
84#13063297—22no—
85#13063296C2×C412yes—
86#13063295—22no—
87#13063295—22no—
88#13063295—22no—
89C4×D172—21no—
90C4×D172—21no—
91C4×D172—21no—
92C4×D172C2×C411yescharacteristic
93C4×D172C2×C412yes—
94C4×D172C2×C411yescharacteristic
95C4×D172C2×C412yes—
96C4×D172D411yescharacteristic
97C4×D172D411yescharacteristic
98C4×D172D412yes—
99#13063287—22no—
100#13063287—22no—
101(C22⋊D43)⋊C4—22no—
102#13063284—21no—
103#13063283C2×C412yes—
104C2×C4⋊Dic43—21no—
105C2×C4⋊Dic43D411yescharacteristic
106C2×Dic43⋊C4—22no—
107C4⋊C4×D43C2×C412yes—
108C2×(C2×D43)⋊C4—22no—
109C2×(C2×D43)⋊C4—22no—
110C2×(C2×D43)⋊C4D412yes—
111C22⋊C4×D43—22no—
112C22⋊C4×D43—22no—
113C2×C4×Dic43—21no—
114C4⋊(C43⋊C8)—21no—
115C22⋊(C43⋊C8)C2312yes—
116(C2×D43)⋊C8—22no—
117(C2×D43)⋊C8—22no—
118#13063236—21no—
119C43⋊#95—22no—
120C43⋊#95C2312yes—
121#126×C43—21no—
122#125×C43C2×C411yescharacteristic
123#124×C43C2×C411yescharacteristic
124#123×C43—21no—
125C22⋊Q8×C43C2311yescharacteristic
126#121×C43C2311yescharacteristic
127C4×Q8×C43C2×C411yescharacteristic
128C4×D4×C43—21no—
129C4×D4×C43C2×C411yescharacteristic
130#117×C43—21no—
131C2×C42×C43—21no—
132C2×C42×C43C2311yescharacteristic
133C4⋊C8×C43—21no—
134C22⋊C8×C43C2311yescharacteristic
135C22⋊C8×C43C2311yescharacteristic
136C4×C8×C43—21no—
137#95×C43—21no—
138#95×C43C2311yescharacteristic
139#95×C43C2311yescharacteristic
140C23×D43—22no—
141C23×D43C2×D412yes—
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×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2411yescharacteristic
151C2×C22⋊D43—22no—
152C2×C22⋊D43—22no—
153C2×C22⋊D43—22no—
154C22×Dic43—22no—
155C22×Dic43C2×D412yes—
156#10621902—82no—
157D4×D43—82no—
158D4×D43—82no—
159D4×D43—82no—
160#10621898—81no—
161#10621898—81no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—22no—
165C2×D172—22no—
166C2×D172—22no—
167C2×D172—42no—
168C2×D172—44no—
169C2×D172C22⋊C411yescharacteristic
170C2×D172C22⋊C411yescharacteristic
171C2×D172C22⋊C412yes—
172C2×D172C22×C412yes—
173C2×C4×D43—22no—
174C2×C4×D43—22no—
175C2×C4×D43—22no—
176C2×C4×D43—82no—
177C2×C4×D43C22×C412yes—
178C2×C4×D43C22×C412yes—
179C2×C4×D43C2×D412yes—
180C2×C4×D43C2×D412yes—
181C2×Dic86—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43C22×C411yescharacteristic
189C4⋊C4×C43C22×C411yescharacteristic
190C22⋊C4×C43—21no—
191C22⋊C4×C43—21no—
192C22⋊C4×C43—21no—
193C22⋊C4×C43—21no—
194C22⋊C4×C43—21no—
195C42×C43—21no—
196C42×C43—42no—
197C42×C43C22×C411yescharacteristic
198C42×C43C22×C411yescharacteristic
199C42×C43C2×D411yescharacteristic
200C42×C43C2×D411yescharacteristic
201C22⋊Dic43—22no—
202(C2×D43)⋊C4—22no—
203(C2×D43)⋊C4—22no—
204(C2×D43)⋊C4—22no—
205(C2×D43)⋊C4—22no—
206(C2×D43)⋊C4—22no—
207(C2×D43)⋊C4—22no—
208(C2×D43)⋊C4—82no—
209(C2×D43)⋊C4—82no—
210(C2×D43)⋊C4C22⋊C412yes—
211(C2×D43)⋊C4C22⋊C412yes—
212(C2×D43)⋊C4C22⋊C412yes—
213(C2×D43)⋊C4C22⋊C412yes—
214C4⋊Dic43—21no—
215C4⋊Dic43—42no—
216C4⋊Dic43C22⋊C411yescharacteristic
217C4⋊Dic43C22⋊C411yescharacteristic
218C4⋊Dic43C22⋊C412yes—
219C4⋊Dic43C22×C412yes—
220Dic43⋊C4—22no—
221Dic43⋊C4—22no—
222Dic43⋊C4—82no—
223C4×Dic43—22no—
224C4×Dic43—81no—
225C2×C43⋊C8—22no—
226#10621872—82no—
227C8×D43—82no—
228C23×C43—21no—
229C23×C43C22×D411yescharacteristic
230C22×D43—22no—
231C22×D43—22no—
232C22×D43—22no—
233C22×D43—42no—
234C22×D43—42no—
235C22×D43—44no—
236C22×D43—82no—
237C22×D43—82no—
238C22×D43C2×C22⋊C412yes—
239C22×D43C2×C22⋊C412yes—
240Q8×C43—41no—
241D4×C43—41no—
242D4×C43—41no—
243D4×C43—41no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—22no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—41no—
251C2×C4×C43—42no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43C2×C22⋊C411yescharacteristic
259C2×C4×C43C2×C22⋊C411yescharacteristic
260C2×C4×C43C2×C22⋊C411yescharacteristic
261C2×C4×C43C2×C22⋊C411yescharacteristic
262C2×C4×C43C23×C411yescharacteristic
263C2×C4×C43C22×D411yescharacteristic
264C22⋊D43—42no—
265C22⋊D43—42no—
266C22⋊D43—82no—
267C22⋊D43—82no—
268C2×Dic43—22no—
269C2×Dic43—42no—
270C2×Dic43—42no—
271C2×Dic43—42no—
272C2×Dic43—42no—
273C2×Dic43C2×C22⋊C412yes—
274C2×Dic43C2×C22⋊C412yes—
275D172—22no—
276D172—22no—
277D172—42no—
278D172—42no—
279D172—44no—
280D172—42no—
281D172—81no—
282D172—82no—
283D172—82no—
284C4×D43—42no—
285C4×D43—42no—
286C4×D43—42no—
287C4×D43—42no—
288C4×D43—82no—
289C4×D43—82no—
290C4×D43—82no—
291Dic86—81no—
292C8×C43—41no—
293C8×C43—41no—
294C43⋊C8—42no—
295#17599—431nomaximal, Sylow
296C22×C43—21no—
297C22×C43—21no—
298C22×C43—41no—
299C22×C43—41no—
300C22×C43—41no—
301C22×C43C22×C22⋊C411yescharacteristic
302C22×C43#57611yescharacteristic
303C22×C43#57711yescharacteristic
304C2×D43—22no—
305C2×D43—22no—
306C2×D43—22no—
307C2×D43—22no—
308C2×D43—22no—
309C2×D43—22no—
310C2×D43—42no—
311C2×D43—42no—
312C2×D43—42no—
313C2×D43—82no—
314C2×D43—82no—
315C2×D43—164no—
316C4×C43—21no—
317C4×C43—21no—
318C4×C43—21no—
319C4×C43—21no—
320C4×C43—21no—
321C4×C43—41no—
322C4×C43—41no—
323C4×C43—41no—
324C4×C43—81no—
325C4×C43—81no—
326C4×C43#42112yes—
327Dic43—22no—
328Dic43—22no—
329Dic43—42no—
330Dic43—82no—
331#3519—431no—
332#2974—431no—
333#2319—431no—
334#1519—432no—
335#1516—432no—
336#1513—432no—
337#1510—432no—
338#1509—431no—
339#1505—431no—
340#1502—431no—
341#1500D4311yescharacteristic, complemented
342C2×C43—21no—
343C2×C43—21no—
344C2×C43—81no—
345C2×C43#288311yescharacteristic
346C2×C43#289711yescharacteristic
347C2×C43C2×#42111yescharacteristic
348D43—42no—
349D43—42no—
350D43—82no—
351#555—431no—
352#554—431no—
353#553—432no—
354#553—861no—
355#550—431no—
356#546—432no—
357#546—862no—
358D42—431no—
359D42—861no—
360#540—861no—
361#538—862no—
362#532—431no—
363#529C2×D4311yescharacteristic
364#525—432no—
365C2×#121—432no—
366#518—861no—
367C2×C4×D4—431no—
368#436—861no—
369#435—862no—
370C8×D4—861no—
371#432—431no—
372#431C2×D4311yescharacteristic, complemented
373#407—432no—
374C2×C22⋊C8—432no—
375#390—861no—
376#389—861no—
377#388—862no—
378#381—432no—
379#380—432no—
380C4×C4⋊C4—431no—
381#376C2×D4311yescharacteristic, complemented
382#328—432no—
383#328C2×D4311yescharacteristic, complemented
384#328C2×D4311yescharacteristic, complemented
385#327—432no—
386#327—432no—
387#327—432no—
388#327—432no—
389#327—432no—
390#327C2×D4311yescharacteristic
391#327C2×D4311yescharacteristic
392C43#1759911yescharacteristic, complemented, Sylow
393C2×#41—432no—
394C2×#41—861no—
395C22×D4—432no—
396C22×D4—431no—
397C22×D4—861no—
398C22×D4—862no—
399C23×C4—432no—
400C2×M16—862no—
401C22×C8—862no—
402C4⋊Q8—431no—
403#127—431no—
404#127—861no—
405#126—21no—
406#126—862no—
407#125—861no—
408#125C4×D4311yescharacteristic
409#124—862no—
410#124—861no—
411#124C4×D4311yescharacteristic
412#123—21no—
413#123—862no—
414#123—862no—
415#123—862no—
416C22⋊Q8—432no—
417C22⋊Q8—862no—
418C22⋊Q8C22×D4311yescharacteristic
419#121—432no—
420#121—432no—
421#121—432no—
422#121—432no—
423#121—862no—
424#121—862no—
425#121—862no—
426#121—862no—
427#121—861no—
428#121—861no—
429#121—862no—
430#121—861no—
431#121C22×D4311yescharacteristic
432#120—862no—
433#120—862no—
434#120—862no—
435C4×Q8C4×D4311yescharacteristic
436C4×D4—21no—
437C4×D4—431no—
438C4×D4—432no—
439C4×D4—431no—
440C4×D4—432no—
441C4×D4—431no—
442C4×D4—432no—
443C4×D4—431no—
444C4×D4—861no—
445C4×D4—861no—
446C4×D4—862no—
447C4×D4—862no—
448C4×D4—862no—
449C4×D4—861no—
450C4×D4C4×D4311yescharacteristic
451#117—21no—
452#117—432no—
453#117—861no—
454C2×C4⋊C4—431no—
455C2×C4⋊C4—432no—
456C2×C4⋊C4—862no—
457C2×C4⋊C4—861no—
458C2×C22⋊C4—432no—
459C2×C22⋊C4—862no—
460C2×C22⋊C4—862no—
461C2×C22⋊C4—862no—
462C2×C22⋊C4—862no—
463C2×C42—21no—
464C2×C42—861no—
465C2×C42C22×D4311yescharacteristic
466C4⋊C8—21no—
467C4⋊C8—861no—
468C22⋊C8—432no—
469C22⋊C8—862no—
470C22⋊C8—862no—
471C22⋊C8C22×D4311yescharacteristic
472C22⋊C8C22×D4311yescharacteristic
473#97—861no—
474C4×C8—21no—
475#95—21no—
476#95—432no—
477#95—862no—
478#95C22×D4311yescharacteristic
479#95C22×D4311yescharacteristic
480C24—432no—
481C24—862no—
482#41—3441no—
483#41—3441no—
484#41—3442no—
485C2×Q8—861no—
486C2×Q8C2×C4×D4311yescharacteristic
487C2×D4—21no—
488C2×D4—431no—
489C2×D4—431no—
490C2×D4—432no—
491C2×D4—432no—
492C2×D4—862no—
493C2×D4—862no—
494C2×D4—862no—
495C2×D4—862no—
496C2×D4—862no—
497C2×D4—862no—
498C2×D4—861no—
499C2×D4—861no—
500C2×D4—3442no—
501C2×D4—3442no—
502C2×D4—3442no—
503C2×D4—1722no—
504C2×D4—1724no—
505C2×D4C2×C4×D4311yescharacteristic
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—432no—
510C22×C4—432no—
511C22×C4—432no—
512C22×C4—432no—
513C22×C4—432no—
514C22×C4—862no—
515C22×C4—862no—
516C22×C4—862no—
517C22×C4—862no—
518C22×C4—3442no—
519C22×C4D4×D4311yescharacteristic
520C22×C4D4×D4311yescharacteristic
521C22×C4C23×D4311yescharacteristic
522M16—3442no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—862no—
526C2×C8—3442no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—431no—
532C4⋊C4—431no—
533C4⋊C4—432no—
534C4⋊C4—432no—
535C4⋊C4—862no—
536C4⋊C4—862no—
537C4⋊C4—861no—
538C4⋊C4—3442no—
539C4⋊C4—1722no—
540C4⋊C4C2×C4×D4311yescharacteristic
541C4⋊C4C2×C4×D4311yescharacteristic
542C22⋊C4—21no—
543C22⋊C4—21no—
544C22⋊C4—21no—
545C22⋊C4—21no—
546C22⋊C4—21no—
547C22⋊C4—432no—
548C22⋊C4—432no—
549C22⋊C4—432no—
550C22⋊C4—432no—
551C22⋊C4—862no—
552C22⋊C4—862no—
553C22⋊C4—862no—
554C22⋊C4—862no—
555C22⋊C4—862no—
556C22⋊C4—862no—
557C22⋊C4—862no—
558C22⋊C4—3442no—
559C22⋊C4—3442no—
560C42—21no—
561C42—42no—
562C42—862no—
563C42—3441no—
564C42C2×C4×D4311yescharacteristic
565C42C2×C4×D4311yescharacteristic
566C42D4×D4311yescharacteristic
567C42D4×D4311yescharacteristic
568C23—21no—
569C23—432no—
570C23—432no—
571C23—862no—
572C23—862no—
573C23—862no—
574C23—3442no—
575C23—3442no—
576C23—1722no—
577C23—1722no—
578C23—1724no—
579C23C2×D4×D4311yescharacteristic
580Q8—41no—
581Q8—3441no—
582D4—41no—
583D4—41no—
584D4—41no—
585D4—862no—
586D4—862no—
587D4—3441no—
588D4—3442no—
589D4—3442no—
590D4—3442no—
591D4—3442no—
592D4—1722no—
593D4—1722no—
594D4—1724no—
595D4—1722no—
596D4—1722no—
597D4—1722no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—41no—
605C2×C4—42no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—432no—
613C2×C4—432no—
614C2×C4—862no—
615C2×C4—3442no—
616C2×C4—3442no—
617C2×C4—3442no—
618C2×C4—1722no—
619C2×C4—1722no—
620C2×C4—1722no—
621C2×C4—1722no—
622C2×C4—1722no—
623C2×C4—1722no—
624C2×C4—1722no—
625C2×C4—1722no—
626C2×C4C22⋊C4×D4311yescharacteristic
627C2×C4C22⋊C4×D4311yescharacteristic
628C2×C4C22⋊C4×D4311yescharacteristic
629C2×C4C22⋊C4×D4311yescharacteristic
630C2×C4C22×C4×D4311yescharacteristic
631C2×C4C2×D4×D4311yescharacteristic
632C8—41no—
633C8—41no—
634C8—1722no—
635C22—21no—
636C22—21no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—862no—
641C22—862no—
642C22—862no—
643C22—862no—
644C22—862no—
645C22—862no—
646C22—3442no—
647C22—3442no—
648C22—1722no—
649C22—1722no—
650C22—1722no—
651C22—6884no—
652C22C2×C22⋊C4×D4311yescharacteristic
653C22#1458370111yescharacteristic
654C22#1458370611yescharacteristic
655C4—21no—
656C4—21no—
657C4—21no—
658C4—21no—
659C4—21no—
660C4—41no—
661C4—41no—
662C4—41no—
663C4—81no—
664C4—81no—
665C4—862no—
666C4—862no—
667C4—3442no—
668C4—1722no—
669C4#1458291412yes—
670C2—21no—
671C2—21no—
672C2—81no—
673C2—3442no—
674C2—1722no—
675C2—1722no—
676C2#1914305411yescharacteristic
677C2#1914311711yescharacteristic
678C2C2×#1458291411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1500C2
socleC22×C43C22×C22⋊C4
prime radical#19148629C2
cosocleC22×C4×C43C24
hypercenter#1500D43
hypocenterC43#17599
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1500

Complements

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

NH ≅ G/Ntype
2. #19143629C2semidirect
3. #19137239C2semidirect
4. #19133161C2semidirect
5. #19133150C2semidirect
6. #19133137C2semidirect
7. #19133122C2semidirect
8. #19133120C2semidirect
9. #19133102C2semidirect
10. #19133091C2semidirect
11. C43×#1500C2semidirect
12. #14583614C4semidirect
13. #14583609C4semidirect
14. #14583602C4semidirect
16. #14583571C4semidirect
17. #14583542C4semidirect
20. D4×D172C4semidirect
31. #14582956C22semidirect
32. #14582861C22semidirect
33. C22⋊C8×D43C22semidirect
37. #14582761C22semidirect
38. #14582758C22semidirect
39. C4×C4⋊Dic43C22semidirect
40. #14582636C22semidirect
41. #14582634C22semidirect
42. #14582634C22semidirect
44. #14582632C22semidirect
45. #14582632C22semidirect
47. C43×#431C22semidirect
48. C43×#376C22semidirect
49. C43×#328C22semidirect
50. C43×#328C22semidirect
341. #1500D43semidirect
372. #431C2×D43semidirect
381. #376C2×D43semidirect
383. #328C2×D43semidirect
384. #328C2×D43semidirect
392. C43#17599semidirect

Maximal subgroups

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

subgroupindex
#191486292
#191436292
#191372392
#191331612
#191331502
#191331372
#191331222
#191331202
#191331022
#191330912
C43×#15002
#1759943