Finite Group Databasebeta

← #25104718

Subgroups — #25104718

Order 11008.

826 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583261C211yesmaximal, characteristic
2#19137306C211yesmaximal, characteristic
3#19135557C211yesmaximal, characteristic, complemented
4#19135404C211yesmaximal, characteristic
5#19135291C211yesmaximal, characteristic
6#19135284C211yesmaximal, characteristic, complemented
7#19135277C211yesmaximal, characteristic
8#19135270C211yesmaximal, characteristic, complemented
9#19134728C211yesmaximal, characteristic, complemented
10#19134428C211yesmaximal, characteristic, complemented
11#19134423C211yesmaximal, characteristic
12C4×#13063248C211yesmaximal, characteristic, complemented
13C4×#13063245C211yesmaximal, characteristic
14#19134282C211yesmaximal, characteristic, complemented
15C43×#2331C211yesmaximal, characteristic, complemented
16C2×#13063313C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19#14583261C418yescomplemented
20C2×#13063248C2211yescharacteristic
21C2×#13063248C2211yescharacteristic
22C2×#13063248C2211yescharacteristic
23C2×#13063248C2211yescharacteristic
24C2×#13063245C2211yescharacteristic
25C2×#13063245C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063236C2211yescharacteristic
29C2×#13063236C2211yescharacteristic
30C2×#13063236C2211yescharacteristic
31C2×C4×C43⋊C8C2211yescharacteristic
32C2×C4×C43⋊C8C2211yescharacteristic
33C2×C4×C43⋊C8C2211yescharacteristic
34#14582805C2211yescharacteristic
35#14582801C2211yescharacteristic
36#14582791—21no—
37#14582791—21no—
38#14582773—21no—
39#14582773—21no—
40#14582769C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49C2×C4⋊Q8×C43C2211yescharacteristic
50C43×#391—21no—
51C43×#391—21no—
52C43×#389C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C43×#387—21no—
55C43×#387—21no—
56C43×#382C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C43×#376C2211yescharacteristic
60C22×Dic86C2311yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C4×D43—21no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063313—22no—
68#13063313C2×C414yes—
69C4×Dic86—22no—
70C4×Dic86—22no—
71C4×D172—22no—
72C4×D172—22no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×C4×Dic43—21no—
84#13063248—22no—
85#13063248—22no—
86#13063248C2×C414yescomplemented
87#13063248C2×C414yescomplemented
88#13063245—22no—
89#13063245—22no—
90#13063245C2×C414yes—
91#13063245C2×C414yes—
92#13063236—22no—
93#13063236—22no—
94#13063236C2×C414yescomplemented
95C4×C43⋊C8—22no—
96C4×C43⋊C8—22no—
97C4×C43⋊C8—22no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C22×Q8×C43—21no—
101C4⋊Q8×C43—22no—
102C4⋊Q8×C43C2×C414yescomplemented
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C42×C43—21no—
111C2×C42×C43—21no—
112C2×C42×C43C2311yescharacteristic
113C2×C42×C43C2311yescharacteristic
114C2×C42×C43C2311yescharacteristic
115#95×C43—21no—
116#95×C43—21no—
117#95×C43—21no—
118#95×C43—21no—
119#95×C43—21no—
120#95×C43—21no—
121#95×C43D411yescharacteristic
122#95×C43D411yescharacteristic
123#95×C43D411yescharacteristic
124#95×C43D411yescharacteristic
125C23×D43—21no—
126C2×Q8×C43—24no—
127C2×Q8×C43—81no—
128C2×Q8×C43—81no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2411yescharacteristic
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172—21no—
147C2×D172—21no—
148C2×D172C22×C412yes—
149C2×C4×D43—42no—
150C2×C4×D43—81no—
151C2×C4×D43—81no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86C22×C412yes—
158C4⋊C4×C43—24no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—81no—
166C4⋊C4×C43—81no—
167C4⋊C4×C43C22×C412yes—
168C4⋊C4×C43C22×C412yes—
169C42×C43—21no—
170C42×C43—21no—
171C42×C43—81no—
172C42×C43—81no—
173C42×C43C22×C412yes—
174C42×C43#4112yes—
175C42×C43#4112yes—
176C42×C43#4112yes—
177(C2×D43)⋊C4—24no—
178(C2×D43)⋊C4—24no—
179(C2×D43)⋊C4—42no—
180(C2×D43)⋊C4—81no—
181(C2×D43)⋊C4—81no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—81no—
187C4⋊Dic43—81no—
188Dic43⋊C4—42no—
189C4×Dic43—42no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8C22×C412yes—
199C2×C43⋊C8C22×C412yes—
200C2×C43⋊C8#4112yes—
201C2×C43⋊C8#4112yes—
202C23×C43C22×D411yescharacteristic
203C22×D43—22no—
204C22×D43—41no—
205C22×D43—41no—
206C22×D43—41no—
207C22×D43—41no—
208C22×D43—41no—
209C22×D43—41no—
210Q8×C43—84no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43C4×D412yes—
238C2×C4×C43C4×D412yes—
239C2×C4×C43#12412yes—
240C2×C4×C43#12412yes—
241C2×C4×C43C23×C411yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×Dic43—22no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256D172—22no—
257D172—22no—
258D172—41no—
259D172—41no—
260C4×D43—84no—
261Dic86—22no—
262Dic86—22no—
263Dic86—41no—
264Dic86—41no—
265C43⋊C8—22no—
266C43⋊C8—22no—
267C43⋊C8—22no—
268C43⋊C8—22no—
269#21654—431nomaximal, Sylow
270C22×C43C2×C4×D411yescharacteristic
271C22×C43C2×#12411yescharacteristic
272C22×C43#53211yescharacteristic
273C22×C43#57611yescharacteristic
274C22×C43#57711yescharacteristic
275C22×C43#57711yescharacteristic
276C22×C43#57811yescharacteristic
277C2×D43—42no—
278C2×D43—42no—
279C2×D43—42no—
280C2×D43—81no—
281C2×D43—81no—
282C2×D43—81no—
283C2×D43—81no—
284C4×C43—22no—
285C4×C43—22no—
286C4×C43—22no—
287C4×C43—22no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—42no—
291C4×C43—42no—
292C4×C43—81no—
293C4×C43—81no—
294C4×C43C4×#4111yescharacteristic
295C4×C43C4×#4111yescharacteristic
296C4×C43#52911yescharacteristic
297C4×C43#52911yescharacteristic
298Dic43—42no—
299Dic43—81no—
300Dic43—81no—
301C2×#489—431no—
302#2331D4311yescharacteristic, complemented
303#2326—431no—
304#1990—431no—
305#1958—431no—
306#1936—431no—
307#1935—431no—
308#1934—431no—
309#1933—431no—
310#1836—431no—
311#1763—431no—
312#1762—431no—
313C4×#103—431no—
314C4×#102—431no—
315#1726—431no—
316C2×C43C4×#12411yescharacteristic
317C2×C43#294611yescharacteristic
318C2×C43#294711yescharacteristic
319C2×C43#313611yescharacteristic
320C2×C43#313711yescharacteristic
321C2×C43#317311yescharacteristic
322C2×C43#317511yescharacteristic
323D43—82no—
324C2×C4⋊Q8C2×D4311yescharacteristic
325C2×#124—431no—
326C2×C4×Q8—431no—
327C2×C4×D4—431no—
328#489—438no—
329C2×#103—431no—
330C2×#103—431no—
331C2×#103—431no—
332C2×#103—431no—
333C2×#102—431no—
334C2×#102—431no—
335C2×#102—431no—
336C2×#102—431no—
337C2×#97—431no—
338C2×#97—431no—
339C2×#97—431no—
340C2×C4×C8—431no—
341C2×C4×C8—431no—
342C2×C4×C8—431no—
343#391—21no—
344#391—21no—
345#391—431no—
346#390—431no—
347#389C2×D4311yescharacteristic
348#389C2×D4311yescharacteristic
349#388—861no—
350#388—861no—
351#387—21no—
352#387—21no—
353#385—861no—
354#385—861no—
355#384—431no—
356#382C2×D4311yescharacteristic
357C4×C4⋊C4C2×D4311yescharacteristic
358C4×C4⋊C4C2×D4311yescharacteristic
359#376C2×D4311yescharacteristic
360#340—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368C43#2165411yescharacteristic, complemented, Sylow
369C22×Q8—21no—
370C22×Q8—431no—
371C22×D4—431no—
372C23×C4—861no—
373C22×C8—431no—
374C22×C8—431no—
375C22×C8—431no—
376C22×C8—431no—
377C4⋊Q8—22no—
378C4⋊Q8C4×D4314yescomplemented
379#124—434no—
380#124—862no—
381C4×Q8—862no—
382C4×Q8—862no—
383C4×D4—862no—
384C4×D4—862no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4C22×D4311yescharacteristic
394C2×C4⋊C4C22×D4311yescharacteristic
395C2×C4⋊C4C22×D4311yescharacteristic
396C2×C4⋊C4C22×D4311yescharacteristic
397C2×C22⋊C4—861no—
398C2×C22⋊C4—861no—
399C2×C22⋊C4—861no—
400C2×C22⋊C4—861no—
401C2×C22⋊C4—861no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—861no—
405C2×C42C22×D4311yescharacteristic
406C2×C42C22×D4311yescharacteristic
407C2×C42C22×D4311yescharacteristic
408#103—434no—
409#103—434no—
410#103—862no—
411#103—862no—
412#102—434no—
413#102—434no—
414#102—862no—
415#102—862no—
416#97—434no—
417#97—862no—
418#97—862no—
419C4×C8—862no—
420C4×C8—862no—
421C4×C8—862no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—861no—
429#95—861no—
430#95C22⋊D4311yescharacteristic
431#95C22⋊D4311yescharacteristic
432#95C22⋊D4311yescharacteristic
433#95C22⋊D4311yescharacteristic
434C24—861no—
435C2×Q8—24no—
436C2×Q8—81no—
437C2×Q8—81no—
438C2×Q8—432no—
439C2×Q8—861no—
440C2×Q8—861no—
441C2×Q8—861no—
442C2×Q8—861no—
443C2×Q8—861no—
444C2×D4—432no—
445C2×D4—861no—
446C2×D4—861no—
447C2×D4—861no—
448C2×D4—861no—
449C2×D4—861no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—3441no—
458C22×C4—3441no—
459C22×C4—1722no—
460C22×C4C2×C22⋊D4311yescharacteristic
461C22×C4C2×C22⋊D4311yescharacteristic
462C22×C4C2×C22⋊D4311yescharacteristic
463C22×C4C2×C22⋊D4311yescharacteristic
464C22×C4C2×C22⋊D4311yescharacteristic
465C22×C4C2×C22⋊D4311yescharacteristic
466C22×C4C23×D4311yescharacteristic
467C2×C8—432no—
468C2×C8—432no—
469C2×C8—432no—
470C2×C8—432no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—861no—
479C4⋊C4—24no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—81no—
487C4⋊C4—81no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—3441no—
493C4⋊C4—3441no—
494C4⋊C4—1722no—
495C4⋊C4C2×C4×D4312yes—
496C4⋊C4C2×C4×D4312yes—
497C22⋊C4—864no—
498C22⋊C4—864no—
499C22⋊C4—3441no—
500C22⋊C4—3441no—
501C22⋊C4—1722no—
502C42—21no—
503C42—21no—
504C42—81no—
505C42—81no—
506C42—1722no—
507C42C2×C4×D4312yes—
508C42#1062189812yes—
509C42#1062190212yes—
510C42#1062190212yes—
511C23—862no—
512C23—1721no—
513C23—1721no—
514C23—1721no—
515C23—1721no—
516C23—1721no—
517C23—1721no—
518C23C22×C22⋊D4311yescharacteristic
519Q8—84no—
520Q8—862no—
521Q8—862no—
522Q8—1721no—
523Q8—1721no—
524D4—862no—
525D4—862no—
526D4—1721no—
527D4—1721no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—862no—
555C2×C4—3444no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4C4×C22⋊D4312yes—
565C2×C4C4×C22⋊D4312yes—
566C2×C4#1306331412yes—
567C2×C4#1306331412yes—
568C2×C4C22×C4×D4311yescharacteristic
569C2×C4#41×D4311yescharacteristic
570C2×C4#41×D4311yescharacteristic
571C2×C4C2×#1062189811yescharacteristic
572C2×C4C2×#1062190211yescharacteristic
573C2×C4C2×#1062190211yescharacteristic
574C8—862no—
575C8—862no—
576C8—862no—
577C8—862no—
578C22—3441no—
579C22—3441no—
580C22—3441no—
581C22—3441no—
582C22—1722no—
583C22—1722no—
584C22—1722no—
585C22C2×C4×C22⋊D4311yescharacteristic
586C22C2×#1306331411yescharacteristic
587C22#1458344511yescharacteristic
588C22#1458370211yescharacteristic
589C22#1458370711yescharacteristic
590C22#1458371011yescharacteristic
591C22#1458371411yescharacteristic
592C4—22no—
593C4—22no—
594C4—22no—
595C4—22no—
596C4—42no—
597C4—42no—
598C4—41no—
599C4—41no—
600C4—81no—
601C4—81no—
602C4—3441no—
603C4—3441no—
604C4—1722no—
605C4C4×#1062190211yescharacteristic
606C4C4×#1062190211yescharacteristic
607C4#1458343611yescharacteristic
608C4#1458343611yescharacteristic
609C2—3442no—
610C2C4×#1306331411yescharacteristic
611C2#1914342711yescharacteristic
612C2#1914343811yescharacteristic
613C2#1914495411yescharacteristic
614C2#1914496511yescharacteristic
615C2#1914520611yescharacteristic
616C2#1914522811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2331C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#2331D43
hypocenterC43#21654
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ #376 ◁ #2331

Complements

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

NH ≅ G/Ntype
3. #19135557C2semidirect
6. #19135284C2semidirect
8. #19135270C2semidirect
9. #19134728C2semidirect
10. #19134428C2semidirect
12. C4×#13063248C2semidirect
14. #19134282C2semidirect
15. C43×#2331C2semidirect
19. #14583261C4semidirect
86. #13063248C2×C4semidirect
87. #13063248C2×C4semidirect
94. #13063236C2×C4semidirect
102. C4⋊Q8×C43C2×C4semidirect
302. #2331D43semidirect
368. C43#21654semidirect
378. C4⋊Q8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145832612
#191373062
#191355572
#191354042
#191352912
#191352842
#191352772
#191352702
#191347282
#191344282
#191344232
C4×#130632482
C4×#130632452
#191342822
C43×#23312
#2165443