Finite Group Databasebeta

← #25104710

Subgroups — #25104710

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×#14583258C211yesmaximal, characteristic
2#19137343C211yesmaximal, characteristic, complemented
3#19135555C211yesmaximal, characteristic, complemented
4#19135407C211yesmaximal, characteristic
5#19135295C211yesmaximal, characteristic
6#19135288C211yesmaximal, characteristic, complemented
7#19135281C211yesmaximal, characteristic
8#19135274C211yesmaximal, characteristic, complemented
9#19134730C211yesmaximal, characteristic, complemented
10#19134425C211yesmaximal, characteristic, complemented
11#19134420C211yesmaximal, characteristic
12C4×#13063249C211yesmaximal, characteristic, complemented
13C4×#13063246C211yesmaximal, characteristic
14#19134282C211yesmaximal, characteristic, complemented
15C43×#2326C211yesmaximal, characteristic
16C2×#13063325C2211yescharacteristic
17#14583258C418yescomplemented
18C2×#13063249C2211yescharacteristic
19C2×#13063249C2211yescharacteristic
20C2×#13063249C2211yescharacteristic
21C2×#13063249C2211yescharacteristic
22C2×#13063246C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063236C2211yescharacteristic
27C2×#13063236C2211yescharacteristic
28C2×#13063236C2211yescharacteristic
29C2×C4×C43⋊C8C2211yescharacteristic
30C2×C4×C43⋊C8C2211yescharacteristic
31C2×C4×C43⋊C8C2211yescharacteristic
32#14582803—21no—
33#14582803—21no—
34#14582797C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582782—21no—
37#14582782—21no—
38#14582765C2211yescharacteristic
39C4×C4⋊Dic43C2211yescharacteristic
40C4×C4⋊Dic43C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49C2×#124×C43C2211yescharacteristic
50C2×C4×Q8×C43C2211yescharacteristic
51C2×C4×D4×C43C2211yescharacteristic
52C43×#391C2211yescharacteristic
53C43×#390C2211yescharacteristic
54C43×#388—21no—
55C43×#388—21no—
56C43×#385—21no—
57C43×#385—21no—
58C43×#384C2211yescharacteristic
59C43×#376C2211yescharacteristic
60C22×Dic86—21no—
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063325—22no—
66#13063325C2×C414yescomplemented
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×C4×Dic43—21no—
75C2×C4×Dic43—21no—
76#13063249—22no—
77#13063249—22no—
78#13063249C2×C414yescomplemented
79#13063249C2×C414yescomplemented
80#13063246—22no—
81#13063246—22no—
82#13063246C2×C414yes—
83#13063246C2×C414yes—
84#13063236—22no—
85#13063236—22no—
86#13063236C2×C414yescomplemented
87C4×C43⋊C8—22no—
88C4×C43⋊C8—22no—
89C4×C43⋊C8—22no—
90C43⋊#95—21no—
91C43⋊#95—21no—
92C43⋊#95—21no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C22×Q8×C43C2311yescharacteristic
97C22×D4×C43C2311yescharacteristic
98C23×C4×C43—21no—
99#124×C43—22no—
100#124×C43C2×C414yes—
101C4×Q8×C43—22no—
102C4×Q8×C43—22no—
103C4×D4×C43—22no—
104C4×D4×C43—22no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C42×C43—21no—
116C2×C42×C43C2311yescharacteristic
117C2×C42×C43C2311yescharacteristic
118C2×C42×C43C2311yescharacteristic
119#95×C43—21no—
120#95×C43—21no—
121#95×C43D411yescharacteristic
122#95×C43D411yescharacteristic
123#95×C43D411yescharacteristic
124#95×C43D411yescharacteristic
125C24×C43—21no—
126C2×Q8×C43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43C22×C412yes—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43C22×C412yes—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—42no—
142C22×C4×C43—81no—
143C22×C4×C43—81no—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2411yescharacteristic
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C2×Dic86—24no—
156C2×Dic86—81no—
157C2×Dic86—81no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—42no—
163C4⋊C4×C43—81no—
164C4⋊C4×C43—81no—
165C22⋊C4×C43—24no—
166C22⋊C4×C43—24no—
167C22⋊C4×C43—42no—
168C22⋊C4×C43—81no—
169C22⋊C4×C43—81no—
170C42×C43—21no—
171C42×C43—21no—
172C42×C43—42no—
173C42×C43C22×C412yes—
174C42×C43#4112yes—
175C42×C43#4112yes—
176C42×C43#4112yes—
177C4⋊Dic43—24no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43C22×C412yes—
185C4⋊Dic43C22×C412yes—
186Dic43⋊C4—81no—
187Dic43⋊C4—81no—
188C4×Dic43—81no—
189C4×Dic43—81no—
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×C43—22no—
203C23×C43—41no—
204C23×C43—41no—
205C23×C43—41no—
206C23×C43—41no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43C22×D411yescharacteristic
210Q8×C43—22no—
211Q8×C43—22no—
212Q8×C43—41no—
213Q8×C43—41no—
214D4×C43—22no—
215D4×C43—22no—
216D4×C43—41no—
217D4×C43—41no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—22no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—41no—
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—84no—
242C2×C4×C43C4×D412yes—
243C2×C4×C43C4×D412yes—
244C2×C4×C43#12412yes—
245C2×C4×C43#12412yes—
246C2×C4×C43C23×C411yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264Dic86—84no—
265C43⋊C8—22no—
266C43⋊C8—22no—
267C43⋊C8—22no—
268C43⋊C8—22no—
269#21654—431nomaximal, Sylow
270C22×C43—42no—
271C22×C43—42no—
272C22×C43—42no—
273C22×C43—81no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43—81no—
277C22×C43C2×C4×D411yescharacteristic
278C22×C43C2×#12411yescharacteristic
279C22×C43#53211yescharacteristic
280C22×C43#57611yescharacteristic
281C22×C43#57711yescharacteristic
282C22×C43#57711yescharacteristic
283C22×C43#57811yescharacteristic
284C4×C43—22no—
285C4×C43—22no—
286C4×C43—22no—
287C4×C43—22no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—42no—
291C4×C43—81no—
292C4×C43—81no—
293C4×C43C4×#4111yescharacteristic
294C4×C43C4×#4111yescharacteristic
295C4×C43#52911yescharacteristic
296C4×C43#52911yescharacteristic
297Dic43—42no—
298Dic43—42no—
299Dic43—81no—
300Dic43—81no—
301C2×#489—431no—
302#2331—431no—
303#2326D4311yescharacteristic
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×C43—82no—
317C2×C43C4×#12411yescharacteristic
318C2×C43#294611yescharacteristic
319C2×C43#294711yescharacteristic
320C2×C43#313611yescharacteristic
321C2×C43#313711yescharacteristic
322C2×C43#317311yescharacteristic
323C2×C43#317511yescharacteristic
324C2×C4⋊Q8—431no—
325C2×#124C2×D4311yescharacteristic
326C2×C4×Q8C2×D4311yescharacteristic
327C2×C4×D4C2×D4311yescharacteristic
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—861no—
344#391—861no—
345#391C2×D4311yescharacteristic
346#390C2×D4311yescharacteristic
347#389—431no—
348#389—431no—
349#388—21no—
350#388—21no—
351#387—861no—
352#387—861no—
353#385—21no—
354#385—21no—
355#384C2×D4311yescharacteristic
356#382—431no—
357C4×C4⋊C4—431no—
358C4×C4⋊C4—431no—
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—861no—
370C22×Q8C22×D4311yescharacteristic
371C22×D4C22×D4311yescharacteristic
372C23×C4—21no—
373C22×C8—431no—
374C22×C8—431no—
375C22×C8—431no—
376C22×C8—431no—
377C4⋊Q8—434no—
378C4⋊Q8—862no—
379#124—22no—
380#124C4×D4314yes—
381C4×Q8—22no—
382C4×Q8—22no—
383C4×D4—22no—
384C4×D4—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—431no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4C22×D4311yescharacteristic
396C2×C4⋊C4C22×D4311yescharacteristic
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C42—21no—
403C2×C42—861no—
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—861no—
425#95—861no—
426#95—861no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95C22⋊D4311yescharacteristic
431#95C22⋊D4311yescharacteristic
432#95C22⋊D4311yescharacteristic
433#95C22⋊D4311yescharacteristic
434C24—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—864no—
441C2×Q8—3441no—
442C2×Q8—3441no—
443C2×Q8C2×C4×D4312yes—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4C2×C4×D4312yes—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—42no—
454C22×C4—81no—
455C22×C4—81no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—861no—
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—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—42no—
484C4⋊C4—81no—
485C4⋊C4—81no—
486C4⋊C4—432no—
487C4⋊C4—432no—
488C4⋊C4—864no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—3441no—
496C4⋊C4—3441no—
497C22⋊C4—24no—
498C22⋊C4—24no—
499C22⋊C4—42no—
500C22⋊C4—81no—
501C22⋊C4—81no—
502C42—21no—
503C42—21no—
504C42—42no—
505C42—3441no—
506C42—3441no—
507C42C2×C4×D4312yes—
508C42#1062189812yes—
509C42#1062190012yes—
510C42#1062190012yes—
511C23—22no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23C22×C22⋊D4311yescharacteristic
519Q8—22no—
520Q8—22no—
521Q8—41no—
522Q8—41no—
523Q8—3444no—
524D4—22no—
525D4—22no—
526D4—41no—
527D4—41no—
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—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—84no—
552C2×C4—862no—
553C2×C4—862no—
554C2×C4—1721no—
555C2×C4—1721no—
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#1306331212yes—
567C2×C4#1306331212yes—
568C2×C4C22×C4×D4311yescharacteristic
569C2×C4#41×D4311yescharacteristic
570C2×C4#41×D4311yescharacteristic
571C2×C4C2×#1062190011yescharacteristic
572C2×C4C2×#1062190011yescharacteristic
573C2×C4C2×#1062189811yescharacteristic
574C8—862no—
575C8—862no—
576C8—862no—
577C8—862no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22C2×C4×C22⋊D4311yescharacteristic
586C22C2×#1306331211yescharacteristic
587C22#1458344511yescharacteristic
588C22#1458370211yescharacteristic
589C22#1458370711yescharacteristic
590C22#1458371011yescharacteristic
591C22#1458371411yescharacteristic
592C4—22no—
593C4—22no—
594C4—22no—
595C4—22no—
596C4—41no—
597C4—42no—
598C4—41no—
599C4—81no—
600C4—81no—
601C4—3441no—
602C4—3441no—
603C4—1722no—
604C4—1722no—
605C4C4×#1062190011yescharacteristic
606C4C4×#1062190011yescharacteristic
607C4#1458343111yescharacteristic
608C4#1458343111yescharacteristic
609C2—82no—
610C2C4×#1306331211yescharacteristic
611C2#1914342311yescharacteristic
612C2#1914343411yescharacteristic
613C2#1914494911yescharacteristic
614C2#1914496011yescharacteristic
615C2#1914520611yescharacteristic
616C2#1914522811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2326C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenter#2326D43
hypocenterC43#21654
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ #376 ◁ #2326

Complements

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

NH ≅ G/Ntype
2. #19137343C2semidirect
3. #19135555C2semidirect
6. #19135288C2semidirect
8. #19135274C2semidirect
9. #19134730C2semidirect
10. #19134425C2semidirect
12. C4×#13063249C2semidirect
14. #19134282C2semidirect
17. #14583258C4semidirect
66. #13063325C2×C4semidirect
78. #13063249C2×C4semidirect
79. #13063249C2×C4semidirect
86. #13063236C2×C4semidirect
368. C43#21654semidirect

Maximal subgroups

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

subgroupindex
C2×#145832582
#191373432
#191355552
#191354072
#191352952
#191352882
#191352812
#191352742
#191347302
#191344252
#191344202
C4×#130632492
C4×#130632462
#191342822
C43×#23262
#2165443