Finite Group Databasebeta

← #25196521

Subgroups — #25196521

Order 11008.

734 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140719C211yesmaximal, characteristic, complemented
2#19137307C211yesmaximal, characteristic
3#19135745C211yesmaximal, characteristic, complemented
4#19135739C211yesmaximal, characteristic
5#19135735C211yesmaximal, characteristic, complemented
6#19135729C211yesmaximal, characteristic
7#19135410C211yesmaximal, characteristic
8#19135405C211yesmaximal, characteristic
9#19134727C211yesmaximal, characteristic, complemented
10#19134721C211yesmaximal, characteristic, complemented
11#19134607C211yesmaximal, characteristic, complemented
12#19134601C211yesmaximal, characteristic, complemented
13#19134595C211yesmaximal, characteristic
14#19134454C211yesmaximal, characteristic, complemented
15C43×#1804C211yesmaximal, characteristic
16C2×#13063324C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×#13063312C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21C2×#13063250C2211yescharacteristic
22C2×#13063250C2211yescharacteristic
23C2×#13063248C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063235C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29#14582833—21no—
30#14582833—21no—
31#14582820—21no—
32#14582820—21no—
33#14582804C2211yescharacteristic
34#14582802C2211yescharacteristic
35#14582787—21no—
36#14582787—21no—
37#14582772—21no—
38#14582772—21no—
39#14582769C2211yescharacteristic
40#14582768C2211yescharacteristic
41#14582768C2211yescharacteristic
42#14582764C2211yescharacteristic
43#14582745C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×C4×D4×C43C2211yescharacteristic
53C2×C4⋊C8×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C43×#382C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86—21no—
60C22×Dic86C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63#13063324—41no—
64#13063324—41no—
65#13063316—41no—
66#13063316—41no—
67#13063312—22no—
68#13063312Q814yescomplemented
69C4×Dic86—22no—
70C4×Dic86—22no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43C2311yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91C4⋊(C43⋊C8)—22no—
92#13063250—41no—
93#13063250—41no—
94#13063248—41no—
95#13063248—41no—
96#13063246—41no—
97#13063246—41no—
98#13063235—22no—
99C8×Dic43—22no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95D411yescharacteristic
105C43⋊#95D411yescharacteristic
106C43⋊#95D411yescharacteristic
107C43⋊#95D411yescharacteristic
108C22×D4×C43C2311yescharacteristic
109C23×C4×C43—21no—
110C22×C8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C4×D4×C43—22no—
113C4×D4×C43—22no—
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C22⋊C4×C43—21no—
118C2×C42×C43C2311yescharacteristic
119C4⋊C8×C43—22no—
120#102×C43—41no—
121#102×C43—41no—
122#95×C43—21no—
123#95×C43—21no—
124C24×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43C2×Q812yes—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—42no—
135C22×C4×C43—81no—
136C22×C4×C43—81no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2411yescharacteristic
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C2×Dic86—21no—
149C2×Dic86—21no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—42no—
154C2×Dic86—81no—
155C2×Dic86—81no—
156C2×Dic86C2×Q812yes—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C22⋊C4×C43—42no—
170C42×C43#4112yes—
171C42×C43#4112yes—
172C22⋊Dic43—24no—
173C22⋊Dic43—24no—
174C22⋊Dic43—81no—
175C22⋊Dic43—81no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—42no—
183C4⋊Dic43—81no—
184C4⋊Dic43—81no—
185Dic43⋊C4—42no—
186Dic43⋊C4—42no—
187Dic43⋊C4—42no—
188Dic43⋊C4—81no—
189Dic43⋊C4—81no—
190Dic43⋊C4—81no—
191Dic43⋊C4—81no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—42no—
195C4×Dic43C2×Q812yes—
196C4×Dic43#4112yes—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C23×C43—22no—
204C23×C43—41no—
205C23×C43—41no—
206C23×C43—41no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43C22×D411yescharacteristic
211D4×C43—22no—
212D4×C43—22no—
213D4×C43—41no—
214D4×C43—41no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—84no—
229C2×C4×C43#12412yes—
230C2×C4×C43#12412yes—
231C2×C4×C43C22×Q811yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43H(5,𝔽2)11yescharacteristic
236C2×C4×C43H(5,𝔽2)11yescharacteristic
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—22no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43C22⋊Q812yes—
260C2×Dic43C22⋊Q812yes—
261Dic86—22no—
262Dic86—22no—
263Dic86—41no—
264Dic86—41no—
265Dic86—84no—
266C8×C43—41no—
267C8×C43—41no—
268C43⋊C8—41no—
269C43⋊C8—41no—
270#29151—431nomaximal, Sylow
271C22×C43—42no—
272C22×C43—42no—
273C22×C43—42no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43—81no—
277C22×C43—81no—
278C22×C43C2×C22⋊Q811yescharacteristic
279C22×C43C2×#12411yescharacteristic
280C22×C43#53511yescharacteristic
281C22×C43#57611yescharacteristic
282C22×C43#57711yescharacteristic
283C22×C43#57711yescharacteristic
284C22×C43#57811yescharacteristic
285C4×C43—22no—
286C4×C43—22no—
287C4×C43—81no—
288C4×C43—81no—
289C4×C43—81no—
290C4×C43#55411yescharacteristic
291C4×C43#55411yescharacteristic
292C4×C43#55511yescharacteristic
293C4×C43#55511yescharacteristic
294Dic43—22no—
295Dic43—22no—
296Dic43—42no—
297Dic43—41no—
298Dic43—41no—
299Dic43—81no—
300Dic43—81no—
301Dic43—81no—
302#2660—431no—
303#2326—431no—
304#2026—431no—
305#2025—431no—
306#2024—431no—
307#2023—431no—
308#1959—431no—
309#1958—431no—
310#1836—431no—
311#1834—431no—
312#1805—431no—
313#1804D4311yescharacteristic
314#1803—431no—
315#1802—431no—
316#1768—431no—
317C2×C43—82no—
318C2×C43#256311yescharacteristic
319C2×C43#308311yescharacteristic
320C2×C43#308411yescharacteristic
321C2×C43#313611yescharacteristic
322C2×C43#313711yescharacteristic
323C2×C43#322411yescharacteristic
324C2×C43#322511yescharacteristic
325C2×C4⋊Q8—431no—
326C2×#125—431no—
327C2×#124—431no—
328C2×C4×Q8—431no—
329C2×C4×D4C2×D4311yescharacteristic
330C2×C4⋊C8—431no—
331C2×C4⋊C8C2×D4311yescharacteristic
332C2×#103—431no—
333C2×#103—431no—
334C2×#103—431no—
335C2×#103—431no—
336C2×#102—431no—
337C2×#102—431no—
338C2×#102C2×D4311yescharacteristic
339C2×#102C2×D4311yescharacteristic
340C2×#97—431no—
341C2×C4×C8—431no—
342#398—861no—
343#398—861no—
344#395—861no—
345#395—861no—
346#391—431no—
347#390—431no—
348#388—861no—
349#388—861no—
350#385—861no—
351#385—861no—
352#384—431no—
353#384—431no—
354#384—431no—
355#382—431no—
356#382C2×D4311yescharacteristic
357#376—431no—
358#340—431no—
359#340—431no—
360#340—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340C2×D4311yescharacteristic
365#340C2×D4311yescharacteristic
366#336—431no—
367#336—431no—
368C43#2915111yescharacteristic, complemented, Sylow
369C22×Q8—431no—
370C22×Q8—861no—
371C22×D4C22×D4311yescharacteristic
372C23×C4—21no—
373C22×C8—431no—
374C22×C8—431no—
375C22×C8C22×D4311yescharacteristic
376C22×C8C22×D4311yescharacteristic
377C4⋊Q8—1721no—
378C4⋊Q8—1721no—
379#125—1721no—
380#125—1721no—
381#124—434no—
382#124—862no—
383C4×Q8—862no—
384C4×Q8—862no—
385C4×D4—22no—
386C4×D4—22no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4C22×D4311yescharacteristic
401C2×C4⋊C4C22×D4311yescharacteristic
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C42—431no—
409C2×C42—431no—
410C2×C42—861no—
411C2×C42C22×D4311yescharacteristic
412C4⋊C8—22no—
413C4⋊C8—862no—
414#103—1721no—
415#103—1721no—
416#103—1721no—
417#103—1721no—
418#102—41no—
419#102—41no—
420#102—1721no—
421#102—1721no—
422#97—862no—
423C4×C8—862no—
424#95—21no—
425#95—21no—
426#95—431no—
427#95—431no—
428#95—431no—
429#95—431no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434C24—21no—
435C2×Q8—432no—
436C2×Q8—861no—
437C2×Q8—861no—
438C2×Q8—861no—
439C2×Q8—861no—
440C2×Q8—861no—
441C2×Q8—3441no—
442C2×Q8—3441no—
443C2×Q8—1722no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4Q8×D4312yes—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—42no—
454C22×C4—81no—
455C22×C4—81no—
456C22×C4—431no—
457C22×C4—431no—
458C22×C4—431no—
459C22×C4—431no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4D4×D4311yescharacteristic
465C22×C4D4×D4311yescharacteristic
466C22×C4C23×D4311yescharacteristic
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
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—21no—
484C4⋊C4—21no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—3441no—
492C4⋊C4—3441no—
493C4⋊C4—3441no—
494C4⋊C4—3441no—
495C4⋊C4—3441no—
496C4⋊C4—3441no—
497C4⋊C4—1722no—
498C4⋊C4—1722no—
499C4⋊C4—1722no—
500C4⋊C4—1722no—
501C22⋊C4—42no—
502C22⋊C4—864no—
503C22⋊C4—864no—
504C22⋊C4—3441no—
505C22⋊C4—3441no—
506C42—432no—
507C42—432no—
508C42—861no—
509C42—861no—
510C42—1722no—
511C42#1062189812yes—
512C42#1062190012yes—
513C23—22no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23C2×D4×D4311yescharacteristic
521Q8—862no—
522Q8—862no—
523Q8—3444no—
524Q8—1721no—
525Q8—1721no—
526D4—22no—
527D4—22no—
528D4—41no—
529D4—41no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—84no—
544C2×C4—432no—
545C2×C4—432no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—862no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4#1306331112yes—
569C2×C4#1306331112yes—
570C2×C4C2×Q8×D4311yescharacteristic
571C2×C4#41×D4311yescharacteristic
572C2×C4C2×#1062190011yescharacteristic
573C2×C4C2×#1062189811yescharacteristic
574C2×C4#1306337011yescharacteristic
575C2×C4#1306337111yescharacteristic
576C8—41no—
577C8—41no—
578C8—1721no—
579C8—1721no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22C22⋊Q8×D4311yescharacteristic
588C22C2×#1306331111yescharacteristic
589C22#1458346511yescharacteristic
590C22#1458370311yescharacteristic
591C22#1458370611yescharacteristic
592C22#1458370911yescharacteristic
593C22#1458371311yescharacteristic
594C4—22no—
595C4—22no—
596C4—81no—
597C4—81no—
598C4—81no—
599C4—862no—
600C4—862no—
601C4—3441no—
602C4—3441no—
603C4—3441no—
604C4—1722no—
605C4—1721no—
606C4—1721no—
607C4#1458360411yescharacteristic
608C4#1458360711yescharacteristic
609C4#1458361211yescharacteristic
610C4#1458361311yescharacteristic
611C2—82no—
612C2#1913976511yescharacteristic
613C2#1914444711yescharacteristic
614C2#1914445811yescharacteristic
615C2#1914494511yescharacteristic
616C2#1914496411yescharacteristic
617C2#1914568811yescharacteristic
618C2#1914570111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1804C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#1804D43
hypocenterC43#29151
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
1. #19140719C2semidirect
3. #19135745C2semidirect
5. #19135735C2semidirect
9. #19134727C2semidirect
10. #19134721C2semidirect
11. #19134607C2semidirect
12. #19134601C2semidirect
14. #19134454C2semidirect
68. #13063312Q8semidirect
368. C43#29151semidirect

Maximal subgroups

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

subgroupindex
#191407192
#191373072
#191357452
#191357392
#191357352
#191357292
#191354102
#191354052
#191347272
#191347212
#191346072
#191346012
#191345952
#191344542
C43×#18042
#2915143