Finite Group Databasebeta

← #25148397

Subgroups — #25148397

Order 11008.

756 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583306C211yesmaximal, characteristic, complemented
2C2×#14583201C211yesmaximal, characteristic
3#19139766C211yesmaximal, characteristic
4#19137690C211yesmaximal, characteristic, complemented
5#19136081C211yesmaximal, characteristic, complemented
6#19136076C211yesmaximal, characteristic, complemented
7#19135981C211yesmaximal, characteristic
8#19135545C211yesmaximal, characteristic, complemented
9#19135365C211yesmaximal, characteristic, complemented
10#19135364C211yesmaximal, characteristic, complemented
11#19135315C211yesmaximal, characteristic, complemented
12#19135225C211yesmaximal, characteristic
13#19135212C211yesmaximal, characteristic
14#19134422C211yesmaximal, characteristic
15C43×#2065C211yesmaximal, characteristic
16C2×#13063324C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19#14583306—24no—
20#14583201—24no—
21C2×#13063259C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063257C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27C2×Dic43⋊C8C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063235C2211yescharacteristic
31#14582811—21no—
32#14582811—21no—
33#14582802C2211yescharacteristic
34#14582795C2211yescharacteristic
35#14582794—21no—
36#14582784—21no—
37#14582781—21no—
38#14582765C2211yescharacteristic
39#14582764C2211yescharacteristic
40#14582757—21no—
41#14582757—21no—
42C4⋊C4×Dic43—21no—
43C4⋊C4×Dic43C2211yescharacteristic
44C4⋊C4×Dic43C2211yescharacteristic
45C4×Dic43⋊C4C2211yescharacteristic
46C4×C4⋊Dic43C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582654C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×#106×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C43×#390C2211yescharacteristic
59C43×#389C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86—21no—
62C23×Dic43—21no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063324—22no—
66#13063324—22no—
67#13063316—22no—
68#13063316D414yes—
69D4×Dic43—22no—
70D4×Dic43—22no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4D411yescharacteristic
80C2×Dic43⋊C4D411yescharacteristic
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43C2311yescharacteristic
88C2×C4×Dic43C2311yescharacteristic
89#13063259—22no—
90#13063258—22no—
91#13063258—22no—
92#13063257—22no—
93#13063256—22no—
94Dic43⋊C8—22no—
95Dic43⋊C8—22no—
96#13063246—22no—
97#13063246Q814yescomplemented
98#13063235—22no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95D411yescharacteristic
108C43⋊#95D411yescharacteristic
109C22×D4×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—21no—
118C2×C42×C43C2311yescharacteristic
119#106×C43—22no—
120C4⋊C8×C43—22no—
121#102×C43—22no—
122#102×C43—22no—
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×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2411yescharacteristic
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—42no—
142C22×Dic43—42no—
143C22×Dic43—42no—
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C2×Dic86—42no—
149C2×Dic86—81no—
150C2×Dic86—81no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43#4112yes—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—42no—
163C4⋊C4×C43C2×D412yes—
164C22⋊C4×C43—81no—
165C22⋊C4×C43—81no—
166C42×C43—21no—
167C42×C43—21no—
168C22⋊Dic43—42no—
169C22⋊Dic43—81no—
170C22⋊Dic43—81no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—24no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43C2×D412yes—
179C4⋊Dic43C2×Q812yes—
180Dic43⋊C4—24no—
181Dic43⋊C4—41no—
182Dic43⋊C4—41no—
183Dic43⋊C4—42no—
184Dic43⋊C4—81no—
185C4×Dic43—21no—
186C4×Dic43—21no—
187C4×Dic43—42no—
188C4×Dic43—81no—
189C4×Dic43—81no—
190C4×Dic43C2×D412yes—
191C4×Dic43#4112yes—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8C2×Q812yes—
198C23×C43—22no—
199C23×C43—41no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43—41no—
203C23×C43—41no—
204C23×C43—41no—
205C23×C43C22×D411yescharacteristic
206D4×C43—22no—
207D4×C43—22no—
208D4×C43—41no—
209D4×C43—41no—
210C2×C4×C43—22no—
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—41no—
218C2×C4×C43—41no—
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×C43C22×D411yescharacteristic
226C2×C4×C43C22×Q811yescharacteristic
227C2×C4×C43C2×#4111yescharacteristic
228C2×C4×C43C2×#4111yescharacteristic
229C2×C4×C432−1+411yescharacteristic
230C2×C4×C432−1+411yescharacteristic
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—22no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—22no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—84no—
254C2×Dic43#12112yes—
255C2×Dic43#12112yes—
256Dic86—84no—
257C8×C43—22no—
258C8×C43—41no—
259C43⋊C8—22no—
260C43⋊C8—41no—
261#25466—431nomaximal, Sylow
262C22×C43—42no—
263C22×C43—42no—
264C22×C43—42no—
265C22×C43—81no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43C2×#12111yescharacteristic
270C22×C43#54711yescharacteristic
271C22×C43D4×Q811yescharacteristic
272C22×C43#57511yescharacteristic
273C22×C43#57511yescharacteristic
274C22×C43#57611yescharacteristic
275C22×C43#57711yescharacteristic
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—42no—
279C4×C43—81no—
280C4×C43—81no—
281C4×C43#53311yescharacteristic
282C4×C43#54111yescharacteristic
283C4×C43#54811yescharacteristic
284C4×C43D4×Q811yescharacteristic
285Dic43—22no—
286Dic43—22no—
287Dic43—41no—
288Dic43—41no—
289Dic43—42no—
290Dic43—42no—
291Dic43—81no—
292Dic43—81no—
293C2×#501—431no—
294C2×#478—431no—
295#2563—431no—
296#2370—431no—
297#2085—431no—
298#2085—431no—
299#2067—431no—
300#2065D4311yescharacteristic
301#1988—431no—
302#1949—431no—
303#1949—431no—
304#1940—431no—
305#1926—431no—
306#1925—431no—
307#1762—431no—
308C2×C43—82no—
309C2×C43#242911yescharacteristic
310C2×C43#304011yescharacteristic
311C2×C43#304511yescharacteristic
312C2×C43#334711yescharacteristic
313C2×C43#334811yescharacteristic
314C2×C43#338811yescharacteristic
315C2×C43#338911yescharacteristic
316C2×C4⋊Q8—431no—
317C2×#125—431no—
318C2×C4×D4—431no—
319#501—864no—
320#478—864no—
321C2×#107—431no—
322C2×#107—431no—
323C2×#107—431no—
324C2×#106—431no—
325C2×#106—431no—
326C2×#106C2×D4311yescharacteristic
327C2×C4⋊C8—431no—
328C2×C4⋊C8—431no—
329C2×C4⋊C8C2×D4311yescharacteristic
330C2×#102—431no—
331C2×#102—431no—
332C2×#102C2×D4311yescharacteristic
333C2×#102C2×D4311yescharacteristic
334C2×#97—431no—
335#393—861no—
336#393—861no—
337#390—431no—
338#390C2×D4311yescharacteristic
339#389—431no—
340#389—861no—
341#389C2×D4311yescharacteristic
342#387—861no—
343#387—861no—
344#382—431no—
345#382—431no—
346#380—861no—
347#380—861no—
348C4×C4⋊C4—431no—
349C4×C4⋊C4—431no—
350C4×C4⋊C4—431no—
351C4×C4⋊C4—431no—
352C4×C4⋊C4—861no—
353#340—431no—
354#340—431no—
355#340—431no—
356#340—431no—
357#340—431no—
358#340C2×D4311yescharacteristic
359#336—431no—
360#336—431no—
361C43#2546611yescharacteristic, complemented, Sylow
362C22×Q8—861no—
363C22×D4C22×D4311yescharacteristic
364C23×C4—861no—
365C22×C8—431no—
366C22×C8—431no—
367C22×C8C22×D4311yescharacteristic
368C22×C8C22×D4311yescharacteristic
369C4⋊Q8—862no—
370C4⋊Q8—862no—
371#125—434no—
372#125—862no—
373C4×D4—862no—
374C4×D4—862no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—431no—
379C2×C4⋊C4—431no—
380C2×C4⋊C4—431no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4C22×D4311yescharacteristic
387C2×C4⋊C4C22×D4311yescharacteristic
388C2×C4⋊C4C22×D4311yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—861no—
392C2×C22⋊C4—861no—
393C2×C22⋊C4—861no—
394C2×C42—431no—
395C2×C42—431no—
396C2×C42—861no—
397C2×C42—861no—
398C2×C42—861no—
399C2×C42C22×D4311yescharacteristic
400#107—862no—
401#107—862no—
402#107—862no—
403#106—22no—
404#106—862no—
405#106—862no—
406C4⋊C8—22no—
407C4⋊C8—862no—
408C4⋊C8—862no—
409#102—22no—
410#102—22no—
411#102—434no—
412#102—862no—
413#97—862no—
414#95—21no—
415#95—431no—
416#95—431no—
417#95—861no—
418#95—861no—
419#95—861no—
420#95—861no—
421#95—861no—
422#95—861no—
423#95—861no—
424#95—861no—
425C24—21no—
426C2×Q8—3441no—
427C2×Q8—3441no—
428C2×Q8—1722no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4Q8×D4312yes—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—431no—
439C22×C4—431no—
440C22×C4—431no—
441C22×C4—431no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4—861no—
446C22×C4—1722no—
447C22×C4—1722no—
448C22×C4—1722no—
449C22×C4D4×D4311yescharacteristic
450C22×C4D4×D4311yescharacteristic
451C22×C4C23×D4311yescharacteristic
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—432no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8#1062190012yes—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—42no—
470C4⋊C4—432no—
471C4⋊C4—432no—
472C4⋊C4—864no—
473C4⋊C4—864no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—3441no—
481C4⋊C4—1721no—
482C4⋊C4—1721no—
483C4⋊C4—1722no—
484C4⋊C4D4×D4312yes—
485C22⋊C4—81no—
486C22⋊C4—81no—
487C22⋊C4—3441no—
488C22⋊C4—3441no—
489C22⋊C4—1722no—
490C42—21no—
491C42—21no—
492C42—432no—
493C42—432no—
494C42—861no—
495C42—861no—
496C42—3441no—
497C42—3441no—
498C42—1722no—
499C23—22no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23C2×D4×D4311yescharacteristic
507Q8—3444no—
508D4—22no—
509D4—22no—
510D4—41no—
511D4—41no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—432no—
528C2×C4—432no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—862no—
534C2×C4—862no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—3444no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4C2×D4×D4311yescharacteristic
553C2×C4C2×Q8×D4311yescharacteristic
554C2×C4#41×D4311yescharacteristic
555C2×C4C2×#1062190011yescharacteristic
556C2×C4#1306337211yescharacteristic
557C2×C4#1306337211yescharacteristic
558C8—22no—
559C8—41no—
560C8—862no—
561C8—1721no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22#121×D4311yescharacteristic
570C22#1458354911yescharacteristic
571C22#1458356211yescharacteristic
572C22#1458369511yescharacteristic
573C22#1458369611yescharacteristic
574C22#1458370311yescharacteristic
575C22#1458370511yescharacteristic
576C4—41no—
577C4—41no—
578C4—42no—
579C4—81no—
580C4—81no—
581C4—862no—
582C4—862no—
583C4—3441no—
584C4—3441no—
585C4—1722no—
586C4—1721no—
587C4—1721no—
588C4—1722no—
589C4#1458345111yescharacteristic
590C4#1458350611yescharacteristic
591C4#1458355511yescharacteristic
592C4#1458356211yescharacteristic
593C2—82no—
594C2#1913818711yescharacteristic
595C2#1914408411yescharacteristic
596C2#1914413111yescharacteristic
597C2#1914709011yescharacteristic
598C2#1914711611yescharacteristic
599C2#1914753311yescharacteristic
600C2#1914755311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2065C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2065D43
hypocenterC43#25466
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2065

Complements

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

NH ≅ G/Ntype
1. C2×#14583306C2semidirect
4. #19137690C2semidirect
5. #19136081C2semidirect
6. #19136076C2semidirect
8. #19135545C2semidirect
9. #19135365C2semidirect
10. #19135364C2semidirect
11. #19135315C2semidirect
97. #13063246Q8semidirect
361. C43#25466semidirect

Maximal subgroups

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

subgroupindex
C2×#145833062
C2×#145832012
#191397662
#191376902
#191360812
#191360762
#191359812
#191355452
#191353652
#191353642
#191353152
#191352252
#191352122
#191344222
C43×#20652
#2546643