Finite Group Databasebeta

← #25165227

Subgroups — #25165227

Order 11008.

704 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
1#19139136C211yesmaximal, characteristic, complemented
2#19137666C211yesmaximal, characteristic
3#19136012C211yesmaximal, characteristic
4#19135964C211yesmaximal, characteristic
5#19135837C211yesmaximal, characteristic
6#19135836C211yesmaximal, characteristic
7#19135272C211yesmaximal, characteristic, complemented
8#19135228C211yesmaximal, characteristic, complemented
9#19135180C211yesmaximal, characteristic, complemented
10#19135151C211yesmaximal, characteristic, complemented
11#19134864C211yesmaximal, characteristic, complemented
12#19134857C211yesmaximal, characteristic
13#19134609C211yesmaximal, characteristic, complemented
14#19134409C211yesmaximal, characteristic
15C43×#1919C211yesmaximal, characteristic, complemented
16C2×#13063313C2211yescharacteristic
17C2×#13063290C2211yescharacteristic
18C2×#13063287C2211yescharacteristic
19C2×#13063256C2211yescharacteristic
20C2×Dic43⋊C8C2211yescharacteristic
21C2×#13063250C2211yescharacteristic
22C2×#13063250C2211yescharacteristic
23C2×#13063248C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30#14582838—21no—
31#14582831—21no—
32#14582804C2211yescharacteristic
33#14582800C2211yescharacteristic
34#14582798C2211yescharacteristic
35#14582798C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582791—21no—
38#14582790—21no—
39#14582786—21no—
40#14582773—21no—
41#14582764—21no—
42#14582764C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45C4×(C2×D43)⋊C4—21no—
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#106×C43C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C4×C4⋊C4×C43C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C4×D43—21no—
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64#13063313—22no—
65#13063313—22no—
66#13063290—22no—
67#13063290—41no—
68#13063287—22no—
69#13063287—41no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43D411yescharacteristic
73C2×C4⋊Dic43D411yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
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—
84C2×C4×Dic43—21no—
85C2×C4×Dic43C2311yescharacteristic
86C2×C4×Dic43C2311yescharacteristic
87#13063256—22no—
88Dic43⋊C8—41no—
89#13063250—22no—
90#13063250—41no—
91#13063248—22no—
92#13063248—22no—
93#13063247—22no—
94#13063247—41no—
95#13063245—22no—
96#13063245—22no—
97C8×Dic43—41no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95D411yescharacteristic
107C43⋊#95D411yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C42×C43—21no—
116C2×C42×C43C2311yescharacteristic
117#106×C43—22no—
118#95×C43—21no—
119#95×C43—21no—
120C23×D43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2411yescharacteristic
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43C2×D411yescharacteristic
132C22×Dic43C2×D411yescharacteristic
133C22×Dic43C2×D411yescharacteristic
134C22×Dic43C2×D411yescharacteristic
135C2×D172—21no—
136C2×D172—21no—
137C2×D172—21no—
138C2×D172—21no—
139C2×D172—21no—
140C2×D172#4112yes—
141C2×C4×D43—42no—
142C2×C4×D43—42no—
143C2×C4×D43—81no—
144C2×Dic86—21no—
145C2×Dic86—21no—
146C2×Dic86—21no—
147C2×Dic86—21no—
148C2×Dic86—21no—
149C2×Dic86#4112yes—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—81no—
163C4⋊C4×C43#4112yes—
164C4⋊C4×C43#4112yes—
165C42×C43—21no—
166C42×C43—21no—
167C42×C43—81no—
168(C2×D43)⋊C4—24no—
169(C2×D43)⋊C4—24no—
170(C2×D43)⋊C4—42no—
171(C2×D43)⋊C4—42no—
172(C2×D43)⋊C4—81no—
173C4⋊Dic43—22no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—41no—
179C4⋊Dic43—81no—
180C4⋊Dic43—81no—
181Dic43⋊C4—42no—
182Dic43⋊C4—42no—
183C4×Dic43—21no—
184C4×Dic43—21no—
185C4×Dic43—21no—
186C4×Dic43—21no—
187C4×Dic43—42no—
188C4×Dic43—42no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C23×C43C22×D411yescharacteristic
196C22×D43—22no—
197C22×D43—41no—
198C22×D43—41no—
199C22×D43—41no—
200C22×D43—41no—
201C22×D43—41no—
202C22×D43—41no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—22no—
206C2×C4×C43—22no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43C2×#4111yescharacteristic
222C2×C4×C43C2×#4111yescharacteristic
223C2×C4×C43C2×#4111yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C2×C4×C43H(5,𝔽2)11yescharacteristic
226C2×C4×C432−1+411yescharacteristic
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—22no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43#13512yes—
248D172—22no—
249D172—22no—
250D172—41no—
251D172—41no—
252C4×D43—84no—
253Dic86—22no—
254Dic86—22no—
255Dic86—41no—
256Dic86—41no—
257C8×C43—41no—
258C8×C43—41no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261#26760—431nomaximal, Sylow
262C22×C43#52511yescharacteristic
263C22×C43#54611yescharacteristic
264C22×C43#54811yescharacteristic
265C22×C43C2×#13511yescharacteristic
266C22×C43#57511yescharacteristic
267C22×C43#57711yescharacteristic
268C22×C43#57711yescharacteristic
269C2×D43—42no—
270C2×D43—42no—
271C2×D43—42no—
272C2×D43—81no—
273C2×D43—81no—
274C2×D43—81no—
275C2×D43—81no—
276C4×C43—41no—
277C4×C43—42no—
278C4×C43—41no—
279C4×C43—42no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43#52911yescharacteristic
283C4×C43#53911yescharacteristic
284C4×C43#55211yescharacteristic
285C4×C43#55311yescharacteristic
286Dic43—22no—
287Dic43—42no—
288Dic43—41no—
289Dic43—41no—
290Dic43—41no—
291Dic43—81no—
292Dic43—81no—
293#2508—431no—
294#2367—431no—
295#2073—431no—
296#2065—431no—
297#2042—431no—
298#2042—431no—
299#1933—431no—
300#1927—431no—
301#1920—431no—
302#1919D4311yescharacteristic, complemented
303#1916—431no—
304#1865—431no—
305#1864—431no—
306#1805—431no—
307C4×#102—431no—
308C2×C43#246011yescharacteristic
309C2×C43#310211yescharacteristic
310C2×C43#312511yescharacteristic
311C2×C43#329611yescharacteristic
312C2×C43#332111yescharacteristic
313C2×C43#336011yescharacteristic
314C2×C43#337111yescharacteristic
315D43—82no—
316C2×#124—431no—
317C2×C4×Q8—431no—
318C2×C4×D4—431no—
319C2×#106—431no—
320C2×#106C2×D4311yescharacteristic
321C2×C4⋊C8—431no—
322C2×#103—431no—
323C2×#103—431no—
324C2×#103—431no—
325C2×#103—431no—
326C2×#102—431no—
327C2×#102—431no—
328C2×#102—431no—
329C2×#102—431no—
330C2×C4×C8—431no—
331#400—861no—
332#398—861no—
333#391—431no—
334#390—431no—
335#389—431no—
336#389—431no—
337#389—431no—
338#389C2×D4311yescharacteristic
339#388—861no—
340#388—861no—
341#387—861no—
342#385—861no—
343#382—431no—
344#382—861no—
345C4×C4⋊C4—431no—
346C4×C4⋊C4—431no—
347C4×C4⋊C4C2×D4311yescharacteristic
348C4×C22⋊C4—861no—
349#340—431no—
350#340—431no—
351#340—431no—
352#340C2×D4311yescharacteristic
353#340C2×D4311yescharacteristic
354#340C2×D4311yescharacteristic
355#336—431no—
356#336—431no—
357#336—431no—
358#336C2×D4311yescharacteristic
359C43#2676011yescharacteristic, complemented, Sylow
360C22×Q8—431no—
361C22×D4—431no—
362C23×C4—861no—
363C22×C8—431no—
364C22×C8—431no—
365C22×C8C22×D4311yescharacteristic
366C22×C8C22×D4311yescharacteristic
367#124—862no—
368#124—862no—
369C4×Q8—862no—
370C4×Q8—1721no—
371C4×D4—862no—
372C4×D4—1721no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—431no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4C22×D4311yescharacteristic
383C2×C4⋊C4C22×D4311yescharacteristic
384C2×C4⋊C4C22×D4311yescharacteristic
385C2×C4⋊C4C22×D4311yescharacteristic
386C2×C22⋊C4—861no—
387C2×C22⋊C4—861no—
388C2×C22⋊C4—861no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—861no—
391C2×C42—21no—
392C2×C42—431no—
393C2×C42—431no—
394C2×C42—861no—
395C2×C42—861no—
396C2×C42C22×D4311yescharacteristic
397#106—22no—
398#106—862no—
399C4⋊C8—1721no—
400#103—862no—
401#103—862no—
402#103—862no—
403#103—1721no—
404#102—862no—
405#102—862no—
406#102—862no—
407#102—1721no—
408C4×C8—1721no—
409#95—21no—
410#95—21no—
411#95—431no—
412#95—431no—
413#95—861no—
414#95—861no—
415#95—861no—
416#95—861no—
417#95—861no—
418#95—861no—
419#95—861no—
420#95—861no—
421C24—861no—
422C2×Q8—432no—
423C2×Q8—861no—
424C2×Q8—861no—
425C2×Q8—861no—
426C2×Q8—861no—
427C2×Q8—861no—
428C2×D4—432no—
429C2×D4—861no—
430C2×D4—861no—
431C2×D4—861no—
432C2×D4—861no—
433C2×D4—861no—
434C22×C4—21no—
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—3441no—
446C22×C4—1722no—
447C22×C4—1722no—
448C22×C4D4×D4311yescharacteristic
449C22×C4D4×D4311yescharacteristic
450C22×C4C23×D4311yescharacteristic
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—861no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—81no—
470C4⋊C4—862no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—3441no—
476C4⋊C4—3441no—
477C4⋊C4—1721no—
478C4⋊C4—1722no—
479C4⋊C4—1722no—
480C4⋊C4#1062189812yes—
481C4⋊C4#1062190212yes—
482C22⋊C4—864no—
483C22⋊C4—864no—
484C22⋊C4—3441no—
485C22⋊C4—1722no—
486C22⋊C4—1722no—
487C42—21no—
488C42—21no—
489C42—81no—
490C42—861no—
491C42—861no—
492C42—861no—
493C42—861no—
494C42—1722no—
495C42—1722no—
496C23—862no—
497C23—1721no—
498C23—1721no—
499C23—1721no—
500C23—1721no—
501C23—1721no—
502C23—1721no—
503C23C2×D4×D4311yescharacteristic
504Q8—862no—
505Q8—862no—
506Q8—1721no—
507Q8—1721no—
508D4—862no—
509D4—862no—
510D4—1721no—
511D4—1721no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—22no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—432no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—862no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—3444no—
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×C4#41×D4311yescharacteristic
553C2×C4#41×D4311yescharacteristic
554C2×C4C2×#1062189811yescharacteristic
555C2×C4C2×#1062190211yescharacteristic
556C2×C4#1306337111yescharacteristic
557C2×C4#1306337211yescharacteristic
558C8—41no—
559C8—41no—
560C8—1721no—
561C8—1721no—
562C22—3441no—
563C22—3441no—
564C22—3441no—
565C22—3441no—
566C22—1722no—
567C22—1722no—
568C22—1722no—
569C22#1458340711yescharacteristic
570C22#1458354011yescharacteristic
571C22#1458355811yescharacteristic
572C22#135×D4311yescharacteristic
573C22#1458369811yescharacteristic
574C22#1458370511yescharacteristic
575C22#1458370911yescharacteristic
576C4—41no—
577C4—41no—
578C4—42no—
579C4—42no—
580C4—81no—
581C4—81no—
582C4—862no—
583C4—3441no—
584C4—3441no—
585C4—1721no—
586C4—1721no—
587C4—1721no—
588C4—1722no—
589C4#1458343611yescharacteristic
590C4#1458349011yescharacteristic
591C4#1458358711yescharacteristic
592C4#1458359311yescharacteristic
593C2—3442no—
594C2#1913854611yescharacteristic
595C2#1914461611yescharacteristic
596C2#1914487511yescharacteristic
597C2#1914642711yescharacteristic
598C2#1914677811yescharacteristic
599C2#1914724511yescharacteristic
600C2#1914736811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1919C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1919D43
hypocenterC43#26760
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1919

Complements

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

NH ≅ G/Ntype
1. #19139136C2semidirect
7. #19135272C2semidirect
8. #19135228C2semidirect
9. #19135180C2semidirect
10. #19135151C2semidirect
11. #19134864C2semidirect
13. #19134609C2semidirect
15. C43×#1919C2semidirect
302. #1919D43semidirect
359. C43#26760semidirect

Maximal subgroups

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

subgroupindex
#191391362
#191376662
#191360122
#191359642
#191358372
#191358362
#191352722
#191352282
#191351802
#191351512
#191348642
#191348572
#191346092
#191344092
C43×#19192
#2676043