Finite Group Databasebeta

← #25169313

Subgroups — #25169313

Order 11008.

728 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139013C211yesmaximal, characteristic
2#19137600C211yesmaximal, characteristic
3#19136007C211yesmaximal, characteristic, complemented
4#19135977C211yesmaximal, characteristic, complemented
5#19135792C211yesmaximal, characteristic
6#19135791C211yesmaximal, characteristic
7#19135357C211yesmaximal, characteristic, complemented
8#19135322C211yesmaximal, characteristic, complemented
9#19135198C211yesmaximal, characteristic
10#19135179C211yesmaximal, characteristic, complemented
11#19135171C211yesmaximal, characteristic, complemented
12#19134864C211yesmaximal, characteristic, complemented
13#19134788C211yesmaximal, characteristic
14#19134414C211yesmaximal, characteristic, complemented
15C43×#1824C211yesmaximal, characteristic
16C2×#13063318—21no—
17C2×#13063304C2211yescharacteristic
18C2×#13063290C2211yescharacteristic
19C2×#13063257C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×Dic43⋊C8C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×C22⋊(C43⋊C8)C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30#14582840—21no—
31#14582827—21no—
32#14582804C2211yescharacteristic
33#14582798C2211yescharacteristic
34#14582795C2211yescharacteristic
35#14582795C2211yescharacteristic
36#14582794—21no—
37#14582786—21no—
38#14582780—21no—
39#14582772—21no—
40#14582768C2211yescharacteristic
41#14582759C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44C4×C22⋊Dic43—21no—
45C4×C22⋊Dic43C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C22×C4⋊C4×C43C2211yescharacteristic
53C2×C22⋊C8×C43C2211yescharacteristic
54C43×#380C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62#13063318—44no—
63#13063304—22no—
64#13063304—22no—
65#13063290—22no—
66#13063290—41no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43D411yescharacteristic
80C2×C22⋊Dic43D411yescharacteristic
81C2×C4×Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43C2311yescharacteristic
85C2×C4×Dic43C2311yescharacteristic
86#13063257—22no—
87#13063256—22no—
88#13063256—22no—
89#13063256—41no—
90Dic43⋊C8—22no—
91#13063250—22no—
92#13063250—41no—
93#13063248—22no—
94#13063248—22no—
95C22⋊(C43⋊C8)—22no—
96C8×Dic43—41no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95D411yescharacteristic
106C43⋊#95D411yescharacteristic
107C23×C4×C43—21no—
108C23×C4×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C2×C4⋊C4×C43—22no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43—41no—
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C22⋊C4×C43—21no—
119C22⋊C8×C43—41no—
120#95×C43—21no—
121C24×C43C2×D411yescharacteristic
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—42no—
133C22×C4×C43—42no—
134C22×C4×C43—81no—
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2411yescharacteristic
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43C2×D411yescharacteristic
142C22×Dic43C2×D411yescharacteristic
143C22×Dic43C2×D411yescharacteristic
144C22×Dic43C2×D411yescharacteristic
145C2×Dic86—21no—
146C2×Dic86—21no—
147C2×Dic86—21no—
148C2×Dic86—21no—
149C2×Dic86—21no—
150C2×Dic86#4112yes—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×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—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—42no—
165C4⋊C4×C43#4112yes—
166C22⋊C4×C43—42no—
167C22⋊Dic43—24no—
168C22⋊Dic43—41no—
169C22⋊Dic43—42no—
170C22⋊Dic43SD1614yes—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—42no—
177C4⋊Dic43#4112yes—
178Dic43⋊C4—24no—
179Dic43⋊C4—42no—
180Dic43⋊C4—42no—
181Dic43⋊C4—42no—
182Dic43⋊C4—42no—
183Dic43⋊C4—81no—
184C4×Dic43—21no—
185C4×Dic43—21no—
186C4×Dic43—21no—
187C4×Dic43—21no—
188C4×Dic43—42no—
189C4×Dic43—42no—
190C4×Dic43—81no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8#4112yes—
197C23×C43—21no—
198C23×C43—21no—
199C23×C43—21no—
200C23×C43—21no—
201C23×C43—21no—
202C23×C43—21no—
203C23×C43C2×SD1612yes—
204C23×C43C22×D411yescharacteristic
205C2×C4×C43—21no—
206C2×C4×C43—22no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
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×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—84no—
225C2×C4×C43C2×#4111yescharacteristic
226C2×C4×C43C2×#4111yescharacteristic
227C2×C4×C43C2×#4111yescharacteristic
228C2×C4×C43C2×#4111yescharacteristic
229C2×C4×C43H(5,𝔽2)11yescharacteristic
230C2×C4×C432−1+411yescharacteristic
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—22no—
236C2×Dic43—22no—
237C2×Dic43—21no—
238C2×Dic43—21no—
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×Dic43C2×SD1612yes—
254C2×Dic43C2×SD1612yes—
255Dic86—22no—
256Dic86—22no—
257Dic86—41no—
258Dic86—41no—
259C8×C43—41no—
260C8×C43—41no—
261C43⋊C8—22no—
262C43⋊C8—41no—
263#27034—431nomaximal, Sylow
264C22×C43—22no—
265C22×C43—22no—
266C22×C43—22no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43#52511yescharacteristic
272C22×C43#54611yescharacteristic
273C22×C43#54711yescharacteristic
274C22×C43C22×SD1611yescharacteristic
275C22×C43#57511yescharacteristic
276C22×C43#57711yescharacteristic
277C22×C43#57811yescharacteristic
278C4×C43—41no—
279C4×C43—42no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43—81no—
283C4×C43#52911yescharacteristic
284C4×C43#53911yescharacteristic
285C4×C43#55311yescharacteristic
286C4×C43#55611yescharacteristic
287Dic43—22no—
288Dic43—22no—
289Dic43—41no—
290Dic43—42no—
291Dic43—42no—
292Dic43—41no—
293Dic43—81no—
294Dic43—81no—
295#2496—431no—
296#2360—431no—
297#2072—431no—
298#2066—431no—
299#2035—431no—
300#2035—431no—
301#1948—431no—
302#1941—431no—
303#1923—431no—
304#1920—431no—
305#1919—431no—
306#1865—431no—
307#1853—431no—
308#1824D4311yescharacteristic
309C4×#103—431no—
310C2×C43—42no—
311C2×C43#246611yescharacteristic
312C2×C43#310311yescharacteristic
313C2×C43#312011yescharacteristic
314C2×C43#329811yescharacteristic
315C2×C43#331111yescharacteristic
316C2×C43#333511yescharacteristic
317C2×C43#335211yescharacteristic
318C2×#126—861no—
319C2×C22⋊Q8—431no—
320C2×C4×Q8—431no—
321C22×C4⋊C4C2×D4311yescharacteristic
322C2×#106—431no—
323C2×#106—431no—
324C2×#106—431no—
325C2×#106—431no—
326C2×C4⋊C8—431no—
327C2×#103—431no—
328C2×#103—431no—
329C2×#103—431no—
330C2×#103—431no—
331C2×C22⋊C8—431no—
332C2×C22⋊C8C2×D4311yescharacteristic
333C2×C4×C8—431no—
334#400—861no—
335#397—861no—
336#391—431no—
337#389—431no—
338#389—431no—
339#389—431no—
340#389—861no—
341#387—861no—
342#387—861no—
343#385—861no—
344#384—431no—
345#380—431no—
346#380C2×D4311yescharacteristic
347C4×C4⋊C4—431no—
348C4×C4⋊C4—431no—
349C4×C22⋊C4—431no—
350C4×C22⋊C4—861no—
351#340—431no—
352#340—431no—
353#340—431no—
354#340—431no—
355#340C2×D4311yescharacteristic
356#340C2×D4311yescharacteristic
357#340C2×D4311yescharacteristic
358#340C2×D4311yescharacteristic
359#336—431no—
360#336—431no—
361C43#2703411yescharacteristic, complemented, Sylow
362C22×Q8—431no—
363C23×C4—21no—
364C23×C4C22×D4311yescharacteristic
365C22×C8—431no—
366C22×C8—431no—
367C22×C8C22×D4311yescharacteristic
368C22×C8C22×D4311yescharacteristic
369#126—1724no—
370C22⋊Q8—862no—
371C22⋊Q8—862no—
372C4×Q8—862no—
373C4×Q8—1721no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—41no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—431no—
379C2×C4⋊C4—431no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4C22×D4311yescharacteristic
388C2×C4⋊C4C22×D4311yescharacteristic
389C2×C4⋊C4C22×D4311yescharacteristic
390C2×C4⋊C4C22×D4311yescharacteristic
391C2×C22⋊C4—21no—
392C2×C22⋊C4—431no—
393C2×C22⋊C4—431no—
394C2×C22⋊C4—861no—
395C2×C22⋊C4—861no—
396C2×C42—431no—
397C2×C42—431no—
398C2×C42—861no—
399C2×C42—861no—
400C2×C42—861no—
401#106—862no—
402#106—862no—
403#106—862no—
404#106—1721no—
405C4⋊C8—862no—
406#103—862no—
407#103—862no—
408#103—862no—
409#103—1721no—
410C22⋊C8—41no—
411C22⋊C8—862no—
412C4×C8—1721no—
413#95—21no—
414#95—431no—
415#95—431no—
416#95—861no—
417#95—861no—
418#95—861no—
419#95—861no—
420#95—861no—
421#95—861no—
422#95—861no—
423#95—861no—
424C24D4×D4311yescharacteristic
425C2×Q8—432no—
426C2×Q8—861no—
427C2×Q8—861no—
428C2×Q8—861no—
429C2×Q8—861no—
430C2×Q8—861no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—81no—
444C22×C4—431no—
445C22×C4—431no—
446C22×C4—431no—
447C22×C4—431no—
448C22×C4—861no—
449C22×C4—861no—
450C22×C4—861no—
451C22×C4—861no—
452C22×C4D4×D4311yescharacteristic
453C22×C4C23×D4311yescharacteristic
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—432no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—42no—
474C4⋊C4—432no—
475C4⋊C4—864no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—3441no—
482C4⋊C4—1722no—
483C4⋊C4—1722no—
484C4⋊C4—1722no—
485C4⋊C4—1722no—
486C4⋊C4—1722no—
487C4⋊C4#1062189812yes—
488C22⋊C4—42no—
489C22⋊C4—434no—
490C22⋊C4—864no—
491C22⋊C4—1721no—
492C22⋊C4—1722no—
493C42—861no—
494C42—861no—
495C42—861no—
496C42—861no—
497C42—3441no—
498C42—1722no—
499C42—1722no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23SD16×D4312yes—
507C23C2×D4×D4311yescharacteristic
508Q8—862no—
509Q8—862no—
510Q8—1721no—
511Q8—1721no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
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—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—84no—
532C2×C4—432no—
533C2×C4—432no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—862no—
539C2×C4—862no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4#41×D4311yescharacteristic
557C2×C4#41×D4311yescharacteristic
558C2×C4#41×D4311yescharacteristic
559C2×C4C2×#1062189811yescharacteristic
560C2×C4#1306337011yescharacteristic
561C2×C4#1306337211yescharacteristic
562C8—41no—
563C8—41no—
564C8—862no—
565C8—1721no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22#1458340711yescharacteristic
574C22#1458353911yescharacteristic
575C22#1458354711yescharacteristic
576C22C2×SD16×D4311yescharacteristic
577C22#1458369511yescharacteristic
578C22#1458370911yescharacteristic
579C22#1458371211yescharacteristic
580C4—41no—
581C4—42no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4—862no—
586C4—862no—
587C4—3441no—
588C4—3441no—
589C4—1722no—
590C4—1722no—
591C4—1721no—
592C4—1721no—
593C4#1458342711yescharacteristic
594C4#1458349211yescharacteristic
595C4#1458359411yescharacteristic
596C4#1458361711yescharacteristic
597C2—42no—
598C2#1913863011yescharacteristic
599C2#1914462311yescharacteristic
600C2#1914480411yescharacteristic
601C2#1914645611yescharacteristic
602C2#1914663211yescharacteristic
603C2#1914695011yescharacteristic
604C2#1914717011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1824C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#1824D43
hypocenterC43#27034
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1824

Complements

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

NH ≅ G/Ntype
3. #19136007C2semidirect
4. #19135977C2semidirect
7. #19135357C2semidirect
8. #19135322C2semidirect
10. #19135179C2semidirect
11. #19135171C2semidirect
12. #19134864C2semidirect
14. #19134414C2semidirect
361. C43#27034semidirect

Maximal subgroups

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

subgroupindex
#191390132
#191376002
#191360072
#191359772
#191357922
#191357912
#191353572
#191353222
#191351982
#191351792
#191351712
#191348642
#191347882
#191344142
C43×#18242
#2703443