Finite Group Databasebeta

← #25100855

Subgroups — #25100855

Order 11008.

814 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582990C211yesmaximal, characteristic
2#19137242C211yesmaximal, characteristic, complemented
3#19137232C211yesmaximal, characteristic
4#19135450C211yesmaximal, characteristic
5#19135448C211yesmaximal, characteristic
6#19135322C211yesmaximal, characteristic, complemented
7#19135320C211yesmaximal, characteristic, complemented
8#19135294C211yesmaximal, characteristic
9#19135285C211yesmaximal, characteristic, complemented
10#19135283C211yesmaximal, characteristic, complemented
11#19134483C211yesmaximal, characteristic, complemented
12#19134424C211yesmaximal, characteristic, complemented
13#19134422C211yesmaximal, characteristic
14#19134283C211yesmaximal, characteristic, complemented
15C43×#1936C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C2×#13063290C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19#14582990C418yescomplemented
20C2×#13063256C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063235C2211yescharacteristic
28C2×#13063235C2211yescharacteristic
29C2×C4×C43⋊C8C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic
32#14582805C2211yescharacteristic
33#14582804C2211yescharacteristic
34#14582802C2211yescharacteristic
35#14582798C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582795C2211yescharacteristic
38#14582793—21no—
39#14582787—21no—
40#14582786—21no—
41#14582780—21no—
42#14582766—21no—
43#14582764—21no—
44#14582760—21no—
45#14582757—21no—
46C4⋊C4×Dic43C2211yescharacteristic
47C4⋊C4×Dic43C2211yescharacteristic
48#14582745C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#97×C43C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×Dic86C2311yescharacteristic
61C23×Dic43—21no—
62C2×#10621883—22no—
63C2×#10621883—22no—
64C2×#10621883C2×C414yes—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063290—22no—
68#13063290C2×C414yes—
69D4×Dic43—22no—
70D4×Dic43C2×C414yes—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43C2311yescharacteristic
85C2×C4×Dic43C2311yescharacteristic
86#13063256—22no—
87#13063256—22no—
88#13063256C2×C414yes—
89#13063250—22no—
90#13063250C2×C414yes—
91#13063248—22no—
92#13063246—22no—
93#13063235—22no—
94#13063235—22no—
95C4×C43⋊C8—22no—
96C8×Dic43—22no—
97C8×Dic43C2×C414yes—
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⋊#95—21no—
107C43⋊#95D411yescharacteristic
108C43⋊#95D411yescharacteristic
109C43⋊#95D411yescharacteristic
110C43⋊#95D411yescharacteristic
111C22×D4×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C22⋊C4×C43—21no—
119C2×C22⋊C4×C43—21no—
120C2×C42×C43C2311yescharacteristic
121#102×C43—22no—
122#102×C43C2×C414yes—
123#97×C43—22no—
124#95×C43—21no—
125C24×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43C22×C412yes—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2411yescharacteristic
138C22×Dic43—24no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—81no—
144C22×Dic43—81no—
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C2×Dic86—21no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86C22×C412yes—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43C22×C412yes—
160C2×C8×C43#4112yes—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—81no—
167C4⋊C4×C43C22×C412yes—
168C22⋊C4×C43—81no—
169C22⋊C4×C43—81no—
170C42×C43—21no—
171C42×C43—21no—
172C22⋊Dic43—24no—
173C22⋊Dic43—81no—
174C22⋊Dic43—81no—
175#10621883—28no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—81no—
182C4⋊Dic43C22×C412yes—
183Dic43⋊C4—24no—
184Dic43⋊C4—81no—
185Dic43⋊C4—81no—
186C4×Dic43—21no—
187C4×Dic43—21no—
188C4×Dic43—24no—
189C4×Dic43—81no—
190C4×Dic43—81no—
191C4×Dic43C22×C412yes—
192C4×Dic43#4112yes—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8C22×C412yes—
196C2×C43⋊C8#4112yes—
197C2×C43⋊C8#4112yes—
198C2×C43⋊C8#4112yes—
199C23×C43—22no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43—41no—
203C23×C43—41no—
204C23×C43—41no—
205C23×C43—41no—
206C23×C43C22×D411yescharacteristic
207D4×C43—22no—
208D4×C43—22no—
209D4×C43—41no—
210D4×C43—41no—
211C2×C4×C43—22no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
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×C43—41no—
226C2×C4×C43C23×C411yescharacteristic
227C2×C4×C43C2×#4111yescharacteristic
228C2×C4×C43C2×#4111yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—22no—
237C2×Dic43—22no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
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—41no—
254C2×Dic43—84no—
255C2×Dic43C4×D412yes—
256C2×Dic43C4×D412yes—
257Dic86—22no—
258Dic86—22no—
259Dic86—41no—
260Dic86—41no—
261C8×C43—22no—
262C8×C43—22no—
263C43⋊C8—22no—
264C43⋊C8#11714yes—
265#21280—431nomaximal, Sylow
266C22×C43—42no—
267C22×C43—42no—
268C22×C43—42no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43—81no—
272C22×C43—81no—
273C22×C43C2×C4×D411yescharacteristic
274C22×C43#53211yescharacteristic
275C22×C43#53211yescharacteristic
276C22×C43#57711yescharacteristic
277C22×C43#57711yescharacteristic
278C22×C43#57711yescharacteristic
279C22×C43#57711yescharacteristic
280C4×C43—41no—
281C4×C43—41no—
282C4×C43—42no—
283C4×C43—81no—
284C4×C43—81no—
285C4×C43C2×#11711yescharacteristic
286C4×C43C4×#4111yescharacteristic
287C4×C43#52911yescharacteristic
288C4×C43#52911yescharacteristic
289Dic43—22no—
290Dic43—22no—
291Dic43—41no—
292Dic43—41no—
293Dic43—42no—
294Dic43—42no—
295Dic43—81no—
296Dic43—81no—
297C2×C4×SD16—431no—
298#2320—431no—
299#2319—431no—
300#1968—431no—
301#1968—431no—
302#1941—431no—
303#1941—431no—
304#1936—431no—
305#1936D4311yescharacteristic
306#1935—431no—
307#1935—431no—
308C4×#106—431no—
309#1763—431no—
310#1762—431no—
311#1726—431no—
312C2×C43—82no—
313C2×C43#229311yescharacteristic
314C2×C43#294911yescharacteristic
315C2×C43#295211yescharacteristic
316C2×C43#317311yescharacteristic
317C2×C43#317311yescharacteristic
318C2×C43#317411yescharacteristic
319C2×C43#317411yescharacteristic
320C22×SD16—431no—
321C2×C4×Q8—431no—
322C2×C4×D4—431no—
323C4×SD16—438no—
324C2×#106—431no—
325C2×#106—431no—
326C2×#106—431no—
327C2×#103—431no—
328C2×#103—431no—
329C2×#103—431no—
330C2×#102—431no—
331C2×#102C2×D4311yescharacteristic
332C2×#102C2×D4311yescharacteristic
333C2×#97—431no—
334C2×#97—431no—
335C2×#97C2×D4311yescharacteristic
336C2×C4×C8—431no—
337C2×C4×C8—431no—
338C2×C4×C8—431no—
339#391—431no—
340#391—431no—
341#390—431no—
342#390C2×D4311yescharacteristic
343#389—431no—
344#389—431no—
345#389—431no—
346#389C2×D4311yescharacteristic
347#388—861no—
348#388—861no—
349#387—861no—
350#387—861no—
351#383—861no—
352#382—861no—
353#381—861no—
354#380—861no—
355C4×C4⋊C4—431no—
356C4×C4⋊C4—431no—
357#376—431no—
358#340—431no—
359#340—431no—
360#340—431no—
361#340—431no—
362#340C2×D4311yescharacteristic
363#340C2×D4311yescharacteristic
364C43#2128011yescharacteristic, complemented, Sylow
365C22×Q8—431no—
366C22×D4C22×D4311yescharacteristic
367C23×C4—861no—
368C2×SD16—434no—
369C2×SD16—862no—
370C2×SD16—862no—
371C22×C8—431no—
372C22×C8—431no—
373C22×C8C22×D4311yescharacteristic
374C22×C8C22×D4311yescharacteristic
375C4×Q8—434no—
376C4×Q8—862no—
377C4×D4—434no—
378C4×D4—862no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—431no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—431no—
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×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—861no—
393C2×C22⋊C4—861no—
394C2×C22⋊C4—861no—
395C2×C42—431no—
396C2×C42—431no—
397C2×C42—861no—
398C2×C42—861no—
399C2×C42—861no—
400C2×C42C22×D4311yescharacteristic
401#106—434no—
402#106—862no—
403#106—862no—
404#103—434no—
405#103—862no—
406#103—862no—
407#102—22no—
408#102—862no—
409#102C4×D4314yes—
410#97—22no—
411#97—862no—
412#97—862no—
413C4×C8—434no—
414C4×C8—862no—
415C4×C8—862no—
416#95—21no—
417#95—431no—
418#95—431no—
419#95—431no—
420#95—431no—
421#95—861no—
422#95—861no—
423#95—861no—
424#95—861no—
425#95—861no—
426#95—861no—
427#95—861no—
428#95—861no—
429#95—861no—
430C24—21no—
431C2×Q8—432no—
432C2×Q8—861no—
433C2×Q8—861no—
434C2×Q8—861no—
435C2×Q8—861no—
436C2×Q8—861no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4C2×C4×D4312yes—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—431no—
447C22×C4—431no—
448C22×C4—431no—
449C22×C4—431no—
450C22×C4—864no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4—3441no—
456C22×C4—3441no—
457C22×C4D4×D4311yescharacteristic
458C22×C4D4×D4311yescharacteristic
459C22×C4C23×D4311yescharacteristic
460SD16—868no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—432no—
466C2×C8—432no—
467C2×C8—432no—
468C2×C8—432no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8C2×C4×D4312yes—
472C2×C8#1062190012yes—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—81no—
479C4⋊C4—432no—
480C4⋊C4—864no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—3441no—
487C4⋊C4—3441no—
488C4⋊C4—3441no—
489C4⋊C4C2×C4×D4312yes—
490C22⋊C4—81no—
491C22⋊C4—81no—
492C22⋊C4—864no—
493C22⋊C4—3441no—
494C22⋊C4—3441no—
495C42—21no—
496C42—21no—
497C42—432no—
498C42—432no—
499C42—864no—
500C42—861no—
501C42—861no—
502C42—3441no—
503C42—3441no—
504C23—22no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23C2×D4×D4311yescharacteristic
512Q8—862no—
513Q8—862no—
514Q8—1721no—
515Q8—1721no—
516D4—22no—
517D4—22no—
518D4—41no—
519D4—41no—
520C2×C4—22no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—432no—
536C2×C4—432no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—862no—
542C2×C4—862no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—3444no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4C22×C4×D4311yescharacteristic
561C2×C4#41×D4311yescharacteristic
562C2×C4#41×D4311yescharacteristic
563C2×C4#41×D4311yescharacteristic
564C2×C4#41×D4311yescharacteristic
565C2×C4C2×#1062190011yescharacteristic
566C8—22no—
567C8—22no—
568C8—434no—
569C8—862no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22C4×D4×D4311yescharacteristic
578C22#1458344411yescharacteristic
579C22#1458344811yescharacteristic
580C22#1458370811yescharacteristic
581C22#1458370911yescharacteristic
582C22#1458370911yescharacteristic
583C22#1458370911yescharacteristic
584C4—41no—
585C4—42no—
586C4—41no—
587C4—81no—
588C4—81no—
589C4—862no—
590C4—862no—
591C4—3441no—
592C4—3441no—
593C4—1721no—
594C4—1722no—
595C4—1722no—
596C4—1721no—
597C4#117×D4311yescharacteristic
598C4C4×#1062190011yescharacteristic
599C4#1458342611yescharacteristic
600C4#1458343211yescharacteristic
601C2—82no—
602C2#1913705511yescharacteristic
603C2#1914345111yescharacteristic
604C2#1914347711yescharacteristic
605C2#1914520711yescharacteristic
606C2#1914521111yescharacteristic
607C2#1914521811yescharacteristic
608C2#1914522211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1936C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenter#1936D43
hypocenterC43#21280
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1936

Complements

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

NH ≅ G/Ntype
2. #19137242C2semidirect
6. #19135322C2semidirect
7. #19135320C2semidirect
9. #19135285C2semidirect
10. #19135283C2semidirect
11. #19134483C2semidirect
12. #19134424C2semidirect
14. #19134283C2semidirect
19. #14582990C4semidirect
364. C43#21280semidirect

Maximal subgroups

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

subgroupindex
C2×#145829902
#191372422
#191372322
#191354502
#191354482
#191353222
#191353202
#191352942
#191352852
#191352832
#191344832
#191344242
#191344222
#191342832
C43×#19362
#2128043