Finite Group Databasebeta

← #25100975

Subgroups — #25100975

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×#14582999C211yesmaximal, characteristic
2#19137247C211yesmaximal, characteristic, complemented
3#19135475C211yesmaximal, characteristic
4#19135448C211yesmaximal, characteristic
5#19135330C211yesmaximal, characteristic, complemented
6#19135325C211yesmaximal, characteristic, complemented
7#19135295C211yesmaximal, characteristic
8#19135284C211yesmaximal, characteristic, complemented
9#19135281C211yesmaximal, characteristic
10#19135270C211yesmaximal, characteristic, complemented
11#19134493C211yesmaximal, characteristic, complemented
12C4×#13063248C211yesmaximal, characteristic, complemented
13C4×#13063246C211yesmaximal, characteristic
14#19134282C211yesmaximal, characteristic, complemented
15C43×#2319C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18#14582999C418yescomplemented
19C2×#13063258C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×#13063248C2211yescharacteristic
23C2×#13063248C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063236C2211yescharacteristic
29C2×#13063236C2211yescharacteristic
30C2×#13063236C2211yescharacteristic
31C2×C4×C43⋊C8C2211yescharacteristic
32C2×C4×C43⋊C8C2211yescharacteristic
33C2×C4×C43⋊C8C2211yescharacteristic
34#14582805C2211yescharacteristic
35#14582805C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582797C2211yescharacteristic
38#14582781—21no—
39#14582781—21no—
40#14582766—21no—
41#14582763—21no—
42C4×C4⋊Dic43C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49C2×C4×D4×C43C2211yescharacteristic
50C43×#390C2211yescharacteristic
51C43×#390C2211yescharacteristic
52C43×#389C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C43×#388—21no—
55C43×#388—21no—
56C43×#381—21no—
57C43×#380—21no—
58C4×C4⋊C4×C43C2211yescharacteristic
59C43×#376C2211yescharacteristic
60C22×Dic86C2311yescharacteristic
61C2×#10621883—22no—
62C2×#10621883—22no—
63C2×#10621883C2×C414yes—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C4×Dic86—22no—
69C4×Dic86C2×C414yes—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×C4×Dic43—21no—
77C2×C4×Dic43—21no—
78#13063258—22no—
79#13063258C2×C414yes—
80#13063256—22no—
81#13063248—22no—
82#13063248—22no—
83#13063248C2×C414yes—
84#13063246—22no—
85#13063246—22no—
86#13063246C2×C414yes—
87#13063236—22no—
88#13063236—22no—
89#13063236C2×C414yes—
90C4×C43⋊C8—22no—
91C4×C43⋊C8—22no—
92C4×C43⋊C8—22no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C22×D4×C43C2311yescharacteristic
101C23×C4×C43—21no—
102C4×D4×C43—22no—
103C4×D4×C43C2×C414yes—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C22⋊C4×C43—21no—
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C42×C43—21no—
115C2×C42×C43C2311yescharacteristic
116C2×C42×C43C2311yescharacteristic
117C2×C42×C43C2311yescharacteristic
118#95×C43—21no—
119#95×C43—21no—
120#95×C43—21no—
121#95×C43D411yescharacteristic
122#95×C43D411yescharacteristic
123#95×C43D411yescharacteristic
124#95×C43D411yescharacteristic
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—24no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—81no—
137C22×C4×C43—81no—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2411yescharacteristic
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C2×Dic86—21no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86C22×C412yes—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—81no—
161C4⋊C4×C43—81no—
162C4⋊C4×C43C22×C412yes—
163C22⋊C4×C43—24no—
164C22⋊C4×C43—81no—
165C22⋊C4×C43—81no—
166C22⋊C4×C43—81no—
167C22⋊C4×C43—81no—
168C42×C43—21no—
169C42×C43—21no—
170C42×C43—21no—
171C42×C43—21no—
172C42×C43—81no—
173C42×C43C22×C412yes—
174C42×C43#4112yes—
175#10621883—28no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43C22×C412yes—
182Dic43⋊C4—24no—
183Dic43⋊C4—81no—
184Dic43⋊C4—81no—
185C4×Dic43—24no—
186C4×Dic43—81no—
187C2×C43⋊C8—21no—
188C2×C43⋊C8—21no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8C22×C412yes—
194C2×C43⋊C8C22×C412yes—
195C2×C43⋊C8#4112yes—
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—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—22no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—84no—
237C2×C4×C43C4×D412yes—
238C2×C4×C43C4×D412yes—
239C2×C4×C43C23×C411yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×Dic43—22no—
246C2×Dic43—22no—
247C2×Dic43—41no—
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—
257Dic86—22no—
258Dic86—22no—
259Dic86—41no—
260Dic86—41no—
261C43⋊C8—22no—
262C43⋊C8—22no—
263C43⋊C8—22no—
264C43⋊C8#11714yes—
265#21291—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#57611yescharacteristic
277C22×C43#57711yescharacteristic
278C22×C43#57711yescharacteristic
279C22×C43#57811yescharacteristic
280C4×C43—22no—
281C4×C43—22no—
282C4×C43—41no—
283C4×C43—41no—
284C4×C43—41no—
285C4×C43—41no—
286C4×C43—42no—
287C4×C43—81no—
288C4×C43—81no—
289C4×C43C2×#11711yescharacteristic
290C4×C43C4×#4111yescharacteristic
291C4×C43#52911yescharacteristic
292C4×C43#52911yescharacteristic
293Dic43—42no—
294Dic43—42no—
295Dic43—81no—
296Dic43—81no—
297C2×#440—431no—
298#2320—431no—
299#2319D4311yescharacteristic
300#1973—431no—
301#1968—431no—
302#1943—431no—
303#1942—431no—
304#1936—431no—
305#1935—431no—
306#1934—431no—
307#1933—431no—
308#1776—431no—
309C4×#103—431no—
310C4×#102—431no—
311#1726—431no—
312C2×C43—82no—
313C2×C43#229311yescharacteristic
314C2×C43#294611yescharacteristic
315C2×C43#294711yescharacteristic
316C2×C43#317411yescharacteristic
317C2×C43#317511yescharacteristic
318C2×C43#317811yescharacteristic
319C2×C43#317911yescharacteristic
320C22×SD16—431no—
321C2×C4×Q8—431no—
322C2×C4×D4C2×D4311yescharacteristic
323#440—438no—
324C2×#107—431no—
325C2×#107—431no—
326C2×#106—431no—
327C2×#103—431no—
328C2×#103—431no—
329C2×#103—431no—
330C2×#102—431no—
331C2×#102—431no—
332C2×#102—431no—
333C2×#97—431no—
334C2×#97—431no—
335C2×#97—431no—
336C2×C4×C8—431no—
337C2×C4×C8—431no—
338C2×C4×C8—431no—
339#391—431no—
340#391—431no—
341#390C2×D4311yescharacteristic
342#390C2×D4311yescharacteristic
343#389—431no—
344#389—431no—
345#389C2×D4311yescharacteristic
346#389C2×D4311yescharacteristic
347#388—21no—
348#388—21no—
349#387—861no—
350#387—861no—
351#383—861no—
352#382—861no—
353#381—21no—
354#380—21no—
355C4×C4⋊C4—431no—
356C4×C4⋊C4C2×D4311yescharacteristic
357#376C2×D4311yescharacteristic
358#340—431no—
359#340—431no—
360#340—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364C43#2129111yescharacteristic, complemented, Sylow
365C22×Q8—431no—
366C22×D4C22×D4311yescharacteristic
367C23×C4—21no—
368C2×SD16—434no—
369C2×SD16—862no—
370C2×SD16—862no—
371C22×C8—431no—
372C22×C8—431no—
373C22×C8—431no—
374C22×C8—431no—
375C4×Q8—434no—
376C4×Q8—862no—
377C4×D4—22no—
378C4×D4C4×D4314yes—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—431no—
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—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C42—21no—
396C2×C42—861no—
397C2×C42—861no—
398C2×C42C22×D4311yescharacteristic
399C2×C42C22×D4311yescharacteristic
400C2×C42C22×D4311yescharacteristic
401#107—434no—
402#107—862no—
403#106—862no—
404#103—434no—
405#103—862no—
406#103—862no—
407#102—434no—
408#102—862no—
409#102—862no—
410#97—434no—
411#97—862no—
412#97—862no—
413C4×C8—862no—
414C4×C8—862no—
415C4×C8—862no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—861no—
420#95—861no—
421#95—861no—
422#95—861no—
423#95—861no—
424#95—861no—
425#95—861no—
426#95C22⋊D4311yescharacteristic
427#95C22⋊D4311yescharacteristic
428#95C22⋊D4311yescharacteristic
429#95C22⋊D4311yescharacteristic
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—24no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—81no—
448C22×C4—81no—
449C22×C4—861no—
450C22×C4—861no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4C2×C22⋊D4311yescharacteristic
454C22×C4C2×C22⋊D4311yescharacteristic
455C22×C4C2×C22⋊D4311yescharacteristic
456C22×C4C2×C22⋊D4311yescharacteristic
457C22×C4C2×C22⋊D4311yescharacteristic
458C22×C4C2×C22⋊D4311yescharacteristic
459C22×C4C23×D4311yescharacteristic
460SD16—868no—
461C2×C8—432no—
462C2×C8—432no—
463C2×C8—432no—
464C2×C8—432no—
465C2×C8—432no—
466C2×C8—432no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—861no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—81no—
479C4⋊C4—81no—
480C4⋊C4—432no—
481C4⋊C4—864no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—3441no—
488C4⋊C4—3441no—
489C4⋊C4C2×C4×D4312yes—
490C22⋊C4—24no—
491C22⋊C4—81no—
492C22⋊C4—81no—
493C22⋊C4—81no—
494C22⋊C4—81no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—81no—
500C42—864no—
501C42—3441no—
502C42C2×C4×D4312yes—
503C42#1062189812yes—
504C23—22no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23C22×C22⋊D4311yescharacteristic
512Q8—862no—
513Q8—862no—
514Q8—1721no—
515Q8—1721no—
516D4—22no—
517D4—22no—
518D4—41no—
519D4—41no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—84no—
546C2×C4—862no—
547C2×C4—862no—
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—1721no—
557C2×C4—1721no—
558C2×C4C4×C22⋊D4312yes—
559C2×C4C4×C22⋊D4312yes—
560C2×C4C22×C4×D4311yescharacteristic
561C2×C4#41×D4311yescharacteristic
562C2×C4#41×D4311yescharacteristic
563C2×C4#41×D4311yescharacteristic
564C2×C4#41×D4311yescharacteristic
565C2×C4C2×#1062189811yescharacteristic
566C8—434no—
567C8—862no—
568C8—862no—
569C8—862no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22C2×C4×C22⋊D4311yescharacteristic
578C22#1458344511yescharacteristic
579C22#1458344511yescharacteristic
580C22#1458370211yescharacteristic
581C22#1458371011yescharacteristic
582C22#1458371011yescharacteristic
583C22#1458371411yescharacteristic
584C4—22no—
585C4—22no—
586C4—41no—
587C4—42no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—81no—
592C4—81no—
593C4—3441no—
594C4—3441no—
595C4—1722no—
596C4—1722no—
597C4#117×D4311yescharacteristic
598C4#1458336711yescharacteristic
599C4#1458342711yescharacteristic
600C4#1458342711yescharacteristic
601C2—82no—
602C2#1913705411yescharacteristic
603C2#1914342711yescharacteristic
604C2#1914343411yescharacteristic
605C2#1914521711yescharacteristic
606C2#1914522811yescharacteristic
607C2#1914525711yescharacteristic
608C2#1914528011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2319C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenter#2319D43
hypocenterC43#21291
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ #376 ◁ #2319

Complements

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

NH ≅ G/Ntype
2. #19137247C2semidirect
5. #19135330C2semidirect
6. #19135325C2semidirect
8. #19135284C2semidirect
10. #19135270C2semidirect
11. #19134493C2semidirect
12. C4×#13063248C2semidirect
14. #19134282C2semidirect
18. #14582999C4semidirect
364. C43#21291semidirect

Maximal subgroups

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

subgroupindex
C2×#145829992
#191372472
#191354752
#191354482
#191353302
#191353252
#191352952
#191352842
#191352812
#191352702
#191344932
C4×#130632482
C4×#130632462
#191342822
C43×#23192
#2129143