Finite Group Databasebeta

← #25100970

Subgroups — #25100970

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×#14583000C211yesmaximal, characteristic
2#19137240C211yesmaximal, characteristic, complemented
3#19137232C211yesmaximal, characteristic
4#19135451C211yesmaximal, characteristic
5#19135333C211yesmaximal, characteristic, complemented
6#19135326C211yesmaximal, characteristic, complemented
7#19135289C211yesmaximal, characteristic
8#19135282C211yesmaximal, characteristic, complemented
9#19135281C211yesmaximal, characteristic
10#19135274C211yesmaximal, characteristic, complemented
11#19134494C211yesmaximal, characteristic, complemented
12#103×Dic43C211yesmaximal, characteristic, complemented
13#102×Dic43C211yesmaximal, characteristic
14#19134283C211yesmaximal, characteristic, complemented
15C43×#1973C211yesmaximal, characteristic
16C2×Q8×Dic43C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18#14583000C418yescomplemented
19C2×#13063259C2211yescharacteristic
20C2×#13063257C2211yescharacteristic
21C2×#13063249C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063235C2211yescharacteristic
26C2×#13063235C2211yescharacteristic
27C2×C4×C43⋊C8C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30#14582806C2211yescharacteristic
31#14582802C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582795C2211yescharacteristic
35#14582795C2211yescharacteristic
36#14582793—21no—
37#14582787—21no—
38#14582784—21no—
39#14582782—21no—
40#14582766—21no—
41#14582763—21no—
42#14582760—21no—
43#14582757—21no—
44C4⋊C4×Dic43C2211yescharacteristic
45C4⋊C4×Dic43C2211yescharacteristic
46#14582745C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53C22×SD16×C43C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#97×C43C2211yescharacteristic
58C43×#391C2211yescharacteristic
59C43×#390C2211yescharacteristic
60C23×Dic43—21no—
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63Q8×Dic43—22no—
64Q8×Dic43C2×C414yes—
65D4×Dic43—22no—
66D4×Dic43C2×C414yes—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C4×Dic43—21no—
80C2×C4×Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43C2311yescharacteristic
83C2×C4×Dic43C2311yescharacteristic
84#13063259C2×C414yes—
85#13063257—22no—
86#13063249—22no—
87#13063249C2×C414yes—
88#13063246—22no—
89#13063246C2×C414yes—
90#13063235—22no—
91#13063235C2×C414yes—
92C4×C43⋊C8—22no—
93C8×Dic43—22no—
94C8×Dic43—22no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95D411yescharacteristic
104C43⋊#95D411yescharacteristic
105C43⋊#95D411yescharacteristic
106C43⋊#95D411yescharacteristic
107C22×Q8×C43C2311yescharacteristic
108C22×D4×C43C2311yescharacteristic
109C2×SD16×C43—22no—
110C2×SD16×C43—22no—
111C2×SD16×C43C2×C414yes—
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—21no—
118C2×C42×C43C2311yescharacteristic
119#107×C43—22no—
120#103×C43—22no—
121#102×C43—22no—
122#97×C43—22no—
123#95×C43—21no—
124#95×C43—21no—
125C24×C43—21no—
126C2×Q8×C43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43C22×C412yes—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43C22×C412yes—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2411yescharacteristic
144C22×Dic43—24no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—81no—
150C22×Dic43—81no—
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155SD16×C43—28no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43C22×C412yes—
159C2×C8×C43#4112yes—
160C2×C8×C43#4112yes—
161C2×C8×C43#4112yes—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C22⋊C4×C43—81no—
167C22⋊C4×C43—81no—
168C42×C43—21no—
169C42×C43—21no—
170C22⋊Dic43—24no—
171C22⋊Dic43—81no—
172C22⋊Dic43—81no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—24no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43C22×C412yes—
181C4⋊Dic43C22×C412yes—
182Dic43⋊C4—81no—
183Dic43⋊C4—81no—
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⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8C22×C412yes—
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
207Q8×C43—22no—
208Q8×C43—22no—
209Q8×C43—41no—
210Q8×C43—41no—
211D4×C43—22no—
212D4×C43—22no—
213D4×C43—41no—
214D4×C43—41no—
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—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43C23×C411yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—22no—
241C2×Dic43—22no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
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—
257C2×Dic43—41no—
258C2×Dic43—84no—
259C2×Dic43C4×D412yes—
260C2×Dic43C4×D412yes—
261C8×C43—22no—
262C8×C43#11714yes—
263C43⋊C8—22no—
264C43⋊C8—22no—
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—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×#440—431no—
298#2320—431no—
299#2319—431no—
300#1973D4311yescharacteristic
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×SD16C2×D4311yescharacteristic
321C2×C4×Q8—431no—
322C2×C4×D4—431no—
323#440—438no—
324C2×#107—431no—
325C2×#107C2×D4311yescharacteristic
326C2×#106—431no—
327C2×#103—431no—
328C2×#103—431no—
329C2×#103C2×D4311yescharacteristic
330C2×#102—431no—
331C2×#102—431no—
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#391C2×D4311yescharacteristic
341#390—431no—
342#390C2×D4311yescharacteristic
343#389—431no—
344#389—431no—
345#389—431no—
346#389—431no—
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#340—431no—
363#340—431no—
364C43#2129111yescharacteristic, complemented, Sylow
365C22×Q8C22×D4311yescharacteristic
366C22×D4C22×D4311yescharacteristic
367C23×C4—861no—
368C2×SD16—22no—
369C2×SD16—22no—
370C2×SD16C4×D4314yes—
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—431no—
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⋊C4—861no—
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#107—22no—
402#107—434no—
403#106—862no—
404#103—22no—
405#103—434no—
406#103—862no—
407#102—22no—
408#102—434no—
409#102—862no—
410#97—22no—
411#97—434no—
412#97—862no—
413C4×C8—862no—
414C4×C8—862no—
415C4×C8—862no—
416#95—21no—
417#95—21no—
418#95—431no—
419#95—431no—
420#95—431no—
421#95—431no—
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—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8C2×C4×D4312yes—
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—28no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—432no—
464C2×C8—432no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8C2×C4×D4312yes—
470C2×C8#1062190012yes—
471C2×C8#1062190012yes—
472C2×C8#1062190012yes—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—432no—
478C4⋊C4—432no—
479C4⋊C4—864no—
480C4⋊C4—861no—
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⋊C4—3441no—
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—22no—
513Q8—22no—
514Q8—41no—
515Q8—41no—
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×C4C2×#1062190011yescharacteristic
564C2×C4C2×#1062190011yescharacteristic
565C2×C4C2×#1062190011yescharacteristic
566C8—22no—
567C8—862no—
568C8—862no—
569C8#1306328114yes—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22C4×D4×D4311yescharacteristic
578C22#1458344411yescharacteristic
579C22#1458344711yescharacteristic
580C22#1458370311yescharacteristic
581C22#1458370811yescharacteristic
582C22#1458370911yescharacteristic
583C22#1458371511yescharacteristic
584C4—41no—
585C4—41no—
586C4—42no—
587C4—81no—
588C4—81no—
589C4—862no—
590C4—862no—
591C4—3441no—
592C4—3441no—
593C4—1722no—
594C4—1722no—
595C4—1721no—
596C4—1721no—
597C4C2×#1306328111yescharacteristic
598C4C4×#1062190011yescharacteristic
599C4#1458342811yescharacteristic
600C4#1458343011yescharacteristic
601C2—82no—
602C2#1913705711yescharacteristic
603C2#1914342611yescharacteristic
604C2#1914343511yescharacteristic
605C2#1914521811yescharacteristic
606C2#1914522911yescharacteristic
607C2#1914526011yescharacteristic
608C2#1914527511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1973C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenter#1973D43
hypocenterC43#21291
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1973

Complements

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

NH ≅ G/Ntype
2. #19137240C2semidirect
5. #19135333C2semidirect
6. #19135326C2semidirect
8. #19135282C2semidirect
10. #19135274C2semidirect
11. #19134494C2semidirect
12. #103×Dic43C2semidirect
14. #19134283C2semidirect
18. #14583000C4semidirect
364. C43#21291semidirect

Maximal subgroups

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

subgroupindex
C2×#145830002
#191372402
#191372322
#191354512
#191353332
#191353262
#191352892
#191352822
#191352812
#191352742
#191344942
#103×Dic432
#102×Dic432
#191342832
C43×#19732
#2129143