Finite Group Databasebeta

← #25116456

Subgroups — #25116456

Order 11008.

810 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583002C211yesmaximal, characteristic
2#19137564C211yesmaximal, characteristic
3#19137551C211yesmaximal, characteristic, complemented
4#19135479C211yesmaximal, characteristic
5#19135446C211yesmaximal, characteristic
6#19135238C211yesmaximal, characteristic, complemented
7#19135221C211yesmaximal, characteristic
8#19135216C211yesmaximal, characteristic
9#19134760C211yesmaximal, characteristic, complemented
10#19134608C211yesmaximal, characteristic, complemented
11#19134594C211yesmaximal, characteristic
12#19134493C211yesmaximal, characteristic, complemented
13#19134487C211yesmaximal, characteristic, complemented
14#19134468C211yesmaximal, characteristic, complemented
15C43×#1927C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C2×Q8×Dic43C2211yescharacteristic
18C2×#13063287C2211yescharacteristic
19#14583002C418yescomplemented
20C2×#13063259C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063236C2211yescharacteristic
30C2×#13063235C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic
32#14582806C2211yescharacteristic
33#14582801C2211yescharacteristic
34#14582800C2211yescharacteristic
35#14582790—21no—
36#14582788—21no—
37#14582784—21no—
38#14582782—21no—
39#14582768C2211yescharacteristic
40#14582764C2211yescharacteristic
41#14582763—21no—
42#14582761—21no—
43C4⋊C4×Dic43C2211yescharacteristic
44C4⋊C4×Dic43C2211yescharacteristic
45C4×Dic43⋊C4C2211yescharacteristic
46C4×C4⋊Dic43C2211yescharacteristic
47#14582750—21no—
48C4×(C2×D43)⋊C4—21no—
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×#106×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C43×#391C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C4×D43—21no—
62C2×#10621884—22no—
63C2×#10621884—22no—
64C2×#10621884C2×C414yes—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67Q8×Dic43—22no—
68Q8×Dic43C2×C414yes—
69#13063287—22no—
70#13063287C2×C414yes—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4D411yescharacteristic
78C2×Dic43⋊C4D411yescharacteristic
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43C2311yescharacteristic
89C2×C4×Dic43C2311yescharacteristic
90#13063259—41no—
91#13063258—22no—
92#13063258C2×C414yes—
93#13063256—22no—
94Dic43⋊C8—22no—
95#13063249—41no—
96#13063247—41no—
97#13063247C2×C414yes—
98#13063245—41no—
99#13063236—22no—
100#13063235C2×C414yes—
101C8×Dic43—22no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95D411yescharacteristic
110C43⋊#95D411yescharacteristic
111C22×Q8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C42×C43—21no—
118C2×C42×C43C2311yescharacteristic
119#106×C43—41no—
120#103×C43—41no—
121#103×C43C2×C414yes—
122#95×C43—21no—
123#95×C43—21no—
124#95×C43—21no—
125C23×D43—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—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43C2×D411yescharacteristic
143C22×Dic43C2×D411yescharacteristic
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C2×D172—21no—
147C2×D172—21no—
148C2×D172—21no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172C22×C412yes—
152C2×C4×D43—24no—
153C2×C4×D43—81no—
154C2×C4×D43—81no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43C22×C412yes—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43C22×C412yes—
167C42×C43—21no—
168C42×C43—21no—
169C42×C43—81no—
170#10621884—28no—
171(C2×D43)⋊C4—24no—
172(C2×D43)⋊C4—42no—
173(C2×D43)⋊C4—42no—
174(C2×D43)⋊C4—81no—
175(C2×D43)⋊C4—81no—
176C4⋊Dic43—21no—
177C4⋊Dic43—24no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43C22×C412yes—
183Dic43⋊C4—22no—
184Dic43⋊C4—41no—
185Dic43⋊C4—42no—
186Dic43⋊C4—81no—
187C4×Dic43—21no—
188C4×Dic43—21no—
189C4×Dic43—24no—
190C4×Dic43—81no—
191C4×Dic43—81no—
192C4×Dic43—81no—
193C4×Dic43C22×C412yes—
194C4×Dic43#4112yes—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8C22×C412yes—
199C2×C43⋊C8#4112yes—
200C2×C43⋊C8#4112yes—
201C23×C43C22×D411yescharacteristic
202C22×D43—22no—
203C22×D43—41no—
204C22×D43—41no—
205C22×D43—41no—
206C22×D43—41no—
207C22×D43—41no—
208C22×D43—41no—
209Q8×C43—22no—
210Q8×C43—22no—
211Q8×C43—41no—
212Q8×C43—41no—
213C2×C4×C43—22no—
214C2×C4×C43—22no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—41no—
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×C43—41no—
231C2×C4×C43C23×C411yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43H(5,𝔽2)11yescharacteristic
236C2×C4×C432−1+411yescharacteristic
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—22no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
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×Dic43C4×D412yes—
256C2×Dic43C4×D412yes—
257C2×Dic43#13712yes—
258D172—22no—
259D172—22no—
260D172—41no—
261D172—41no—
262C4×D43—84no—
263C8×C43—22no—
264C8×C43—41no—
265C43⋊C8—41no—
266C43⋊C8#11714yes—
267#22819—431nomaximal, Sylow
268C22×C43C2×C4×D411yescharacteristic
269C22×C43#54711yescharacteristic
270C22×C43#55011yescharacteristic
271C22×C43C2×#13711yescharacteristic
272C22×C43#57511yescharacteristic
273C22×C43#57611yescharacteristic
274C22×C43#57711yescharacteristic
275C2×D43—42no—
276C2×D43—42no—
277C2×D43—42no—
278C2×D43—81no—
279C2×D43—81no—
280C2×D43—81no—
281C2×D43—81no—
282C4×C43—41no—
283C4×C43—41no—
284C4×C43—42no—
285C4×C43—42no—
286C4×C43—81no—
287C4×C43—81no—
288C4×C43C2×#11711yescharacteristic
289C4×C43#52011yescharacteristic
290C4×C43#55511yescharacteristic
291C4×C43#55611yescharacteristic
292Dic43—22no—
293Dic43—22no—
294Dic43—22no—
295Dic43—41no—
296Dic43—42no—
297Dic43—81no—
298Dic43—81no—
299C2×#440—431no—
300#2357—431no—
301#2355—431no—
302#1973—431no—
303#1968—431no—
304#1928—431no—
305#1927D4311yescharacteristic, complemented
306#1926—431no—
307#1925—431no—
308#1847—431no—
309#1805—431no—
310#1802—431no—
311#1776—431no—
312C4×#107—431no—
313#1771—431no—
314C2×C43#235411yescharacteristic
315C2×C43C4×#13711yescharacteristic
316C2×C43#294611yescharacteristic
317C2×C43#334611yescharacteristic
318C2×C43#335011yescharacteristic
319C2×C43#340011yescharacteristic
320C2×C43#340311yescharacteristic
321D43—82no—
322C22×SD16—431no—
323C2×C4×Q8—431no—
324C2×C4×D4—431no—
325#440—438no—
326C2×#107—431no—
327C2×#107—431no—
328C2×#107—431no—
329C2×#106—431no—
330C2×#106C2×D4311yescharacteristic
331C2×C4⋊C8—431no—
332C2×#103—431no—
333C2×#103C2×D4311yescharacteristic
334C2×#103C2×D4311yescharacteristic
335C2×#102—431no—
336C2×#102—431no—
337C2×#102—431no—
338C2×#97—431no—
339C2×#97—431no—
340C2×C4×C8—431no—
341#391—431no—
342#391C2×D4311yescharacteristic
343#390—431no—
344#390—431no—
345#388—861no—
346#388—861no—
347#387—861no—
348#387—861no—
349#384—431no—
350#382—431no—
351#382—861no—
352#381—861no—
353C4×C4⋊C4—431no—
354C4×C4⋊C4—431no—
355C4×C4⋊C4—431no—
356C4×C4⋊C4—431no—
357C4×C4⋊C4—861no—
358C4×C4⋊C4C2×D4311yescharacteristic
359C4×C22⋊C4—861no—
360#340—431no—
361#340—431no—
362#340—431no—
363#340C2×D4311yescharacteristic
364#336—431no—
365#336C2×D4311yescharacteristic
366C43#2281911yescharacteristic, complemented, Sylow
367C22×Q8C22×D4311yescharacteristic
368C22×D4—431no—
369C23×C4—861no—
370C2×SD16—434no—
371C2×SD16—862no—
372C2×SD16—862no—
373C22×C8—431no—
374C22×C8—431no—
375C22×C8C22×D4311yescharacteristic
376C22×C8C22×D4311yescharacteristic
377C4×Q8—434no—
378C4×Q8—862no—
379C4×D4—434no—
380C4×D4—862no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—431no—
384C2×C4⋊C4—431no—
385C2×C4⋊C4—431no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4—861no—
389C2×C4⋊C4C22×D4311yescharacteristic
390C2×C4⋊C4C22×D4311yescharacteristic
391C2×C4⋊C4C22×D4311yescharacteristic
392C2×C22⋊C4—861no—
393C2×C22⋊C4—861no—
394C2×C22⋊C4—861no—
395C2×C22⋊C4—861no—
396C2×C22⋊C4—861no—
397C2×C42—21no—
398C2×C42—431no—
399C2×C42—431no—
400C2×C42—861no—
401C2×C42—861no—
402C2×C42—861no—
403C2×C42—861no—
404C2×C42C22×D4311yescharacteristic
405#107—434no—
406#107—862no—
407#107—1721no—
408#106—41no—
409#106—862no—
410C4⋊C8—862no—
411#103—41no—
412#103—1721no—
413#103C4×D4314yes—
414#102—434no—
415#102—1721no—
416#102—1721no—
417#97—434no—
418#97—862no—
419C4×C8—862no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—431no—
424#95—431no—
425#95—861no—
426#95—861no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95—861no—
431#95—861no—
432C24—861no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8C2×C4×D4312yes—
439C2×D4—432no—
440C2×D4—861no—
441C2×D4—861no—
442C2×D4—861no—
443C2×D4—861no—
444C2×D4—861no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—431no—
450C22×C4—431no—
451C22×C4—431no—
452C22×C4—431no—
453C22×C4—864no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—3441no—
458C22×C4—3441no—
459C22×C4D4×D4311yescharacteristic
460C22×C4D4×D4311yescharacteristic
461C22×C4C23×D4311yescharacteristic
462SD16—868no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—432no—
469C2×C8—432no—
470C2×C8—432no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8C2×C4×D4312yes—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—432no—
481C4⋊C4—862no—
482C4⋊C4—864no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—3441no—
489C4⋊C4—1721no—
490C4⋊C4—1722no—
491C4⋊C4C2×C4×D4312yes—
492C22⋊C4—864no—
493C22⋊C4—3441no—
494C22⋊C4—3441no—
495C22⋊C4—1722no—
496C22⋊C4—1722no—
497C42—21no—
498C42—21no—
499C42—81no—
500C42—432no—
501C42—432no—
502C42—864no—
503C42—861no—
504C42—861no—
505C42—3441no—
506C42—3441no—
507C42—3441no—
508C23—862no—
509C23—1721no—
510C23—1721no—
511C23—1721no—
512C23—1721no—
513C23—1721no—
514C23—1721no—
515C23C2×D4×D4311yescharacteristic
516Q8—22no—
517Q8—22no—
518Q8—41no—
519Q8—41no—
520D4—862no—
521D4—862no—
522D4—1721no—
523D4—1721no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—432no—
543C2×C4—432no—
544C2×C4—432no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—862no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—3444no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4C22×C4×D4311yescharacteristic
565C2×C4#41×D4311yescharacteristic
566C2×C4#41×D4311yescharacteristic
567C2×C4#41×D4311yescharacteristic
568C2×C4#1306337011yescharacteristic
569C2×C4#1306337211yescharacteristic
570C8—22no—
571C8—41no—
572C8—434no—
573C8—1721no—
574C22—3441no—
575C22—3441no—
576C22—3441no—
577C22—3441no—
578C22—1722no—
579C22—1722no—
580C22—1722no—
581C22C4×D4×D4311yescharacteristic
582C22#1458354711yescharacteristic
583C22#1458356711yescharacteristic
584C22#137×D4311yescharacteristic
585C22#1458369811yescharacteristic
586C22#1458370111yescharacteristic
587C22#1458370511yescharacteristic
588C4—42no—
589C4—41no—
590C4—41no—
591C4—42no—
592C4—81no—
593C4—81no—
594C4—862no—
595C4—862no—
596C4—862no—
597C4—3441no—
598C4—3441no—
599C4—1721no—
600C4—1722no—
601C4#117×D4311yescharacteristic
602C4#1458337811yescharacteristic
603C4#1458361111yescharacteristic
604C4#1458361611yescharacteristic
605C2—3442no—
606C2#1913754111yescharacteristic
607C2#1914341111yescharacteristic
608C2#1914342211yescharacteristic
609C2#1914707311yescharacteristic
610C2#1914714311yescharacteristic
611C2#1914764311yescharacteristic
612C2#1914768211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1927C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#1927D43
hypocenterC43#22819
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1927

Complements

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

NH ≅ G/Ntype
3. #19137551C2semidirect
6. #19135238C2semidirect
9. #19134760C2semidirect
10. #19134608C2semidirect
12. #19134493C2semidirect
13. #19134487C2semidirect
14. #19134468C2semidirect
15. C43×#1927C2semidirect
19. #14583002C4semidirect
305. #1927D43semidirect
366. C43#22819semidirect

Maximal subgroups

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

subgroupindex
C2×#145830022
#191375642
#191375512
#191354792
#191354462
#191352382
#191352212
#191352162
#191347602
#191346082
#191345942
#191344932
#191344872
#191344682
C43×#19272
#2281943