Finite Group Databasebeta

← #25099666

Subgroups — #25099666

Order 11008.

890 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582996C211yesmaximal, characteristic
2#19137242C211yesmaximal, characteristic, complemented
3#19136956C211yesmaximal, characteristic
4#19135235C211yesmaximal, characteristic, complemented
5#19135230C211yesmaximal, characteristic, complemented
6#19135184C211yesmaximal, characteristic, complemented
7#19135169C211yesmaximal, characteristic, complemented
8#19134929C211yesmaximal, characteristic
9#19134927C211yesmaximal, characteristic
10#19134858C211yesmaximal, characteristic
11#19134494C211yesmaximal, characteristic, complemented
12#19134414C211yesmaximal, characteristic, complemented
13#102×Dic43C211yesmaximal, characteristic
14#19134345C211yesmaximal, characteristic, complemented
15C43×#1862C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C2×#13063290C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic
20#14582996C418yescomplemented
21C2×#13063258C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063235C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29#14582805C2211yescharacteristic
30#14582804C2211yescharacteristic
31#14582798C2211yescharacteristic
32#14582786—21no—
33#14582780—21no—
34#14582766—21no—
35#14582764—21no—
36C4⋊C4×Dic43C2211yescharacteristic
37C4⋊C4×Dic43C2211yescharacteristic
38C4⋊C4×Dic43C2211yescharacteristic
39C4×C4⋊Dic43C2211yescharacteristic
40C22⋊C4×Dic43—21no—
41C22⋊C4×Dic43—21no—
42C4×C22⋊Dic43—21no—
43#14582745C2211yescharacteristic
44C2×C43⋊#95—21no—
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C22×Dic86C2311yescharacteristic
61C23×Dic43—21no—
62C23×Dic43—21no—
63C2×#10621883—22no—
64C2×#10621883—22no—
65C2×#10621883C2×C414yes—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063290—22no—
69#13063290C2×C414yescomplemented
70D4×Dic43—22no—
71D4×Dic43—22no—
72D4×Dic43—22no—
73D4×Dic43C2×C414yes—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×Dic43⋊C4—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43C2311yescharacteristic
87C2×C4×Dic43C2311yescharacteristic
88#13063258C2×C414yescomplemented
89#13063257—22no—
90#13063250—22no—
91#13063250C2×C414yescomplemented
92#13063248—22no—
93#13063246—22no—
94#13063235C2×C414yescomplemented
95C8×Dic43—22no—
96C43⋊#95—21no—
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
107C43⋊#95D411yescharacteristic
108C43⋊#95D411yescharacteristic
109C22×D4×C43C2311yescharacteristic
110C23×C4×C43—21no—
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C4×D4×C43—22no—
114C4×D4×C43—22no—
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C22⋊C4×C43—21no—
120C2×C42×C43C2311yescharacteristic
121#107×C43—22no—
122#102×C43—22no—
123#102×C43C2×C414yes—
124#95×C43—21no—
125C24×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43C22×C412yes—
130C2×D4×C43#4112yes—
131C2×D4×C43#4112yes—
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×C43C2411yescharacteristic
141C22×Dic43—24no—
142C22×Dic43—24no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—81no—
148C22×Dic43—81no—
149C22×Dic43—81no—
150C22×Dic43—81no—
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86C22×C412yes—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43C22×C412yes—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—81no—
172C4⋊C4×C43C22×C412yes—
173C4⋊C4×C43#4112yes—
174C22⋊C4×C43—24no—
175C42×C43—21no—
176C42×C43—21no—
177C22⋊Dic43—24no—
178C22⋊Dic43—24no—
179#10621883—28no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—81no—
185C4⋊Dic43C22×C412yes—
186C4⋊Dic43#4112yes—
187Dic43⋊C4—24no—
188C4×Dic43—21no—
189C4×Dic43—21no—
190C4×Dic43—24no—
191C4×Dic43—81no—
192C4×Dic43—81no—
193C4×Dic43—81no—
194C4×Dic43—81no—
195C4×Dic43C22×C412yes—
196C4×Dic43#4112yes—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8C22×C412yes—
203C23×C43—22no—
204C23×C43—22no—
205C23×C43—22no—
206C23×C43—41no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43C22×D411yescharacteristic
211D4×C43—22no—
212D4×C43—22no—
213D4×C43—22no—
214D4×C43#11714yes—
215C2×C4×C43—22no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—22no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
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—84no—
231C2×C4×C43C23×C411yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—22no—
242C2×Dic43—22no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—22no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
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—41no—
259C2×Dic43—84no—
260C2×Dic43—84no—
261C2×Dic43C4×D412yes—
262C2×Dic43C4×D412yes—
263Dic86—22no—
264Dic86—22no—
265Dic86—41no—
266Dic86—41no—
267C8×C43—22no—
268C8×C43—41no—
269C43⋊C8—22no—
270C43⋊C8—41no—
271#21125—431nomaximal, Sylow
272C22×C43—24no—
273C22×C43—42no—
274C22×C43—42no—
275C22×C43—42no—
276C22×C43—42no—
277C22×C43—42no—
278C22×C43—42no—
279C22×C43C2×C4×D411yescharacteristic
280C22×C43#52511yescharacteristic
281C22×C43#52511yescharacteristic
282C22×C43#57611yescharacteristic
283C22×C43#57711yescharacteristic
284C22×C43#57711yescharacteristic
285C22×C43#57811yescharacteristic
286C4×C43—41no—
287C4×C43—42no—
288C4×C43—41no—
289C4×C43—42no—
290C4×C43—81no—
291C4×C43C2×#11711yescharacteristic
292C4×C43C4×#4111yescharacteristic
293C4×C43#52911yescharacteristic
294C4×C43#52911yescharacteristic
295Dic43—22no—
296Dic43—22no—
297Dic43—41no—
298Dic43—42no—
299Dic43—41no—
300Dic43—42no—
301Dic43—42no—
302Dic43—81no—
303C2×#440—431no—
304#2320—431no—
305#2275—431no—
306#1928—431no—
307#1927—431no—
308#1921—431no—
309#1918—431no—
310#1877—431no—
311#1877—431no—
312#1864—431no—
313#1862D4311yescharacteristic
314#1776—431no—
315C4×#103—431no—
316C4×#102—431no—
317#1746—431no—
318C2×C43—44no—
319C2×C43#229011yescharacteristic
320C2×C43#294611yescharacteristic
321C2×C43#294711yescharacteristic
322C2×C43#311811yescharacteristic
323C2×C43#312011yescharacteristic
324C2×C43#312311yescharacteristic
325C2×C43#312411yescharacteristic
326C22×SD16—431no—
327C2×C4×Q8—431no—
328C2×C4×D4—431no—
329C2×C4×D4—431no—
330C2×C4×D4C2×D4311yescharacteristic
331#440—438no—
332C2×#107—431no—
333C2×#107C2×D4311yescharacteristic
334C2×#106—431no—
335C2×#103—431no—
336C2×#103—431no—
337C2×#103—431no—
338C2×#102—431no—
339C2×#102C2×D4311yescharacteristic
340C2×#102C2×D4311yescharacteristic
341C2×#97—431no—
342C2×C4×C8—431no—
343#391—431no—
344#391—431no—
345#389—431no—
346#389C2×D4311yescharacteristic
347#387—861no—
348#387—861no—
349#383—861no—
350#382—861no—
351C4×C4⋊C4—431no—
352C4×C4⋊C4—431no—
353C4×C4⋊C4—431no—
354C4×C4⋊C4—431no—
355C4×C22⋊C4—861no—
356C4×C22⋊C4—861no—
357C4×C22⋊C4—861no—
358#376—431no—
359C2×#95—861no—
360#340—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340C2×D4311yescharacteristic
366#336—431no—
367#336—431no—
368#336—431no—
369#336C2×D4311yescharacteristic
370C43#2112511yescharacteristic, complemented, Sylow
371C22×Q8—431no—
372C22×D4C22×D4311yescharacteristic
373C23×C4—21no—
374C23×C4—861no—
375C23×C4—861no—
376C2×SD16—434no—
377C2×SD16—862no—
378C2×SD16—862no—
379C22×C8—431no—
380C22×C8—431no—
381C22×C8C22×D4311yescharacteristic
382C22×C8C22×D4311yescharacteristic
383C4×Q8—434no—
384C4×Q8—862no—
385C4×D4—22no—
386C4×D4—22no—
387C4×D4—434no—
388C4×D4—862no—
389C4×D4—862no—
390C4×D4—862no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4C22×D4311yescharacteristic
398C2×C4⋊C4C22×D4311yescharacteristic
399C2×C4⋊C4C22×D4311yescharacteristic
400C2×C22⋊C4—21no—
401C2×C22⋊C4—861no—
402C2×C22⋊C4—861no—
403C2×C42—431no—
404C2×C42—431no—
405C2×C42—861no—
406C2×C42—861no—
407C2×C42—861no—
408C2×C42—861no—
409C2×C42—861no—
410C2×C42C22×D4311yescharacteristic
411#107—22no—
412#107—434no—
413#106—862no—
414#103—434no—
415#103—862no—
416#103—862no—
417#102—22no—
418#102—862no—
419#102C4×D4314yes—
420#97—434no—
421C4×C8—862no—
422#95—21no—
423#95—431no—
424#95—431no—
425#95—431no—
426#95—431no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436C24—21no—
437C2×Q8—432no—
438C2×Q8—861no—
439C2×Q8—861no—
440C2×Q8—861no—
441C2×Q8—861no—
442C2×Q8—861no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4C2×C4×D4312yes—
447C2×D4#1062190012yes—
448C2×D4#1062190212yes—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—24no—
452C22×C4—21no—
453C22×C4—81no—
454C22×C4—81no—
455C22×C4—431no—
456C22×C4—431no—
457C22×C4—431no—
458C22×C4—431no—
459C22×C4—864no—
460C22×C4—864no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—3441no—
466C22×C4—3441no—
467C22×C4—3441no—
468C22×C4—3441no—
469C22×C4D4×D4311yescharacteristic
470C22×C4D4×D4311yescharacteristic
471C22×C4C23×D4311yescharacteristic
472SD16—868no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—432no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8C2×C4×D4312yes—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—81no—
490C4⋊C4—432no—
491C4⋊C4—432no—
492C4⋊C4—864no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—3441no—
498C4⋊C4C2×C4×D4312yes—
499C4⋊C4#1062190012yes—
500C22⋊C4—24no—
501C22⋊C4—864no—
502C22⋊C4—864no—
503C42—21no—
504C42—21no—
505C42—432no—
506C42—432no—
507C42—864no—
508C42—861no—
509C42—861no—
510C42—3441no—
511C42—3441no—
512C42—3441no—
513C42—3441no—
514C23—22no—
515C23—22no—
516C23—22no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23C2×D4×D4311yescharacteristic
522Q8—862no—
523Q8—862no—
524Q8—1721no—
525Q8—1721no—
526D4—22no—
527D4—22no—
528D4—22no—
529D4#1306328314yes—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
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—432no—
547C2×C4—432no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—862no—
553C2×C4—862no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—862no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—861no—
561C2×C4—3444no—
562C2×C4—3444no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4C22×C4×D4311yescharacteristic
573C2×C4#41×D4311yescharacteristic
574C2×C4#41×D4311yescharacteristic
575C2×C4C2×#1062190011yescharacteristic
576C2×C4C2×#1062190011yescharacteristic
577C2×C4C2×#1062190211yescharacteristic
578C8—22no—
579C8—41no—
580C8—862no—
581C8—1721no—
582C22—24no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22C4×D4×D4311yescharacteristic
590C22#1458340511yescharacteristic
591C22#1458341211yescharacteristic
592C22#1458370011yescharacteristic
593C22#1458370611yescharacteristic
594C22#1458370911yescharacteristic
595C22#1458371511yescharacteristic
596C4—41no—
597C4—42no—
598C4—41no—
599C4—42no—
600C4—81no—
601C4—862no—
602C4—862no—
603C4—3441no—
604C4—1722no—
605C4—1721no—
606C4—1722no—
607C4—1721no—
608C4—1722no—
609C4C2×#1306328311yescharacteristic
610C4C4×#1062190011yescharacteristic
611C4#1458342611yescharacteristic
612C4#1458343511yescharacteristic
613C2—44no—
614C2#1913703111yescharacteristic
615C2#1914342011yescharacteristic
616C2#1914343511yescharacteristic
617C2#1914477211yescharacteristic
618C2#1914480211yescharacteristic
619C2#1914484911yescharacteristic
620C2#1914486211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1862C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenter#1862D43
hypocenterC43#21125
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1862

Complements

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

NH ≅ G/Ntype
2. #19137242C2semidirect
4. #19135235C2semidirect
5. #19135230C2semidirect
6. #19135184C2semidirect
7. #19135169C2semidirect
11. #19134494C2semidirect
12. #19134414C2semidirect
14. #19134345C2semidirect
20. #14582996C4semidirect
69. #13063290C2×C4semidirect
88. #13063258C2×C4semidirect
91. #13063250C2×C4semidirect
94. #13063235C2×C4semidirect
370. C43#21125semidirect

Maximal subgroups

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

subgroupindex
C2×#145829962
#191372422
#191369562
#191352352
#191352302
#191351842
#191351692
#191349292
#191349272
#191348582
#191344942
#191344142
#102×Dic432
#191343452
C43×#18622
#2112543