Finite Group Databasebeta

← #25064235

Subgroups — #25064235

Order 11008.

990 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148330C211yesmaximal, characteristic
2#19143253C211yesmaximal, characteristic, complemented
3#19133170C212yesmaximal, complemented
4#19133162C211yesmaximal, characteristic, complemented
5#19133141C212yesmaximal, complemented
6#19133136C211yesmaximal, characteristic, complemented
7#19133118C212yesmaximal, complemented
8#19133110C211yesmaximal, characteristic, complemented
9#19133089C212yesmaximal, complemented
10#19133084C211yesmaximal, characteristic, complemented
11C43×#2347C211yesmaximal, characteristic, complemented
12#14583612—21no—
13#14583597—21no—
14#14583593—21no—
15#14583573—22no—
16#14583550—21no—
17#14583539—22no—
18#14583527C411yescharacteristic, complemented
19#14583520C412yescomplemented
20#14583504C412yescomplemented
21#14583468C411yescharacteristic, complemented
22#14583449C2212yes—
23#14583433C2212yes—
24#14583410C2211yescharacteristic
25C2×#13063299C2211yescharacteristic
26#14583379C411yescharacteristic, complemented
27#14583373C411yescharacteristic, complemented
28#14582960—22no—
29#14582956C2212yescomplemented
30#14582952C2212yescomplemented
31#14582926—21no—
32#14582863C2211yescharacteristic
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34#14582855—21no—
35#14582635C2211yescharacteristic, complemented
36#14582635C2211yescharacteristic, complemented
37#14582635C2212yescomplemented
38#14582632C2212yes—
39#14582632C2212yes—
40#14582632C2212yes—
41#14582632C2212yes—
42#14582632C2211yescharacteristic, complemented
43#14582632C2211yescharacteristic, complemented
44#14582632C2212yescomplemented
45C2×#117×C43C2211yescharacteristic
46C43×#389—21no—
47C43×#388—22no—
48C43×#383C2212yescomplemented
49C43×#380C2211yescharacteristic
50C4×C4⋊C4×C43—21no—
51C4×C4⋊C4×C43C2212yescomplemented
52C4×C22⋊C4×C43C2211yescharacteristic
53C2×#10621898—22no—
54C2×#10621898C2×C411yescharacteristic
55C22×D172C2×C411yescharacteristic
56C22×C22⋊D43—21no—
57C2×#10621877—21no—
58C22×C43⋊C8—21no—
59#13063325C2×C412yes—
60#13063324—21no—
61#13063322C2×C412yes—
62#13063320—22no—
63#13063319—22no—
64#13063317C2×C412yes—
65#13063316—21no—
66#13063313—22no—
67#13063313C2×C412yes—
68#13063311—22no—
69#13063310—22no—
70#13063310—22no—
71#13063308—21no—
72#13063308—22no—
73#13063307—22no—
74#13063304C2×C411yescharacteristic
75#13063304C2311yescharacteristic
76#13063303—22no—
77#13063302—22no—
78#13063300—21no—
79#13063300—21no—
80#13063299—21no—
81#13063299—21no—
82#13063299—22no—
83#13063299C2×C412yes—
84#13063299C2×C411yescharacteristic
85#13063299C2312yes—
86#13063299C2311yescharacteristic
87#13063298—22no—
88#13063298—22no—
89#13063295—22no—
90#13063294—21no—
91C4×Dic86C2×C412yes—
92C4×D172—22no—
93C4×D172C2×C412yes—
94C4×D172C2×C412yes—
95C4×D172C2×C412yes—
96#13063287—21no—
97#13063287—21no—
98C4×C22⋊D43—21no—
99C4×C22⋊D43—21no—
100C4×C22⋊D43—22no—
101(C22⋊D43)⋊C4—22no—
102#13063284C2×C411yescharacteristic
103#13063283—21no—
104#13063282—22no—
105C2×C4⋊Dic43C2×C411yescharacteristic
106C4⋊C4×D43—21no—
107C2×(C2×D43)⋊C4—21no—
108C22⋊C4×D43—22no—
109C4⋊(C43⋊C8)—22no—
110C4⋊(C43⋊C8)—22no—
111C22⋊(C43⋊C8)—21no—
112C22⋊(C43⋊C8)—21no—
113C22⋊(C43⋊C8)C2311yescharacteristic
114C22⋊(C43⋊C8)C2311yescharacteristic
115C22⋊(C43⋊C8)C2312yes—
116#13063236—22no—
117C4×C43⋊C8—22no—
118C23×C4×C43C2311yescharacteristic
119#117×C43C2×C411yescharacteristic
120#117×C43C2×C411yescharacteristic
121#117×C43C2×C412yes—
122#117×C43D412yes—
123#117×C43D411yescharacteristic
124#117×C43D411yescharacteristic
125C2×C4⋊C4×C43—21no—
126C2×C4⋊C4×C43—22no—
127C2×C4⋊C4×C43D411yescharacteristic
128C2×C4⋊C4×C43D411yescharacteristic
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43D412yes—
132C2×C42×C43—21no—
133C2×C42×C43—22no—
134C2×C42×C43C2312yes—
135#95×C43—22no—
136#95×C43—22no—
137#95×C43C2311yescharacteristic
138#95×C43C2311yescharacteristic
139#95×C43C2312yes—
140C24×C43C2×D411yescharacteristic
141C23×D43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—22no—
145C22×C4×C43—42no—
146C22×C4×C43C22×C411yescharacteristic
147C22×C4×C43C22×C411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D412yes—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D412yes—
153C22×C4×C43C2411yescharacteristic
154C2×C22⋊D43—21no—
155C2×C22⋊D43—21no—
156C2×C22⋊D43—22no—
157C2×C22⋊D43—21no—
158C2×C22⋊D43—22no—
159C2×C22⋊D43—81no—
160C2×C22⋊D43—81no—
161C22×Dic43—21no—
162#10621898—42no—
163#10621898—82no—
164#10621898—82no—
165C2×D172—21no—
166C2×D172—22no—
167C2×D172—22no—
168C2×D172—42no—
169C2×D172C22×C412yes—
170C2×D172C22×C411yescharacteristic
171C2×C4×D43—21no—
172C2×C4×D43—22no—
173C2×C4×D43—22no—
174C2×C4×D43—22no—
175C2×Dic86—22no—
176C2×Dic86C22×C411yescharacteristic
177C4⋊C4×C43—42no—
178C4⋊C4×C43—44no—
179C4⋊C4×C43C22⋊C411yescharacteristic
180C4⋊C4×C43C22⋊C411yescharacteristic
181C4⋊C4×C43C22⋊C411yescharacteristic
182C4⋊C4×C43C22⋊C411yescharacteristic
183C4⋊C4×C43C22⋊C412yes—
184C4⋊C4×C43C22⋊C412yes—
185C22⋊C4×C43—42no—
186C22⋊C4×C43—81no—
187C22⋊C4×C43C22⋊C412yes—
188C22⋊C4×C43C22⋊C412yes—
189C22⋊C4×C43C22⋊C412yes—
190C22⋊C4×C43C22⋊C412yes—
191C42×C43—42no—
192C42×C43—82no—
193C42×C43C22×C412yes—
194C42×C43C22×C412yes—
195C42×C43C2×D412yes—
196C42×C43C2×D412yes—
197C22⋊Dic43—21no—
198C22⋊Dic43—21no—
199C22⋊Dic43—21no—
200(C2×D43)⋊C4—22no—
201(C2×D43)⋊C4—22no—
202(C2×D43)⋊C4—22no—
203(C2×D43)⋊C4—22no—
204(C2×D43)⋊C4—22no—
205(C2×D43)⋊C4—22no—
206(C2×D43)⋊C4—21no—
207(C2×D43)⋊C4—22no—
208(C2×D43)⋊C4—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—22no—
211C4⋊Dic43C22×C412yes—
212C4⋊Dic43C22×C411yescharacteristic
213C4⋊Dic43C22×C411yescharacteristic
214Dic43⋊C4—22no—
215Dic43⋊C4—22no—
216Dic43⋊C4—22no—
217Dic43⋊C4—21no—
218Dic43⋊C4—21no—
219C4×Dic43—22no—
220C4×Dic43—21no—
221#10621877—42no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—22no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—42no—
226C23×C43—21no—
227C23×C43—21no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43C2×C22⋊C411yescharacteristic
231C23×C43C2×C22⋊C411yescharacteristic
232C23×C43C22×D411yescharacteristic
233C22×D43—22no—
234C22×D43—21no—
235C22×D43—42no—
236C22×D43—81no—
237C22×D43—81no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
244C2×C4×C43—42no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—42no—
253C2×C4×C43—42no—
254C2×C4×C43—42no—
255C2×C4×C43—41no—
256C2×C4×C43C2×C22⋊C412yes—
257C2×C4×C43C2×C22⋊C412yes—
258C2×C4×C43C2×C22⋊C411yescharacteristic
259C2×C4×C43C2×C22⋊C412yes—
260C2×C4×C43C2×C22⋊C412yes—
261C2×C4×C43C2×C22⋊C411yescharacteristic
262C2×C4×C43C23×C411yescharacteristic
263C2×C4×C43C22×D411yescharacteristic
264C22⋊D43—42no—
265C22⋊D43—41no—
266C22⋊D43—42no—
267C22⋊D43—41no—
268C22⋊D43—42no—
269C22⋊D43—81no—
270C22⋊D43—82no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—22no—
274C2×Dic43—21no—
275C2×Dic43—81no—
276D172—42no—
277D172—41no—
278D172—42no—
279D172—82no—
280D172—82no—
281C4×D43—42no—
282C4×D43—82no—
283C4×D43—82no—
284C4×D43—82no—
285Dic86—41no—
286Dic86—82no—
287C43⋊C8—41no—
288C43⋊C8—41no—
289C43⋊C8—42no—
290#17607—431nomaximal, Sylow
291C22×C43—21no—
292C22×C43—21no—
293C22×C43—21no—
294C22×C43—21no—
295C22×C43—21no—
296C22×C43—21no—
297C22×C43—21no—
298C22×C43—21no—
299C22×C43—81no—
300C22×C43—81no—
301C22×C43C22×C22⋊C411yescharacteristic
302C22×C43#57611yescharacteristic
303C22×C43#57711yescharacteristic
304C2×D43—42no—
305C2×D43—41no—
306C2×D43—42no—
307C2×D43—41no—
308C2×D43—42no—
309C2×D43—41no—
310C2×D43—162no—
311C4×C43—21no—
312C4×C43—21no—
313C4×C43—21no—
314C4×C43—22no—
315C4×C43—22no—
316C4×C43—22no—
317C4×C43—22no—
318C4×C43—42no—
319C4×C43—82no—
320C4×C43—81no—
321C4×C43#41012yes—
322Dic43—41no—
323Dic43—41no—
324Dic43—42no—
325Dic43—41no—
326#3494—431no—
327#2924—431no—
328#2347D4311yescharacteristic, complemented
329#1521—432no—
330#1519—431no—
331#1514—432no—
332#1513—431no—
333#1509—432no—
334#1507—431no—
335#1502—432no—
336#1501—431no—
337C2×C43—21no—
338C2×C43—21no—
339C2×C43—41no—
340C2×C43—41no—
341C2×C43C2×#41011yescharacteristic
342C2×C43#289711yescharacteristic
343C2×C43#290111yescharacteristic
344D43—81no—
345D43—82no—
346#555—861no—
347#553—861no—
348#553—861no—
349#551—862no—
350#547—861no—
351#546—862no—
352#544—431no—
353#542—432no—
354#540—432no—
355#535—431no—
356#532—432no—
357#529—432no—
358#525—431no—
359C2×#121—431no—
360#520—431no—
361#518—431no—
362C2×#117C2×D4311yescharacteristic
363#433—862no—
364#432—432no—
365#431—432no—
366#424—861no—
367#407—431no—
368C2×C22⋊C8—431no—
369#405—861no—
370#389—21no—
371#388—22no—
372#383C2×D4312yescomplemented
373#380C2×D4311yescharacteristic
374C4×C4⋊C4—21no—
375C4×C4⋊C4C2×D4312yescomplemented
376C4×C22⋊C4C2×D4311yescharacteristic
377#328—431no—
378#328—431no—
379#328—432no—
380#327—432no—
381#327—432no—
382#327—432no—
383#327—432no—
384#327—431no—
385#327—431no—
386#327—432no—
387C43#1760711yescharacteristic, complemented, Sylow
388C2×#41—431no—
389C2×#41—862no—
390C22×D4—431no—
391C22×D4—861no—
392C23×C4C22×D4311yescharacteristic
393C2×M16—861no—
394C22×C8—861no—
395C4⋊Q8—432no—
396C4⋊Q8—861no—
397#127—432no—
398#126—862no—
399#126—862no—
400#125—432no—
401#125—861no—
402#124—432no—
403#124—862no—
404#124—862no—
405#123—861no—
406#123—862no—
407#123—862no—
408#123—862no—
409#123—862no—
410C22⋊Q8—431no—
411C22⋊Q8—431no—
412C22⋊Q8—862no—
413C22⋊Q8—862no—
414#121—432no—
415#121—431no—
416#121—432no—
417#121—431no—
418#121—861no—
419#121—861no—
420#121—862no—
421#121—861no—
422#121—861no—
423#121—862no—
424#121—862no—
425#120—861no—
426#120—862no—
427C4×Q8—432no—
428C4×D4—432no—
429C4×D4—432no—
430C4×D4—432no—
431C4×D4—861no—
432C4×D4—861no—
433C4×D4—862no—
434C4×D4—861no—
435C4×D4—861no—
436C4×D4—862no—
437C4×D4—862no—
438#117—431no—
439#117—861no—
440#117—862no—
441#117C4×D4311yescharacteristic
442#117C4×D4311yescharacteristic
443#117C4×D4312yes—
444#117D17212yes—
445#117D17211yescharacteristic
446#117D17211yescharacteristic
447C2×C4⋊C4—21no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—431no—
450C2×C4⋊C4—861no—
451C2×C4⋊C4C22⋊D4311yescharacteristic
452C2×C4⋊C4C22⋊D4311yescharacteristic
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—861no—
456C2×C22⋊C4—862no—
457C2×C22⋊C4C22⋊D4312yes—
458C2×C42—21no—
459C2×C42—22no—
460C2×C42C22×D4312yes—
461C4⋊C8—862no—
462C4⋊C8—862no—
463C22⋊C8—431no—
464C22⋊C8—431no—
465C22⋊C8—432no—
466C22⋊C8—861no—
467C22⋊C8—861no—
468#97—862no—
469C4×C8—862no—
470#95—22no—
471#95—22no—
472#95C22×D4311yescharacteristic
473#95C22×D4311yescharacteristic
474#95C22×D4312yes—
475C24—861no—
476C24C2×C22⋊D4311yescharacteristic
477#41—3442no—
478#41—3442no—
479#41—1722no—
480C2×Q8—431no—
481C2×Q8—862no—
482C2×D4—432no—
483C2×D4—431no—
484C2×D4—861no—
485C2×D4—862no—
486C2×D4—861no—
487C2×D4—861no—
488C2×D4—862no—
489C2×D4—862no—
490C2×D4—862no—
491C2×D4—861no—
492C2×D4—3441no—
493C2×D4—3441no—
494C2×D4—1722no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—42no—
499C22×C4—861no—
500C22×C4—862no—
501C22×C4—862no—
502C22×C4—862no—
503C22×C4—861no—
504C22×C4C2×C4×D4311yescharacteristic
505C22×C4C2×C4×D4311yescharacteristic
506C22×C4C2×D17211yescharacteristic
507C22×C4C2×D17211yescharacteristic
508C22×C4C2×C22⋊D4312yes—
509C22×C4C2×C22⋊D4311yescharacteristic
510C22×C4C2×C22⋊D4312yes—
511C22×C4C23×D4311yescharacteristic
512M16—1722no—
513C2×C8—861no—
514C2×C8—862no—
515C2×C8—861no—
516C2×C8—1722no—
517C4⋊C4—42no—
518C4⋊C4—44no—
519C4⋊C4—432no—
520C4⋊C4—431no—
521C4⋊C4—431no—
522C4⋊C4—861no—
523C4⋊C4—862no—
524C4⋊C4—862no—
525C4⋊C4—862no—
526C4⋊C4—862no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4(C2×D43)⋊C411yescharacteristic
530C4⋊C4(C2×D43)⋊C411yescharacteristic
531C4⋊C4(C2×D43)⋊C411yescharacteristic
532C4⋊C4(C2×D43)⋊C411yescharacteristic
533C4⋊C4(C2×D43)⋊C412yes—
534C4⋊C4(C2×D43)⋊C412yes—
535C22⋊C4—42no—
536C22⋊C4—81no—
537C22⋊C4—861no—
538C22⋊C4—861no—
539C22⋊C4—861no—
540C22⋊C4—862no—
541C22⋊C4—862no—
542C22⋊C4—862no—
543C22⋊C4—862no—
544C22⋊C4—862no—
545C22⋊C4—862no—
546C22⋊C4—861no—
547C22⋊C4—862no—
548C22⋊C4—861no—
549C22⋊C4(C2×D43)⋊C412yes—
550C22⋊C4(C2×D43)⋊C412yes—
551C22⋊C4(C2×D43)⋊C412yes—
552C22⋊C4(C2×D43)⋊C412yes—
553C42—42no—
554C42—82no—
555C42—861no—
556C42—862no—
557C42C2×C4×D4312yes—
558C42C2×C4×D4312yes—
559C42C2×D17212yes—
560C42C2×D17212yes—
561C23—21no—
562C23—21no—
563C23—41no—
564C23—41no—
565C23—862no—
566C23—861no—
567C23—3441no—
568C23—3441no—
569C23—1722no—
570C23C2×(C2×D43)⋊C411yescharacteristic
571C23C2×(C2×D43)⋊C411yescharacteristic
572C23C22×C22⋊D4311yescharacteristic
573Q8—3442no—
574Q8—1721no—
575D4—3442no—
576D4—3442no—
577D4—3442no—
578D4—3441no—
579D4—1722no—
580D4—1721no—
581D4—1722no—
582D4—1722no—
583D4—1721no—
584D4—1722no—
585D4—1721no—
586D4—1722no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—42no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—41no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—862no—
609C2×C4—3442no—
610C2×C4—3442no—
611C2×C4—3442no—
612C2×C4—3441no—
613C2×C4—1722no—
614C2×C4C2×(C2×D43)⋊C412yes—
615C2×C4C2×(C2×D43)⋊C412yes—
616C2×C4C2×(C2×D43)⋊C412yes—
617C2×C4C2×(C2×D43)⋊C412yes—
618C2×C4C2×(C2×D43)⋊C411yescharacteristic
619C2×C4C2×(C2×D43)⋊C411yescharacteristic
620C2×C4C22×C4×D4311yescharacteristic
621C2×C4C22×D17211yescharacteristic
622C8—1721no—
623C8—1721no—
624C8—1722no—
625C22—21no—
626C22—21no—
627C22—21no—
628C22—21no—
629C22—21no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—81no—
634C22—81no—
635C22—1721no—
636C22—1722no—
637C22—1721no—
638C22—1722no—
639C22—1722no—
640C22—1721no—
641C22—6882no—
642C22C22×(C2×D43)⋊C411yescharacteristic
643C22#1458370211yescharacteristic
644C22#1458370711yescharacteristic
645C4—21no—
646C4—21no—
647C4—21no—
648C4—22no—
649C4—22no—
650C4—22no—
651C4—22no—
652C4—42no—
653C4—82no—
654C4—81no—
655C4—1721no—
656C4—1722no—
657C4—1721no—
658C4—1721no—
659C4#1458287212yes—
660C2—21no—
661C2—21no—
662C2—41no—
663C2—41no—
664C2—3442no—
665C2—3441no—
666C2C2×#1458287211yescharacteristic
667C2#1914311811yescharacteristic
668C2#1914314311yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2347C2
socleC22×C43C22×C22⋊C4
prime radical#19148330C2
cosocleC22×C4×C43C24
hypercenter#2347D43
hypocenterC43#17607
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2347

Complements

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

NH ≅ G/Ntype
2. #19143253C2semidirect
3. #19133170C2semidirect
4. #19133162C2semidirect
5. #19133141C2semidirect
6. #19133136C2semidirect
7. #19133118C2semidirect
8. #19133110C2semidirect
9. #19133089C2semidirect
10. #19133084C2semidirect
11. C43×#2347C2semidirect
18. #14583527C4semidirect
19. #14583520C4semidirect
20. #14583504C4semidirect
21. #14583468C4semidirect
26. #14583379C4semidirect
27. #14583373C4semidirect
29. #14582956C22semidirect
30. #14582952C22semidirect
35. #14582635C22semidirect
36. #14582635C22semidirect
37. #14582635C22semidirect
42. #14582632C22semidirect
43. #14582632C22semidirect
44. #14582632C22semidirect
48. C43×#383C22semidirect
51. C4×C4⋊C4×C43C22semidirect
328. #2347D43semidirect
372. #383C2×D43semidirect
375. C4×C4⋊C4C2×D43semidirect
387. C43#17607semidirect

Maximal subgroups

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

subgroupindex
#191483302
#191432532
#191331702
#191331622
#191331412
#191331362
#191331182
#191331102
#191330892
#191330842
C43×#23472
#1760743