Finite Group Databasebeta

← #25062880

Subgroups — #25062880

Order 11008.

922 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583587C211yesmaximal, characteristic
2#19143685C211yesmaximal, characteristic, complemented
3#19143682C211yesmaximal, characteristic, complemented
4#19132963C212yesmaximal, complemented
5#19132963C212yesmaximal, complemented
6#19132951C211yesmaximal, characteristic, complemented
7#19132935C211yesmaximal, characteristic
8#19132928C212yesmaximal, complemented
9#19132915C211yesmaximal, characteristic
10#19132908C212yesmaximal, complemented
11C43×#1470C211yesmaximal, characteristic, complemented
12#14583587—21no—
13#14583587—21no—
14#14583587—21no—
15#14583587—22no—
16#14583587—22no—
17#14583587—21no—
18C2×#13063320C2212yes—
19C2×#13063316C412yes—
20C2×#13063310C412yes—
21C2×#13063305C411yescharacteristic
22C2×#13063305C411yescharacteristic
23C2×C4×Dic86C2211yescharacteristic
24C2×C4×D172C2211yescharacteristic
25C2×#13063283C411yescharacteristic
26C2×#13063283C2212yes—
27C2×C4⋊C4×D43C411yescharacteristic
28#14583029—21no—
29#14583028—22no—
30#14583027—22no—
31#14583026—21no—
32C8×Dic86—21no—
33#14583023—21no—
34#14582956C2211yescharacteristic
35#14582953C2212yes—
36#14582953C2212yes—
37#14582952C2211yescharacteristic
38#14582949C2212yes—
39#14582949C2212yes—
40#14582625C2212yes—
41#14582625C2212yes—
42#14582622C2211yescharacteristic
43#14582622C2212yes—
44#14582622C2212yes—
45#14582622C2211yescharacteristic
46#14582622C2211yescharacteristic
47#14582622C2211yescharacteristic
48C2×#125×C43C2211yescharacteristic
49C43×#432C2211yescharacteristic
50C43×#431C2211yescharacteristic
51C43×#324C2212yes—
52C43×#324C2212yes—
53C22×Dic86C2×C411yescharacteristic
54C22×D172C2×C411yescharacteristic
55C22×C4×D43C2×C412yes—
56C22×C4×D43C2×C411yescharacteristic
57C22×C4×D43C2×C411yescharacteristic
58#13063320—22no—
59#13063320—22no—
60#13063320—22no—
61#13063320—22no—
62#13063316—22no—
63#13063316—22no—
64#13063316—22no—
65#13063316—22no—
66#13063310—22no—
67#13063310—22no—
68#13063310—22no—
69#13063310—22no—
70#13063305—21no—
71#13063305—21no—
72#13063305—22no—
73#13063305—21no—
74#13063305—21no—
75#13063305—22no—
76C4×Dic86D411yescharacteristic
77C4×Dic86D411yescharacteristic
78C4×Dic86D411yescharacteristic
79C4×Dic86D412yes—
80C4×Dic86D412yes—
81C4×Dic86D411yescharacteristic
82C4×D172—21no—
83C4×D172—21no—
84C4×D172—21no—
85C4×D172—21no—
86#13063283—22no—
87#13063283—21no—
88#13063283—21no—
89#13063283—22no—
90#13063283—22no—
91#13063283—22no—
92#13063283—22no—
93C2×C4⋊Dic43C2×C412yes—
94C2×C4⋊Dic43C2×C411yescharacteristic
95C2×C4⋊Dic43C2×C412yes—
96C2×C4⋊Dic43C2×C411yescharacteristic
97C2×Dic43⋊C4C2×C412yes—
98C2×Dic43⋊C4C2×C412yes—
99C4⋊C4×D43—22no—
100C4⋊C4×D43—21no—
101C4⋊C4×D43—21no—
102C2×(C2×D43)⋊C4C2×C412yes—
103C2×(C2×D43)⋊C4C2×C412yes—
104C2×(C2×D43)⋊C4C2×C412yes—
105C2×(C2×D43)⋊C4C2311yescharacteristic
106C2×(C2×D43)⋊C4C2311yescharacteristic
107C2×C4×Dic43C2×C412yes—
108C2×C4×Dic43C2312yes—
109C4⋊(C43⋊C8)—21no—
110C4⋊(C43⋊C8)—21no—
111Dic43⋊C8—22no—
112Dic43⋊C8—22no—
113Dic43⋊C8—22no—
114Dic43⋊C8—22no—
115C22⋊(C43⋊C8)C2311yescharacteristic
116C22⋊(C43⋊C8)C2312yes—
117C22⋊(C43⋊C8)C2311yescharacteristic
118#13063236—21no—
119#13063235—22no—
120#13063235—22no—
121C4×C43⋊C8—21no—
122C8×Dic43—22no—
123C8×Dic43—22no—
124#125×C43—21no—
125#125×C43—21no—
126#125×C43—21no—
127#125×C43—21no—
128C2×C4⋊C4×C43C2×C411yescharacteristic
129C2×C4⋊C4×C43C2×C411yescharacteristic
130C2×C4⋊C4×C43C2×C412yes—
131C2×C4⋊C4×C43C2312yes—
132C2×C42×C43C2311yescharacteristic
133C4⋊C8×C43—21no—
134C4⋊C8×C43—21no—
135C22⋊C8×C43C2311yescharacteristic
136C22⋊C8×C43C2312yes—
137C22⋊C8×C43C2311yescharacteristic
138#97×C43—21no—
139C4×C8×C43—21no—
140C23×D43C22×C411yescharacteristic
141C23×D43C22×C411yescharacteristic
142C22×C4×C43C22×C412yes—
143C22×C4×C43C22×C411yescharacteristic
144C22×C4×C43C22×C411yescharacteristic
145C22×C4×C43C22×C412yes—
146C22×C4×C43C2411yescharacteristic
147C22×Dic43C22×C412yes—
148C22×Dic43C22×C411yescharacteristic
149C22×Dic43C22×C411yescharacteristic
150C22×Dic43C22×C412yes—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—22no—
154C2×D172—41no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—22no—
160C2×C4×D43—22no—
161C2×C4×D43—24no—
162C2×C4×D43—42no—
163C2×C4×D43—42no—
164C2×C4×D43—42no—
165C2×Dic86—42no—
166C2×Dic86C22⋊C411yescharacteristic
167C2×Dic86C22⋊C411yescharacteristic
168C2×Dic86C22⋊C412yes—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—22no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—22no—
177C4⋊C4×C43—22no—
178C4⋊C4×C43—22no—
179C4⋊C4×C43—22no—
180C42×C43C2×D411yescharacteristic
181C42×C43C2×D411yescharacteristic
182C42×C43C2×D411yescharacteristic
183C42×C43C2×D411yescharacteristic
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—21no—
186(C2×D43)⋊C4—21no—
187(C2×D43)⋊C4—21no—
188(C2×D43)⋊C4—22no—
189(C2×D43)⋊C4—22no—
190(C2×D43)⋊C4—22no—
191(C2×D43)⋊C4—22no—
192(C2×D43)⋊C4—22no—
193(C2×D43)⋊C4—22no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—22no—
197C4⋊Dic43—22no—
198C4⋊Dic43—22no—
199C4⋊Dic43—22no—
200C4⋊Dic43C22⋊C412yes—
201C4⋊Dic43C22⋊C411yescharacteristic
202C4⋊Dic43C22⋊C411yescharacteristic
203Dic43⋊C4—22no—
204Dic43⋊C4—22no—
205Dic43⋊C4C22⋊C412yes—
206Dic43⋊C4C22⋊C412yes—
207Dic43⋊C4C22⋊C412yes—
208Dic43⋊C4C22⋊C412yes—
209C4×Dic43—22no—
210C4×Dic43—22no—
211C4×Dic43C2×D412yes—
212C4×Dic43C2×D412yes—
213C4×Dic43C2×D412yes—
214C4×Dic43C2×D412yes—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—22no—
217C2×C43⋊C8—21no—
218C23×C43C23×C411yescharacteristic
219C22×D43—21no—
220C22×D43—21no—
221C22×D43—21no—
222C22×D43—21no—
223C22×D43—21no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43#13112yes—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—22no—
235C2×C4×C43—22no—
236C2×C4×C43—41no—
237C2×C4×C43—42no—
238C2×C4×C43C2×C22⋊C411yescharacteristic
239C2×C4×C43C2×C22⋊C411yescharacteristic
240C2×C4×C43C2×C22⋊C411yescharacteristic
241C2×C4×C43C2×C22⋊C411yescharacteristic
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C22×D411yescharacteristic
244C2×Dic43—22no—
245C2×Dic43—22no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—42no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43C2×C22⋊C412yes—
252C2×Dic43C2×C22⋊C412yes—
253C2×Dic43C2×C22⋊C412yes—
254C2×Dic43C2×C22⋊C412yes—
255D172—42no—
256D172—42no—
257C4×D43—44no—
258C4×D43—44no—
259C4×D43—42no—
260C4×D43—42no—
261C4×D43—42no—
262C4×D43—42no—
263Dic86—22no—
264Dic86—22no—
265Dic86—42no—
266C8×C43—41no—
267C8×C43—41no—
268C8×C43—42no—
269C43⋊C8—41no—
270C43⋊C8—42no—
271C43⋊C8—41no—
272#17423—431nomaximal, Sylow
273C22×C43—21no—
274C22×C43—21no—
275C22×C43C22×C22⋊C411yescharacteristic
276C22×C43C2×#13111yescharacteristic
277C22×C43#56811yescharacteristic
278C2×D43—22no—
279C2×D43—42no—
280C2×D43—41no—
281C2×D43—41no—
282C2×D43—42no—
283C2×D43—41no—
284C2×D43—41no—
285C2×D43—41no—
286C2×D43—81no—
287C2×D43—81no—
288C4×C43—21no—
289C4×C43—21no—
290C4×C43—21no—
291C4×C43—21no—
292C4×C43—21no—
293C4×C43—42no—
294C4×C43—42no—
295C4×C43#41312yes—
296Dic43—22no—
297Dic43—22no—
298Dic43—22no—
299Dic43—22no—
300Dic43—41no—
301Dic43—41no—
302C2×#552—431no—
303#2984—431no—
304#2984—431no—
305#1473—432no—
306#1473—432no—
307#1470—431no—
308#1470D4311yescharacteristic, complemented
309#1466—431no—
310#1464—432no—
311#1460—431no—
312#1458—432no—
313C2×C43—21no—
314C2×C43—21no—
315C2×C43#288011yescharacteristic
316C2×C43#288411yescharacteristic
317C2×C43C2×#41311yescharacteristic
318D43—42no—
319D43—81no—
320#552—861no—
321#552—861no—
322#552—862no—
323#552—862no—
324#552—861no—
325#552—861no—
326C2×#126—432no—
327C2×#125—432no—
328C2×#125C2×D4311yescharacteristic
329C2×#123—432no—
330C2×C22⋊Q8—431no—
331C2×C22⋊Q8—431no—
332C2×C4×Q8—431no—
333C2×C4×D4—431no—
334C2×#117—432no—
335C2×#117—431no—
336C22×C4⋊C4—431no—
337#446—861no—
338#446—862no—
339#446—861no—
340#446—862no—
341C8×Q8—861no—
342C8×Q8—861no—
343#432—431no—
344#432—432no—
345#432—432no—
346#432C2×D4311yescharacteristic
347#431—431no—
348#431—432no—
349#431—432no—
350#431C2×D4311yescharacteristic
351#324—432no—
352#324—432no—
353#324C2×D4312yes—
354#324C2×D4312yes—
355#323—431no—
356#323—432no—
357#323—431no—
358#323—431no—
359#323—431no—
360#323—432no—
361C43#1742311yescharacteristic, complemented, Sylow
362C22×Q8—431no—
363C22×D4—431no—
364C23×C4—432no—
365C23×C4—431no—
366C23×C4—431no—
367#126—862no—
368#126—862no—
369#126—862no—
370#126—862no—
371#125—21no—
372#125—21no—
373#125—21no—
374#125—21no—
375#125—862no—
376#125—862no—
377#125—862no—
378#125—862no—
379#123—862no—
380#123—862no—
381#123—862no—
382#123—862no—
383C22⋊Q8—861no—
384C22⋊Q8—861no—
385C22⋊Q8—862no—
386C22⋊Q8—861no—
387C22⋊Q8—861no—
388C22⋊Q8—862no—
389C4×Q8—431no—
390C4×Q8—431no—
391C4×Q8—432no—
392C4×Q8—432no—
393C4×Q8—431no—
394C4×Q8—431no—
395C4×D4—861no—
396C4×D4—861no—
397C4×D4—861no—
398C4×D4—861no—
399#117—862no—
400#117—862no—
401#117—862no—
402#117—862no—
403#117—862no—
404#117—861no—
405#117—861no—
406C2×C4⋊C4—431no—
407C2×C4⋊C4—432no—
408C2×C4⋊C4—432no—
409C2×C4⋊C4—432no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—432no—
412C2×C4⋊C4—862no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4C4×D4311yescharacteristic
416C2×C4⋊C4C4×D4311yescharacteristic
417C2×C4⋊C4C4×D4312yes—
418C2×C4⋊C4C22×D4312yes—
419C2×C22⋊C4—432no—
420C2×C22⋊C4—432no—
421C2×C22⋊C4—432no—
422C2×C22⋊C4—431no—
423C2×C22⋊C4—431no—
424C2×C42—432no—
425C2×C42—432no—
426C2×C42C22×D4311yescharacteristic
427C4⋊C8—21no—
428C4⋊C8—21no—
429C4⋊C8—862no—
430C4⋊C8—862no—
431C4⋊C8—862no—
432C4⋊C8—862no—
433C4⋊C8—861no—
434C4⋊C8—861no—
435C22⋊C8—431no—
436C22⋊C8—432no—
437C22⋊C8—431no—
438C22⋊C8C22×D4311yescharacteristic
439C22⋊C8C22×D4312yes—
440C22⋊C8C22×D4311yescharacteristic
441#97—21no—
442#97—862no—
443#97—862no—
444#97—861no—
445C4×C8—21no—
446C4×C8—862no—
447C4×C8—862no—
448C4×C8—861no—
449C24—431no—
450C24—431no—
451C2×Q8—431no—
452C2×Q8—431no—
453C2×Q8—432no—
454C2×Q8—1722no—
455C2×D4—862no—
456C2×D4—861no—
457C2×D4—861no—
458C2×D4—1721no—
459C22×C4—432no—
460C22×C4—432no—
461C22×C4—431no—
462C22×C4—431no—
463C22×C4—862no—
464C22×C4—862no—
465C22×C4—864no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—1722no—
471C22×C4—1722no—
472C22×C4—1722no—
473C22×C4C2×C4×D4312yes—
474C22×C4C2×C4×D4311yescharacteristic
475C22×C4C2×C4×D4311yescharacteristic
476C22×C4C2×C4×D4312yes—
477C22×C4C23×D4311yescharacteristic
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—22no—
481C2×C8—861no—
482C2×C8—862no—
483C2×C8—861no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—432no—
493C4⋊C4—431no—
494C4⋊C4—431no—
495C4⋊C4—432no—
496C4⋊C4—432no—
497C4⋊C4—432no—
498C4⋊C4—432no—
499C4⋊C4—862no—
500C4⋊C4—862no—
501C4⋊C4—862no—
502C4⋊C4—862no—
503C4⋊C4—862no—
504C4⋊C4—862no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C22⋊C4—862no—
508C22⋊C4—862no—
509C22⋊C4—862no—
510C22⋊C4—862no—
511C22⋊C4—862no—
512C22⋊C4—862no—
513C22⋊C4—861no—
514C22⋊C4—861no—
515C22⋊C4—861no—
516C22⋊C4—861no—
517C42—432no—
518C42—432no—
519C42—432no—
520C42—432no—
521C42—862no—
522C42—862no—
523C42D4×D4311yescharacteristic
524C42D4×D4311yescharacteristic
525C42D4×D4311yescharacteristic
526C42D4×D4311yescharacteristic
527C23—432no—
528C23—861no—
529C23—861no—
530C23—861no—
531C23—861no—
532C23—861no—
533C23—1721no—
534C23—1721no—
535C23—1721no—
536C23—1721no—
537C23C22×C4×D4311yescharacteristic
538Q8—862no—
539Q8—862no—
540Q8—1722no—
541D4—1722no—
542D4—1722no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—41no—
551C2×C4—42no—
552C2×C4—432no—
553C2×C4—432no—
554C2×C4—432no—
555C2×C4—432no—
556C2×C4—862no—
557C2×C4—862no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—1722no—
561C2×C4—1722no—
562C2×C4—1724no—
563C2×C4—1724no—
564C2×C4—1722no—
565C2×C4—1722no—
566C2×C4—1722no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4C22⋊C4×D4311yescharacteristic
570C2×C4C22⋊C4×D4311yescharacteristic
571C2×C4C22⋊C4×D4311yescharacteristic
572C2×C4C22⋊C4×D4311yescharacteristic
573C2×C4C2×D4×D4311yescharacteristic
574C2×C4C2×D4×D4311yescharacteristic
575C8—41no—
576C8—41no—
577C8—42no—
578C8—1721no—
579C8—1722no—
580C8—1721no—
581C22—21no—
582C22—21no—
583C22—862no—
584C22—3441no—
585C22—3441no—
586C22—1722no—
587C22—1722no—
588C22—1721no—
589C22—1721no—
590C22—1721no—
591C22—1721no—
592C22—1721no—
593C22C2×C22⋊C4×D4311yescharacteristic
594C22#131×D4311yescharacteristic
595C22#1458366411yescharacteristic
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—21no—
601C4—42no—
602C4—42no—
603C4—862no—
604C4—862no—
605C4—862no—
606C4—862no—
607C4—1721no—
608C4—1721no—
609C4#1458288212yes—
610C2—21no—
611C2—21no—
612C2—3441no—
613C2—1722no—
614C2#1914304311yescharacteristic
615C2#1914305711yescharacteristic
616C2C2×#1458288211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1470C2
socleC22×C43C22×C22⋊C4
prime radicalC22×D172C2×C4
cosocleC22×C4×C43C24
hypercenter#1470D43
hypocenterC43#17423
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1470

Complements

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

NH ≅ G/Ntype
2. #19143685C2semidirect
3. #19143682C2semidirect
4. #19132963C2semidirect
5. #19132963C2semidirect
6. #19132951C2semidirect
8. #19132928C2semidirect
10. #19132908C2semidirect
11. C43×#1470C2semidirect
308. #1470D43semidirect
361. C43#17423semidirect

Maximal subgroups

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

subgroupindex
C2×#145835872
#191436852
#191436822
#191329632
#191329512
#191329352
#191329282
#191329152
#191329082
C43×#14702
#1742343