Finite Group Databasebeta

← #25125397

Subgroups — #25125397

Order 11008.

962 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582906C211yesmaximal, characteristic
2C2×#103×D43C211yesmaximal, characteristic
3#19137220C211yesmaximal, characteristic
4#19137178C211yesmaximal, characteristic
5#19136017C211yesmaximal, characteristic, complemented
6#19136016C211yesmaximal, characteristic, complemented
7#19136014C211yesmaximal, characteristic, complemented
8#19136007C211yesmaximal, characteristic, complemented
9#19136006C211yesmaximal, characteristic, complemented
10#19136005C211yesmaximal, characteristic, complemented
11#19136003C211yesmaximal, characteristic, complemented
12#19134313C211yesmaximal, characteristic
13#19134310C211yesmaximal, characteristic
14#19134290C211yesmaximal, characteristic
15C43×#2074C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19C2×#13063283C2211yescharacteristic
20C2×#13063283C2211yescharacteristic
21C2×#13063282C2211yescharacteristic
22C2×C4⋊C4×D43C2211yescharacteristic
23#14582906—24no—
24C2×#13063250C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30#103×D43—24no—
31#14582806C2211yescharacteristic
32#14582805C2211yescharacteristic
33#14582804C2211yescharacteristic
34#14582803—21no—
35#14582803—21no—
36#14582796—21no—
37#14582796—21no—
38#14582773—21no—
39#14582773—21no—
40#14582769C2211yescharacteristic
41#14582768C2211yescharacteristic
42#14582764C2211yescharacteristic
43#14582761—21no—
44#14582761—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C43×#391C2211yescharacteristic
57C43×#382C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×Dic86—21no—
62C22×Dic86C2311yescharacteristic
63C2×Q8×D43—22no—
64C2×Q8×D43—22no—
65C2×Q8×D43—22no—
66C2×Q8×D43—22no—
67C2×Q8×D43—22no—
68C2×Q8×D43D414yes—
69C22×C4×D43—21no—
70C22×C4×D43—21no—
71C22×C4×D43C2311yescharacteristic
72C2×#10621872—22no—
73C2×#10621872—22no—
74C2×#10621872—22no—
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77C2×C8×D43—22no—
78C2×C8×D43—22no—
79C2×C8×D43—22no—
80#13063283—22no—
81#13063283—22no—
82#13063283—22no—
83#13063283—22no—
84#13063282—22no—
85#13063282—22no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4D411yescharacteristic
95C2×Dic43⋊C4D411yescharacteristic
96C4⋊C4×D43—22no—
97C4⋊C4×D43—22no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4D411yescharacteristic
101C2×(C2×D43)⋊C4D411yescharacteristic
102C2×C4×Dic43—21no—
103C2×C4×Dic43—21no—
104C2×C4×Dic43C2311yescharacteristic
105#13063250—22no—
106#13063250—22no—
107#13063249—22no—
108#13063249—22no—
109#13063248—22no—
110#13063248—22no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C22×Q8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C42×C43C2311yescharacteristic
126#103×C43—22no—
127#103×C43—22no—
128#95×C43—21no—
129#95×C43—21no—
130#95×C43—21no—
131#95×C43—21no—
132C23×D43C2×D411yescharacteristic
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43C2×D412yes—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153Q8×D43—28no—
154Q8×D43—28no—
155Q8×D43—44no—
156Q8×D43—44no—
157C2×C4×D43—24no—
158C2×C4×D43—42no—
159C2×C4×D43—42no—
160C2×C4×D43—42no—
161C2×C4×D43—81no—
162C2×C4×D43—81no—
163C2×C4×D43C2×D412yes—
164C2×C4×D43#4112yes—
165C2×C4×D43#4112yes—
166C2×C4×D43#4112yes—
167C2×C4×D43#4112yes—
168C2×C4×D43#4112yes—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86—21no—
174C2×Dic86—24no—
175C2×Dic86—42no—
176C2×Dic86—42no—
177C2×Dic86C2×D412yes—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C42×C43—21no—
191C42×C43—21no—
192(C2×D43)⋊C4—22no—
193(C2×D43)⋊C4—22no—
194(C2×D43)⋊C4—42no—
195(C2×D43)⋊C4—42no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—81no—
203C4⋊Dic43—81no—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—42no—
207Dic43⋊C4—81no—
208Dic43⋊C4—81no—
209C4×Dic43—21no—
210C4×Dic43—21no—
211C4×Dic43—42no—
212C4×Dic43—42no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219#10621872—44no—
220C8×D43—44no—
221C23×C43C22×D411yescharacteristic
222C22×D43—21no—
223C22×D43—21no—
224C22×D43—21no—
225C22×D43—21no—
226C22×D43#12112yes—
227C22×D43#12312yes—
228C22×D43#12412yes—
229Q8×C43—22no—
230Q8×C43—22no—
231Q8×C43—41no—
232Q8×C43—41no—
233C2×C4×C43—22no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
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×C43C22×D411yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×Dic43—22no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43#12112yes—
276C2×Dic43#12312yes—
277C2×Dic43#12412yes—
278C4×D43—48no—
279C4×D43—84no—
280C4×D43#12314yes—
281C4×D43#12314yes—
282C4×D43#12614yes—
283C4×D43#12614yes—
284Dic86—22no—
285Dic86—22no—
286Dic86—41no—
287Dic86—41no—
288Dic86—48no—
289C8×C43—41no—
290C8×C43—41no—
291C43⋊C8—41no—
292C43⋊C8—41no—
293#23633—431nomaximal, Sylow
294C22×C43C2×#12111yescharacteristic
295C22×C43C2×#12311yescharacteristic
296C22×C43C2×#12411yescharacteristic
297C22×C43#57711yescharacteristic
298C22×C43#57711yescharacteristic
299C22×C43#57811yescharacteristic
300C22×C43#57811yescharacteristic
301C2×D43—22no—
302C2×D43—22no—
303C2×D43—22no—
304C2×D43—22no—
305C2×D43—22no—
306C2×D43—22no—
307C2×D43#39714yes—
308C4×C43—41no—
309C4×C43—41no—
310C4×C43—42no—
311C4×C43—81no—
312C4×C43—81no—
313C4×C43—81no—
314C4×C43C2×#12311yescharacteristic
315C4×C43C2×#12311yescharacteristic
316C4×C43C2×#12611yescharacteristic
317C4×C43C2×#12611yescharacteristic
318Dic43—41no—
319Dic43—41no—
320Dic43—42no—
321Dic43—81no—
322Dic43—81no—
323Dic43—81no—
324Dic43#39714yes—
325C2×#419—431no—
326C22×#103—431no—
327#2317—431no—
328#2310—431no—
329#2074—431no—
330#2074—431no—
331#2074—431no—
332#2074D4311yescharacteristic, complemented
333#2072—431no—
334#2072—431no—
335#2072—431no—
336#2072—431no—
337#1736—431no—
338#1735—431no—
339#1729—431no—
340C2×C43C2×#39711yescharacteristic
341C2×C43#304311yescharacteristic
342C2×C43#304411yescharacteristic
343C2×C43#309711yescharacteristic
344C2×C43#309711yescharacteristic
345C2×C43#313711yescharacteristic
346C2×C43#313711yescharacteristic
347D43—24no—
348C23×Q8—431no—
349C22×M16—431no—
350C23×C8—431no—
351C2×#117—431no—
352C2×#117—431no—
353C2×#117—431no—
354C22×C4⋊C4—431no—
355#419—864no—
356C2×#103—431no—
357C2×#103—431no—
358C2×#103—431no—
359C2×#103—431no—
360C2×#103—431no—
361C2×#103—431no—
362C2×#103—864no—
363C2×#103C2×D4311yescharacteristic
364C2×#103C2×D4311yescharacteristic
365#391—431no—
366#391—431no—
367#391—431no—
368#391—861no—
369#391—861no—
370#391C2×D4311yescharacteristic
371#389—861no—
372#389—861no—
373#385—861no—
374#385—861no—
375#384—431no—
376#384—431no—
377#382—431no—
378#382C2×D4311yescharacteristic
379#381—861no—
380#381—861no—
381#340—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340—431no—
387#340C2×D4311yescharacteristic
388#340C2×D4311yescharacteristic
389#336—431no—
390#336—431no—
391#336—431no—
392#336C2×D4311yescharacteristic
393C43#2363311yescharacteristic, complemented, Sylow
394C22×Q8—434no—
395C22×Q8—431no—
396C22×Q8—861no—
397C22×Q8—862no—
398C22×Q8—862no—
399C22×Q8—862no—
400C22×Q8—862no—
401C22×Q8—862no—
402C22×Q8C22×D4311yescharacteristic
403C23×C4—431no—
404C23×C4—861no—
405C23×C4—861no—
406C2×M16—862no—
407C2×M16—862no—
408C2×M16—862no—
409C22×C8—431no—
410C22×C8—431no—
411C22×C8—862no—
412C22×C8—862no—
413C22×C8—862no—
414C22×C8C22×D4311yescharacteristic
415C22×C8C22×D4311yescharacteristic
416#117—862no—
417#117—862no—
418#117—862no—
419#117—862no—
420#117—862no—
421#117—862no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—862no—
428C2×C4⋊C4—862no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4C22×D4311yescharacteristic
435C2×C4⋊C4C22×D4311yescharacteristic
436C2×C4⋊C4C22×D4311yescharacteristic
437C2×C22⋊C4—431no—
438C2×C22⋊C4—431no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4—861no—
441C2×C42—431no—
442C2×C42—861no—
443C2×C42—861no—
444C2×C42C22×D4311yescharacteristic
445#103—22no—
446#103—22no—
447#103—862no—
448#103—862no—
449#103—862no—
450#103—862no—
451#103—862no—
452#103—862no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—861no—
458#95—861no—
459#95—861no—
460#95—861no—
461#95—861no—
462#95—861no—
463#95—861no—
464#95—861no—
465C24—431no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—432no—
472C2×Q8—864no—
473C2×Q8—868no—
474C2×Q8—868no—
475C2×Q8—861no—
476C2×Q8—861no—
477C2×Q8—861no—
478C2×Q8—861no—
479C2×Q8—861no—
480C2×Q8—1722no—
481C2×Q8—1722no—
482C2×Q8—1724no—
483C2×Q8—1724no—
484C2×Q8D4×D4312yes—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—431no—
490C22×C4—432no—
491C22×C4—432no—
492C22×C4—432no—
493C22×C4—432no—
494C22×C4—432no—
495C22×C4—432no—
496C22×C4—431no—
497C22×C4—431no—
498C22×C4—864no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—3441no—
504C22×C4—3441no—
505C22×C4—1722no—
506C22×C4—1722no—
507C22×C4—1722no—
508C22×C4D4×D4311yescharacteristic
509C22×C4D4×D4311yescharacteristic
510C22×C4C23×D4311yescharacteristic
511M16—1724no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8—861no—
524C2×C8—1724no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—862no—
532C4⋊C4—862no—
533C4⋊C4—861no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—861no—
539C4⋊C4—3441no—
540C4⋊C4—3441no—
541C4⋊C4—3441no—
542C4⋊C4—3441no—
543C4⋊C4—1722no—
544C22⋊C4—862no—
545C22⋊C4—862no—
546C22⋊C4—1722no—
547C22⋊C4—1722no—
548C42—21no—
549C42—21no—
550C42—861no—
551C42—861no—
552C42—1722no—
553C42—1722no—
554C23—432no—
555C23—432no—
556C23—432no—
557C23—861no—
558C23—861no—
559C23—861no—
560C23—861no—
561C23C2×D4×D4311yescharacteristic
562Q8—22no—
563Q8—22no—
564Q8—41no—
565Q8—41no—
566Q8—862no—
567Q8—862no—
568Q8—1728no—
569Q8—1721no—
570Q8—1721no—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—432no—
590C2×C4—432no—
591C2×C4—432no—
592C2×C4—434no—
593C2×C4—434no—
594C2×C4—434no—
595C2×C4—434no—
596C2×C4—862no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—3444no—
604C2×C4—1728no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4C2×D4×D4311yescharacteristic
617C2×C4#41×D4311yescharacteristic
618C2×C4#41×D4311yescharacteristic
619C2×C4#41×D4311yescharacteristic
620C2×C4#41×D4311yescharacteristic
621C2×C4#41×D4311yescharacteristic
622C8—41no—
623C8—41no—
624C8—1721no—
625C8—1721no—
626C22—434no—
627C22—862no—
628C22—862no—
629C22—862no—
630C22—862no—
631C22—862no—
632C22—862no—
633C22#121×D4311yescharacteristic
634C22#123×D4311yescharacteristic
635C22#124×D4311yescharacteristic
636C22#1458370611yescharacteristic
637C22#1458370811yescharacteristic
638C22#1458371311yescharacteristic
639C22#1458371511yescharacteristic
640C4—42no—
641C4—41no—
642C4—41no—
643C4—81no—
644C4—81no—
645C4—81no—
646C4—434no—
647C4—3441no—
648C4—3441no—
649C4—3441no—
650C4—1722no—
651C4—1721no—
652C4—1721no—
653C4#123×D4311yescharacteristic
654C4#123×D4311yescharacteristic
655C4#126×D4311yescharacteristic
656C4#126×D4311yescharacteristic
657C2—864no—
658C2#397×D4311yescharacteristic
659C2#1914411411yescharacteristic
660C2#1914412311yescharacteristic
661C2#1914455911yescharacteristic
662C2#1914456111yescharacteristic
663C2#1914495911yescharacteristic
664C2#1914496111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2074C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#2074D43
hypocenterC43#23633
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2074

Complements

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

NH ≅ G/Ntype
5. #19136017C2semidirect
6. #19136016C2semidirect
7. #19136014C2semidirect
8. #19136007C2semidirect
9. #19136006C2semidirect
10. #19136005C2semidirect
11. #19136003C2semidirect
15. C43×#2074C2semidirect
332. #2074D43semidirect
393. C43#23633semidirect

Maximal subgroups

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

subgroupindex
C2×#145829062
C2×#103×D432
#191372202
#191371782
#191360172
#191360162
#191360142
#191360072
#191360062
#191360052
#191360032
#191343132
#191343102
#191342902
C43×#20742
#2363343