Finite Group Databasebeta

← #25124638

Subgroups — #25124638

Order 11008.

1154 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583455C211yesmaximal, characteristic
2C2×#14582936C211yesmaximal, characteristic
3C2×#14582934C211yesmaximal, characteristic
4#19137076C211yesmaximal, characteristic
5#19135934C211yesmaximal, characteristic, complemented
6#19135933C211yesmaximal, characteristic, complemented
7#19135930C211yesmaximal, characteristic, complemented
8#19135927C211yesmaximal, characteristic, complemented
9#19135926C211yesmaximal, characteristic, complemented
10#19135922C211yesmaximal, characteristic, complemented
11#19135921C211yesmaximal, characteristic, complemented
12#19134310C211yesmaximal, characteristic
13#19134310C211yesmaximal, characteristic
14#336×D43C211yesmaximal, characteristic
15C43×#2059C211yesmaximal, characteristic, complemented
16C22×C8×D43C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18#14583455—24no—
19#14583455—24no—
20C2×#13063324C2211yescharacteristic
21C2×#13063324C2211yescharacteristic
22C2×#13063317C2211yescharacteristic
23C2×#13063303—21no—
24C2×#13063303—21no—
25C2×#13063290—21no—
26C2×#13063290—21no—
27C2×#13063283C2211yescharacteristic
28C2×#13063283C2211yescharacteristic
29C2×#13063283C2211yescharacteristic
30C2×#13063283C2211yescharacteristic
31C2×C42×D43C2211yescharacteristic
32#14582936—24no—
33#14582934—24no—
34C2×#13063259C2211yescharacteristic
35C2×#13063258C2211yescharacteristic
36C2×#13063258C2211yescharacteristic
37C2×#13063257C2211yescharacteristic
38C2×#13063256C2211yescharacteristic
39C2×#13063256C2211yescharacteristic
40#14582798C2211yescharacteristic
41#14582797C2211yescharacteristic
42#14582795C2211yescharacteristic
43#14582773—21no—
44#14582770—21no—
45C4⋊C4×Dic43—21no—
46#14582750—21no—
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582654C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C2×#125×C43C2211yescharacteristic
57C2×#107×C43C2211yescharacteristic
58C2×#106×C43C2211yescharacteristic
59C43×#389C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86—21no—
65C22×C4×D43D411yescharacteristic
66C22×C4×D43D411yescharacteristic
67C22×C4×D43C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C2×C8×D43—22no—
71C2×C8×D43—22no—
72C2×C8×D43—22no—
73C2×C8×D43—22no—
74C2×C8×D43Q814yescomplemented
75C2×C8×D43Q814yescomplemented
76#13063324—22no—
77#13063324—22no—
78#13063324—22no—
79#13063324—22no—
80#13063317—22no—
81#13063317—22no—
82#13063303—28no—
83#13063303—28no—
84#13063290—28no—
85#13063290—28no—
86#13063283—22no—
87#13063283—22no—
88#13063283—22no—
89#13063283—22no—
90#13063283—22no—
91#13063283D414yes—
92#13063283D414yes—
93#13063283Q814yescomplemented
94C2×C4⋊Dic43—21no—
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×C4×Dic43—21no—
110C2×C4×Dic43—21no—
111C2×C4×Dic43—21no—
112C2×C4×Dic43—21no—
113C2×C4×Dic43D411yescharacteristic
114C2×C4×Dic43D411yescharacteristic
115C2×C4×Dic43C2311yescharacteristic
116C42×D43—22no—
117C42×D43—22no—
118#13063259—22no—
119#13063258—22no—
120#13063258—22no—
121#13063257—22no—
122#13063256—22no—
123#13063256—22no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C22×C8×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129#125×C43—22no—
130#125×C43—22no—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C42×C43C2311yescharacteristic
139#107×C43—22no—
140#106×C43—22no—
141#95×C43—21no—
142C23×D43C2×D411yescharacteristic
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2411yescharacteristic
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157C2×C4×D43—22no—
158C2×C4×D43—22no—
159C2×C4×D43—22no—
160C2×C4×D43—22no—
161C2×C4×D43—41no—
162C2×C4×D43—41no—
163C2×C4×D43C2×D412yes—
164C2×C4×D43C2×D412yes—
165C2×C4×D43C2×Q812yes—
166C2×C4×D43C2×Q812yes—
167C2×C4×D43C2×Q812yes—
168C2×C4×D43#4112yes—
169C2×Dic86—24no—
170C2×Dic86—24no—
171C2×Dic86—42no—
172C2×Dic86—42no—
173C2×Dic86—42no—
174C2×Dic86—42no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43C2×Q812yes—
180C2×C8×C43C2×Q812yes—
181C4⋊C4×C43—24no—
182C4⋊C4×C43—24no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—42no—
189C4⋊C4×C43C2×D412yes—
190C4⋊C4×C43C2×D412yes—
191C4⋊C4×C43C2×Q812yes—
192C42×C43—21no—
193C42×C43—21no—
194(C2×D43)⋊C4—24no—
195(C2×D43)⋊C4—24no—
196(C2×D43)⋊C4—24no—
197(C2×D43)⋊C4—42no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—42no—
204C4⋊Dic43C2×D412yes—
205C4⋊Dic43C2×D412yes—
206C4⋊Dic43C2×Q812yes—
207Dic43⋊C4—24no—
208Dic43⋊C4—24no—
209Dic43⋊C4—24no—
210Dic43⋊C4—24no—
211Dic43⋊C4—42no—
212Dic43⋊C4—42no—
213C4×Dic43—21no—
214C4×Dic43—21no—
215C4×Dic43—22no—
216C4×Dic43—22no—
217C4×Dic43—24no—
218C4×Dic43—24no—
219C4×Dic43—24no—
220C4×Dic43—42no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8C2×Q812yes—
226C2×C43⋊C8C2×Q812yes—
227C8×D43—28no—
228C8×D43—28no—
229C23×C43C22×D411yescharacteristic
230C22×D43—21no—
231C22×D43—21no—
232C22×D43—21no—
233C22×D43—21no—
234C22×D43#12012yes—
235C22×D43C22⋊Q812yes—
236C22×D43C4⋊Q812yes—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
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—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C22×Q811yescharacteristic
258C2×C4×C43C22×Q811yescharacteristic
259C2×C4×C43C22×Q811yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—22no—
266C2×Dic43—22no—
267C2×Dic43—22no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43#12012yes—
278C2×Dic43C22⋊Q812yes—
279C2×Dic43C4⋊Q812yes—
280C2×Dic43#13512yes—
281C2×Dic43#13512yes—
282C4×D43—44no—
283C4×D43—44no—
284C4×D43C22⋊Q814yes—
285C4×D43C22⋊Q814yes—
286C4×D43C4⋊Q814yes—
287C4×D43C4⋊Q814yes—
288Dic86—48no—
289Dic86—48no—
290C8×C43—22no—
291C8×C43—22no—
292C43⋊C8—22no—
293C43⋊C8—22no—
294#23551—431nomaximal, Sylow
295C22×C43C2×#12011yescharacteristic
296C22×C43C2×C22⋊Q811yescharacteristic
297C22×C43C2×C4⋊Q811yescharacteristic
298C22×C43C2×#13511yescharacteristic
299C22×C43C2×#13511yescharacteristic
300C22×C43#57511yescharacteristic
301C22×C43#57511yescharacteristic
302C2×D43—22no—
303C2×D43—22no—
304C2×D43—22no—
305C2×D43—22no—
306C2×D43—22no—
307C2×D43—22no—
308C2×D43#39514yes—
309C4×C43—42no—
310C4×C43—42no—
311C4×C43—42no—
312C4×C43—41no—
313C4×C43—41no—
314C4×C43—81no—
315C4×C43C2×C22⋊Q811yescharacteristic
316C4×C43C2×C22⋊Q811yescharacteristic
317C4×C43C2×C4⋊Q811yescharacteristic
318C4×C43C2×C4⋊Q811yescharacteristic
319Dic43—22no—
320Dic43—22no—
321Dic43—42no—
322Dic43—42no—
323Dic43—42no—
324Dic43—81no—
325Dic43#39514yes—
326C2×#533—431no—
327C2×#427—431no—
328C2×#427—431no—
329#2296—431no—
330#2059—431no—
331#2059—431no—
332#2059—431no—
333#2059D4311yescharacteristic, complemented
334#2058—431no—
335#2058—431no—
336#2057—431no—
337#2057—431no—
338#1735—431no—
339#1735—431no—
340C2×#336—431no—
341C2×C43C2×#39511yescharacteristic
342C2×C43#300211yescharacteristic
343C2×C43#300211yescharacteristic
344C2×C43#307611yescharacteristic
345C2×C43#307611yescharacteristic
346C2×C43#316011yescharacteristic
347C2×C43#316211yescharacteristic
348D43—24no—
349C23×C8—431no—
350C23×C8—431no—
351#533—864no—
352#533—864no—
353C2×C4⋊Q8—431no—
354C2×C4⋊Q8—431no—
355C2×#125—431no—
356C2×#125C2×D4311yescharacteristic
357C2×C22⋊Q8—861no—
358C2×C22⋊Q8—861no—
359C2×C4×Q8—861no—
360C2×C4×Q8—861no—
361C2×#117—431no—
362C2×#117—431no—
363C2×#117—431no—
364C2×#117—431no—
365C22×C42—431no—
366#427—864no—
367#427—864no—
368C2×#107—431no—
369C2×#107—431no—
370C2×#107—431no—
371C2×#107C2×D4311yescharacteristic
372C2×#106—431no—
373C2×#106—431no—
374C2×#106—431no—
375C2×#106C2×D4311yescharacteristic
376#389—431no—
377#389—431no—
378#389—431no—
379#389C2×D4311yescharacteristic
380#385—861no—
381#385—861no—
382C4×C4⋊C4—861no—
383C4×C4⋊C4—861no—
384#340—431no—
385#340—431no—
386#340—431no—
387#340—431no—
388#340—431no—
389#340—431no—
390#340C2×D4311yescharacteristic
391#340C2×D4311yescharacteristic
392#336—431no—
393#336—431no—
394#336—431no—
395#336C2×D4311yescharacteristic
396C43#2355111yescharacteristic, complemented, Sylow
397C22×Q8—861no—
398C22×Q8—861no—
399C23×C4—431no—
400C23×C4—431no—
401C23×C4—431no—
402C22×C8—431no—
403C22×C8—431no—
404C22×C8—434no—
405C22×C8—434no—
406C22×C8—862no—
407C22×C8—862no—
408C22×C8—862no—
409C22×C8—862no—
410C22×C8C22×D4311yescharacteristic
411C22×C8C22×D4311yescharacteristic
412C4⋊Q8—862no—
413C4⋊Q8—862no—
414C4⋊Q8—862no—
415C4⋊Q8—862no—
416#125—22no—
417#125—22no—
418#125—862no—
419#125—862no—
420C22⋊Q8—868no—
421C22⋊Q8—868no—
422C4×Q8—868no—
423C4×Q8—868no—
424#117—434no—
425#117—434no—
426#117—434no—
427#117—862no—
428#117—862no—
429#117—862no—
430#117—862no—
431#117—862no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—431no—
436C2×C4⋊C4—431no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—861no—
440C2×C4⋊C4—861no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4—861no—
446C2×C4⋊C4C22×D4311yescharacteristic
447C2×C4⋊C4C22×D4311yescharacteristic
448C2×C4⋊C4C22×D4311yescharacteristic
449C2×C4⋊C4C22×D4311yescharacteristic
450C2×C22⋊C4—861no—
451C2×C22⋊C4—861no—
452C2×C22⋊C4—861no—
453C2×C22⋊C4—861no—
454C2×C42—431no—
455C2×C42—431no—
456C2×C42—431no—
457C2×C42—862no—
458C2×C42—862no—
459C2×C42—861no—
460C2×C42—861no—
461C2×C42—861no—
462C2×C42—861no—
463C2×C42C22×D4311yescharacteristic
464#107—22no—
465#107—862no—
466#107—862no—
467#107—862no—
468#106—22no—
469#106—862no—
470#106—862no—
471#106—862no—
472#95—21no—
473#95—861no—
474#95—861no—
475#95—861no—
476C24—431no—
477C2×Q8—864no—
478C2×Q8—864no—
479C2×Q8—1722no—
480C2×Q8—1722no—
481C2×Q8—1722no—
482C2×Q8—1722no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—431no—
488C22×C4—432no—
489C22×C4—432no—
490C22×C4—432no—
491C22×C4—432no—
492C22×C4—432no—
493C22×C4—432no—
494C22×C4—431no—
495C22×C4—431no—
496C22×C4—862no—
497C22×C4—862no—
498C22×C4—862no—
499C22×C4—862no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—1721no—
505C22×C4—1721no—
506C22×C4D4×D4311yescharacteristic
507C22×C4D4×D4311yescharacteristic
508C22×C4C23×D4311yescharacteristic
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—432no—
514C2×C8—432no—
515C2×C8—868no—
516C2×C8—868no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8Q8×D4312yes—
522C2×C8Q8×D4312yes—
523C4⋊C4—24no—
524C4⋊C4—24no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—42no—
531C4⋊C4—432no—
532C4⋊C4—432no—
533C4⋊C4—432no—
534C4⋊C4—864no—
535C4⋊C4—864no—
536C4⋊C4—864no—
537C4⋊C4—864no—
538C4⋊C4—861no—
539C4⋊C4—861no—
540C4⋊C4—861no—
541C4⋊C4—861no—
542C4⋊C4—861no—
543C4⋊C4—1722no—
544C4⋊C4—1722no—
545C4⋊C4—1722no—
546C4⋊C4D4×D4312yes—
547C4⋊C4D4×D4312yes—
548C4⋊C4Q8×D4312yes—
549C22⋊C4—864no—
550C22⋊C4—864no—
551C22⋊C4—864no—
552C22⋊C4—1722no—
553C42—21no—
554C42—21no—
555C42—862no—
556C42—862no—
557C42—864no—
558C42—864no—
559C42—864no—
560C42—861no—
561C42—861no—
562C42—1722no—
563C23—432no—
564C23—432no—
565C23—432no—
566C23—861no—
567C23—861no—
568C23—861no—
569C23—861no—
570C23C2×D4×D4311yescharacteristic
571Q8—1728no—
572Q8—1728no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—432no—
592C2×C4—432no—
593C2×C4—432no—
594C2×C4—434no—
595C2×C4—434no—
596C2×C4—434no—
597C2×C4—434no—
598C2×C4—432no—
599C2×C4—432no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—862no—
605C2×C4—862no—
606C2×C4—862no—
607C2×C4—1724no—
608C2×C4—1724no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4C2×D4×D4311yescharacteristic
619C2×C4C2×D4×D4311yescharacteristic
620C2×C4C2×Q8×D4311yescharacteristic
621C2×C4C2×Q8×D4311yescharacteristic
622C2×C4C2×Q8×D4311yescharacteristic
623C2×C4#41×D4311yescharacteristic
624C8—22no—
625C8—22no—
626C8—862no—
627C8—862no—
628C22—434no—
629C22—862no—
630C22—862no—
631C22—862no—
632C22—862no—
633C22—862no—
634C22—862no—
635C22#120×D4311yescharacteristic
636C22C22⋊Q8×D4311yescharacteristic
637C22C4⋊Q8×D4311yescharacteristic
638C22#135×D4311yescharacteristic
639C22#135×D4311yescharacteristic
640C22#1458369511yescharacteristic
641C22#1458369811yescharacteristic
642C4—41no—
643C4—42no—
644C4—41no—
645C4—42no—
646C4—42no—
647C4—81no—
648C4—434no—
649C4—862no—
650C4—862no—
651C4—3441no—
652C4—1722no—
653C4—1722no—
654C4—1722no—
655C4C22⋊Q8×D4311yescharacteristic
656C4C22⋊Q8×D4311yescharacteristic
657C4C4⋊Q8×D4311yescharacteristic
658C4C4⋊Q8×D4311yescharacteristic
659C2—864no—
660C2#395×D4311yescharacteristic
661C2#1914381011yescharacteristic
662C2#1914381611yescharacteristic
663C2#1914438011yescharacteristic
664C2#1914438211yescharacteristic
665C2#1914510811yescharacteristic
666C2#1914511611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2059C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#2059D43
hypocenterC43#23551
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2059

Complements

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

NH ≅ G/Ntype
5. #19135934C2semidirect
6. #19135933C2semidirect
7. #19135930C2semidirect
8. #19135927C2semidirect
9. #19135926C2semidirect
10. #19135922C2semidirect
11. #19135921C2semidirect
15. C43×#2059C2semidirect
74. C2×C8×D43Q8semidirect
75. C2×C8×D43Q8semidirect
93. #13063283Q8semidirect
333. #2059D43semidirect
396. C43#23551semidirect

Maximal subgroups

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

subgroupindex
C2×#145834552
C2×#145829362
C2×#145829342
#191370762
#191359342
#191359332
#191359302
#191359272
#191359262
#191359222
#191359212
#191343102
#336×D432
C43×#20592
#2355143