Finite Group Databasebeta

← #25103000

Subgroups — #25103000

Order 11008.

1008 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×#14583102C211yesmaximal, characteristic
2C2×C4×#10621883C211yesmaximal, characteristic
3#19137311C211yesmaximal, characteristic, complemented
4#19136956C211yesmaximal, characteristic
5#19135516C211yesmaximal, characteristic, complemented
6#19135360C211yesmaximal, characteristic, complemented
7#19135235C211yesmaximal, characteristic, complemented
8#19135232C211yesmaximal, characteristic, complemented
9#19134931C211yesmaximal, characteristic
10#19134927C211yesmaximal, characteristic
11#19134603C211yesmaximal, characteristic
12#19134455C211yesmaximal, characteristic, complemented
13#19134426C211yesmaximal, characteristic, complemented
14C4×#13063249C211yesmaximal, characteristic, complemented
15C2×C43×#440C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C2×#13063323C2211yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic
20C2×D4×Dic43C2211yescharacteristic
21#14583102C418yescomplemented
22C4×#10621883—24no—
23C2×#13063256C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×C4×C43⋊C8C2211yescharacteristic
33#14582806C2211yescharacteristic
34#14582804C2211yescharacteristic
35#14582783—21no—
36#14582783—21no—
37#14582780—21no—
38#14582780—21no—
39#14582764C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic
43C22⋊C4×Dic43—21no—
44C22⋊C4×Dic43—21no—
45C4×C22⋊Dic43—21no—
46#14582745C2211yescharacteristic
47C2×C43⋊#95—21no—
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C22×SD16×C43C2211yescharacteristic
55C2×C4×Q8×C43C2211yescharacteristic
56C2×C4×D4×C43C2211yescharacteristic
57C43×#440—24no—
58C2×#107×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×#97×C43C2211yescharacteristic
62C22×Dic86C2311yescharacteristic
63C23×Dic43—21no—
64C23×Dic43—21no—
65C2×#10621883—22no—
66C2×#10621883—22no—
67C2×#10621883C2×C414yes—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063323—22no—
71#13063323C2×C414yescomplemented
72C4×Dic86—22no—
73C4×Dic86—22no—
74D4×Dic43—22no—
75D4×Dic43—22no—
76D4×Dic43—22no—
77D4×Dic43C2×C414yes—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43C2311yescharacteristic
91C2×C4×Dic43C2311yescharacteristic
92#13063256—22no—
93Dic43⋊C8—22no—
94Dic43⋊C8C2×C414yescomplemented
95#13063250—22no—
96#13063250C2×C414yescomplemented
97#13063249—22no—
98#13063249C2×C414yescomplemented
99#13063248—22no—
100#13063246—22no—
101C4×C43⋊C8—22no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95D411yescharacteristic
112C43⋊#95D411yescharacteristic
113C43⋊#95D411yescharacteristic
114C43⋊#95D411yescharacteristic
115C22×Q8×C43C2311yescharacteristic
116C22×D4×C43C2311yescharacteristic
117C23×C4×C43—21no—
118C2×SD16×C43—22no—
119C2×SD16×C43—22no—
120C2×SD16×C43C2×C414yes—
121C22×C8×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C4×Q8×C43—22no—
124C4×Q8×C43—22no—
125C4×D4×C43—22no—
126C4×D4×C43D414yes—
127C2×C4⋊C4×C43—21no—
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C22⋊C4×C43—21no—
131C2×C42×C43—21no—
132C2×C42×C43C2311yescharacteristic
133#107×C43—22no—
134#103×C43—22no—
135#102×C43—22no—
136#97×C43—22no—
137C24×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43C22×C412yes—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43C22×C412yes—
148C2×D4×C43C2×D412yes—
149C2×D4×C43#4112yes—
150C22×C4×C43—24no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—81no—
155C22×C4×C43—81no—
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2411yescharacteristic
159C22×Dic43—24no—
160C22×Dic43—24no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—81no—
166C22×Dic43—81no—
167C22×Dic43—81no—
168C22×Dic43—81no—
169C22×Dic43C2×D411yescharacteristic
170C22×Dic43C2×D411yescharacteristic
171C22×Dic43C2×D411yescharacteristic
172C22×Dic43C2×D411yescharacteristic
173C2×Dic86—21no—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86—21no—
178C2×Dic86C22×C412yes—
179SD16×C43—28no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43C22×C412yes—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—42no—
190C4⋊C4×C43C2×D412yes—
191C22⋊C4×C43—24no—
192C42×C43—42no—
193C42×C43C2×D412yes—
194C42×C43#4112yes—
195C22⋊Dic43—24no—
196C22⋊Dic43—24no—
197#10621883—28no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43C22×C412yes—
203C4⋊Dic43#4112yes—
204Dic43⋊C4—24no—
205Dic43⋊C4—24no—
206Dic43⋊C4—42no—
207C4×Dic43—21no—
208C4×Dic43—21no—
209C4×Dic43—42no—
210C4×Dic43—81no—
211C4×Dic43—81no—
212C4×Dic43—81no—
213C4×Dic43C22×C412yes—
214C4×Dic43#4112yes—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8C22×C412yes—
221C23×C43—22no—
222C23×C43—22no—
223C23×C43—22no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43C22×D411yescharacteristic
229Q8×C43—22no—
230Q8×C43—22no—
231Q8×C43—41no—
232Q8×C43—41no—
233D4×C43—22no—
234D4×C43—22no—
235D4×C43—22no—
236D4×C43C4×D414yes—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
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—84no—
251C2×C4×C43#12112yes—
252C2×C4×C43#12112yes—
253C2×C4×C43C23×C411yescharacteristic
254C2×C4×C43C22×D411yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—22no—
264C2×Dic43—22no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—22no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—84no—
282C2×Dic43—84no—
283C2×Dic43C4×D412yes—
284C2×Dic43C4×D412yes—
285Dic86—22no—
286Dic86—22no—
287Dic86—41no—
288Dic86—41no—
289C8×C43—22no—
290C8×C43—41no—
291C43⋊C8—22no—
292C43⋊C8—41no—
293#21514—431nomaximal, Sylow
294C22×C43—24no—
295C22×C43—42no—
296C22×C43—42no—
297C22×C43—42no—
298C22×C43—42no—
299C22×C43—42no—
300C22×C43—42no—
301C22×C43C2×C4×D411yescharacteristic
302C22×C43C2×#12111yescharacteristic
303C22×C43#52511yescharacteristic
304C22×C43#57711yescharacteristic
305C22×C43#57711yescharacteristic
306C22×C43#57711yescharacteristic
307C22×C43#57811yescharacteristic
308C4×C43—22no—
309C4×C43—22no—
310C4×C43—42no—
311C4×C43—42no—
312C4×C43—81no—
313C4×C43C2×C4×D411yescharacteristic
314C4×C43C4×#4111yescharacteristic
315C4×C43#52911yescharacteristic
316C4×C43#53211yescharacteristic
317Dic43—22no—
318Dic43—22no—
319Dic43—41no—
320Dic43—41no—
321Dic43—42no—
322Dic43—42no—
323Dic43—42no—
324Dic43—81no—
325C2×#461—431no—
326C2×#440D4311yescharacteristic
327C2×C4×SD16—431no—
328#2327—431no—
329#2275—431no—
330#1981—431no—
331#1949—431no—
332#1928—431no—
333#1927—431no—
334#1877—431no—
335#1877—431no—
336#1804—431no—
337#1768—431no—
338#1763—431no—
339C4×#103—431no—
340C2×C43—44no—
341C2×C43C4×#12111yescharacteristic
342C2×C43#294711yescharacteristic
343C2×C43#294911yescharacteristic
344C2×C43#304211yescharacteristic
345C2×C43#304611yescharacteristic
346C2×C43#312011yescharacteristic
347C2×C43#312311yescharacteristic
348C22×SD16—431no—
349C22×SD16C2×D4311yescharacteristic
350C2×C4⋊Q8—431no—
351C2×C4×Q8—431no—
352C2×C4×Q8C2×D4311yescharacteristic
353C2×C4×D4—431no—
354C2×C4×D4—431no—
355C2×C4×D4C2×D4311yescharacteristic
356#461—438no—
357#440—24no—
358C4×SD16—864no—
359C2×#107C2×D4311yescharacteristic
360C2×#106—431no—
361C2×C4⋊C8—431no—
362C2×C4⋊C8—431no—
363C2×#103—431no—
364C2×#103—431no—
365C2×#103—431no—
366C2×#103—431no—
367C2×#103—431no—
368C2×#103C2×D4311yescharacteristic
369C2×#102—431no—
370C2×#102C2×D4311yescharacteristic
371C2×#97C2×D4311yescharacteristic
372C2×C4×C8—431no—
373#391—431no—
374#391—431no—
375#387—861no—
376#387—861no—
377#387—861no—
378#387—861no—
379#382—431no—
380C4×C4⋊C4—431no—
381C4×C4⋊C4—431no—
382C4×C4⋊C4—431no—
383C4×C22⋊C4—861no—
384C4×C22⋊C4—861no—
385C4×C22⋊C4—861no—
386#376—431no—
387C2×#95—861no—
388#340—431no—
389#340—431no—
390#340—431no—
391#340—431no—
392#336—431no—
393#336—431no—
394C43#2151411yescharacteristic, complemented, Sylow
395C22×Q8—431no—
396C22×Q8C22×D4311yescharacteristic
397C22×D4C22×D4311yescharacteristic
398C23×C4—21no—
399C23×C4—861no—
400C23×C4—861no—
401C2×SD16—22no—
402C2×SD16—22no—
403C2×SD16—434no—
404C2×SD16—862no—
405C2×SD16—862no—
406C2×SD16C4×D4314yes—
407C22×C8—431no—
408C22×C8—431no—
409C22×C8C22×D4311yescharacteristic
410C22×C8C22×D4311yescharacteristic
411C4⋊Q8—434no—
412C4⋊Q8—862no—
413C4×Q8—22no—
414C4×Q8—22no—
415C4×Q8—862no—
416C4×Q8—862no—
417C4×D4—22no—
418C4×D4—434no—
419C4×D4—862no—
420C4×D4—862no—
421C4×D4—862no—
422C4×D4C22⋊D4314yes—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4C22×D4311yescharacteristic
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C42—21no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—861no—
439C2×C42—861no—
440C2×C42—861no—
441C2×C42—861no—
442C2×C42C22×D4311yescharacteristic
443#107—22no—
444#106—862no—
445C4⋊C8—434no—
446C4⋊C8—862no—
447#103—22no—
448#103—434no—
449#103—434no—
450#103—862no—
451#103—862no—
452#103—862no—
453#102—22no—
454#102—862no—
455#97—22no—
456C4×C8—862no—
457#95—431no—
458#95—431no—
459#95—431no—
460#95—431no—
461#95—861no—
462#95—861no—
463#95—861no—
464#95—861no—
465#95—861no—
466#95—861no—
467#95—861no—
468#95—861no—
469#95—861no—
470C24—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—432no—
477C2×Q8—861no—
478C2×Q8—861no—
479C2×Q8—861no—
480C2×Q8—861no—
481C2×Q8—861no—
482C2×Q8C2×C4×D4312yes—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4C2×C4×D4312yes—
487C2×D4#1062189812yes—
488C2×D4C2×C22⋊D4312yes—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—24no—
492C22×C4—21no—
493C22×C4—81no—
494C22×C4—81no—
495C22×C4—431no—
496C22×C4—431no—
497C22×C4—431no—
498C22×C4—431no—
499C22×C4—864no—
500C22×C4—864no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—3441no—
506C22×C4—3441no—
507C22×C4—3441no—
508C22×C4—3441no—
509C22×C4D4×D4311yescharacteristic
510C22×C4D4×D4311yescharacteristic
511C22×C4C23×D4311yescharacteristic
512SD16—28no—
513SD16—868no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—432no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8—861no—
524C2×C8—861no—
525C2×C8C2×C4×D4312yes—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—42no—
530C4⋊C4—432no—
531C4⋊C4—432no—
532C4⋊C4—864no—
533C4⋊C4—864no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—1722no—
539C4⋊C4C2×C22⋊D4312yes—
540C22⋊C4—24no—
541C22⋊C4—864no—
542C22⋊C4—864no—
543C42—42no—
544C42—432no—
545C42—432no—
546C42—861no—
547C42—861no—
548C42—3441no—
549C42—3441no—
550C42—3441no—
551C42—1722no—
552C42#1062190012yes—
553C42C2×C22⋊D4312yes—
554C23—22no—
555C23—22no—
556C23—22no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23C2×D4×D4311yescharacteristic
562Q8—22no—
563Q8—22no—
564Q8—41no—
565Q8—41no—
566Q8—862no—
567Q8—862no—
568Q8—1721no—
569Q8—1721no—
570D4—22no—
571D4—22no—
572D4—22no—
573D4C4×C22⋊D4314yes—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—84no—
588C2×C4—432no—
589C2×C4—432no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—862no—
595C2×C4—862no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—862no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—3444no—
604C2×C4—3444no—
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#1306329712yes—
615C2×C4#1306329712yes—
616C2×C4C22×C4×D4311yescharacteristic
617C2×C4C22×C22⋊D4311yescharacteristic
618C2×C4#41×D4311yescharacteristic
619C2×C4#41×D4311yescharacteristic
620C2×C4C2×#1062190011yescharacteristic
621C2×C4C2×#1062189811yescharacteristic
622C8—22no—
623C8—41no—
624C8—862no—
625C8—1721no—
626C22—24no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—42no—
633C22C4×D4×D4311yescharacteristic
634C22C2×#1306329711yescharacteristic
635C22#1458340811yescharacteristic
636C22#1458370811yescharacteristic
637C22#1458370911yescharacteristic
638C22#1458370911yescharacteristic
639C22#1458371511yescharacteristic
640C4—22no—
641C4—22no—
642C4—42no—
643C4—42no—
644C4—81no—
645C4—862no—
646C4—862no—
647C4—3441no—
648C4—1722no—
649C4—1722no—
650C4—1721no—
651C4—1721no—
652C4—1722no—
653C4C2×C4×C22⋊D4311yescharacteristic
654C4C4×#1062190011yescharacteristic
655C4#1458342911yescharacteristic
656C4#1458344511yescharacteristic
657C2—44no—
658C2C4×#1306329711yescharacteristic
659C2#1914343511yescharacteristic
660C2#1914345111yescharacteristic
661C2#1914410911yescharacteristic
662C2#1914414911yescharacteristic
663C2#1914481311yescharacteristic
664C2#1914484611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#440C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenterC2×#440D43
hypocenterC43#21514
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
3. #19137311C2semidirect
5. #19135516C2semidirect
6. #19135360C2semidirect
7. #19135235C2semidirect
8. #19135232C2semidirect
12. #19134455C2semidirect
13. #19134426C2semidirect
14. C4×#13063249C2semidirect
21. #14583102C4semidirect
71. #13063323C2×C4semidirect
94. Dic43⋊C8C2×C4semidirect
96. #13063250C2×C4semidirect
98. #13063249C2×C4semidirect
394. C43#21514semidirect

Maximal subgroups

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

subgroupindex
C2×#145831022
C2×C4×#106218832
#191373112
#191369562
#191355162
#191353602
#191352352
#191352322
#191349312
#191349272
#191346032
#191344552
#191344262
C4×#130632492
C2×C43×#4402
#2151443