Finite Group Databasebeta

← #25064069

Subgroups — #25064069

Order 11008.

992 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583451C211yesmaximal, characteristic
2#19143224C211yesmaximal, characteristic
3#19136986C211yesmaximal, characteristic
4#19133157C214yesmaximal, complemented
5#19133129C211yesmaximal, characteristic
6#19133128C211yesmaximal, characteristic
7#19133127C211yesmaximal, characteristic
8#19133105C214yesmaximal, complemented
9C43×#1511C211yesmaximal, characteristic
10#14583451—21no—
11#14583451—21no—
12#14583451—21no—
13#14583451—21no—
14#14583451C412yescomplemented
15#14583451C412yescomplemented
16#14583451C2212yes—
17#14583451C2212yes—
18C2×#13063324C411yescharacteristic, complemented
19C2×#13063323C411yescharacteristic, complemented
20C2×#13063315—21no—
21C2×#13063304C2211yescharacteristic
22C2×#13063302—21no—
23C2×Q8×Dic43C411yescharacteristic, complemented
24C2×#13063290—21no—
25C2×#13063290C411yescharacteristic, complemented
26C2×#13063281—21no—
27C22×C4×Dic43C2211yescharacteristic
28#14582953—21no—
29#14582953C2212yes—
30#14582949—21no—
31#14582949C2212yes—
32#14582922—21no—
33#14582863C2211yescharacteristic
34M16×Dic43—21no—
35#14582766—21no—
36#14582763C2212yes—
37#14582762C2211yescharacteristic
38#14582757—21no—
39#14582750—21no—
40C22⋊C4×Dic43—21no—
41#14582744C2212yes—
42#14582637C2214yes—
43#14582636C2214yes—
44#14582635C2214yes—
45C2×C22⋊Q8×C43C2211yescharacteristic
46C43×#407C2211yescharacteristic
47C43×#381C2211yescharacteristic
48C43×#328C2214yes—
49C22×Dic86—21no—
50C22×Dic86C2×C411yescharacteristic
51C23×Dic43D411yescharacteristic
52C23×Dic43D411yescharacteristic
53C2×#10621877—21no—
54#13063324—21no—
55#13063324—21no—
56#13063324C2×C412yes—
57#13063324C2×C412yes—
58#13063323—21no—
59#13063323—21no—
60#13063323C2×C412yes—
61#13063323C2×C412yes—
62#13063315—22no—
63#13063315—22no—
64#13063315—22no—
65#13063315—22no—
66#13063304—21no—
67#13063304—21no—
68#13063304C2×C412yes—
69#13063304C2312yes—
70#13063302—22no—
71#13063302—22no—
72#13063302—22no—
73#13063302—22no—
74Q8×Dic43—21no—
75Q8×Dic43—21no—
76Q8×Dic43C2×C412yes—
77Q8×Dic43C2×C412yes—
78#13063290—22no—
79#13063290—22no—
80#13063290—21no—
81#13063290—21no—
82#13063290—22no—
83#13063290—22no—
84#13063290C2×C412yes—
85#13063290C2×C412yes—
86#13063281—22no—
87#13063281—22no—
88#13063281—22no—
89#13063281—22no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43C2×C411yescharacteristic
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—22no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43—22no—
103C2×C4×Dic43C2×C411yescharacteristic
104C2×C4×Dic43C2×C411yescharacteristic
105C2×C4×Dic43C2×C411yescharacteristic
106C2×C4×Dic43C2×C411yescharacteristic
107C2×C4×Dic43D411yescharacteristic
108C2×C4×Dic43D411yescharacteristic
109C2×C4×Dic43D411yescharacteristic
110C2×C4×Dic43D411yescharacteristic
111C2×C4×Dic43D411yescharacteristic
112C2×C4×Dic43D411yescharacteristic
113C2×C4×Dic43C2311yescharacteristic
114C2×C4×Dic43C2311yescharacteristic
115Dic43⋊C8—22no—
116Dic43⋊C8—22no—
117C22⋊(C43⋊C8)—21no—
118C22⋊(C43⋊C8)C2312yes—
119#13063235—22no—
120C8×Dic43—22no—
121C43⋊#95—21no—
122C43⋊#95—22no—
123C43⋊#95—22no—
124C43⋊#95C2312yes—
125C22×Q8×C43C2×C411yescharacteristic
126C23×C4×C43C2311yescharacteristic
127C2×M16×C43—21no—
128C22⋊Q8×C43—21no—
129C22⋊Q8×C43—21no—
130C22⋊Q8×C43C2×C412yes—
131C22⋊Q8×C43C2312yes—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43C2×C411yescharacteristic
134C2×C22⋊C4×C43—21no—
135C2×C22⋊C4×C43—21no—
136C22⋊C8×C43—21no—
137C22⋊C8×C43C2312yes—
138#95×C43—21no—
139#95×C43C2312yes—
140C24×C43C2×D411yescharacteristic
141C2×Q8×C43—21no—
142C2×Q8×C43—42no—
143C2×Q8×C43C22×C412yes—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—22no—
147C22×C4×C43—42no—
148C22×C4×C43C22×C411yescharacteristic
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2411yescharacteristic
154C22×Dic43—24no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—22no—
158C22×Dic43—42no—
159C22×Dic43C22⋊C411yescharacteristic
160C22×Dic43C22⋊C411yescharacteristic
161C22×Dic43C22⋊C411yescharacteristic
162C22×Dic43C22⋊C411yescharacteristic
163C22×Dic43C22⋊C411yescharacteristic
164C22×Dic43C22⋊C411yescharacteristic
165C22×Dic43C22⋊C411yescharacteristic
166C22×Dic43C22⋊C411yescharacteristic
167C22×Dic43C2×D411yescharacteristic
168C22×Dic43C2×D411yescharacteristic
169C22×Dic43C2×D411yescharacteristic
170C22×Dic43C2×D411yescharacteristic
171C2×Dic86—21no—
172C2×Dic86—22no—
173C2×Dic86—22no—
174C2×Dic86—44no—
175C2×Dic86—42no—
176C2×Dic86C22×C412yes—
177M16×C43—42no—
178C2×C8×C43—22no—
179C4⋊C4×C43—22no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—22no—
182C4⋊C4×C43C22×C412yes—
183C22⋊C4×C43—22no—
184C22⋊C4×C43—22no—
185C22⋊C4×C43—42no—
186C22⋊Dic43—22no—
187C22⋊Dic43—22no—
188C22⋊Dic43—42no—
189C4⋊Dic43—21no—
190C4⋊Dic43—22no—
191C4⋊Dic43—22no—
192C4⋊Dic43C22×C412yes—
193Dic43⋊C4—22no—
194Dic43⋊C4—22no—
195Dic43⋊C4—22no—
196Dic43⋊C4—22no—
197Dic43⋊C4—22no—
198Dic43⋊C4—22no—
199Dic43⋊C4—22no—
200Dic43⋊C4—22no—
201Dic43⋊C4—22no—
202Dic43⋊C4—22no—
203Dic43⋊C4—44no—
204C4×Dic43—22no—
205C4×Dic43—22no—
206C4×Dic43—22no—
207C4×Dic43—22no—
208C4×Dic43—44no—
209C4×Dic43C22⋊C411yescharacteristic
210C4×Dic43C22⋊C411yescharacteristic
211C4×Dic43C22⋊C411yescharacteristic
212C4×Dic43C22⋊C411yescharacteristic
213C4×Dic43C22⋊C411yescharacteristic
214C4×Dic43C22⋊C411yescharacteristic
215C4×Dic43C22⋊C411yescharacteristic
216C4×Dic43C22⋊C411yescharacteristic
217C4×Dic43C22×C411yescharacteristic
218C4×Dic43C22×C411yescharacteristic
219C4×Dic43C22×C411yescharacteristic
220C4×Dic43C22×C411yescharacteristic
221C4×Dic43C2×D411yescharacteristic
222C4×Dic43C2×D411yescharacteristic
223C4×Dic43C2×D411yescharacteristic
224C4×Dic43C2×D411yescharacteristic
225#10621877—42no—
226C2×C43⋊C8—22no—
227C23×C43—22no—
228C23×C43—22no—
229C23×C43—41no—
230C23×C43C2×C22⋊C411yescharacteristic
231C23×C43C2×C22⋊C411yescharacteristic
232C23×C43C22×D411yescharacteristic
233Q8×C43—42no—
234Q8×C43—42no—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—42no—
244C2×C4×C43—42no—
245C2×C4×C43—42no—
246C2×C4×C43—42no—
247C2×C4×C43—42no—
248C2×C4×C43C2×C22⋊C411yescharacteristic
249C2×C4×C43C2×C22⋊C411yescharacteristic
250C2×C4×C43C23×C411yescharacteristic
251C2×C4×C43C22×D411yescharacteristic
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—22no—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—42no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43—42no—
269C2×Dic43—42no—
270C2×Dic43C2×C22⋊C411yescharacteristic
271C2×Dic43C2×C22⋊C411yescharacteristic
272C2×Dic43C2×C22⋊C411yescharacteristic
273C2×Dic43C2×C22⋊C411yescharacteristic
274C2×Dic43C2×C22⋊C411yescharacteristic
275C2×Dic43C2×C22⋊C411yescharacteristic
276C2×Dic43C2×C22⋊C411yescharacteristic
277C2×Dic43C2×C22⋊C411yescharacteristic
278C2×Dic43#13714yes—
279Dic86—44no—
280Dic86—42no—
281Dic86—44no—
282Dic86—42no—
283C8×C43—42no—
284C43⋊C8—42no—
285#17590—431nomaximal, Sylow
286C22×C43—21no—
287C22×C43—21no—
288C22×C43—21no—
289C22×C43—21no—
290C22×C43—21no—
291C22×C43—21no—
292C22×C43—21no—
293C22×C43—44no—
294C22×C43#41012yes—
295C22×C43C22×C22⋊C411yescharacteristic
296C22×C43C2×#13712yes—
297C4×C43—21no—
298C4×C43—21no—
299C4×C43—21no—
300C4×C43—21no—
301C4×C43—42no—
302C4×C43—42no—
303C4×C43—82no—
304Dic43—21no—
305Dic43—21no—
306Dic43—21no—
307Dic43—21no—
308Dic43—21no—
309Dic43—42no—
310Dic43—42no—
311Dic43—82no—
312Dic43#41912yes—
313Dic43#41912yes—
314Dic43#42112yes—
315C2×#533—431no—
316#2920—431no—
317#2283—431no—
318#1518—434no—
319#1511—431no—
320#1511—431no—
321#1511—431no—
322#1511D4311yescharacteristic
323#1506—434no—
324C2×C43—22no—
325C2×C43—22no—
326C2×C43—41no—
327C2×C43C2×#41011yescharacteristic
328C2×C43C2×#41911yescharacteristic
329C2×C43C2×#42111yescharacteristic
330#533—432no—
331#533—432no—
332#533—432no—
333#533—432no—
334#533—861no—
335#533—861no—
336#533—861no—
337#533—861no—
338C2×C4⋊Q8—431no—
339C2×C4⋊Q8—431no—
340C2×#125—861no—
341C2×C22⋊Q8—431no—
342C2×C22⋊Q8—861no—
343C2×C22⋊Q8C2×D4311yescharacteristic
344C2×C4×Q8—431no—
345C2×C4×Q8—431no—
346C2×C4×Q8—861no—
347C2×#117—861no—
348C22×C42—431no—
349#432—432no—
350#432—861no—
351#431—432no—
352#431—861no—
353#423—861no—
354#407—431no—
355#407C2×D4311yescharacteristic
356C4×M16—861no—
357#383—861no—
358#382—432no—
359#381—431no—
360#381C2×D4311yescharacteristic
361#380—861no—
362C4×C4⋊C4—861no—
363C4×C22⋊C4—861no—
364#376—432no—
365#328—434no—
366#328—434no—
367#328—434no—
368#328C2×D4314yes—
369C43#1759011yescharacteristic, complemented, Sylow
370C22×Q8—431no—
371C22×Q8—861no—
372C22×Q8C4×D4311yescharacteristic
373C23×C4—431no—
374C23×C4—431no—
375C23×C4C22×D4311yescharacteristic
376C2×M16—21no—
377C2×M16—861no—
378C4⋊Q8—432no—
379C4⋊Q8—432no—
380C4⋊Q8—432no—
381C4⋊Q8—432no—
382C4⋊Q8—861no—
383C4⋊Q8—861no—
384C4⋊Q8—861no—
385C4⋊Q8—861no—
386#125—862no—
387#125—862no—
388#125—862no—
389#125—862no—
390C22⋊Q8—21no—
391C22⋊Q8—21no—
392C22⋊Q8—432no—
393C22⋊Q8—432no—
394C22⋊Q8—862no—
395C22⋊Q8—862no—
396C22⋊Q8—862no—
397C22⋊Q8—862no—
398C22⋊Q8—861no—
399C22⋊Q8—861no—
400C22⋊Q8C4×D4312yes—
401C22⋊Q8C22×D4312yes—
402C4×Q8—432no—
403C4×Q8—432no—
404C4×Q8—432no—
405C4×Q8—432no—
406C4×Q8—861no—
407C4×Q8—861no—
408C4×Q8—862no—
409C4×Q8—862no—
410C4×Q8—862no—
411C4×Q8—862no—
412C4×Q8—861no—
413C4×Q8—861no—
414#117—862no—
415#117—862no—
416#117—862no—
417#117—862no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—862no—
427C2×C4⋊C4C4×D4311yescharacteristic
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C42—431no—
433C2×C42—431no—
434C2×C42—431no—
435C2×C42—431no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—431no—
439C2×C42—431no—
440C2×C42—431no—
441C2×C42—431no—
442C2×C42—431no—
443C2×C42—431no—
444C2×C42—861no—
445C2×C42—861no—
446C2×C42—862no—
447C4⋊C8—862no—
448C4⋊C8—862no—
449C22⋊C8—21no—
450C22⋊C8—432no—
451C22⋊C8—861no—
452C22⋊C8C22×D4312yes—
453#97—862no—
454C4×C8—862no—
455#95—21no—
456#95—432no—
457#95—862no—
458#95—862no—
459#95—861no—
460#95C22×D4312yes—
461C24D4×D4311yescharacteristic
462C2×Q8—21no—
463C2×Q8—42no—
464C2×Q8—432no—
465C2×Q8—862no—
466C2×Q8—862no—
467C2×Q8—861no—
468C2×Q8—1722no—
469C2×Q8—1724no—
470C2×Q8C2×C4×D4312yes—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—42no—
475C22×C4—431no—
476C22×C4—431no—
477C22×C4—431no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—864no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—862no—
491C22×C4—1722no—
492C22×C4C2×C4×D4311yescharacteristic
493C22×C4C2×C4×D4311yescharacteristic
494C22×C4D4×D4311yescharacteristic
495C22×C4D4×D4311yescharacteristic
496C22×C4D4×D4311yescharacteristic
497C22×C4C23×D4311yescharacteristic
498M16—42no—
499M16—1722no—
500C2×C8—22no—
501C2×C8—862no—
502C4⋊C4—22no—
503C4⋊C4—21no—
504C4⋊C4—22no—
505C4⋊C4—432no—
506C4⋊C4—862no—
507C4⋊C4—862no—
508C4⋊C4—862no—
509C4⋊C4—862no—
510C4⋊C4—862no—
511C4⋊C4—862no—
512C4⋊C4—862no—
513C4⋊C4—862no—
514C4⋊C4—862no—
515C4⋊C4—862no—
516C4⋊C4—861no—
517C4⋊C4—862no—
518C4⋊C4—862no—
519C4⋊C4—1724no—
520C4⋊C4C2×C4×D4312yes—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—42no—
524C22⋊C4—862no—
525C22⋊C4—862no—
526C22⋊C4—1722no—
527C42—431no—
528C42—431no—
529C42—431no—
530C42—431no—
531C42—431no—
532C42—431no—
533C42—431no—
534C42—431no—
535C42—431no—
536C42—431no—
537C42—431no—
538C42—431no—
539C42—431no—
540C42—431no—
541C42—431no—
542C42—431no—
543C42—862no—
544C42—862no—
545C42—862no—
546C42—862no—
547C42—1724no—
548C23—22no—
549C23—22no—
550C23—41no—
551C23C22⋊C4×D4311yescharacteristic
552C23C22⋊C4×D4311yescharacteristic
553C23C2×D4×D4311yescharacteristic
554Q8—42no—
555Q8—42no—
556Q8—1722no—
557Q8—1722no—
558Q8—1724no—
559Q8—1724no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—431no—
574C2×C4—431no—
575C2×C4—431no—
576C2×C4—434no—
577C2×C4—431no—
578C2×C4—431no—
579C2×C4—431no—
580C2×C4—431no—
581C2×C4—431no—
582C2×C4—862no—
583C2×C4—862no—
584C2×C4—862no—
585C2×C4—862no—
586C2×C4—862no—
587C2×C4—862no—
588C2×C4—862no—
589C2×C4—862no—
590C2×C4—862no—
591C2×C4—862no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1722no—
596C2×C4—1722no—
597C2×C4—1722no—
598C2×C4—1722no—
599C2×C4—1722no—
600C2×C4C22⋊C4×D4311yescharacteristic
601C2×C4C22⋊C4×D4311yescharacteristic
602C2×C4C22×C4×D4311yescharacteristic
603C2×C4C2×D4×D4311yescharacteristic
604C8—42no—
605C8—1722no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—44no—
614C22#1458287112yes—
615C22C2×C22⋊C4×D4311yescharacteristic
616C22#137×D4312yes—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—21no—
621C4—42no—
622C4—42no—
623C4—82no—
624C4—432no—
625C4—432no—
626C4—432no—
627C4—861no—
628C4—861no—
629C4—861no—
630C4—861no—
631C4—861no—
632C4—3442no—
633C4—1722no—
634C4—1722no—
635C2—22no—
636C2—22no—
637C2—41no—
638C2C2×#1458287111yescharacteristic
639C2#419×D4311yescharacteristic
640C2#421×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1511C2
socleC22×C43C22×C22⋊C4
prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenter#1511D43
hypocenterC43#17590
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1511

Complements

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

NH ≅ G/Ntype
4. #19133157C2semidirect
8. #19133105C2semidirect
14. #14583451C4semidirect
15. #14583451C4semidirect
18. C2×#13063324C4semidirect
19. C2×#13063323C4semidirect
23. C2×Q8×Dic43C4semidirect
25. C2×#13063290C4semidirect
369. C43#17590semidirect

Maximal subgroups

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

subgroupindex
C2×#145834512
#191432242
#191369862
#191331572
#191331292
#191331282
#191331272
#191331052
C43×#15112
#1759043