Finite Group Databasebeta

← #25063920

Subgroups — #25063920

Order 11008.

1046 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583430C211yesmaximal, characteristic
2C2×#14582949C211yesmaximal, characteristic, complemented
3#19136990C211yesmaximal, characteristic, complemented
4#19133169C214yesmaximal, complemented
5#19133168C211yesmaximal, characteristic, complemented
6#19133166C211yesmaximal, characteristic, complemented
7#19133163C211yesmaximal, characteristic
8#19133078C214yesmaximal, complemented
9C43×#1519C211yesmaximal, characteristic
10#14583430—21no—
11#14583430—21no—
12#14583430—21no—
13#14583430—21no—
14#14583430C412yescomplemented
15#14583430C412yescomplemented
16#14583430C2212yes—
17#14583430C2212yes—
18C2×#13063318—21no—
19C2×#13063316C411yescharacteristic, complemented
20C2×#13063312C411yescharacteristic, complemented
21C2×#13063306—21no—
22C2×#13063304C2211yescharacteristic
23C2×#13063290C411yescharacteristic, complemented
24C2×D4×Dic43—21no—
25C2×D4×Dic43C411yescharacteristic, complemented
26C2×#13063281—21no—
27C22×C4×Dic43C2211yescharacteristic
28#14582949—21no—
29#14582949—21no—
30#14582949C2212yescomplemented
31#14582949C2212yescomplemented
32C2×Dic43⋊C8—21no—
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34C2×C8×Dic43—21no—
35#14582766C2212yescomplemented
36#14582764—21no—
37#14582760—21no—
38#14582759C2211yescharacteristic
39C4⋊C4×Dic43—21no—
40C22⋊C4×Dic43—21no—
41#14582744C2212yescomplemented
42#14582637C2214yescomplemented
43#14582635C2214yescomplemented
44#14582633C2214yes—
45C2×#121×C43C2211yescharacteristic
46C2×C22⋊C8×C43C2211yescharacteristic
47C43×#380C2211yescharacteristic
48C43×#327C2214yes—
49C22×Dic86C2×C411yescharacteristic
50C23×Dic43—21no—
51C23×Dic43D411yescharacteristic
52C23×Dic43D411yescharacteristic
53C22×C43⋊C8—21no—
54#13063318—22no—
55#13063318—22no—
56#13063318—22no—
57#13063318—22no—
58#13063316—21no—
59#13063316—21no—
60#13063316C2×C412yes—
61#13063316C2×C412yes—
62#13063312—21no—
63#13063312—21no—
64#13063312C2×C412yes—
65#13063312C2×C412yes—
66#13063306—22no—
67#13063306—22no—
68#13063306—22no—
69#13063306—22no—
70#13063304—21no—
71#13063304—21no—
72#13063304C2×C412yes—
73#13063304C2312yes—
74#13063290—21no—
75#13063290—21no—
76#13063290C2×C412yes—
77#13063290C2×C412yes—
78D4×Dic43—22no—
79D4×Dic43—22no—
80D4×Dic43—22no—
81D4×Dic43—22no—
82D4×Dic43—21no—
83D4×Dic43—21no—
84D4×Dic43C2×C412yes—
85D4×Dic43C2×C412yes—
86#13063281—22no—
87#13063281—22no—
88#13063281—22no—
89#13063281—22no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43C2×C411yescharacteristic
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×C22⋊Dic43—21no—
97C2×C22⋊Dic43—21no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43—21no—
100C2×C22⋊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—
119C8×Dic43—22no—
120C8×Dic43—22no—
121C43⋊#95—22no—
122C43⋊#95—22no—
123C43⋊#95—22no—
124C43⋊#95C2312yes—
125C22×D4×C43—21no—
126C22×D4×C43C2×C411yescharacteristic
127C23×C4×C43C2311yescharacteristic
128C22×C8×C43—21no—
129#121×C43—21no—
130#121×C43—21no—
131#121×C43C2×C412yes—
132#121×C43C2312yes—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43C2×C411yescharacteristic
135C2×C22⋊C4×C43—21no—
136C2×C22⋊C4×C43—21no—
137C22⋊C8×C43—21no—
138C22⋊C8×C43C2312yes—
139#95×C43C2312yes—
140C24×C43—21no—
141C24×C43C2×D411yescharacteristic
142C2×D4×C43—21no—
143C2×D4×C43—22no—
144C2×D4×C43—22no—
145C2×D4×C43—42no—
146C2×D4×C43—42no—
147C2×D4×C43—42no—
148C2×D4×C43C22×C412yes—
149C22×C4×C43—21no—
150C22×C4×C43—22no—
151C22×C4×C43—42no—
152C22×C4×C43C22×C411yescharacteristic
153C22×C4×C43C22×C411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2411yescharacteristic
158C22×Dic43—22no—
159C22×Dic43—22no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—22no—
163C22×Dic43—22no—
164C22×Dic43—22no—
165C22×Dic43—42no—
166C22×Dic43—44no—
167C22×Dic43C22⋊C411yescharacteristic
168C22×Dic43C22⋊C411yescharacteristic
169C22×Dic43C22⋊C411yescharacteristic
170C22×Dic43C22⋊C411yescharacteristic
171C22×Dic43C22⋊C411yescharacteristic
172C22×Dic43C22⋊C411yescharacteristic
173C22×Dic43C22⋊C411yescharacteristic
174C22×Dic43C22⋊C411yescharacteristic
175C22×Dic43C2×D411yescharacteristic
176C22×Dic43C2×D411yescharacteristic
177C22×Dic43C2×D411yescharacteristic
178C22×Dic43C2×D411yescharacteristic
179C2×Dic86—21no—
180C2×Dic86—42no—
181C2×Dic86C22×C412yes—
182C2×C8×C43—22no—
183C2×C8×C43—42no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—42no—
186C4⋊C4×C43C22×C412yes—
187C22⋊C4×C43—22no—
188C22⋊C4×C43—22no—
189C22⋊C4×C43—42no—
190C22⋊Dic43—22no—
191C22⋊Dic43—22no—
192C22⋊Dic43—22no—
193C22⋊Dic43—22no—
194C22⋊Dic43—22no—
195C22⋊Dic43—22no—
196C22⋊Dic43—22no—
197C22⋊Dic43—22no—
198C22⋊Dic43—42no—
199C4⋊Dic43—21no—
200C4⋊Dic43—22no—
201C4⋊Dic43—22no—
202C4⋊Dic43—42no—
203C4⋊Dic43C22×C412yes—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210C4×Dic43—22no—
211C4×Dic43—22no—
212C4×Dic43—44no—
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×Dic43C22×C411yescharacteristic
222C4×Dic43C22×C411yescharacteristic
223C4×Dic43C22×C411yescharacteristic
224C4×Dic43C22×C411yescharacteristic
225C4×Dic43C2×D411yescharacteristic
226C4×Dic43C2×D411yescharacteristic
227C4×Dic43C2×D411yescharacteristic
228C4×Dic43C2×D411yescharacteristic
229C2×C43⋊C8—22no—
230C2×C43⋊C8—42no—
231C23×C43—22no—
232C23×C43—41no—
233C23×C43—41no—
234C23×C43—42no—
235C23×C43—42no—
236C23×C43—42no—
237C23×C43C2×C22⋊C411yescharacteristic
238C23×C43C2×C22⋊C411yescharacteristic
239C23×C43#13512yes—
240C23×C43#13512yes—
241C23×C43C22×D411yescharacteristic
242D4×C43—42no—
243D4×C43—42no—
244D4×C43—42no—
245D4×C43—44no—
246D4×C43—42no—
247C2×C4×C43—22no—
248C2×C4×C43—22no—
249C2×C4×C43—22no—
250C2×C4×C43—22no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—42no—
255C2×C4×C43—42no—
256C2×C4×C43—42no—
257C2×C4×C43—42no—
258C2×C4×C43C2×C22⋊C411yescharacteristic
259C2×C4×C43C2×C22⋊C411yescharacteristic
260C2×C4×C43C23×C411yescharacteristic
261C2×C4×C43C22×D411yescharacteristic
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—22no—
267C2×Dic43—22no—
268C2×Dic43—22no—
269C2×Dic43—22no—
270C2×Dic43—22no—
271C2×Dic43—22no—
272C2×Dic43—22no—
273C2×Dic43—22no—
274C2×Dic43—22no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—44no—
279C2×Dic43—42no—
280C2×Dic43—42no—
281C2×Dic43—44no—
282C2×Dic43—42no—
283C2×Dic43—42no—
284C2×Dic43—42no—
285C2×Dic43C2×C22⋊C411yescharacteristic
286C2×Dic43C2×C22⋊C411yescharacteristic
287C2×Dic43C2×C22⋊C411yescharacteristic
288C2×Dic43C2×C22⋊C411yescharacteristic
289C2×Dic43C2×C22⋊C411yescharacteristic
290C2×Dic43C2×C22⋊C411yescharacteristic
291C2×Dic43C2×C22⋊C411yescharacteristic
292C2×Dic43C2×C22⋊C411yescharacteristic
293Dic86—42no—
294Dic86—42no—
295C8×C43—42no—
296C43⋊C8—42no—
297#17567—431nomaximal, Sylow
298C22×C43—21no—
299C22×C43—21no—
300C22×C43—21no—
301C22×C43—21no—
302C22×C43—21no—
303C22×C43—21no—
304C22×C43—42no—
305C22×C43—42no—
306C22×C43—42no—
307C22×C43—42no—
308C22×C43—42no—
309C22×C43—84no—
310C22×C43#41612yes—
311C22×C43#41612yes—
312C22×C43C22×C22⋊C411yescharacteristic
313C22×C43C2×#13511yescharacteristic
314C22×C43C2×#13511yescharacteristic
315C4×C43—21no—
316C4×C43—21no—
317C4×C43—21no—
318C4×C43—42no—
319C4×C43—82no—
320C4×C43#41012yes—
321Dic43—21no—
322Dic43—21no—
323Dic43—21no—
324Dic43—21no—
325Dic43—21no—
326Dic43—21no—
327Dic43—21no—
328Dic43—42no—
329Dic43—42no—
330Dic43—82no—
331Dic43#42112yes—
332C2×#529—431no—
333C2×#431—431no—
334#2283—431no—
335#1521—434no—
336#1520—431no—
337#1520—431no—
338#1519—431no—
339#1519D4311yescharacteristic
340#1500—434no—
341C2×C43—21no—
342C2×C43—21no—
343C2×C43—22no—
344C2×C43—22no—
345C2×C43—82no—
346C2×C43C2×#41011yescharacteristic
347C2×C43C2×#41611yescharacteristic
348C2×C43C2×#42111yescharacteristic
349#529—432no—
350#529—432no—
351#529—432no—
352#529—432no—
353#529—861no—
354#529—861no—
355#529—861no—
356#529—861no—
357C2×#126—861no—
358C2×#125—431no—
359C2×#124—431no—
360C2×#123—861no—
361C2×C22⋊Q8—431no—
362C2×#121C2×D4311yescharacteristic
363C2×C4×Q8—431no—
364C2×C4×D4—431no—
365C2×C4×D4—861no—
366C2×#117—861no—
367C22×C42—431no—
368#431—432no—
369#431—432no—
370#431—861no—
371#431—861no—
372C2×C4⋊C8—861no—
373C2×C22⋊C8—431no—
374C2×C22⋊C8C2×D4311yescharacteristic
375C2×C4×C8—861no—
376#383—432no—
377#382—861no—
378#381—861no—
379#380—431no—
380#380C2×D4311yescharacteristic
381C4×C4⋊C4—861no—
382C4×C22⋊C4—861no—
383#376—432no—
384#328—434no—
385#328—434no—
386#327—434no—
387#327C2×D4314yes—
388C43#1756711yescharacteristic, complemented, Sylow
389C22×Q8—431no—
390C22×D4—21no—
391C22×D4C4×D4311yescharacteristic
392C23×C4—431no—
393C23×C4—431no—
394C23×C4—861no—
395C23×C4C22×D4311yescharacteristic
396C22×C8—21no—
397C22×C8—861no—
398#126—862no—
399#126—862no—
400#126—862no—
401#126—862no—
402#125—432no—
403#125—432no—
404#125—861no—
405#125—861no—
406#124—432no—
407#124—432no—
408#124—861no—
409#124—861no—
410#123—862no—
411#123—862no—
412#123—862no—
413#123—862no—
414C22⋊Q8—432no—
415C22⋊Q8—432no—
416C22⋊Q8—861no—
417C22⋊Q8—861no—
418#121—21no—
419#121—21no—
420#121C4×D4312yes—
421#121C22×D4312yes—
422C4×Q8—432no—
423C4×Q8—432no—
424C4×Q8—861no—
425C4×Q8—861no—
426C4×D4—432no—
427C4×D4—432no—
428C4×D4—861no—
429C4×D4—861no—
430C4×D4—862no—
431C4×D4—862no—
432C4×D4—862no—
433C4×D4—862no—
434#117—862no—
435#117—862no—
436#117—862no—
437#117—862no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—431no—
440C2×C4⋊C4—861no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4C4×D4311yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—861no—
449C2×C22⋊C4—861no—
450C2×C22⋊C4—861no—
451C2×C22⋊C4—861no—
452C2×C22⋊C4—861no—
453C2×C42—431no—
454C2×C42—431no—
455C2×C42—431no—
456C2×C42—431no—
457C2×C42—431no—
458C2×C42—431no—
459C2×C42—431no—
460C2×C42—431no—
461C2×C42—431no—
462C2×C42—431no—
463C2×C42—431no—
464C2×C42—431no—
465C2×C42—861no—
466C2×C42—862no—
467C4⋊C8—862no—
468C4⋊C8—862no—
469C22⋊C8—21no—
470C22⋊C8—432no—
471C22⋊C8—861no—
472C22⋊C8C22×D4312yes—
473C4×C8—862no—
474C4×C8—862no—
475#95—432no—
476#95—862no—
477#95—862no—
478#95—862no—
479#95C22×D4312yes—
480C24—21no—
481C24D4×D4311yescharacteristic
482C2×Q8—432no—
483C2×Q8—861no—
484C2×Q8—1722no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—21no—
488C2×D4—42no—
489C2×D4—42no—
490C2×D4—42no—
491C2×D4C2×C4×D4312yes—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—42no—
495C22×C4—431no—
496C22×C4—431no—
497C22×C4—431no—
498C22×C4—431no—
499C22×C4—431no—
500C22×C4—431no—
501C22×C4—431no—
502C22×C4—431no—
503C22×C4—431no—
504C22×C4—431no—
505C22×C4—431no—
506C22×C4—431no—
507C22×C4—862no—
508C22×C4—862no—
509C22×C4—862no—
510C22×C4—862no—
511C22×C4—861no—
512C22×C4—861no—
513C22×C4—862no—
514C22×C4—1722no—
515C22×C4—1724no—
516C22×C4C2×C4×D4311yescharacteristic
517C22×C4C2×C4×D4311yescharacteristic
518C22×C4D4×D4311yescharacteristic
519C22×C4D4×D4311yescharacteristic
520C22×C4D4×D4311yescharacteristic
521C22×C4C23×D4311yescharacteristic
522C2×C8—22no—
523C2×C8—42no—
524C2×C8—862no—
525C2×C8—1722no—
526C4⋊C4—21no—
527C4⋊C4—42no—
528C4⋊C4—432no—
529C4⋊C4—862no—
530C4⋊C4—862no—
531C4⋊C4—862no—
532C4⋊C4—862no—
533C4⋊C4—862no—
534C4⋊C4—862no—
535C4⋊C4—861no—
536C4⋊C4—862no—
537C4⋊C4—862no—
538C4⋊C4—1722no—
539C4⋊C4C2×C4×D4312yes—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—42no—
543C22⋊C4—862no—
544C22⋊C4—862no—
545C22⋊C4—862no—
546C22⋊C4—862no—
547C22⋊C4—862no—
548C22⋊C4—862no—
549C22⋊C4—862no—
550C22⋊C4—862no—
551C22⋊C4—1722no—
552C42—431no—
553C42—431no—
554C42—431no—
555C42—431no—
556C42—431no—
557C42—431no—
558C42—431no—
559C42—431no—
560C42—431no—
561C42—431no—
562C42—431no—
563C42—431no—
564C42—431no—
565C42—431no—
566C42—431no—
567C42—431no—
568C42—862no—
569C42—862no—
570C42—1724no—
571C23—22no—
572C23—41no—
573C23—41no—
574C23—42no—
575C23—42no—
576C23—42no—
577C23C22⋊C4×D4311yescharacteristic
578C23C22⋊C4×D4311yescharacteristic
579C23#1306334412yes—
580C23#1306334612yes—
581C23C2×D4×D4311yescharacteristic
582Q8—1722no—
583Q8—1722no—
584D4—42no—
585D4—44no—
586D4—42no—
587D4—42no—
588D4—42no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—431no—
601C2×C4—431no—
602C2×C4—431no—
603C2×C4—431no—
604C2×C4—431no—
605C2×C4—431no—
606C2×C4—431no—
607C2×C4—431no—
608C2×C4—862no—
609C2×C4—862no—
610C2×C4—862no—
611C2×C4—862no—
612C2×C4—862no—
613C2×C4—862no—
614C2×C4—862no—
615C2×C4—861no—
616C2×C4—861no—
617C2×C4—861no—
618C2×C4—861no—
619C2×C4—862no—
620C2×C4—862no—
621C2×C4—1724no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4—1724no—
626C2×C4—1722no—
627C2×C4—1722no—
628C2×C4—1722no—
629C2×C4—1722no—
630C2×C4—1722no—
631C2×C4C22⋊C4×D4311yescharacteristic
632C2×C4C22⋊C4×D4311yescharacteristic
633C2×C4C22×C4×D4311yescharacteristic
634C2×C4C2×D4×D4311yescharacteristic
635C8—42no—
636C8—1722no—
637C22—21no—
638C22—21no—
639C22—21no—
640C22—21no—
641C22—21no—
642C22—21no—
643C22—42no—
644C22—42no—
645C22—42no—
646C22—42no—
647C22—42no—
648C22—84no—
649C22#1458289212yes—
650C22#1458289212yes—
651C22C2×C22⋊C4×D4311yescharacteristic
652C22C2×#1306334411yescharacteristic
653C22C2×#1306334611yescharacteristic
654C4—21no—
655C4—21no—
656C4—21no—
657C4—42no—
658C4—82no—
659C4—432no—
660C4—861no—
661C4—861no—
662C4—861no—
663C4—861no—
664C4—861no—
665C4—861no—
666C4—861no—
667C4—3442no—
668C4—1722no—
669C4—1722no—
670C4#1458287112yes—
671C2—21no—
672C2—21no—
673C2—22no—
674C2—22no—
675C2—82no—
676C2C2×#1458287111yescharacteristic
677C2C2×#1458289211yescharacteristic
678C2#421×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1519C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#121×C43C22
cosocleC22×C4×C43C24
hypercenter#1519D43
hypocenterC43#17567
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1519

Complements

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

NH ≅ G/Ntype
2. C2×#14582949C2semidirect
3. #19136990C2semidirect
4. #19133169C2semidirect
5. #19133168C2semidirect
6. #19133166C2semidirect
8. #19133078C2semidirect
14. #14583430C4semidirect
15. #14583430C4semidirect
19. C2×#13063316C4semidirect
20. C2×#13063312C4semidirect
23. C2×#13063290C4semidirect
25. C2×D4×Dic43C4semidirect
30. #14582949C22semidirect
31. #14582949C22semidirect
35. #14582766C22semidirect
41. #14582744C22semidirect
42. #14582637C22semidirect
43. #14582635C22semidirect
388. C43#17567semidirect

Maximal subgroups

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

subgroupindex
C2×#145834302
C2×#145829492
#191369902
#191331692
#191331682
#191331662
#191331632
#191330782
C43×#15192
#1756743