Finite Group Databasebeta

← #25063841

Subgroups — #25063841

Order 11008.

1024 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583430C211yesmaximal, characteristic
2#19143224C211yesmaximal, characteristic, complemented
3#19136986C211yesmaximal, characteristic, complemented
4#19133130C214yesmaximal, complemented
5#19133129C211yesmaximal, characteristic, complemented
6#19133127C211yesmaximal, characteristic, complemented
7#19133124C211yesmaximal, characteristic
8#19133078C214yesmaximal, complemented
9C43×#1510C211yesmaximal, 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#14582953—21no—
29#14582953C2212yescomplemented
30#14582949—21no—
31#14582949C2212yescomplemented
32#14582922—21no—
33#14582863C2211yescharacteristic
34M16×Dic43—21no—
35#14582766—21no—
36#14582763C2212yescomplemented
37#14582762C2211yescharacteristic
38#14582757—21no—
39#14582750—21no—
40C22⋊C4×Dic43—21no—
41#14582744C2212yescomplemented
42#14582637C2214yescomplemented
43#14582635C2214yescomplemented
44#14582633C2214yes—
45C2×#121×C43C2211yescharacteristic
46C43×#407C2211yescharacteristic
47C43×#381C2211yescharacteristic
48C43×#327C2214yes—
49C22×Dic86C2×C411yescharacteristic
50C23×Dic43—21no—
51C23×Dic43D411yescharacteristic
52C23×Dic43D411yescharacteristic
53C2×#10621877—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⋊Dic43C2×C411yescharacteristic
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—22no—
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—
119#13063235—22no—
120C8×Dic43—22no—
121C43⋊#95—21no—
122C43⋊#95—22no—
123C43⋊#95—22no—
124C43⋊#95C2312yes—
125C22×D4×C43—21no—
126C22×D4×C43C2×C411yescharacteristic
127C23×C4×C43C2311yescharacteristic
128C2×M16×C43—21no—
129#121×C43—21no—
130#121×C43—21no—
131#121×C43C2×C412yes—
132#121×C43C2312yes—
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×C43—21no—
141C24×C43C2×D411yescharacteristic
142C2×D4×C43—21no—
143C2×D4×C43—22no—
144C2×D4×C43—22no—
145C2×D4×C43—44no—
146C2×D4×C43—42no—
147C2×D4×C43C22×C412yes—
148C22×C4×C43—21no—
149C22×C4×C43—22no—
150C22×C4×C43—42no—
151C22×C4×C43C22×C411yescharacteristic
152C22×C4×C43C22×C411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2411yescharacteristic
157C22×Dic43—22no—
158C22×Dic43—22no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—22no—
162C22×Dic43—42no—
163C22×Dic43—42no—
164C22×Dic43—44no—
165C22×Dic43C22⋊C411yescharacteristic
166C22×Dic43C22⋊C411yescharacteristic
167C22×Dic43C22⋊C411yescharacteristic
168C22×Dic43C22⋊C411yescharacteristic
169C22×Dic43C22⋊C411yescharacteristic
170C22×Dic43C22⋊C411yescharacteristic
171C22×Dic43C22⋊C411yescharacteristic
172C22×Dic43C22⋊C411yescharacteristic
173C22×Dic43C2×D411yescharacteristic
174C22×Dic43C2×D411yescharacteristic
175C22×Dic43C2×D411yescharacteristic
176C22×Dic43C2×D411yescharacteristic
177C2×Dic86—21no—
178C2×Dic86—42no—
179C2×Dic86C22×C412yes—
180M16×C43—42no—
181C2×C8×C43—22no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43C22×C412yes—
184C22⋊C4×C43—22no—
185C22⋊C4×C43—22no—
186C22⋊C4×C43—42no—
187C22⋊Dic43—22no—
188C22⋊Dic43—22no—
189C22⋊Dic43—22no—
190C22⋊Dic43—22no—
191C22⋊Dic43—22no—
192C22⋊Dic43—22no—
193C22⋊Dic43—22no—
194C22⋊Dic43—22no—
195C22⋊Dic43—42no—
196C4⋊Dic43—21no—
197C4⋊Dic43—22no—
198C4⋊Dic43—22no—
199C4⋊Dic43C22×C412yes—
200Dic43⋊C4—22no—
201Dic43⋊C4—22no—
202Dic43⋊C4—22no—
203Dic43⋊C4—22no—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—44no—
207C4×Dic43—22no—
208C4×Dic43—22no—
209C4×Dic43—44no—
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×Dic43C22×C411yescharacteristic
222C4×Dic43C2×D411yescharacteristic
223C4×Dic43C2×D411yescharacteristic
224C4×Dic43C2×D411yescharacteristic
225C4×Dic43C2×D411yescharacteristic
226#10621877—42no—
227C2×C43⋊C8—22no—
228C23×C43—22no—
229C23×C43—22no—
230C23×C43—22no—
231C23×C43—41no—
232C23×C43—42no—
233C23×C43—42no—
234C23×C43—42no—
235C23×C43C2×C22⋊C411yescharacteristic
236C23×C43C2×C22⋊C411yescharacteristic
237C23×C43C22×D411yescharacteristic
238D4×C43—42no—
239D4×C43—42no—
240D4×C43—44no—
241D4×C43—44no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
244C2×C4×C43—22no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—42no—
250C2×C4×C43—42no—
251C2×C4×C43—42no—
252C2×C4×C43—42no—
253C2×C4×C43C2×C22⋊C411yescharacteristic
254C2×C4×C43C2×C22⋊C411yescharacteristic
255C2×C4×C43C23×C411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—44no—
272C2×Dic43—42no—
273C2×Dic43—42no—
274C2×Dic43—44no—
275C2×Dic43—42no—
276C2×Dic43—42no—
277C2×Dic43—42no—
278C2×Dic43C2×C22⋊C411yescharacteristic
279C2×Dic43C2×C22⋊C411yescharacteristic
280C2×Dic43C2×C22⋊C411yescharacteristic
281C2×Dic43C2×C22⋊C411yescharacteristic
282C2×Dic43C2×C22⋊C411yescharacteristic
283C2×Dic43C2×C22⋊C411yescharacteristic
284C2×Dic43C2×C22⋊C411yescharacteristic
285C2×Dic43C2×C22⋊C411yescharacteristic
286Dic86—42no—
287Dic86—42no—
288C8×C43—42no—
289C43⋊C8—42no—
290#17554—431nomaximal, Sylow
291C22×C43—21no—
292C22×C43—21no—
293C22×C43—21no—
294C22×C43—21no—
295C22×C43—21no—
296C22×C43—21no—
297C22×C43—21no—
298C22×C43—44no—
299C22×C43—42no—
300C22×C43—42no—
301C22×C43—42no—
302C22×C43—84no—
303C22×C43#41012yes—
304C22×C43C22×C22⋊C411yescharacteristic
305C22×C43#57512yes—
306C4×C43—21no—
307C4×C43—21no—
308C4×C43—21no—
309C4×C43—21no—
310C4×C43—42no—
311C4×C43—82no—
312Dic43—21no—
313Dic43—21no—
314Dic43—21no—
315Dic43—21no—
316Dic43—21no—
317Dic43—21no—
318Dic43—21no—
319Dic43—42no—
320Dic43—42no—
321Dic43—82no—
322Dic43#42112yes—
323C2×#529—431no—
324#2920—431no—
325#2283—431no—
326#1512—434no—
327#1511—431no—
328#1511—431no—
329#1510—431no—
330#1510D4311yescharacteristic
331#1500—434no—
332C2×C43—22no—
333C2×C43—22no—
334C2×C43—41no—
335C2×C43—82no—
336C2×C43C2×#41011yescharacteristic
337C2×C43#289611yescharacteristic
338C2×C43C2×#42111yescharacteristic
339#529—432no—
340#529—432no—
341#529—432no—
342#529—432no—
343#529—861no—
344#529—861no—
345#529—861no—
346#529—861no—
347C2×#126—861no—
348C2×#125—431no—
349C2×#124—431no—
350C2×#123—861no—
351C2×C22⋊Q8—431no—
352C2×#121C2×D4311yescharacteristic
353C2×C4×Q8—431no—
354C2×C4×D4—431no—
355C2×C4×D4—861no—
356C2×#117—861no—
357C22×C42—431no—
358#432—432no—
359#432—861no—
360#431—432no—
361#431—861no—
362#423—861no—
363#407—431no—
364#407C2×D4311yescharacteristic
365C4×M16—861no—
366#383—861no—
367#382—432no—
368#381—431no—
369#381C2×D4311yescharacteristic
370#380—861no—
371C4×C4⋊C4—861no—
372C4×C22⋊C4—861no—
373#376—432no—
374#328—434no—
375#328—434no—
376#327—434no—
377#327C2×D4314yes—
378C43#1755411yescharacteristic, complemented, Sylow
379C22×Q8—431no—
380C22×D4—21no—
381C22×D4C4×D4311yescharacteristic
382C23×C4—431no—
383C23×C4—431no—
384C23×C4—861no—
385C23×C4C22×D4311yescharacteristic
386C2×M16—21no—
387C2×M16—861no—
388#126—862no—
389#126—862no—
390#126—862no—
391#126—862no—
392#125—432no—
393#125—432no—
394#125—861no—
395#125—861no—
396#124—432no—
397#124—432no—
398#124—861no—
399#124—861no—
400#123—862no—
401#123—862no—
402#123—862no—
403#123—862no—
404C22⋊Q8—432no—
405C22⋊Q8—432no—
406C22⋊Q8—861no—
407C22⋊Q8—861no—
408#121—21no—
409#121—21no—
410#121C4×D4312yes—
411#121C22×D4312yes—
412C4×Q8—432no—
413C4×Q8—432no—
414C4×Q8—861no—
415C4×Q8—861no—
416C4×D4—432no—
417C4×D4—432no—
418C4×D4—861no—
419C4×D4—861no—
420C4×D4—862no—
421C4×D4—862no—
422C4×D4—862no—
423C4×D4—862no—
424#117—862no—
425#117—862no—
426#117—862no—
427#117—862no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—862no—
434C2×C4⋊C4C4×D4311yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—861no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4—861no—
441C2×C22⋊C4—861no—
442C2×C42—431no—
443C2×C42—431no—
444C2×C42—431no—
445C2×C42—431no—
446C2×C42—431no—
447C2×C42—431no—
448C2×C42—431no—
449C2×C42—431no—
450C2×C42—431no—
451C2×C42—431no—
452C2×C42—431no—
453C2×C42—431no—
454C2×C42—861no—
455C2×C42—862no—
456C4⋊C8—862no—
457C4⋊C8—862no—
458C22⋊C8—21no—
459C22⋊C8—432no—
460C22⋊C8—861no—
461C22⋊C8C22×D4312yes—
462#97—862no—
463C4×C8—862no—
464#95—21no—
465#95—432no—
466#95—862no—
467#95—862no—
468#95—861no—
469#95C22×D4312yes—
470C24—21no—
471C24D4×D4311yescharacteristic
472C2×Q8—432no—
473C2×Q8—861no—
474C2×Q8—1722no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—21no—
478C2×D4—42no—
479C2×D4—44no—
480C2×D4C2×C4×D4312yes—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—42no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—431no—
494C22×C4—431no—
495C22×C4—431no—
496C22×C4—862no—
497C22×C4—862no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—862no—
501C22×C4—1722no—
502C22×C4—1722no—
503C22×C4—1724no—
504C22×C4C2×C4×D4311yescharacteristic
505C22×C4C2×C4×D4311yescharacteristic
506C22×C4D4×D4311yescharacteristic
507C22×C4D4×D4311yescharacteristic
508C22×C4D4×D4311yescharacteristic
509C22×C4C23×D4311yescharacteristic
510M16—42no—
511M16—1722no—
512C2×C8—22no—
513C2×C8—862no—
514C4⋊C4—21no—
515C4⋊C4—432no—
516C4⋊C4—862no—
517C4⋊C4—862no—
518C4⋊C4—862no—
519C4⋊C4—862no—
520C4⋊C4—862no—
521C4⋊C4—862no—
522C4⋊C4—861no—
523C4⋊C4—862no—
524C4⋊C4—862no—
525C4⋊C4—1724no—
526C4⋊C4C2×C4×D4312yes—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—42no—
530C22⋊C4—862no—
531C22⋊C4—862no—
532C22⋊C4—862no—
533C22⋊C4—862no—
534C22⋊C4—862no—
535C22⋊C4—862no—
536C22⋊C4—862no—
537C22⋊C4—862no—
538C22⋊C4—1722no—
539C42—431no—
540C42—431no—
541C42—431no—
542C42—431no—
543C42—431no—
544C42—431no—
545C42—431no—
546C42—431no—
547C42—431no—
548C42—431no—
549C42—431no—
550C42—431no—
551C42—431no—
552C42—431no—
553C42—431no—
554C42—431no—
555C42—862no—
556C42—862no—
557C42—1724no—
558C23—22no—
559C23—22no—
560C23—22no—
561C23—41no—
562C23—42no—
563C23—42no—
564C23—42no—
565C23C22⋊C4×D4311yescharacteristic
566C23C22⋊C4×D4311yescharacteristic
567C23C2×D4×D4311yescharacteristic
568Q8—1722no—
569Q8—1722no—
570D4—42no—
571D4—42no—
572D4—44no—
573D4—44no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—431no—
586C2×C4—431no—
587C2×C4—431no—
588C2×C4—431no—
589C2×C4—431no—
590C2×C4—431no—
591C2×C4—431no—
592C2×C4—431no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—862no—
596C2×C4—862no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—862no—
600C2×C4—1724no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1724no—
609C2×C4—1722no—
610C2×C4—1722no—
611C2×C4—1722no—
612C2×C4—1722no—
613C2×C4—1722no—
614C2×C4C22⋊C4×D4311yescharacteristic
615C2×C4C22⋊C4×D4311yescharacteristic
616C2×C4C22×C4×D4311yescharacteristic
617C2×C4C2×D4×D4311yescharacteristic
618C8—42no—
619C8—1722no—
620C22—21no—
621C22—21no—
622C22—21no—
623C22—21no—
624C22—21no—
625C22—21no—
626C22—21no—
627C22—44no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—84no—
632C22#1458287112yes—
633C22C2×C22⋊C4×D4311yescharacteristic
634C22#1458369512yes—
635C4—21no—
636C4—21no—
637C4—21no—
638C4—21no—
639C4—42no—
640C4—82no—
641C4—432no—
642C4—861no—
643C4—861no—
644C4—861no—
645C4—861no—
646C4—861no—
647C4—861no—
648C4—861no—
649C4—3442no—
650C4—1722no—
651C4—1722no—
652C2—22no—
653C2—22no—
654C2—41no—
655C2—82no—
656C2C2×#1458287111yescharacteristic
657C2#1914310911yescharacteristic
658C2#421×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1510C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#121×C43C22
cosocleC22×C4×C43C24
hypercenter#1510D43
hypocenterC43#17554
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1510

Complements

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

NH ≅ G/Ntype
2. #19143224C2semidirect
3. #19136986C2semidirect
4. #19133130C2semidirect
5. #19133129C2semidirect
6. #19133127C2semidirect
8. #19133078C2semidirect
14. #14583430C4semidirect
15. #14583430C4semidirect
19. C2×#13063316C4semidirect
20. C2×#13063312C4semidirect
23. C2×#13063290C4semidirect
25. C2×D4×Dic43C4semidirect
29. #14582953C22semidirect
31. #14582949C22semidirect
36. #14582763C22semidirect
41. #14582744C22semidirect
42. #14582637C22semidirect
43. #14582635C22semidirect
378. C43#17554semidirect

Maximal subgroups

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

subgroupindex
C2×#145834302
#191432242
#191369862
#191331302
#191331292
#191331272
#191331242
#191330782
C43×#15102
#1755443