Finite Group Databasebeta

← #25062598

Subgroups — #25062598

Order 11008.

1020 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583431C211yesmaximal, characteristic
2#19143223C211yesmaximal, characteristic, complemented
3#431×D43C211yesmaximal, characteristic, complemented
4#19132961C214yesmaximal, complemented
5#19132940C214yesmaximal, complemented
6#19132918C211yesmaximal, characteristic, complemented
7#19132918C211yesmaximal, characteristic, complemented
8#19132916C211yesmaximal, characteristic, complemented
9C43×#1460C211yesmaximal, characteristic, complemented
10#14583431—21no—
11#14583431—21no—
12#14583431—21no—
13#14583431—21no—
14#14583431—21no—
15#14583431—21no—
16#14583431—21no—
17#14583431—21no—
18C2×#13063318C2212yes—
19C2×#13063316C411yescharacteristic
20C2×#13063312C411yescharacteristic
21C2×#13063307C2212yes—
22C2×#13063305C411yescharacteristic
23C2×#13063296C411yescharacteristic
24C2×C4×Dic86C2211yescharacteristic
25C2×C4×C22⋊D43C412yes—
26C2×#13063284C412yes—
27C2×C42×D43C2211yescharacteristic
28#14582955—21no—
29#14582953C2212yes—
30#14582952C2211yescharacteristic
31#14582952C2211yescharacteristic
32#14582951—21no—
33#14582950—21no—
34#14582950—21no—
35#14582949C2212yes—
36#14582921—21no—
37C4⋊C8×D43—21no—
38#14582861C2212yes—
39C22⋊C8×D43C2212yes—
40C4×#10621872—21no—
41C4×C8×D43—21no—
42#14582624C2214yes—
43#14582624C2214yes—
44#14582623C2214yes—
45C2×C4×D4×C43C2211yescharacteristic
46C43×#431C2211yescharacteristic
47C43×#431C2211yescharacteristic
48C43×#323C2214yes—
49C22×Dic86C2×C411yescharacteristic
50C22×C22⋊D43C2×C412yes—
51C22×C4×D43C2×C411yescharacteristic
52C22×C4×D43C2×C411yescharacteristic
53C22×C4×D43C2311yescharacteristic
54C2×#10621872—22no—
55C2×C8×D43—22no—
56#13063318—22no—
57#13063318—22no—
58#13063318—22no—
59#13063318—22no—
60#13063316—21no—
61#13063316—21no—
62#13063316—21no—
63#13063316—21no—
64#13063312—21no—
65#13063312—21no—
66#13063312—21no—
67#13063312—21no—
68#13063307—22no—
69#13063307—22no—
70#13063307—22no—
71#13063307—22no—
72#13063305—21no—
73#13063305—21no—
74#13063305—21no—
75#13063305—21no—
76#13063296—21no—
77#13063296—21no—
78#13063296—21no—
79#13063296—21no—
80C4×Dic86—21no—
81C4×Dic86—21no—
82C4×Dic86—21no—
83C4×Dic86—21no—
84C4×C22⋊D43—22no—
85C4×C22⋊D43—22no—
86C4×C22⋊D43—22no—
87C4×C22⋊D43—22no—
88#13063284—22no—
89#13063284—22no—
90#13063284—22no—
91#13063284—22no—
92C2×C4⋊Dic43C2×C412yes—
93C2×C4⋊Dic43C2×C412yes—
94C2×C4⋊Dic43C2×C411yescharacteristic
95C2×Dic43⋊C4C2×C412yes—
96C2×Dic43⋊C4C2312yes—
97C2×C22⋊Dic43C2×C412yes—
98C2×C22⋊Dic43C2×C412yes—
99C2×C22⋊Dic43C2×C412yes—
100C2×(C2×D43)⋊C4C2×C412yes—
101C2×C4×Dic43C2×C412yes—
102C2×C4×Dic43C2×C411yescharacteristic
103C2×C4×Dic43C2×C411yescharacteristic
104C2×C4×Dic43C2311yescharacteristic
105C42×D43D411yescharacteristic
106C42×D43D411yescharacteristic
107C42×D43D411yescharacteristic
108C42×D43D411yescharacteristic
109C42×D43D411yescharacteristic
110C42×D43D411yescharacteristic
111C42×D43D411yescharacteristic
112C42×D43D411yescharacteristic
113C4⋊(C43⋊C8)—21no—
114C4⋊(C43⋊C8)—21no—
115Dic43⋊C8—22no—
116Dic43⋊C8—22no—
117C22⋊(C43⋊C8)C2312yes—
118C22⋊(C43⋊C8)C2312yes—
119(C2×D43)⋊C8—22no—
120(C2×D43)⋊C8—22no—
121#13063235—22no—
122C4×C43⋊C8—21no—
123C4×C43⋊C8—21no—
124C8×Dic43—22no—
125C22×D4×C43C2×C411yescharacteristic
126C23×C4×C43C2×C412yes—
127C4×D4×C43—21no—
128C4×D4×C43—21no—
129C4×D4×C43—21no—
130C4×D4×C43—21no—
131C2×C4⋊C4×C43C2×C411yescharacteristic
132C2×C22⋊C4×C43C2312yes—
133C2×C42×C43C2311yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43—21no—
136C22⋊C8×C43C2312yes—
137C22⋊C8×C43C2312yes—
138C4×C8×C43—21no—
139C4×C8×C43—21no—
140C24×C43C22×C412yes—
141C23×D43C22×C411yescharacteristic
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—22no—
145C2×D4×C43—22no—
146C22×C4×C43—22no—
147C22×C4×C43—22no—
148C22×C4×C43—44no—
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C22×C412yes—
151C22×C4×C43C22×C411yescharacteristic
152C22×C4×C43C2411yescharacteristic
153C2×C22⋊D43—22no—
154C2×C22⋊D43—22no—
155C2×C22⋊D43—44no—
156C22×Dic43C22×C412yes—
157C22×Dic43C22×C411yescharacteristic
158C22×Dic43C22×C412yes—
159C22×Dic43C22×C411yescharacteristic
160C22×Dic43C22×C411yescharacteristic
161C2×C4×D43—22no—
162C2×C4×D43—22no—
163C2×C4×D43—42no—
164C2×C4×D43—42no—
165C2×C4×D43C22⋊C411yescharacteristic
166C2×C4×D43C22⋊C411yescharacteristic
167C2×C4×D43C22⋊C411yescharacteristic
168C2×C4×D43C22⋊C411yescharacteristic
169C2×C4×D43C22⋊C411yescharacteristic
170C2×C4×D43C22⋊C411yescharacteristic
171C2×C4×D43C22⋊C411yescharacteristic
172C2×C4×D43C22⋊C411yescharacteristic
173C2×C4×D43C2×D411yescharacteristic
174C2×C4×D43C2×D411yescharacteristic
175C2×C4×D43C2×D411yescharacteristic
176C2×C4×D43C2×D411yescharacteristic
177C2×Dic86—21no—
178C2×Dic86—21no—
179C2×Dic86—22no—
180C2×Dic86—22no—
181C2×C8×C43—22no—
182C2×C8×C43—22no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C22⋊C4×C43—22no—
186C22⋊C4×C43—22no—
187C42×C43C2×D411yescharacteristic
188C42×C43C2×D411yescharacteristic
189C42×C43C2×D411yescharacteristic
190C42×C43C2×D411yescharacteristic
191C22⋊Dic43—22no—
192C22⋊Dic43—22no—
193C22⋊Dic43—22no—
194C22⋊Dic43—22no—
195C22⋊Dic43—22no—
196C22⋊Dic43—22no—
197(C2×D43)⋊C4—22no—
198(C2×D43)⋊C4—22no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—22no—
202C4⋊Dic43—22no—
203C4⋊Dic43—22no—
204C4⋊Dic43—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208Dic43⋊C4—22no—
209C4×Dic43—22no—
210C4×Dic43—22no—
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×Dic43C2×D411yescharacteristic
220C4×Dic43C2×D411yescharacteristic
221C4×Dic43C2×D411yescharacteristic
222C4×Dic43C2×D411yescharacteristic
223C2×C43⋊C8—22no—
224C2×C43⋊C8—22no—
225#10621872—44no—
226C8×D43—44no—
227C23×C43—22no—
228C23×C43—22no—
229C23×C43—22no—
230C23×C43—42no—
231C23×C43—42no—
232C23×C43C23×C411yescharacteristic
233C22×D43—21no—
234C22×D43—21no—
235C22×D43—22no—
236C22×D43—41no—
237C22×D43C2×C22⋊C411yescharacteristic
238C22×D43C2×C22⋊C411yescharacteristic
239D4×C43—42no—
240D4×C43—42no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—41no—
244C2×C4×C43—44no—
245C2×C4×C43—44no—
246C2×C4×C43—42no—
247C2×C4×C43C2×C22⋊C411yescharacteristic
248C2×C4×C43C2×C22⋊C411yescharacteristic
249C2×C4×C43C2×C22⋊C411yescharacteristic
250C2×C4×C43C2×C22⋊C411yescharacteristic
251C2×C4×C43#13112yes—
252C2×C4×C43#13112yes—
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C22×D411yescharacteristic
255C22⋊D43—44no—
256C22⋊D43—44no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—22no—
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—42no—
266C2×Dic43C2×C22⋊C411yescharacteristic
267C2×Dic43C2×C22⋊C411yescharacteristic
268C2×Dic43C2×C22⋊C411yescharacteristic
269C2×Dic43C2×C22⋊C411yescharacteristic
270C2×Dic43C2×C22⋊C411yescharacteristic
271C2×Dic43C2×C22⋊C411yescharacteristic
272C4×D43—22no—
273C4×D43—22no—
274C4×D43—22no—
275C4×D43—22no—
276C4×D43—22no—
277C4×D43—22no—
278C4×D43—22no—
279C4×D43—22no—
280C4×D43—41no—
281C4×D43—41no—
282C4×D43—41no—
283C4×D43—41no—
284Dic86—42no—
285Dic86—42no—
286C8×C43—42no—
287C8×C43—42no—
288C43⋊C8—42no—
289C43⋊C8—42no—
290#17383—431nomaximal, Sylow
291C22×C43—21no—
292C22×C43—21no—
293C22×C43—42no—
294C22×C43—42no—
295C22×C43—42no—
296C22×C43—82no—
297C22×C43—82no—
298C22×C43C22×C22⋊C411yescharacteristic
299C22×C43C2×#13111yescharacteristic
300C22×C43C2×#13111yescharacteristic
301C2×D43—21no—
302C2×D43—21no—
303C2×D43—21no—
304C2×D43—21no—
305C2×D43—21no—
306C2×D43—42no—
307C2×D43—42no—
308C2×D43#41012yes—
309C4×C43—21no—
310C4×C43—21no—
311C4×C43—21no—
312C4×C43—42no—
313C4×C43#40812yes—
314C4×C43#40812yes—
315C4×C43#41312yes—
316Dic43—21no—
317Dic43—21no—
318Dic43—21no—
319Dic43—21no—
320Dic43—21no—
321Dic43—21no—
322Dic43—42no—
323Dic43—42no—
324C2×#529—431no—
325#2920—431no—
326C2×#431—431no—
327#1473—434no—
328#1468—434no—
329#1461—431no—
330#1461—431no—
331#1460—431no—
332#1460D4311yescharacteristic, complemented
333C2×C43—21no—
334C2×C43—21no—
335C2×C43—82no—
336C2×C43C2×#40811yescharacteristic
337C2×C43C2×#41011yescharacteristic
338C2×C43C2×#41311yescharacteristic
339D43—22no—
340D43—41no—
341#529—861no—
342#529—861no—
343#529—861no—
344#529—861no—
345#529—861no—
346#529—861no—
347#529—861no—
348#529—861no—
349C2×#126—432no—
350C2×#125—431no—
351C2×#124—431no—
352C2×#123—432no—
353C2×C22⋊Q8—431no—
354C2×#121—431no—
355C2×C4×Q8—431no—
356C2×C4×D4—432no—
357C2×C4×D4C2×D4311yescharacteristic
358C2×#117—432no—
359C22×C42—431no—
360#432—432no—
361#432—861no—
362#431—431no—
363#431—431no—
364#431—432no—
365#431—861no—
366#431—861no—
367#431—861no—
368#431C2×D4311yescharacteristic
369#431C2×D4311yescharacteristic
370#423—861no—
371C2×C4⋊C8—861no—
372#407—432no—
373C2×C22⋊C8—432no—
374C4×M16—861no—
375C2×C4×C8—861no—
376#324—434no—
377#324—434no—
378#323—434no—
379#323C2×D4314yes—
380C43#1738311yescharacteristic, complemented, Sylow
381C22×Q8—431no—
382C22×D4—432no—
383C22×D4C4×D4311yescharacteristic
384C23×C4—431no—
385C23×C4—431no—
386C23×C4—431no—
387C23×C4C4×D4312yes—
388C2×M16—862no—
389C22×C8—862no—
390#126—862no—
391#126—862no—
392#126—862no—
393#126—862no—
394#125—861no—
395#125—861no—
396#125—861no—
397#125—861no—
398#124—861no—
399#124—861no—
400#124—861no—
401#124—861no—
402#123—862no—
403#123—862no—
404#123—862no—
405#123—862no—
406C22⋊Q8—861no—
407C22⋊Q8—861no—
408C22⋊Q8—861no—
409C22⋊Q8—861no—
410#121—861no—
411#121—861no—
412#121—861no—
413#121—861no—
414C4×Q8—861no—
415C4×Q8—861no—
416C4×Q8—861no—
417C4×Q8—861no—
418C4×D4—21no—
419C4×D4—21no—
420C4×D4—21no—
421C4×D4—21no—
422C4×D4—862no—
423C4×D4—862no—
424C4×D4—862no—
425C4×D4—862no—
426#117—862no—
427#117—862no—
428#117—862no—
429#117—862no—
430C2×C4⋊C4—432no—
431C2×C4⋊C4—432no—
432C2×C4⋊C4—432no—
433C2×C4⋊C4—431no—
434C2×C4⋊C4—432no—
435C2×C4⋊C4C4×D4311yescharacteristic
436C2×C22⋊C4—432no—
437C2×C22⋊C4—432no—
438C2×C22⋊C4—432no—
439C2×C22⋊C4—432no—
440C2×C22⋊C4C22×D4312yes—
441C2×C42—431no—
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—432no—
453C2×C42C22×D4311yescharacteristic
454C4⋊C8—21no—
455C4⋊C8—21no—
456C4⋊C8—862no—
457C4⋊C8—862no—
458C4⋊C8—861no—
459C4⋊C8—861no—
460C22⋊C8—432no—
461C22⋊C8—432no—
462C22⋊C8—862no—
463C22⋊C8—862no—
464C22⋊C8C22×D4312yes—
465C22⋊C8C22×D4312yes—
466#97—862no—
467C4×C8—21no—
468C4×C8—21no—
469C4×C8—862no—
470C4×C8—861no—
471C4×C8—861no—
472C24—431no—
473C24C2×C4×D4312yes—
474C2×Q8—861no—
475C2×Q8—861no—
476C2×Q8—862no—
477C2×Q8—862no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—862no—
483C2×D4—862no—
484C2×D4—1724no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—44no—
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—431no—
497C22×C4—431no—
498C22×C4—431no—
499C22×C4—431no—
500C22×C4—431no—
501C22×C4—431no—
502C22×C4—431no—
503C22×C4—432no—
504C22×C4—432no—
505C22×C4—862no—
506C22×C4—862no—
507C22×C4—1722no—
508C22×C4—1722no—
509C22×C4C2×C4×D4311yescharacteristic
510C22×C4C2×C4×D4312yes—
511C22×C4C2×C4×D4311yescharacteristic
512C22×C4C23×D4311yescharacteristic
513M16—1724no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—862no—
517C2×C8—862no—
518C2×C8—1724no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—862no—
522C4⋊C4—862no—
523C4⋊C4—862no—
524C4⋊C4—862no—
525C4⋊C4—862no—
526C4⋊C4—862no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—862no—
530C4⋊C4—862no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—862no—
534C22⋊C4—862no—
535C22⋊C4—862no—
536C22⋊C4—862no—
537C22⋊C4—862no—
538C22⋊C4—862no—
539C22⋊C4—862no—
540C22⋊C4—862no—
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—862no—
554C42—862no—
555C42D4×D4311yescharacteristic
556C42D4×D4311yescharacteristic
557C42D4×D4311yescharacteristic
558C42D4×D4311yescharacteristic
559C23—22no—
560C23—22no—
561C23—22no—
562C23—42no—
563C23—42no—
564C23—431no—
565C23—431no—
566C23—862no—
567C23—861no—
568C23—861no—
569C23—1721no—
570C23C22×C4×D4311yescharacteristic
571Q8—1722no—
572Q8—1722no—
573D4—42no—
574D4—42no—
575D4—1724no—
576D4—1724no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—41no—
580C2×C4—44no—
581C2×C4—44no—
582C2×C4—42no—
583C2×C4—431no—
584C2×C4—431no—
585C2×C4—431no—
586C2×C4—431no—
587C2×C4—431no—
588C2×C4—431no—
589C2×C4—862no—
590C2×C4—862no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—862no—
596C2×C4—862no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—862no—
600C2×C4—862no—
601C2×C4—862no—
602C2×C4—862no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1722no—
610C2×C4C22⋊C4×D4311yescharacteristic
611C2×C4C22⋊C4×D4311yescharacteristic
612C2×C4C22⋊C4×D4311yescharacteristic
613C2×C4C22⋊C4×D4311yescharacteristic
614C2×C4#1306333112yes—
615C2×C4#1306333312yes—
616C2×C4C2×D4×D4311yescharacteristic
617C2×C4C2×D4×D4311yescharacteristic
618C8—42no—
619C8—42no—
620C8—1722no—
621C8—1722no—
622C22—21no—
623C22—21no—
624C22—42no—
625C22—42no—
626C22—42no—
627C22—82no—
628C22—82no—
629C22—432no—
630C22—861no—
631C22—861no—
632C22—861no—
633C22—861no—
634C22—861no—
635C22—1722no—
636C22—1722no—
637C22C2×C22⋊C4×D4311yescharacteristic
638C22C2×#1306333111yescharacteristic
639C22C2×#1306333311yescharacteristic
640C4—21no—
641C4—21no—
642C4—21no—
643C4—42no—
644C4—861no—
645C4—861no—
646C4—861no—
647C4—861no—
648C4—861no—
649C4—861no—
650C4—1722no—
651C4—1722no—
652C4#1458286412yes—
653C4#1458286412yes—
654C4#1458288012yes—
655C2—21no—
656C2—21no—
657C2—82no—
658C2—862no—
659C2—1721no—
660C2C2×#1458286411yescharacteristic
661C2#410×D4311yescharacteristic
662C2C2×#1458288011yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1460C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063296C4
cosocleC22×C4×C43C24
hypercenter#1460D43
hypocenterC43#17383
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1460

Complements

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

NH ≅ G/Ntype
2. #19143223C2semidirect
3. #431×D43C2semidirect
4. #19132961C2semidirect
5. #19132940C2semidirect
6. #19132918C2semidirect
7. #19132918C2semidirect
8. #19132916C2semidirect
9. C43×#1460C2semidirect
332. #1460D43semidirect
380. C43#17383semidirect

Maximal subgroups

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

subgroupindex
C2×#145834312
#191432232
#431×D432
#191329612
#191329402
#191329182
#191329162
C43×#14602
#1738343