Finite Group Databasebeta

← #25066784

Subgroups — #25066784

Order 11008.

734 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
1#19144593C211yesmaximal, characteristic
2#19143302C211yesmaximal, characteristic, complemented
3#436×D43C211yesmaximal, characteristic, complemented
4#19133480C211yesmaximal, characteristic, complemented
5#19133479C211yesmaximal, characteristic, complemented
6#19133477C211yesmaximal, characteristic, complemented
7#19133477C211yesmaximal, characteristic, complemented
8#19133426C211yesmaximal, characteristic, complemented
9#19133424C211yesmaximal, characteristic, complemented
10#19133422C211yesmaximal, characteristic, complemented
11#19133368C211yesmaximal, characteristic, complemented
12#19133018C211yesmaximal, characteristic, complemented
13#19132992C211yesmaximal, characteristic, complemented
14#19132880C211yesmaximal, characteristic, complemented
15C43×#1581C211yesmaximal, characteristic, complemented
16C2×#13063331—21no—
17C2×M16×D43—21no—
18#14583446C2211yescharacteristic
19C4×D4×D43C2211yescharacteristic
20#14583214C411yescharacteristic
21#14583211C411yescharacteristic
22#14583178C411yescharacteristic
23#14583177C411yescharacteristic
24#14583093C411yescharacteristic
25#14583092C411yescharacteristic
26#14583034C411yescharacteristic
27#14583031C411yescharacteristic
28C4×D344C2211yescharacteristic
29C4×#10621882C2211yescharacteristic
30C4×#10621882C2211yescharacteristic
31#14582978C2211yescharacteristic
32#14582977C2211yescharacteristic
33#14582977C2211yescharacteristic, complemented
34#14582976C2211yescharacteristic
35#14582976C2211yescharacteristic, complemented
36#14582975—21no—
37#14582974—21no—
38#14582974—21no—
39C8×D172C2211yescharacteristic, complemented
40C8×C22⋊D43—21no—
41#14582950C2211yescharacteristic
42#14582950C2211yescharacteristic
43#14582921C2211yescharacteristic
44C4⋊C8×D43C2211yescharacteristic
45#14582864—21no—
46C22⋊C8×D43—21no—
47C4×C8×D43C2211yescharacteristic
48#14582652C2211yescharacteristic, complemented
49#14582651C2211yescharacteristic, complemented
50#14582651C2211yescharacteristic, complemented
51#14582628C2211yescharacteristic
52#14582628C2211yescharacteristic, complemented
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic, complemented
55#14582626C2211yescharacteristic
56#14582626C2211yescharacteristic, complemented
57#14582620C2211yescharacteristic, complemented
58C8×C43⋊C8C2211yescharacteristic, complemented
59C8×C43⋊C8C2211yescharacteristic, complemented
60C4×D8×C43C2211yescharacteristic
61C43×#436C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic, complemented
63C43×#335C2211yescharacteristic, complemented
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic, complemented
66C43×#322C2211yescharacteristic, complemented
67C2×#10621898—21no—
68C2×D4×D43C2×C411yescharacteristic
69C22×C4×D43—21no—
70C2×D344C2×C411yescharacteristic
71C2×#10621882C2×C411yescharacteristic
72C2×#10621882C2×C411yescharacteristic
73#13063331—44no—
74C2×#10621877—21no—
75C2×#10621877—21no—
76C2×#10621872—21no—
77C2×#10621872—21no—
78C2×#10621872—21no—
79C2×#10621872—21no—
80M16×D43—44no—
81C2×C8×D43—21no—
82C2×C8×D43—21no—
83C2×C8×D43D411yescharacteristic
84C2×C8×D43D411yescharacteristic
85#13063324C2×C411yescharacteristic
86#13063321C2×C411yescharacteristic
87#13063311—21no—
88#13063300C2×C411yescharacteristic
89#13063298—21no—
90#13063296C2×C411yescharacteristic
91C4×D172C2311yescharacteristic
92C4×D172C2311yescharacteristic
93D4×Dic43C2×C411yescharacteristic
94#13063287C2×C411yescharacteristic
95C4×C22⋊D43—21no—
96C4×C22⋊D43—21no—
97(C22⋊D43)⋊C4—21no—
98C4⋊C4×D43C2×C411yescharacteristic
99C22⋊C4×D43—21no—
100C42×D43C2311yescharacteristic
101#13063259C2×C411yescharacteristic
102#13063258C2×C411yescharacteristic
103#13063258C2×C411yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8C2×C411yescharacteristic
110Dic43⋊C8C2×C411yescharacteristic
111#13063247C2×C411yescharacteristic
112#13063247C2×C411yescharacteristic
113#13063246C2×C411yescharacteristic
114#13063246C2×C411yescharacteristic
115#13063245C2×C411yescharacteristic
116#13063245C2×C411yescharacteristic
117C22⋊(C43⋊C8)—21no—
118C22⋊(C43⋊C8)—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8—21no—
123(C2×D43)⋊C8—21no—
124(C2×D43)⋊C8C2×C411yescharacteristic
125(C2×D43)⋊C8C2×C411yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C4×C43⋊C8C2311yescharacteristic
128C4×C43⋊C8C2311yescharacteristic
129C8×Dic43D411yescharacteristic
130C8×Dic43D411yescharacteristic
131C2×D8×C43C2×C411yescharacteristic
132C2×M16×C43—21no—
133C22×C8×C43—21no—
134C4×D4×C43C2311yescharacteristic
135C4×D4×C43C2311yescharacteristic
136#107×C43C2×C411yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#102×C43C2×C411yescharacteristic
140#102×C43C2×C411yescharacteristic
141C22⋊C8×C43—21no—
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C4×C8×C43C2311yescharacteristic
146C23×D43—21no—
147C2×D4×C43C22×C411yescharacteristic
148C2×D4×C43C22×C411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C2×C22⋊D43—21no—
152C2×C22⋊D43—21no—
153C2×C22⋊D43—21no—
154C2×C22⋊D43—21no—
155C22×Dic43—21no—
156D4×D43—41no—
157D4×D43—41no—
158#10621898—42no—
159#10621898—42no—
160C2×D172—21no—
161C2×D172C22×C411yescharacteristic
162C2×D172C22×C411yescharacteristic
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×C4×D43—21no—
167C2×C4×D43—42no—
168C2×C4×D43—42no—
169C2×C4×D43C22×C411yescharacteristic
170C2×C4×D43C2×D411yescharacteristic
171C2×C4×D43#4111yescharacteristic
172C2×Dic86—21no—
173D8×C43—41no—
174M16×C43—42no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—42no—
179C2×C8×C43C22×C411yescharacteristic
180C2×C8×C43C22×C411yescharacteristic
181C2×C8×C43C2×D411yescharacteristic
182C2×C8×C43C2×D411yescharacteristic
183C4⋊C4×C43C22×C411yescharacteristic
184C4⋊C4×C43C22×C411yescharacteristic
185C22⋊C4×C43—21no—
186C22⋊C4×C43—21no—
187C42×C43C2411yescharacteristic
188C22⋊Dic43—21no—
189C22⋊Dic43—21no—
190#10621882—41no—
191#10621882—41no—
192(C2×D43)⋊C4—21no—
193(C2×D43)⋊C4—21no—
194(C2×D43)⋊C4—21no—
195(C2×D43)⋊C4—21no—
196C4⋊Dic43C22×C411yescharacteristic
197C4⋊Dic43C22×C411yescharacteristic
198Dic43⋊C4—21no—
199Dic43⋊C4—21no—
200C4×Dic43C22×C411yescharacteristic
201C4×Dic43C2×D411yescharacteristic
202C4×Dic43#4111yescharacteristic
203#10621877—42no—
204#10621877—42no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8C22×C411yescharacteristic
209C2×C43⋊C8C22×C411yescharacteristic
210C2×C43⋊C8C2×D411yescharacteristic
211C2×C43⋊C8C2×D411yescharacteristic
212D344—41no—
213#10621872—42no—
214#10621872—42no—
215#10621872—42no—
216#10621872—42no—
217C8×D43—22no—
218C8×D43—42no—
219C8×D43—42no—
220C8×D43D814yescomplemented
221C23×C43—21no—
222C23×C43—21no—
223C22×D43—21no—
224C22×D43—21no—
225C22×D43—42no—
226C22×D43—42no—
227C22×D43—42no—
228C22×D43C4×D411yescharacteristic
229D4×C43—21no—
230D4×C43—21no—
231D4×C43—21no—
232D4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43C23×C411yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C22⋊D43—42no—
243C22⋊D43—42no—
244C22⋊D43—42no—
245C22⋊D43—42no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—42no—
249C2×Dic43C4×D411yescharacteristic
250C2×Dic43C4×D411yescharacteristic
251C2×Dic43C4×D411yescharacteristic
252D172—21no—
253D172—21no—
254D172—21no—
255D172—21no—
256D172—42no—
257C4×D43—21no—
258C4×D43—21no—
259C4×D43—41no—
260C4×D43—42no—
261C4×D43—41no—
262C4×D43—41no—
263C4×D43—41no—
264C4×D43—41no—
265C4×D43—42no—
266C4×D43C2×D812yes—
267C4×D43#13512yes—
268Dic86—42no—
269C8×C43—21no—
270C8×C43—21no—
271C8×C43—21no—
272C8×C43—41no—
273C8×C43—41no—
274C8×C43—41no—
275C8×C43C2×D812yes—
276C43⋊C8—21no—
277C43⋊C8—21no—
278C43⋊C8—21no—
279C43⋊C8—41no—
280C43⋊C8—41no—
281C43⋊C8—41no—
282C43⋊C8C2×D812yes—
283#17928—431nomaximal, Sylow
284C22×C43—41no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43—41no—
290C22×C43C2×C4×D411yescharacteristic
291C2×D43—21no—
292C2×D43—21no—
293C2×D43—41no—
294C2×D43—41no—
295C2×D43—41no—
296C2×D43—41no—
297C2×D43—41no—
298C2×D43—41no—
299C2×D43—84no—
300C2×D43C4×D812yes—
301C4×C43—21no—
302C4×C43—41no—
303C4×C43—41no—
304C4×C43#56811yescharacteristic
305C4×C43#56811yescharacteristic
306C4×C43C22×D811yescharacteristic
307C4×C43C2×#13511yescharacteristic
308Dic43—21no—
309Dic43—21no—
310Dic43—41no—
311Dic43—41no—
312Dic43C4×D812yes—
313#3100—431no—
314#2931—431no—
315C2×#436—431no—
316#1589—431no—
317#1589—431no—
318#1589—431no—
319#1589—431no—
320#1581—431no—
321#1581—431no—
322#1581—431no—
323#1581D4311yescharacteristic, complemented
324#1571—431no—
325#1486—431no—
326#1480—431no—
327#1450—431no—
328C2×C43—81no—
329C2×C43—81no—
330C2×C43#293011yescharacteristic
331C2×C43C2×C4×D811yescharacteristic
332C2×C43#295511yescharacteristic
333D43—22no—
334D43—81no—
335D43—81no—
336C2×#131—861no—
337C22×M16—861no—
338#532—431no—
339C2×C4×D4—431no—
340#480—431no—
341#480—431no—
342#474—431no—
343#474—431no—
344#459—431no—
345#459—431no—
346#447—431no—
347#447—431no—
348C4×D8—431no—
349C4×D8—431no—
350C4×D8—431no—
351C4×D8C2×D4311yescharacteristic
352#436—431no—
353#436—431no—
354#436—431no—
355#436—431no—
356#436—431no—
357#436—861no—
358#436—861no—
359#436—861no—
360#436C2×D4311yescharacteristic
361C8×D4—431no—
362C8×D4—861no—
363C8×D4C2×D4311yescharacteristic, complemented
364#431—431no—
365#431—431no—
366#423—431no—
367C2×C4⋊C8—431no—
368#408—861no—
369C2×C22⋊C8—861no—
370C2×C4×C8—431no—
371#335—431no—
372#335—431no—
373#335—431no—
374#335C2×D4311yescharacteristic, complemented
375D4⋊C8—431no—
376D4⋊C8—431no—
377D4⋊C8—431no—
378D4⋊C8—431no—
379D4⋊C8—431no—
380D4⋊C8—431no—
381D4⋊C8C2×D4311yescharacteristic
382D4⋊C8C2×D4311yescharacteristic, complemented
383#322—431no—
384#322C2×D4311yescharacteristic, complemented
385C82—431no—
386C82—431no—
387C43#1792811yescharacteristic, complemented, Sylow
388C2×#41—861no—
389C22×D4—431no—
390C23×C4—861no—
391C2×D8—431no—
392C2×D8—431no—
393C2×D8—431no—
394C2×D8C4×D4311yescharacteristic
395#131—1724no—
396C2×M16—21no—
397C2×M16—861no—
398C2×M16—861no—
399C2×M16—861no—
400C2×M16—861no—
401C2×M16—861no—
402C2×M16—861no—
403C2×M16—1724no—
404C22×C8—21no—
405C22×C8—431no—
406C22×C8—431no—
407C22×C8—861no—
408C22×C8—861no—
409C4⋊Q8—431no—
410#127—431no—
411#124—861no—
412#121—431no—
413#121—431no—
414#121—861no—
415C4×D4—431no—
416C4×D4—431no—
417C4×D4—431no—
418C4×D4—431no—
419C4×D4—861no—
420C4×D4—861no—
421C4×D4—861no—
422C4×D4C22×D4311yescharacteristic
423C4×D4C22×D4311yescharacteristic
424C2×C4⋊C4—431no—
425C2×C22⋊C4—861no—
426C2×C42—431no—
427#107—431no—
428#107—431no—
429#107—431no—
430#107C4×D4311yescharacteristic
431C4⋊C8—431no—
432C4⋊C8—431no—
433C4⋊C8—431no—
434C4⋊C8—431no—
435C4⋊C8—861no—
436C4⋊C8—861no—
437C4⋊C8—861no—
438C4⋊C8C22×D4311yescharacteristic
439C4⋊C8C22×D4311yescharacteristic
440#102—431no—
441#102—431no—
442#102—431no—
443#102—431no—
444#102—431no—
445#102—431no—
446#102C4×D4311yescharacteristic
447#102C4×D4311yescharacteristic
448C22⋊C8—21no—
449C22⋊C8—21no—
450C22⋊C8—431no—
451C22⋊C8—431no—
452C22⋊C8—861no—
453C22⋊C8—861no—
454C22⋊C8—861no—
455C22⋊C8—861no—
456C22⋊C8—861no—
457C22⋊C8—861no—
458C22⋊C8—861no—
459C4×C8—431no—
460C4×C8—431no—
461C4×C8—431no—
462C4×C8—431no—
463C4×C8—431no—
464C4×C8C22×D4311yescharacteristic
465C4×C8C22×D4311yescharacteristic
466C4×C8C22×D4311yescharacteristic
467C24—861no—
468#41—1722no—
469#41—1722no—
470C2×Q8—861no—
471C2×D4—431no—
472C2×D4—431no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—861no—
476C2×D4—861no—
477C2×D4—861no—
478C2×D4—1721no—
479C2×D4—1721no—
480C2×D4C2×C4×D4311yescharacteristic
481C2×D4C2×C4×D4311yescharacteristic
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—1722no—
493C22×C4—1722no—
494D8—41no—
495D8—1721no—
496D8—1721no—
497D8—1721no—
498M16—42no—
499M16—1722no—
500M16—1722no—
501M16—1722no—
502M16—1722no—
503M16—1722no—
504M16—1722no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—42no—
509C2×C8—431no—
510C2×C8—434no—
511C2×C8—431no—
512C2×C8—431no—
513C2×C8—431no—
514C2×C8—862no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—1722no—
519C2×C8—1722no—
520C2×C8C2×C4×D4311yescharacteristic
521C2×C8C2×C4×D4311yescharacteristic
522C2×C8D4×D4311yescharacteristic
523C2×C8D4×D4311yescharacteristic
524C4⋊C4—431no—
525C4⋊C4—431no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4C2×C4×D4311yescharacteristic
529C4⋊C4C2×C4×D4311yescharacteristic
530C22⋊C4—21no—
531C22⋊C4—21no—
532C22⋊C4—861no—
533C22⋊C4—861no—
534C22⋊C4—861no—
535C22⋊C4—861no—
536C22⋊C4—861no—
537C22⋊C4—861no—
538C42—431no—
539C42—431no—
540C42—431no—
541C42C23×D4311yescharacteristic
542C23—21no—
543C23—21no—
544C23—431no—
545C23—861no—
546C23—861no—
547C23—1722no—
548C23—1722no—
549C23—1722no—
550Q8—1722no—
551D4—21no—
552D4—21no—
553D4—21no—
554D4—21no—
555D4—861no—
556D4—861no—
557D4—861no—
558D4—861no—
559D4—1722no—
560D4—1722no—
561D4—1722no—
562D4—1722no—
563D4—1722no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—431no—
571C2×C4—432no—
572C2×C4—432no—
573C2×C4—431no—
574C2×C4—431no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—1721no—
580C2×C4—1722no—
581C2×C4—1722no—
582C2×C4—1722no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4C22×C4×D4311yescharacteristic
588C2×C4C2×D4×D4311yescharacteristic
589C2×C4#41×D4311yescharacteristic
590C8—21no—
591C8—21no—
592C8—21no—
593C8—41no—
594C8—41no—
595C8—41no—
596C8—432no—
597C8—861no—
598C8—861no—
599C8—861no—
600C8—1721no—
601C8—1721no—
602C8—1721no—
603C8D8×D4312yes—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—432no—
611C22—861no—
612C22—861no—
613C22—3444no—
614C22—1721no—
615C22—1721no—
616C22—1721no—
617C22—1721no—
618C22—1721no—
619C22—1721no—
620C22C4×D4×D4311yescharacteristic
621C4—21no—
622C4—41no—
623C4—41no—
624C4—432no—
625C4—861no—
626C4—861no—
627C4—1721no—
628C4—1721no—
629C4#1458366411yescharacteristic
630C4#1458366511yescharacteristic
631C4C2×D8×D4311yescharacteristic
632C4#135×D4311yescharacteristic
633C2—81no—
634C2—81no—
635C2—862no—
636C2—3441no—
637C2—3441no—
638C2#1914329311yescharacteristic
639C2C4×D8×D4311yescharacteristic
640C2#1914349511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1581C2
socleC22×C43C2×C4×D4
prime radical#19144593C2
cosocleC42×C43C24
hypercenter#1581D43
hypocenterC43#17928
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1581

Complements

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

NH ≅ G/Ntype
2. #19143302C2semidirect
3. #436×D43C2semidirect
4. #19133480C2semidirect
5. #19133479C2semidirect
6. #19133477C2semidirect
7. #19133477C2semidirect
8. #19133426C2semidirect
9. #19133424C2semidirect
10. #19133422C2semidirect
11. #19133368C2semidirect
12. #19133018C2semidirect
13. #19132992C2semidirect
14. #19132880C2semidirect
15. C43×#1581C2semidirect
33. #14582977C22semidirect
35. #14582976C22semidirect
39. C8×D172C22semidirect
48. #14582652C22semidirect
49. #14582651C22semidirect
50. #14582651C22semidirect
52. #14582628C22semidirect
54. D4⋊(C43⋊C8)C22semidirect
56. #14582626C22semidirect
57. #14582620C22semidirect
58. C8×C43⋊C8C22semidirect
59. C8×C43⋊C8C22semidirect
62. C8×D4×C43C22semidirect
63. C43×#335C22semidirect
65. C43×D4⋊C8C22semidirect
66. C43×#322C22semidirect
220. C8×D43D8semidirect
323. #1581D43semidirect
363. C8×D4C2×D43semidirect
374. #335C2×D43semidirect
382. D4⋊C8C2×D43semidirect
384. #322C2×D43semidirect
387. C43#17928semidirect

Maximal subgroups

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

subgroupindex
#191445932
#191433022
#436×D432
#191334802
#191334792
#191334772
#191334262
#191334242
#191334222
#191333682
#191330182
#191329922
#191328802
C43×#15812
#1792843