Finite Group Databasebeta

← #25063488

Subgroups — #25063488

Order 11008.

970 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148192C211yesmaximal, characteristic
2C8×#10621898C211yesmaximal, characteristic, complemented
3#19143263C211yesmaximal, characteristic, complemented
4#19133052C212yesmaximal, complemented
5#19133026C212yesmaximal, complemented
6#19133023C211yesmaximal, characteristic, complemented
7#19133000C212yesmaximal, complemented
8#19132994C211yesmaximal, characteristic, complemented
9#19132974C212yesmaximal, complemented
10C2×#14582631C211yesmaximal, characteristic, complemented
11C43×#1492C211yesmaximal, characteristic, complemented
12#14583635C411yescharacteristic
13#14583631—21no—
14#14583624C411yescharacteristic
15#14583623C411yescharacteristic
16#14583618—21no—
17#14583601C412yes—
18#14583592—22no—
19#14583569C411yescharacteristic
20#14583555C412yes—
21#14583445—21no—
22#14583431C2212yes—
23#14583429—22no—
24#41×Dic43—21no—
25C4×#10621898C2211yescharacteristic
26C4×#10621900C2212yes—
27C2×C4×Dic86C2211yescharacteristic
28C8×Dic86—21no—
29C8×D172—21no—
30C8×C22⋊D43—22no—
31#14582959—22no—
32#14582955C2212yes—
33#14582952C2211yescharacteristic
34#14582951C2212yes—
35#14582950C2212yes—
36C2×C4⋊(C43⋊C8)C2211yescharacteristic
37#14582867—21no—
38#14582857—21no—
39C4×C8×D43C2212yes—
40#14582631C2211yescharacteristic
41#14582631C2211yescharacteristic
42#14582631C2211yescharacteristic
43#14582631C2211yescharacteristic
44#14582629C2212yes—
45#14582629C2212yes—
46D4⋊(C43⋊C8)C2212yes—
47D4⋊(C43⋊C8)C2212yes—
48C43×#532C2211yescharacteristic
49C43×#423C2211yescharacteristic
50C2×C4×C8×C43C2211yescharacteristic
51C43×D4⋊C8C2212yes—
52C43×D4⋊C8C2212yes—
53C2×#10621898D411yescharacteristic
54C2×#10621900C2×C412yes—
55C22×Dic86C2×C411yescharacteristic
56C22×C43⋊C8—21no—
57C2×C8×D43—22no—
58#13063323—21no—
59#13063321—21no—
60#13063320—22no—
61#13063318—22no—
62#13063318—22no—
63#13063316C2×C412yes—
64#13063315—22no—
65#13063314—21no—
66#13063312—21no—
67#13063312C2×C412yes—
68#13063311—22no—
69#13063309—22no—
70#13063307—22no—
71#13063306—22no—
72#13063305C2×C412yes—
73#13063302—22no—
74#13063297—22no—
75#13063297—22no—
76#13063297—22no—
77#13063296C2×C412yes—
78Q8×Dic43—21no—
79Q8×Dic43—21no—
80C4×Dic86—21no—
81C4×Dic86—21no—
82C4×Dic86C2×C411yescharacteristic
83C4×Dic86C2×C411yescharacteristic
84C4×Dic86C2×C411yescharacteristic
85C4×Dic86D411yescharacteristic
86C4×Dic86C2311yescharacteristic
87C4×Dic86C2311yescharacteristic
88#13063290C2×C412yes—
89C4×D172C2×C411yescharacteristic
90C4×D172D411yescharacteristic
91D4×Dic43—22no—
92D4×Dic43—22no—
93D4×Dic43—21no—
94D4×Dic43—21no—
95D4×Dic43C2×C412yes—
96C4×C22⋊D43—22no—
97C4×C22⋊D43—22no—
98C4×C22⋊D43C2×C412yes—
99C4×C22⋊D43D412yes—
100(C22⋊D43)⋊C4—22no—
101#13063284—22no—
102#13063284D411yescharacteristic
103#13063283C2×C412yes—
104#13063282D412yes—
105#13063281—22no—
106C2×C4⋊Dic43C2×C411yescharacteristic
107C2×Dic43⋊C4—21no—
108C2×C4×Dic43—21no—
109C2×C4×Dic43—22no—
110C42×D43C2312yes—
111C4⋊(C43⋊C8)—21no—
112C4⋊(C43⋊C8)—21no—
113C4⋊(C43⋊C8)C2311yescharacteristic
114C4⋊(C43⋊C8)C2311yescharacteristic
115Dic43⋊C8—22no—
116C22⋊(C43⋊C8)—21no—
117(C2×D43)⋊C8—22no—
118(C2×D43)⋊C8—22no—
119(C2×D43)⋊C8—22no—
120#13063235—22no—
121C4×C43⋊C8C2312yes—
122C8×Dic43—22no—
123C8×Dic43—22no—
124C2×#41×C43—21no—
125C2×M16×C43—21no—
126C22×C8×C43—21no—
127C4⋊Q8×C43C2×C411yescharacteristic
128#127×C43C2×C411yescharacteristic
129#124×C43—21no—
130#121×C43—21no—
131#121×C43C2×C412yes—
132C4×D4×C43—21no—
133C4×D4×C43C2312yes—
134C2×C42×C43C2311yescharacteristic
135C4⋊C8×C43—21no—
136C4⋊C8×C43C2312yes—
137C4×C8×C43—21no—
138C4×C8×C43C2311yescharacteristic
139C4×C8×C43C2311yescharacteristic
140#41×C43—42no—
141#41×C43—42no—
142C2×Q8×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—22no—
146C2×D4×C43C22×C412yes—
147C22×C4×C43—22no—
148C22×C4×C43C22×C411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C2×C22⋊D43—22no—
152C2×C22⋊D43—22no—
153C2×C22⋊D43C22⋊C412yes—
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158#10621900—24no—
159#10621900—42no—
160#10621898—22no—
161#10621898—22no—
162C2×D172C22⋊C411yescharacteristic
163C2×C4×D43C22×C412yes—
164C2×C4×D43C2×D412yes—
165C2×C4×D43C2×D412yes—
166C2×Dic86—22no—
167C2×Dic86—21no—
168C2×Dic86—41no—
169C2×Dic86C22⋊C411yescharacteristic
170C2×Dic86C22×C411yescharacteristic
171C2×Dic86C22×C411yescharacteristic
172M16×C43—42no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—22no—
176C2×C8×C43—42no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43C22×C412yes—
179C22⋊C4×C43—22no—
180C22⋊C4×C43—22no—
181C42×C43C22×C411yescharacteristic
182C42×C43C2×D411yescharacteristic
183C42×C43C2×D411yescharacteristic
184C42×C43C2411yescharacteristic
185C22⋊Dic43—22no—
186C22⋊Dic43—22no—
187C22⋊Dic43—22no—
188C22⋊Dic43—22no—
189C22⋊Dic43C22⋊C412yes—
190(C2×D43)⋊C4—22no—
191(C2×D43)⋊C4—22no—
192(C2×D43)⋊C4C22⋊C412yes—
193(C2×D43)⋊C4C22⋊C412yes—
194C4⋊Dic43—21no—
195C4⋊Dic43—22no—
196C4⋊Dic43—22no—
197C4⋊Dic43C22⋊C411yescharacteristic
198C4⋊Dic43C22⋊C411yescharacteristic
199C4⋊Dic43C22×C411yescharacteristic
200C4⋊Dic43C22×C411yescharacteristic
201Dic43⋊C4—21no—
202Dic43⋊C4—21no—
203Dic43⋊C4—21no—
204Dic43⋊C4—21no—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207Dic43⋊C4C22⋊C412yes—
208Dic43⋊C4C22⋊C412yes—
209C4×Dic43—21no—
210C4×Dic43—21no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C4×Dic43—22no—
214C4×Dic43—22no—
215C4×Dic43C22×C412yes—
216C4×Dic43C2×D412yes—
217C4×Dic43C2×D412yes—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—22no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—42no—
222C8×D43—44no—
223C23×C43—22no—
224C23×C43C2×C22⋊C411yescharacteristic
225C22×D43C2×C22⋊C412yes—
226Q8×C43—42no—
227D4×C43—22no—
228D4×C43—22no—
229D4×C43—44no—
230D4×C43—42no—
231D4×C43—81no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—22no—
235C2×C4×C43—41no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43C2×C22⋊C411yescharacteristic
239C2×C4×C43C2×C22⋊C411yescharacteristic
240C2×C4×C43C2×C22⋊C411yescharacteristic
241C2×C4×C43#13512yes—
242C2×C4×C43#13512yes—
243C2×C4×C43C23×C411yescharacteristic
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43C22×D411yescharacteristic
246C22⋊D43—24no—
247C22⋊D43—44no—
248C22⋊D43—82no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—44no—
254C2×Dic43—42no—
255C2×Dic43—82no—
256C2×Dic43—81no—
257C2×Dic43C2×C22⋊C412yes—
258C2×Dic43C2×C22⋊C412yes—
259C2×Dic43C2×C22⋊C412yes—
260D172—22no—
261C4×D43—22no—
262C4×D43—22no—
263C4×D43—22no—
264C4×D43—22no—
265C4×D43—42no—
266Dic86—21no—
267Dic86—22no—
268Dic86—21no—
269Dic86—21no—
270Dic86—42no—
271Dic86#13112yes—
272C8×C43—22no—
273C8×C43—41no—
274C8×C43—42no—
275C43⋊C8—42no—
276C43⋊C8—41no—
277C43⋊C8—41no—
278#17510—431nomaximal, Sylow
279C22×C43—21no—
280C22×C43—21no—
281C22×C43—42no—
282C22×C43—42no—
283C22×C43—42no—
284C22×C43#41612yes—
285C22×C43C22×C22⋊C411yescharacteristic
286C2×D43—22no—
287C2×D43—22no—
288C2×D43—22no—
289C4×C43—21no—
290C4×C43—21no—
291C4×C43—21no—
292C4×C43—42no—
293C4×C43#41612yes—
294C4×C43C2×#13111yescharacteristic
295C4×C43#56811yescharacteristic
296C4×C43C2×#13511yescharacteristic
297C4×C43C2×#13511yescharacteristic
298Dic43—22no—
299Dic43—22no—
300Dic43—22no—
301Dic43—22no—
302Dic43—41no—
303Dic43—41no—
304Dic43—41no—
305#3480—431no—
306C8×#41—431no—
307#2925—431no—
308#1494—432no—
309#1492D4311yescharacteristic, complemented
310#1488—432no—
311#1487—431no—
312#1482—432no—
313#1480—431no—
314#1476—432no—
315C2×Q8⋊C8—431no—
316C2×C43—22no—
317C2×C43—82no—
318C2×C43#288011yescharacteristic
319C2×C43C2×#41611yescharacteristic
320C2×C43#290111yescharacteristic
321D43—42no—
322#559—431no—
323#559—861no—
324#557—431no—
325#556—431no—
326#556—861no—
327#553—432no—
328#553—862no—
329#550—431no—
330#548—432no—
331#532—861no—
332#532C2×D4311yescharacteristic
333#529—432no—
334#529—862no—
335C4×#41—431no—
336C4×#41—432no—
337C4×#41—861no—
338C2×C4×Q8—431no—
339C8×Q8—861no—
340C8×D4—861no—
341C8×D4—862no—
342#433—862no—
343#432—432no—
344#431—431no—
345#431—432no—
346#431—432no—
347#423C2×D4311yescharacteristic
348C2×C4⋊C8—431no—
349#408—861no—
350#405—861no—
351C2×C4×C8—432no—
352C2×C4×C8C2×D4311yescharacteristic
353Q8⋊C8—432no—
354Q8⋊C8—432no—
355Q8⋊C8—431no—
356Q8⋊C8—431no—
357Q8⋊C8—431no—
358Q8⋊C8—431no—
359D4⋊C8—432no—
360D4⋊C8—432no—
361D4⋊C8C2×D4312yes—
362D4⋊C8C2×D4312yes—
363C43#1751011yescharacteristic, complemented, Sylow
364C2×#41—21no—
365C2×#41—431no—
366C2×#41—432no—
367C22×Q8—431no—
368C2×M16—21no—
369C22×C8—21no—
370C22×C8—862no—
371C22×C8—861no—
372C4⋊Q8—861no—
373C4⋊Q8C4×D4311yescharacteristic
374#127—861no—
375#127C4×D4311yescharacteristic
376#126—862no—
377#126—862no—
378#126—862no—
379#125—432no—
380#125—862no—
381#124—21no—
382#124—432no—
383#124—862no—
384#124—861no—
385#124—861no—
386#123—862no—
387#123—862no—
388#123—862no—
389C22⋊Q8—432no—
390C22⋊Q8—862no—
391#121—21no—
392#121—432no—
393#121—862no—
394#121—862no—
395#121—862no—
396#121C4×D4312yes—
397C4×Q8—431no—
398C4×Q8—431no—
399C4×Q8—432no—
400C4×Q8—431no—
401C4×Q8—431no—
402C4×Q8—431no—
403C4×Q8—431no—
404C4×Q8—861no—
405C4×Q8—861no—
406C4×Q8—861no—
407C4×Q8—861no—
408C4×D4—21no—
409C4×D4—432no—
410C4×D4—432no—
411C4×D4—432no—
412C4×D4—431no—
413C4×D4—431no—
414C4×D4—862no—
415C4×D4—862no—
416C4×D4—862no—
417C4×D4—861no—
418C4×D4—861no—
419C4×D4—862no—
420C4×D4—862no—
421C4×D4C22×D4312yes—
422#117—431no—
423#117—432no—
424#117—432no—
425#117—862no—
426#117—862no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—861no—
429C2×C42—432no—
430C2×C42—862no—
431C2×C42—861no—
432C2×C42C22×D4311yescharacteristic
433C4⋊C8—21no—
434C4⋊C8—431no—
435C4⋊C8—431no—
436C4⋊C8—862no—
437C4⋊C8—861no—
438C4⋊C8—861no—
439C4⋊C8C22×D4312yes—
440C22⋊C8—862no—
441C22⋊C8—862no—
442C22⋊C8—862no—
443C22⋊C8—861no—
444#97—862no—
445C4×C8—21no—
446C4×C8—432no—
447C4×C8—862no—
448C4×C8—862no—
449C4×C8C22×D4311yescharacteristic
450C4×C8C22×D4311yescharacteristic
451#41—42no—
452#41—42no—
453#41—862no—
454#41—862no—
455#41—864no—
456#41—1722no—
457C2×Q8—21no—
458C2×Q8—431no—
459C2×Q8—431no—
460C2×Q8—431no—
461C2×Q8—862no—
462C2×Q8—861no—
463C2×Q8—1721no—
464C2×D4—22no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—432no—
468C2×D4—431no—
469C2×D4—862no—
470C2×D4—862no—
471C2×D4C2×C4×D4312yes—
472C22×C4—22no—
473C22×C4—432no—
474C22×C4—432no—
475C22×C4—432no—
476C22×C4—862no—
477C22×C4—862no—
478C22×C4—861no—
479C22×C4—861no—
480C22×C4C2×C4×D4311yescharacteristic
481C22×C4D4×D4311yescharacteristic
482C22×C4D4×D4311yescharacteristic
483M16—42no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—22no—
487C2×C8—42no—
488C2×C8—862no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—1724no—
492C2×C8—1722no—
493C4⋊C4—21no—
494C4⋊C4—431no—
495C4⋊C4—431no—
496C4⋊C4—432no—
497C4⋊C4—432no—
498C4⋊C4—431no—
499C4⋊C4—431no—
500C4⋊C4—862no—
501C4⋊C4—862no—
502C4⋊C4—862no—
503C4⋊C4—862no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4C2×C4×D4312yes—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—432no—
513C22⋊C4—432no—
514C22⋊C4—432no—
515C22⋊C4—862no—
516C22⋊C4—862no—
517C22⋊C4—862no—
518C22⋊C4—862no—
519C22⋊C4—862no—
520C22⋊C4—862no—
521C42—432no—
522C42—432no—
523C42—432no—
524C42—862no—
525C42—862no—
526C42—861no—
527C42—861no—
528C42—861no—
529C42—861no—
530C42C2×C4×D4311yescharacteristic
531C42D4×D4311yescharacteristic
532C42D4×D4311yescharacteristic
533C42C23×D4311yescharacteristic
534C23—22no—
535C23—432no—
536C23C22⋊C4×D4311yescharacteristic
537Q8—42no—
538Q8—432no—
539Q8—862no—
540Q8—861no—
541Q8—861no—
542Q8—861no—
543Q8—1722no—
544D4—22no—
545D4—22no—
546D4—44no—
547D4—42no—
548D4—81no—
549D4—864no—
550D4—862no—
551D4—3442no—
552D4—1724no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—432no—
560C2×C4—432no—
561C2×C4—432no—
562C2×C4—861no—
563C2×C4—862no—
564C2×C4—862no—
565C2×C4—862no—
566C2×C4—862no—
567C2×C4—861no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—3442no—
571C2×C4—3441no—
572C2×C4—1722no—
573C2×C4—1724no—
574C2×C4—1722no—
575C2×C4C22⋊C4×D4311yescharacteristic
576C2×C4C22⋊C4×D4311yescharacteristic
577C2×C4C22⋊C4×D4311yescharacteristic
578C2×C4#1306334412yes—
579C2×C4#1306334612yes—
580C2×C4C22×C4×D4311yescharacteristic
581C2×C4C2×D4×D4311yescharacteristic
582C2×C4C2×D4×D4311yescharacteristic
583C8—22no—
584C8—41no—
585C8—42no—
586C8—1722no—
587C8—1721no—
588C8—1721no—
589C22—21no—
590C22—21no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22—862no—
595C22—862no—
596C22—862no—
597C22#1458289212yes—
598C22C2×C22⋊C4×D4311yescharacteristic
599C4—21no—
600C4—21no—
601C4—21no—
602C4—42no—
603C4—862no—
604C4—862no—
605C4—862no—
606C4—862no—
607C4—1721no—
608C4—1721no—
609C4—1721no—
610C4#1458289212yes—
611C4#131×D4311yescharacteristic
612C4#1458366411yescharacteristic
613C4C2×#1306334411yescharacteristic
614C4C2×#1306334611yescharacteristic
615C2—22no—
616C2—82no—
617C2—1722no—
618C2#1914304311yescharacteristic
619C2C2×#1458289211yescharacteristic
620C2#1914313911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1492C2
socleC22×C43C22×C22⋊C4
prime radical#19148192C2
cosocleC42×C43C24
hypercenter#1492D43
hypocenterC43#17510
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1492

Complements

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

NH ≅ G/Ntype
2. C8×#10621898C2semidirect
3. #19143263C2semidirect
4. #19133052C2semidirect
5. #19133026C2semidirect
6. #19133023C2semidirect
7. #19133000C2semidirect
8. #19132994C2semidirect
9. #19132974C2semidirect
10. C2×#14582631C2semidirect
11. C43×#1492C2semidirect
309. #1492D43semidirect
363. C43#17510semidirect

Maximal subgroups

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

subgroupindex
#191481922
C8×#106218982
#191432632
#191330522
#191330262
#191330232
#191330002
#191329942
#191329742
C2×#145826312
C43×#14922
#1751043