Finite Group Databasebeta

← #25063163

Subgroups — #25063163

Order 11008.

1010 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147890C211yesmaximal, characteristic
2#19143226C211yesmaximal, characteristic, complemented
3#431×D43C211yesmaximal, characteristic, complemented
4#19133017C211yesmaximal, characteristic, complemented
5#19133015C211yesmaximal, characteristic, complemented
6#19133012C211yesmaximal, characteristic, complemented
7#19133000C214yesmaximal, complemented
8#19132979C214yesmaximal, complemented
9C43×#1484C211yesmaximal, characteristic, complemented
10#14583456C2211yescharacteristic
11#14583454C411yescharacteristic
12#14583454C411yescharacteristic
13#14583447C411yescharacteristic
14#14583447C411yescharacteristic
15#14583431—21no—
16#14583431C2212yes—
17#14583430—21no—
18#14583430C412yes—
19#14583428—21no—
20#14583428—21no—
21#14583409—21no—
22#14583409C412yes—
23#14583406—21no—
24#41×Dic43—21no—
25C4×#10621900—21no—
26C4×#10621900C2212yes—
27C2×C42×D43C2211yescharacteristic
28#14582954—21no—
29#14582954—21no—
30#14582952C2211yescharacteristic
31#14582951C2212yes—
32#14582950—21no—
33#14582950C2212yes—
34#14582950C2212yes—
35#14582949—21no—
36#14582922—21no—
37C4⋊C8×D43C2212yes—
38#14582862—21no—
39C22⋊C8×D43—21no—
40C4×#10621877C2211yescharacteristic
41C4×C8×D43—21no—
42#14582631C2214yescomplemented
43#14582629C2214yescomplemented
44D4⋊(C43⋊C8)C2214yescomplemented
45C43×#532C2211yescharacteristic
46C43×#431C2211yescharacteristic
47C4×M16×C43C2211yescharacteristic
48C43×D4⋊C8C2214yescomplemented
49C2×#10621900—21no—
50C2×#10621900C2×C412yes—
51C22×C4×D43C2×C411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43D411yescharacteristic
54C2×#10621877—21no—
55C2×C8×D43—22no—
56#13063325C2×C411yescharacteristic
57#13063325C2×C411yescharacteristic
58#13063318—22no—
59#13063318—22no—
60#13063317—21no—
61#13063316—21no—
62#13063316C2×C412yes—
63#13063312—21no—
64#13063312C2×C412yes—
65#13063307—22no—
66#13063307—22no—
67#13063306—22no—
68#13063305—21no—
69#13063305C2×C412yes—
70#13063304—21no—
71#13063304C2×C412yes—
72#13063301—21no—
73#13063301—21no—
74#13063296—21no—
75#13063296—21no—
76#13063296—21no—
77#13063296C2×C412yes—
78#13063293—22no—
79Q8×Dic43—21no—
80Q8×Dic43—21no—
81C4×Dic86—21no—
82C4×Dic86C2312yes—
83#13063290—21no—
84#13063290C2×C412yes—
85D4×Dic43—22no—
86D4×Dic43—22no—
87D4×Dic43—21no—
88D4×Dic43—21no—
89D4×Dic43—21no—
90D4×Dic43C2×C412yes—
91C4×C22⋊D43—22no—
92C4×C22⋊D43—22no—
93(C22⋊D43)⋊C4—22no—
94(C22⋊D43)⋊C4—22no—
95#13063284—21no—
96#13063284—22no—
97#13063283—21no—
98#13063283C2×C412yes—
99#13063281—22no—
100#13063281—22no—
101C2×C4×Dic43—22no—
102C2×C4×Dic43C2×C411yescharacteristic
103C2×C4×Dic43D411yescharacteristic
104C2×C4×Dic43D411yescharacteristic
105C42×D43C2×C411yescharacteristic
106C42×D43C2×C411yescharacteristic
107C42×D43D411yescharacteristic
108C42×D43D411yescharacteristic
109C42×D43D411yescharacteristic
110C42×D43D411yescharacteristic
111C42×D43C2311yescharacteristic
112C42×D43C2311yescharacteristic
113C4⋊(C43⋊C8)C2312yes—
114Dic43⋊C8—22no—
115Dic43⋊C8—22no—
116Dic43⋊C8—22no—
117C22⋊(C43⋊C8)—21no—
118(C2×D43)⋊C8—22no—
119(C2×D43)⋊C8—22no—
120(C2×D43)⋊C8—22no—
121#13063236—21no—
122C4×C43⋊C8—21no—
123C4×C43⋊C8C2312yes—
124C8×Dic43—22no—
125C2×#41×C43—21no—
126C2×M16×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×C43C2312yes—
136C22⋊C8×C43—21no—
137#97×C43—21no—
138C4×C8×C43—21no—
139C4×C8×C43C2312yes—
140C23×D43C22⋊C411yescharacteristic
141#41×C43—44no—
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—
153C22×Dic43—22no—
154C22×Dic43—22no—
155C22×Dic43C22⋊C411yescharacteristic
156C22×Dic43C22⋊C411yescharacteristic
157C22×Dic43C22⋊C411yescharacteristic
158#10621900—28no—
159#10621900—44no—
160C2×C4×D43—24no—
161C2×C4×D43—42no—
162C2×C4×D43—42no—
163C2×C4×D43C22⋊C411yescharacteristic
164C2×C4×D43C22⋊C411yescharacteristic
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×D43C2×D411yescharacteristic
172C2×C4×D43C2×D411yescharacteristic
173C2×C4×D43C2×D411yescharacteristic
174C2×C4×D43C2×D411yescharacteristic
175C2×Dic86—21no—
176C2×Dic86C22×C412yes—
177M16×C43—42no—
178C2×C8×C43—22no—
179C2×C8×C43—22no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43C22×C412yes—
182C22⋊C4×C43—22no—
183C22⋊C4×C43—22no—
184C42×C43C22×C411yescharacteristic
185C42×C43C2×D411yescharacteristic
186C42×C43C2×D411yescharacteristic
187C42×C43C2411yescharacteristic
188C22⋊Dic43—22no—
189C22⋊Dic43—22no—
190C22⋊Dic43—22no—
191C22⋊Dic43—22no—
192C22⋊Dic43—22no—
193(C2×D43)⋊C4—22no—
194(C2×D43)⋊C4—22no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—22no—
199C4⋊Dic43—22no—
200C4⋊Dic43C22×C412yes—
201Dic43⋊C4—22no—
202Dic43⋊C4—22no—
203Dic43⋊C4—22no—
204Dic43⋊C4—22no—
205C4×Dic43—22no—
206C4×Dic43—22no—
207C4×Dic43—22no—
208C4×Dic43C22⋊C411yescharacteristic
209C4×Dic43C22⋊C411yescharacteristic
210C4×Dic43C22⋊C411yescharacteristic
211C4×Dic43C22⋊C411yescharacteristic
212C4×Dic43C22⋊C411yescharacteristic
213C4×Dic43C22⋊C411yescharacteristic
214C4×Dic43C22×C411yescharacteristic
215C4×Dic43C22×C411yescharacteristic
216C4×Dic43C2×D411yescharacteristic
217C4×Dic43C2×D411yescharacteristic
218C4×Dic43C2×D411yescharacteristic
219C4×Dic43C2×D411yescharacteristic
220#10621877—42no—
221C2×C43⋊C8—22no—
222C2×C43⋊C8—22no—
223C8×D43—44no—
224C23×C43—22no—
225C23×C43C2×C22⋊C411yescharacteristic
226C22×D43—22no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43C2×C22⋊C411yescharacteristic
230C22×D43C2×C22⋊C411yescharacteristic
231Q8×C43—42no—
232D4×C43—24no—
233D4×C43—42no—
234D4×C43—44no—
235D4×C43—42no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—44no—
241C2×C4×C43C2×C22⋊C411yescharacteristic
242C2×C4×C43C2×C22⋊C411yescharacteristic
243C2×C4×C43C2×C22⋊C411yescharacteristic
244C2×C4×C43C23×C411yescharacteristic
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C22⋊D43—44no—
248C22⋊D43—44no—
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—44no—
255C2×Dic43—44no—
256C2×Dic43C2×C22⋊C411yescharacteristic
257C2×Dic43C2×C22⋊C411yescharacteristic
258C2×Dic43C2×C22⋊C411yescharacteristic
259C2×Dic43C2×C22⋊C411yescharacteristic
260C2×Dic43C2×C22⋊C411yescharacteristic
261C2×Dic43C2×C22⋊C411yescharacteristic
262C4×D43—22no—
263C4×D43—22no—
264C4×D43—22no—
265C4×D43—22no—
266C4×D43—22no—
267C4×D43—22no—
268C4×D43—22no—
269C4×D43—41no—
270C4×D43—41no—
271C4×D43—41no—
272C4×D43—41no—
273C4×D43#13114yes—
274Dic86—24no—
275Dic86—42no—
276C8×C43—42no—
277C8×C43—42no—
278C43⋊C8—42no—
279C43⋊C8—42no—
280#17467—431nomaximal, Sylow
281C22×C43—21no—
282C22×C43—21no—
283C22×C43—21no—
284C22×C43—42no—
285C22×C43—42no—
286C22×C43—42no—
287C22×C43C22×C22⋊C411yescharacteristic
288C2×D43—21no—
289C2×D43—21no—
290C2×D43—21no—
291C2×D43—21no—
292C2×D43—21no—
293C2×D43—44no—
294C2×D43#40812yes—
295C4×C43—21no—
296C4×C43—21no—
297C4×C43—21no—
298C4×C43—42no—
299C4×C43#42112yes—
300C4×C43C2×#13112yes—
301C4×C43#57512yes—
302Dic43—21no—
303Dic43—21no—
304Dic43—21no—
305Dic43—21no—
306Dic43—21no—
307Dic43—42no—
308Dic43—42no—
309Dic43#40812yes—
310#3444—431no—
311#2920—431no—
312C2×#431—431no—
313#1485—431no—
314#1485—431no—
315#1484—431no—
316#1484D4311yescharacteristic, complemented
317#1482—434no—
318#1477—434no—
319C2×C43—41no—
320C2×C43—82no—
321C2×C43C2×#40811yescharacteristic
322C2×C43#289611yescharacteristic
323C2×C43C2×#42111yescharacteristic
324D43—22no—
325D43—41no—
326#533—431no—
327#533—431no—
328#533—431no—
329#532—431no—
330#532—431no—
331#532C2×D4311yescharacteristic
332#529—432no—
333#529—432no—
334#529—861no—
335#529—861no—
336#529—861no—
337#529—861no—
338#525—432no—
339#525—861no—
340#525—861no—
341C4×#41—432no—
342C4×#41—861no—
343C4×#41—861no—
344C22×C42—431no—
345#432—861no—
346#432—861no—
347#431—432no—
348#431—432no—
349#431—431no—
350#431—432no—
351#431—861no—
352#431—861no—
353#431C2×D4311yescharacteristic
354#423—861no—
355C2×C4⋊C8—432no—
356#407—861no—
357C2×C22⋊C8—861no—
358C4×M16—431no—
359C4×M16C2×D4311yescharacteristic
360C2×C4×C8—861no—
361Q8⋊C8—434no—
362Q8⋊C8—434no—
363D4⋊C8—434no—
364D4⋊C8C2×D4314yescomplemented
365C43#1746711yescharacteristic, complemented, Sylow
366C2×#41—21no—
367C2×#41—432no—
368C2×#41—861no—
369C23×C4—431no—
370C23×C4—431no—
371C23×C4—431no—
372C2×M16—21no—
373C2×M16—861no—
374C22×C8—862no—
375C4⋊Q8—431no—
376C4⋊Q8—431no—
377C4⋊Q8C4×D4311yescharacteristic
378#127C4×D4311yescharacteristic
379#126—862no—
380#126—862no—
381#125—432no—
382#125—861no—
383#125—861no—
384#124—21no—
385#124—432no—
386#124—861no—
387#123—862no—
388#123—862no—
389#123—862no—
390C22⋊Q8—432no—
391C22⋊Q8—432no—
392C22⋊Q8—861no—
393C22⋊Q8—861no—
394C22⋊Q8—861no—
395C22⋊Q8—861no—
396#121—21no—
397#121—432no—
398#121—861no—
399#121—861no—
400#121—861no—
401#121C4×D4312yes—
402#120—862no—
403C4×Q8—432no—
404C4×Q8—432no—
405C4×Q8—861no—
406C4×Q8—861no—
407C4×Q8—861no—
408C4×Q8—861no—
409C4×D4—21no—
410C4×D4—432no—
411C4×D4—861no—
412C4×D4—861no—
413C4×D4—861no—
414C4×D4—862no—
415C4×D4—862no—
416C4×D4—862no—
417C4×D4—862no—
418C4×D4—862no—
419C4×D4—862no—
420C4×D4C22×D4312yes—
421#117—432no—
422#117—862no—
423#117—862no—
424#117—862no—
425#117—861no—
426#117—861no—
427C2×C42—431no—
428C2×C42—431no—
429C2×C42—431no—
430C2×C42—431no—
431C2×C42—431no—
432C2×C42—431no—
433C2×C42—431no—
434C2×C42—431no—
435C2×C42—431no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—862no—
439C2×C42C22×D4311yescharacteristic
440C4⋊C8—432no—
441C4⋊C8—862no—
442C4⋊C8—862no—
443C4⋊C8—862no—
444C4⋊C8C22×D4312yes—
445C22⋊C8—21no—
446C22⋊C8—862no—
447C22⋊C8—862no—
448C22⋊C8—862no—
449C22⋊C8—861no—
450#97—21no—
451#97—861no—
452C4×C8—21no—
453C4×C8—432no—
454C4×C8—862no—
455C4×C8—861no—
456C4×C8C22×D4312yes—
457C24—431no—
458#41—44no—
459#41—868no—
460#41—1724no—
461C2×Q8—21no—
462C2×Q8—432no—
463C2×Q8—861no—
464C2×D4—22no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—862no—
468C2×D4—862no—
469C2×D4C2×C4×D4312yes—
470C22×C4—22no—
471C22×C4—431no—
472C22×C4—431no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—431no—
477C22×C4—431no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—864no—
487C22×C4—862no—
488C22×C4—862no—
489C22×C4—1722no—
490C22×C4—1722no—
491C22×C4C2×C4×D4311yescharacteristic
492C22×C4D4×D4311yescharacteristic
493C22×C4D4×D4311yescharacteristic
494M16—42no—
495M16—1722no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—862no—
499C2×C8—862no—
500C2×C8—1724no—
501C4⋊C4—21no—
502C4⋊C4—432no—
503C4⋊C4—862no—
504C4⋊C4—862no—
505C4⋊C4—862no—
506C4⋊C4—862no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—862no—
511C4⋊C4—862no—
512C4⋊C4C2×C4×D4312yes—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—862no—
516C22⋊C4—862no—
517C22⋊C4—862no—
518C22⋊C4—862no—
519C22⋊C4—862no—
520C22⋊C4—862no—
521C22⋊C4—862no—
522C42—431no—
523C42—431no—
524C42—431no—
525C42—431no—
526C42—431no—
527C42—431no—
528C42—431no—
529C42—431no—
530C42—431no—
531C42—431no—
532C42—431no—
533C42—431no—
534C42—862no—
535C42—862no—
536C42—862no—
537C42C2×C4×D4311yescharacteristic
538C42D4×D4311yescharacteristic
539C42D4×D4311yescharacteristic
540C42C23×D4311yescharacteristic
541C23—22no—
542C23—431no—
543C23—431no—
544C23—862no—
545C23—1721no—
546C23—1721no—
547C23C22⋊C4×D4311yescharacteristic
548Q8—42no—
549Q8—864no—
550Q8—1722no—
551D4—24no—
552D4—42no—
553D4—44no—
554D4—42no—
555D4—1724no—
556D4—1724no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—44no—
562C2×C4—431no—
563C2×C4—434no—
564C2×C4—431no—
565C2×C4—431no—
566C2×C4—431no—
567C2×C4—431no—
568C2×C4—431no—
569C2×C4—862no—
570C2×C4—862no—
571C2×C4—862no—
572C2×C4—862no—
573C2×C4—862no—
574C2×C4—862no—
575C2×C4—862no—
576C2×C4—862no—
577C2×C4—862no—
578C2×C4—862no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1724no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1724no—
587C2×C4C22⋊C4×D4311yescharacteristic
588C2×C4C22⋊C4×D4311yescharacteristic
589C2×C4C22⋊C4×D4311yescharacteristic
590C2×C4C22×C4×D4311yescharacteristic
591C2×C4C2×D4×D4311yescharacteristic
592C2×C4C2×D4×D4311yescharacteristic
593C8—42no—
594C8—42no—
595C8—1722no—
596C8—1722no—
597C22—21no—
598C22—21no—
599C22—21no—
600C22—42no—
601C22—42no—
602C22—42no—
603C22—432no—
604C22—861no—
605C22—861no—
606C22—861no—
607C22—861no—
608C22—861no—
609C22—1724no—
610C22C2×C22⋊C4×D4311yescharacteristic
611C4—21no—
612C4—21no—
613C4—21no—
614C4—42no—
615C4—432no—
616C4—861no—
617C4—861no—
618C4—861no—
619C4—861no—
620C4—861no—
621C4—1722no—
622C4—1722no—
623C4#1458291412yes—
624C4#131×D4312yes—
625C4#1458369512yes—
626C2—41no—
627C2—82no—
628C2—862no—
629C2—1721no—
630C2#408×D4311yescharacteristic
631C2#1914310911yescharacteristic
632C2C2×#1458291411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1484C2
socleC22×C43C22×C22⋊C4
prime radical#19147890C2
cosocleC42×C43C24
hypercenter#1484D43
hypocenterC43#17467
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1484

Complements

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

NH ≅ G/Ntype
2. #19143226C2semidirect
3. #431×D43C2semidirect
4. #19133017C2semidirect
5. #19133015C2semidirect
6. #19133012C2semidirect
7. #19133000C2semidirect
8. #19132979C2semidirect
9. C43×#1484C2semidirect
42. #14582631C22semidirect
43. #14582629C22semidirect
44. D4⋊(C43⋊C8)C22semidirect
48. C43×D4⋊C8C22semidirect
316. #1484D43semidirect
364. D4⋊C8C2×D43semidirect
365. C43#17467semidirect

Maximal subgroups

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

subgroupindex
#191478902
#191432262
#431×D432
#191330172
#191330152
#191330122
#191330002
#191329792
C43×#14842
#1746743