Finite Group Databasebeta

← #25067708

Subgroups — #25067708

Order 11008.

660 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144655C211yesmaximal, characteristic
2#19143341C211yesmaximal, characteristic, complemented
3#19133507C211yesmaximal, characteristic, complemented
4#19133478C211yesmaximal, characteristic, complemented
5#19133473C211yesmaximal, characteristic, complemented
6#19133457C211yesmaximal, characteristic, complemented
7#19133438C211yesmaximal, characteristic, complemented
8#19133422C211yesmaximal, characteristic, complemented
9#19133405C211yesmaximal, characteristic, complemented
10C8×#10621884C211yesmaximal, characteristic, complemented
11#19133381C211yesmaximal, characteristic, complemented
12#19133063C211yesmaximal, characteristic, complemented
13#19132982C211yesmaximal, characteristic, complemented
14#19132892C211yesmaximal, characteristic, complemented
15C43×#2971C211yesmaximal, characteristic, complemented
16C2×#13063333—21no—
17#14583449C2211yescharacteristic
18#14583223C411yescharacteristic
19#14583223C411yescharacteristic
20#14583194C411yescharacteristic
21#14583189C411yescharacteristic
22#14583099C411yescharacteristic
23#14583094C411yescharacteristic
24#14583044C411yescharacteristic
25#14583044C411yescharacteristic
26C4×#10621884C2211yescharacteristic
27C4×#10621884C2211yescharacteristic
28C4×#10621882C2211yescharacteristic
29C4×#10621882C2211yescharacteristic
30#14582978C2211yescharacteristic
31#14582978C2211yescharacteristic
32#14582972—21no—
33#14582972—21no—
34C8×D172C2211yescharacteristic
35C8×D172C2211yescharacteristic
36#14582952C2211yescharacteristic
37#14582952C2211yescharacteristic
38C2×C4⋊(C43⋊C8)C2211yescharacteristic
39#14582867—21no—
40#14582651C2211yescharacteristic
41#14582651C2211yescharacteristic
42#14582649C2211yescharacteristic
43#14582649C2211yescharacteristic
44Q8⋊(C43⋊C8)C2211yescharacteristic
45Q8⋊(C43⋊C8)C2211yescharacteristic
46D4⋊(C43⋊C8)C2211yescharacteristic
47D4⋊(C43⋊C8)C2211yescharacteristic
48#14582626C2211yescharacteristic
49#14582626C2211yescharacteristic
50#14582626C2211yescharacteristic
51#14582626C2211yescharacteristic
52#14582621C2211yescharacteristic
53#14582621C2211yescharacteristic
54#14582620C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic
56C4×#41×C43C2211yescharacteristic
57C8×Q8×C43C2211yescharacteristic
58C8×Q8×C43C2211yescharacteristic
59C43×#436—21no—
60C43×#436—21no—
61C43×#436C2211yescharacteristic
62C43×#436C2211yescharacteristic
63C43×#432—21no—
64C43×#432C2211yescharacteristic
65C4×M16×C43—21no—
66C4×M16×C43C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621884C2×C411yescharacteristic
69C2×#10621884C2×C411yescharacteristic
70C2×#10621882C2×C411yescharacteristic
71C2×#10621882C2×C411yescharacteristic
72#13063333—44no—
73C2×#10621872—21no—
74C2×#10621872—21no—
75C22×C43⋊C8—21no—
76C2×C8×D43—21no—
77C2×C8×D43—21no—
78#13063325C2×C411yescharacteristic
79#13063322C2×C411yescharacteristic
80#13063313—21no—
81#13063299—21no—
82#13063299C2×C411yescharacteristic
83#13063299C2×C411yescharacteristic
84C4×D172—21no—
85C4×D172C2311yescharacteristic
86C4×D172C2311yescharacteristic
87#13063258C2×C411yescharacteristic
88#13063258C2×C411yescharacteristic
89#13063256C2×C411yescharacteristic
90#13063256C2×C411yescharacteristic
91C4⋊(C43⋊C8)—21no—
92C4⋊(C43⋊C8)—21no—
93C4⋊(C43⋊C8)C2×C411yescharacteristic
94C4⋊(C43⋊C8)C2×C411yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97#13063249C2×C411yescharacteristic
98#13063249C2×C411yescharacteristic
99#13063246C2×C411yescharacteristic
100#13063246C2×C411yescharacteristic
101#13063245C2×C411yescharacteristic
102#13063245C2×C411yescharacteristic
103#13063245C2×C411yescharacteristic
104#13063245C2×C411yescharacteristic
105C22⋊(C43⋊C8)—21no—
106C22⋊(C43⋊C8)C2×C411yescharacteristic
107C22⋊(C43⋊C8)C2×C411yescharacteristic
108(C2×D43)⋊C8—21no—
109(C2×D43)⋊C8—21no—
110(C2×D43)⋊C8—21no—
111(C2×D43)⋊C8—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C2×#41×C43C2×C411yescharacteristic
117C2×M16×C43—21no—
118C2×M16×C43—21no—
119C2×M16×C43D411yescharacteristic
120C2×M16×C43D411yescharacteristic
121C4×Q8×C43C2×C411yescharacteristic
122C4×Q8×C43C2311yescharacteristic
123C4×D4×C43—21no—
124C4×D4×C43—21no—
125C4×D4×C43C2×C411yescharacteristic
126C4×D4×C43C2311yescharacteristic
127#117×C43—21no—
128#117×C43C2×C411yescharacteristic
129C2×C42×C43—21no—
130C2×C42×C43C2311yescharacteristic
131C4⋊C8×C43—21no—
132C4⋊C8×C43—21no—
133C4⋊C8×C43C2311yescharacteristic
134C4⋊C8×C43C2311yescharacteristic
135C22⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138#97×C43—21no—
139#97×C43D411yescharacteristic
140#97×C43D411yescharacteristic
141C4×C8×C43—21no—
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145#41×C43—22no—
146#41×C43—41no—
147C2×Q8×C43C22×C411yescharacteristic
148C2×D4×C43—21no—
149C2×D4×C43C22×C411yescharacteristic
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43C22×C411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43#4111yescharacteristic
156C2×C22⋊D43—21no—
157C2×C22⋊D43—21no—
158#10621898—42no—
159#10621898—42no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172C22×C411yescharacteristic
163C2×D172C22×C411yescharacteristic
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×Dic86—21no—
167M16×C43—22no—
168M16×C43—41no—
169M16×C43—42no—
170M16×C43—42no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43C2×D411yescharacteristic
174C2×C8×C43C2×D411yescharacteristic
175C2×C8×C43C2×D411yescharacteristic
176C2×C8×C43C2×D411yescharacteristic
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43C22×C411yescharacteristic
180C4⋊C4×C43C22×C411yescharacteristic
181C22⋊C4×C43—21no—
182C22⋊C4×C43—21no—
183C22⋊C4×C43—21no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43—21no—
187C42×C43C22×C411yescharacteristic
188C42×C43C2×D411yescharacteristic
189C42×C43#4111yescharacteristic
190C42×C43C2411yescharacteristic
191#10621884—22no—
192#10621884—22no—
193#10621882—41no—
194#10621882—41no—
195(C2×D43)⋊C4—21no—
196(C2×D43)⋊C4—21no—
197(C2×D43)⋊C4—21no—
198(C2×D43)⋊C4—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43C22×C411yescharacteristic
201C4⋊Dic43C22×C411yescharacteristic
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—42no—
207C2×C43⋊C8C22×C411yescharacteristic
208C2×C43⋊C8C22×C411yescharacteristic
209C2×C43⋊C8C22×C411yescharacteristic
210C2×C43⋊C8C22×C411yescharacteristic
211#10621872—42no—
212#10621872—42no—
213C8×D43—42no—
214C8×D43—42no—
215C23×C43—21no—
216C23×C43C4×D411yescharacteristic
217C22×D43—21no—
218C22×D43—21no—
219Q8×C43—21no—
220Q8×C43#13112yescomplemented
221D4×C43—21no—
222D4×C43—21no—
223D4×C43—42no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—41no—
232C2×C4×C43—42no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—81no—
236C2×C4×C43C4×D411yescharacteristic
237C2×C4×C43C4×D411yescharacteristic
238C2×C4×C43C4×D411yescharacteristic
239C2×C4×C43C23×C411yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C22⋊D43—42no—
243C22⋊D43—42no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246D172—21no—
247D172—21no—
248D172—21no—
249D172—21no—
250D172—42no—
251D172—81no—
252C4×D43—41no—
253C4×D43—41no—
254C4×D43—41no—
255C4×D43—41no—
256Dic86—42no—
257C8×C43—21no—
258C8×C43—21no—
259C8×C43—21no—
260C8×C43—41no—
261C8×C43—41no—
262C8×C43AGL(1,ℤ/8)12yes—
263C43⋊C8—21no—
264C43⋊C8—21no—
265C43⋊C8—21no—
266C43⋊C8—21no—
267C43⋊C8—41no—
268C43⋊C8—41no—
269C43⋊C8—41no—
270C43⋊C8—41no—
271#18011—431nomaximal, Sylow
272C22×C43—21no—
273C22×C43—21no—
274C22×C43—21no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43C2×C4×D411yescharacteristic
279C2×D43—41no—
280C2×D43—41no—
281C2×D43—41no—
282C2×D43—41no—
283C2×D43—41no—
284C2×D43—41no—
285C4×C43—21no—
286C4×C43—22no—
287C4×C43—21no—
288C4×C43—21no—
289C4×C43—21no—
290C4×C43—41no—
291C4×C43—41no—
292C4×C43C2×#13111yescharacteristic
293C4×C43#56811yescharacteristic
294C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
295C4×C43#57511yescharacteristic
296Dic43—41no—
297Dic43—41no—
298#3106—431no—
299#2971D4311yescharacteristic, complemented
300#2935—431no—
301#1594—431no—
302#1589—431no—
303#1588—431no—
304#1586—431no—
305#1583—431no—
306#1581—431no—
307SD16⋊C8—431no—
308C8×SD16—431no—
309#1573—431no—
310#1496—431no—
311#1477—431no—
312#1453—431no—
313C2×C43—41no—
314C2×C43—81no—
315C2×C43#293311yescharacteristic
316C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
317C2×C43#295711yescharacteristic
318D43—81no—
319D43—81no—
320C2×#131—861no—
321#532—431no—
322C4×#41C2×D4311yescharacteristic
323#482—431no—
324#482—431no—
325#477—431no—
326#476—431no—
327#460—431no—
328#459—431no—
329#449—431no—
330#449—431no—
331C8×Q8C2×D4311yescharacteristic
332C8×Q8C2×D4311yescharacteristic
333C4×SD16—431no—
334C4×SD16—431no—
335C4×D8—431no—
336C4×D8—431no—
337#436—21no—
338#436—21no—
339#436—431no—
340#436—431no—
341#436C2×D4311yescharacteristic
342#436C2×D4311yescharacteristic
343#435—861no—
344#435—861no—
345C8×D4—431no—
346C8×D4—431no—
347#432—21no—
348#432C2×D4311yescharacteristic
349#431—431no—
350#431—431no—
351C2×C4⋊C8—431no—
352#408—861no—
353C4×M16—21no—
354C4×M16C2×D4311yescharacteristic
355#335—431no—
356#335—431no—
357#334—431no—
358#334—431no—
359Q8⋊C8—431no—
360Q8⋊C8—431no—
361D4⋊C8—431no—
362D4⋊C8—431no—
363D4⋊C8—431no—
364D4⋊C8—431no—
365D4⋊C8—431no—
366D4⋊C8—431no—
367#322—431no—
368#322—431no—
369#322—431no—
370C82—431no—
371C43#1801111yescharacteristic, complemented, Sylow
372C2×#41—861no—
373C2×#41C4×D4311yescharacteristic
374C2×SD16—431no—
375C2×SD16—431no—
376C2×D8—431no—
377C2×D8—431no—
378#131—1724no—
379C2×M16—21no—
380C2×M16—21no—
381C2×M16—861no—
382C2×M16—861no—
383C2×M16C22⋊D4311yescharacteristic
384C2×M16C22⋊D4311yescharacteristic
385C22×C8—861no—
386C22×C8—861no—
387C22×C8—861no—
388C4⋊Q8—431no—
389#127—431no—
390#124—861no—
391#121—431no—
392#121—431no—
393#121—861no—
394C4×Q8C4×D4311yescharacteristic
395C4×Q8C22×D4311yescharacteristic
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—431no—
399C4×D4—431no—
400C4×D4—861no—
401C4×D4C4×D4311yescharacteristic
402C4×D4C22×D4311yescharacteristic
403#117—21no—
404#117C4×D4311yescharacteristic
405C2×C42—21no—
406C2×C42C22×D4311yescharacteristic
407#107—431no—
408#107—431no—
409#106—431no—
410#106—431no—
411C4⋊C8—21no—
412C4⋊C8—21no—
413C4⋊C8—431no—
414C4⋊C8—431no—
415C4⋊C8—431no—
416C4⋊C8—431no—
417C4⋊C8—861no—
418C4⋊C8—861no—
419C4⋊C8C22×D4311yescharacteristic
420C4⋊C8C22×D4311yescharacteristic
421#103—431no—
422#103—431no—
423#102—431no—
424#102—431no—
425#102—431no—
426#102—431no—
427#102—431no—
428#102—431no—
429C22⋊C8—21no—
430C22⋊C8—21no—
431C22⋊C8—21no—
432C22⋊C8—431no—
433C22⋊C8—431no—
434C22⋊C8—861no—
435C22⋊C8—861no—
436C22⋊C8—861no—
437C22⋊C8—861no—
438C22⋊C8—861no—
439#97—21no—
440#97C22⋊D4311yescharacteristic
441#97C22⋊D4311yescharacteristic
442C4×C8—21no—
443C4×C8—21no—
444C4×C8—431no—
445C4×C8—431no—
446C4×C8—431no—
447C4×C8—431no—
448C4×C8C22×D4311yescharacteristic
449C4×C8C22×D4311yescharacteristic
450#41—22no—
451#41—41no—
452#41—1722no—
453#41—1722no—
454C2×Q8—861no—
455C2×Q8C2×C4×D4311yescharacteristic
456C2×D4—21no—
457C2×D4—431no—
458C2×D4—431no—
459C2×D4—861no—
460C2×D4—861no—
461C2×D4—861no—
462C2×D4—861no—
463C2×D4C2×C4×D4311yescharacteristic
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4C2×C4×D4311yescharacteristic
470C22×C4#1062189811yescharacteristic
471C22×C4C2×C22⋊D4311yescharacteristic
472SD16—862no—
473SD16—862no—
474D8—1721no—
475D8—1721no—
476M16—22no—
477M16—41no—
478M16—42no—
479M16—42no—
480M16—1722no—
481M16—1722no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—431no—
485C2×C8—431no—
486C2×C8—431no—
487C2×C8—431no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8—1722no—
493C2×C8—1722no—
494C2×C8—1722no—
495C2×C8C2×C22⋊D4311yescharacteristic
496C2×C8C2×C22⋊D4311yescharacteristic
497C2×C8C2×C22⋊D4311yescharacteristic
498C2×C8C2×C22⋊D4311yescharacteristic
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—431no—
502C4⋊C4—431no—
503C4⋊C4—861no—
504C4⋊C4C2×C4×D4311yescharacteristic
505C4⋊C4C2×C4×D4311yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—861no—
510C22⋊C4—861no—
511C22⋊C4—861no—
512C22⋊C4—861no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42C2×C4×D4311yescharacteristic
517C42#1062189811yescharacteristic
518C42C2×C22⋊D4311yescharacteristic
519C42C23×D4311yescharacteristic
520C23—21no—
521C23—861no—
522C23—861no—
523C23C4×C22⋊D4311yescharacteristic
524Q8—21no—
525Q8—1722no—
526Q8#1306333312yescomplemented
527D4—21no—
528D4—21no—
529D4—42no—
530D4—861no—
531D4—861no—
532D4—861no—
533D4—861no—
534D4—3441no—
535D4—1722no—
536D4—1722no—
537D4—1722no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—81no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4C4×C22⋊D4311yescharacteristic
557C2×C4C4×C22⋊D4311yescharacteristic
558C2×C4C4×C22⋊D4311yescharacteristic
559C2×C4C22×C4×D4311yescharacteristic
560C2×C4C22×C22⋊D4311yescharacteristic
561C2×C4C2×#1062189811yescharacteristic
562C8—21no—
563C8—21no—
564C8—21no—
565C8—41no—
566C8—41no—
567C8—861no—
568C8—861no—
569C8—861no—
570C8—861no—
571C8—1721no—
572C8—1721no—
573C8—1721no—
574C8—1721no—
575C8#1306335012yes—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—1721no—
583C22—1721no—
584C22—1721no—
585C22—1721no—
586C22—1721no—
587C22—1721no—
588C22C2×C4×C22⋊D4311yescharacteristic
589C4—21no—
590C4—21no—
591C4—21no—
592C4—22no—
593C4—21no—
594C4—41no—
595C4—41no—
596C4—1721no—
597C4—1721no—
598C4C2×#1306333311yescharacteristic
599C4#1458366511yescharacteristic
600C4C2×#1306335011yescharacteristic
601C4#1458369711yescharacteristic
602C2—41no—
603C2—81no—
604C2—3441no—
605C2—3441no—
606C2#1914332011yescharacteristic
607C2C4×#1306335011yescharacteristic
608C2#1914351011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#2971C2
socleC22×C43C2×C4×D4
prime radical#19144655C2
cosocleC42×C43C24
hypercenter#2971D43
hypocenterC43#18011
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2971

Complements

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

NH ≅ G/Ntype
2. #19143341C2semidirect
3. #19133507C2semidirect
4. #19133478C2semidirect
5. #19133473C2semidirect
6. #19133457C2semidirect
7. #19133438C2semidirect
8. #19133422C2semidirect
9. #19133405C2semidirect
10. C8×#10621884C2semidirect
11. #19133381C2semidirect
12. #19133063C2semidirect
13. #19132982C2semidirect
14. #19132892C2semidirect
15. C43×#2971C2semidirect
220. Q8×C43#131semidirect
299. #2971D43semidirect
371. C43#18011semidirect
526. Q8#13063333semidirect

Maximal subgroups

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

subgroupindex
#191446552
#191433412
#191335072
#191334782
#191334732
#191334572
#191334382
#191334222
#191334052
C8×#106218842
#191333812
#191330632
#191329822
#191328922
C43×#29712
#1801143