Finite Group Databasebeta

← #25067702

Subgroups — #25067702

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#19143615C211yesmaximal, characteristic, complemented
3#19143338C211yesmaximal, characteristic, complemented
4#19133506C211yesmaximal, characteristic, complemented
5#19133477C211yesmaximal, characteristic, complemented
6#19133470C211yesmaximal, characteristic, complemented
7#19133462C211yesmaximal, characteristic, complemented
8#19133435C211yesmaximal, characteristic, complemented
9#19133427C211yesmaximal, characteristic, complemented
10#19133410C211yesmaximal, characteristic, complemented
11#19133392C211yesmaximal, characteristic, complemented
12#19133378C211yesmaximal, characteristic, complemented
13#19133065C211yesmaximal, characteristic, complemented
14#19132890C211yesmaximal, characteristic, complemented
15C43×#1477C211yesmaximal, characteristic, complemented
16C2×#13063331—21no—
17#14583449C2211yescharacteristic
18#14583223C411yescharacteristic
19#14583223C411yescharacteristic
20#14583194C411yescharacteristic
21#14583189C411yescharacteristic
22#14583099C411yescharacteristic
23#14583094C411yescharacteristic
24#14583044C411yescharacteristic
25#14583044C411yescharacteristic
26Q8×C43⋊C8C2211yescharacteristic
27Q8×C43⋊C8C2211yescharacteristic
28C4×#10621884C2211yescharacteristic
29C4×#10621884C2211yescharacteristic
30C4×#10621882C2211yescharacteristic
31C4×#10621882C2211yescharacteristic
32#14582977—21no—
33#14582977—21no—
34#14582977C2211yescharacteristic
35#14582977C2211yescharacteristic
36#14582976C2211yescharacteristic
37#14582976C2211yescharacteristic
38#14582969—21no—
39#14582969—21no—
40#14582964C2211yescharacteristic
41#14582964C2211yescharacteristic
42#14582956—21no—
43#14582956C2211yescharacteristic
44#14582952C2211yescharacteristic
45#14582865—21no—
46C4×#10621877—21no—
47C4×#10621877C2211yescharacteristic
48#14582651C2211yescharacteristic
49#14582651C2211yescharacteristic
50#14582649C2211yescharacteristic
51#14582649C2211yescharacteristic
52#14582628C2211yescharacteristic
53#14582628C2211yescharacteristic
54#14582628C2211yescharacteristic
55#14582628C2211yescharacteristic
56#14582621C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582620C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C4×#41×C43C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C2×C4⋊C8×C43C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×D4⋊C8C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621884C2×C411yescharacteristic
69C2×#10621884C2×C411yescharacteristic
70C2×#10621882C2×C411yescharacteristic
71C2×#10621882C2×C411yescharacteristic
72#13063331—44no—
73C2×#10621877—21no—
74C2×#10621877—21no—
75C2×#10621877D411yescharacteristic
76C2×#10621877D411yescharacteristic
77C2×#10621872—21no—
78C2×#10621872—21no—
79C2×C8×D43—21no—
80C2×C8×D43—21no—
81#13063325C2×C411yescharacteristic
82#13063322C2×C411yescharacteristic
83#13063313—21no—
84#13063299—21no—
85#13063299C2×C411yescharacteristic
86#13063299C2×C411yescharacteristic
87C4×D172—21no—
88C4×D172C2311yescharacteristic
89C4×D172C2311yescharacteristic
90#13063258C2×C411yescharacteristic
91#13063258C2×C411yescharacteristic
92#13063256C2×C411yescharacteristic
93#13063256C2×C411yescharacteristic
94C4⋊(C43⋊C8)—21no—
95C4⋊(C43⋊C8)—21no—
96C4⋊(C43⋊C8)C2×C411yescharacteristic
97C4⋊(C43⋊C8)C2×C411yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100#13063249C2×C411yescharacteristic
101#13063249C2×C411yescharacteristic
102#13063246C2×C411yescharacteristic
103#13063246C2×C411yescharacteristic
104#13063245C2×C411yescharacteristic
105#13063245C2×C411yescharacteristic
106#13063245C2×C411yescharacteristic
107#13063245C2×C411yescharacteristic
108C22⋊(C43⋊C8)—21no—
109C22⋊(C43⋊C8)—21no—
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)C2×C411yescharacteristic
112C22⋊(C43⋊C8)C2×C411yescharacteristic
113(C2×D43)⋊C8—21no—
114(C2×D43)⋊C8—21no—
115(C2×D43)⋊C8—21no—
116(C2×D43)⋊C8—21no—
117#13063236—21no—
118#13063236D411yescharacteristic
119#13063236D411yescharacteristic
120C4×C43⋊C8—21no—
121C4×C43⋊C8—21no—
122C4×C43⋊C8C2311yescharacteristic
123C4×C43⋊C8C2311yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C2×#41×C43C2×C411yescharacteristic
127C22×C8×C43—21no—
128C4×Q8×C43C2×C411yescharacteristic
129C4×Q8×C43C2311yescharacteristic
130C4×D4×C43—21no—
131C4×D4×C43—21no—
132C4×D4×C43C2×C411yescharacteristic
133C4×D4×C43C2311yescharacteristic
134#117×C43—21no—
135#117×C43C2×C411yescharacteristic
136C2×C42×C43—21no—
137C2×C42×C43C2311yescharacteristic
138C4⋊C8×C43—21no—
139C4⋊C8×C43—21no—
140C4⋊C8×C43C2311yescharacteristic
141C4⋊C8×C43C2311yescharacteristic
142C22⋊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—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—42no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43C22×C411yescharacteristic
175C4⋊C4×C43C22×C411yescharacteristic
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C22⋊C4×C43—21no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43C22×C411yescharacteristic
183C42×C43C2×D411yescharacteristic
184C42×C43#4111yescharacteristic
185C42×C43C2411yescharacteristic
186#10621884—22no—
187#10621884—22no—
188#10621882—41no—
189#10621882—41no—
190(C2×D43)⋊C4—21no—
191(C2×D43)⋊C4—21no—
192(C2×D43)⋊C4—21no—
193(C2×D43)⋊C4—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43C22×C411yescharacteristic
196C4⋊Dic43C22×C411yescharacteristic
197#10621877—22no—
198#10621877—41no—
199#10621877—42no—
200#10621877—42no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8C22×C411yescharacteristic
204C2×C43⋊C8C22×C411yescharacteristic
205C2×C43⋊C8C22×C411yescharacteristic
206C2×C43⋊C8C22×C411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209C2×C43⋊C8C2×D411yescharacteristic
210C2×C43⋊C8C2×D411yescharacteristic
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—41no—
258C8×C43—41no—
259C8×C43—41no—
260C8×C43—41no—
261C43⋊C8—21no—
262C43⋊C8—21no—
263C43⋊C8—21no—
264C43⋊C8—21no—
265C43⋊C8—21no—
266C43⋊C8—21no—
267C43⋊C8—21no—
268C43⋊C8—41no—
269C43⋊C8—41no—
270C43⋊C8AGL(1,ℤ/8)12yes—
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#2971—431no—
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#1477D4311yescharacteristic, complemented
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×Q8—431no—
332C8×Q8—431no—
333C4×SD16—431no—
334C4×SD16—431no—
335C4×D8—431no—
336C4×D8—431no—
337#436—431no—
338#436—431no—
339#436—431no—
340#436—431no—
341#436—861no—
342#436—861no—
343#435—861no—
344#435—861no—
345C8×D4—431no—
346C8×D4—431no—
347#432—431no—
348#432—861no—
349#431—431no—
350#431C2×D4311yescharacteristic
351C2×C4⋊C8C2×D4311yescharacteristic
352#408—861no—
353C4×M16—431no—
354C4×M16—861no—
355#335—431no—
356#335—431no—
357#334—431no—
358#334—431no—
359Q8⋊C8C2×D4311yescharacteristic
360Q8⋊C8C2×D4311yescharacteristic
361D4⋊C8—431no—
362D4⋊C8—431no—
363D4⋊C8—431no—
364D4⋊C8—431no—
365D4⋊C8C2×D4311yescharacteristic
366D4⋊C8C2×D4311yescharacteristic
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—431no—
380C2×M16—431no—
381C2×M16—861no—
382C2×M16—861no—
383C2×M16—861no—
384C2×M16—861no—
385C22×C8—21no—
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—431no—
431C22⋊C8—431no—
432C22⋊C8—861no—
433C22⋊C8—861no—
434C22⋊C8—861no—
435C22⋊C8—861no—
436C22⋊C8—861no—
437C22⋊C8—861no—
438C22⋊C8—861no—
439#97—431no—
440#97—431no—
441#97—861no—
442C4×C8—431no—
443C4×C8—431no—
444C4×C8—431no—
445C4×C8—431no—
446C4×C8—861no—
447C4×C8—861no—
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×C4D4×D4311yescharacteristic
471C22×C4#1062190011yescharacteristic
472SD16—862no—
473SD16—862no—
474D8—1721no—
475D8—1721no—
476M16—862no—
477M16—1722no—
478M16—1722no—
479M16—1722no—
480M16—1721no—
481M16—1722no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—42no—
487C2×C8—431no—
488C2×C8—431no—
489C2×C8—431no—
490C2×C8—431no—
491C2×C8—431no—
492C2×C8—431no—
493C2×C8—431no—
494C2×C8—431no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8—1722no—
498C2×C8—1722no—
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
517C42D4×D4311yescharacteristic
518C42#1062190011yescharacteristic
519C42C23×D4311yescharacteristic
520C23—21no—
521C23—861no—
522C23—861no—
523C23(C22⋊D43)⋊C411yescharacteristic
524Q8—21no—
525Q8—1722no—
526Q8#1306333112yescomplemented
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×C4(C22⋊D43)⋊C411yescharacteristic
557C2×C4(C22⋊D43)⋊C411yescharacteristic
558C2×C4(C22⋊D43)⋊C411yescharacteristic
559C2×C4C22×C4×D4311yescharacteristic
560C2×C4C2×D4×D4311yescharacteristic
561C2×C4C2×#1062190011yescharacteristic
562C8—41no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—432no—
567C8—861no—
568C8—861no—
569C8—861no—
570C8—861no—
571C8—861no—
572C8—861no—
573C8—861no—
574C8—1721no—
575C8—1721no—
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×(C22⋊D43)⋊C411yescharacteristic
589C4—21no—
590C4—21no—
591C4—21no—
592C4—22no—
593C4—21no—
594C4—41no—
595C4—41no—
596C4—1721no—
597C4—1721no—
598C4C2×#1306333111yescharacteristic
599C4#1458366511yescharacteristic
600C4AGL(1,ℤ/8)×D4311yescharacteristic
601C4#1458369811yescharacteristic
602C2—41no—
603C2—81no—
604C2—3441no—
605C2—3441no—
606C2#1914331611yescharacteristic
607C2#1914340811yescharacteristic
608C2#1914350811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1477C2
socleC22×C43C2×C4×D4
prime radical#19144655C2
cosocleC42×C43C24
hypercenter#1477D43
hypocenterC43#18011
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1477

Complements

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

NH ≅ G/Ntype
2. #19143615C2semidirect
3. #19143338C2semidirect
4. #19133506C2semidirect
5. #19133477C2semidirect
6. #19133470C2semidirect
7. #19133462C2semidirect
8. #19133435C2semidirect
9. #19133427C2semidirect
10. #19133410C2semidirect
11. #19133392C2semidirect
12. #19133378C2semidirect
13. #19133065C2semidirect
14. #19132890C2semidirect
15. C43×#1477C2semidirect
220. Q8×C43#131semidirect
311. #1477D43semidirect
371. C43#18011semidirect
526. Q8#13063331semidirect

Maximal subgroups

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

subgroupindex
#191446552
#191436152
#191433382
#191335062
#191334772
#191334702
#191334622
#191334352
#191334272
#191334102
#191333922
#191333782
#191330652
#191328902
C43×#14772
#1801143