Finite Group Databasebeta

← #25067714

Subgroups — #25067714

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#19144649C211yesmaximal, characteristic
2#19143612C211yesmaximal, characteristic, complemented
3#19143339C211yesmaximal, characteristic, complemented
4#19133506C211yesmaximal, characteristic, complemented
5#19133477C211yesmaximal, characteristic, complemented
6#19133476C211yesmaximal, characteristic, complemented
7#19133456C211yesmaximal, characteristic, complemented
8#19133441C211yesmaximal, characteristic, complemented
9#19133421C211yesmaximal, characteristic, complemented
10#19133404C211yesmaximal, characteristic, complemented
11#19133398C211yesmaximal, characteristic, complemented
12#19133381C211yesmaximal, characteristic, complemented
13#19132983C211yesmaximal, characteristic, complemented
14#19132890C211yesmaximal, characteristic, complemented
15C43×#1496C211yesmaximal, characteristic, complemented
16C2×#13063332—21no—
17C4×#10621898C2211yescharacteristic
18#14583220C411yescharacteristic
19#14583220C411yescharacteristic
20#14583191C411yescharacteristic
21#14583186C411yescharacteristic
22#14583096C411yescharacteristic
23#14583091C411yescharacteristic
24#14583042C411yescharacteristic
25#14583042C411yescharacteristic
26#14583023C2211yescharacteristic
27#14583023C2211yescharacteristic
28C4×#10621883C2211yescharacteristic
29C4×#10621883C2211yescharacteristic
30C4×#10621882C2211yescharacteristic
31C4×#10621882C2211yescharacteristic
32#14582977C2211yescharacteristic
33#14582977C2211yescharacteristic
34#14582976C2211yescharacteristic
35#14582976C2211yescharacteristic
36#14582974—21no—
37#14582974—21no—
38#14582971—21no—
39#14582971—21no—
40D4×C43⋊C8C2211yescharacteristic
41D4×C43⋊C8C2211yescharacteristic
42#14582954—21no—
43#14582952C2211yescharacteristic
44C2×C4⋊(C43⋊C8)C2211yescharacteristic
45#14582866—21no—
46C4×#10621877C2211yescharacteristic
47#14582851—21no—
48#14582651C2211yescharacteristic
49#14582651C2211yescharacteristic
50#14582649C2211yescharacteristic
51#14582649C2211yescharacteristic
52#14582631C2211yescharacteristic
53#14582631C2211yescharacteristic
54#14582628C2211yescharacteristic
55#14582628C2211yescharacteristic
56#14582621C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582620C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C43×#532C2211yescharacteristic
61C43×#432C2211yescharacteristic
62C43×#431C2211yescharacteristic
63C43×D4⋊C8C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×D4⋊C8C2211yescharacteristic
67C2×#10621898C2×C411yescharacteristic
68C2×#10621883C2×C411yescharacteristic
69C2×#10621883C2×C411yescharacteristic
70C2×#10621882C2×C411yescharacteristic
71C2×#10621882C2×C411yescharacteristic
72#13063332—44no—
73C2×#10621877—21no—
74C2×#10621877—21no—
75C2×#10621877D411yescharacteristic
76C2×#10621877D411yescharacteristic
77C2×#10621872—21no—
78C2×#10621872—21no—
79C22×C43⋊C8—21no—
80C22×C43⋊C8—21no—
81C22×C43⋊C8—21no—
82C4×Dic86C2×C411yescharacteristic
83C4×Dic86C2311yescharacteristic
84C4×D172C2×C411yescharacteristic
85C4×D172C2311yescharacteristic
86C4×C22⋊D43—21no—
87C4×C22⋊D43—21no—
88#13063284C2×C411yescharacteristic
89#13063282—21no—
90C42×D43—21no—
91#13063258C2×C411yescharacteristic
92#13063258C2×C411yescharacteristic
93#13063256C2×C411yescharacteristic
94#13063256C2×C411yescharacteristic
95C4⋊(C43⋊C8)—21no—
96C4⋊(C43⋊C8)C2×C411yescharacteristic
97C4⋊(C43⋊C8)C2×C411yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100Dic43⋊C8—21no—
101Dic43⋊C8—21no—
102#13063248C2×C411yescharacteristic
103#13063248C2×C411yescharacteristic
104#13063246C2×C411yescharacteristic
105#13063246C2×C411yescharacteristic
106#13063246C2×C411yescharacteristic
107#13063246C2×C411yescharacteristic
108#13063245C2×C411yescharacteristic
109#13063245C2×C411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112C22⋊(C43⋊C8)—21no—
113C22⋊(C43⋊C8)—21no—
114C22⋊(C43⋊C8)C2×C411yescharacteristic
115C22⋊(C43⋊C8)C2×C411yescharacteristic
116(C2×D43)⋊C8—21no—
117(C2×D43)⋊C8—21no—
118#13063236D411yescharacteristic
119#13063236D411yescharacteristic
120C4×C43⋊C8C2311yescharacteristic
121C4×C43⋊C8C2311yescharacteristic
122C4×C43⋊C8C2311yescharacteristic
123C4×C43⋊C8C2311yescharacteristic
124C8×Dic43—21no—
125C8×Dic43—21no—
126C2×#41×C43—21no—
127C4⋊Q8×C43C2×C411yescharacteristic
128#127×C43C2×C411yescharacteristic
129#124×C43—21no—
130#121×C43—21no—
131#121×C43C2×C411yescharacteristic
132#121×C43C2×C411yescharacteristic
133C4×D4×C43—21no—
134C4×D4×C43C2311yescharacteristic
135C4×D4×C43C2311yescharacteristic
136C2×C42×C43C2311yescharacteristic
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C22⋊C8×C43—21no—
141C22⋊C8×C43—21no—
142#97×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145#41×C43—42no—
146#41×C43—42no—
147C2×Q8×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43C22×C411yescharacteristic
153C2×D4×C43C22×C411yescharacteristic
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43C22×C411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43#4111yescharacteristic
159C2×C22⋊D43—21no—
160#10621898—22no—
161#10621898—41no—
162C2×D172C22×C411yescharacteristic
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×Dic86C22×C411yescharacteristic
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43C22×C411yescharacteristic
173C4⋊C4×C43C22×C411yescharacteristic
174C22⋊C4×C43—21no—
175C22⋊C4×C43—21no—
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C42×C43C22×C411yescharacteristic
179C42×C43C2×D411yescharacteristic
180C42×C43#4111yescharacteristic
181C42×C43C2411yescharacteristic
182C22⋊Dic43—21no—
183#10621883—22no—
184#10621883—22no—
185#10621882—41no—
186#10621882—41no—
187(C2×D43)⋊C4—21no—
188(C2×D43)⋊C4—21no—
189C4⋊Dic43C22×C411yescharacteristic
190C4⋊Dic43C22×C411yescharacteristic
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196#10621877—22no—
197#10621877—41no—
198#10621877—42no—
199#10621877—42no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—42no—
203C2×C43⋊C8—42no—
204C2×C43⋊C8—42no—
205C2×C43⋊C8C22×C411yescharacteristic
206C2×C43⋊C8C22×C411yescharacteristic
207C2×C43⋊C8C22×C411yescharacteristic
208C2×C43⋊C8C22×C411yescharacteristic
209C2×C43⋊C8C2×D411yescharacteristic
210C2×C43⋊C8C2×D411yescharacteristic
211C2×C43⋊C8C2×D411yescharacteristic
212C2×C43⋊C8C2×D411yescharacteristic
213#10621872—42no—
214#10621872—42no—
215C23×C43—21no—
216C23×C43—21no—
217C23×C43C4×D411yescharacteristic
218C22×D43—21no—
219Q8×C43—42no—
220D4×C43—21no—
221D4×C43—21no—
222D4×C43—21no—
223D4×C43—21no—
224D4×C43—42no—
225D4×C43—42no—
226D4×C43—42no—
227D4×C43—81no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43C4×D411yescharacteristic
240C2×C4×C43C4×D411yescharacteristic
241C2×C4×C43C4×D411yescharacteristic
242C2×C4×C43C23×C411yescharacteristic
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C22⋊D43—42no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249D172—21no—
250D172—21no—
251C4×D43—42no—
252C4×D43—41no—
253C4×D43—41no—
254C4×D43—81no—
255Dic86—21no—
256Dic86#13112yescomplemented
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×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43C2×C4×D411yescharacteristic
282C2×D43—41no—
283C2×D43—41no—
284C2×D43—41no—
285C4×C43—21no—
286C4×C43—21no—
287C4×C43—21no—
288C4×C43—21no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43C2×#13111yescharacteristic
292C4×C43#56811yescharacteristic
293C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
294C4×C43#57511yescharacteristic
295Dic43—22no—
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#1496D4311yescharacteristic, complemented
311#1477—431no—
312#1453—431no—
313C2×C43—41no—
314C2×C43—81no—
315C2×C43—81no—
316C2×C43#293311yescharacteristic
317C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
318C2×C43#295711yescharacteristic
319D43—81no—
320C2×#131—861no—
321#532C2×D4311yescharacteristic
322C4×#41—431no—
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—861no—
348#432C2×D4311yescharacteristic
349#431—431no—
350#431C2×D4311yescharacteristic
351C2×C4⋊C8—431no—
352#408—861no—
353C4×M16—431no—
354C4×M16—861no—
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⋊C8C2×D4311yescharacteristic
364D4⋊C8C2×D4311yescharacteristic
365D4⋊C8C2×D4311yescharacteristic
366D4⋊C8C2×D4311yescharacteristic
367#322—431no—
368#322—431no—
369#322—431no—
370C82—431no—
371C43#1801111yescharacteristic, complemented, Sylow
372C2×#41—21no—
373C2×#41—431no—
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—861no—
386C22×C8—861no—
387C22×C8—861no—
388C4⋊Q8C4×D4311yescharacteristic
389#127C4×D4311yescharacteristic
390#124—21no—
391#121—21no—
392#121C4×D4311yescharacteristic
393#121C4×D4311yescharacteristic
394C4×Q8—431no—
395C4×Q8—431no—
396C4×D4—21no—
397C4×D4—431no—
398C4×D4—431no—
399C4×D4—861no—
400C4×D4—861no—
401C4×D4C22×D4311yescharacteristic
402C4×D4C22×D4311yescharacteristic
403#117—431no—
404#117—861no—
405C2×C42—861no—
406C2×C42C22×D4311yescharacteristic
407#107—431no—
408#107—431no—
409#106—431no—
410#106—431no—
411C4⋊C8—21no—
412C4⋊C8—431no—
413C4⋊C8—431no—
414C4⋊C8—431no—
415C4⋊C8—431no—
416C4⋊C8—861no—
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—431no—
432C22⋊C8—431no—
433C22⋊C8—861no—
434C22⋊C8—861no—
435C22⋊C8—861no—
436C22⋊C8—861no—
437C22⋊C8—861no—
438C22⋊C8—861no—
439#97—21no—
440#97—431no—
441#97—431no—
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—42no—
451#41—42no—
452#41—862no—
453#41—1721no—
454C2×Q8—21no—
455C2×Q8—431no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—431no—
461C2×D4—861no—
462C2×D4C2×C4×D4311yescharacteristic
463C2×D4C2×C4×D4311yescharacteristic
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—861no—
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—431no—
487C2×C8—431no—
488C2×C8—431no—
489C2×C8—431no—
490C2×C8—431no—
491C2×C8—431no—
492C2×C8—431no—
493C2×C8—431no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8—1722no—
497C2×C8—1722no—
498C2×C8—1722no—
499C4⋊C4—21no—
500C4⋊C4—431no—
501C4⋊C4—431no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4C2×C4×D4311yescharacteristic
505C4⋊C4C2×C4×D4311yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—861no—
511C22⋊C4—861no—
512C22⋊C4—861no—
513C42—861no—
514C42—861no—
515C42—861no—
516C42C2×C4×D4311yescharacteristic
517C42D4×D4311yescharacteristic
518C42#1062190011yescharacteristic
519C42C23×D4311yescharacteristic
520C23—21no—
521C23—21no—
522C23—861no—
523C23(C22⋊D43)⋊C411yescharacteristic
524Q8—42no—
525Q8—432no—
526Q8—861no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—42no—
532D4—42no—
533D4—42no—
534D4—81no—
535D4—861no—
536D4—861no—
537D4—1722no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—3441no—
553C2×C4—1722no—
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—41no—
583C22—41no—
584C22—41no—
585C22—1721no—
586C22—1721no—
587C22—1721no—
588C22C2×(C22⋊D43)⋊C411yescharacteristic
589C4—21no—
590C4—21no—
591C4—21no—
592C4—21no—
593C4—41no—
594C4—41no—
595C4—862no—
596C4—1721no—
597C4—1721no—
598C4#131×D4311yescharacteristic
599C4#1458366411yescharacteristic
600C4AGL(1,ℤ/8)×D4311yescharacteristic
601C4#1458369511yescharacteristic
602C2—41no—
603C2—81no—
604C2—81no—
605C2—3441no—
606C2#1914332511yescharacteristic
607C2#1914339911yescharacteristic
608C2#1914350811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1496C2
socleC22×C43C2×C4×D4
prime radical#19144649C2
cosocleC42×C43C24
hypercenter#1496D43
hypocenterC43#18011
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1496

Complements

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

NH ≅ G/Ntype
2. #19143612C2semidirect
3. #19143339C2semidirect
4. #19133506C2semidirect
5. #19133477C2semidirect
6. #19133476C2semidirect
7. #19133456C2semidirect
8. #19133441C2semidirect
9. #19133421C2semidirect
10. #19133404C2semidirect
11. #19133398C2semidirect
12. #19133381C2semidirect
13. #19132983C2semidirect
14. #19132890C2semidirect
15. C43×#1496C2semidirect
256. Dic86#131semidirect
310. #1496D43semidirect
371. C43#18011semidirect

Maximal subgroups

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

subgroupindex
#191446492
#191436122
#191433392
#191335062
#191334772
#191334762
#191334562
#191334412
#191334212
#191334042
#191333982
#191333812
#191329832
#191328902
C43×#14962
#1801143