Finite Group Databasebeta

← #25081735

Subgroups — #25081735

Order 11008.

594 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145958C211yesmaximal, characteristic
2#19145816C211yesmaximal, characteristic, complemented
3#19144991C211yesmaximal, characteristic, complemented
4#19143593C211yesmaximal, characteristic, complemented
5#19134180C211yesmaximal, characteristic, complemented
6#19134173C211yesmaximal, characteristic, complemented
7#19134138C211yesmaximal, characteristic, complemented
8#19134131C211yesmaximal, characteristic, complemented
9#19134056C211yesmaximal, characteristic, complemented
10#19134049C211yesmaximal, characteristic, complemented
11#19134014C211yesmaximal, characteristic, complemented
12#19134007C211yesmaximal, characteristic, complemented
13#19133360C211yesmaximal, characteristic, complemented
14#19133298C211yesmaximal, characteristic, complemented
15C43×#1548C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17#14583433C2211yescharacteristic
18#14583305—21no—
19#14583261—21no—
20#14583261—21no—
21#14583261—21no—
22#14583251C2211yescharacteristic
23#14583251C2211yescharacteristic
24#14583247C2211yescharacteristic
25#14583247C2211yescharacteristic
26#14583229—21no—
27#14583212—21no—
28#14583200—21no—
29#14583191C2211yescharacteristic
30#14583191C2211yescharacteristic
31#14583186C2211yescharacteristic
32#14583186C2211yescharacteristic
33#14583185C2211yescharacteristic
34#14583180C2211yescharacteristic
35#14583152—21no—
36#14583145—21no—
37#14583115—21no—
38#14583100C2211yescharacteristic
39#14583095C2211yescharacteristic
40#14583026C2211yescharacteristic
41#14583023C2211yescharacteristic
42#14582976C2211yescharacteristic
43#14582974—21no—
44#14582973—21no—
45#14582964C2211yescharacteristic
46#14582958—21no—
47#14582956C2211yescharacteristic
48#14582898—21no—
49#14582898—21no—
50#14582853—21no—
51C4×#10621877C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582649C2211yescharacteristic
55#14582649C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582646C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C2×C4⋊Q8×C43C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C43×#423C2211yescharacteristic
63C43×#333C2211yescharacteristic
64C43×#333C2211yescharacteristic
65C43×#333C2211yescharacteristic
66C43×#333C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621873—21no—
69C2×D344—21no—
70C2×#10621877D411yescharacteristic
71C2×#10621877D411yescharacteristic
72C2×#10621872—21no—
73C2×C8×D43—21no—
74#13063325C2311yescharacteristic
75#13063322C2311yescharacteristic
76#13063319—21no—
77#13063317D411yescharacteristic
78#13063313—21no—
79#13063313D411yescharacteristic
80#13063308—21no—
81#13063304D411yescharacteristic
82#13063299—21no—
83#13063299—21no—
84#13063299D411yescharacteristic
85C4×Dic86C2311yescharacteristic
86C4×D172—21no—
87C4×D172—21no—
88C4×D172C2311yescharacteristic
89C4×C22⋊D43—21no—
90#13063282—21no—
91#13063259—21no—
92#13063258—21no—
93#13063258—21no—
94#13063257—21no—
95#13063256—21no—
96#13063256—21no—
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99Dic43⋊C8—21no—
100Dic43⋊C8—21no—
101#13063250—21no—
102#13063248—21no—
103#13063248—21no—
104#13063248—21no—
105#13063248—21no—
106#13063248—21no—
107#13063248—21no—
108#13063247—21no—
109#13063247—21no—
110#13063247—21no—
111#13063245—21no—
112#13063245—21no—
113#13063245—21no—
114#13063245—21no—
115#13063245—21no—
116#13063245—21no—
117C22⋊(C43⋊C8)—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120#13063236—21no—
121#13063236D411yescharacteristic
122#13063236D411yescharacteristic
123#13063235—21no—
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C22×Q8×C43—21no—
128C2×M16×C43—21no—
129C4⋊Q8×C43—21no—
130C4⋊Q8×C43—21no—
131C4⋊Q8×C43—21no—
132C4⋊Q8×C43C2311yescharacteristic
133C4⋊Q8×C43C2311yescharacteristic
134C2×C4⋊C4×C43—21no—
135C2×C4⋊C4×C43—21no—
136C2×C42×C43C2311yescharacteristic
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141C4⋊C8×C43C2311yescharacteristic
142C22⋊C8×C43—21no—
143C4×C8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—41no—
147C2×Q8×C43—82no—
148C22×C4×C43—41no—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43#4111yescharacteristic
152C2×C22⋊D43—21no—
153C2×C22⋊D43—41no—
154#10621898—42no—
155#10621898—42no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172C2×D411yescharacteristic
160C2×C4×D43—21no—
161C2×C4×D43—41no—
162C2×Dic86—21no—
163C2×Dic86C2×D411yescharacteristic
164M16×C43—81no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—41no—
174C4⋊C4×C43—41no—
175C42×C43C2×D411yescharacteristic
176C42×C43C2×D411yescharacteristic
177C42×C43#4111yescharacteristic
178C42×C43C2411yescharacteristic
179C22⋊Dic43—21no—
180(C2×D43)⋊C4—21no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—41no—
185(C2×D43)⋊C4—41no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43C2×D411yescharacteristic
189C4⋊Dic43C2×D411yescharacteristic
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194C4×Dic43—21no—
195#10621877—41no—
196#10621877—41no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8C2×D411yescharacteristic
200C2×C43⋊C8C2×D411yescharacteristic
201C2×C43⋊C8C2×D411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203D344—81no—
204#10621873—81no—
205#10621872—42no—
206C8×D43—42no—
207C23×C43#12111yescharacteristic
208C22×D43—21no—
209C22×D43—41no—
210Q8×C43—81no—
211Q8×C43—81no—
212Q8×C43—82no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—82no—
221C2×C4×C43#12111yescharacteristic
222C2×C4×C43#12111yescharacteristic
223C2×C4×C43#12111yescharacteristic
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C22×D411yescharacteristic
226C2×C4×C43C2×#4111yescharacteristic
227C22⋊D43—81no—
228C22⋊D43—82no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—41no—
233D172—21no—
234D172—21no—
235D172—41no—
236D172—41no—
237D172—41no—
238D172—41no—
239D172—81no—
240C4×D43—41no—
241C4×D43—41no—
242C4×D43—82no—
243Dic86—21no—
244Dic86—21no—
245Dic86—41no—
246Dic86—41no—
247C8×C43—41no—
248C8×C43—41no—
249C8×C43—41no—
250C8×C43—41no—
251C43⋊C8—21no—
252C43⋊C8—21no—
253C43⋊C8—21no—
254C43⋊C8—21no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257#19382—431nomaximal, Sylow
258C22×C43—21no—
259C22×C43—21no—
260C22×C43—21no—
261C22×C43C2×#12111yescharacteristic
262C2×D43—41no—
263C2×D43—41no—
264C2×D43—41no—
265C2×D43—81no—
266C2×D43—81no—
267C2×D43—81no—
268C4×C43—21no—
269C4×C43—21no—
270C4×C43—21no—
271C4×C43—21no—
272C4×C43—81no—
273C4×C43—81no—
274C4×C43#57511yescharacteristic
275C4×C43#57511yescharacteristic
276C4×C43#57711yescharacteristic
277C4×C43#57811yescharacteristic
278Dic43—41no—
279Dic43—41no—
280Dic43—41no—
281Dic43—81no—
282#3251—431no—
283#3238—431no—
284#3141—431no—
285#2969—431no—
286#1704—431no—
287#1703—431no—
288#1698—431no—
289#1697—431no—
290#1684—431no—
291#1683—431no—
292#1678—431no—
293#1677—431no—
294#1569—431no—
295#1553—431no—
296#1548D4311yescharacteristic, complemented
297C2×C43—41no—
298C2×C43#304011yescharacteristic
299C2×C43#306311yescharacteristic
300C2×C43#306811yescharacteristic
301D43—81no—
302D43—161no—
303#532—431no—
304C2×C4⋊Q8C2×D4311yescharacteristic
305#529—431no—
306#501—861no—
307#489—861no—
308#489—861no—
309#489—861no—
310#487—431no—
311#487—431no—
312#486—431no—
313#486—431no—
314#483—861no—
315#480—861no—
316#478—861no—
317#477—431no—
318#477—431no—
319#476—431no—
320#476—431no—
321#475—431no—
322#474—431no—
323#469—861no—
324#468—861no—
325#463—861no—
326#460—431no—
327#459—431no—
328#446—431no—
329C8×Q8—431no—
330#436—431no—
331#436—861no—
332#435—861no—
333C8×D4—431no—
334#433—861no—
335#432—431no—
336#431C2×D4311yescharacteristic
337#423C2×D4311yescharacteristic
338#417—861no—
339#417—861no—
340#405—861no—
341C4×M16—431no—
342#335—431no—
343#335—431no—
344#334—431no—
345#334—431no—
346#333C2×D4311yescharacteristic
347#333C2×D4311yescharacteristic
348#333C2×D4311yescharacteristic
349#333C2×D4311yescharacteristic
350#332—431no—
351#332—431no—
352#331—431no—
353#331—431no—
354C43#1938211yescharacteristic, complemented, Sylow
355C2×#41—861no—
356C22×Q8—21no—
357C2×SD16—861no—
358C2×D8—861no—
359C2×M16—21no—
360C2×M16—431no—
361C2×M16—431no—
362C2×M16—861no—
363C22×C8—861no—
364C4⋊Q8—21no—
365C4⋊Q8—21no—
366C4⋊Q8—21no—
367C4⋊Q8—431no—
368C4⋊Q8C22×D4311yescharacteristic
369C4⋊Q8C22×D4311yescharacteristic
370#127—431no—
371#126—861no—
372#125—431no—
373#124—431no—
374#124—861no—
375#123—861no—
376C22⋊Q8—431no—
377#121—431no—
378#121—861no—
379#121—861no—
380C4×Q8—431no—
381C4×D4—431no—
382C4×D4—861no—
383C4×D4—861no—
384C4×D4—861no—
385#117—861no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C42C22×D4311yescharacteristic
389#107—861no—
390#107—861no—
391#107—861no—
392#106—861no—
393#106—861no—
394#106—861no—
395C4⋊C8—21no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—861no—
399C4⋊C8—861no—
400C4⋊C8C22×D4311yescharacteristic
401C4⋊C8C22×D4311yescharacteristic
402C4⋊C8C22×D4311yescharacteristic
403C4⋊C8C22×D4311yescharacteristic
404#103—861no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#102—861no—
412#102—861no—
413#102—861no—
414#102—861no—
415#102—861no—
416#102—861no—
417#102—861no—
418#102—861no—
419#102—861no—
420C22⋊C8—21no—
421C22⋊C8—861no—
422C22⋊C8—861no—
423C22⋊C8—861no—
424#97—431no—
425#97—431no—
426#97—861no—
427#97—861no—
428C4×C8—21no—
429C4×C8—431no—
430C4×C8—431no—
431C4×C8—861no—
432#41—1722no—
433#41—1722no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—41no—
437C2×Q8—82no—
438C2×Q8—431no—
439C2×Q8—861no—
440C2×D4—431no—
441C2×D4—861no—
442C2×D4—861no—
443C2×D4—861no—
444C2×D4—861no—
445C2×D4—1721no—
446C22×C4—41no—
447C22×C4—861no—
448C22×C4—1721no—
449C22×C4#1062189811yescharacteristic
450C22×C4D4×D4311yescharacteristic
451C22×C4D4×D4311yescharacteristic
452SD16—3441no—
453D8—3441no—
454M16—81no—
455M16—1722no—
456M16—1721no—
457M16—1721no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—431no—
463C2×C8—431no—
464C2×C8—431no—
465C2×C8—431no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—1722no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4—431no—
476C4⋊C4—431no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C22⋊C4—861no—
484C22⋊C4—861no—
485C22⋊C4—861no—
486C22⋊C4—861no—
487C22⋊C4—861no—
488C22⋊C4—1721no—
489C22⋊C4—1721no—
490C42—861no—
491C42#1062189811yescharacteristic
492C42D4×D4311yescharacteristic
493C42D4×D4311yescharacteristic
494C42C23×D4311yescharacteristic
495C23—861no—
496C23—1721no—
497C23#1306329811yescharacteristic
498Q8—81no—
499Q8—81no—
500Q8—82no—
501Q8—861no—
502Q8—861no—
503Q8—1721no—
504Q8—1721no—
505D4—861no—
506D4—861no—
507D4—3441no—
508D4—3442no—
509D4—3441no—
510D4—1721no—
511D4—1721no—
512D4—1721no—
513D4—1721no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—82no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—3442no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4#1306329811yescharacteristic
530C2×C4#1306329811yescharacteristic
531C2×C4#1306329811yescharacteristic
532C2×C4C2×D4×D4311yescharacteristic
533C2×C4C2×D4×D4311yescharacteristic
534C2×C4C2×#1062189811yescharacteristic
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—861no—
540C8—861no—
541C8—861no—
542C8—861no—
543C8—1721no—
544C8—1721no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—3441no—
549C22—3441no—
550C22—3441no—
551C22—1721no—
552C22—1721no—
553C22—1721no—
554C22C2×#1306329811yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—81no—
560C4—81no—
561C4—3441no—
562C4—1721no—
563C4—1721no—
564C4—1721no—
565C4#1458369811yescharacteristic
566C4#1458369811yescharacteristic
567C4#1458370511yescharacteristic
568C4#1458371211yescharacteristic
569C2—41no—
570C2—3441no—
571C2—6881no—
572C2#1914409211yescharacteristic
573C2#1914428411yescharacteristic
574C2#1914432211yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1548C2
socleC22×C43C2×#121
prime radical#19145958C2
hypercenter#1548D43
hypocenterC43#19382
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
2. #19145816C2semidirect
3. #19144991C2semidirect
4. #19143593C2semidirect
5. #19134180C2semidirect
6. #19134173C2semidirect
7. #19134138C2semidirect
8. #19134131C2semidirect
9. #19134056C2semidirect
10. #19134049C2semidirect
11. #19134014C2semidirect
12. #19134007C2semidirect
13. #19133360C2semidirect
14. #19133298C2semidirect
15. C43×#1548C2semidirect
296. #1548D43semidirect
354. C43#19382semidirect

Maximal subgroups

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

subgroupindex
#191459582
#191458162
#191449912
#191435932
#191341802
#191341732
#191341382
#191341312
#191340562
#191340492
#191340142
#191340072
#191333602
#191332982
C43×#15482
#1938243