Finite Group Databasebeta

← #25084185

Subgroups — #25084185

Order 11008.

568 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145933C211yesmaximal, characteristic
2#19145816C211yesmaximal, characteristic
3#19145739C211yesmaximal, characteristic, complemented
4#19143751C211yesmaximal, characteristic
5#19134180C211yesmaximal, characteristic, complemented
6#19134173C211yesmaximal, characteristic, complemented
7#19134104C211yesmaximal, characteristic, complemented
8#19134097C211yesmaximal, characteristic, complemented
9#19134056C211yesmaximal, characteristic, complemented
10#19134049C211yesmaximal, characteristic, complemented
11#19133980C211yesmaximal, characteristic, complemented
12#19133973C211yesmaximal, characteristic, complemented
13#19133378C211yesmaximal, characteristic, complemented
14#19133293C211yesmaximal, characteristic, complemented
15C2×C43×#333C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17#14583433C2211yescharacteristic
18#14583305—21no—
19#14583295C2211yescharacteristic
20#14583295C2211yescharacteristic
21#14583261—21no—
22#14583251C2211yescharacteristic
23#14583251C2211yescharacteristic
24#14583229—21no—
25#14583229—21no—
26#14583229—21no—
27#14583212—21no—
28#14583207—21no—
29#14583191C2211yescharacteristic
30#14583191C2211yescharacteristic
31#14583186C2211yescharacteristic
32#14583186C2211yescharacteristic
33#14583185C2211yescharacteristic
34#14583181—21no—
35#14583181—21no—
36#14583180C2211yescharacteristic
37#14583140—21no—
38#14583128—21no—
39#14583122—21no—
40#14583110C2211yescharacteristic
41#14583105C2211yescharacteristic
42#14583026C2211yescharacteristic
43#14583023C2211yescharacteristic
44#14582976C2211yescharacteristic
45#14582970—21no—
46#14582964C2211yescharacteristic
47C8×C22⋊D43—21no—
48#14582959—21no—
49#14582956C2211yescharacteristic
50#14582952C2211yescharacteristic
51#14582924—21no—
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582649C2211yescharacteristic
55#14582649C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582646C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582644C2211yescharacteristic
60C2×C4⋊Q8×C43C2211yescharacteristic
61C2×C4⋊C8×C43C2211yescharacteristic
62C2×C4⋊C8×C43C2211yescharacteristic
63C43×#333C2211yescharacteristic
64C43×#333C2211yescharacteristic
65C43×#333C2211yescharacteristic
66C43×#333C2211yescharacteristic
67C2×Dic172—21no—
68C2×#10621873—21no—
69C2×#10621872—21no—
70C2×C8×D43—21no—
71#13063325C2311yescharacteristic
72#13063325C2311yescharacteristic
73#13063319—21no—
74#13063317—21no—
75#13063317D411yescharacteristic
76#13063313D411yescharacteristic
77#13063308—21no—
78#13063304—21no—
79#13063304—21no—
80#13063304D411yescharacteristic
81#13063299D411yescharacteristic
82C4×Dic86—21no—
83C4×Dic86—21no—
84C4×Dic86C2311yescharacteristic
85C4×D172C2311yescharacteristic
86C4×C22⋊D43—21no—
87#13063284—21no—
88#13063282—21no—
89#13063259—21no—
90#13063258—21no—
91#13063258—21no—
92#13063257—21no—
93#13063256—21no—
94#13063256—21no—
95#13063256—21no—
96#13063256—21no—
97#13063256—21no—
98#13063256—21no—
99C4⋊(C43⋊C8)D411yescharacteristic
100C4⋊(C43⋊C8)D411yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105#13063250—21no—
106#13063250—21no—
107#13063250—21no—
108#13063248—21no—
109#13063248—21no—
110#13063248—21no—
111#13063248—21no—
112#13063248—21no—
113#13063248—21no—
114#13063247—21no—
115#13063245—21no—
116#13063245—21no—
117C22⋊(C43⋊C8)—21no—
118C22⋊(C43⋊C8)D411yescharacteristic
119C22⋊(C43⋊C8)D411yescharacteristic
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122#13063236—21no—
123#13063235—21no—
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C22×Q8×C43—21no—
128C22×C8×C43—21no—
129C22×C8×C43—21no—
130C4⋊Q8×C43—21no—
131C4⋊Q8×C43—21no—
132C4⋊Q8×C43—21no—
133C4⋊Q8×C43C2311yescharacteristic
134C4⋊Q8×C43C2311yescharacteristic
135C2×C4⋊C4×C43—21no—
136C2×C4⋊C4×C43—21no—
137C2×C42×C43C2311yescharacteristic
138C4⋊C8×C43—21no—
139C4⋊C8×C43—21no—
140C4⋊C8×C43C2311yescharacteristic
141C4⋊C8×C43C2311yescharacteristic
142C4⋊C8×C43C2311yescharacteristic
143C4⋊C8×C43C2311yescharacteristic
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×D172C2×D411yescharacteristic
154C2×C4×D43—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86C2×D411yescharacteristic
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—81no—
163C2×C8×C43—81no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—41no—
169C4⋊C4×C43—41no—
170C42×C43C2×D411yescharacteristic
171C42×C43C2×D411yescharacteristic
172C42×C43#4111yescharacteristic
173C42×C43C2411yescharacteristic
174C22⋊Dic43—21no—
175C22⋊Dic43—41no—
176(C2×D43)⋊C4—21no—
177(C2×D43)⋊C4—21no—
178(C2×D43)⋊C4—21no—
179(C2×D43)⋊C4—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43C2×D411yescharacteristic
185C4⋊Dic43C2×D411yescharacteristic
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190Dic43⋊C4—41no—
191Dic43⋊C4—41no—
192C4×Dic43—21no—
193C4×Dic43—41no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8C2×D411yescharacteristic
197C2×C43⋊C8C2×D411yescharacteristic
198C2×C43⋊C8C2×D411yescharacteristic
199C2×C43⋊C8C2×D411yescharacteristic
200Dic172—81no—
201#10621873—81no—
202#10621872—81no—
203C8×D43—81no—
204C23×C43#12111yescharacteristic
205C22×D43—21no—
206Q8×C43—81no—
207Q8×C43—81no—
208Q8×C43—82no—
209C2×C4×C43—22no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—82no—
217C2×C4×C43#12111yescharacteristic
218C2×C4×C43#12111yescharacteristic
219C2×C4×C43#12111yescharacteristic
220C2×C4×C43C22×D411yescharacteristic
221C2×C4×C43C22×D411yescharacteristic
222C2×C4×C43C2×#4111yescharacteristic
223C22⋊D43—42no—
224C2×Dic43—21no—
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—41no—
228C2×Dic43—41no—
229D172—21no—
230D172—21no—
231C4×D43—41no—
232C4×D43—41no—
233Dic86—21no—
234Dic86—21no—
235Dic86—41no—
236Dic86—41no—
237Dic86—41no—
238Dic86—41no—
239C8×C43—41no—
240C8×C43—41no—
241C8×C43—41no—
242C8×C43—41no—
243C43⋊C8—21no—
244C43⋊C8—21no—
245C43⋊C8—21no—
246C43⋊C8—21no—
247C43⋊C8—41no—
248C43⋊C8—41no—
249#19588—431nomaximal, Sylow
250C22×C43—21no—
251C22×C43—21no—
252C22×C43#47112yes—
253C22×C43C2×#12111yescharacteristic
254C2×D43—41no—
255C2×D43—41no—
256C2×D43—41no—
257C4×C43—21no—
258C4×C43—21no—
259C4×C43—21no—
260C4×C43—21no—
261C4×C43—81no—
262C4×C43—81no—
263C4×C43#57711yescharacteristic
264C4×C43#57711yescharacteristic
265C4×C43#57811yescharacteristic
266C4×C43#57811yescharacteristic
267Dic43—41no—
268Dic43—41no—
269Dic43—41no—
270Dic43—81no—
271Dic43—81no—
272#3248—431no—
273#3238—431no—
274#3229—431no—
275#2994—431no—
276#1704—431no—
277#1703—431no—
278#1692—431no—
279#1691—431no—
280#1684—431no—
281#1683—431no—
282#1672—431no—
283#1671—431no—
284#1573—431no—
285#1552—431no—
286C2×#333D4311yescharacteristic, complemented
287C2×C43—22no—
288C2×C43#304611yescharacteristic
289C2×C43#306311yescharacteristic
290C2×C43C2×#47111yescharacteristic
291D43—81no—
292#533—431no—
293C2×C4⋊Q8C2×D4311yescharacteristic
294#529—431no—
295#501—861no—
296#498—431no—
297#498—431no—
298#489—861no—
299#487—431no—
300#487—431no—
301#483—861no—
302#483—861no—
303#483—861no—
304#480—861no—
305#479—861no—
306#477—431no—
307#477—431no—
308#476—431no—
309#476—431no—
310#475—431no—
311#475—861no—
312#475—861no—
313#474—431no—
314#467—861no—
315#465—861no—
316#464—861no—
317#462—431no—
318#461—431no—
319#446—431no—
320C8×Q8—431no—
321#436—431no—
322#435—861no—
323C8×D4—431no—
324C8×D4—861no—
325#433—861no—
326#432—431no—
327#431—431no—
328#424—861no—
329C2×C4⋊C8C2×D4311yescharacteristic
330C2×C4⋊C8C2×D4311yescharacteristic
331#335—431no—
332#335—431no—
333#334—431no—
334#334—431no—
335#333C2×D4311yescharacteristic
336#333C2×D4311yescharacteristic
337#333C2×D4311yescharacteristic
338#333C2×D4311yescharacteristic
339#332—431no—
340#332—431no—
341#332—431no—
342#332—431no—
343C43#1958811yescharacteristic, complemented, Sylow
344C22×Q8—21no—
345C2×Q16—861no—
346C2×SD16—861no—
347C2×M16—861no—
348C22×C8—21no—
349C22×C8—21no—
350C22×C8—861no—
351C4⋊Q8—21no—
352C4⋊Q8—21no—
353C4⋊Q8—21no—
354C4⋊Q8—431no—
355C4⋊Q8—431no—
356C4⋊Q8C22×D4311yescharacteristic
357C4⋊Q8C22×D4311yescharacteristic
358#126—861no—
359#125—431no—
360#125—861no—
361#124—431no—
362#123—861no—
363C22⋊Q8—431no—
364C22⋊Q8—861no—
365C22⋊Q8—861no—
366#121—431no—
367C4×Q8—431no—
368C4×Q8—861no—
369C4×Q8—861no—
370C4×D4—431no—
371C4×D4—861no—
372#117—861no—
373#117—861no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C42C22×D4311yescharacteristic
377#107—861no—
378#107—861no—
379#107—861no—
380#106—861no—
381#106—861no—
382#106—861no—
383#106—861no—
384#106—861no—
385#106—861no—
386#106—861no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—431no—
390C4⋊C8—431no—
391C4⋊C8—431no—
392C4⋊C8—431no—
393C4⋊C8—861no—
394C4⋊C8—861no—
395C4⋊C8C22×D4311yescharacteristic
396C4⋊C8C22×D4311yescharacteristic
397C4⋊C8C22×D4311yescharacteristic
398C4⋊C8C22×D4311yescharacteristic
399#103—861no—
400#103—861no—
401#103—861no—
402#103—861no—
403#103—861no—
404#103—861no—
405#103—861no—
406#103—861no—
407#103—861no—
408#102—861no—
409#102—861no—
410#102—861no—
411C22⋊C8—431no—
412C22⋊C8—431no—
413C22⋊C8—861no—
414C22⋊C8—861no—
415C22⋊C8—861no—
416#97—861no—
417#97—861no—
418C4×C8—431no—
419C4×C8—431no—
420C4×C8—861no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—41no—
424C2×Q8—82no—
425C2×Q8—431no—
426C2×Q8—861no—
427C2×Q8—861no—
428C2×D4—431no—
429C2×D4—861no—
430C22×C4—41no—
431C22×C4—861no—
432C22×C4#1062189811yescharacteristic
433C22×C4D4×D4311yescharacteristic
434C22×C4D4×D4311yescharacteristic
435Q16—3441no—
436SD16—3441no—
437M16—3441no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—81no—
443C2×C8—81no—
444C2×C8—431no—
445C2×C8—431no—
446C2×C8—431no—
447C2×C8—431no—
448C2×C8—861no—
449C2×C8—861no—
450C2×C8—3441no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—431no—
458C4⋊C4—431no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—1721no—
468C4⋊C4—1721no—
469C22⋊C4—861no—
470C22⋊C4—861no—
471C22⋊C4—861no—
472C22⋊C4—861no—
473C22⋊C4—861no—
474C22⋊C4—1721no—
475C42—861no—
476C42—1721no—
477C42#1062189811yescharacteristic
478C42D4×D4311yescharacteristic
479C42D4×D4311yescharacteristic
480C42C23×D4311yescharacteristic
481C23—861no—
482C23#1306329811yescharacteristic
483Q8—81no—
484Q8—81no—
485Q8—82no—
486Q8—861no—
487Q8—861no—
488Q8—1721no—
489Q8—1721no—
490Q8—1721no—
491Q8—1721no—
492D4—861no—
493D4—861no—
494D4—1722no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—82no—
503C2×C4—861no—
504C2×C4—861no—
505C2×C4—861no—
506C2×C4—1721no—
507C2×C4—1721no—
508C2×C4—1721no—
509C2×C4—1721no—
510C2×C4#1306329811yescharacteristic
511C2×C4#1306329811yescharacteristic
512C2×C4#1306329811yescharacteristic
513C2×C4C2×D4×D4311yescharacteristic
514C2×C4C2×D4×D4311yescharacteristic
515C2×C4C2×#1062189811yescharacteristic
516C8—41no—
517C8—41no—
518C8—41no—
519C8—41no—
520C8—861no—
521C8—861no—
522C8—861no—
523C8—861no—
524C8—1721no—
525C8—1721no—
526C22—21no—
527C22—21no—
528C22—1721no—
529C22—1721no—
530C22—1721no—
531C22#1458316112yes—
532C22C2×#1306329811yescharacteristic
533C4—21no—
534C4—21no—
535C4—21no—
536C4—21no—
537C4—81no—
538C4—81no—
539C4—3441no—
540C4—3441no—
541C4—1721no—
542C4—1721no—
543C4—1721no—
544C4#1458370511yescharacteristic
545C4#1458370511yescharacteristic
546C4#1458371211yescharacteristic
547C4#1458371211yescharacteristic
548C2—22no—
549C2—3441no—
550C2#1914415011yescharacteristic
551C2#1914428411yescharacteristic
552C2C2×#1458316111yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#333C2
socleC22×C43C2×#121
prime radical#13063299D4
hypercenterC2×#333D43
hypocenterC43#19588
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
3. #19145739C2semidirect
5. #19134180C2semidirect
6. #19134173C2semidirect
7. #19134104C2semidirect
8. #19134097C2semidirect
9. #19134056C2semidirect
10. #19134049C2semidirect
11. #19133980C2semidirect
12. #19133973C2semidirect
13. #19133378C2semidirect
14. #19133293C2semidirect
15. C2×C43×#333C2semidirect
286. C2×#333D43semidirect
343. C43#19588semidirect

Maximal subgroups

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

subgroupindex
#191459332
#191458162
#191457392
#191437512
#191341802
#191341732
#191341042
#191340972
#191340562
#191340492
#191339802
#191339732
#191333782
#191332932
C2×C43×#3332
#1958843