Finite Group Databasebeta

← #25093907

Subgroups — #25093907

Order 11008.

570 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147505C211yesmaximal, characteristic, complemented
2#19147503C211yesmaximal, characteristic, complemented
3#19147215C211yesmaximal, characteristic
4#19134212C211yesmaximal, characteristic, complemented
5#19134121C211yesmaximal, characteristic, complemented
6#19134120C211yesmaximal, characteristic, complemented
7#19134118C211yesmaximal, characteristic, complemented
8#19134116C211yesmaximal, characteristic, complemented
9#19133740C211yesmaximal, characteristic
10#19133734C211yesmaximal, characteristic, complemented
11#19133729C211yesmaximal, characteristic, complemented
12#19133727C211yesmaximal, characteristic, complemented
13#19133486C211yesmaximal, characteristic, complemented
14#19133483C211yesmaximal, characteristic, complemented
15C43×#3357C211yesmaximal, characteristic
16Q8×Dic86C2211yescharacteristic
17#14583606C2211yescharacteristic
18#14583309—21no—
19#14583306—21no—
20#14583304C2211yescharacteristic
21#14583302C2211yescharacteristic
22#14583302C2211yescharacteristic
23#14583278C2211yescharacteristic
24#14583278C2211yescharacteristic
25#14583240—21no—
26#14583210—21no—
27#14583208—21no—
28#14583203—21no—
29#14583194C2211yescharacteristic
30#14583191C2211yescharacteristic
31#14583191C2211yescharacteristic
32#14583189C2211yescharacteristic
33#14583189C2211yescharacteristic
34#14583189C2211yescharacteristic
35#14583179—21no—
36#14583177—21no—
37#14583143—21no—
38#14583030C2211yescharacteristic
39#14583029C2211yescharacteristic
40#14583000—21no—
41#14582999—21no—
42C4×#10621883C2211yescharacteristic
43#14582977C2211yescharacteristic
44#14582942—21no—
45#14582650C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582647C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52#14582629C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic
56C43×#555C2211yescharacteristic
57C43×#554C2211yescharacteristic
58C43×#500C2211yescharacteristic
59C43×#485—21no—
60C43×#480—21no—
61C43×#477C2211yescharacteristic
62C43×#476C2211yescharacteristic
63C43×#468—21no—
64C4×SD16×C43C2211yescharacteristic
65C43×#436C2211yescharacteristic
66C43×#428—21no—
67C2×#10621885—41no—
68C2×#10621885—41no—
69C2×#10621883D411yescharacteristic
70C2×#10621877—21no—
71#13063325—21no—
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063324—21no—
75#13063324—41no—
76#13063316—21no—
77#13063304—21no—
78#13063302—41no—
79Q8×Dic43—21no—
80C4×Dic86—21no—
81C4×Dic86C2311yescharacteristic
82D4×Dic43—21no—
83C2×C4⋊Dic43—21no—
84#13063259—21no—
85#13063259—21no—
86#13063258—21no—
87#13063258—21no—
88#13063258—21no—
89#13063258—21no—
90#13063258—21no—
91#13063258—21no—
92#13063258—21no—
93#13063256—21no—
94#13063256—21no—
95#13063256—21no—
96#13063256D411yescharacteristic
97C4⋊(C43⋊C8)—21no—
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101Dic43⋊C8—21no—
102#13063249—21no—
103#13063248—21no—
104#13063248—21no—
105#13063248D411yescharacteristic
106#13063246—21no—
107#13063246—21no—
108#13063246—21no—
109#13063246D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111#13063236—21no—
112#13063235—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×SD16×C43D411yescharacteristic
116C2×M16×C43—21no—
117C4⋊Q8×C43C2311yescharacteristic
118C4⋊Q8×C43C2311yescharacteristic
119#125×C43—21no—
120#124×C43—41no—
121C22⋊Q8×C43—21no—
122C22⋊Q8×C43—41no—
123#121×C43—21no—
124#121×C43—21no—
125C4×Q8×C43C2311yescharacteristic
126C4×D4×C43—21no—
127C4×D4×C43C2311yescharacteristic
128C4×D4×C43C2311yescharacteristic
129#117×C43—21no—
130#117×C43—21no—
131C2×C4⋊C4×C43—21no—
132#107×C43—21no—
133#107×C43—21no—
134#107×C43—21no—
135#106×C43—21no—
136#106×C43D411yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43D411yescharacteristic
140#102×C43—21no—
141#102×C43D411yescharacteristic
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×D4×C43—41no—
148C2×D4×C43C2×D411yescharacteristic
149C2×D4×C43C2×D411yescharacteristic
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—41no—
153C22×Dic43—41no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—41no—
157C2×Dic86C2×D411yescharacteristic
158SD16×C43—22no—
159M16×C43—42no—
160C2×C8×C43—21no—
161C2×C8×C43C2×D411yescharacteristic
162C2×C8×C43C2×D411yescharacteristic
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—41no—
169C4⋊C4×C43—41no—
170C4⋊C4×C43C2×D411yescharacteristic
171C4⋊C4×C43C2×D411yescharacteristic
172C4⋊C4×C43C2×D411yescharacteristic
173C22⋊C4×C43—21no—
174C22⋊C4×C43—21no—
175C22⋊C4×C43—41no—
176C22⋊C4×C43—41no—
177C22⋊C4×C43—41no—
178C42×C43—21no—
179C42×C43—41no—
180C42×C43C2411yescharacteristic
181C22⋊Dic43—41no—
182#10621885—82no—
183#10621885—82no—
184#10621883—22no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—41no—
190C4⋊Dic43—41no—
191C4⋊Dic43C2×D411yescharacteristic
192Dic43⋊C4—21no—
193Dic43⋊C4—41no—
194Dic43⋊C4—41no—
195C4×Dic43—21no—
196C4×Dic43—41no—
197#10621877—42no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204C23×C43—21no—
205C23×C43—21no—
206Q8×C43—21no—
207Q8×C43—21no—
208Q8×C43—81no—
209Q8×C43—81no—
210D4×C43—21no—
211D4×C43—21no—
212D4×C43—21no—
213D4×C43—21no—
214D4×C43—161no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—161no—
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43H(5,𝔽2)11yescharacteristic
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—161no—
234Dic86—21no—
235Dic86—21no—
236Dic86—81no—
237Dic86—81no—
238Dic86—161no—
239C8×C43—21no—
240C8×C43—41no—
241C8×C43#13712yes—
242C43⋊C8—22no—
243C43⋊C8—21no—
244C43⋊C8—41no—
245C43⋊C8—41no—
246C43⋊C8—41no—
247C43⋊C8#13712yes—
248#20324—431nomaximal, Sylow
249C22×C43—41no—
250C22×C43—41no—
251C22×C43—41no—
252C22×C43—41no—
253C22×C43—41no—
254C22×C43—41no—
255C22×C43D4211yescharacteristic
256C4×C43—21no—
257C4×C43—41no—
258C4×C43—41no—
259C4×C43—41no—
260C4×C43—41no—
261C4×C43—81no—
262C4×C43—81no—
263C4×C43C2×#13711yescharacteristic
264C4×C43C2×#13711yescharacteristic
265C4×C43#57811yescharacteristic
266C4×C43#57811yescharacteristic
267Dic43—41no—
268Dic43—41no—
269Dic43—81no—
270Dic43—81no—
271#3385—431no—
272#3385—431no—
273#3357—431no—
274#3357D4311yescharacteristic
275#1713—431no—
276#1696—431no—
277#1696—431no—
278#1695—431no—
279#1695—431no—
280#1634—431no—
281#1633—431no—
282#1632—431no—
283#1632—431no—
284#1590—431no—
285#1590—431no—
286C2×C43—81no—
287C2×C43—81no—
288C2×C43#327611yescharacteristic
289C2×C43#327611yescharacteristic
290C2×C43#329211yescharacteristic
291Q82—431no—
292#555C2×D4311yescharacteristic
293#554—431no—
294#554C2×D4311yescharacteristic
295#501—861no—
296#501—861no—
297#500—431no—
298#500—431no—
299#500—431no—
300#500C2×D4311yescharacteristic
301#494—431no—
302#494—431no—
303#485—21no—
304#485—861no—
305#480—21no—
306#480—861no—
307#479—861no—
308#479—861no—
309#477—431no—
310#477—431no—
311#477—431no—
312#477C2×D4311yescharacteristic
313#476—431no—
314#476—431no—
315#476—431no—
316#476C2×D4311yescharacteristic
317#474—861no—
318#474—861no—
319#468—21no—
320#468—861no—
321#446—431no—
322#446—431no—
323#440—861no—
324#440—861no—
325C4×SD16—431no—
326C4×SD16C2×D4311yescharacteristic
327#436—431no—
328#436C2×D4311yescharacteristic
329#428—21no—
330#428—861no—
331#334—431no—
332#334—431no—
333#333—431no—
334#333—431no—
335#333—431no—
336#333—431no—
337Q8⋊C8—431no—
338Q8⋊C8—431no—
339D4⋊C8—431no—
340D4⋊C8—431no—
341C82—431no—
342C43#2032411yescharacteristic, complemented, Sylow
343C2×Q16—1721no—
344C2×Q16—1721no—
345C2×SD16—431no—
346C2×SD16C22⋊D4311yescharacteristic
347C2×M16—21no—
348C2×M16—861no—
349C4⋊Q8—431no—
350C4⋊Q8—431no—
351C4⋊Q8—861no—
352C4⋊Q8—861no—
353C4⋊Q8—1721no—
354C4⋊Q8C22×D4311yescharacteristic
355C4⋊Q8C22×D4311yescharacteristic
356#125—21no—
357#125—861no—
358#124—41no—
359C22⋊Q8—21no—
360C22⋊Q8—41no—
361C22⋊Q8—861no—
362C22⋊Q8—1721no—
363#121—21no—
364#121—21no—
365C4×Q8—431no—
366C4×Q8—861no—
367C4×Q8—861no—
368C4×Q8C22×D4311yescharacteristic
369C4×D4—21no—
370C4×D4—861no—
371C4×D4C22×D4311yescharacteristic
372C4×D4C22×D4311yescharacteristic
373#117—21no—
374#117—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—861no—
377#107—21no—
378#107—21no—
379#107—21no—
380#107—861no—
381#107—861no—
382#107—861no—
383#107—861no—
384#107—861no—
385#107—861no—
386#107—861no—
387#107—861no—
388#107—861no—
389#106—21no—
390#106—431no—
391#106—861no—
392#106—861no—
393#106—861no—
394#106C22⋊D4311yescharacteristic
395C4⋊C8—431no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—861no—
399C4⋊C8—861no—
400C4⋊C8C22×D4311yescharacteristic
401#103—21no—
402#103—431no—
403#103—861no—
404#103—861no—
405#103—861no—
406#103C22⋊D4311yescharacteristic
407#102—21no—
408#102—431no—
409#102—861no—
410#102—861no—
411#102—861no—
412#102C22⋊D4311yescharacteristic
413C22⋊C8—21no—
414C22⋊C8—861no—
415#97—861no—
416#97—861no—
417C4×C8—431no—
418C4×C8—431no—
419C4×C8C22×D4311yescharacteristic
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—431no—
423C2×Q8—861no—
424C2×Q8—861no—
425C2×Q8—1721no—
426C2×Q8C2×C22⋊D4311yescharacteristic
427C2×D4—41no—
428C2×D4D4×D4311yescharacteristic
429C2×D4C2×C22⋊D4311yescharacteristic
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—41no—
433C22×C4—1721no—
434Q16—3442no—
435Q16—3442no—
436SD16—22no—
437SD16—862no—
438M16—42no—
439M16—1722no—
440C2×C8—21no—
441C2×C8—431no—
442C2×C8—431no—
443C2×C8—861no—
444C2×C8—861no—
445C2×C8—861no—
446C2×C8—861no—
447C2×C8C2×C22⋊D4311yescharacteristic
448C2×C8C2×C22⋊D4311yescharacteristic
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—41no—
455C4⋊C4—41no—
456C4⋊C4—431no—
457C4⋊C4—861no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—1721no—
463C4⋊C4—1721no—
464C4⋊C4—1721no—
465C4⋊C4—1721no—
466C4⋊C4D4×D4311yescharacteristic
467C4⋊C4C2×C22⋊D4311yescharacteristic
468C4⋊C4C2×C22⋊D4311yescharacteristic
469C22⋊C4—21no—
470C22⋊C4—21no—
471C22⋊C4—41no—
472C22⋊C4—41no—
473C22⋊C4—41no—
474C22⋊C4—1721no—
475C42—21no—
476C42—41no—
477C42—861no—
478C42—1721no—
479C42C23×D4311yescharacteristic
480C23—21no—
481C23—21no—
482Q8—21no—
483Q8—21no—
484Q8—81no—
485Q8—81no—
486Q8—861no—
487Q8—861no—
488Q8—3441no—
489Q8—3441no—
490Q8—6881no—
491D4—21no—
492D4—21no—
493D4—21no—
494D4—21no—
495D4—161no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—161no—
507C2×C4—861no—
508C2×C4—861no—
509C2×C4—1721no—
510C2×C4—1721no—
511C2×C4—6881no—
512C2×C4C2×D4×D4311yescharacteristic
513C2×C4C22×C22⋊D4311yescharacteristic
514C2×C4#1306337011yescharacteristic
515C8—21no—
516C8—41no—
517C8—432no—
518C8—862no—
519C8—861no—
520C8—1721no—
521C8—1721no—
522C8—1721no—
523C8#1306335512yes—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22D4×C22⋊D4311yescharacteristic
531C4—21no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—81no—
537C4—81no—
538C4—3441no—
539C4—3441no—
540C4—1721no—
541C4—1721no—
542C4#137×D4311yescharacteristic
543C4C2×#1306335511yescharacteristic
544C4#1458371411yescharacteristic
545C4#1458371511yescharacteristic
546C2—81no—
547C2—81no—
548C2#1914623511yescharacteristic
549C2#1914623711yescharacteristic
550C2#1914639211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3357C2
socleC22×C43D42
prime radicalC43×#555C22
hypercenter#3357D43
hypocenterC43#20324
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3357

Complements

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

NH ≅ G/Ntype
1. #19147505C2semidirect
2. #19147503C2semidirect
4. #19134212C2semidirect
5. #19134121C2semidirect
6. #19134120C2semidirect
7. #19134118C2semidirect
8. #19134116C2semidirect
10. #19133734C2semidirect
11. #19133729C2semidirect
12. #19133727C2semidirect
13. #19133486C2semidirect
14. #19133483C2semidirect
342. C43#20324semidirect

Maximal subgroups

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

subgroupindex
#191475052
#191475032
#191472152
#191342122
#191341212
#191341202
#191341182
#191341162
#191337402
#191337342
#191337292
#191337272
#191334862
#191334832
C43×#33572
#2032443