Finite Group Databasebeta

← #25086799

Subgroups — #25086799

Order 11008.

616 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147514C211yesmaximal, characteristic
2#19147273C211yesmaximal, characteristic, complemented
3D4×#10621885C211yesmaximal, characteristic
4#19134269C211yesmaximal, characteristic, complemented
5#19134098C211yesmaximal, characteristic, complemented
6#19134048C211yesmaximal, characteristic
7#19133989C211yesmaximal, characteristic, complemented
8#19133963C211yesmaximal, characteristic, complemented
9#19133844C211yesmaximal, characteristic
10#19133836C211yesmaximal, characteristic, complemented
11#19133816C211yesmaximal, characteristic, complemented
12#19133759C211yesmaximal, characteristic
13#19133445C211yesmaximal, characteristic, complemented
14SD16⋊(C43⋊C8)C211yesmaximal, characteristic
15Q8×SD16×C43C211yesmaximal, characteristic
16C22×#10621885—21no—
17#14583628C2211yescharacteristic
18D4×Dic86C2211yescharacteristic
19#14583306—21no—
20#14583304C2211yescharacteristic
21#14583302C2211yescharacteristic
22#14583278C2211yescharacteristic
23#14583251—21no—
24#14583251C2211yescharacteristic
25#14583249C2211yescharacteristic
26#14583197—21no—
27#14583192—21no—
28#14583191—21no—
29#14583191C2211yescharacteristic
30#14583184C2211yescharacteristic
31#14583179C2211yescharacteristic
32#14583138—21no—
33#14583109—21no—
34#14583109C2211yescharacteristic
35#14583109C2211yescharacteristic
36#14583106C2211yescharacteristic
37#14583055—21no—
38#14583054—21no—
39#14583029C2211yescharacteristic
40Q8×C43⋊C8C2211yescharacteristic
41#14583000—21no—
42C4×#10621885—21no—
43C4×#10621885C2211yescharacteristic
44D4×C43⋊C8C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582651C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582645C2211yescharacteristic
49#14582644C2211yescharacteristic
50#14582644C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53#14582629C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582620C2211yescharacteristic
56Q82×C43C2211yescharacteristic
57D4×Q8×C43C2211yescharacteristic
58C43×#498—21no—
59C43×#498C2211yescharacteristic
60C43×#476—21no—
61C43×#476C2211yescharacteristic
62C43×#475—21no—
63C43×#475C2211yescharacteristic
64C8×Q8×C43C2211yescharacteristic
65C4×SD16×C43—21no—
66C4×SD16×C43C2211yescharacteristic
67C22×Dic86—21no—
68C2×#10621885—21no—
69C2×#10621885—21no—
70C2×#10621885—21no—
71C2×#10621885—21no—
72C2×#10621885—21no—
73C2×#10621885—44no—
74C2×#10621885D411yescharacteristic
75C22×C43⋊C8—21no—
76#13063325—21no—
77#13063325C2311yescharacteristic
78#13063325C2311yescharacteristic
79#13063324—21no—
80#13063316—21no—
81#13063316—41no—
82#13063304—21no—
83#13063302—41no—
84Q8×Dic43—21no—
85C4×Dic86—21no—
86C4×Dic86C2311yescharacteristic
87D4×Dic43—21no—
88#13063259—21no—
89#13063259—21no—
90#13063258—21no—
91#13063258—21no—
92#13063258—41no—
93#13063258D411yescharacteristic
94#13063256—21no—
95C4⋊(C43⋊C8)—21no—
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99Dic43⋊C8—21no—
100#13063249—21no—
101#13063249—21no—
102#13063249—41no—
103#13063249D411yescharacteristic
104#13063248—21no—
105#13063248—21no—
106#13063248—21no—
107#13063248—21no—
108#13063248—21no—
109#13063248D411yescharacteristic
110#13063246—21no—
111C22⋊(C43⋊C8)—21no—
112#13063235—21no—
113C4×C43⋊C8—21no—
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C22×Q8×C43—21no—
117C2×SD16×C43D411yescharacteristic
118C4⋊Q8×C43—21no—
119C4⋊Q8×C43—21no—
120C4⋊Q8×C43—21no—
121C4⋊Q8×C43—41no—
122C4⋊Q8×C43C2311yescharacteristic
123C4⋊Q8×C43C2311yescharacteristic
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—41no—
126C4×Q8×C43—21no—
127C4×Q8×C43—21no—
128C4×Q8×C43C2311yescharacteristic
129C4×Q8×C43C2311yescharacteristic
130C4×D4×C43—21no—
131C4×D4×C43C2311yescharacteristic
132#106×C43—21no—
133#106×C43—21no—
134#106×C43—21no—
135#106×C43—21no—
136#106×C43D411yescharacteristic
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139#103×C43—21no—
140#103×C43D411yescharacteristic
141#102×C43—21no—
142#102×C43D411yescharacteristic
143C4×C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—41no—
148C2×Q8×C43—41no—
149C2×Q8×C43—42no—
150C2×Q8×C43—81no—
151C2×Q8×C43C2×D411yescharacteristic
152C2×Q8×C43C2×D411yescharacteristic
153C2×D4×C43C2×D411yescharacteristic
154C22×C4×C43—21no—
155C22×C4×C43—41no—
156C22×Dic43—41no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—42no—
160C2×Dic86—41no—
161C2×Dic86—81no—
162C2×Dic86C2×D411yescharacteristic
163SD16×C43Q1614yescomplemented
164C2×C8×C43—21no—
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C4⋊C4×C43—21no—
168C4⋊C4×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—
175C4⋊C4×C43—41no—
176C4⋊C4×C43C2×D411yescharacteristic
177C4⋊C4×C43C2×D411yescharacteristic
178C4⋊C4×C43C2×D411yescharacteristic
179C22⋊C4×C43—21no—
180C22⋊C4×C43—41no—
181C42×C43—21no—
182C42×C43—21no—
183C42×C43—41no—
184C42×C43C2411yescharacteristic
185C22⋊Dic43—41no—
186#10621885—22no—
187#10621885—42no—
188#10621885—42no—
189#10621885—42no—
190#10621885—42no—
191#10621885—81no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—41no—
197C4⋊Dic43—41no—
198C4⋊Dic43C2×D411yescharacteristic
199Dic43⋊C4—21no—
200Dic43⋊C4—41no—
201Dic43⋊C4—41no—
202C4×Dic43—21no—
203C4×Dic43—41no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—42no—
209C2×C43⋊C8C2×D411yescharacteristic
210C2×C43⋊C8C2×D411yescharacteristic
211C23×C43—21no—
212Q8×C43—21no—
213Q8×C43—21no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—82no—
217Q8×C43—81no—
218Q8×C43—161no—
219Q8×C43C2×Q1612yescomplemented
220Q8×C43AGL(1,ℤ/8)12yes—
221D4×C43—21no—
222D4×C43C2×Q1612yes—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—82no—
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43H(5,𝔽2)11yescharacteristic
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—82no—
241Dic86—21no—
242Dic86—21no—
243Dic86—41no—
244Dic86—41no—
245Dic86—41no—
246Dic86—41no—
247Dic86—82no—
248C8×C43—21no—
249C8×C43—41no—
250C8×C43C2×Q1612yescomplemented
251C43⋊C8—21no—
252C43⋊C8—21no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257#19812—431nomaximal, Sylow
258C22×C43—22no—
259C22×C43—41no—
260C22×C43—41no—
261C22×C43D4211yescharacteristic
262C4×C43—22no—
263C4×C43—22no—
264C4×C43—21no—
265C4×C43—41no—
266C4×C43—41no—
267C4×C43—41no—
268C4×C43—81no—
269C4×C43—81no—
270C4×C43C22×Q1611yescharacteristic
271C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
272C4×C43#57711yescharacteristic
273C4×C43#57811yescharacteristic
274Dic43—41no—
275Dic43—41no—
276Dic43—81no—
277Dic43—81no—
278#3386—431no—
279Q8×SD16D4311yescharacteristic
280#3363—431no—
281D4×Q16—431no—
282#1723—431no—
283#1692—431no—
284#1683—431no—
285#1674—431no—
286#1670—431no—
287#1649—431no—
288#1648—431no—
289#1645—431no—
290#1637—431no—
291#1584—431no—
292SD16⋊C8—431no—
293C2×C43—42no—
294C2×C43#326511yescharacteristic
295C2×C43D4×Q1611yescharacteristic
296C2×C43#328911yescharacteristic
297C22×Q16—861no—
298Q82C2×D4311yescharacteristic
299#557—431no—
300D4×Q8—431no—
301D4×Q8C2×D4311yescharacteristic
302#501—861no—
303#500—431no—
304#500—431no—
305#498—21no—
306#498C2×D4311yescharacteristic
307#494—431no—
308#487—431no—
309#487—431no—
310#487—861no—
311#478—861no—
312#477—431no—
313#477—861no—
314#477—861no—
315#476—21no—
316#476C2×D4311yescharacteristic
317#475—21no—
318#475—431no—
319#475C2×D4311yescharacteristic
320#474—431no—
321#467—861no—
322#462—431no—
323#462—431no—
324#462—431no—
325#462—861no—
326#451—861no—
327#451—861no—
328#446—431no—
329C8×Q8—431no—
330C8×Q8C2×D4311yescharacteristic
331#440—861no—
332C4×Q16—431no—
333C4×Q16—861no—
334C4×SD16—21no—
335C4×SD16C2×D4311yescharacteristic
336C8×D4—431no—
337#335—431no—
338#335—431no—
339#333—431no—
340#332—431no—
341#332—431no—
342#332—431no—
343Q8⋊C8—431no—
344Q8⋊C8—431no—
345Q8⋊C8—431no—
346D4⋊C8—431no—
347#322—431no—
348C43#1981211yescharacteristic, complemented, Sylow
349C22×Q8—21no—
350C22×Q8—861no—
351C2×Q16—431no—
352C2×Q16—861no—
353C2×Q16—861no—
354C2×Q16—861no—
355C2×Q16—861no—
356C2×Q16—861no—
357C2×Q16—1724no—
358C2×SD16C22⋊D4311yescharacteristic
359C22×C8—861no—
360C4⋊Q8—21no—
361C4⋊Q8—21no—
362C4⋊Q8—21no—
363C4⋊Q8—41no—
364C4⋊Q8—431no—
365C4⋊Q8—431no—
366C4⋊Q8—861no—
367C4⋊Q8—861no—
368C4⋊Q8C22×D4311yescharacteristic
369C4⋊Q8C22×D4311yescharacteristic
370#125—861no—
371#125—1721no—
372C22⋊Q8—21no—
373C22⋊Q8—41no—
374C22⋊Q8—861no—
375C22⋊Q8—1721no—
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8—431no—
379C4×Q8—861no—
380C4×Q8—861no—
381C4×Q8C22×D4311yescharacteristic
382C4×Q8C22×D4311yescharacteristic
383C4×D4—21no—
384C4×D4—861no—
385C4×D4C22×D4311yescharacteristic
386#107—431no—
387#107—861no—
388#107—861no—
389#107—861no—
390#107—861no—
391#107—1721no—
392#106—21no—
393#106—21no—
394#106—21no—
395#106—21no—
396#106—861no—
397#106C22⋊D4311yescharacteristic
398C4⋊C8—21no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—431no—
402C4⋊C8—861no—
403C4⋊C8—861no—
404C4⋊C8C22×D4311yescharacteristic
405#103—21no—
406#103—431no—
407#103—431no—
408#103—861no—
409#103—861no—
410#103—861no—
411#103—861no—
412#103—861no—
413#103—861no—
414#103—861no—
415#103—1721no—
416#103C22⋊D4311yescharacteristic
417#102—21no—
418#102—861no—
419#102C22⋊D4311yescharacteristic
420C22⋊C8—861no—
421#97—861no—
422C4×C8—21no—
423C4×C8—431no—
424C4×C8—431no—
425C4×C8—861no—
426C4×C8C22×D4311yescharacteristic
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—41no—
430C2×Q8—41no—
431C2×Q8—42no—
432C2×Q8—81no—
433C2×Q8—431no—
434C2×Q8—861no—
435C2×Q8—861no—
436C2×Q8—3441no—
437C2×Q8—1721no—
438C2×Q8—1722no—
439C2×Q8D4×D4311yescharacteristic
440C2×Q8C2×C22⋊D4311yescharacteristic
441C2×D4C2×C22⋊D4311yescharacteristic
442C22×C4—21no—
443C22×C4—41no—
444C22×C4—1721no—
445Q16—862no—
446Q16—3441no—
447Q16—1722no—
448Q16—1722no—
449Q16—1722no—
450Q16—1722no—
451SD16#1062188514yescomplemented
452C2×C8—21no—
453C2×C8—431no—
454C2×C8—431no—
455C2×C8—861no—
456C2×C8—861no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8—1722no—
460C2×C8C2×C22⋊D4311yescharacteristic
461C2×C8C2×C22⋊D4311yescharacteristic
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—431no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—1721no—
478C4⋊C4—1721no—
479C4⋊C4—1721no—
480C4⋊C4—1721no—
481C4⋊C4D4×D4311yescharacteristic
482C4⋊C4C2×C22⋊D4311yescharacteristic
483C4⋊C4C2×C22⋊D4311yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—41no—
486C22⋊C4—1721no—
487C42—21no—
488C42—21no—
489C42—41no—
490C42—861no—
491C42—1721no—
492C42C23×D4311yescharacteristic
493C23—21no—
494Q8—21no—
495Q8—21no—
496Q8—41no—
497Q8—41no—
498Q8—82no—
499Q8—81no—
500Q8—161no—
501Q8—861no—
502Q8—861no—
503Q8—3442no—
504Q8—1721no—
505Q8—1721no—
506Q8—1721no—
507Q8—1721no—
508Q8C2×#1062188512yescomplemented
509Q8#1306335212yes—
510D4—21no—
511D4C2×#1062188512yes—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—82no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—3442no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4C2×D4×D4311yescharacteristic
528C2×C4C22×C22⋊D4311yescharacteristic
529C2×C4#1306337011yescharacteristic
530C8—21no—
531C8—41no—
532C8—861no—
533C8—861no—
534C8—1721no—
535C8—1721no—
536C8—1721no—
537C8—1721no—
538C8C2×#1062188512yescomplemented
539C22—22no—
540C22—41no—
541C22—41no—
542C22D4×C22⋊D4311yescharacteristic
543C4—22no—
544C4—22no—
545C4—21no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—81no—
550C4—81no—
551C4—3441no—
552C4—3441no—
553C4—1721no—
554C4—1721no—
555C4C22×#1062188511yescharacteristic
556C4C2×#1306335211yescharacteristic
557C4#1458370511yescharacteristic
558C4#1458371411yescharacteristic
559C2—42no—
560C2#1914609011yescharacteristic
561C2D4×#1062188511yescharacteristic
562C2#1914636811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingQ8×SD16×C43C2
socleC22×C43D42
prime radicalC2×D4×C43C2×D4
hypercenterQ8×SD16D43
hypocenterC43#19812
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ Q8×SD16

Complements

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

NH ≅ G/Ntype
2. #19147273C2semidirect
4. #19134269C2semidirect
5. #19134098C2semidirect
7. #19133989C2semidirect
8. #19133963C2semidirect
10. #19133836C2semidirect
11. #19133816C2semidirect
13. #19133445C2semidirect
163. SD16×C43Q16semidirect
219. Q8×C43C2×Q16semidirect
250. C8×C43C2×Q16semidirect
348. C43#19812semidirect
451. SD16#10621885semidirect
508. Q8C2×#10621885semidirect
538. C8C2×#10621885semidirect

Maximal subgroups

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

subgroupindex
#191475142
#191472732
D4×#106218852
#191342692
#191340982
#191340482
#191339892
#191339632
#191338442
#191338362
#191338162
#191337592
#191334452
SD16⋊(C43⋊C8)2
Q8×SD16×C432
#1981243