Finite Group Databasebeta

← #25086808

Subgroups — #25086808

Order 11008.

580 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#10621885C211yesmaximal, characteristic, complemented
2SD16×Dic86C211yesmaximal, characteristic
3#19146465C211yesmaximal, characteristic
4#19134273C211yesmaximal, characteristic, complemented
5#19134101C211yesmaximal, characteristic, complemented
6#19134055C211yesmaximal, characteristic, complemented
7#19133996C211yesmaximal, characteristic, complemented
8#19133992C211yesmaximal, characteristic
9#19133816C211yesmaximal, characteristic, complemented
10#19133759C211yesmaximal, characteristic
11#19133734C211yesmaximal, characteristic, complemented
12#19133729C211yesmaximal, characteristic
13#19133443C211yesmaximal, characteristic, complemented
14SD16⋊(C43⋊C8)C211yesmaximal, characteristic
15C43×#3385C211yesmaximal, characteristic
16Q8×Dic86C2211yescharacteristic
17D4×Dic86C2211yescharacteristic
18#14583302—21no—
19#14583302C2211yescharacteristic
20#14583297C2211yescharacteristic
21#14583296—21no—
22#14583278C2211yescharacteristic
23#14583251C2211yescharacteristic
24#14583249C2211yescharacteristic
25#14583234—21no—
26#14583194—21no—
27#14583194C2211yescharacteristic
28#14583191—21no—
29#14583191C2211yescharacteristic
30#14583191C2211yescharacteristic
31#14583189C2211yescharacteristic
32#14583187—21no—
33#14583184C2211yescharacteristic
34#14583182—21no—
35#14583138—21no—
36#14583109C2211yescharacteristic
37#14583054—21no—
38Q8×C43⋊C8C2211yescharacteristic
39C8×Dic86C2211yescharacteristic
40C4×#10621885—21no—
41C4×#10621885C2211yescharacteristic
42SD16×Dic43—21no—
43D4×C43⋊C8C2211yescharacteristic
44C2×#13063248—21no—
45#14582652C2211yescharacteristic
46#14582651C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582644C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53#14582629C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582620C2211yescharacteristic
56Q82×C43C2211yescharacteristic
57C43×#554C2211yescharacteristic
58C43×#501—21no—
59C43×#500C2211yescharacteristic
60C43×#479—21no—
61C43×#477C2211yescharacteristic
62C43×#476C2211yescharacteristic
63C43×#474—21no—
64C43×#446C2211yescharacteristic
65C43×#440—21no—
66C4×SD16×C43C2211yescharacteristic
67C22×Dic86—21no—
68C2×#10621885—21no—
69C2×#10621885—41no—
70C2×#10621885D411yescharacteristic
71C22×C43⋊C8—21no—
72#13063325—21no—
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063324—21no—
76#13063324—21no—
77#13063324—41no—
78#13063304—21no—
79#13063302—41no—
80Q8×Dic43—21no—
81C4×Dic86—21no—
82C4×Dic86C2311yescharacteristic
83D4×Dic43—21no—
84#13063258—21no—
85#13063258—21no—
86#13063258—21no—
87#13063258—21no—
88#13063258—21no—
89#13063258D411yescharacteristic
90#13063257—21no—
91#13063257—21no—
92#13063256—21no—
93#13063256—21no—
94C4⋊(C43⋊C8)—21no—
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98Dic43⋊C8—21no—
99#13063249—21no—
100#13063249—21no—
101#13063249—41no—
102#13063249D411yescharacteristic
103#13063248—21no—
104#13063248—21no—
105#13063248—21no—
106#13063248—21no—
107#13063248—21no—
108#13063248D411yescharacteristic
109#13063246—21no—
110C22⋊(C43⋊C8)—21no—
111C4×C43⋊C8—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C2×SD16×C43D411yescharacteristic
116C4⋊Q8×C43—21no—
117C4⋊Q8×C43—21no—
118C4⋊Q8×C43—41no—
119C4⋊Q8×C43C2311yescharacteristic
120C4⋊Q8×C43C2311yescharacteristic
121#125×C43—21no—
122C22⋊Q8×C43—21no—
123C22⋊Q8×C43—41no—
124C4×Q8×C43—21no—
125C4×Q8×C43—21no—
126C4×Q8×C43C2311yescharacteristic
127C4×Q8×C43C2311yescharacteristic
128C4×D4×C43—21no—
129C4×D4×C43C2311yescharacteristic
130C2×C4⋊C4×C43—21no—
131#107×C43—21no—
132#107×C43—21no—
133#107×C43—21no—
134#106×C43—21no—
135#106×C43D411yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43D411yescharacteristic
140#102×C43—21no—
141#102×C43D411yescharacteristic
142#97×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—41no—
147C2×Q8×C43C2×D411yescharacteristic
148C2×Q8×C43C2×D411yescharacteristic
149C2×D4×C43C2×D411yescharacteristic
150C22×C4×C43—21no—
151C22×C4×C43—41no—
152C22×Dic43—41no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—42no—
156C2×Dic86—41no—
157C2×Dic86—41no—
158C2×Dic86—81no—
159C2×Dic86C2×D411yescharacteristic
160SD16×C43Q1614yescomplemented
161C2×C8×C43—21no—
162C2×C8×C43C2×D411yescharacteristic
163C2×C8×C43C2×D411yescharacteristic
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—41no—
171C4⋊C4×C43—41no—
172C4⋊C4×C43—41no—
173C4⋊C4×C43—41no—
174C4⋊C4×C43C2×D411yescharacteristic
175C4⋊C4×C43C2×D411yescharacteristic
176C4⋊C4×C43C2×D411yescharacteristic
177C22⋊C4×C43—21no—
178C22⋊C4×C43—41no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43—41no—
182C42×C43C2411yescharacteristic
183C22⋊Dic43—41no—
184#10621885—22no—
185#10621885—81no—
186#10621885—82no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—41no—
192C4⋊Dic43C2×D411yescharacteristic
193Dic43⋊C4—21no—
194Dic43⋊C4—41no—
195Dic43⋊C4—41no—
196C4×Dic43—21no—
197C4×Dic43—41no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—81no—
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C23×C43—21no—
206Q8×C43—21no—
207Q8×C43—21no—
208Q8×C43—21no—
209Q8×C43—81no—
210Q8×C43—81no—
211Q8×C43—161no—
212Q8×C43C2×Q1612yes—
213D4×C43—21no—
214D4×C43C2×Q1612yes—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—161no—
225C2×C4×C43C22×D411yescharacteristic
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43H(5,𝔽2)11yescharacteristic
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—41no—
231C2×Dic43—41no—
232C2×Dic43—82no—
233Dic86—21no—
234Dic86—41no—
235Dic86—41no—
236Dic86—82no—
237Dic86—81no—
238Dic86—161no—
239Dic86#13712yes—
240C8×C43—21no—
241C8×C43—41no—
242C8×C43C2×Q1612yes—
243C43⋊C8—21no—
244C43⋊C8—21no—
245C43⋊C8—41no—
246C43⋊C8—41no—
247C43⋊C8—41no—
248C43⋊C8—41no—
249#19813—431nomaximal, Sylow
250C22×C43—22no—
251C22×C43—41no—
252C22×C43—41no—
253C22×C43D4211yescharacteristic
254C4×C43—22no—
255C4×C43—21no—
256C4×C43—41no—
257C4×C43—41no—
258C4×C43—41no—
259C4×C43—41no—
260C4×C43—81no—
261C4×C43—81no—
262C4×C43C22×Q1611yescharacteristic
263C4×C43C2×#13711yescharacteristic
264C4×C43#57711yescharacteristic
265C4×C43#57811yescharacteristic
266Dic43—22no—
267Dic43—41no—
268Dic43—81no—
269Dic43—81no—
270#3385D4311yescharacteristic
271Q8×Q16—431no—
272Q8×SD16—431no—
273#3299—431no—
274#1723—431no—
275#1692—431no—
276#1684—431no—
277#1676—431no—
278#1675—431no—
279#1645—431no—
280#1637—431no—
281#1633—431no—
282#1632—431no—
283#1584—431no—
284SD16⋊C8—431no—
285C2×C43—42no—
286C2×C43#326611yescharacteristic
287C2×C43D4×Q1611yescharacteristic
288C2×C43#328811yescharacteristic
289Q82—431no—
290Q82C2×D4311yescharacteristic
291#554C2×D4311yescharacteristic
292D4×Q8—431no—
293#501—21no—
294#500—431no—
295#500—861no—
296#500C2×D4311yescharacteristic
297#498—431no—
298#498—861no—
299#494—431no—
300#487—431no—
301#487—431no—
302#484—861no—
303#479—21no—
304#477—431no—
305#477—431no—
306#477—431no—
307#477—861no—
308#477—861no—
309#477C2×D4311yescharacteristic
310#476—431no—
311#476—861no—
312#476C2×D4311yescharacteristic
313#475—431no—
314#475—861no—
315#474—21no—
316#467—861no—
317#462—431no—
318#451—861no—
319#446C2×D4311yescharacteristic
320C8×Q8—431no—
321C8×Q8—431no—
322#440—21no—
323C4×Q16—431no—
324C4×Q16—861no—
325C4×SD16—861no—
326C4×SD16C2×D4311yescharacteristic
327C8×D4—431no—
328C2×#103—861no—
329#335—431no—
330#335—431no—
331#333—431no—
332#333—431no—
333#333—431no—
334#332—431no—
335Q8⋊C8—431no—
336Q8⋊C8—431no—
337Q8⋊C8—431no—
338D4⋊C8—431no—
339#322—431no—
340C43#1981311yescharacteristic, complemented, Sylow
341C22×Q8—861no—
342C2×Q16—431no—
343C2×Q16—861no—
344C2×Q16—1721no—
345C2×SD16C22⋊D4311yescharacteristic
346C22×C8—861no—
347C4⋊Q8—21no—
348C4⋊Q8—21no—
349C4⋊Q8—41no—
350C4⋊Q8—431no—
351C4⋊Q8—431no—
352C4⋊Q8—861no—
353C4⋊Q8—861no—
354C4⋊Q8—861no—
355C4⋊Q8—1721no—
356C4⋊Q8C22×D4311yescharacteristic
357C4⋊Q8C22×D4311yescharacteristic
358#125—21no—
359C22⋊Q8—21no—
360C22⋊Q8—41no—
361C22⋊Q8—861no—
362C22⋊Q8—1721no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—431no—
366C4×Q8—861no—
367C4×Q8—861no—
368C4×Q8C22×D4311yescharacteristic
369C4×Q8C22×D4311yescharacteristic
370C4×D4—21no—
371C4×D4—861no—
372C4×D4C22×D4311yescharacteristic
373C2×C4⋊C4—21no—
374#107—21no—
375#107—21no—
376#107—21no—
377#107—431no—
378#107—861no—
379#107—861no—
380#107—861no—
381#107—861no—
382#107—861no—
383#106—21no—
384#106—861no—
385#106—861no—
386#106—861no—
387#106—861no—
388#106C22⋊D4311yescharacteristic
389C4⋊C8—21no—
390C4⋊C8—431no—
391C4⋊C8—431no—
392C4⋊C8—431no—
393C4⋊C8—861no—
394C4⋊C8—861no—
395C4⋊C8C22×D4311yescharacteristic
396#103—21no—
397#103—431no—
398#103—431no—
399#103—861no—
400#103—861no—
401#103—861no—
402#103—861no—
403#103—861no—
404#103—861no—
405#103—861no—
406#103—1721no—
407#103C22⋊D4311yescharacteristic
408#102—21no—
409#102—861no—
410#102C22⋊D4311yescharacteristic
411C22⋊C8—861no—
412#97—21no—
413C4×C8—431no—
414C4×C8—431no—
415C4×C8—861no—
416C4×C8—861no—
417C4×C8C22×D4311yescharacteristic
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—41no—
421C2×Q8—431no—
422C2×Q8—861no—
423C2×Q8—861no—
424C2×Q8—3441no—
425C2×Q8—1721no—
426C2×Q8—1721no—
427C2×Q8—1722no—
428C2×Q8D4×D4311yescharacteristic
429C2×Q8C2×C22⋊D4311yescharacteristic
430C2×D4C2×C22⋊D4311yescharacteristic
431C22×C4—21no—
432C22×C4—41no—
433C22×C4—1721no—
434Q16—862no—
435Q16—3441no—
436Q16—3442no—
437SD16#1062188514yescomplemented
438C2×C8—21no—
439C2×C8—431no—
440C2×C8—431no—
441C2×C8—861no—
442C2×C8—861no—
443C2×C8—861no—
444C2×C8—861no—
445C2×C8—3441no—
446C2×C8C2×C22⋊D4311yescharacteristic
447C2×C8C2×C22⋊D4311yescharacteristic
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—41no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4—431no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—1721no—
465C4⋊C4—1721no—
466C4⋊C4—1721no—
467C4⋊C4D4×D4311yescharacteristic
468C4⋊C4C2×C22⋊D4311yescharacteristic
469C4⋊C4C2×C22⋊D4311yescharacteristic
470C22⋊C4—21no—
471C22⋊C4—41no—
472C22⋊C4—1721no—
473C42—21no—
474C42—21no—
475C42—41no—
476C42—861no—
477C42—1721no—
478C42C23×D4311yescharacteristic
479C23—21no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—81no—
484Q8—81no—
485Q8—161no—
486Q8—432no—
487Q8—861no—
488Q8—3441no—
489Q8—3442no—
490Q8—1721no—
491Q8—1721no—
492Q8—6881no—
493Q8C2×#1062188512yes—
494D4—21no—
495D4C2×#1062188512yes—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—161no—
506C2×C4—861no—
507C2×C4—861no—
508C2×C4—3442no—
509C2×C4—1721no—
510C2×C4—1721no—
511C2×C4C2×D4×D4311yescharacteristic
512C2×C4C22×C22⋊D4311yescharacteristic
513C2×C4#1306337011yescharacteristic
514C8—21no—
515C8—41no—
516C8—861no—
517C8—861no—
518C8—1721no—
519C8—1721no—
520C8—1721no—
521C8—1721no—
522C8C2×#1062188512yes—
523C22—22no—
524C22—41no—
525C22—41no—
526C22D4×C22⋊D4311yescharacteristic
527C4—22no—
528C4—21no—
529C4—41no—
530C4—41no—
531C4—41no—
532C4—41no—
533C4—81no—
534C4—81no—
535C4—862no—
536C4—3441no—
537C4—3441no—
538C4—1721no—
539C4C22×#1062188511yescharacteristic
540C4#137×D4311yescharacteristic
541C4#1458370811yescharacteristic
542C4#1458371411yescharacteristic
543C2—42no—
544C2#1914609911yescharacteristic
545C2D4×#1062188511yescharacteristic
546C2#1914635911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3385C2
socleC22×C43D42
prime radicalC2×D4×C43C2×D4
hypercenter#3385D43
hypocenterC43#19813
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3385

Complements

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

NH ≅ G/Ntype
1. Q8×#10621885C2semidirect
4. #19134273C2semidirect
5. #19134101C2semidirect
6. #19134055C2semidirect
7. #19133996C2semidirect
9. #19133816C2semidirect
11. #19133734C2semidirect
13. #19133443C2semidirect
160. SD16×C43Q16semidirect
340. C43#19813semidirect
437. SD16#10621885semidirect

Maximal subgroups

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

subgroupindex
Q8×#106218852
SD16×Dic862
#191464652
#191342732
#191341012
#191340552
#191339962
#191339922
#191338162
#191337592
#191337342
#191337292
#191334432
SD16⋊(C43⋊C8)2
C43×#33852
#1981343