Finite Group Databasebeta

← #25087594

Subgroups — #25087594

Order 11008.

572 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#19147458C211yesmaximal, characteristic
2#19147244C211yesmaximal, characteristic
3#19147212C211yesmaximal, characteristic, complemented
4#19134273C211yesmaximal, characteristic, complemented
5#19134115C211yesmaximal, characteristic, complemented
6#19134055C211yesmaximal, characteristic, complemented
7#19133997C211yesmaximal, characteristic, complemented
8#19133970C211yesmaximal, characteristic, complemented
9#19133802C211yesmaximal, characteristic, complemented
10#19133766C211yesmaximal, characteristic, complemented
11#19133729C211yesmaximal, characteristic, complemented
12#19133728C211yesmaximal, characteristic, complemented
13#19133424C211yesmaximal, characteristic
14#19133414C211yesmaximal, characteristic, complemented
15C43×#3338C211yesmaximal, characteristic, complemented
16#14583622C2211yescharacteristic
17#14583609C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583298—21no—
20#14583297C2211yescharacteristic
21#14583278C2211yescharacteristic
22#14583256—21no—
23#14583251C2211yescharacteristic
24#14583249C2211yescharacteristic
25#14583238—21no—
26#14583228—21no—
27#14583203—21no—
28#14583199—21no—
29#14583196—21no—
30#14583194C2211yescharacteristic
31#14583189C2211yescharacteristic
32#14583186C2211yescharacteristic
33#14583186C2211yescharacteristic
34#14583184C2211yescharacteristic
35#14583154—21no—
36#14583114—21no—
37#14583104C2211yescharacteristic
38Q8×C43⋊C8C2211yescharacteristic
39Q8×C43⋊C8C2211yescharacteristic
40C4×#10621883—21no—
41C4×#10621882—21no—
42C4×#10621882C2211yescharacteristic
43#14582978C2211yescharacteristic
44#14582940—21no—
45#14582651C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582644C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582620C2211yescharacteristic
56C43×#554C2211yescharacteristic
57C43×#554C2211yescharacteristic
58C43×#500C2211yescharacteristic
59C43×#484—21no—
60C43×#484—21no—
61C43×#477C2211yescharacteristic
62C43×#477C2211yescharacteristic
63C43×#467—21no—
64C4×Q16×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic
66C2×#107×C43—21no—
67C2×#10621885—41no—
68C2×#10621883—21no—
69C2×#10621882D411yescharacteristic
70C2×#10621872—21no—
71#13063325C2311yescharacteristic
72#13063325C2311yescharacteristic
73#13063320—41no—
74#13063317—21no—
75#13063313—21no—
76#13063303—41no—
77#13063301—21no—
78#13063301—21no—
79C4×Dic86—21no—
80C4×D172—21no—
81C4×D172C2311yescharacteristic
82#13063283—21no—
83C4⋊C4×D43—21no—
84#13063258—21no—
85#13063258—21no—
86#13063258—21no—
87#13063258D411yescharacteristic
88#13063257—21no—
89#13063257—21no—
90#13063256—21no—
91#13063256—21no—
92#13063256—21no—
93#13063256—21no—
94C4⋊(C43⋊C8)—21no—
95C4⋊(C43⋊C8)—21no—
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99#13063249—21no—
100#13063249—21no—
101#13063249—41no—
102#13063248—21no—
103#13063248—21no—
104#13063248—21no—
105#13063246—21no—
106#13063246D411yescharacteristic
107#13063245—21no—
108#13063245—21no—
109#13063245D411yescharacteristic
110(C2×D43)⋊C8—21no—
111C4×C43⋊C8—21no—
112C4×C43⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×Q16×C43D411yescharacteristic
116C22×C8×C43—21no—
117C4⋊Q8×C43C2311yescharacteristic
118C4⋊Q8×C43C2311yescharacteristic
119#125×C43—21no—
120#125×C43—21no—
121C22⋊Q8×C43—21no—
122C22⋊Q8×C43—21no—
123C22⋊Q8×C43—41no—
124C22⋊Q8×C43—41no—
125C4×Q8×C43C2311yescharacteristic
126C4×Q8×C43C2311yescharacteristic
127C4×D4×C43—21no—
128C4×D4×C43—21no—
129C4×D4×C43C2311yescharacteristic
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43—21no—
132#107×C43—21no—
133#107×C43—21no—
134#107×C43—21no—
135#107×C43—21no—
136#107×C43D411yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#103×C43D411yescharacteristic
141#103×C43D411yescharacteristic
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×Q8×C43C2×D411yescharacteristic
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43—41no—
151C22×C4×C43—41no—
152C2×D172C2×D411yescharacteristic
153C2×C4×D43—21no—
154C2×C4×D43—41no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157Q16×C43—22no—
158C2×C8×C43—21no—
159C2×C8×C43—42no—
160C2×C8×C43C2×D411yescharacteristic
161C2×C8×C43C2×D411yescharacteristic
162C4⋊C4×C43—21no—
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×C43—41no—
171C4⋊C4×C43—41no—
172C4⋊C4×C43C2×D411yescharacteristic
173C4⋊C4×C43C2×D411yescharacteristic
174C4⋊C4×C43C2×D411yescharacteristic
175C22⋊C4×C43—21no—
176C22⋊C4×C43—41no—
177C22⋊C4×C43—41no—
178C42×C43—21no—
179C42×C43—21no—
180C42×C43C2411yescharacteristic
181#10621885—82no—
182#10621883—42no—
183#10621882—22no—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—41no—
186(C2×D43)⋊C4—41no—
187(C2×D43)⋊C4—41no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43C2×D411yescharacteristic
193Dic43⋊C4—41no—
194Dic43⋊C4—41no—
195Dic43⋊C4—41no—
196C4×Dic43—41no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8C2×D411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203#10621872—42no—
204C23×C43—21no—
205C22×D43—21no—
206Q8×C43—21no—
207Q8×C43—21no—
208Q8×C43—21no—
209Q8×C43—21no—
210Q8×C43—81no—
211Q8×C43—81no—
212D4×C43—21no—
213D4×C43#13712yes—
214C2×C4×C43—21no—
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—161no—
224C2×C4×C43—161no—
225C2×C4×C43C22×D411yescharacteristic
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43H(5,𝔽2)11yescharacteristic
228C2×Dic43—21no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231D172—21no—
232D172—21no—
233C4×D43—41no—
234C4×D43—41no—
235C4×D43—161no—
236Dic86—41no—
237Dic86—41no—
238Dic86—81no—
239C8×C43—21no—
240C8×C43—41no—
241C8×C43#13512yes—
242C43⋊C8—21no—
243C43⋊C8—21no—
244C43⋊C8—41no—
245C43⋊C8—41no—
246C43⋊C8—41no—
247C43⋊C8—41no—
248#19865—431nomaximal, Sylow
249C22×C43—22no—
250C22×C43—41no—
251C22×C43—41no—
252C22×C43D4211yescharacteristic
253C2×D43—41no—
254C2×D43—41no—
255C2×D43—41no—
256C4×C43—21no—
257C4×C43—41no—
258C4×C43—41no—
259C4×C43—41no—
260C4×C43—41no—
261C4×C43—41no—
262C4×C43—81no—
263C4×C43—81no—
264C4×C43C2×#13511yescharacteristic
265C4×C43C2×#13711yescharacteristic
266C4×C43#57811yescharacteristic
267C4×C43#57811yescharacteristic
268Dic43—41no—
269Dic43—81no—
270Dic43—81no—
271#3380—431no—
272#3360—431no—
273#3356—431no—
274#3338D4311yescharacteristic, complemented
275#1723—431no—
276#1695—431no—
277#1684—431no—
278#1676—431no—
279#1671—431no—
280#1643—431no—
281#1638—431no—
282#1632—431no—
283#1632—431no—
284#1581—431no—
285#1579—431no—
286C2×C43—42no—
287C2×C43#327011yescharacteristic
288C2×C43#328311yescharacteristic
289C2×C43#328811yescharacteristic
290D43—81no—
291#556—431no—
292#554—431no—
293#554C2×D4311yescharacteristic
294#554C2×D4311yescharacteristic
295#500—431no—
296#500C2×D4311yescharacteristic
297#499—861no—
298#498—431no—
299#494—431no—
300#488—861no—
301#487—431no—
302#487—431no—
303#485—861no—
304#484—21no—
305#484—21no—
306#483—861no—
307#479—861no—
308#478—861no—
309#478—861no—
310#477—431no—
311#477C2×D4311yescharacteristic
312#477C2×D4311yescharacteristic
313#476—431no—
314#476—431no—
315#476—431no—
316#475—431no—
317#470—861no—
318#467—21no—
319#463—861no—
320#461—431no—
321C8×Q8—431no—
322C8×Q8—431no—
323C4×Q16C2×D4311yescharacteristic
324C4×SD16—861no—
325C4×D8—431no—
326C4×D8—861no—
327#436—431no—
328C8×D4C2×D4311yescharacteristic
329#428—861no—
330C2×#107—21no—
331#335—431no—
332#334—431no—
333#333—431no—
334#333—431no—
335#333—431no—
336#332—431no—
337Q8⋊C8—431no—
338Q8⋊C8—431no—
339D4⋊C8—431no—
340D4⋊C8—431no—
341#322—431no—
342C43#1986511yescharacteristic, complemented, Sylow
343C2×Q16—1721no—
344C2×Q16C22⋊D4311yescharacteristic
345C2×SD16—861no—
346C2×D8—431no—
347C2×M16—861no—
348C22×C8—21no—
349C4⋊Q8—431no—
350C4⋊Q8—431no—
351C4⋊Q8C22×D4311yescharacteristic
352C4⋊Q8C22×D4311yescharacteristic
353#126—1721no—
354#125—21no—
355#125—21no—
356#125—861no—
357#124—861no—
358C22⋊Q8—21no—
359C22⋊Q8—21no—
360C22⋊Q8—41no—
361C22⋊Q8—41no—
362C22⋊Q8—861no—
363C22⋊Q8—861no—
364C22⋊Q8—1721no—
365C4×Q8—861no—
366C4×Q8C22×D4311yescharacteristic
367C4×Q8C22×D4311yescharacteristic
368C4×D4—21no—
369C4×D4—21no—
370C4×D4—431no—
371C4×D4—861no—
372C4×D4C22×D4311yescharacteristic
373#117—861no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—861no—
377#107—21no—
378#107—21no—
379#107—21no—
380#107—21no—
381#107—431no—
382#107—861no—
383#107—861no—
384#107—861no—
385#107C22⋊D4311yescharacteristic
386#106—861no—
387#106—861no—
388#106—861no—
389#106—861no—
390#106—861no—
391#106—861no—
392C4⋊C8—431no—
393C4⋊C8—431no—
394C4⋊C8—431no—
395C4⋊C8—861no—
396C4⋊C8—861no—
397C4⋊C8C22×D4311yescharacteristic
398#103—21no—
399#103—21no—
400#103—861no—
401#103—861no—
402#103—861no—
403#103—861no—
404#103—861no—
405#103—1721no—
406#103C22⋊D4311yescharacteristic
407#103C22⋊D4311yescharacteristic
408#102—431no—
409#102—431no—
410#102—861no—
411#102—861no—
412#102—861no—
413C22⋊C8—21no—
414C22⋊C8—861no—
415C4×C8—431no—
416C4×C8—431no—
417C4×C8—861no—
418C4×C8—861no—
419C4×C8C22×D4311yescharacteristic
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—861no—
423C2×Q8—861no—
424C2×Q8C2×C22⋊D4311yescharacteristic
425C2×Q8C2×C22⋊D4311yescharacteristic
426C2×D4—431no—
427C2×D4D4×D4311yescharacteristic
428C22×C4—21no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—861no—
432C22×C4—1721no—
433Q16—22no—
434Q16—3442no—
435SD16—1722no—
436D8—862no—
437M16—1722no—
438C2×C8—21no—
439C2×C8—42no—
440C2×C8—431no—
441C2×C8—431no—
442C2×C8—861no—
443C2×C8—861no—
444C2×C8—861no—
445C2×C8—861no—
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—1721no—
464C4⋊C4—1721no—
465C4⋊C4—1721no—
466C4⋊C4D4×D4311yescharacteristic
467C4⋊C4C2×C22⋊D4311yescharacteristic
468C4⋊C4C2×C22⋊D4311yescharacteristic
469C22⋊C4—21no—
470C22⋊C4—41no—
471C22⋊C4—41no—
472C22⋊C4—861no—
473C22⋊C4—1721no—
474C22⋊C4—1721no—
475C22⋊C4—1721no—
476C42—21no—
477C42—21no—
478C42—1721no—
479C42C23×D4311yescharacteristic
480C23—21no—
481C23—861no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—21no—
486Q8—81no—
487Q8—81no—
488Q8—3441no—
489Q8—1721no—
490Q8—1721no—
491D4—21no—
492D4—861no—
493D4—861no—
494D4#1306335712yes—
495C2×C4—21no—
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—161no—
505C2×C4—161no—
506C2×C4—861no—
507C2×C4—1721no—
508C2×C4—1721no—
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—861no—
518C8—861no—
519C8—1721no—
520C8—1721no—
521C8—1721no—
522C8—1721no—
523C8#1306334512yes—
524C22—22no—
525C22—41no—
526C22—41no—
527C22—1721no—
528C22—1721no—
529C22—1721no—
530C22D4×C22⋊D4311yescharacteristic
531C4—21no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—81no—
538C4—81no—
539C4—3441no—
540C4—3441no—
541C4—1721no—
542C4C2×#1306334511yescharacteristic
543C4C2×#1306335711yescharacteristic
544C4#1458371211yescharacteristic
545C4#1458371411yescharacteristic
546C2—42no—
547C2—3441no—
548C2#1914616511yescharacteristic
549C2#1914631311yescharacteristic
550C2#1914635911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3338C2
socleC22×C43D42
prime radicalC2×#10621882D4
hypercenter#3338D43
hypocenterC43#19865
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3338

Complements

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

NH ≅ G/Ntype
3. #19147212C2semidirect
4. #19134273C2semidirect
5. #19134115C2semidirect
6. #19134055C2semidirect
7. #19133997C2semidirect
8. #19133970C2semidirect
9. #19133802C2semidirect
10. #19133766C2semidirect
11. #19133729C2semidirect
12. #19133728C2semidirect
14. #19133414C2semidirect
15. C43×#3338C2semidirect
274. #3338D43semidirect
342. C43#19865semidirect

Maximal subgroups

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

subgroupindex
#191474582
#191472442
#191472122
#191342732
#191341152
#191340552
#191339972
#191339702
#191338022
#191337662
#191337292
#191337282
#191334242
#191334142
C43×#33382
#1986543