Finite Group Databasebeta

← #25067809

Subgroups — #25067809

Order 11008.

598 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144664C211yesmaximal, characteristic
2#19143726C211yesmaximal, characteristic
3#19143695C211yesmaximal, characteristic, complemented
4#19133487C211yesmaximal, characteristic, complemented
5#19133482C211yesmaximal, characteristic, complemented
6#19133473C211yesmaximal, characteristic, complemented
7#19133472C211yesmaximal, characteristic, complemented
8#19133467C211yesmaximal, characteristic, complemented
9#19133466C211yesmaximal, characteristic, complemented
10#19133399C211yesmaximal, characteristic, complemented
11#19133385C211yesmaximal, characteristic, complemented
12#19133048C211yesmaximal, characteristic, complemented
13#19132976C211yesmaximal, characteristic
14#19132877C211yesmaximal, characteristic, complemented
15C8×Q16×C43C211yesmaximal, characteristic, complemented
16#14583453C2211yescharacteristic
17C4×#10621902C2211yescharacteristic
18#14583242C411yescharacteristic
19#14583238C411yescharacteristic
20#14583182C411yescharacteristic
21#14583178C411yescharacteristic
22#14583107C411yescharacteristic
23#14583103C411yescharacteristic
24#14583064C411yescharacteristic
25#14583060C411yescharacteristic
26#14583030C2211yescharacteristic
27#14583029C2211yescharacteristic
28#14583028—21no—
29Q8×C43⋊C8C2211yescharacteristic
30C8×Dic86—21no—
31#14583023C2211yescharacteristic
32C4×#10621885C2211yescharacteristic
33C4×#10621873C2211yescharacteristic
34C4×#10621884C2211yescharacteristic
35#14582978—21no—
36#14582978C2211yescharacteristic
37#14582976—21no—
38#14582976C2211yescharacteristic
39#14582959—21no—
40#14582958—21no—
41#14582951C2211yescharacteristic
42#14582950—21no—
43#14582950C2211yescharacteristic
44#14582950C2211yescharacteristic
45#14582921—21no—
46#14582921C2211yescharacteristic
47C4×C8×D43C2211yescharacteristic
48#14582651C2211yescharacteristic
49#14582650C2211yescharacteristic
50#14582649C2211yescharacteristic
51#14582631C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53Q8⋊(C43⋊C8)C2211yescharacteristic
54#14582629C2211yescharacteristic
55#14582628C2211yescharacteristic
56#14582626C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582621C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C8×Q8×C43C2211yescharacteristic
61C8×Q8×C43C2211yescharacteristic
62C4×Q16×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×Q8⋊C8C2211yescharacteristic
66C82×C43C2211yescharacteristic
67C2×#10621902C2×C411yescharacteristic
68C2×#10621885C2×C411yescharacteristic
69C2×#10621873C2×C411yescharacteristic
70C2×#10621884C2×C411yescharacteristic
71C2×#10621872—21no—
72C2×#10621872—21no—
73C2×#10621872—21no—
74C2×C8×D43—21no—
75#13063324C2×C411yescharacteristic
76#13063323C2×C411yescharacteristic
77#13063315—21no—
78#13063305C2×C411yescharacteristic
79#13063303—21no—
80#13063301C2×C411yescharacteristic
81Q8×Dic43C2×C411yescharacteristic
82C4×Dic86—21no—
83C4×Dic86C2311yescharacteristic
84C4×D172—21no—
85C4×D172C2311yescharacteristic
86#13063287—21no—
87#13063287C2×C411yescharacteristic
88#13063283—21no—
89#13063283C2×C411yescharacteristic
90#13063282—21no—
91C42×D43—21no—
92C42×D43C2311yescharacteristic
93#13063258C2×C411yescharacteristic
94#13063257C2×C411yescharacteristic
95#13063256C2×C411yescharacteristic
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)—21no—
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100Dic43⋊C8—21no—
101Dic43⋊C8—21no—
102Dic43⋊C8—21no—
103Dic43⋊C8C2×C411yescharacteristic
104Dic43⋊C8C2×C411yescharacteristic
105Dic43⋊C8D411yescharacteristic
106Dic43⋊C8D411yescharacteristic
107#13063250C2×C411yescharacteristic
108#13063249C2×C411yescharacteristic
109#13063249C2×C411yescharacteristic
110#13063248C2×C411yescharacteristic
111#13063247C2×C411yescharacteristic
112#13063245C2×C411yescharacteristic
113(C2×D43)⋊C8—21no—
114(C2×D43)⋊C8—21no—
115(C2×D43)⋊C8—21no—
116(C2×D43)⋊C8C2×C411yescharacteristic
117(C2×D43)⋊C8C2×C411yescharacteristic
118(C2×D43)⋊C8D411yescharacteristic
119(C2×D43)⋊C8D411yescharacteristic
120#13063236—21no—
121#13063235—21no—
122C4×C43⋊C8—21no—
123C4×C43⋊C8C2311yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×Q16×C43C2×C411yescharacteristic
130C4×Q8×C43C2311yescharacteristic
131C4×Q8×C43C2311yescharacteristic
132#107×C43C2×C411yescharacteristic
133C4⋊C8×C43—21no—
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#103×C43C2×C411yescharacteristic
138#103×C43C2×C411yescharacteristic
139C4×C8×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C22×C411yescharacteristic
145C2×Q8×C43C22×C411yescharacteristic
146#10621902—22no—
147#10621902—41no—
148C2×D172—21no—
149C2×D172C22×C411yescharacteristic
150C2×C4×D43—21no—
151C2×C4×D43—21no—
152C2×C4×D43—21no—
153C2×C4×D43C22×C411yescharacteristic
154C2×C4×D43C2×D411yescharacteristic
155C2×C4×D43#4111yescharacteristic
156C2×Dic86—21no—
157C2×Dic86C22×C411yescharacteristic
158Q16×C43—22no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43C22×C411yescharacteristic
163C2×C8×C43C22×C411yescharacteristic
164C2×C8×C43C2×D411yescharacteristic
165C2×C8×C43C2×D411yescharacteristic
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43C22×C411yescharacteristic
169C4⋊C4×C43C22×C411yescharacteristic
170C42×C43—21no—
171C42×C43—21no—
172C42×C43C2411yescharacteristic
173#10621885—22no—
174#10621884—41no—
175(C2×D43)⋊C4—21no—
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⋊Dic43C22×C411yescharacteristic
183C4⋊Dic43C22×C411yescharacteristic
184Dic43⋊C4—21no—
185Dic43⋊C4—21no—
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189C4×Dic43—21no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43C22×C411yescharacteristic
193C4×Dic43C2×D411yescharacteristic
194C4×Dic43#4111yescharacteristic
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8C22×C411yescharacteristic
199C2×C43⋊C8C22×C411yescharacteristic
200C2×C43⋊C8C2×D411yescharacteristic
201C2×C43⋊C8C2×D411yescharacteristic
202#10621873—41no—
203#10621872—81no—
204#10621872—81no—
205#10621872—81no—
206C8×D43—24no—
207C22×D43—21no—
208C22×D43C4×D411yescharacteristic
209Q8×C43—21no—
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43#13112yes—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43C23×C411yescharacteristic
218C2×C4×C43C22×D411yescharacteristic
219C2×C4×C43C2×#4111yescharacteristic
220C2×Dic43—21no—
221C2×Dic43—21no—
222C2×Dic43—21no—
223C2×Dic43C4×D411yescharacteristic
224C2×Dic43C4×D411yescharacteristic
225C2×Dic43C4×D411yescharacteristic
226D172—21no—
227D172—21no—
228D172—42no—
229C4×D43—21no—
230C4×D43—21no—
231C4×D43—21no—
232C4×D43—21no—
233C4×D43—22no—
234C4×D43—42no—
235C4×D43—41no—
236C4×D43—41no—
237C4×D43—42no—
238Dic86—21no—
239Dic86—21no—
240Dic86—42no—
241C8×C43—22no—
242C8×C43—21no—
243C8×C43—21no—
244C8×C43—21no—
245C8×C43—21no—
246C8×C43—41no—
247C8×C43—41no—
248C43⋊C8—22no—
249C43⋊C8—21no—
250C43⋊C8—21no—
251C43⋊C8—21no—
252C43⋊C8—21no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255#18019—431nomaximal, Sylow
256C22×C43C2×C4×D411yescharacteristic
257C2×D43—21no—
258C2×D43—21no—
259C2×D43—21no—
260C2×D43—41no—
261C2×D43—41no—
262C2×D43—41no—
263C4×C43—22no—
264C4×C43—21no—
265C4×C43—41no—
266C4×C43—41no—
267C4×C43—41no—
268C4×C43C2×#13111yescharacteristic
269C4×C43#56811yescharacteristic
270C4×C43#57711yescharacteristic
271C4×C43#57811yescharacteristic
272Dic43—21no—
273Dic43—21no—
274Dic43—41no—
275Dic43—41no—
276Dic43—41no—
277Dic43#44312yes—
278#3107—431no—
279#2991—431no—
280#2986—431no—
281#1590—431no—
282#1590—431no—
283#1588—431no—
284#1588—431no—
285#1587—431no—
286#1587—431no—
287C8×Q16—431no—
288C8×Q16D4311yescharacteristic, complemented
289#1574—431no—
290#1493—431no—
291#1476—431no—
292#1450—431no—
293C2×C43#293311yescharacteristic
294C2×C43#294711yescharacteristic
295C2×C43C2×#44311yescharacteristic
296D43—41no—
297D43—81no—
298#533—431no—
299C4×#41—431no—
300#485—431no—
301#485—431no—
302#475—431no—
303#474—431no—
304#462—431no—
305#461—431no—
306#452—431no—
307#452—431no—
308#446—431no—
309#446—431no—
310#446—861no—
311C8×Q8—431no—
312C8×Q8—431no—
313C8×Q8—861no—
314C8×Q8C2×D4311yescharacteristic
315C8×Q8C2×D4311yescharacteristic
316C4×Q16—431no—
317C4×Q16C2×D4311yescharacteristic
318C4×SD16—431no—
319C4×SD16—431no—
320#436—431no—
321#436—431no—
322#436—861no—
323#436—861no—
324#433—861no—
325#433—861no—
326#431—431no—
327#431—431no—
328#431—431no—
329#431—861no—
330#423—431no—
331#423—861no—
332C2×C4×C8—431no—
333#335—431no—
334#335C2×D4311yescharacteristic
335#334—431no—
336#334—431no—
337Q8⋊C8—431no—
338Q8⋊C8—431no—
339Q8⋊C8—431no—
340Q8⋊C8—431no—
341Q8⋊C8C2×D4311yescharacteristic
342Q8⋊C8C2×D4311yescharacteristic
343D4⋊C8—431no—
344D4⋊C8—431no—
345#322—431no—
346#322—431no—
347C82—431no—
348C82C2×D4311yescharacteristic
349C43#1801911yescharacteristic, complemented, Sylow
350C2×#41—431no—
351C2×Q16—431no—
352C2×Q16C4×D4311yescharacteristic
353C2×SD16—431no—
354C2×SD16—431no—
355C2×M16—861no—
356C2×M16—861no—
357C2×M16—861no—
358C22×C8—861no—
359C4⋊Q8—431no—
360C4⋊Q8—431no—
361#125—861no—
362C22⋊Q8—431no—
363C22⋊Q8—431no—
364C22⋊Q8—861no—
365C4×Q8—431no—
366C4×Q8—431no—
367C4×Q8—861no—
368C4×Q8C22×D4311yescharacteristic
369C4×Q8C22×D4311yescharacteristic
370C4×D4—431no—
371C4×D4—431no—
372C4×D4—861no—
373C4×D4—861no—
374#117—431no—
375#117—861no—
376#117—861no—
377C2×C42—431no—
378C2×C42—861no—
379#107—431no—
380#107C4×D4311yescharacteristic
381#106—431no—
382#106—431no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—431no—
386C4⋊C8—431no—
387C4⋊C8—431no—
388C4⋊C8—431no—
389C4⋊C8—431no—
390C4⋊C8—431no—
391C4⋊C8—861no—
392C4⋊C8—861no—
393C4⋊C8—861no—
394C4⋊C8—861no—
395C4⋊C8—861no—
396C4⋊C8C22×D4311yescharacteristic
397C4⋊C8C22×D4311yescharacteristic
398#103—431no—
399#103—431no—
400#103—431no—
401#103—431no—
402#103C4×D4311yescharacteristic
403#103C4×D4311yescharacteristic
404#102—431no—
405#102—431no—
406C22⋊C8—431no—
407C22⋊C8—431no—
408C22⋊C8—431no—
409C22⋊C8—431no—
410C22⋊C8—861no—
411C22⋊C8—861no—
412C22⋊C8—861no—
413#97—861no—
414#97—861no—
415C4×C8—21no—
416C4×C8—21no—
417C4×C8—431no—
418C4×C8—431no—
419C4×C8—431no—
420C4×C8—861no—
421C4×C8—861no—
422C4×C8—861no—
423C4×C8—861no—
424C4×C8C22×D4311yescharacteristic
425C4×C8C22×D4311yescharacteristic
426C4×C8C22×D4311yescharacteristic
427#41—862no—
428#41—1721no—
429C2×Q8—431no—
430C2×Q8—861no—
431C2×Q8C2×C4×D4311yescharacteristic
432C2×Q8C2×C4×D4311yescharacteristic
433C2×D4—431no—
434C2×D4—861no—
435C22×C4—431no—
436C22×C4—431no—
437C22×C4—431no—
438C22×C4—861no—
439C22×C4—861no—
440C22×C4—861no—
441Q16—22no—
442Q16—862no—
443SD16—1721no—
444SD16—1721no—
445M16—3441no—
446M16—3441no—
447M16—3441no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—431no—
452C2×C8—431no—
453C2×C8—431no—
454C2×C8—431no—
455C2×C8—864no—
456C2×C8—861no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8C2×C4×D4311yescharacteristic
460C2×C8C2×C4×D4311yescharacteristic
461C2×C8D4×D4311yescharacteristic
462C2×C8D4×D4311yescharacteristic
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—431no—
466C4⋊C4—431no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4C2×C4×D4311yescharacteristic
475C4⋊C4C2×C4×D4311yescharacteristic
476C22⋊C4—861no—
477C22⋊C4—861no—
478C22⋊C4—861no—
479C22⋊C4—861no—
480C22⋊C4—861no—
481C42—21no—
482C42—21no—
483C42—431no—
484C42—431no—
485C42—431no—
486C42—861no—
487C42—861no—
488C42—861no—
489C42C23×D4311yescharacteristic
490C23—431no—
491C23—861no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—861no—
496Q8—861no—
497Q8—1722no—
498Q8#1306333112yes—
499D4—861no—
500D4—861no—
501D4—1722no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—431no—
507C2×C4—431no—
508C2×C4—431no—
509C2×C4—862no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—861no—
516C2×C4—861no—
517C2×C4—1722no—
518C2×C4—1722no—
519C2×C4—1721no—
520C2×C4—1721no—
521C2×C4C22×C4×D4311yescharacteristic
522C2×C4C2×D4×D4311yescharacteristic
523C2×C4#41×D4311yescharacteristic
524C8—22no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—862no—
532C8—861no—
533C8—861no—
534C8—861no—
535C8—861no—
536C8—1721no—
537C8—1721no—
538C22—861no—
539C22—861no—
540C22—861no—
541C22—1721no—
542C22—1721no—
543C22—1721no—
544C22C4×D4×D4311yescharacteristic
545C4—21no—
546C4—22no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—432no—
551C4—861no—
552C4—861no—
553C4—1721no—
554C4—1721no—
555C4—1721no—
556C4C2×#1306333111yescharacteristic
557C4#1458366411yescharacteristic
558C4#1458370611yescharacteristic
559C4#1458371211yescharacteristic
560C2—3441no—
561C2—1721no—
562C2#1914331511yescharacteristic
563C2#1914343311yescharacteristic
564C2#443×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC8×Q16×C43C2
socleC22×C43C2×C4×D4
prime radicalC2×#10621902C2×C4
cosocleC42×C43C24
hypercenterC8×Q16D43
hypocenterC43#18019
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×Q16

Complements

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

NH ≅ G/Ntype
3. #19143695C2semidirect
4. #19133487C2semidirect
5. #19133482C2semidirect
6. #19133473C2semidirect
7. #19133472C2semidirect
8. #19133467C2semidirect
9. #19133466C2semidirect
10. #19133399C2semidirect
11. #19133385C2semidirect
12. #19133048C2semidirect
14. #19132877C2semidirect
15. C8×Q16×C43C2semidirect
288. C8×Q16D43semidirect
349. C43#18019semidirect

Maximal subgroups

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

subgroupindex
#191446642
#191437262
#191436952
#191334872
#191334822
#191334732
#191334722
#191334672
#191334662
#191333992
#191333852
#191330482
#191329762
#191328772
C8×Q16×C432
#1801943