Finite Group Databasebeta

← #25067991

Subgroups — #25067991

Order 11008.

566 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
1#19144634C211yesmaximal, characteristic
2#19143696C211yesmaximal, characteristic
3#19133502C211yesmaximal, characteristic, complemented
4#19133490C211yesmaximal, characteristic, complemented
5#19133466C211yesmaximal, characteristic, complemented
6#19133464C211yesmaximal, characteristic, complemented
7#19133445C211yesmaximal, characteristic, complemented
8#19133443C211yesmaximal, characteristic, complemented
9#19133412C211yesmaximal, characteristic, complemented
10C8×#10621885C211yesmaximal, characteristic, complemented
11#19133376C211yesmaximal, characteristic
12#19133067C211yesmaximal, characteristic
13#19132990C211yesmaximal, characteristic
14#19132895C211yesmaximal, characteristic
15C43×#2984C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17#14583234C411yescharacteristic
18#14583234C411yescharacteristic
19#14583194C411yescharacteristic
20#14583194C411yescharacteristic
21#14583109C411yescharacteristic
22#14583109C411yescharacteristic
23#14583055C411yescharacteristic
24#14583055C411yescharacteristic
25#14583029C2211yescharacteristic
26#14583029C2211yescharacteristic
27#14583026—21no—
28C8×Dic86C2211yescharacteristic
29C8×Dic86C2211yescharacteristic
30#14583023—21no—
31C4×#10621885C2211yescharacteristic
32C4×#10621885C2211yescharacteristic
33C4×#10621885C2211yescharacteristic
34C4×#10621885C2211yescharacteristic
35#14582957—21no—
36#14582957—21no—
37#14582952C2211yescharacteristic
38#14582952C2211yescharacteristic
39#14582952C2211yescharacteristic
40#14582651C2211yescharacteristic
41#14582651C2211yescharacteristic
42#14582649C2211yescharacteristic
43#14582649C2211yescharacteristic
44Q8⋊(C43⋊C8)C2211yescharacteristic
45Q8⋊(C43⋊C8)C2211yescharacteristic
46Q8⋊(C43⋊C8)C2211yescharacteristic
47Q8⋊(C43⋊C8)C2211yescharacteristic
48#14582629C2211yescharacteristic
49#14582629C2211yescharacteristic
50#14582629C2211yescharacteristic
51#14582629C2211yescharacteristic
52#14582621C2211yescharacteristic
53#14582621C2211yescharacteristic
54#14582620C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic
56C2×C4×Q8×C43C2211yescharacteristic
57C43×#446—21no—
58C43×#446—21no—
59C43×#446C2211yescharacteristic
60C43×#446C2211yescharacteristic
61C8×Q8×C43C2211yescharacteristic
62C8×Q8×C43C2211yescharacteristic
63C43×#432—21no—
64C43×#432C2211yescharacteristic
65C43×#431—21no—
66C43×#431C2211yescharacteristic
67C2×#10621885C2×C411yescharacteristic
68C2×#10621885C2×C411yescharacteristic
69C2×#10621885C2×C411yescharacteristic
70C2×#10621885C2×C411yescharacteristic
71#13063325C2×C411yescharacteristic
72#13063325C2×C411yescharacteristic
73#13063317—21no—
74#13063304—21no—
75#13063304C2×C411yescharacteristic
76#13063304C2×C411yescharacteristic
77C4×Dic86—21no—
78C4×Dic86C2311yescharacteristic
79C4×Dic86C2311yescharacteristic
80#13063284—21no—
81#13063258C2×C411yescharacteristic
82#13063258C2×C411yescharacteristic
83#13063258C2×C411yescharacteristic
84#13063258C2×C411yescharacteristic
85C4⋊(C43⋊C8)—21no—
86C4⋊(C43⋊C8)C2×C411yescharacteristic
87C4⋊(C43⋊C8)C2×C411yescharacteristic
88C4⋊(C43⋊C8)C2311yescharacteristic
89C4⋊(C43⋊C8)C2311yescharacteristic
90Dic43⋊C8—21no—
91Dic43⋊C8—21no—
92Dic43⋊C8—21no—
93Dic43⋊C8—21no—
94#13063249C2×C411yescharacteristic
95#13063249C2×C411yescharacteristic
96#13063249C2×C411yescharacteristic
97#13063249C2×C411yescharacteristic
98#13063248C2×C411yescharacteristic
99#13063248C2×C411yescharacteristic
100#13063248C2×C411yescharacteristic
101#13063248C2×C411yescharacteristic
102C22⋊(C43⋊C8)—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)C2×C411yescharacteristic
105C22⋊(C43⋊C8)C2×C411yescharacteristic
106#13063235—21no—
107#13063235—21no—
108C4×C43⋊C8—21no—
109C4×C43⋊C8C2311yescharacteristic
110C4×C43⋊C8C2311yescharacteristic
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C8×Dic43—21no—
114C8×Dic43—21no—
115C22×Q8×C43C2×C411yescharacteristic
116C4×Q8×C43—21no—
117C4×Q8×C43—21no—
118C4×Q8×C43C2×C411yescharacteristic
119C4×Q8×C43C2×C411yescharacteristic
120C4×Q8×C43C2311yescharacteristic
121C4×Q8×C43C2311yescharacteristic
122C2×C4⋊C4×C43—21no—
123C2×C4⋊C4×C43C2×C411yescharacteristic
124C2×C42×C43—21no—
125C2×C42×C43C2311yescharacteristic
126C4⋊C8×C43—21no—
127C4⋊C8×C43—21no—
128C4⋊C8×C43—21no—
129C4⋊C8×C43—21no—
130C4⋊C8×C43D411yescharacteristic
131C4⋊C8×C43D411yescharacteristic
132C4⋊C8×C43C2311yescharacteristic
133C4⋊C8×C43C2311yescharacteristic
134C22⋊C8×C43—21no—
135C22⋊C8×C43D411yescharacteristic
136C22⋊C8×C43D411yescharacteristic
137#97×C43—21no—
138#97×C43—21no—
139#97×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—22no—
146C2×Q8×C43—41no—
147C2×Q8×C43C22×C411yescharacteristic
148C2×Q8×C43C22×C411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43C22×C411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43#4111yescharacteristic
154C2×Dic86—21no—
155C2×Dic86C22×C411yescharacteristic
156C2×Dic86C22×C411yescharacteristic
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43C2×D411yescharacteristic
160C2×C8×C43C2×D411yescharacteristic
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×C43C22×C411yescharacteristic
169C4⋊C4×C43C22×C411yescharacteristic
170C42×C43—21no—
171C42×C43—21no—
172C42×C43—21no—
173C42×C43—21no—
174C42×C43C22×C411yescharacteristic
175C42×C43C2×D411yescharacteristic
176C42×C43#4111yescharacteristic
177C42×C43C2411yescharacteristic
178C22⋊Dic43—21no—
179C22⋊Dic43—21no—
180#10621885—22no—
181#10621885—22no—
182#10621885—41no—
183#10621885—41no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43C22×C411yescharacteristic
188C4⋊Dic43C22×C411yescharacteristic
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8C22×C411yescharacteristic
200C2×C43⋊C8C22×C411yescharacteristic
201C2×C43⋊C8C22×C411yescharacteristic
202C2×C43⋊C8C22×C411yescharacteristic
203C23×C43C4×D411yescharacteristic
204Q8×C43—21no—
205Q8×C43—21no—
206Q8×C43—21no—
207Q8×C43—42no—
208Q8×C43#13112yes—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—41no—
218C2×C4×C43—42no—
219C2×C4×C43—42no—
220C2×C4×C43C4×D411yescharacteristic
221C2×C4×C43C4×D411yescharacteristic
222C2×C4×C43C4×D411yescharacteristic
223C2×C4×C43C23×C411yescharacteristic
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230Dic86—21no—
231Dic86—21no—
232Dic86—21no—
233Dic86—21no—
234Dic86—42no—
235C8×C43—21no—
236C8×C43—21no—
237C8×C43—21no—
238C8×C43—21no—
239C8×C43—41no—
240C8×C43—41no—
241C43⋊C8—21no—
242C43⋊C8—21no—
243C43⋊C8—21no—
244C43⋊C8—21no—
245C43⋊C8—41no—
246C43⋊C8—41no—
247C43⋊C8—41no—
248C43⋊C8—41no—
249#18032—431nomaximal, Sylow
250C22×C43—21no—
251C22×C43—21no—
252C22×C43—21no—
253C22×C43C2×C4×D411yescharacteristic
254C4×C43—21no—
255C4×C43—22no—
256C4×C43—21no—
257C4×C43—21no—
258C4×C43—21no—
259C4×C43—41no—
260C4×C43—41no—
261C4×C43—41no—
262C4×C43C2×#13111yescharacteristic
263C4×C43#56811yescharacteristic
264C4×C43#57811yescharacteristic
265C4×C43#57811yescharacteristic
266Dic43—41no—
267Dic43—41no—
268Dic43—41no—
269Dic43—41no—
270#3104—431no—
271#2986—431no—
272#2984D4311yescharacteristic
273#1593—431no—
274#1591—431no—
275#1587—431no—
276#1587—431no—
277#1584—431no—
278#1584—431no—
279#1579—431no—
280C8×Q16—431no—
281#1572—431no—
282#1497—431no—
283#1479—431no—
284#1454—431no—
285C2×C43—41no—
286C2×C43#293311yescharacteristic
287C2×C43#295011yescharacteristic
288C2×C43#295511yescharacteristic
289#533—431no—
290C2×C4×Q8C2×D4311yescharacteristic
291#484—431no—
292#484—431no—
293#477—431no—
294#477—431no—
295#462—431no—
296#462—431no—
297#451—431no—
298#451—431no—
299#446—21no—
300#446—21no—
301#446—431no—
302#446—431no—
303#446—861no—
304#446C2×D4311yescharacteristic
305#446C2×D4311yescharacteristic
306C8×Q8—431no—
307C8×Q8—431no—
308C8×Q8—861no—
309C8×Q8C2×D4311yescharacteristic
310C8×Q8C2×D4311yescharacteristic
311C4×Q16—431no—
312C4×Q16—431no—
313C4×Q16—431no—
314C4×Q16—431no—
315#433—861no—
316#433—861no—
317#432—21no—
318#432C2×D4311yescharacteristic
319#431—21no—
320#431—431no—
321#431—431no—
322#431—431no—
323#431C2×D4311yescharacteristic
324#335—431no—
325#335—431no—
326#334—431no—
327#334—431no—
328Q8⋊C8—431no—
329Q8⋊C8—431no—
330Q8⋊C8—431no—
331Q8⋊C8—431no—
332Q8⋊C8—431no—
333Q8⋊C8—431no—
334Q8⋊C8—431no—
335Q8⋊C8—431no—
336#322—431no—
337#322—431no—
338#322—431no—
339C82—431no—
340C43#1803211yescharacteristic, complemented, Sylow
341C22×Q8C4×D4311yescharacteristic
342C2×Q16—431no—
343C2×Q16—431no—
344C2×Q16—431no—
345C2×Q16—431no—
346C4⋊Q8—431no—
347C4⋊Q8—431no—
348#125—861no—
349C22⋊Q8—431no—
350C22⋊Q8—431no—
351C22⋊Q8—861no—
352C4×Q8—21no—
353C4×Q8—21no—
354C4×Q8—431no—
355C4×Q8—431no—
356C4×Q8—861no—
357C4×Q8C4×D4311yescharacteristic
358C4×Q8C4×D4311yescharacteristic
359C4×Q8C22×D4311yescharacteristic
360C4×Q8C22×D4311yescharacteristic
361#117—861no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4C4×D4311yescharacteristic
364C2×C42—21no—
365C2×C42C22×D4311yescharacteristic
366#107—431no—
367#107—431no—
368#107—431no—
369#107—431no—
370C4⋊C8—21no—
371C4⋊C8—21no—
372C4⋊C8—21no—
373C4⋊C8—21no—
374C4⋊C8—431no—
375C4⋊C8—431no—
376C4⋊C8—431no—
377C4⋊C8—431no—
378C4⋊C8—861no—
379C4⋊C8—861no—
380C4⋊C8—861no—
381C4⋊C8—861no—
382C4⋊C8—861no—
383C4⋊C8C22⋊D4311yescharacteristic
384C4⋊C8C22⋊D4311yescharacteristic
385C4⋊C8C22×D4311yescharacteristic
386C4⋊C8C22×D4311yescharacteristic
387#103—431no—
388#103—431no—
389#103—431no—
390#103—431no—
391#103—431no—
392#103—431no—
393#103—431no—
394#103—431no—
395C22⋊C8—21no—
396C22⋊C8—431no—
397C22⋊C8—431no—
398C22⋊C8—861no—
399C22⋊C8—861no—
400C22⋊C8C22⋊D4311yescharacteristic
401C22⋊C8C22⋊D4311yescharacteristic
402#97—21no—
403#97—21no—
404#97—21no—
405#97—861no—
406#97—861no—
407C4×C8—21no—
408C4×C8—21no—
409C4×C8—431no—
410C4×C8—431no—
411C4×C8—431no—
412C4×C8—431no—
413C4×C8—861no—
414C4×C8—861no—
415C4×C8—861no—
416C4×C8C22×D4311yescharacteristic
417C4×C8C22×D4311yescharacteristic
418C2×Q8—21no—
419C2×Q8—22no—
420C2×Q8—41no—
421C2×Q8—431no—
422C2×Q8—431no—
423C2×Q8—861no—
424C2×Q8C2×C4×D4311yescharacteristic
425C2×Q8C2×C4×D4311yescharacteristic
426C22×C4—21no—
427C22×C4—21no—
428C22×C4C2×C4×D4311yescharacteristic
429C22×C4#1062189811yescharacteristic
430C22×C4C2×C22⋊D4311yescharacteristic
431Q16—862no—
432Q16—862no—
433Q16—1721no—
434Q16—1721no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—431no—
438C2×C8—431no—
439C2×C8—431no—
440C2×C8—431no—
441C2×C8—861no—
442C2×C8—861no—
443C2×C8—861no—
444C2×C8—861no—
445C2×C8C2×C22⋊D4311yescharacteristic
446C2×C8C2×C22⋊D4311yescharacteristic
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—431no—
455C4⋊C4—431no—
456C4⋊C4—861no—
457C4⋊C4—861no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4C2×C4×D4311yescharacteristic
464C4⋊C4C2×C4×D4311yescharacteristic
465C22⋊C4—861no—
466C22⋊C4—861no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—21no—
471C42—861no—
472C42—861no—
473C42C2×C4×D4311yescharacteristic
474C42#1062189811yescharacteristic
475C42C2×C22⋊D4311yescharacteristic
476C42C23×D4311yescharacteristic
477C23C4×C22⋊D4311yescharacteristic
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—42no—
482Q8—861no—
483Q8—861no—
484Q8—861no—
485Q8—861no—
486Q8—1722no—
487Q8#1306333312yes—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—861no—
500C2×C4—861no—
501C2×C4—861no—
502C2×C4—861no—
503C2×C4C4×C22⋊D4311yescharacteristic
504C2×C4C4×C22⋊D4311yescharacteristic
505C2×C4C4×C22⋊D4311yescharacteristic
506C2×C4C22×C4×D4311yescharacteristic
507C2×C4C22×C22⋊D4311yescharacteristic
508C2×C4C2×#1062189811yescharacteristic
509C8—21no—
510C8—21no—
511C8—21no—
512C8—21no—
513C8—41no—
514C8—41no—
515C8—861no—
516C8—861no—
517C8—861no—
518C8—861no—
519C8—1721no—
520C8—1721no—
521C8—1721no—
522C8—1721no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22C2×C4×C22⋊D4311yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—22no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—1721no—
536C4—1721no—
537C4—1721no—
538C4—1721no—
539C4C2×#1306333311yescharacteristic
540C4#1458366511yescharacteristic
541C4#1458371411yescharacteristic
542C4#1458371411yescharacteristic
543C2—41no—
544C2#1914332011yescharacteristic
545C2#1914346111yescharacteristic
546C2#1914349611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#2984C2
socleC22×C43C2×C4×D4
prime radicalC23×C43C4×D4
cosocleC42×C43C24
hypercenter#2984D43
hypocenterC43#18032
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2984

Complements

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

NH ≅ G/Ntype
3. #19133502C2semidirect
4. #19133490C2semidirect
5. #19133466C2semidirect
6. #19133464C2semidirect
7. #19133445C2semidirect
8. #19133443C2semidirect
9. #19133412C2semidirect
10. C8×#10621885C2semidirect
340. C43#18032semidirect

Maximal subgroups

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

subgroupindex
#191446342
#191436962
#191335022
#191334902
#191334662
#191334642
#191334452
#191334432
#191334122
C8×#106218852
#191333762
#191330672
#191329902
#191328952
C43×#29842
#1803243