Finite Group Databasebeta

← #25067786

Subgroups — #25067786

Order 11008.

600 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#19144671C211yesmaximal, characteristic
2#19143682C211yesmaximal, characteristic, complemented
3#19133490C211yesmaximal, characteristic, complemented
4#19133483C211yesmaximal, characteristic, complemented
5#19133471C211yesmaximal, characteristic, complemented
6#19133466C211yesmaximal, characteristic, complemented
7#19133464C211yesmaximal, characteristic, complemented
8#19133452C211yesmaximal, characteristic, complemented
9C8×#10621885C211yesmaximal, characteristic, complemented
10C8×#10621883C211yesmaximal, characteristic, complemented
11#19133378C211yesmaximal, characteristic, complemented
12#19133055C211yesmaximal, characteristic
13C2×#14582629C211yesmaximal, characteristic, complemented
14#19132879C211yesmaximal, characteristic, complemented
15C43×#2994C211yesmaximal, characteristic
16C2×C4×Dic86C2211yescharacteristic
17#14583227C411yescharacteristic
18#14583210C411yescharacteristic
19#14583203C411yescharacteristic
20#14583203C411yescharacteristic
21#14583118C411yescharacteristic
22#14583118C411yescharacteristic
23#14583054C411yescharacteristic
24#14583037C411yescharacteristic
25#14583029C2211yescharacteristic
26#14583029C2211yescharacteristic
27#14583028—21no—
28#14583028—21no—
29C8×Dic86C2211yescharacteristic
30C8×Dic86C2211yescharacteristic
31C4×#10621885C2211yescharacteristic
32C4×#10621885C2211yescharacteristic
33C4×#10621883C2211yescharacteristic
34C4×#10621883C2211yescharacteristic
35#14582956C2211yescharacteristic
36#14582953—21no—
37#14582952C2211yescharacteristic
38#14582949—21no—
39C2×C4×C43⋊C8C2211yescharacteristic
40#14582651C2211yescharacteristic
41#14582651C2211yescharacteristic
42#14582649C2211yescharacteristic
43#14582649C2211yescharacteristic
44Q8⋊(C43⋊C8)C2211yescharacteristic
45Q8⋊(C43⋊C8)C2211yescharacteristic
46#14582629C2211yescharacteristic
47#14582629C2211yescharacteristic
48#14582629C2211yescharacteristic
49#14582629C2211yescharacteristic
50D4⋊(C43⋊C8)C2211yescharacteristic
51D4⋊(C43⋊C8)C2211yescharacteristic
52#14582621C2211yescharacteristic
53#14582621C2211yescharacteristic
54C8×C43⋊C8C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic
56C43×#529C2211yescharacteristic
57C43×#446C2211yescharacteristic
58C8×Q8×C43C2211yescharacteristic
59C43×#436C2211yescharacteristic
60C43×#435—21no—
61C8×D4×C43—21no—
62C8×D4×C43C2211yescharacteristic
63C43×#433—21no—
64C43×#431C2211yescharacteristic
65C43×#424—21no—
66C2×C4⋊C8×C43C2211yescharacteristic
67C22×Dic86C2×C411yescharacteristic
68C2×#10621885C2×C411yescharacteristic
69C2×#10621885C2×C411yescharacteristic
70C2×#10621883C2×C411yescharacteristic
71C2×#10621883C2×C411yescharacteristic
72C22×C43⋊C8—21no—
73C4×Dic86—21no—
74C4×Dic86—21no—
75C4×Dic86C2×C411yescharacteristic
76C4×Dic86C2×C411yescharacteristic
77C4×Dic86C2311yescharacteristic
78C4×Dic86C2311yescharacteristic
79C2×C4⋊Dic43C2×C411yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×C4×Dic43—21no—
82#13063258C2×C411yescharacteristic
83#13063258C2×C411yescharacteristic
84#13063256C2×C411yescharacteristic
85#13063256C2×C411yescharacteristic
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#13063248C2×C411yescharacteristic
97#13063248C2×C411yescharacteristic
98#13063248C2×C411yescharacteristic
99#13063248C2×C411yescharacteristic
100#13063246C2×C411yescharacteristic
101#13063246C2×C411yescharacteristic
102C22⋊(C43⋊C8)—21no—
103C22⋊(C43⋊C8)C2×C411yescharacteristic
104C22⋊(C43⋊C8)C2×C411yescharacteristic
105#13063236—21no—
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—
115C2×M16×C43—21no—
116C22×C8×C43—21no—
117C22×C8×C43—21no—
118#126×C43—21no—
119#125×C43C2×C411yescharacteristic
120#124×C43C2×C411yescharacteristic
121#123×C43—21no—
122C22⋊Q8×C43C2×C411yescharacteristic
123#121×C43C2×C411yescharacteristic
124C4×Q8×C43C2311yescharacteristic
125C4×D4×C43—21no—
126C4×D4×C43C2311yescharacteristic
127#117×C43—21no—
128C2×C42×C43C2311yescharacteristic
129C4⋊C8×C43—21no—
130C4⋊C8×C43—21no—
131C4⋊C8×C43—21no—
132C4⋊C8×C43D411yescharacteristic
133C4⋊C8×C43D411yescharacteristic
134C4⋊C8×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138C22⋊C8×C43D411yescharacteristic
139C22⋊C8×C43D411yescharacteristic
140#97×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C22×C411yescharacteristic
145C2×D4×C43—21no—
146C2×D4×C43C22×C411yescharacteristic
147C22×C4×C43—21no—
148C22×C4×C43C22×C411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43#4111yescharacteristic
151C22×Dic43—21no—
152C22×Dic43—21no—
153C2×Dic86—22no—
154C2×Dic86—21no—
155C2×Dic86—41no—
156C2×Dic86C22×C411yescharacteristic
157C2×Dic86C22×C411yescharacteristic
158M16×C43—81no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—81no—
162C2×C8×C43—81no—
163C2×C8×C43C2×D411yescharacteristic
164C2×C8×C43C2×D411yescharacteristic
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×C43C22×C411yescharacteristic
172C4⋊C4×C43C22×C411yescharacteristic
173C22⋊C4×C43—21no—
174C22⋊C4×C43—21no—
175C22⋊C4×C43—21no—
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C42×C43—21no—
179C42×C43C22×C411yescharacteristic
180C42×C43C2×D411yescharacteristic
181C42×C43#4111yescharacteristic
182C42×C43C2411yescharacteristic
183#10621885—22no—
184#10621885—41no—
185#10621883—22no—
186#10621883—41no—
187C4⋊Dic43—21no—
188C4⋊Dic43C22×C411yescharacteristic
189C4⋊Dic43C22×C411yescharacteristic
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C2×C43⋊C8—24no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8C22×C411yescharacteristic
204C2×C43⋊C8C22×C411yescharacteristic
205C2×C43⋊C8C22×C411yescharacteristic
206C2×C43⋊C8C22×C411yescharacteristic
207C23×C43—21no—
208C23×C43C4×D411yescharacteristic
209Q8×C43—21no—
210Q8×C43—21no—
211D4×C43—21no—
212D4×C43—21no—
213D4×C43—42no—
214C2×C4×C43—22no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43C4×D411yescharacteristic
225C2×C4×C43C4×D411yescharacteristic
226C2×C4×C43C4×D411yescharacteristic
227C2×C4×C43C23×C411yescharacteristic
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—42no—
235C2×Dic43—42no—
236Dic86—21no—
237Dic86—21no—
238Dic86—21no—
239Dic86—42no—
240Dic86#13112yes—
241C8×C43—21no—
242C8×C43—21no—
243C8×C43—21no—
244C8×C43—21no—
245C8×C43—41no—
246C8×C43—41no—
247C43⋊C8—22no—
248C43⋊C8—22no—
249C43⋊C8—21no—
250C43⋊C8—21no—
251C43⋊C8—21no—
252C43⋊C8—21no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255#18017—431nomaximal, Sylow
256C22×C43—21no—
257C22×C43—21no—
258C22×C43—41no—
259C22×C43—41no—
260C22×C43—41no—
261C22×C43#44312yes—
262C22×C43C2×C4×D411yescharacteristic
263C4×C43—21no—
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—21no—
267C4×C43—41no—
268C4×C43—41no—
269C4×C43—41no—
270C4×C43C2×#13111yescharacteristic
271C4×C43#56811yescharacteristic
272C4×C43#57711yescharacteristic
273C4×C43#57811yescharacteristic
274Dic43—22no—
275Dic43—41no—
276Dic43—41no—
277Dic43—41no—
278#3108—431no—
279#2994D4311yescharacteristic
280#2984—431no—
281#1591—431no—
282#1590—431no—
283#1588—431no—
284#1587—431no—
285#1587—431no—
286#1585—431no—
287C8×Q16—431no—
288C8×SD16—431no—
289#1573—431no—
290#1494—431no—
291C2×Q8⋊C8—431no—
292#1450—431no—
293C2×C43—22no—
294C2×C43—81no—
295C2×C43#293311yescharacteristic
296C2×C43#294711yescharacteristic
297C2×C43C2×#44311yescharacteristic
298#529C2×D4311yescharacteristic
299C2×C4×Q8—431no—
300#483—431no—
301#480—431no—
302#479—431no—
303#479—431no—
304#464—431no—
305#464—431no—
306#451—431no—
307#448—431no—
308#446—431no—
309#446—431no—
310#446—861no—
311#446—861no—
312#446C2×D4311yescharacteristic
313C8×Q8—431no—
314C8×Q8—431no—
315C8×Q8C2×D4311yescharacteristic
316C4×Q16—431no—
317C4×Q16—431no—
318C4×SD16—431no—
319C4×SD16—431no—
320#436C2×D4311yescharacteristic
321#435—21no—
322C8×D4—21no—
323C8×D4C2×D4311yescharacteristic
324#433—21no—
325#432—431no—
326#432—861no—
327#431—431no—
328#431—861no—
329#431C2×D4311yescharacteristic
330#424—21no—
331C2×C4⋊C8C2×D4311yescharacteristic
332C2×C4×C8—431no—
333#335—431no—
334#335—431no—
335#334—431no—
336#334—431no—
337Q8⋊C8—431no—
338Q8⋊C8—431no—
339Q8⋊C8—431no—
340Q8⋊C8—431no—
341Q8⋊C8—431no—
342Q8⋊C8—431no—
343D4⋊C8—431no—
344D4⋊C8—431no—
345#322—431no—
346#322—431no—
347C82—431no—
348C82—431no—
349C43#1801711yescharacteristic, complemented, Sylow
350C22×Q8—431no—
351C2×Q16—431no—
352C2×Q16—431no—
353C2×SD16—431no—
354C2×SD16—431no—
355C2×M16—21no—
356C22×C8—21no—
357C22×C8—21no—
358C22×C8—861no—
359#126—21no—
360#125C4×D4311yescharacteristic
361#124C4×D4311yescharacteristic
362#123—21no—
363C22⋊Q8C4×D4311yescharacteristic
364#121C4×D4311yescharacteristic
365C4×Q8—431no—
366C4×Q8—431no—
367C4×Q8—431no—
368C4×Q8—431no—
369C4×Q8—861no—
370C4×Q8—861no—
371C4×Q8C22×D4311yescharacteristic
372C4×D4—21no—
373C4×D4C22×D4311yescharacteristic
374#117—21no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—861no—
377C2×C42—861no—
378C2×C42C22×D4311yescharacteristic
379#107—431no—
380#107—431no—
381#106—431no—
382#106—431no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—431no—
387C4⋊C8—431no—
388C4⋊C8—431no—
389C4⋊C8—431no—
390C4⋊C8—861no—
391C4⋊C8—861no—
392C4⋊C8—861no—
393C4⋊C8—861no—
394C4⋊C8C22⋊D4311yescharacteristic
395C4⋊C8C22⋊D4311yescharacteristic
396C4⋊C8C22×D4311yescharacteristic
397C4⋊C8C22×D4311yescharacteristic
398#103—431no—
399#103—431no—
400#103—431no—
401#103—431no—
402#103—431no—
403#103—431no—
404#102—431no—
405#102—431no—
406C22⋊C8—21no—
407C22⋊C8—21no—
408C22⋊C8—431no—
409C22⋊C8—431no—
410C22⋊C8—861no—
411C22⋊C8C22⋊D4311yescharacteristic
412C22⋊C8C22⋊D4311yescharacteristic
413#97—21no—
414#97—861no—
415#97—861no—
416#97—861no—
417C4×C8—21no—
418C4×C8—431no—
419C4×C8—431no—
420C4×C8—431no—
421C4×C8—431no—
422C4×C8—861no—
423C4×C8—861no—
424C4×C8—861no—
425C4×C8C22×D4311yescharacteristic
426C4×C8C22×D4311yescharacteristic
427C2×Q8—431no—
428C2×Q8—431no—
429C2×Q8—862no—
430C2×Q8—861no—
431C2×Q8—1721no—
432C2×Q8C2×C4×D4311yescharacteristic
433C2×D4—21no—
434C2×D4C2×C4×D4311yescharacteristic
435C22×C4—21no—
436C22×C4—861no—
437C22×C4—861no—
438C22×C4C2×C4×D4311yescharacteristic
439C22×C4#1062189811yescharacteristic
440C22×C4C2×C22⋊D4311yescharacteristic
441Q16—862no—
442Q16—1721no—
443SD16—862no—
444SD16—1721no—
445M16—81no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—81no—
449C2×C8—81no—
450C2×C8—431no—
451C2×C8—431no—
452C2×C8—431no—
453C2×C8—431no—
454C2×C8—864no—
455C2×C8—861no—
456C2×C8—861no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8C2×C22⋊D4311yescharacteristic
460C2×C8C2×C22⋊D4311yescharacteristic
461C2×C8C2×C22⋊D4311yescharacteristic
462C2×C8C2×C22⋊D4311yescharacteristic
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—431no—
468C4⋊C4—431no—
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—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C42—21no—
482C42—861no—
483C42—861no—
484C42—861no—
485C42—861no—
486C42C2×C4×D4311yescharacteristic
487C42#1062189811yescharacteristic
488C42C2×C22⋊D4311yescharacteristic
489C42C23×D4311yescharacteristic
490C23—21no—
491C23C4×C22⋊D4311yescharacteristic
492Q8—21no—
493Q8—21no—
494Q8—432no—
495Q8—861no—
496Q8—861no—
497Q8—861no—
498Q8—1722no—
499D4—21no—
500D4—21no—
501D4—42no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—861no—
516C2×C4—1722no—
517C2×C4—1722no—
518C2×C4C4×C22⋊D4311yescharacteristic
519C2×C4C4×C22⋊D4311yescharacteristic
520C2×C4C4×C22⋊D4311yescharacteristic
521C2×C4C22×C4×D4311yescharacteristic
522C2×C4C22×C22⋊D4311yescharacteristic
523C2×C4C2×#1062189811yescharacteristic
524C8—21no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—41no—
529C8—41no—
530C8—862no—
531C8—862no—
532C8—861no—
533C8—861no—
534C8—861no—
535C8—861no—
536C8—1721no—
537C8—1721no—
538C22—21no—
539C22—21no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22#1458301412yes—
544C22C2×C4×C22⋊D4311yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—862no—
553C4—1721no—
554C4—1721no—
555C4—1721no—
556C4#131×D4311yescharacteristic
557C4#1458366411yescharacteristic
558C4#1458371011yescharacteristic
559C4#1458371411yescharacteristic
560C2—22no—
561C2—81no—
562C2#1914331711yescharacteristic
563C2#1914343411yescharacteristic
564C2C2×#1458301411yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#2994C2
socleC22×C43C2×C4×D4
prime radical#121×C43C2×C4
cosocleC42×C43C24
hypercenter#2994D43
hypocenterC43#18017
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2994

Complements

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

NH ≅ G/Ntype
2. #19143682C2semidirect
3. #19133490C2semidirect
4. #19133483C2semidirect
5. #19133471C2semidirect
6. #19133466C2semidirect
7. #19133464C2semidirect
8. #19133452C2semidirect
9. C8×#10621885C2semidirect
10. C8×#10621883C2semidirect
11. #19133378C2semidirect
13. C2×#14582629C2semidirect
14. #19132879C2semidirect
349. C43#18017semidirect

Maximal subgroups

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

subgroupindex
#191446712
#191436822
#191334902
#191334832
#191334712
#191334662
#191334642
#191334522
C8×#106218852
C8×#106218832
#191333782
#191330552
C2×#145826292
#191328792
C43×#29942
#1801743