Finite Group Databasebeta

← #25067433

Subgroups — #25067433

Order 11008.

566 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145202C211yesmaximal, characteristic
2#19143744C211yesmaximal, characteristic
3#19143692C211yesmaximal, characteristic, complemented
4#19133476C211yesmaximal, characteristic, complemented
5#19133469C211yesmaximal, characteristic, complemented
6#19133463C211yesmaximal, characteristic, complemented
7#19133449C211yesmaximal, characteristic, complemented
8#19133448C211yesmaximal, characteristic, complemented
9#19133442C211yesmaximal, characteristic, complemented
10#19133441C211yesmaximal, characteristic, complemented
11#19133428C211yesmaximal, characteristic, complemented
12#19133363C211yesmaximal, characteristic, complemented
13#19133051C211yesmaximal, characteristic, complemented
14#19132884C211yesmaximal, characteristic, complemented
15C43×#1494C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17#14583309C411yescharacteristic
18#14583294C411yescharacteristic
19#14583269C411yescharacteristic
20#14583258C411yescharacteristic
21#14583155C411yescharacteristic
22#14583155C411yescharacteristic
23#14583143C411yescharacteristic
24#14583143C411yescharacteristic
25#14583030C2211yescharacteristic
26#14583027—21no—
27#14583027—21no—
28#14583026C2211yescharacteristic
29#14583026C2211yescharacteristic
30Q8×C43⋊C8C2211yescharacteristic
31#14583023C2211yescharacteristic
32#14583023C2211yescharacteristic
33C4×#10621885C2211yescharacteristic
34C4×#10621885C2211yescharacteristic
35C4×#10621883C2211yescharacteristic
36C4×#10621883C2211yescharacteristic
37#14582977—21no—
38#14582977C2211yescharacteristic
39#14582971—21no—
40D4×C43⋊C8C2211yescharacteristic
41#14582960—21no—
42#14582957—21no—
43#14582957—21no—
44#14582952C2211yescharacteristic
45#14582926—21no—
46#14582923C2211yescharacteristic
47C4×#10621877C2211yescharacteristic
48#14582651C2211yescharacteristic
49#14582651C2211yescharacteristic
50#14582649C2211yescharacteristic
51#14582649C2211yescharacteristic
52#14582631C2211yescharacteristic
53#14582631C2211yescharacteristic
54#14582631C2211yescharacteristic
55#14582631C2211yescharacteristic
56#14582621C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582620C2211yescharacteristic
59#14582620C2211yescharacteristic
60C43×#529C2211yescharacteristic
61C43×#432C2211yescharacteristic
62C2×C4×C8×C43C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×D4⋊C8C2211yescharacteristic
67C2×#10621885C2×C411yescharacteristic
68C2×#10621885C2×C411yescharacteristic
69C2×#10621883C2×C411yescharacteristic
70C2×#10621883C2×C411yescharacteristic
71C2×#10621877—21no—
72C2×#10621877—21no—
73C2×#10621877C2×C411yescharacteristic
74C2×#10621877C2×C411yescharacteristic
75C22×C43⋊C8—21no—
76#13063325C2×C411yescharacteristic
77#13063325C2×C411yescharacteristic
78#13063317—21no—
79#13063304—21no—
80#13063304C2×C411yescharacteristic
81#13063304C2×C411yescharacteristic
82C4×Dic86—21no—
83C4×Dic86C2311yescharacteristic
84C4×Dic86C2311yescharacteristic
85#13063284—21no—
86#13063258C2×C411yescharacteristic
87#13063258C2×C411yescharacteristic
88#13063256C2×C411yescharacteristic
89#13063256C2×C411yescharacteristic
90C4⋊(C43⋊C8)—21no—
91C4⋊(C43⋊C8)—21no—
92C4⋊(C43⋊C8)—21no—
93C4⋊(C43⋊C8)D411yescharacteristic
94C4⋊(C43⋊C8)D411yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97Dic43⋊C8—21no—
98Dic43⋊C8—21no—
99Dic43⋊C8—21no—
100Dic43⋊C8—21no—
101#13063249C2×C411yescharacteristic
102#13063249C2×C411yescharacteristic
103#13063248C2×C411yescharacteristic
104#13063248C2×C411yescharacteristic
105#13063248C2×C411yescharacteristic
106#13063248C2×C411yescharacteristic
107#13063246C2×C411yescharacteristic
108#13063246C2×C411yescharacteristic
109C22⋊(C43⋊C8)—21no—
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)D411yescharacteristic
112C22⋊(C43⋊C8)D411yescharacteristic
113#13063236—21no—
114#13063236C2×C411yescharacteristic
115#13063236C2×C411yescharacteristic
116#13063235—21no—
117#13063235—21no—
118C4×C43⋊C8—21no—
119C4×C43⋊C8C2311yescharacteristic
120C4×C43⋊C8C2311yescharacteristic
121C4×C43⋊C8C2311yescharacteristic
122C4×C43⋊C8C2311yescharacteristic
123C8×Dic43—21no—
124C8×Dic43—21no—
125C22×C8×C43—21no—
126#126×C43—21no—
127#125×C43C2×C411yescharacteristic
128#124×C43C2×C411yescharacteristic
129#123×C43—21no—
130C22⋊Q8×C43C2×C411yescharacteristic
131#121×C43C2×C411yescharacteristic
132C4×Q8×C43C2311yescharacteristic
133C4×D4×C43—21no—
134C4×D4×C43C2311yescharacteristic
135#117×C43—21no—
136C2×C42×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C22⋊C8×C43—21no—
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
151C2×Dic86—21no—
152C2×Dic86C22×C411yescharacteristic
153C2×Dic86C22×C411yescharacteristic
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—42no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43C22×C411yescharacteristic
164C4⋊C4×C43C22×C411yescharacteristic
165C22⋊C4×C43—21no—
166C22⋊C4×C43—21no—
167C22⋊C4×C43—21no—
168C22⋊C4×C43—21no—
169C22⋊C4×C43—21no—
170C42×C43—21no—
171C42×C43C22×C411yescharacteristic
172C42×C43C2×D411yescharacteristic
173C42×C43#4111yescharacteristic
174C42×C43C2411yescharacteristic
175C22⋊Dic43—21no—
176C22⋊Dic43—21no—
177#10621885—41no—
178#10621885—41no—
179#10621883—41no—
180#10621883—41no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43C22×C411yescharacteristic
185C4⋊Dic43C22×C411yescharacteristic
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192#10621877—41no—
193#10621877—41no—
194#10621877—81no—
195#10621877—81no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—81no—
199C2×C43⋊C8C22×C411yescharacteristic
200C2×C43⋊C8C22×C411yescharacteristic
201C2×C43⋊C8C22×C411yescharacteristic
202C2×C43⋊C8C22×C411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C23×C43—21no—
208C23×C43C4×D411yescharacteristic
209Q8×C43—21no—
210Q8×C43—21no—
211D4×C43—21no—
212D4×C43—21no—
213D4×C43—81no—
214C2×C4×C43—21no—
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—41no—
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—
234Dic86—21no—
235Dic86—21no—
236Dic86—21no—
237Dic86—21no—
238Dic86—81no—
239C8×C43—22no—
240C8×C43—41no—
241C8×C43—41no—
242C8×C43—41no—
243C43⋊C8—21no—
244C43⋊C8—21no—
245C43⋊C8—21no—
246C43⋊C8—21no—
247C43⋊C8—21no—
248C43⋊C8—21no—
249C43⋊C8—21no—
250C43⋊C8—21no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253#17988—431nomaximal, Sylow
254C22×C43—21no—
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—41no—
258C22×C43—41no—
259C22×C43—41no—
260C22×C43C2×C4×D411yescharacteristic
261C4×C43—21no—
262C4×C43—21no—
263C4×C43—21no—
264C4×C43—21no—
265C4×C43—41no—
266C4×C43—41no—
267C4×C43—41no—
268C4×C43#56811yescharacteristic
269C4×C43#56811yescharacteristic
270C4×C43#57711yescharacteristic
271C4×C43#57811yescharacteristic
272Dic43—41no—
273Dic43—41no—
274Dic43—41no—
275Dic43—41no—
276#3172—431no—
277#2993—431no—
278#2985—431no—
279#1588—431no—
280#1587—431no—
281#1587—431no—
282#1585—431no—
283#1584—431no—
284#1584—431no—
285#1583—431no—
286#1582—431no—
287#1569—431no—
288#1494D4311yescharacteristic
289#1493—431no—
290#1451—431no—
291C2×C43—41no—
292C2×C43—81no—
293C2×C43#293211yescharacteristic
294C2×C43#294711yescharacteristic
295C2×C43#295611yescharacteristic
296#533—431no—
297#529C2×D4311yescharacteristic
298#501—431no—
299#497—431no—
300#491—431no—
301#489—431no—
302#470—431no—
303#470—431no—
304#468—431no—
305#468—431no—
306#446—431no—
307#446—431no—
308#446—431no—
309#446—861no—
310#446—861no—
311C8×Q8—431no—
312C8×Q8—431no—
313C8×Q8—431no—
314C4×Q16—431no—
315C4×Q16—431no—
316C4×SD16—431no—
317C4×SD16—431no—
318#436—431no—
319#436—861no—
320#435—861no—
321C8×D4—431no—
322#433—861no—
323#433—861no—
324#433—861no—
325#432C2×D4311yescharacteristic
326#431—431no—
327#424—861no—
328#423—431no—
329C4×M16—431no—
330C2×C4×C8C2×D4311yescharacteristic
331#335—431no—
332#335—431no—
333#334—431no—
334#334—431no—
335Q8⋊C8—431no—
336Q8⋊C8—431no—
337Q8⋊C8—431no—
338Q8⋊C8—431no—
339Q8⋊C8C2×D4311yescharacteristic
340Q8⋊C8C2×D4311yescharacteristic
341D4⋊C8C2×D4311yescharacteristic
342D4⋊C8C2×D4311yescharacteristic
343#322—431no—
344#322—431no—
345#322—431no—
346#322—431no—
347C43#1798811yescharacteristic, complemented, Sylow
348C2×Q16—431no—
349C2×Q16—431no—
350C2×SD16—431no—
351C2×SD16—431no—
352C2×M16—431no—
353C2×M16—431no—
354C2×M16—861no—
355C2×M16—861no—
356C22×C8—21no—
357C22×C8—861no—
358C4⋊Q8—431no—
359C4⋊Q8—431no—
360#126—21no—
361#125—861no—
362#125C4×D4311yescharacteristic
363#124C4×D4311yescharacteristic
364#123—21no—
365C22⋊Q8—431no—
366C22⋊Q8—431no—
367C22⋊Q8—861no—
368C22⋊Q8C4×D4311yescharacteristic
369#121C4×D4311yescharacteristic
370C4×Q8—431no—
371C4×Q8—431no—
372C4×Q8—861no—
373C4×Q8C22×D4311yescharacteristic
374C4×D4—21no—
375C4×D4C22×D4311yescharacteristic
376#117—21no—
377#117—861no—
378C2×C42C22×D4311yescharacteristic
379#107—431no—
380#107—431no—
381#106—431no—
382#106—431no—
383C4⋊C8—431no—
384C4⋊C8—431no—
385C4⋊C8—431no—
386C4⋊C8—431no—
387C4⋊C8—861no—
388C4⋊C8—861no—
389C4⋊C8—861no—
390C4⋊C8—861no—
391C4⋊C8—861no—
392C4⋊C8—861no—
393C4⋊C8—861no—
394C4⋊C8C22×D4311yescharacteristic
395C4⋊C8C22×D4311yescharacteristic
396#103—431no—
397#103—431no—
398#103—431no—
399#103—431no—
400#103—431no—
401#103—431no—
402#102—431no—
403#102—431no—
404C22⋊C8—21no—
405C22⋊C8—431no—
406C22⋊C8—431no—
407C22⋊C8—861no—
408C22⋊C8—861no—
409#97—21no—
410#97—431no—
411#97—431no—
412#97—861no—
413#97—861no—
414#97—861no—
415C4×C8—21no—
416C4×C8—431no—
417C4×C8—431no—
418C4×C8—431no—
419C4×C8—431no—
420C4×C8—861no—
421C4×C8—861no—
422C4×C8—861no—
423C4×C8C22×D4311yescharacteristic
424C4×C8C22×D4311yescharacteristic
425C2×Q8—431no—
426C2×Q8—431no—
427C2×Q8—861no—
428C2×Q8C2×C4×D4311yescharacteristic
429C2×D4—21no—
430C2×D4C2×C4×D4311yescharacteristic
431C22×C4—21no—
432C22×C4C2×C4×D4311yescharacteristic
433C22×C4D4×D4311yescharacteristic
434C22×C4#1062190011yescharacteristic
435Q16—1721no—
436Q16—1721no—
437SD16—1721no—
438SD16—1721no—
439M16—3441no—
440M16—3441no—
441M16—1721no—
442M16—1721no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—42no—
448C2×C8—431no—
449C2×C8—431no—
450C2×C8—431no—
451C2×C8—431no—
452C2×C8—431no—
453C2×C8—431no—
454C2×C8—431no—
455C2×C8—431no—
456C2×C8—861no—
457C2×C8—861no—
458C2×C8—3441no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—431no—
464C4⋊C4—431no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4C2×C4×D4311yescharacteristic
473C4⋊C4C2×C4×D4311yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—861no—
480C22⋊C4—861no—
481C42—21no—
482C42—861no—
483C42—861no—
484C42C2×C4×D4311yescharacteristic
485C42D4×D4311yescharacteristic
486C42#1062190011yescharacteristic
487C42C23×D4311yescharacteristic
488C23—21no—
489C23(C22⋊D43)⋊C411yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—861no—
493Q8—861no—
494Q8—861no—
495Q8—861no—
496Q8—3441no—
497D4—21no—
498D4—21no—
499D4—81no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4(C22⋊D43)⋊C411yescharacteristic
515C2×C4(C22⋊D43)⋊C411yescharacteristic
516C2×C4(C22⋊D43)⋊C411yescharacteristic
517C2×C4C22×C4×D4311yescharacteristic
518C2×C4C2×D4×D4311yescharacteristic
519C2×C4C2×#1062190011yescharacteristic
520C8—22no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8—861no—
525C8—861no—
526C8—861no—
527C8—861no—
528C8—861no—
529C8—861no—
530C8—861no—
531C8—861no—
532C8—1721no—
533C8—1721no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22C2×(C22⋊D43)⋊C411yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—1721no—
549C4—1721no—
550C4—1721no—
551C4—1721no—
552C4#1458366411yescharacteristic
553C4#1458366411yescharacteristic
554C4#1458370611yescharacteristic
555C4#1458371311yescharacteristic
556C2—41no—
557C2—81no—
558C2#1914331011yescharacteristic
559C2#1914344111yescharacteristic
560C2#1914350111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1494C2
socleC22×C43C2×C4×D4
prime radical#121×C43C2×C4
cosocleC42×C43C24
hypercenter#1494D43
hypocenterC43#17988
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1494

Complements

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

NH ≅ G/Ntype
3. #19143692C2semidirect
4. #19133476C2semidirect
5. #19133469C2semidirect
6. #19133463C2semidirect
7. #19133449C2semidirect
8. #19133448C2semidirect
9. #19133442C2semidirect
10. #19133441C2semidirect
11. #19133428C2semidirect
12. #19133363C2semidirect
13. #19133051C2semidirect
14. #19132884C2semidirect
347. C43#17988semidirect

Maximal subgroups

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

subgroupindex
#191452022
#191437442
#191436922
#191334762
#191334692
#191334632
#191334492
#191334482
#191334422
#191334412
#191334282
#191333632
#191330512
#191328842
C43×#14942
#1798843