Finite Group Databasebeta

← #14724918

Subgroups — #14724918

Order 2816.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078688C211yesmaximal, characteristic
2#13077634C211yesmaximal, characteristic
3#13077563C211yesmaximal, characteristic, complemented
4#13067520C211yesmaximal, characteristic, complemented
5#13067508C211yesmaximal, characteristic, complemented
6#13067496C211yesmaximal, characteristic, complemented
7#13067489C211yesmaximal, characteristic, complemented
8#13067468C211yesmaximal, characteristic, complemented
9#13067461C211yesmaximal, characteristic, complemented
10#13067436C211yesmaximal, characteristic, complemented
11C8×Dic44C211yesmaximal, characteristic, complemented
12#13067401C211yesmaximal, characteristic, complemented
13#13067090C211yesmaximal, characteristic, complemented
14#13067004C211yesmaximal, characteristic
15C11×#1453C211yesmaximal, characteristic, complemented
16C4×#4339C2211yescharacteristic
17#10623001C2211yescharacteristic
18C11×#431C2211yescharacteristic
19C11×#431C2211yescharacteristic
20C4×C11×M16C2211yescharacteristic
21#10622741—21no—
22#10622741—21no—
23#10622735—21no—
24#10622732—21no—
25#10622539C2211yescharacteristic
26C2×C4⋊(C11⋊C8)C2211yescharacteristic
27#10622464C411yescharacteristic
28#10622462C411yescharacteristic
29#10622459C411yescharacteristic
30#10622454C411yescharacteristic
31#10622346C411yescharacteristic
32#10622346C411yescharacteristic
33#10622336C411yescharacteristic
34#10622336C411yescharacteristic
35#10622320—21no—
36#10622318—21no—
37#10622314—21no—
38#10622314—21no—
39C4×Dic44C2211yescharacteristic
40C4×Dic44C2211yescharacteristic
41C4×#4314C2211yescharacteristic
42C4×#4314C2211yescharacteristic
43#10622301C2211yescharacteristic
44#10622301C2211yescharacteristic
45#10622292C2211yescharacteristic
46#10622292C2211yescharacteristic
47C8×Dic22C2211yescharacteristic
48C8×Dic22C2211yescharacteristic
49C8×Dic22C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51C11×#322C2211yescharacteristic
52C11×#322C2211yescharacteristic
53C11×#322C2211yescharacteristic
54C82×C11C2211yescharacteristic
55#10622097C2211yescharacteristic
56#10622097C2211yescharacteristic
57#10622096C2211yescharacteristic
58#10622096C2211yescharacteristic
59#10622095C2211yescharacteristic
60#10622095C2211yescharacteristic
61#10622094C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622094C2211yescharacteristic
65#10622094C2211yescharacteristic
66#10622094C2211yescharacteristic
67C2×#4339C2×C411yescharacteristic
68C2×C11×M16D411yescharacteristic
69C2×C11×M16D411yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C4×C22⋊D11—21no—
72C4×C22⋊D11—21no—
73#66979—21no—
74#66979C2×C411yescharacteristic
75#66977—21no—
76#66977C2×C411yescharacteristic
77#66977C2×C411yescharacteristic
78C22×C11⋊C8—21no—
79C2×Dic44C2×C411yescharacteristic
80C2×Dic44C2×C411yescharacteristic
81C2×#4314C2×C411yescharacteristic
82C2×#4314C2×C411yescharacteristic
83C2×#4313—21no—
84C2×#4313—21no—
85C4×D44C2×C411yescharacteristic
86C4×D44C2311yescharacteristic
87#66925—21no—
88C42×D11—21no—
89#66923—21no—
90#66922C2×C411yescharacteristic
91#66922C2×C411yescharacteristic
92C4×Dic22—21no—
93C4×Dic22C2×C411yescharacteristic
94C4×Dic22C2311yescharacteristic
95C4×Dic22C2311yescharacteristic
96C4×Dic22C2311yescharacteristic
97C11×C4⋊C8—21no—
98C11×C4⋊C8C2×C411yescharacteristic
99C11×C4⋊C8C2×C411yescharacteristic
100C11×C22⋊C8—21no—
101C11×C22⋊C8C2×C411yescharacteristic
102C11×C22⋊C8C2×C411yescharacteristic
103C11×#97D411yescharacteristic
104C11×#97D411yescharacteristic
105C4×C8×C11C2311yescharacteristic
106C4×C8×C11C2311yescharacteristic
107C4×C8×C11C2311yescharacteristic
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111C22⋊(C11⋊C8)—21no—
112#66885C2×C411yescharacteristic
113#66885C2×C411yescharacteristic
114(C2×D11)⋊C8—21no—
115(C2×D11)⋊C8—21no—
116#66882C2×C411yescharacteristic
117#66882C2×C411yescharacteristic
118#66881C2×C411yescharacteristic
119#66881C2×C411yescharacteristic
120#66880C2×C411yescharacteristic
121#66880C2×C411yescharacteristic
122#66880C2×C411yescharacteristic
123#66880C2×C411yescharacteristic
124#66880C2×C411yescharacteristic
125#66880C2×C411yescharacteristic
126#66879—21no—
127#66879—21no—
128Dic11⋊C8—21no—
129Dic11⋊C8—21no—
130Dic11⋊C8—21no—
131Dic11⋊C8—21no—
132Dic11⋊C8—21no—
133Dic11⋊C8—21no—
134C8×Dic11—21no—
135C8×Dic11—21no—
136C8×Dic11—21no—
137C8×Dic11—21no—
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143#66867—21no—
144#18013—111nomaximal, Sylow
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11#4111yescharacteristic
148C2×C22⋊D11—21no—
149#4339—22no—
150#4339—41no—
151C2×D44C22×C411yescharacteristic
152C2×C4×D11—21no—
153C2×C4×D11—21no—
154C2×C4×D11—21no—
155C2×Dic22—21no—
156C2×Dic22C22×C411yescharacteristic
157C2×Dic22C22×C411yescharacteristic
158C2×Dic22C22×C411yescharacteristic
159C11×M16—22no—
160C11×M16—41no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11C22×C411yescharacteristic
164C2×C8×C11C22×C411yescharacteristic
165C2×C8×C11C22×C411yescharacteristic
166C2×C8×C11C22×C411yescharacteristic
167C2×C8×C11C2×D411yescharacteristic
168C2×C8×C11C2×D411yescharacteristic
169C2×C8×C11C2×D411yescharacteristic
170C2×C8×C11C2×D411yescharacteristic
171C42×C11C22×C411yescharacteristic
172C42×C11C2×D411yescharacteristic
173C42×C11#4111yescharacteristic
174C42×C11C2411yescharacteristic
175C22⋊Dic11—21no—
176C22⋊Dic11—21no—
177C22⋊Dic11—21no—
178(C2×D11)⋊C4—21no—
179(C2×D11)⋊C4—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11C22×C411yescharacteristic
184C4⋊Dic11C22×C411yescharacteristic
185C4⋊Dic11C22×C411yescharacteristic
186C4⋊Dic11C22×C411yescharacteristic
187Dic11⋊C4—21no—
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—42no—
203Dic44—22no—
204Dic44—22no—
205#4314—41no—
206#4314—41no—
207#4313—42no—
208#4313—42no—
209#3107—111no—
210#2971—111no—
211#2962—111no—
212#1592—111no—
213#1590—111no—
214#1588—111no—
215#1587—111no—
216#1584—111no—
217#1583—111no—
218#1579—111no—
219C8×Q16—111no—
220#1573—111no—
221#1497—111no—
222#1477—111no—
223#1453D1111yescharacteristic, complemented
224C23×C11C4×D411yescharacteristic
225C22×D11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—41no—
231C2×C4×C11C4×D411yescharacteristic
232C2×C4×C11C4×D411yescharacteristic
233C2×C4×C11C4×D411yescharacteristic
234C2×C4×C11C23×C411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C22⋊D11—42no—
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245D44—21no—
246D44—21no—
247C4×D11—42no—
248C4×D11—41no—
249C4×D11—41no—
250C4×D11—81no—
251Dic22—21no—
252Dic22—21no—
253Dic22—21no—
254Dic22—21no—
255Dic22—21no—
256Dic22—81no—
257Dic22#13112yes—
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—21no—
261C8×C11—21no—
262C8×C11—21no—
263C8×C11—21no—
264C8×C11—21no—
265C8×C11—41no—
266C8×C11—41no—
267C8×C11#13712yes—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272#533—111no—
273C4×#41—111no—
274#485—111no—
275#485—111no—
276#475—111no—
277#474—111no—
278#462—111no—
279#461—111no—
280#452—111no—
281#452—111no—
282#446—111no—
283#446—111no—
284#446—221no—
285#446—221no—
286C8×Q8—111no—
287C8×Q8—111no—
288C8×Q8—111no—
289C8×Q8—111no—
290C4×Q16—111no—
291C4×Q16—111no—
292C4×SD16—111no—
293C4×SD16—111no—
294#436—111no—
295#436—111no—
296#436—221no—
297#436—221no—
298#432—111no—
299#432—221no—
300#431C2×D1111yescharacteristic
301#431C2×D1111yescharacteristic
302#424—221no—
303C2×C4⋊C8—111no—
304#405—221no—
305C4×M16—221no—
306C4×M16C2×D1111yescharacteristic
307#335—111no—
308#335—111no—
309#334—111no—
310#334—111no—
311Q8⋊C8—111no—
312Q8⋊C8—111no—
313Q8⋊C8—111no—
314Q8⋊C8—111no—
315Q8⋊C8—111no—
316Q8⋊C8—111no—
317D4⋊C8—111no—
318D4⋊C8—111no—
319#322C2×D1111yescharacteristic
320#322C2×D1111yescharacteristic
321#322C2×D1111yescharacteristic
322C82C2×D1111yescharacteristic
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11C2×C4×D411yescharacteristic
327C2×D11—41no—
328C2×D11—41no—
329C2×D11—41no—
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—21no—
333C4×C11—21no—
334C4×C11C2×#13111yescharacteristic
335C4×C11#56811yescharacteristic
336C4×C11C2×#13711yescharacteristic
337C4×C11#57511yescharacteristic
338Dic11—22no—
339Dic11—41no—
340Dic11—41no—
341Dic11—41no—
342Dic11—41no—
343Dic11—41no—
344Dic11—41no—
345C2×#41—111no—
346C2×Q16—111no—
347C2×Q16—111no—
348C2×SD16—111no—
349C2×SD16—111no—
350C2×M16—221no—
351C2×M16—221no—
352C2×M16D4411yescharacteristic
353C2×M16D4411yescharacteristic
354C22×C8—221no—
355C4⋊Q8—111no—
356C4⋊Q8—111no—
357#125—221no—
358C22⋊Q8—111no—
359C22⋊Q8—111no—
360C22⋊Q8—221no—
361C4×Q8—111no—
362C4×Q8—111no—
363C4×Q8—111no—
364C4×Q8—111no—
365C4×Q8—221no—
366C4×D4—111no—
367C4×D4—111no—
368C4×D4—221no—
369C4×D4—221no—
370#117—111no—
371#117—221no—
372#117—221no—
373C2×C42—221no—
374C2×C42C22×D1111yescharacteristic
375#107—111no—
376#107—111no—
377#106—111no—
378#106—111no—
379C4⋊C8—21no—
380C4⋊C8—111no—
381C4⋊C8—111no—
382C4⋊C8—111no—
383C4⋊C8—111no—
384C4⋊C8—221no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387C4⋊C8—221no—
388C4⋊C8—221no—
389C4⋊C8—221no—
390C4⋊C8—221no—
391C4⋊C8C4×D1111yescharacteristic
392C4⋊C8C4×D1111yescharacteristic
393#103—111no—
394#103—111no—
395#103—111no—
396#103—111no—
397#103—111no—
398#103—111no—
399#102—111no—
400#102—111no—
401C22⋊C8—21no—
402C22⋊C8—221no—
403C22⋊C8—221no—
404C22⋊C8—221no—
405C22⋊C8C4×D1111yescharacteristic
406C22⋊C8C4×D1111yescharacteristic
407#97—221no—
408#97—221no—
409#97—221no—
410#97D4411yescharacteristic
411#97D4411yescharacteristic
412C4×C8—221no—
413C4×C8—221no—
414C4×C8—221no—
415C4×C8—221no—
416C4×C8C22×D1111yescharacteristic
417C4×C8C22×D1111yescharacteristic
418C4×C8C22×D1111yescharacteristic
419C4×C8C22×D1111yescharacteristic
420C4×C8C22×D1111yescharacteristic
421C4×C8C22×D1111yescharacteristic
422C2×C11—41no—
423C2×C11#293311yescharacteristic
424C2×C11C4×#13711yescharacteristic
425C2×C11#295711yescharacteristic
426D11—81no—
427#41—222no—
428#41—441no—
429C2×Q8—111no—
430C2×Q8—111no—
431C2×Q8—111no—
432C2×Q8—221no—
433C2×D4—111no—
434C2×D4—221no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4C2×C4×D1111yescharacteristic
439C22×C4C2×D4411yescharacteristic
440C22×C4#433911yescharacteristic
441Q16—222no—
442Q16—222no—
443SD16—441no—
444SD16—441no—
445M16—22no—
446M16—41no—
447M16—442no—
448M16—442no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—442no—
456C2×C8C2×C4×D1111yescharacteristic
457C2×C8C2×C4×D1111yescharacteristic
458C2×C8C2×C4×D1111yescharacteristic
459C2×C8C2×C4×D1111yescharacteristic
460C2×C8C2×D4411yescharacteristic
461C2×C8C2×D4411yescharacteristic
462C2×C8C2×D4411yescharacteristic
463C2×C8C2×D4411yescharacteristic
464C4⋊C4—111no—
465C4⋊C4—111no—
466C4⋊C4—111no—
467C4⋊C4—111no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C22⋊C4—221no—
478C22⋊C4—221no—
479C22⋊C4—221no—
480C22⋊C4—221no—
481C22⋊C4—221no—
482C42—221no—
483C42—221no—
484C42—221no—
485C42—221no—
486C42—221no—
487C42C2×C4×D1111yescharacteristic
488C42C2×D4411yescharacteristic
489C42#433911yescharacteristic
490C42C23×D1111yescharacteristic
491C11#1801311yescharacteristic, complemented, Sylow
492C23—221no—
493C23C4×D4411yescharacteristic
494Q8—112no—
495Q8—221no—
496Q8—221no—
497Q8—221no—
498Q8—221no—
499Q8—221no—
500Q8—881no—
501D4—221no—
502D4—221no—
503D4—442no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—221no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—442no—
517C2×C4—441no—
518C2×C4—441no—
519C2×C4—881no—
520C2×C4C4×D4411yescharacteristic
521C2×C4C4×D4411yescharacteristic
522C2×C4C4×D4411yescharacteristic
523C2×C4C22×C4×D1111yescharacteristic
524C2×C4C22×D4411yescharacteristic
525C2×C4C2×#433911yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—21no—
531C8—21no—
532C8—21no—
533C8—41no—
534C8—41no—
535C8—441no—
536C8—441no—
537C8—441no—
538C8—441no—
539C8#6696212yes—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—441no—
544C22—441no—
545C22—441no—
546C22C2×C4×D4411yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—222no—
552C4—441no—
553C4—441no—
554C4—441no—
555C4—441no—
556C4—441no—
557C4—441no—
558C4C2×#6696211yescharacteristic
559C4#1062327911yescharacteristic
560C4D11×#13111yescharacteristic
561C4#1062328111yescharacteristic
562C2—41no—
563C2—881no—
564C2#1307734411yescharacteristic
565C2C4×#6696211yescharacteristic
566C2#1307753411yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1453C2
socleC22×C11C2×C4×D4
prime radicalC2×#4339C2×C4
cosocleC42×C11C24
hypercenter#1453D11
hypocenterC11#18013
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #1453

Complements

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

NH ≅ G/Ntype
3. #13077563C2semidirect
4. #13067520C2semidirect
5. #13067508C2semidirect
6. #13067496C2semidirect
7. #13067489C2semidirect
8. #13067468C2semidirect
9. #13067461C2semidirect
10. #13067436C2semidirect
11. C8×Dic44C2semidirect
12. #13067401C2semidirect
13. #13067090C2semidirect
15. C11×#1453C2semidirect
223. #1453D11semidirect
491. C11#18013semidirect

Maximal subgroups

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

subgroupindex
#130786882
#130776342
#130775632
#130675202
#130675082
#130674962
#130674892
#130674682
#130674612
#130674362
C8×Dic442
#130674012
#130670902
#130670042
C11×#14532
#1801311