Finite Group Databasebeta

← #14725646

Subgroups — #14725646

Order 2816.

588 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#13079222C211yesmaximal, characteristic
2#13077620C211yesmaximal, characteristic
3#13077563C211yesmaximal, characteristic, complemented
4#13067520C211yesmaximal, characteristic, complemented
5#13067514C211yesmaximal, characteristic, complemented
6#13067496C211yesmaximal, characteristic, complemented
7#13067489C211yesmaximal, characteristic, complemented
8#13067468C211yesmaximal, characteristic, complemented
9#13067454C211yesmaximal, characteristic, complemented
10#13067436C211yesmaximal, characteristic, complemented
11C8×#4314C211yesmaximal, characteristic, complemented
12#13067368C211yesmaximal, characteristic, complemented
13#13067038C211yesmaximal, characteristic, complemented
14#13067030C211yesmaximal, characteristic
15C11×#1455C211yesmaximal, characteristic, complemented
16#10623010C2211yescharacteristic
17#10623001C2211yescharacteristic
18C4×C11×M16C2211yescharacteristic
19C4×C11×M16C2211yescharacteristic
20C4×C11×M16C2211yescharacteristic
21#10622750C411yescharacteristic
22#10622750C411yescharacteristic
23#10622747C411yescharacteristic
24#10622747C411yescharacteristic
25#10622741—21no—
26#10622740—21no—
27#10622735—21no—
28#10622732—21no—
29#10622538C2211yescharacteristic
30C2×C4⋊(C11⋊C8)C2211yescharacteristic
31#10622328C411yescharacteristic
32#10622327C411yescharacteristic
33#10622322—21no—
34#10622321—21no—
35#10622316C411yescharacteristic
36#10622315C411yescharacteristic
37#10622314—21no—
38#10622314—21no—
39C4×Dic44C2211yescharacteristic
40C4×Dic44C2211yescharacteristic
41C4×#4314C2211yescharacteristic
42C4×#4314C2211yescharacteristic
43#10622301C2211yescharacteristic
44C8×D44C2211yescharacteristic
45#10622292C2211yescharacteristic
46#10622292C2211yescharacteristic
47#10622292C2211yescharacteristic
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×C11×M16—21no—
68C2×C11×M16C2×C411yescharacteristic
69C2×C11×M16C2×C411yescharacteristic
70C2×C11×M16D411yescharacteristic
71C2×C11×M16D411yescharacteristic
72C2×C42×C11C2311yescharacteristic
73#66983C2×C411yescharacteristic
74#66982—21no—
75C4×C22⋊D11—21no—
76#66979—21no—
77#66977—21no—
78#66977C2×C411yescharacteristic
79#66977C2×C411yescharacteristic
80#66977C2×C411yescharacteristic
81C22×C11⋊C8—21no—
82C2×Dic44C2×C411yescharacteristic
83C2×Dic44C2×C411yescharacteristic
84C2×#4314C2×C411yescharacteristic
85C2×#4314C2×C411yescharacteristic
86C2×#4313—21no—
87C2×C8×D11—21no—
88#66929—21no—
89#66928C2×C411yescharacteristic
90C4×D44C2311yescharacteristic
91#66925—21no—
92#66923—21no—
93#66923C2×C411yescharacteristic
94#66922C2×C411yescharacteristic
95#66922C2×C411yescharacteristic
96C4×Dic22—21no—
97C4×Dic22C2311yescharacteristic
98C4×Dic22C2311yescharacteristic
99C4×Dic22C2311yescharacteristic
100C11×#97—21no—
101C11×#97C2×C411yescharacteristic
102C11×#97C2×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—
128#66879—21no—
129Dic11⋊C8—21no—
130Dic11⋊C8—21no—
131Dic11⋊C8—21no—
132Dic11⋊C8—21no—
133Dic11⋊C8—21no—
134Dic11⋊C8—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
143C4×C11⋊C8—21no—
144#18077—111nomaximal, Sylow
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11#4111yescharacteristic
148C2×C22⋊D11—21no—
149C2×D44C22×C411yescharacteristic
150C2×C4×D11—21no—
151C2×Dic22—21no—
152C2×Dic22C22×C411yescharacteristic
153C2×Dic22C22×C411yescharacteristic
154C2×Dic22C22×C411yescharacteristic
155C11×M16—22no—
156C11×M16—22no—
157C11×M16—41no—
158C11×M16—41no—
159C11×M16—42no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11C22×C411yescharacteristic
163C2×C8×C11C22×C411yescharacteristic
164C2×C8×C11C22×C411yescharacteristic
165C2×C8×C11C22×C411yescharacteristic
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2×D411yescharacteristic
168C2×C8×C11C2×D411yescharacteristic
169C2×C8×C11C2×D411yescharacteristic
170C42×C11C22×C411yescharacteristic
171C42×C11C2×D411yescharacteristic
172C42×C11#4111yescharacteristic
173C42×C11C2411yescharacteristic
174C22⋊Dic11—21no—
175C22⋊Dic11—21no—
176C22⋊Dic11—21no—
177(C2×D11)⋊C4—21no—
178(C2×D11)⋊C4—21no—
179(C2×D11)⋊C4—21no—
180(C2×D11)⋊C4—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11C22×C411yescharacteristic
185C4⋊Dic11C22×C411yescharacteristic
186C4⋊Dic11C22×C411yescharacteristic
187C4⋊Dic11C22×C411yescharacteristic
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194Dic11⋊C4—21no—
195Dic11⋊C4—21no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—42no—
204Dic44—22no—
205Dic44—41no—
206#4314—22no—
207#4314—41no—
208#4313—42no—
209C8×D11—42no—
210#3172—111no—
211#2969—111no—
212#2962—111no—
213#1592—111no—
214#1591—111no—
215#1588—111no—
216#1587—111no—
217#1584—111no—
218#1582—111no—
219#1579—111no—
220C8×SD16—111no—
221#1565—111no—
222#1485—111no—
223#1483—111no—
224#1455D1111yescharacteristic, complemented
225C23×C11C4×D411yescharacteristic
226C22×D11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—41no—
232C2×C4×C11C4×D411yescharacteristic
233C2×C4×C11C4×D411yescharacteristic
234C2×C4×C11C4×D411yescharacteristic
235C2×C4×C11C23×C411yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C22⋊D11—81no—
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246D44—21no—
247D44—21no—
248C4×D11—41no—
249C4×D11—41no—
250Dic22—21no—
251Dic22—21no—
252Dic22—21no—
253Dic22—21no—
254Dic22—21no—
255Dic22—21no—
256Dic22—81no—
257C8×C11—22no—
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—21no—
261C8×C11—21no—
262C8×C11—21no—
263C8×C11—21no—
264C8×C11—41no—
265C8×C11#13112yes—
266C8×C11#13712yes—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271#533—111no—
272#529—111no—
273#501—111no—
274#497—111no—
275#491—111no—
276#489—111no—
277#470—111no—
278#470—111no—
279#468—111no—
280#468—111no—
281#446—111no—
282#446—111no—
283#446—111no—
284#446—221no—
285#446—221no—
286C8×Q8—111no—
287C8×Q8—111no—
288C8×Q8—111no—
289C4×Q16—111no—
290C4×Q16—111no—
291C4×SD16—111no—
292C4×SD16—111no—
293#436—111no—
294#436—221no—
295#435—221no—
296C8×D4—111no—
297#433—221no—
298#431—111no—
299#424—221no—
300C2×C4⋊C8—111no—
301#405—221no—
302#405—221no—
303C4×M16C2×D1111yescharacteristic
304C4×M16C2×D1111yescharacteristic
305C4×M16C2×D1111yescharacteristic
306#335—111no—
307#335—111no—
308#334—111no—
309#334—111no—
310Q8⋊C8—111no—
311Q8⋊C8—111no—
312Q8⋊C8—111no—
313Q8⋊C8—111no—
314Q8⋊C8—111no—
315Q8⋊C8—111no—
316D4⋊C8—111no—
317D4⋊C8—111no—
318#322C2×D1111yescharacteristic
319#322C2×D1111yescharacteristic
320#322C2×D1111yescharacteristic
321C82C2×D1111yescharacteristic
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11C2×C4×D411yescharacteristic
326C2×D11—41no—
327C2×D11—41no—
328C2×D11—41no—
329C4×C11—21no—
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—21no—
333C4×C11C2×#13111yescharacteristic
334C4×C11#56811yescharacteristic
335C4×C11C2×#13711yescharacteristic
336C4×C11#57511yescharacteristic
337Dic11—41no—
338Dic11—41no—
339Dic11—41no—
340Dic11—41no—
341Dic11—41no—
342Dic11—41no—
343Dic11—41no—
344C2×Q16—111no—
345C2×Q16—111no—
346C2×SD16—111no—
347C2×SD16—111no—
348C2×M16—21no—
349C2×M16—221no—
350C2×M16C4×D1111yescharacteristic
351C2×M16C4×D1111yescharacteristic
352C2×M16D4411yescharacteristic
353C2×M16D4411yescharacteristic
354C22×C8—221no—
355C22×C8—221no—
356C4⋊Q8—111no—
357C4⋊Q8—111no—
358#126—221no—
359#125—111no—
360#125—221no—
361#124—111no—
362#123—221no—
363C22⋊Q8—111no—
364C22⋊Q8—111no—
365C22⋊Q8—111no—
366C22⋊Q8—221no—
367#121—111no—
368C4×Q8—111no—
369C4×Q8—111no—
370C4×Q8—111no—
371C4×Q8—221no—
372C4×D4—111no—
373C4×D4—221no—
374#117—221no—
375#117—221no—
376C2×C42C22×D1111yescharacteristic
377#107—111no—
378#107—111no—
379#106—111no—
380#106—111no—
381C4⋊C8—111no—
382C4⋊C8—111no—
383C4⋊C8—111no—
384C4⋊C8—111no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387C4⋊C8—221no—
388C4⋊C8—221no—
389C4⋊C8—221no—
390C4⋊C8—221no—
391C4⋊C8—221no—
392#103—111no—
393#103—111no—
394#103—111no—
395#103—111no—
396#103—111no—
397#103—111no—
398#102—111no—
399#102—111no—
400C22⋊C8—221no—
401C22⋊C8—221no—
402C22⋊C8—221no—
403#97—21no—
404#97—221no—
405#97—221no—
406#97—221no—
407#97C4×D1111yescharacteristic
408#97C4×D1111yescharacteristic
409#97D4411yescharacteristic
410#97D4411yescharacteristic
411C4×C8—221no—
412C4×C8—221no—
413C4×C8—221no—
414C4×C8—221no—
415C4×C8C22×D1111yescharacteristic
416C4×C8C22×D1111yescharacteristic
417C4×C8C22×D1111yescharacteristic
418C4×C8C22×D1111yescharacteristic
419C4×C8C22×D1111yescharacteristic
420C4×C8C22×D1111yescharacteristic
421C2×C11—41no—
422C2×C11#293511yescharacteristic
423C2×C11C4×#13711yescharacteristic
424C2×C11#295611yescharacteristic
425D11—81no—
426C2×Q8—111no—
427C2×Q8—111no—
428C2×Q8—111no—
429C2×Q8—221no—
430C2×D4—111no—
431C2×D4—221no—
432C22×C4—221no—
433C22×C4C2×C4×D1111yescharacteristic
434C22×C4C2×D4411yescharacteristic
435C22×C4#433911yescharacteristic
436Q16—222no—
437Q16—441no—
438SD16—222no—
439SD16—441no—
440M16—22no—
441M16—22no—
442M16—41no—
443M16—41no—
444M16—42no—
445M16—442no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—442no—
453C2×C8—442no—
454C2×C8C2×C4×D1111yescharacteristic
455C2×C8C2×C4×D1111yescharacteristic
456C2×C8C2×C4×D1111yescharacteristic
457C2×C8C2×C4×D1111yescharacteristic
458C2×C8C2×D4411yescharacteristic
459C2×C8C2×D4411yescharacteristic
460C2×C8C2×D4411yescharacteristic
461C2×C8C2×D4411yescharacteristic
462C4⋊C4—111no—
463C4⋊C4—111no—
464C4⋊C4—111no—
465C4⋊C4—111no—
466C4⋊C4—221no—
467C4⋊C4—221no—
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—
482C22⋊C4—221no—
483C22⋊C4—221no—
484C42—221no—
485C42—221no—
486C42—221no—
487C42C2×C4×D1111yescharacteristic
488C42C2×D4411yescharacteristic
489C42#433911yescharacteristic
490C42C23×D1111yescharacteristic
491C11#1807711yescharacteristic, complemented, Sylow
492C23—221no—
493C23C4×D4411yescharacteristic
494Q8—221no—
495Q8—221no—
496Q8—221no—
497Q8—221no—
498Q8—221no—
499Q8—221no—
500Q8—881no—
501D4—221no—
502D4—221no—
503D4—881no—
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—441no—
517C2×C4—441no—
518C2×C4C4×D4411yescharacteristic
519C2×C4C4×D4411yescharacteristic
520C2×C4C4×D4411yescharacteristic
521C2×C4C22×C4×D1111yescharacteristic
522C2×C4C22×D4411yescharacteristic
523C2×C4C2×#433911yescharacteristic
524C8—22no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—21no—
531C8—41no—
532C8—441no—
533C8—441no—
534C8—441no—
535C8—441no—
536C8#6696012yes—
537C8#6696212yes—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—441no—
542C22—441no—
543C22—441no—
544C22C2×C4×D4411yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—441no—
550C4—441no—
551C4—441no—
552C4—441no—
553C4—441no—
554C4—441no—
555C4—441no—
556C4C2×#6696011yescharacteristic
557C4#1062327611yescharacteristic
558C4C2×#6696211yescharacteristic
559C4#1062327911yescharacteristic
560C2—41no—
561C2—881no—
562C2#1307736211yescharacteristic
563C2C4×#6696211yescharacteristic
564C2#1307752711yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1455C2
socleC22×C11C2×C4×D4
prime radical#66983C2×C4
cosocleC42×C11C24
hypercenter#1455D11
hypocenterC11#18077
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #1455

Complements

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

NH ≅ G/Ntype
3. #13077563C2semidirect
4. #13067520C2semidirect
5. #13067514C2semidirect
6. #13067496C2semidirect
7. #13067489C2semidirect
8. #13067468C2semidirect
9. #13067454C2semidirect
10. #13067436C2semidirect
11. C8×#4314C2semidirect
12. #13067368C2semidirect
13. #13067038C2semidirect
15. C11×#1455C2semidirect
224. #1455D11semidirect
491. C11#18077semidirect

Maximal subgroups

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

subgroupindex
#130792222
#130776202
#130775632
#130675202
#130675142
#130674962
#130674892
#130674682
#130674542
#130674362
C8×#43142
#130673682
#130670382
#130670302
C11×#14552
#1807711