Finite Group Databasebeta

← #14724895

Subgroups — #14724895

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#13078692C211yesmaximal, characteristic
2M16×Dic22C211yesmaximal, characteristic, complemented
3#13067523C211yesmaximal, characteristic, complemented
4#13067504C211yesmaximal, characteristic, complemented
5#13067485C211yesmaximal, characteristic, complemented
6#13067473C211yesmaximal, characteristic, complemented
7#13067466C211yesmaximal, characteristic, complemented
8#13067457C211yesmaximal, characteristic, complemented
9#13067428C211yesmaximal, characteristic, complemented
10C8×#4326C211yesmaximal, characteristic, complemented
11#13067404C211yesmaximal, characteristic, complemented
12#13067081C211yesmaximal, characteristic
13#13067010C211yesmaximal, characteristic, complemented
14#13066913C211yesmaximal, characteristic, complemented
15C11×#2969C211yesmaximal, characteristic
16C11×#529C2211yescharacteristic
17C2×C4×Dic22C2211yescharacteristic
18C11×#446C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C11×#436—21no—
21C11×#436C2211yescharacteristic
22C11×#435—21no—
23C8×D4×C11C2211yescharacteristic
24C11×#433—21no—
25C11×#431C2211yescharacteristic
26C11×#405—21no—
27C4×C11×M16C2211yescharacteristic
28#10622731—21no—
29M16×Dic11—21no—
30#10622676C411yescharacteristic
31#10622676C411yescharacteristic
32#10622667C411yescharacteristic
33#10622667C411yescharacteristic
34#10622663C411yescharacteristic
35#10622656C411yescharacteristic
36#10622653C411yescharacteristic
37#10622646C411yescharacteristic
38C4×#4326C2211yescharacteristic
39C4×#4326C2211yescharacteristic
40C4×#4324C2211yescharacteristic
41C4×#4324C2211yescharacteristic
42#10622538C2211yescharacteristic
43#10622538C2211yescharacteristic
44#10622537C2211yescharacteristic
45#10622314—21no—
46#10622314—21no—
47#10622292C2211yescharacteristic
48#10622292C2211yescharacteristic
49C8×Dic22C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51Q8⋊(C11⋊C8)C2211yescharacteristic
52Q8⋊(C11⋊C8)C2211yescharacteristic
53D4⋊(C11⋊C8)C2211yescharacteristic
54D4⋊(C11⋊C8)C2211yescharacteristic
55#10622122C2211yescharacteristic
56#10622122C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622122C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622118C2211yescharacteristic
61#10622117C2211yescharacteristic
62#10622117C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C22×Dic22C2×C411yescharacteristic
68C2×C11×M16—21no—
69C2×C11×M16D411yescharacteristic
70C2×C11×M16D411yescharacteristic
71C22×C8×C11—21no—
72C11×#126—21no—
73C11×#125C2×C411yescharacteristic
74C11×#124C2×C411yescharacteristic
75C11×#123—21no—
76C11×C22⋊Q8C2×C411yescharacteristic
77C11×#121C2×C411yescharacteristic
78C4×Q8×C11C2311yescharacteristic
79C4×D4×C11—21no—
80C4×D4×C11C2311yescharacteristic
81C11×#117—21no—
82C2×C42×C11C2311yescharacteristic
83C2×#4326C2×C411yescharacteristic
84C2×#4326C2×C411yescharacteristic
85C2×#4324C2×C411yescharacteristic
86C2×#4324C2×C411yescharacteristic
87C2×C4⋊Dic11C2×C411yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×C4×Dic11—21no—
90C2×#4318—21no—
91C4×Dic22—21no—
92C4×Dic22—21no—
93C4×Dic22C2×C411yescharacteristic
94C4×Dic22C2×C411yescharacteristic
95C4×Dic22C2311yescharacteristic
96C4×Dic22C2311yescharacteristic
97C11×C4⋊C8—21no—
98C11×C4⋊C8—21no—
99C11×C4⋊C8C2311yescharacteristic
100C11×C4⋊C8C2311yescharacteristic
101C11×C22⋊C8—21no—
102C11×C22⋊C8—21no—
103C11×C22⋊C8—21no—
104C11×#97—21no—
105C11×#97D411yescharacteristic
106C11×#97D411yescharacteristic
107C4×C8×C11—21no—
108C4×C8×C11—21no—
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111#66899C2×C411yescharacteristic
112#66899C2×C411yescharacteristic
113#66896C2×C411yescharacteristic
114#66896C2×C411yescharacteristic
115C22⋊(C11⋊C8)—21no—
116C22⋊(C11⋊C8)C2×C411yescharacteristic
117C22⋊(C11⋊C8)C2×C411yescharacteristic
118#66879—21no—
119#66879—21no—
120Dic11⋊C8—21no—
121Dic11⋊C8—21no—
122Dic11⋊C8—21no—
123Dic11⋊C8—21no—
124C8×Dic11—21no—
125C8×Dic11—21no—
126#66874C2×C411yescharacteristic
127#66874C2×C411yescharacteristic
128#66874C2×C411yescharacteristic
129#66874C2×C411yescharacteristic
130#66872C2×C411yescharacteristic
131#66872C2×C411yescharacteristic
132#66871C2×C411yescharacteristic
133#66871C2×C411yescharacteristic
134C4⋊(C11⋊C8)—21no—
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)C2×C411yescharacteristic
137C4⋊(C11⋊C8)C2×C411yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18012—111nomaximal, Sylow
145C2×Q8×C11C22×C411yescharacteristic
146C2×D4×C11—21no—
147C2×D4×C11C22×C411yescharacteristic
148C22×C4×C11—21no—
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11#4111yescharacteristic
152C22×Dic11—21no—
153C22×Dic11—21no—
154C2×Dic22—22no—
155C2×Dic22—21no—
156C2×Dic22—41no—
157C2×Dic22C22×C411yescharacteristic
158C2×Dic22C22×C411yescharacteristic
159C11×M16—22no—
160C11×M16—41no—
161C11×M16—42no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—42no—
165C2×C8×C11C2×D411yescharacteristic
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2×D411yescharacteristic
168C2×C8×C11C2×D411yescharacteristic
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4C22×C411yescharacteristic
174C11×C4⋊C4C22×C411yescharacteristic
175C11×C22⋊C4—21no—
176C11×C22⋊C4—21no—
177C11×C22⋊C4—21no—
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C42×C11—21no—
181C42×C11C22×C411yescharacteristic
182C42×C11C2×D411yescharacteristic
183C42×C11#4111yescharacteristic
184C42×C11C2411yescharacteristic
185#4326—22no—
186#4326—41no—
187#4324—22no—
188#4324—41no—
189C4⋊Dic11—21no—
190C4⋊Dic11C22×C411yescharacteristic
191C4⋊Dic11C22×C411yescharacteristic
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194Dic11⋊C4—21no—
195Dic11⋊C4—21no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200#4318—42no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C22×C411yescharacteristic
207C2×C11⋊C8C22×C411yescharacteristic
208C2×C11⋊C8C22×C411yescharacteristic
209#3108—111no—
210#2969D1111yescharacteristic
211Q8×M16—111no—
212#1593—111no—
213#1590—111no—
214#1587—111no—
215#1585—111no—
216#1584—111no—
217#1583—111no—
218SD16⋊C8—111no—
219C8×Q16—111no—
220#1574—111no—
221#1495—111no—
222#1479—111no—
223#1453—111no—
224C23×C11—21no—
225C23×C11C4×D411yescharacteristic
226Q8×C11—21no—
227Q8×C11—21no—
228D4×C11—21no—
229D4×C11—21no—
230D4×C11—81no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11C4×D411yescharacteristic
242C2×C4×C11C4×D411yescharacteristic
243C2×C4×C11C4×D411yescharacteristic
244C2×C4×C11C23×C411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—42no—
252C2×Dic11—81no—
253Dic22—21no—
254Dic22—21no—
255Dic22—21no—
256Dic22—42no—
257Dic22#13112yes—
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—21no—
261C8×C11—41no—
262C8×C11—41no—
263C8×C11#13712yes—
264C11⋊C8—21no—
265C11⋊C8—21no—
266C11⋊C8—21no—
267C11⋊C8—21no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272#529C2×D1111yescharacteristic
273C2×C4×Q8—111no—
274#483—111no—
275#480—111no—
276#479—111no—
277#479—111no—
278#464—111no—
279#464—111no—
280#451—111no—
281#448—111no—
282#446—111no—
283#446—111no—
284#446—221no—
285#446—221no—
286#446C2×D1111yescharacteristic
287C8×Q8—111no—
288C8×Q8—111no—
289C8×Q8C2×D1111yescharacteristic
290C4×Q16—111no—
291C4×Q16—111no—
292C4×SD16—111no—
293C4×SD16—111no—
294#436—21no—
295#436C2×D1111yescharacteristic
296#435—21no—
297C8×D4C2×D1111yescharacteristic
298#433—21no—
299#431—111no—
300#431—111no—
301#431C2×D1111yescharacteristic
302#423—111no—
303#423—221no—
304#405—21no—
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#322—111no—
320#322—111no—
321#322—111no—
322C82—111no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11—41no—
327C22×C11—41no—
328C22×C11—41no—
329C22×C11C2×C4×D411yescharacteristic
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—21no—
333C4×C11—21no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11C2×#13111yescharacteristic
338C4×C11#56811yescharacteristic
339C4×C11C2×#13711yescharacteristic
340C4×C11#57511yescharacteristic
341Dic11—22no—
342Dic11—41no—
343Dic11—41no—
344Dic11—41no—
345C22×Q8—111no—
346C2×Q16—111no—
347C2×Q16—111no—
348C2×SD16—111no—
349C2×SD16—111no—
350C2×M16—21no—
351C2×M16—221no—
352C2×M16C22⋊D1111yescharacteristic
353C2×M16C22⋊D1111yescharacteristic
354C22×C8—21no—
355#126—21no—
356#125C4×D1111yescharacteristic
357#124C4×D1111yescharacteristic
358#123—21no—
359C22⋊Q8C4×D1111yescharacteristic
360#121C4×D1111yescharacteristic
361C4×Q8—111no—
362C4×Q8—111no—
363C4×Q8—111no—
364C4×Q8—111no—
365C4×Q8—221no—
366C4×Q8—221no—
367C4×Q8C22×D1111yescharacteristic
368C4×D4—21no—
369C4×D4C22×D1111yescharacteristic
370#117—21no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—221no—
373C2×C42—221no—
374C2×C42C22×D1111yescharacteristic
375#107—111no—
376#107—111no—
377#106—111no—
378#106—111no—
379C4⋊C8—21no—
380C4⋊C8—21no—
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⋊C8C22×D1111yescharacteristic
392C4⋊C8C22×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—21no—
403C22⋊C8—21no—
404C22⋊C8—111no—
405C22⋊C8—111no—
406C22⋊C8—221no—
407#97—21no—
408#97—221no—
409#97—221no—
410#97C22⋊D1111yescharacteristic
411#97C22⋊D1111yescharacteristic
412C4×C8—21no—
413C4×C8—21no—
414C4×C8—111no—
415C4×C8—111no—
416C4×C8—111no—
417C4×C8—111no—
418C4×C8—221no—
419C4×C8—221no—
420C4×C8C22×D1111yescharacteristic
421C4×C8C22×D1111yescharacteristic
422C2×C11—41no—
423C2×C11—81no—
424C2×C11#293311yescharacteristic
425C2×C11C4×#13711yescharacteristic
426C2×C11#295711yescharacteristic
427C2×Q8—111no—
428C2×Q8—111no—
429C2×Q8—222no—
430C2×Q8—221no—
431C2×Q8—441no—
432C2×Q8C2×C4×D1111yescharacteristic
433C2×D4—21no—
434C2×D4C2×C4×D1111yescharacteristic
435C22×C4—21no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4C2×C4×D1111yescharacteristic
439C22×C4#433911yescharacteristic
440C22×C4C2×C22⋊D1111yescharacteristic
441Q16—222no—
442Q16—441no—
443SD16—222no—
444SD16—441no—
445M16—22no—
446M16—41no—
447M16—42no—
448M16—442no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—42no—
452C2×C8—111no—
453C2×C8—111no—
454C2×C8—111no—
455C2×C8—111no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8C2×C22⋊D1111yescharacteristic
461C2×C8C2×C22⋊D1111yescharacteristic
462C2×C8C2×C22⋊D1111yescharacteristic
463C2×C8C2×C22⋊D1111yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—111no—
469C4⋊C4—111no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4C2×C4×D1111yescharacteristic
476C4⋊C4C2×C4×D1111yescharacteristic
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C42—21no—
483C42—221no—
484C42—221no—
485C42—221no—
486C42—221no—
487C42C2×C4×D1111yescharacteristic
488C42#433911yescharacteristic
489C42C2×C22⋊D1111yescharacteristic
490C42C23×D1111yescharacteristic
491C11#1801211yescharacteristic, complemented, Sylow
492C23—21no—
493C23C4×C22⋊D1111yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—112no—
497Q8—221no—
498Q8—221no—
499Q8—221no—
500Q8—442no—
501D4—21no—
502D4—21no—
503D4—81no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—221no—
517C2×C4—221no—
518C2×C4—442no—
519C2×C4—881no—
520C2×C4C4×C22⋊D1111yescharacteristic
521C2×C4C4×C22⋊D1111yescharacteristic
522C2×C4C4×C22⋊D1111yescharacteristic
523C2×C4C22×C4×D1111yescharacteristic
524C2×C4C2×#433911yescharacteristic
525C2×C4C22×C22⋊D1111yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—221no—
532C8—221no—
533C8—221no—
534C8—221no—
535C8—441no—
536C8—441no—
537C8—441no—
538C8—441no—
539C8#6700412yes—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22C2×C4×C22⋊D1111yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—222no—
555C4—441no—
556C4—441no—
557C4—441no—
558C4D11×#13111yescharacteristic
559C4#1062328111yescharacteristic
560C4#1062335311yescharacteristic
561C4C2×#6700411yescharacteristic
562C2—41no—
563C2—81no—
564C2#1307733811yescharacteristic
565C2C4×#6700411yescharacteristic
566C2#1307753111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2969C2
socleC22×C11C2×C4×D4
prime radicalC11×#121C2×C4
cosocleC42×C11C24
hypercenter#2969D11
hypocenterC11#18012
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2969

Complements

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

NH ≅ G/Ntype
2. M16×Dic22C2semidirect
3. #13067523C2semidirect
4. #13067504C2semidirect
5. #13067485C2semidirect
6. #13067473C2semidirect
7. #13067466C2semidirect
8. #13067457C2semidirect
9. #13067428C2semidirect
10. C8×#4326C2semidirect
11. #13067404C2semidirect
13. #13067010C2semidirect
14. #13066913C2semidirect
491. C11#18012semidirect

Maximal subgroups

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

subgroupindex
#130786922
M16×Dic222
#130675232
#130675042
#130674852
#130674732
#130674662
#130674572
#130674282
C8×#43262
#130674042
#130670812
#130670102
#130669132
C11×#29692
#1801211