Finite Group Databasebeta

← #14724906

Subgroups — #14724906

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#13078700C211yesmaximal, characteristic
2#13077622C211yesmaximal, characteristic
3#13077568C211yesmaximal, characteristic, complemented
4#13067503C211yesmaximal, characteristic, complemented
5#13067485C211yesmaximal, characteristic, complemented
6#13067471C211yesmaximal, characteristic, complemented
7#13067467C211yesmaximal, characteristic, complemented
8#13067458C211yesmaximal, characteristic, complemented
9#13067430C211yesmaximal, characteristic, complemented
10#13067420C211yesmaximal, characteristic, complemented
11#13067403C211yesmaximal, characteristic, complemented
12#13067080C211yesmaximal, characteristic
13#13067009C211yesmaximal, characteristic, complemented
14#13066912C211yesmaximal, characteristic, complemented
15C11×#1593C211yesmaximal, characteristic, complemented
16#10623111C2211yescharacteristic
17C4×Q8×D11C2211yescharacteristic
18C11×#446C2211yescharacteristic
19C11×#446C2211yescharacteristic
20C4×C11×Q16C2211yescharacteristic
21#10622799C411yescharacteristic
22#10622798C411yescharacteristic
23C4×#4326C2211yescharacteristic
24C4×#4325C2211yescharacteristic
25#10622637C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27#10622495C411yescharacteristic
28#10622490C411yescharacteristic
29#10622453—21no—
30#10622451—21no—
31#10622451C2211yescharacteristic
32#10622450—21no—
33#10622450C2211yescharacteristic
34#10622446C2211yescharacteristic
35#10622443C2211yescharacteristic
36#10622441—21no—
37#10622419C411yescharacteristic
38#10622418C411yescharacteristic
39#10622412C411yescharacteristic
40#10622411C411yescharacteristic
41#10622321—21no—
42#10622320—21no—
43#10622319—21no—
44#10622314—21no—
45C4×#4314C2211yescharacteristic
46C4×#4313C2211yescharacteristic
47C8×D44C2211yescharacteristic
48#10622298C2211yescharacteristic
49#10622298C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51C11×#334C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×Q8⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56Q8⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622096C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×Q8×D11C2×C411yescharacteristic
68C2×C11×Q16C2×C411yescharacteristic
69C4×Q8×C11C2311yescharacteristic
70C4×Q8×C11C2311yescharacteristic
71#67000C2×C411yescharacteristic
72#66999C2×C411yescharacteristic
73Q8×Dic11C2×C411yescharacteristic
74C2×#4326C2×C411yescharacteristic
75C2×#4325C2×C411yescharacteristic
76C2×#4314C2×C411yescharacteristic
77C2×#4313—21no—
78C2×#4313—21no—
79C2×#4313D411yescharacteristic
80C2×#4313D411yescharacteristic
81C2×C8×D11—21no—
82#66951—21no—
83#66948C2×C411yescharacteristic
84#66947—21no—
85C4⋊C4×D11—21no—
86C4⋊C4×D11C2×C411yescharacteristic
87#66943C2×C411yescharacteristic
88#66940—21no—
89#66940C2×C411yescharacteristic
90C4×D44—21no—
91C4×D44C2311yescharacteristic
92#66925—21no—
93C42×D11—21no—
94C42×D11C2311yescharacteristic
95C4×Dic22—21no—
96C4×Dic22C2311yescharacteristic
97C11×#107C2×C411yescharacteristic
98C11×C4⋊C8—21no—
99C11×C4⋊C8—21no—
100C11×C4⋊C8C2311yescharacteristic
101C11×C4⋊C8C2311yescharacteristic
102C11×#103C2×C411yescharacteristic
103C11×#103C2×C411yescharacteristic
104C11×#97—21no—
105C11×#97—21no—
106C4×C8×C11C2311yescharacteristic
107C4×C8×C11C2311yescharacteristic
108C4×C8×C11C2311yescharacteristic
109#66899C2×C411yescharacteristic
110#66899C2×C411yescharacteristic
111#66885C2×C411yescharacteristic
112(C2×D11)⋊C8—21no—
113(C2×D11)⋊C8—21no—
114(C2×D11)⋊C8—21no—
115(C2×D11)⋊C8—21no—
116(C2×D11)⋊C8C2×C411yescharacteristic
117(C2×D11)⋊C8C2×C411yescharacteristic
118#66881C2×C411yescharacteristic
119#66880C2×C411yescharacteristic
120#66879D411yescharacteristic
121#66879D411yescharacteristic
122Dic11⋊C8—21no—
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8C2×C411yescharacteristic
127Dic11⋊C8C2×C411yescharacteristic
128C8×Dic11—21no—
129C8×Dic11—21no—
130C8×Dic11—21no—
131#66874C2×C411yescharacteristic
132#66873C2×C411yescharacteristic
133#66872C2×C411yescharacteristic
134#66871C2×C411yescharacteristic
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139#66867—21no—
140C4×C11⋊C8—21no—
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18012—111nomaximal, Sylow
145C2×Q8×C11C22×C411yescharacteristic
146C2×Q8×C11C22×C411yescharacteristic
147Q8×D11—22no—
148Q8×D11—41no—
149C2×D44—21no—
150C2×D44C22×C411yescharacteristic
151C2×C4×D11—21no—
152C2×C4×D11—21no—
153C2×C4×D11—21no—
154C2×C4×D11C22×C411yescharacteristic
155C2×C4×D11C2×D411yescharacteristic
156C2×C4×D11#4111yescharacteristic
157C2×Dic22—21no—
158C2×Dic22C22×C411yescharacteristic
159C11×Q16—41no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11C22×C411yescharacteristic
164C2×C8×C11C22×C411yescharacteristic
165C2×C8×C11C2×D411yescharacteristic
166C2×C8×C11C2×D411yescharacteristic
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4C22×C411yescharacteristic
170C11×C4⋊C4C22×C411yescharacteristic
171C42×C11—21no—
172C42×C11—21no—
173C42×C11C2411yescharacteristic
174#4326—22no—
175#4325—41no—
176(C2×D11)⋊C4—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⋊Dic11C22×C411yescharacteristic
184C4⋊Dic11C22×C411yescharacteristic
185Dic11⋊C4—21no—
186Dic11⋊C4—21no—
187Dic11⋊C4—21no—
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11C22×C411yescharacteristic
194C4×Dic11C2×D411yescharacteristic
195C4×Dic11#4111yescharacteristic
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8C22×C411yescharacteristic
200C2×C11⋊C8C22×C411yescharacteristic
201C2×C11⋊C8C2×D411yescharacteristic
202C2×C11⋊C8C2×D411yescharacteristic
203#4314—22no—
204#4313—22no—
205#4313—41no—
206#4313—42no—
207#4313—42no—
208C8×D11—42no—
209#3108—111no—
210#2969—111no—
211Q8×M16—111no—
212#1593D1111yescharacteristic, complemented
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—
224C22×D11—21no—
225C22×D11C4×D411yescharacteristic
226Q8×C11—21no—
227Q8×C11—21no—
228Q8×C11—21no—
229Q8×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11C23×C411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×Dic11—21no—
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11C4×D411yescharacteristic
241C2×Dic11C4×D411yescharacteristic
242C2×Dic11C4×D411yescharacteristic
243D44—21no—
244D44—21no—
245D44—81no—
246C4×D11—21no—
247C4×D11—21no—
248C4×D11—21no—
249C4×D11—21no—
250C4×D11—41no—
251C4×D11—42no—
252C4×D11—41no—
253C4×D11—41no—
254C4×D11—81no—
255Dic22—21no—
256Dic22—42no—
257Dic22#13112yes—
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—21no—
261C8×C11—21no—
262C8×C11—41no—
263C8×C11—41no—
264C8×C11—41no—
265C11⋊C8—21no—
266C11⋊C8—21no—
267C11⋊C8—21no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C11⋊C8#13712yes—
272#529—111no—
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—221no—
284#446—221no—
285#446C2×D1111yescharacteristic
286#446C2×D1111yescharacteristic
287C8×Q8—111no—
288C8×Q8—111no—
289C8×Q8—111no—
290C4×Q16—111no—
291C4×Q16C2×D1111yescharacteristic
292C4×SD16—111no—
293C4×SD16—111no—
294#436—111no—
295#436—221no—
296#435—221no—
297C8×D4—111no—
298#433—221no—
299#431—111no—
300#431—111no—
301#431—111no—
302#423—111no—
303#423—221no—
304#405—221no—
305C4×M16—111no—
306C4×M16—221no—
307#335—111no—
308#335—111no—
309#334—111no—
310#334C2×D1111yescharacteristic
311Q8⋊C8—111no—
312Q8⋊C8—111no—
313Q8⋊C8—111no—
314Q8⋊C8—111no—
315Q8⋊C8C2×D1111yescharacteristic
316Q8⋊C8C2×D1111yescharacteristic
317D4⋊C8—111no—
318D4⋊C8—111no—
319#322—111no—
320#322—111no—
321#322C2×D1111yescharacteristic
322C82—111no—
323C22×C11C2×C4×D411yescharacteristic
324C2×D11—21no—
325C2×D11—21no—
326C2×D11—21no—
327C2×D11—41no—
328C2×D11—41no—
329C2×D11—41no—
330C4×C11—21no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11C2×#13111yescharacteristic
336C4×C11#56811yescharacteristic
337C4×C11C2×#13711yescharacteristic
338C4×C11#57511yescharacteristic
339Dic11—22no—
340Dic11—21no—
341Dic11—21no—
342Dic11—21no—
343Dic11—41no—
344Dic11—41no—
345C22×Q8—111no—
346C2×Q16—111no—
347C2×Q16C4×D1111yescharacteristic
348C2×SD16—111no—
349C2×SD16—111no—
350C2×M16—111no—
351C2×M16—111no—
352C2×M16—221no—
353C2×M16—221no—
354C22×C8—221no—
355#126—221no—
356#125—111no—
357#124—111no—
358#123—221no—
359C22⋊Q8—111no—
360#121—111no—
361C4×Q8—111no—
362C4×Q8—111no—
363C4×Q8—111no—
364C4×Q8—221no—
365C4×Q8—221no—
366C4×Q8C22×D1111yescharacteristic
367C4×Q8C22×D1111yescharacteristic
368C4×D4—111no—
369C4×D4—221no—
370#117—221no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—221no—
373C2×C42—111no—
374C2×C42—221no—
375#107—111no—
376#107C4×D1111yescharacteristic
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#103C4×D1111yescharacteristic
398#103C4×D1111yescharacteristic
399#102—111no—
400#102—111no—
401C22⋊C8—111no—
402C22⋊C8—111no—
403C22⋊C8—221no—
404C22⋊C8—221no—
405C22⋊C8—221no—
406C22⋊C8—221no—
407#97—21no—
408#97—21no—
409#97—111no—
410#97—111no—
411#97—221no—
412C4×C8—111no—
413C4×C8—111no—
414C4×C8—111no—
415C4×C8—221no—
416C4×C8—221no—
417C4×C8—221no—
418C4×C8—221no—
419C4×C8C22×D1111yescharacteristic
420C4×C8C22×D1111yescharacteristic
421C4×C8C22×D1111yescharacteristic
422C2×C11#293311yescharacteristic
423C2×C11C4×#13711yescharacteristic
424C2×C11#295711yescharacteristic
425D11—41no—
426D11—81no—
427C2×Q8—111no—
428C2×Q8—221no—
429C2×Q8—222no—
430C2×Q8—441no—
431C2×Q8C2×C4×D1111yescharacteristic
432C2×Q8C2×C4×D1111yescharacteristic
433C2×D4—111no—
434C2×D4—221no—
435C22×C4—111no—
436C22×C4—111no—
437C22×C4—111no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4—221no—
441Q16—41no—
442Q16—222no—
443SD16—222no—
444SD16—441no—
445M16—222no—
446M16—441no—
447M16—442no—
448M16—442no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—111no—
453C2×C8—111no—
454C2×C8—111no—
455C2×C8—111no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—442no—
460C2×C8C2×C4×D1111yescharacteristic
461C2×C8C2×C4×D1111yescharacteristic
462C2×C8D4×D1111yescharacteristic
463C2×C8D4×D1111yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
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⋊C4C2×C4×D1111yescharacteristic
476C4⋊C4C2×C4×D1111yescharacteristic
477C22⋊C4—221no—
478C22⋊C4—221no—
479C22⋊C4—221no—
480C22⋊C4—221no—
481C22⋊C4—221no—
482C42—21no—
483C42—21no—
484C42—111no—
485C42—111no—
486C42—111no—
487C42—221no—
488C42—221no—
489C42—221no—
490C42C23×D1111yescharacteristic
491C11#1801211yescharacteristic, complemented, Sylow
492C23—111no—
493C23—221no—
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—112no—
499Q8—221no—
500Q8—442no—
501D4—221no—
502D4—221no—
503D4—881no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—111no—
509C2×C4—111no—
510C2×C4—111no—
511C2×C4—221no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—221no—
517C2×C4—221no—
518C2×C4—441no—
519C2×C4—442no—
520C2×C4—441no—
521C2×C4—441no—
522C2×C4—881no—
523C2×C4C22×C4×D1111yescharacteristic
524C2×C4C2×D4×D1111yescharacteristic
525C2×C4#41×D1111yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8—112no—
534C8—221no—
535C8—221no—
536C8—221no—
537C8—441no—
538C8—441no—
539C8—441no—
540C22—221no—
541C22—221no—
542C22—221no—
543C22—441no—
544C22—441no—
545C22—441no—
546C22C4×D4×D1111yescharacteristic
547C4—21no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—221no—
553C4—221no—
554C4—222no—
555C4—221no—
556C4—441no—
557C4—441no—
558C4#1062327611yescharacteristic
559C4D11×#13111yescharacteristic
560C4D11×#13711yescharacteristic
561C4#1062330811yescharacteristic
562C2—441no—
563C2—881no—
564C2#1307734511yescharacteristic
565C2#1307743211yescharacteristic
566C2#1307753011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1593C2
socleC22×C11C2×C4×D4
prime radical#66948C2×C4
cosocleC42×C11C24
hypercenter#1593D11
hypocenterC11#18012
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1593

Complements

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

NH ≅ G/Ntype
3. #13077568C2semidirect
4. #13067503C2semidirect
5. #13067485C2semidirect
6. #13067471C2semidirect
7. #13067467C2semidirect
8. #13067458C2semidirect
9. #13067430C2semidirect
10. #13067420C2semidirect
11. #13067403C2semidirect
13. #13067009C2semidirect
14. #13066912C2semidirect
15. C11×#1593C2semidirect
212. #1593D11semidirect
491. C11#18012semidirect

Maximal subgroups

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

subgroupindex
#130787002
#130776222
#130775682
#130675032
#130674852
#130674712
#130674672
#130674582
#130674302
#130674202
#130674032
#130670802
#130670092
#130669122
C11×#15932
#1801211