Finite Group Databasebeta

← #14725725

Subgroups — #14725725

Order 2816.

572 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079220C211yesmaximal, characteristic
2#13077775C211yesmaximal, characteristic
3#13077716C211yesmaximal, characteristic, complemented
4#13067525C211yesmaximal, characteristic, complemented
5#13067508C211yesmaximal, characteristic, complemented
6#13067494C211yesmaximal, characteristic, complemented
7#13067487C211yesmaximal, characteristic, complemented
8#13067469C211yesmaximal, characteristic, complemented
9#13067455C211yesmaximal, characteristic, complemented
10#13067427C211yesmaximal, characteristic, complemented
11#13067367C211yesmaximal, characteristic, complemented
12#13067023C211yesmaximal, characteristic
13#13067017C211yesmaximal, characteristic, complemented
14#13066910C211yesmaximal, characteristic, complemented
15C8×C11×Q16C211yesmaximal, characteristic, complemented
16#10623111C2211yescharacteristic
17#10623109C2211yescharacteristic
18C8×Q8×C11C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C4×C11×Q16C2211yescharacteristic
21#10622803C411yescharacteristic
22#10622802C411yescharacteristic
23C4×#4326C2211yescharacteristic
24C4×#4325C2211yescharacteristic
25#10622637C2211yescharacteristic
26#10622637C2211yescharacteristic
27#10622499C411yescharacteristic
28#10622489C411yescharacteristic
29#10622453—21no—
30#10622452—21no—
31#10622449—21no—
32#10622447C2211yescharacteristic
33#10622446C2211yescharacteristic
34D11×C4⋊C8C2211yescharacteristic
35#10622443C2211yescharacteristic
36#10622441—21no—
37#10622429C411yescharacteristic
38#10622425C411yescharacteristic
39#10622410C411yescharacteristic
40#10622408C411yescharacteristic
41C4×#4314C2211yescharacteristic
42#10622303—21no—
43#10622303—21no—
44#10622301C2211yescharacteristic
45C4×#4313C2211yescharacteristic
46C8×D44—21no—
47#10622298C2211yescharacteristic
48#10622298C2211yescharacteristic
49#10622292C2211yescharacteristic
50C8×Dic22—21no—
51C11×#335C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×Q8⋊C8C2211yescharacteristic
54C82×C11C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56Q8⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622095C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622093C2211yescharacteristic
65#10622092C2211yescharacteristic
66#10622092C2211yescharacteristic
67C2×C11×Q16C2×C411yescharacteristic
68C4×Q8×C11C2311yescharacteristic
69C4×Q8×C11C2311yescharacteristic
70#67000C2×C411yescharacteristic
71#66999C2×C411yescharacteristic
72#66999C2×C411yescharacteristic
73#66997C2×C411yescharacteristic
74C2×#4326C2×C411yescharacteristic
75C2×#4325C2×C411yescharacteristic
76C2×#4314C2×C411yescharacteristic
77C2×#4313—21no—
78C2×#4313C2×C411yescharacteristic
79C2×#4313C2×C411yescharacteristic
80C2×C8×D11—21no—
81C2×C8×D11—21no—
82#66951—21no—
83#66950C2×C411yescharacteristic
84#66949—21no—
85#66948C2×C411yescharacteristic
86#66947—21no—
87#66943C2×C411yescharacteristic
88#66942—21no—
89#66941C2×C411yescharacteristic
90C4×D44—21no—
91C4×D44C2311yescharacteristic
92#66925—21no—
93#66925—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
104C4×C8×C11—21no—
105C4×C8×C11—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)⋊C8D411yescharacteristic
117(C2×D11)⋊C8D411yescharacteristic
118#66881C2×C411yescharacteristic
119#66880C2×C411yescharacteristic
120#66879—21no—
121#66879C2×C411yescharacteristic
122#66879C2×C411yescharacteristic
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127Dic11⋊C8D411yescharacteristic
128Dic11⋊C8D411yescharacteristic
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—
140#66867—21no—
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18083—111nomaximal, Sylow
145C2×Q8×C11C22×C411yescharacteristic
146C2×Q8×C11C22×C411yescharacteristic
147C2×D44—21no—
148C2×D44C22×C411yescharacteristic
149C2×C4×D11—21no—
150C2×C4×D11C22×C411yescharacteristic
151C2×C4×D11C2×D411yescharacteristic
152C2×C4×D11#4111yescharacteristic
153C2×Dic22—21no—
154C2×Dic22C22×C411yescharacteristic
155C11×Q16—22no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11C22×C411yescharacteristic
160C2×C8×C11C22×C411yescharacteristic
161C2×C8×C11C2×D411yescharacteristic
162C2×C8×C11C2×D411yescharacteristic
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4C22×C411yescharacteristic
166C11×C4⋊C4C22×C411yescharacteristic
167C42×C11—21no—
168C42×C11—21no—
169C42×C11C2411yescharacteristic
170#4326—41no—
171#4325—41no—
172(C2×D11)⋊C4—21no—
173(C2×D11)⋊C4—21no—
174(C2×D11)⋊C4—21no—
175(C2×D11)⋊C4—21no—
176(C2×D11)⋊C4—21no—
177(C2×D11)⋊C4—21no—
178(C2×D11)⋊C4—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11C22×C411yescharacteristic
182C4⋊Dic11C22×C411yescharacteristic
183Dic11⋊C4—21no—
184Dic11⋊C4—21no—
185Dic11⋊C4—21no—
186Dic11⋊C4—21no—
187Dic11⋊C4—21no—
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190C4×Dic11—21no—
191C4×Dic11C22×C411yescharacteristic
192C4×Dic11C2×D411yescharacteristic
193C4×Dic11#4111yescharacteristic
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8C22×C411yescharacteristic
198C2×C11⋊C8C22×C411yescharacteristic
199C2×C11⋊C8C2×D411yescharacteristic
200C2×C11⋊C8C2×D411yescharacteristic
201#4314—22no—
202#4313—22no—
203#4313—41no—
204#4313—81no—
205C8×D11—81no—
206C8×D11—81no—
207#3172—111no—
208#2994—111no—
209#2986—111no—
210#1593—111no—
211#1590—111no—
212#1588—111no—
213#1587—111no—
214#1584—111no—
215#1582—111no—
216SD16⋊C8—111no—
217C8×Q16D1111yescharacteristic, complemented
218#1565—111no—
219#1482—111no—
220#1481—111no—
221#1453—111no—
222C22×D11—21no—
223C22×D11C4×D411yescharacteristic
224Q8×C11—21no—
225Q8×C11—21no—
226Q8×C11—21no—
227Q8×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11C23×C411yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×Dic11—21no—
236C2×Dic11—21no—
237C2×Dic11—21no—
238C2×Dic11C4×D411yescharacteristic
239C2×Dic11C4×D411yescharacteristic
240C2×Dic11C4×D411yescharacteristic
241D44—21no—
242D44—21no—
243D44—42no—
244C4×D11—21no—
245C4×D11—21no—
246C4×D11—21no—
247C4×D11—21no—
248C4×D11—41no—
249C4×D11—41no—
250C4×D11—41no—
251Dic22—21no—
252Dic22—21no—
253Dic22—42no—
254C8×C11—21no—
255C8×C11—21no—
256C8×C11—21no—
257C8×C11—41no—
258C8×C11—41no—
259C8×C11—41no—
260C8×C11#13112yes—
261C11⋊C8—21no—
262C11⋊C8—21no—
263C11⋊C8—21no—
264C11⋊C8—21no—
265C11⋊C8—41no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268#533—111no—
269#529—111no—
270#501—111no—
271#497—111no—
272#491—111no—
273#489—111no—
274#470—111no—
275#470—111no—
276#468—111no—
277#468—111no—
278#446—111no—
279#446—111no—
280#446—111no—
281#446—221no—
282C8×Q8—111no—
283C8×Q8—221no—
284C8×Q8C2×D1111yescharacteristic
285C8×Q8C2×D1111yescharacteristic
286C4×Q16—111no—
287C4×Q16C2×D1111yescharacteristic
288C4×SD16—111no—
289C4×SD16—111no—
290#436—111no—
291#435—221no—
292C8×D4—111no—
293C8×D4—221no—
294#433—221no—
295#433—221no—
296#433—221no—
297#431—111no—
298#431—111no—
299#431—111no—
300#424—221no—
301C2×C4⋊C8—111no—
302C4×M16—111no—
303#335—111no—
304#335C2×D1111yescharacteristic
305#334—111no—
306#334—111no—
307Q8⋊C8—111no—
308Q8⋊C8—111no—
309Q8⋊C8—111no—
310Q8⋊C8—111no—
311Q8⋊C8C2×D1111yescharacteristic
312Q8⋊C8C2×D1111yescharacteristic
313D4⋊C8—111no—
314D4⋊C8—111no—
315#322—111no—
316#322—111no—
317#322—111no—
318C82C2×D1111yescharacteristic
319C22×C11C2×C4×D411yescharacteristic
320C2×D11—21no—
321C2×D11—21no—
322C2×D11—21no—
323C2×D11—41no—
324C2×D11—41no—
325C2×D11—41no—
326C4×C11—21no—
327C4×C11—41no—
328C4×C11—41no—
329C4×C11—41no—
330C4×C11—41no—
331C4×C11C2×#13111yescharacteristic
332C4×C11#56811yescharacteristic
333C4×C11#57711yescharacteristic
334C4×C11#57811yescharacteristic
335Dic11—21no—
336Dic11—21no—
337Dic11—21no—
338Dic11—41no—
339Dic11—41no—
340Dic11—41no—
341C2×Q16—111no—
342C2×Q16C4×D1111yescharacteristic
343C2×SD16—111no—
344C2×SD16—111no—
345C2×M16—111no—
346C2×M16—111no—
347C2×M16—221no—
348C22×C8—221no—
349C22×C8—221no—
350C4⋊Q8—111no—
351C4⋊Q8—111no—
352#126—221no—
353#125—111no—
354#125—221no—
355#124—111no—
356#123—221no—
357C22⋊Q8—111no—
358C22⋊Q8—111no—
359C22⋊Q8—111no—
360C22⋊Q8—221no—
361#121—111no—
362C4×Q8—111no—
363C4×Q8—221no—
364C4×Q8C22×D1111yescharacteristic
365C4×Q8C22×D1111yescharacteristic
366C4×D4—111no—
367C4×D4—221no—
368#117—221no—
369#117—221no—
370C2×C42—111no—
371#107—111no—
372#107C4×D1111yescharacteristic
373#106—111no—
374#106—111no—
375C4⋊C8—21no—
376C4⋊C8—21no—
377C4⋊C8—111no—
378C4⋊C8—111no—
379C4⋊C8—111no—
380C4⋊C8—111no—
381C4⋊C8—221no—
382C4⋊C8—221no—
383C4⋊C8—221no—
384C4⋊C8—221no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387C4⋊C8C22×D1111yescharacteristic
388C4⋊C8C22×D1111yescharacteristic
389#103—111no—
390#103—111no—
391#103—111no—
392#103—111no—
393#103C4×D1111yescharacteristic
394#103C4×D1111yescharacteristic
395#102—111no—
396#102—111no—
397C22⋊C8—111no—
398C22⋊C8—111no—
399C22⋊C8—221no—
400C22⋊C8—221no—
401C22⋊C8—221no—
402C22⋊C8—221no—
403#97—111no—
404#97—111no—
405#97—221no—
406#97—221no—
407#97—221no—
408C4×C8—21no—
409C4×C8—21no—
410C4×C8—111no—
411C4×C8—111no—
412C4×C8—111no—
413C4×C8—221no—
414C4×C8—221no—
415C4×C8C22×D1111yescharacteristic
416C4×C8C22×D1111yescharacteristic
417C4×C8C22×D1111yescharacteristic
418C2×C11#293511yescharacteristic
419C2×C11#294711yescharacteristic
420C2×C11#295511yescharacteristic
421D11—41no—
422D11—81no—
423C2×Q8—111no—
424C2×Q8—221no—
425C2×Q8C2×C4×D1111yescharacteristic
426C2×Q8C2×C4×D1111yescharacteristic
427C2×D4—111no—
428C2×D4—221no—
429C22×C4—111no—
430C22×C4—111no—
431C22×C4—111no—
432C22×C4—221no—
433Q16—22no—
434Q16—441no—
435SD16—222no—
436SD16—441no—
437M16—222no—
438M16—441no—
439M16—881no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—111no—
444C2×C8—111no—
445C2×C8—111no—
446C2×C8—111no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—881no—
451C2×C8—881no—
452C2×C8C2×C4×D1111yescharacteristic
453C2×C8C2×C4×D1111yescharacteristic
454C2×C8D4×D1111yescharacteristic
455C2×C8D4×D1111yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—111no—
459C4⋊C4—111no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4C2×C4×D1111yescharacteristic
470C4⋊C4C2×C4×D1111yescharacteristic
471C22⋊C4—221no—
472C22⋊C4—221no—
473C22⋊C4—221no—
474C22⋊C4—221no—
475C22⋊C4—221no—
476C22⋊C4—221no—
477C22⋊C4—221no—
478C42—21no—
479C42—21no—
480C42—111no—
481C42—111no—
482C42—111no—
483C42—221no—
484C42C23×D1111yescharacteristic
485C11#1808311yescharacteristic, complemented, Sylow
486C23—111no—
487C23—221no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—221no—
493Q8—221no—
494Q8—442no—
495D4—221no—
496D4—221no—
497D4—442no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—111no—
503C2×C4—111no—
504C2×C4—111no—
505C2×C4—221no—
506C2×C4—221no—
507C2×C4—221no—
508C2×C4—221no—
509C2×C4—221no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—441no—
513C2×C4—441no—
514C2×C4—441no—
515C2×C4C22×C4×D1111yescharacteristic
516C2×C4C2×D4×D1111yescharacteristic
517C2×C4#41×D1111yescharacteristic
518C8—21no—
519C8—21no—
520C8—21no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8—221no—
525C8—221no—
526C8—221no—
527C8—221no—
528C8—441no—
529C8—441no—
530C8—441no—
531C8#6695412yes—
532C22—221no—
533C22—221no—
534C22—221no—
535C22—441no—
536C22—441no—
537C22—441no—
538C22C4×D4×D1111yescharacteristic
539C4—21no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—41no—
544C4—221no—
545C4—221no—
546C4—221no—
547C4—441no—
548C4—441no—
549C4—441no—
550C4C2×#6695411yescharacteristic
551C4#1062328111yescharacteristic
552C4#1062329711yescharacteristic
553C4#1062330111yescharacteristic
554C2—441no—
555C2—881no—
556C2#1307735511yescharacteristic
557C2#1307745411yescharacteristic
558C2#1307751411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC8×C11×Q16C2
socleC22×C11C2×C4×D4
prime radical#66948C2×C4
cosocleC42×C11C24
hypercenterC8×Q16D11
hypocenterC11#18083
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×Q16

Complements

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

NH ≅ G/Ntype
3. #13077716C2semidirect
4. #13067525C2semidirect
5. #13067508C2semidirect
6. #13067494C2semidirect
7. #13067487C2semidirect
8. #13067469C2semidirect
9. #13067455C2semidirect
10. #13067427C2semidirect
11. #13067367C2semidirect
13. #13067017C2semidirect
14. #13066910C2semidirect
15. C8×C11×Q16C2semidirect
217. C8×Q16D11semidirect
485. C11#18083semidirect

Maximal subgroups

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

subgroupindex
#130792202
#130777752
#130777162
#130675252
#130675082
#130674942
#130674872
#130674692
#130674552
#130674272
#130673672
#130670232
#130670172
#130669102
C8×C11×Q162
#1808311