Finite Group Databasebeta

← #14725726

Subgroups — #14725726

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#13079216C211yesmaximal, characteristic
2#13077772C211yesmaximal, characteristic
3#13077718C211yesmaximal, characteristic, complemented
4#13067522C211yesmaximal, characteristic, complemented
5#13067503C211yesmaximal, characteristic, complemented
6#13067491C211yesmaximal, characteristic, complemented
7#13067490C211yesmaximal, characteristic, complemented
8#13067463C211yesmaximal, characteristic, complemented
9#13067455C211yesmaximal, characteristic, complemented
10#13067431C211yesmaximal, characteristic, complemented
11#13067420C211yesmaximal, characteristic, complemented
12#13067366C211yesmaximal, characteristic, complemented
13#13067025C211yesmaximal, characteristic
14#13066911C211yesmaximal, characteristic, complemented
15C11×#1481C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17#10623010C2211yescharacteristic
18C11×#431C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20#10622724—21no—
21C8×C22⋊D11—21no—
22#10622702C411yescharacteristic
23#10622699C411yescharacteristic
24#10622695C411yescharacteristic
25#10622693C411yescharacteristic
26#10622665C411yescharacteristic
27#10622665C411yescharacteristic
28#10622662C411yescharacteristic
29#10622662C411yescharacteristic
30C4×#4326C2211yescharacteristic
31C4×#4326C2211yescharacteristic
32C4×#4325C2211yescharacteristic
33C4×#4325C2211yescharacteristic
34#10622637—21no—
35#10622637C2211yescharacteristic
36#10622637C2211yescharacteristic
37Q8×C11⋊C8—21no—
38Q8×C11⋊C8C2211yescharacteristic
39Q8×C11⋊C8C2211yescharacteristic
40#10622613—21no—
41#10622613—21no—
42#10622538C2211yescharacteristic
43#10622538C2211yescharacteristic
44C4×#4318C2211yescharacteristic
45#10622453—21no—
46#10622452—21no—
47#10622451C2211yescharacteristic
48#10622447C2211yescharacteristic
49#10622444C2211yescharacteristic
50#10622443C2211yescharacteristic
51C11×Q8⋊C8C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×Q8⋊C8C2211yescharacteristic
54C11×Q8⋊C8C2211yescharacteristic
55#10622118C2211yescharacteristic
56#10622118C2211yescharacteristic
57#10622117C2211yescharacteristic
58#10622117C2211yescharacteristic
59#10622097C2211yescharacteristic
60#10622097C2211yescharacteristic
61#10622094C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C22×C8×C11—21no—
68C11×C4⋊Q8C2×C411yescharacteristic
69C11×C4⋊Q8C2×C411yescharacteristic
70C11×#125—21no—
71C11×C22⋊Q8—21no—
72C11×C22⋊Q8C2×C411yescharacteristic
73C11×C22⋊Q8C2×C411yescharacteristic
74C4×Q8×C11—21no—
75C4×Q8×C11C2311yescharacteristic
76C4×Q8×C11C2311yescharacteristic
77C11×#117—21no—
78C2×C42×C11C2311yescharacteristic
79C2×#4326C2×C411yescharacteristic
80C2×#4326C2×C411yescharacteristic
81C2×#4325C2×C411yescharacteristic
82C2×#4325C2×C411yescharacteristic
83#66983C2×C411yescharacteristic
84#66982—21no—
85C4×C22⋊D11—21no—
86#66977C2×C411yescharacteristic
87C2×#4318C2×C411yescharacteristic
88C2×#4318C2×C411yescharacteristic
89C2×#4313—21no—
90C2×C8×D11—21no—
91#66929—21no—
92#66928C2×C411yescharacteristic
93C4×D44C2311yescharacteristic
94#66925—21no—
95#66923C2×C411yescharacteristic
96C4×Dic22C2311yescharacteristic
97C11×C4⋊C8—21no—
98C11×C4⋊C8—21no—
99C11×C4⋊C8C2311yescharacteristic
100C11×C4⋊C8C2311yescharacteristic
101C11×C22⋊C8—21no—
102C4×C8×C11C2311yescharacteristic
103C4×C8×C11C2311yescharacteristic
104#66899C2×C411yescharacteristic
105#66899C2×C411yescharacteristic
106#66899C2×C411yescharacteristic
107#66899C2×C411yescharacteristic
108C22⋊(C11⋊C8)—21no—
109C22⋊(C11⋊C8)D411yescharacteristic
110C22⋊(C11⋊C8)D411yescharacteristic
111(C2×D11)⋊C8—21no—
112(C2×D11)⋊C8—21no—
113#66879—21no—
114Dic11⋊C8—21no—
115Dic11⋊C8—21no—
116C8×Dic11—21no—
117#66874C2×C411yescharacteristic
118#66874C2×C411yescharacteristic
119#66873C2×C411yescharacteristic
120#66873C2×C411yescharacteristic
121#66872C2×C411yescharacteristic
122#66872C2×C411yescharacteristic
123#66871C2×C411yescharacteristic
124#66871C2×C411yescharacteristic
125C4⋊(C11⋊C8)—21no—
126C4⋊(C11⋊C8)—21no—
127C4⋊(C11⋊C8)—21no—
128C4⋊(C11⋊C8)—21no—
129C4⋊(C11⋊C8)D411yescharacteristic
130C4⋊(C11⋊C8)D411yescharacteristic
131C4⋊(C11⋊C8)C2311yescharacteristic
132C4⋊(C11⋊C8)C2311yescharacteristic
133#66867—21no—
134#66867—21no—
135#66867C2×C411yescharacteristic
136#66867C2×C411yescharacteristic
137C4×C11⋊C8—21no—
138C4×C11⋊C8—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18083—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11C22×C411yescharacteristic
147C2×Q8×C11C22×C411yescharacteristic
148C22×C4×C11C22×C411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11#4111yescharacteristic
151C2×C22⋊D11—21no—
152C2×D44C22×C411yescharacteristic
153C2×C4×D11—21no—
154C2×Dic22C22×C411yescharacteristic
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—81no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4C22×C411yescharacteristic
168C11×C4⋊C4C22×C411yescharacteristic
169C11×C22⋊C4—21no—
170C11×C22⋊C4—21no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11C22×C411yescharacteristic
174C42×C11C2×D411yescharacteristic
175C42×C11#4111yescharacteristic
176C42×C11C2411yescharacteristic
177C22⋊Dic11—21no—
178#4326—22no—
179#4326—41no—
180#4325—22no—
181#4325—41no—
182(C2×D11)⋊C4—21no—
183(C2×D11)⋊C4—21no—
184(C2×D11)⋊C4—21no—
185(C2×D11)⋊C4—21no—
186C4⋊Dic11C22×C411yescharacteristic
187C4⋊Dic11C22×C411yescharacteristic
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192C4×Dic11—21no—
193#4318—22no—
194#4318—41no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8C22×C411yescharacteristic
198C2×C11⋊C8C22×C411yescharacteristic
199C2×C11⋊C8C22×C411yescharacteristic
200C2×C11⋊C8C22×C411yescharacteristic
201C2×C11⋊C8C2×D411yescharacteristic
202C2×C11⋊C8C2×D411yescharacteristic
203C2×C11⋊C8C2×D411yescharacteristic
204C2×C11⋊C8C2×D411yescharacteristic
205#4313—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×Q16—111no—
218#1565—111no—
219#1482—111no—
220#1481D1111yescharacteristic, complemented
221#1453—111no—
222C23×C11C4×D411yescharacteristic
223C22×D11—21no—
224Q8×C11—21no—
225Q8×C11—21no—
226Q8×C11—21no—
227Q8×C11—21no—
228Q8×C11—42no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
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—41no—
238C2×C4×C11C4×D411yescharacteristic
239C2×C4×C11C4×D411yescharacteristic
240C2×C4×C11C4×D411yescharacteristic
241C2×C4×C11C23×C411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C22⋊D11—42no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248D44—21no—
249D44—21no—
250C4×D11—41no—
251C4×D11—41no—
252Dic22—21no—
253Dic22—21no—
254C8×C11—41no—
255C8×C11—41no—
256C8×C11—41no—
257C8×C11—41no—
258C11⋊C8—21no—
259C11⋊C8—21no—
260C11⋊C8—21no—
261C11⋊C8—21no—
262C11⋊C8—21no—
263C11⋊C8—21no—
264C11⋊C8—21no—
265C11⋊C8—41no—
266C11⋊C8—41no—
267C11⋊C8#13112yes—
268#533C2×D1111yescharacteristic
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—111no—
284C8×Q8—111no—
285C8×Q8—221no—
286C4×Q16—111no—
287C4×Q16—111no—
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#431C2×D1111yescharacteristic
300#424—221no—
301C2×C4⋊C8C2×D1111yescharacteristic
302C4×M16—111no—
303#335—111no—
304#335—111no—
305#334—111no—
306#334—111no—
307Q8⋊C8—111no—
308Q8⋊C8—111no—
309Q8⋊C8C2×D1111yescharacteristic
310Q8⋊C8C2×D1111yescharacteristic
311Q8⋊C8C2×D1111yescharacteristic
312Q8⋊C8C2×D1111yescharacteristic
313D4⋊C8—111no—
314D4⋊C8—111no—
315#322—111no—
316#322—111no—
317#322—111no—
318C82—111no—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11C2×C4×D411yescharacteristic
323C2×D11—41no—
324C2×D11—41no—
325C2×D11—41no—
326C4×C11—21no—
327C4×C11—21no—
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11C2×#13111yescharacteristic
335C4×C11#56811yescharacteristic
336C4×C11#57711yescharacteristic
337C4×C11#57811yescharacteristic
338Dic11—41no—
339Dic11—41no—
340Dic11—41no—
341C2×Q16—111no—
342C2×Q16—111no—
343C2×SD16—111no—
344C2×SD16—111no—
345C2×M16—111no—
346C2×M16—111no—
347C2×M16—221no—
348C22×C8—21no—
349C22×C8—221no—
350C4⋊Q8C4×D1111yescharacteristic
351C4⋊Q8C4×D1111yescharacteristic
352#126—221no—
353#125—21no—
354#125—111no—
355#124—111no—
356#123—221no—
357C22⋊Q8—21no—
358C22⋊Q8—111no—
359C22⋊Q8C4×D1111yescharacteristic
360C22⋊Q8C4×D1111yescharacteristic
361#121—111no—
362C4×Q8—21no—
363C4×Q8—111no—
364C4×Q8C22×D1111yescharacteristic
365C4×Q8C22×D1111yescharacteristic
366C4×D4—111no—
367C4×D4—221no—
368#117—21no—
369#117—221no—
370C2×C42C22×D1111yescharacteristic
371#107—111no—
372#107—111no—
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#103—111no—
394#103—111no—
395#102—111no—
396#102—111no—
397C22⋊C8—21no—
398C22⋊C8—111no—
399C22⋊C8—111no—
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—111no—
409C4×C8—111no—
410C4×C8—111no—
411C4×C8—111no—
412C4×C8—221no—
413C4×C8—221no—
414C4×C8—221no—
415C4×C8—221no—
416C4×C8C22×D1111yescharacteristic
417C4×C8C22×D1111yescharacteristic
418C2×C11—41no—
419C2×C11#293511yescharacteristic
420C2×C11#294711yescharacteristic
421C2×C11#295511yescharacteristic
422D11—81no—
423C2×Q8—21no—
424C2×Q8—111no—
425C2×Q8C2×C4×D1111yescharacteristic
426C2×Q8C2×C4×D1111yescharacteristic
427C2×D4—111no—
428C2×D4—221no—
429C22×C4—221no—
430C22×C4C2×C4×D1111yescharacteristic
431C22×C4D4×D1111yescharacteristic
432C22×C4#434111yescharacteristic
433Q16—222no—
434Q16—441no—
435SD16—222no—
436SD16—441no—
437M16—222no—
438M16—441no—
439M16—881no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—81no—
445C2×C8—111no—
446C2×C8—111no—
447C2×C8—111no—
448C2×C8—111no—
449C2×C8—111no—
450C2×C8—111no—
451C2×C8—111no—
452C2×C8—111no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—881no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—111no—
464C4⋊C4—111no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4C2×C4×D1111yescharacteristic
470C4⋊C4C2×C4×D1111yescharacteristic
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—221no—
474C22⋊C4—221no—
475C22⋊C4—221no—
476C22⋊C4—221no—
477C22⋊C4—221no—
478C42—21no—
479C42—21no—
480C42—221no—
481C42C2×C4×D1111yescharacteristic
482C42D4×D1111yescharacteristic
483C42#434111yescharacteristic
484C42C23×D1111yescharacteristic
485C11#1808311yescharacteristic, complemented, Sylow
486C23—221no—
487C23(C22⋊D11)⋊C411yescharacteristic
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—42no—
493Q8—221no—
494Q8—221no—
495D4—221no—
496D4—221no—
497D4—442no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—41no—
507C2×C4—221no—
508C2×C4—221no—
509C2×C4—221no—
510C2×C4—441no—
511C2×C4—441no—
512C2×C4(C22⋊D11)⋊C411yescharacteristic
513C2×C4(C22⋊D11)⋊C411yescharacteristic
514C2×C4(C22⋊D11)⋊C411yescharacteristic
515C2×C4C22×C4×D1111yescharacteristic
516C2×C4C2×D4×D1111yescharacteristic
517C2×C4C2×#434111yescharacteristic
518C8—41no—
519C8—41no—
520C8—41no—
521C8—41no—
522C8—112no—
523C8—221no—
524C8—221no—
525C8—221no—
526C8—221no—
527C8—221no—
528C8—221no—
529C8—221no—
530C8—441no—
531C8—441no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—441no—
536C22—441no—
537C22—441no—
538C22C2×(C22⋊D11)⋊C411yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—441no—
548C4—441no—
549C4—441no—
550C4D11×#13111yescharacteristic
551C4#1062328111yescharacteristic
552C4#1062329311yescharacteristic
553C4#1062329711yescharacteristic
554C2—41no—
555C2—881no—
556C2#1307735611yescharacteristic
557C2#1307745311yescharacteristic
558C2#1307751511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1481C2
socleC22×C11C2×C4×D4
prime radical#66983C2×C4
cosocleC42×C11C24
hypercenter#1481D11
hypocenterC11#18083
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
3. #13077718C2semidirect
4. #13067522C2semidirect
5. #13067503C2semidirect
6. #13067491C2semidirect
7. #13067490C2semidirect
8. #13067463C2semidirect
9. #13067455C2semidirect
10. #13067431C2semidirect
11. #13067420C2semidirect
12. #13067366C2semidirect
14. #13066911C2semidirect
15. C11×#1481C2semidirect
220. #1481D11semidirect
485. C11#18083semidirect

Maximal subgroups

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

subgroupindex
#130792162
#130777722
#130777182
#130675222
#130675032
#130674912
#130674902
#130674632
#130674552
#130674312
#130674202
#130673662
#130670252
#130669112
C11×#14812
#1808311