Finite Group Databasebeta

← #14724168

Subgroups — #14724168

Order 2816.

568 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078692C211yesmaximal, characteristic
2#13077699C211yesmaximal, characteristic, complemented
3#13067523C211yesmaximal, characteristic, complemented
4#13067518C211yesmaximal, characteristic, complemented
5#13067511C211yesmaximal, characteristic, complemented
6#13067504C211yesmaximal, characteristic, complemented
7#13067487C211yesmaximal, characteristic, complemented
8#13067473C211yesmaximal, characteristic, complemented
9#13067466C211yesmaximal, characteristic, complemented
10#13067452C211yesmaximal, characteristic, complemented
11#13067407C211yesmaximal, characteristic, complemented
12#13067044C211yesmaximal, characteristic, complemented
13#13067024C211yesmaximal, characteristic
14#13066916C211yesmaximal, characteristic, complemented
15C11×#2993C211yesmaximal, 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×#424—21no—
27C11×#423C2211yescharacteristic
28#10622676C411yescharacteristic
29#10622676C411yescharacteristic
30#10622667C411yescharacteristic
31#10622667C411yescharacteristic
32#10622663C411yescharacteristic
33#10622656C411yescharacteristic
34#10622653C411yescharacteristic
35#10622646C411yescharacteristic
36C4×#4326C2211yescharacteristic
37C4×#4326C2211yescharacteristic
38C4×#4324C2211yescharacteristic
39C4×#4324C2211yescharacteristic
40#10622538C2211yescharacteristic
41#10622538C2211yescharacteristic
42#10622538C2211yescharacteristic
43#10622444—21no—
44#10622444—21no—
45#10622332—21no—
46#10622332—21no—
47#10622292C2211yescharacteristic
48#10622292C2211yescharacteristic
49#10622292C2211yescharacteristic
50#10622292C2211yescharacteristic
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×M16—21no—
70C22×C8×C11—21no—
71C11×#126—21no—
72C11×#125C2×C411yescharacteristic
73C11×#124C2×C411yescharacteristic
74C11×#123—21no—
75C11×C22⋊Q8C2×C411yescharacteristic
76C11×#121C2×C411yescharacteristic
77C4×Q8×C11C2311yescharacteristic
78C4×D4×C11—21no—
79C4×D4×C11C2311yescharacteristic
80C11×#117—21no—
81C2×C42×C11C2311yescharacteristic
82C2×#4326C2×C411yescharacteristic
83C2×#4326C2×C411yescharacteristic
84C2×#4324C2×C411yescharacteristic
85C2×#4324C2×C411yescharacteristic
86C2×C4⋊Dic11C2×C411yescharacteristic
87C2×Dic11⋊C4—21no—
88C2×C4×Dic11—21no—
89C4×Dic22—21no—
90C4×Dic22—21no—
91C4×Dic22C2×C411yescharacteristic
92C4×Dic22C2×C411yescharacteristic
93C4×Dic22C2311yescharacteristic
94C4×Dic22C2311yescharacteristic
95C11×C4⋊C8—21no—
96C11×C4⋊C8—21no—
97C11×C4⋊C8—21no—
98C11×C4⋊C8D411yescharacteristic
99C11×C4⋊C8D411yescharacteristic
100C11×C4⋊C8C2311yescharacteristic
101C11×C4⋊C8C2311yescharacteristic
102C11×C22⋊C8—21no—
103C11×C22⋊C8—21no—
104C11×C22⋊C8D411yescharacteristic
105C11×C22⋊C8D411yescharacteristic
106C11×#97—21no—
107C4×C8×C11—21no—
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110#66899C2×C411yescharacteristic
111#66899C2×C411yescharacteristic
112#66896C2×C411yescharacteristic
113#66896C2×C411yescharacteristic
114C22⋊(C11⋊C8)—21no—
115C22⋊(C11⋊C8)—21no—
116C22⋊(C11⋊C8)C2×C411yescharacteristic
117C22⋊(C11⋊C8)C2×C411yescharacteristic
118#66879—21no—
119#66879—21no—
120#66879—21no—
121#66879—21no—
122Dic11⋊C8—21no—
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125Dic11⋊C8—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)C2×C411yescharacteristic
136C4⋊(C11⋊C8)C2×C411yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4×C11⋊C8—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17947—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—21no—
155C2×Dic22—41no—
156C2×Dic22—41no—
157C2×Dic22C22×C411yescharacteristic
158C2×Dic22C22×C411yescharacteristic
159C11×M16—81no—
160C11×M16—81no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—81no—
164C2×C8×C11C2×D411yescharacteristic
165C2×C8×C11C2×D411yescharacteristic
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2×D411yescharacteristic
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4C22×C411yescharacteristic
173C11×C4⋊C4C22×C411yescharacteristic
174C11×C22⋊C4—21no—
175C11×C22⋊C4—21no—
176C11×C22⋊C4—21no—
177C11×C22⋊C4—21no—
178C11×C22⋊C4—21no—
179C42×C11—21no—
180C42×C11C22×C411yescharacteristic
181C42×C11C2×D411yescharacteristic
182C42×C11#4111yescharacteristic
183C42×C11C2411yescharacteristic
184#4326—41no—
185#4326—41no—
186#4324—41no—
187#4324—41no—
188C4⋊Dic11—21no—
189C4⋊Dic11C22×C411yescharacteristic
190C4⋊Dic11C22×C411yescharacteristic
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194Dic11⋊C4—21no—
195C4×Dic11—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⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C22×C411yescharacteristic
207#3108—111no—
208#2993D1111yescharacteristic
209#2983—111no—
210#1593—111no—
211#1592—111no—
212#1591—111no—
213#1590—111no—
214#1587—111no—
215#1585—111no—
216#1584—111no—
217#1582—111no—
218#1574—111no—
219#1487—111no—
220#1482—111no—
221#1454—111no—
222C23×C11—21no—
223C23×C11C4×D411yescharacteristic
224Q8×C11—21no—
225Q8×C11—21no—
226D4×C11—21no—
227D4×C11—21no—
228D4×C11—81no—
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—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11C4×D411yescharacteristic
240C2×C4×C11C4×D411yescharacteristic
241C2×C4×C11C4×D411yescharacteristic
242C2×C4×C11C23×C411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—42no—
250C2×Dic11—81no—
251Dic22—21no—
252Dic22—21no—
253Dic22—21no—
254Dic22—21no—
255Dic22—42no—
256C8×C11—21no—
257C8×C11—21no—
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—41no—
261C8×C11—41no—
262C11⋊C8—21no—
263C11⋊C8—21no—
264C11⋊C8—21no—
265C11⋊C8—21no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270#529C2×D1111yescharacteristic
271C2×C4×Q8—111no—
272#483—111no—
273#480—111no—
274#479—111no—
275#479—111no—
276#464—111no—
277#464—111no—
278#451—111no—
279#448—111no—
280#446—111no—
281#446—111no—
282#446—111no—
283#446—111no—
284#446—221no—
285#446—221no—
286#446C2×D1111yescharacteristic
287C8×Q8C2×D1111yescharacteristic
288C4×Q16—111no—
289C4×Q16—111no—
290C4×SD16—111no—
291C4×SD16—111no—
292#436—21no—
293#436C2×D1111yescharacteristic
294#435—21no—
295C8×D4C2×D1111yescharacteristic
296#433—21no—
297#432—221no—
298#432—221no—
299#431—111no—
300#431—111no—
301#431—111no—
302#431C2×D1111yescharacteristic
303#424—21no—
304#423C2×D1111yescharacteristic
305#335—111no—
306#335—111no—
307#334—111no—
308#334—111no—
309Q8⋊C8—111no—
310Q8⋊C8—111no—
311Q8⋊C8—111no—
312Q8⋊C8—111no—
313Q8⋊C8—111no—
314Q8⋊C8—111no—
315D4⋊C8—111no—
316D4⋊C8—111no—
317#322—111no—
318#322—111no—
319#322—111no—
320C82—111no—
321C22×C11—21no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—41no—
325C22×C11—41no—
326C22×C11—41no—
327C22×C11C2×C4×D411yescharacteristic
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11#56811yescharacteristic
336C4×C11#56811yescharacteristic
337C4×C11#57711yescharacteristic
338C4×C11#57811yescharacteristic
339Dic11—41no—
340Dic11—41no—
341Dic11—41no—
342Dic11—41no—
343C22×Q8—111no—
344C2×Q16—111no—
345C2×Q16—111no—
346C2×SD16—111no—
347C2×SD16—111no—
348C2×M16—21no—
349C2×M16—21no—
350C22×C8—21no—
351#126—21no—
352#125C4×D1111yescharacteristic
353#124C4×D1111yescharacteristic
354#123—21no—
355C22⋊Q8C4×D1111yescharacteristic
356#121C4×D1111yescharacteristic
357C4×Q8—111no—
358C4×Q8—111no—
359C4×Q8—111no—
360C4×Q8—111no—
361C4×Q8—221no—
362C4×Q8—221no—
363C4×Q8C22×D1111yescharacteristic
364C4×D4—21no—
365C4×D4C22×D1111yescharacteristic
366#117—21no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—221no—
369C2×C42—221no—
370C2×C42C22×D1111yescharacteristic
371#107—111no—
372#107—111no—
373#106—111no—
374#106—111no—
375C4⋊C8—21no—
376C4⋊C8—21no—
377C4⋊C8—21no—
378C4⋊C8—111no—
379C4⋊C8—111no—
380C4⋊C8—111no—
381C4⋊C8—111no—
382C4⋊C8—221no—
383C4⋊C8—221no—
384C4⋊C8—221no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387C4⋊C8C22⋊D1111yescharacteristic
388C4⋊C8C22⋊D1111yescharacteristic
389C4⋊C8C22×D1111yescharacteristic
390C4⋊C8C22×D1111yescharacteristic
391#103—111no—
392#103—111no—
393#103—111no—
394#103—111no—
395#103—111no—
396#103—111no—
397#102—111no—
398#102—111no—
399C22⋊C8—21no—
400C22⋊C8—21no—
401C22⋊C8—111no—
402C22⋊C8—111no—
403C22⋊C8—221no—
404C22⋊C8—221no—
405C22⋊C8C22⋊D1111yescharacteristic
406C22⋊C8C22⋊D1111yescharacteristic
407#97—21no—
408#97—221no—
409#97—221no—
410#97—221no—
411#97—221no—
412C4×C8—21no—
413C4×C8—111no—
414C4×C8—111no—
415C4×C8—111no—
416C4×C8—111no—
417C4×C8—221no—
418C4×C8C22×D1111yescharacteristic
419C4×C8C22×D1111yescharacteristic
420C2×C11—41no—
421C2×C11—81no—
422C2×C11#293011yescharacteristic
423C2×C11#294711yescharacteristic
424C2×C11#295711yescharacteristic
425C2×Q8—111no—
426C2×Q8—111no—
427C2×Q8—221no—
428C2×Q8—441no—
429C2×Q8—441no—
430C2×Q8C2×C4×D1111yescharacteristic
431C2×D4—21no—
432C2×D4C2×C4×D1111yescharacteristic
433C22×C4—21no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4C2×C4×D1111yescharacteristic
437C22×C4#433911yescharacteristic
438C22×C4C2×C22⋊D1111yescharacteristic
439Q16—441no—
440Q16—441no—
441SD16—441no—
442SD16—441no—
443M16—81no—
444M16—81no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—81no—
448C2×C8—111no—
449C2×C8—111no—
450C2×C8—111no—
451C2×C8—111no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8C2×C22⋊D1111yescharacteristic
457C2×C8C2×C22⋊D1111yescharacteristic
458C2×C8C2×C22⋊D1111yescharacteristic
459C2×C8C2×C22⋊D1111yescharacteristic
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—111no—
465C4⋊C4—111no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4C2×C4×D1111yescharacteristic
472C4⋊C4C2×C4×D1111yescharacteristic
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C42—21no—
479C42—221no—
480C42—221no—
481C42—221no—
482C42—221no—
483C42C2×C4×D1111yescharacteristic
484C42#433911yescharacteristic
485C42C2×C22⋊D1111yescharacteristic
486C42C23×D1111yescharacteristic
487C11#1794711yescharacteristic, complemented, Sylow
488C23—21no—
489C23C4×C22⋊D1111yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—221no—
493Q8—221no—
494Q8—221no—
495Q8—221no—
496Q8—442no—
497D4—21no—
498D4—21no—
499D4—81no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—442no—
515C2×C4—881no—
516C2×C4C4×C22⋊D1111yescharacteristic
517C2×C4C4×C22⋊D1111yescharacteristic
518C2×C4C4×C22⋊D1111yescharacteristic
519C2×C4C22×C4×D1111yescharacteristic
520C2×C4C2×#433911yescharacteristic
521C2×C4C22×C22⋊D1111yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—221no—
529C8—221no—
530C8—221no—
531C8—221no—
532C8—441no—
533C8—441no—
534C8—441no—
535C8—441no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22C2×C4×C22⋊D1111yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—441no—
551C4—441no—
552C4—441no—
553C4—441no—
554C4#1062328111yescharacteristic
555C4#1062328111yescharacteristic
556C4#1062336711yescharacteristic
557C4#1062336911yescharacteristic
558C2—41no—
559C2—81no—
560C2#1307731711yescharacteristic
561C2#1307745511yescharacteristic
562C2#1307753111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2993C2
socleC22×C11C2×C4×D4
prime radicalC11×#121C2×C4
cosocleC42×C11C24
hypercenter#2993D11
hypocenterC11#17947
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2993

Complements

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

NH ≅ G/Ntype
2. #13077699C2semidirect
3. #13067523C2semidirect
4. #13067518C2semidirect
5. #13067511C2semidirect
6. #13067504C2semidirect
7. #13067487C2semidirect
8. #13067473C2semidirect
9. #13067466C2semidirect
10. #13067452C2semidirect
11. #13067407C2semidirect
12. #13067044C2semidirect
14. #13066916C2semidirect
487. C11#17947semidirect

Maximal subgroups

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

subgroupindex
#130786922
#130776992
#130675232
#130675182
#130675112
#130675042
#130674872
#130674732
#130674662
#130674522
#130674072
#130670442
#130670242
#130669162
C11×#29932
#1794711