Finite Group Databasebeta

← #14721521

Subgroups — #14721521

Order 2816.

1202 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082382C211yesmaximal, characteristic
2#13077696C211yesmaximal, characteristic, complemented
3#13071533C211yesmaximal, characteristic, complemented
4#13067175C211yesmaximal, characteristic, complemented
5#13067174C214yesmaximal, complemented
6#13067112C211yesmaximal, characteristic, complemented
7#13067111C211yesmaximal, characteristic, complemented
8#13067109C214yesmaximal, complemented
9C11×#1517C211yesmaximal, characteristic, complemented
10C2×#67043—21no—
11C11×#532C2211yescharacteristic
12#10623364—21no—
13#10623258C412yescomplemented
14#10623249C412yescomplemented
15#10623208—22no—
16#10623128—22no—
17#10623127C2214yes—
18#10623084C412yescomplemented
19#10623083—22no—
20D4×Dic22C412yescomplemented
21C2×#66940—21no—
22#10623008C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C11×#431C2211yescharacteristic
25C11×#382C2211yescharacteristic
26#10622586—21no—
27C4×C4⋊Dic11C2211yescharacteristic
28#10622538C2211yescharacteristic
29#10622443—22no—
30#10622331C2214yes—
31C8×Dic22—22no—
32#10622263C2212yes—
33#10622262C2212yes—
34#10622260—22no—
35C11×#327C2214yes—
36#10622175C2212yes—
37#10622175C2212yes—
38#10622108C2212yes—
39#10622108C2212yes—
40#10622089C2214yes—
41C2×C11×#41—21no—
42#67043—44no—
43#67043—44no—
44C2×Q8×D11—22no—
45C2×#4341—24no—
46C2×#4341—22no—
47C2×#4339—21no—
48C2×#4339—22no—
49C22×Dic22—22no—
50C22×Dic22D411yescharacteristic
51C11×C4⋊Q8C2×C411yescharacteristic
52C11×#127C2×C411yescharacteristic
53C11×#124—21no—
54C11×#121—21no—
55C11×#121C2312yes—
56C4×D4×C11—21no—
57C4×D4×C11C2×C412yes—
58C2×C11×C4⋊C4—21no—
59C2×C42×C11C2311yescharacteristic
60#66999—22no—
61#66993C2×C414yes—
62#66992—24no—
63#66992—24no—
64#66991—22no—
65D4×Dic11C2×C414yes—
66#66983—21no—
67#66983—22no—
68#66983C2312yes—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11D411yescharacteristic
71#66977—22no—
72C2×Dic11⋊C4—22no—
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4D412yes—
75C2×C4×Dic11—21no—
76C2×C4×Dic11—22no—
77C2×C4×Dic11C2312yes—
78#66949—24no—
79#66946C2×C414yes—
80#66941C2×C414yes—
81#66940—44no—
82#66938—24no—
83#66937—24no—
84(C22⋊D11)⋊C4—24no—
85#66931—24no—
86#66928—21no—
87#66927C2×C411yescharacteristic
88C4×D44—21no—
89C4×D44C2×C412yes—
90#66922C2×C411yescharacteristic
91C4×Dic22C2×C412yes—
92C4×Dic22C2×C412yes—
93C4×Dic22D412yes—
94C4×Dic22D412yes—
95C11×C4⋊C8—21no—
96C11×C22⋊C8C2312yes—
97C4×C8×C11—21no—
98C11×#95—21no—
99C11×#95C2312yes—
100C11⋊#95—22no—
101C11⋊#95C2311yescharacteristic
102C11⋊#95C2311yescharacteristic
103C22⋊(C11⋊C8)C2312yes—
104Dic11⋊C8—24no—
105C8×Dic11—24no—
106C4⋊(C11⋊C8)—21no—
107C4×C11⋊C8—21no—
108#17618—111nomaximal, Sylow
109C11×#41—42no—
110C11×#41—42no—
111C2×Q8×C11—21no—
112C2×D4×C11—22no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11C22×C412yes—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2411yescharacteristic
121C2×C22⋊D11—24no—
122C2×C22⋊D11—24no—
123C2×C22⋊D11—22no—
124C22×Dic11—24no—
125C22×Dic11—21no—
126C22×Dic11—21no—
127C22×Dic11C2×D412yes—
128C22×Dic11C2×D412yes—
129Q8×D11—48no—
130#4341—48no—
131#4341—48no—
132#4341—48no—
133#4339—48no—
134#4339—42no—
135#4339—42no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44C22×C412yes—
139C2×C4×D11—24no—
140C2×C4×D11—22no—
141C2×Dic22—24no—
142C2×Dic22—21no—
143C2×Dic22—48no—
144C2×Dic22C22⋊C412yes—
145C2×Dic22C22⋊C412yes—
146C2×Dic22D814yes—
147C2×Dic22SD1614yes—
148C2×C8×C11—22no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—42no—
151C11×C4⋊C4C22×C412yes—
152C11×C22⋊C4—22no—
153C11×C22⋊C4—22no—
154C42×C11C22×C411yescharacteristic
155C42×C11C22×C411yescharacteristic
156C42×C11C2×D411yescharacteristic
157C42×C11C2×D411yescharacteristic
158C22⋊Dic11—24no—
159(C2×D11)⋊C4—24no—
160(C2×D11)⋊C4—22no—
161(C2×D11)⋊C4—22no—
162C4⋊Dic11—21no—
163C4⋊Dic11—42no—
164C4⋊Dic11C22⋊C412yes—
165C4⋊Dic11C22⋊C412yes—
166C4⋊Dic11C22×C412yes—
167Dic11⋊C4—24no—
168Dic11⋊C4—44no—
169Dic11⋊C4—44no—
170Dic11⋊C4C22⋊C414yes—
171Dic11⋊C4C22⋊C414yes—
172C4×Dic11—44no—
173C4×Dic11—42no—
174C4×Dic11C22×C414yes—
175C4×Dic11C2×D414yes—
176C2×C11⋊C8—22no—
177#3497—111no—
178#2982—111no—
179#2351—111no—
180#1517—111no—
181#1517—114no—
182#1517D1111yescharacteristic, complemented
183#1502—111no—
184#1502—114no—
185#1502—111no—
186C23×C11—22no—
187C23×C11C22×D411yescharacteristic
188C22×D11—22no—
189Q8×C11—42no—
190D4×C11—42no—
191D4×C11—42no—
192D4×C11—42no—
193D4×C11—42no—
194D4×C11—81no—
195C2×C4×C11—22no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—44no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11C2×C22⋊C411yescharacteristic
203C2×C4×C11C2×C22⋊C411yescharacteristic
204C2×C4×C11C2×C22⋊C411yescharacteristic
205C2×C4×C11C2×C22⋊C411yescharacteristic
206C2×C4×C11C2×D812yes—
207C2×C4×C11C2×SD1612yes—
208C2×C4×C11C23×C411yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C22⋊D11—42no—
211C22⋊D11—42no—
212C22⋊D11—48no—
213C22⋊D11—84no—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—42no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—48no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11C2×C22⋊C414yes—
224C2×Dic11C2×C22⋊C414yes—
225C2×Dic11C2×D814yes—
226C2×Dic11C2×SD1614yes—
227D44—42no—
228D44—42no—
229D44—81no—
230C4×D11—44no—
231C4×D11—48no—
232Dic22—42no—
233Dic22—48no—
234Dic22#10218yes—
235Dic22#10218yes—
236C8×C11—42no—
237C11⋊C8—42no—
238C2×2−1+4—221no—
239#550—112no—
240#550—112no—
241D4×Q8—112no—
242D4×Q8—112no—
243#548—222no—
244#548—222no—
245#537—222no—
246#537—221no—
247#532—114no—
248#532—111no—
249#532C2×D1111yescharacteristic
250C2×C4×Q8—111no—
251C2×C4×Q8—221no—
252C8×Q8—222no—
253C8×Q8—222no—
254#431—111no—
255#431—114no—
256#431C2×D1111yescharacteristic
257#389—222no—
258#389—221no—
259#382—112no—
260#382C2×D1111yescharacteristic
261C4×C4⋊C4—111no—
262C4×C4⋊C4—112no—
263#327—112no—
264#327—112no—
265#327—112no—
266#327—112no—
267#327—114no—
268#327C2×D1114yes—
269C22×C11—21no—
270C22×C11—21no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—42no—
274C22×C11C22×C22⋊C411yescharacteristic
275C22×C11C22×D811yescharacteristic
276C22×C11C22×SD1611yescharacteristic
277C2×D11—42no—
278C2×D11—42no—
279C2×D11—42no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—21no—
284C4×C11—42no—
285C4×C11—82no—
286C4×C11C2×#10212yes—
287C4×C11C2×#10212yes—
288Dic11—24no—
289Dic11—42no—
290Dic11—42no—
291Dic11—81no—
292Dic11C2×#10218yes—
2932−1+4—444no—
2942−1+4—444no—
295C2×#41—21no—
296C2×#41—222no—
297C2×#41—224no—
298C2×#41—222no—
299C2×#41—221no—
300C22×Q8—111no—
301C22×Q8—222no—
302C22×Q8—222no—
303C4⋊Q8—114no—
304C4⋊Q8—111no—
305C4⋊Q8C4×D1111yescharacteristic
306#127—114no—
307#127—111no—
308#127C4×D1111yescharacteristic
309#124—21no—
310#124—224no—
311#124—221no—
312C22⋊Q8—224no—
313C22⋊Q8—224no—
314C22⋊Q8—222no—
315C22⋊Q8—222no—
316#121—21no—
317#121—112no—
318#121—224no—
319#121—222no—
320#121—222no—
321#121—224no—
322#121—224no—
323#121—221no—
324#121C22×D1112yes—
325C4×Q8—112no—
326C4×Q8—112no—
327C4×Q8—112no—
328C4×Q8—112no—
329C4×Q8—444no—
330C4×D4—21no—
331C4×D4—114no—
332C4×D4—114no—
333C4×D4—112no—
334C4×D4—224no—
335C4×D4—221no—
336C4×D4C4×D1112yes—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—112no—
339C2×C4⋊C4—111no—
340C2×C4⋊C4—222no—
341C2×C4⋊C4—222no—
342C2×C4⋊C4—221no—
343C2×C42—112no—
344C2×C42—222no—
345C2×C42—221no—
346C2×C42C22×D1111yescharacteristic
347C4⋊C8—21no—
348C4⋊C8—224no—
349C4⋊C8—221no—
350C22⋊C8—112no—
351C22⋊C8C22×D1112yes—
352C4×C8—21no—
353C4×C8—224no—
354C4×C8—221no—
355#95—21no—
356#95—111no—
357#95—111no—
358#95—222no—
359#95C22×D1112yes—
360C2×C11—21no—
361C2×C11—21no—
362C2×C11—82no—
363C2×C11#288411yescharacteristic
364C2×C11C22×#10211yescharacteristic
365C2×C11#290111yescharacteristic
366D11—82no—
367#41—42no—
368#41—42no—
369#41—448no—
370#41—448no—
371#41—448no—
372#41—448no—
373#41—442no—
374#41—442no—
375C2×Q8—21no—
376C2×Q8—112no—
377C2×Q8—112no—
378C2×Q8—114no—
379C2×Q8—114no—
380C2×Q8—224no—
381C2×Q8—221no—
382C2×Q8—448no—
383C2×Q8—448no—
384C2×D4—22no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—112no—
388C2×D4—224no—
389C2×D4—224no—
390C2×D4—222no—
391C2×D4—221no—
392C2×D4—221no—
393C2×D4C2×C4×D1112yes—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—112no—
397C22×C4—112no—
398C22×C4—224no—
399C22×C4—224no—
400C22×C4—221no—
401C22×C4—222no—
402C22×C4—221no—
403C22×C4D4×D1111yescharacteristic
404C22×C4D4×D1111yescharacteristic
405C22×C4C23×D1111yescharacteristic
406C2×C8—22no—
407C2×C8—222no—
408C4⋊C4—21no—
409C4⋊C4—42no—
410C4⋊C4—114no—
411C4⋊C4—114no—
412C4⋊C4—112no—
413C4⋊C4—112no—
414C4⋊C4—112no—
415C4⋊C4—224no—
416C4⋊C4—221no—
417C4⋊C4—444no—
418C4⋊C4—444no—
419C4⋊C4—442no—
420C4⋊C4C2×C4×D1112yes—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C22⋊C4—224no—
424C22⋊C4—224no—
425C22⋊C4—222no—
426C22⋊C4—222no—
427C42—114no—
428C42—114no—
429C42—444no—
430C42—442no—
431C42C2×C4×D1111yescharacteristic
432C42C2×C4×D1111yescharacteristic
433C42D4×D1111yescharacteristic
434C42D4×D1111yescharacteristic
435C11#1761811yescharacteristic, complemented, Sylow
436C23—22no—
437C23—222no—
438C23C2×D4×D1111yescharacteristic
439Q8—42no—
440Q8—118no—
441Q8—118no—
442Q8—448no—
443Q8—442no—
444D4—42no—
445D4—42no—
446D4—42no—
447D4—42no—
448D4—81no—
449D4—442no—
450D4—448no—
451D4—442no—
452D4—442no—
453D4—442no—
454D4—881no—
455D4—884no—
456C2×C4—22no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—44no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—114no—
464C2×C4—114no—
465C2×C4—114no—
466C2×C4—114no—
467C2×C4—222no—
468C2×C4—222no—
469C2×C4—448no—
470C2×C4—448no—
471C2×C4—442no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—444no—
475C2×C4—441no—
476C2×C4—441no—
477C2×C4—441no—
478C2×C4C22⋊C4×D1111yescharacteristic
479C2×C4C22⋊C4×D1111yescharacteristic
480C2×C4C22⋊C4×D1111yescharacteristic
481C2×C4C22⋊C4×D1111yescharacteristic
482C2×C4D8×D1112yes—
483C2×C4SD16×D1112yes—
484C2×C4C22×C4×D1111yescharacteristic
485C2×C4C2×D4×D1111yescharacteristic
486C8—42no—
487C8—442no—
488C22—21no—
489C22—21no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—442no—
494C22—442no—
495C22—442no—
496C22C2×C22⋊C4×D1111yescharacteristic
497C22C2×D8×D1111yescharacteristic
498C22C2×SD16×D1111yescharacteristic
499C4—21no—
500C4—21no—
501C4—21no—
502C4—21no—
503C4—42no—
504C4—82no—
505C4—118no—
506C4—224no—
507C4—442no—
508C4—442no—
509C4—881no—
510C4D11×#10212yes—
511C4D11×#10212yes—
512C2—21no—
513C2—21no—
514C2—82no—
515C2—882no—
516C2#1307707811yescharacteristic
517C2C2×D11×#10211yescharacteristic
518C2#1307716211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1517C2
socleC22×C11C22×C22⋊C4
prime radical#13082382C2
cosocleC22×C4×C11C24
hypercenter#1517D11
hypocenterC11#17618
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1517

Complements

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

NH ≅ G/Ntype
2. #13077696C2semidirect
3. #13071533C2semidirect
4. #13067175C2semidirect
5. #13067174C2semidirect
6. #13067112C2semidirect
7. #13067111C2semidirect
8. #13067109C2semidirect
9. C11×#1517C2semidirect
13. #10623258C4semidirect
14. #10623249C4semidirect
18. #10623084C4semidirect
20. D4×Dic22C4semidirect
182. #1517D11semidirect
435. C11#17618semidirect

Maximal subgroups

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

subgroupindex
#130823822
#130776962
#130715332
#130671752
#130671742
#130671122
#130671112
#130671092
C11×#15172
#1761811