Finite Group Databasebeta

← #14916652

Subgroups — #14916652

Order 2816.

2238 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic
2#13071797C211yesmaximal, characteristic, complemented
3#13071796C211yesmaximal, characteristic, complemented
4#13071796C211yesmaximal, characteristic, complemented
5#13071671C214yesmaximal, complemented
6#13071490C214yesmaximal
7#13071450C214yesmaximal
8#13071359C214yesmaximal, complemented
9#13071331C214yesmaximal, complemented
10#13071215C214yesmaximal
11#13071013C211yesmaximal, characteristic
12#13071013C211yesmaximal, characteristic
13C11×#2381C211yesmaximal, characteristic, complemented
14C22×Q8×D11C2212yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×#66997C2212yes—
17D11×C4⋊Q8C4116yescomplemented
18C2×C4⋊C4×D11C2212yes—
19C2×C4⋊C4×D11C2212yes—
20C2×#66941C2212yes—
21C2×#66941C2212yes—
22C2×#66940C2214yes—
23C2×C42×D11C2211yescharacteristic
24C2×#66922C2211yescharacteristic
25C2×C4×Dic22C2214yes—
26C11×#391C2214yes—
27C11×#387C2214yes—
28C11×#387C2214yes—
29C11×#383C2211yescharacteristic
30C11×#383C2211yescharacteristic
31#10622843C2214yes—
32#10622600C2214yes—
33#10622594C2214yes—
34#10622594C2214yes—
35#10622591C2214yes—
36#10622585C2214yes—
37C4×(C2×D11)⋊C4C2214yes—
38#10622550C2211yescharacteristic
39#10622550C2211yescharacteristic
40#10622546C2214yes—
41C4×Dic11⋊C4C2214yes—
42#10622280C2212yes—
43#10622280C2214yes—
44#10622280C2212yes—
45#10622279C2212yes—
46#10622279C2214yes—
47#10622279C2212yes—
48#10622277C2212yes—
49#10622277C2212yes—
50#10622268C2214yes—
51#10622267C2214yes—
52#10622267C2214yes—
53#10622266C2214yes—
54#10622266C2214yes—
55#10622265C2214yes—
56#10622263C2212yes—
57#10622263C2212yes—
58#10622262C2212yes—
59#10622262C2212yes—
60#10622262C2214yes—
61#10622261C2212yes—
62#10622261C2212yes—
63#10622260C2214yes—
64#10622259C2214yes—
65#10622259C2214yes—
66#10622259C2214yes—
67#10622259C2214yes—
68C22×Q8×C11C2312yes—
69C2×Q8×D11—44no—
70C2×Q8×D11—44no—
71C2×Q8×D11C2×C4116yes—
72C22×C4×D11C2311yescharacteristic
73C22×C4×D11C2311yescharacteristic
74C22×C4×D11C2311yescharacteristic
75C22×C4×D11C2314yes—
76C22×Dic22C2314yes—
77C22×Dic22C2312yes—
78C11×C4⋊Q8C2×C418yes—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C4⋊C4C2312yes—
81C2×C11×C4⋊C4C2312yes—
82C2×C42×C11C2314yes—
83C2×C42×C11C2311yescharacteristic
84#66997C2×C4116yes—
85C2×(C2×D11)⋊C4C2314yes—
86C2×(C2×D11)⋊C4C2314yes—
87C2×C4⋊Dic11C2314yes—
88C2×C4⋊Dic11C2312yes—
89C2×C4⋊Dic11C2312yes—
90C2×Dic11⋊C4C2314yes—
91C2×Dic11⋊C4C2314yes—
92C2×Dic11⋊C4C2314yes—
93C2×Dic11⋊C4C2314yes—
94C2×Dic11⋊C4C2314yes—
95C2×Dic11⋊C4C2314yes—
96C2×C4×Dic11C2314yes—
97C2×C4×Dic11C2314yes—
98C2×C4×Dic11C2314yes—
99C2×C4×Dic11C2314yes—
100C2×C4×Dic11C2314yes—
101C2×C4×Dic11C2311yescharacteristic
102C2×C4×Dic11C2311yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C4⋊C4×D11C2×C4116yes—
105C4⋊C4×D11C2×C4116yes—
106#66941C2×C4116yes—
107#66941C2×C4116yes—
108#66940—48no—
109C42×D11C2×C418yes—
110#66922C2×C418yes—
111C4×Dic22—48no—
112C11×#95C2312yes—
113C11×#95C2312yes—
114C11×#95C2314yes—
115C11×#95C2314yes—
116C11×#95C2312yes—
117C11×#95C2312yes—
118C11×#95C2312yes—
119C11×#95C2312yes—
120C11⋊#95C2314yes—
121C11⋊#95C2312yes—
122C11⋊#95C2314yes—
123C11⋊#95C2312yes—
124C11⋊#95C2314yes—
125C11⋊#95C2314yes—
126C11⋊#95C2314yes—
127C11⋊#95C2314yes—
128C11⋊#95C2314yes—
129C11⋊#95C2314yes—
130C11⋊#95C2312yes—
131C11⋊#95C2312yes—
132C11⋊#95C2312yes—
133C11⋊#95C2312yes—
134#34371—111nomaximal, Sylow
135C23×D11C2411yescharacteristic
136C2×Q8×C11—42no—
137C2×Q8×C11—42no—
138C2×Q8×C11C22×C418yes—
139C22×C4×C11C2414yes—
140C22×C4×C11C2414yes—
141C22×C4×C11C2411yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C22×C4×C11C2414yes—
145C22×Dic11C2414yes—
146C22×Dic11C2414yes—
147C22×Dic11C2411yescharacteristic
148C22×Dic11C2414yes—
149C22×Dic11C2411yescharacteristic
150C22×Dic11C2411yescharacteristic
151Q8×D11—432no—
152C2×C4×D11—24no—
153C2×C4×D11—24no—
154C2×C4×D11—24no—
155C2×C4×D11—44no—
156C2×C4×D11—44no—
157C2×C4×D11C22×C414yes—
158C2×C4×D11C22×C414yes—
159C2×C4×D11C22×C414yes—
160C2×C4×D11C22×C4116yes—
161C2×Dic22—28no—
162C2×Dic22—28no—
163C2×Dic22—42no—
164C2×Dic22—42no—
165C2×Dic22C22×C4116yes—
166C2×Dic22C22×C418yes—
167C11×C4⋊C4—44no—
168C11×C4⋊C4C22×C418yes—
169C11×C4⋊C4C22×C418yes—
170C42×C11—44no—
171C42×C11C22×C414yes—
172(C2×D11)⋊C4—28no—
173(C2×D11)⋊C4—28no—
174C4⋊Dic11—44no—
175C4⋊Dic11C22×C418yes—
176C4⋊Dic11C22×C418yes—
177Dic11⋊C4—28no—
178Dic11⋊C4—28no—
179Dic11⋊C4—44no—
180Dic11⋊C4—44no—
181Dic11⋊C4C22×C4116yes—
182Dic11⋊C4C22×C4116yes—
183C4×Dic11—28no—
184C4×Dic11—28no—
185C4×Dic11—44no—
186C4×Dic11—44no—
187C4×Dic11—44no—
188C4×Dic11C22×C414yes—
189C4×Dic11C22×C414yes—
190C4×Dic11C22×C414yes—
191C22×C4⋊Q8—111no—
192#2381—111no—
193#2381—111no—
194#2381—111no—
195#2381D1111yescharacteristic, complemented
196#2365—114no—
197#2345—114no—
198Q8×C22⋊C4—114no—
199#2331—114no—
200#2327—114no—
201#2313—114no—
202#2283—111no—
203#2283—111no—
204C23×C11C2511yescharacteristic
205C22×D11—22no—
206C22×D11—22no—
207C22×D11C23×C412yes—
208C22×D112−1+414yes—
209Q8×C11—48no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11C23×C412yes—
222C2×C4×C11C23×C412yes—
223C2×C4×C11C23×C412yes—
224C2×C4×C11C23×C418yes—
225C2×Dic11—24no—
226C2×Dic11—24no—
227C2×Dic11—22no—
228C2×Dic11—24no—
229C2×Dic11—24no—
230C2×Dic11—24no—
231C2×Dic11—24no—
232C2×Dic11—24no—
233C2×Dic11—24no—
234C2×Dic11C23×C412yes—
235C2×Dic11C23×C418yes—
236C2×Dic11C23×C412yes—
237C2×Dic11C23×C412yes—
238C2×Dic11H(5,𝔽2)14yes—
239C2×Dic112−1+414yes—
240C4×D11—28no—
241C4×D11—28no—
242C4×D11—28no—
243C4×D11—416no—
244Dic22—232no—
245Dic22—48no—
246C23×Q8—112no—
247C2×C4⋊Q8—112no—
248C2×C4⋊Q8—1116no—
249C2×C4⋊Q8—112no—
250C2×C4⋊Q8—112no—
251C2×C4⋊Q8—111no—
252C2×C4⋊Q8C2×D1111yescharacteristic
253C2×C4×Q8—114no—
254C2×C4×Q8—114no—
255C22×C4⋊C4—112no—
256C22×C4⋊C4—112no—
257C22×C42—111no—
258#391—114no—
259#391—114no—
260#391—114no—
261#391—114no—
262#391—114no—
263#391C2×D1114yes—
264#389—114no—
265#389—114no—
266#387—114no—
267#387—114no—
268#387—114no—
269#387—114no—
270#387—114no—
271#387—114no—
272#387—114no—
273#387—114no—
274#387—114no—
275#387—114no—
276#387C2×D1114yes—
277#387C2×D1114yes—
278#383—111no—
279#383—111no—
280#383C2×D1111yescharacteristic
281#383C2×D1111yescharacteristic
282#382—112no—
283#382—112no—
284#381—112no—
285#381—112no—
286#380—114no—
287#380—114no—
288#380—112no—
289#380—112no—
290C4×C4⋊C4—114no—
291C4×C4⋊C4—114no—
292C4×C4⋊C4—112no—
293C4×C4⋊C4—112no—
294C4×C22⋊C4—114no—
295C4×C22⋊C4—114no—
296C4×C22⋊C4—112no—
297C4×C22⋊C4—112no—
298#376—112no—
299#376—112no—
300C22×C11C24×C411yescharacteristic
301C22×C11C2×H(5,𝔽2)12yes—
302C22×C11C2×2−1+412yes—
303C22×C11C2×2−1+412yes—
304C2×D11—22no—
305C2×D11—22no—
306C2×D11—28no—
307C2×D11#51914yes—
308C4×C11—22no—
309C4×C11—28no—
310C4×C11—22no—
311C4×C11—22no—
312C4×C11—44no—
313C4×C11—44no—
314Dic11—28no—
315Dic11—22no—
316Dic11—44no—
317Dic11—44no—
318Dic11#51814yes—
319Dic11#51914yes—
320C22×Q8—1116no—
321C22×Q8—114no—
322C22×Q8—112no—
323C22×Q8—444no—
324C22×Q8—444no—
325C22×Q8C22×D1112yes—
326C23×C4—111no—
327C23×C4—111no—
328C23×C4—111no—
329C23×C4—114no—
330C4⋊Q8—1116no—
331C4⋊Q8—1116no—
332C4⋊Q8—1116no—
333C4⋊Q8—118no—
334C4⋊Q8C4×D1118yes—
335C4×Q8—448no—
336C4×Q8—448no—
337C2×C4⋊C4—114no—
338C2×C4⋊C4—114no—
339C2×C4⋊C4—112no—
340C2×C4⋊C4—112no—
341C2×C4⋊C4—1116no—
342C2×C4⋊C4—1116no—
343C2×C4⋊C4—114no—
344C2×C4⋊C4—114no—
345C2×C4⋊C4—114no—
346C2×C4⋊C4—114no—
347C2×C4⋊C4—114no—
348C2×C4⋊C4C22×D1114yes—
349C2×C4⋊C4C22×D1112yes—
350C2×C4⋊C4C22×D1112yes—
351C2×C22⋊C4—114no—
352C2×C22⋊C4—114no—
353C2×C42—111no—
354C2×C42—111no—
355C2×C42—111no—
356C2×C42—118no—
357C2×C42—114no—
358C2×C42—114no—
359C2×C42—114no—
360C2×C42—114no—
361C2×C42—114no—
362C2×C42C22×D1114yes—
363C2×C42C22×D1111yescharacteristic
364#95—112no—
365#95—112no—
366#95—114no—
367#95—114no—
368#95—112no—
369#95—112no—
370#95—114no—
371#95—114no—
372#95—114no—
373#95—114no—
374#95—114no—
375#95—114no—
376#95—112no—
377#95—112no—
378#95C22×D1112yes—
379#95C22×D1112yes—
380#95C22×D1112yes—
381#95C22×D1112yes—
382#95C22×D1114yes—
383#95C22×D1114yes—
384#95C22×D1112yes—
385#95C22×D1112yes—
386C2×C11C2×#51811yescharacteristic
387C2×C11C2×#51911yescharacteristic
388C2×C11C2×#51911yescharacteristic
389C2×C11#355214yes—
390D11—24no—
391C24—111no—
392C2×Q8—42no—
393C2×Q8—42no—
394C2×Q8—1116no—
395C2×Q8—118no—
396C2×Q8—228no—
397C2×Q8—228no—
398C2×Q8—442no—
399C2×Q8—442no—
400C2×Q8—4432no—
401C2×Q8C2×C4×D1118yes—
402C22×C4—111no—
403C22×C4—111no—
404C22×C4—111no—
405C22×C4—114no—
406C22×C4—114no—
407C22×C4—114no—
408C22×C4—114no—
409C22×C4—1116no—
410C22×C4—114no—
411C22×C4—114no—
412C22×C4—224no—
413C22×C4—224no—
414C22×C4—224no—
415C22×C4—444no—
416C22×C4—444no—
417C22×C4C23×D1114yes—
418C22×C4C23×D1114yes—
419C22×C4C23×D1111yescharacteristic
420C22×C4C23×D1111yescharacteristic
421C22×C4C23×D1111yescharacteristic
422C22×C4C23×D1114yes—
423C4⋊C4—44no—
424C4⋊C4—1116no—
425C4⋊C4—1116no—
426C4⋊C4—118no—
427C4⋊C4—118no—
428C4⋊C4—228no—
429C4⋊C4—228no—
430C4⋊C4—444no—
431C4⋊C4—444no—
432C4⋊C4—444no—
433C4⋊C4C2×C4×D1118yes—
434C4⋊C4C2×C4×D1118yes—
435C22⋊C4—228no—
436C22⋊C4—228no—
437C42—44no—
438C42—114no—
439C42—114no—
440C42—114no—
441C42—228no—
442C42—228no—
443C42—444no—
444C42—444no—
445C42—444no—
446C42C2×C4×D1114yes—
447C11#3437111yescharacteristic, complemented, Sylow
448C23—112no—
449C23—114no—
450C23—222no—
451C23—222no—
452C23C24×D1111yescharacteristic
453Q8—48no—
454Q8—2232no—
455Q8—448no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—112no—
468C2×C4—112no—
469C2×C4—114no—
470C2×C4—114no—
471C2×C4—112no—
472C2×C4—118no—
473C2×C4—228no—
474C2×C4—228no—
475C2×C4—228no—
476C2×C4—224no—
477C2×C4—224no—
478C2×C4—222no—
479C2×C4—224no—
480C2×C4—224no—
481C2×C4—224no—
482C2×C4—224no—
483C2×C4—224no—
484C2×C4—224no—
485C2×C4—4416no—
486C2×C4C22×C4×D1112yes—
487C2×C4C22×C4×D1112yes—
488C2×C4C22×C4×D1112yes—
489C2×C4C22×C4×D1118yes—
490C22—114no—
491C22—228no—
492C22—222no—
493C22—222no—
494C22C23×C4×D1111yescharacteristic
495C22D11×H(5,𝔽2)12yes—
496C22D11×2−1+412yes—
497C22D11×2−1+412yes—
498C4—22no—
499C4—28no—
500C4—22no—
501C4—22no—
502C4—44no—
503C4—44no—
504C4—114no—
505C4—114no—
506C4—228no—
507C4—222no—
508C4—444no—
509C4—444no—
510C2—224no—
511C2D11×#51811yescharacteristic
512C2D11×#51911yescharacteristic
513C2D11×#51911yescharacteristic
514C2#1308305014yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2381C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2381D11
hypocenterC11#34371
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2381

Complements

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

NH ≅ G/Ntype
2. #13071797C2semidirect
3. #13071796C2semidirect
4. #13071796C2semidirect
5. #13071671C2semidirect
8. #13071359C2semidirect
9. #13071331C2semidirect
13. C11×#2381C2semidirect
17. D11×C4⋊Q8C4semidirect
195. #2381D11semidirect
447. C11#34371semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
#130717972
#130717962
#130716712
#130714902
#130714502
#130713592
#130713312
#130712152
#130710132
C11×#23812
#3437111