Finite Group Databasebeta

← #14916883

Subgroups — #14916883

Order 2816.

1926 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic
2#13071797C211yesmaximal, characteristic, complemented
3#13071796C211yesmaximal, characteristic, complemented
4#13071796C211yesmaximal, characteristic, complemented
5#13071698C214yesmaximal
6#13071580C214yesmaximal, complemented
7#13071475C214yesmaximal
8#13071416C214yesmaximal, complemented
9#13071348C214yesmaximal
10#13071265C214yesmaximal, complemented
11#13071013C211yesmaximal, characteristic
12D11×#383C211yesmaximal, characteristic
13C11×#2381C211yesmaximal, characteristic, complemented
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×#66999C2212yes—
16C2×Q8×Dic11C2212yes—
17#10623259C4116yescomplemented
18C2×#66950C2212yes—
19C2×#66945C2212yes—
20C2×#66943C2212yes—
21C2×#66940C2212yes—
22C2×C42×D11C2211yescharacteristic
23C2×#66922C2211yescharacteristic
24C11×#391C2214yes—
25C11×#387C2214yes—
26C11×#387C2214yes—
27C11×#383C2211yescharacteristic
28C11×#383C2211yescharacteristic
29#10622843C2214yes—
30#10622602C2214yes—
31#10622594C2214yes—
32#10622594C2214yes—
33#10622590C2214yes—
34C4⋊C4×Dic11C2214yes—
35#10622585C2214yes—
36C4×(C2×D11)⋊C4C2214yes—
37#10622550C2211yescharacteristic
38#10622550C2211yescharacteristic
39C4×C4⋊Dic11C2214yes—
40#10622546C2214yes—
41C4×Dic11⋊C4C2214yes—
42#10622281C2214yes—
43#10622280C2212yes—
44#10622279C2212yes—
45#10622279C2214yes—
46#10622277C2212yes—
47D11×#95C2212yes—
48D11×#95C2212yes—
49D11×#95C2212yes—
50#10622267C2214yes—
51#10622267C2214yes—
52#10622267C2214yes—
53#10622266C2214yes—
54#10622266C2214yes—
55#10622266C2214yes—
56#10622265C2214yes—
57#10622264C2212yes—
58#10622264C2214yes—
59#10622264C2212yes—
60#10622264C2212yes—
61#10622263C2212yes—
62#10622262C2212yes—
63#10622261C2214yes—
64#10622261C2212yes—
65#10622260C2214yes—
66#10622259C2214yes—
67#10622259C2214yes—
68C22×Q8×C11C2312yes—
69C22×C4×D11C2311yescharacteristic
70C22×C4×D11C2314yes—
71C22×C4×D11C2311yescharacteristic
72C22×C4×D11C2311yescharacteristic
73C22×Dic22C2312yes—
74C11×C4⋊Q8C2×C418yescomplemented
75C2×C11×C4⋊C4C2314yes—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2312yes—
78C2×C42×C11C2314yes—
79C2×C42×C11C2311yescharacteristic
80#66999C2×C4116yes—
81Q8×Dic11C2×C4116yescomplemented
82C2×(C2×D11)⋊C4C2314yes—
83C2×(C2×D11)⋊C4C2314yes—
84C2×C4⋊Dic11C2314yes—
85C2×C4⋊Dic11C2312yes—
86C2×C4⋊Dic11C2312yes—
87C2×C4⋊Dic11C2314yes—
88C2×Dic11⋊C4C2314yes—
89C2×Dic11⋊C4C2314yes—
90C2×Dic11⋊C4C2314yes—
91C2×Dic11⋊C4C2314yes—
92C2×C4×Dic11C2314yes—
93C2×C4×Dic11C2314yes—
94C2×C4×Dic11C2314yes—
95C2×C4×Dic11C2314yes—
96C2×C4×Dic11C2311yescharacteristic
97C2×C4×Dic11C2311yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C2×C4×Dic11C2314yes—
100#66950C2×C4116yes—
101#66945C2×C4116yes—
102#66943C2×C4116yescomplemented
103#66940C2×C4116yescomplemented
104C42×D11C2×C418yes—
105#66922C2×C418yescomplemented
106C11×#95C2312yes—
107C11×#95C2312yes—
108C11×#95C2314yes—
109C11×#95C2314yes—
110C11×#95C2312yes—
111C11×#95C2312yes—
112C11×#95C2312yes—
113C11×#95C2312yes—
114C11⋊#95C2312yes—
115C11⋊#95C2312yes—
116C11⋊#95C2314yes—
117C11⋊#95C2314yes—
118C11⋊#95C2314yes—
119C11⋊#95C2314yes—
120C11⋊#95C2314yes—
121C11⋊#95C2314yes—
122C11⋊#95C2314yes—
123C11⋊#95C2312yes—
124C11⋊#95C2314yes—
125C11⋊#95C2312yes—
126C11⋊#95C2314yes—
127C11⋊#95C2312yes—
128C11⋊#95C2314yes—
129C11⋊#95C2312yes—
130#34389—111nomaximal, Sylow
131C23×D11C2411yescharacteristic
132C2×Q8×C11—42no—
133C2×Q8×C11—42no—
134C2×Q8×C11C22×C418yes—
135C22×C4×C11C2414yes—
136C22×C4×C11C2414yes—
137C22×C4×C11C2411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×C4×C11C2414yes—
141C22×Dic11C2414yes—
142C22×Dic11C2414yes—
143C22×Dic11C2411yescharacteristic
144C22×Dic11C2411yescharacteristic
145C22×Dic11C2414yes—
146C22×Dic11C2411yescharacteristic
147C2×C4×D11—24no—
148C2×C4×D11—28no—
149C2×C4×D11—42no—
150C2×C4×D11—42no—
151C2×C4×D11—44no—
152C2×C4×D11—44no—
153C2×C4×D11C22×C414yes—
154C2×C4×D11C22×C414yes—
155C2×C4×D11C22×C414yes—
156C2×Dic22—42no—
157C2×Dic22—42no—
158C2×Dic22C22×C418yes—
159C11×C4⋊C4—44no—
160C11×C4⋊C4C22×C418yes—
161C11×C4⋊C4C22×C418yes—
162C42×C11—44no—
163C42×C11C22×C414yes—
164(C2×D11)⋊C4—28no—
165(C2×D11)⋊C4C22×C4116yes—
166C4⋊Dic11—44no—
167C4⋊Dic11C22×C418yes—
168C4⋊Dic11C22×C418yes—
169C4⋊Dic11C22×C4116yes—
170Dic11⋊C4—44no—
171Dic11⋊C4—44no—
172Dic11⋊C4—44no—
173Dic11⋊C4C22×C4116yes—
174C4×Dic11—44no—
175C4×Dic11—44no—
176C4×Dic11—44no—
177C4×Dic11—44no—
178C4×Dic11C22×C414yes—
179C4×Dic11C22×C414yes—
180C4×Dic11C22×C414yes—
181C4×Dic11C22×C4116yes—
182C2×#533—111no—
183#2381—111no—
184#2381—111no—
185#2381—111no—
186#2381D1111yescharacteristic, complemented
187#2368—114no—
188#2356—114no—
189#2343—114no—
190#2336—114no—
191#2329—114no—
192#2320—114no—
193#2283—111no—
194C2×#383—111no—
195C23×C11C2511yescharacteristic
196C22×D11—22no—
197C22×D11—22no—
198C22×D11C23×C412yes—
199C22×D112−1+414yes—
200Q8×C11—48no—
201C2×C4×C11—22no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11C23×C418yes—
213C2×C4×C11C23×C412yes—
214C2×C4×C11C23×C412yes—
215C2×C4×C11C23×C412yes—
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—24no—
219C2×Dic11—24no—
220C2×Dic11—22no—
221C2×Dic11—24no—
222C2×Dic11—24no—
223C2×Dic11—24no—
224C2×Dic11—24no—
225C2×Dic11—24no—
226C2×Dic11—24no—
227C2×Dic11C23×C412yes—
228C2×Dic11C23×C412yes—
229C2×Dic11C23×C412yes—
230C2×Dic11C23×C418yes—
231C4×D11—28no—
232C4×D11—44no—
233C4×D11—44no—
234C4×D11—88no—
235Dic22—48no—
236#533—1116no—
237C2×C4⋊Q8—111no—
238C2×C4⋊Q8C2×D1111yescharacteristic
239C2×#125—112no—
240C2×C22⋊Q8—112no—
241C2×C22⋊Q8—112no—
242C2×C4×Q8—112no—
243C2×C4×Q8—112no—
244C2×#117—112no—
245C22×C42—111no—
246#391—114no—
247#391—114no—
248#391—114no—
249#391C2×D1114yes—
250#389—114no—
251#389—114no—
252#387—114no—
253#387—114no—
254#387—114no—
255#387—114no—
256#387—114no—
257#387—114no—
258#387—114no—
259#387—114no—
260#387—114no—
261#387—114no—
262#387C2×D1114yes—
263#387C2×D1114yes—
264#385—114no—
265#385—114no—
266#383—111no—
267#383—111no—
268#383—112no—
269#383—114no—
270#383—112no—
271#383—112no—
272#383C2×D1111yescharacteristic
273#383C2×D1111yescharacteristic
274#382—114no—
275#382—112no—
276#381—112no—
277#380—112no—
278C4×C4⋊C4—114no—
279C4×C4⋊C4—114no—
280C4×C4⋊C4—114no—
281C4×C4⋊C4—112no—
282C4×C22⋊C4—114no—
283C4×C22⋊C4—114no—
284C4×C22⋊C4—112no—
285#376—114no—
286#376—112no—
287C2×#95—112no—
288C2×#95—112no—
289C2×#95—112no—
290C22×C11C24×C411yescharacteristic
291C22×C11C2×2−1+412yes—
292C22×C11#58512yes—
293C22×C11#58512yes—
294C2×D11—22no—
295C2×D11—22no—
296C2×D11—28no—
297C2×D11#51914yes—
298C4×C11—22no—
299C4×C11—28no—
300C4×C11—22no—
301C4×C11—22no—
302C4×C11—44no—
303C4×C11—44no—
304Dic11—22no—
305Dic11—28no—
306Dic11—22no—
307Dic11—22no—
308Dic11—44no—
309Dic11—44no—
310C22×Q8—112no—
311C22×Q8C22×D1112yes—
312C23×C4—111no—
313C23×C4—111no—
314C23×C4—111no—
315C23×C4—114no—
316C4⋊Q8—118no—
317C4⋊Q8C4×D1118yescomplemented
318#125—1116no—
319C22⋊Q8—1116no—
320C22⋊Q8—1116no—
321C4×Q8—1116no—
322C4×Q8—1116no—
323#117—1116no—
324C2×C4⋊C4—112no—
325C2×C4⋊C4—114no—
326C2×C4⋊C4—114no—
327C2×C4⋊C4—112no—
328C2×C4⋊C4—114no—
329C2×C4⋊C4—114no—
330C2×C4⋊C4—114no—
331C2×C4⋊C4—114no—
332C2×C4⋊C4C22×D1114yes—
333C2×C4⋊C4C22×D1112yes—
334C2×C4⋊C4C22×D1112yes—
335C2×C22⋊C4—114no—
336C2×C22⋊C4—114no—
337C2×C42—114no—
338C2×C42—111no—
339C2×C42—111no—
340C2×C42—111no—
341C2×C42—118no—
342C2×C42—114no—
343C2×C42—114no—
344C2×C42—114no—
345C2×C42—114no—
346C2×C42C22×D1114yes—
347C2×C42C22×D1111yescharacteristic
348#95—114no—
349#95—114no—
350#95—112no—
351#95—114no—
352#95—112no—
353#95—112no—
354#95—114no—
355#95—112no—
356#95—114no—
357#95—112no—
358#95—114no—
359#95—114no—
360#95—114no—
361#95—112no—
362#95—114no—
363#95—114no—
364#95C22×D1112yes—
365#95C22×D1112yes—
366#95C22×D1112yes—
367#95C22×D1112yes—
368#95C22×D1114yes—
369#95C22×D1112yes—
370#95C22×D1114yes—
371#95C22×D1112yes—
372C2×C11C2×#51911yescharacteristic
373C2×C11#342811yescharacteristic
374C2×C11#342811yescharacteristic
375C2×C11#356414yes—
376D11—24no—
377C24—111no—
378C2×Q8—42no—
379C2×Q8—42no—
380C2×Q8—118no—
381C2×Q8—442no—
382C2×Q8—442no—
383C2×Q8C2×C4×D1118yes—
384C22×C4—111no—
385C22×C4—111no—
386C22×C4—114no—
387C22×C4—111no—
388C22×C4—114no—
389C22×C4—114no—
390C22×C4—114no—
391C22×C4—114no—
392C22×C4—114no—
393C22×C4—224no—
394C22×C4—228no—
395C22×C4—442no—
396C22×C4—442no—
397C22×C4—444no—
398C22×C4—444no—
399C22×C4C23×D1114yes—
400C22×C4C23×D1114yes—
401C22×C4C23×D1111yescharacteristic
402C22×C4C23×D1111yescharacteristic
403C22×C4C23×D1111yescharacteristic
404C22×C4C23×D1114yes—
405C4⋊C4—44no—
406C4⋊C4—118no—
407C4⋊C4—1116no—
408C4⋊C4—1116no—
409C4⋊C4—118no—
410C4⋊C4—444no—
411C4⋊C4—444no—
412C4⋊C4—444no—
413C4⋊C4—444no—
414C4⋊C4C2×C4×D1118yes—
415C4⋊C4C2×C4×D1118yes—
416C22⋊C4—1116no—
417C22⋊C4—228no—
418C42—44no—
419C42—114no—
420C42—114no—
421C42—114no—
422C42—1116no—
423C42—444no—
424C42—444no—
425C42—444no—
426C42—444no—
427C42C2×C4×D1114yes—
428C11#3438911yescharacteristic, complemented, Sylow
429C23—112no—
430C23—114no—
431C23—222no—
432C23—222no—
433C23C24×D1111yescharacteristic
434Q8—48no—
435Q8—448no—
436C2×C4—24no—
437C2×C4—24no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—24no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—112no—
448C2×C4—112no—
449C2×C4—112no—
450C2×C4—118no—
451C2×C4—228no—
452C2×C4—222no—
453C2×C4—222no—
454C2×C4—222no—
455C2×C4—224no—
456C2×C4—224no—
457C2×C4—224no—
458C2×C4—224no—
459C2×C4—224no—
460C2×C4—224no—
461C2×C4—224no—
462C2×C4—224no—
463C2×C4—444no—
464C2×C4—444no—
465C2×C4—888no—
466C2×C4C22×C4×D1112yes—
467C2×C4C22×C4×D1112yes—
468C2×C4C22×C4×D1112yes—
469C2×C4C22×C4×D1118yes—
470C22—114no—
471C22—228no—
472C22—222no—
473C22—222no—
474C22C23×C4×D1111yescharacteristic
475C22#1062345512yes—
476C22D11×2−1+412yes—
477C22#1062345712yes—
478C4—22no—
479C4—22no—
480C4—28no—
481C4—22no—
482C4—44no—
483C4—44no—
484C4—222no—
485C4—222no—
486C4—222no—
487C4—228no—
488C4—444no—
489C4—444no—
490C2—224no—
491C2D11×#51911yescharacteristic
492C2#1308181411yescharacteristic
493C2#1308181811yescharacteristic
494C2#1308323114yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2381C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2381D11
hypocenterC11#34389
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
6. #13071580C2semidirect
8. #13071416C2semidirect
10. #13071265C2semidirect
13. C11×#2381C2semidirect
17. #10623259C4semidirect
74. C11×C4⋊Q8C2×C4semidirect
81. Q8×Dic11C2×C4semidirect
102. #66943C2×C4semidirect
103. #66940C2×C4semidirect
105. #66922C2×C4semidirect
186. #2381D11semidirect
317. C4⋊Q8C4×D11semidirect
428. C11#34389semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
#130717972
#130717962
#130716982
#130715802
#130714752
#130714162
#130713482
#130712652
#130710132
D11×#3832
C11×#23812
#3438911