Finite Group Databasebeta

← #14645697

Subgroups — #14645697

Order 2816.

756 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069565C211yesmaximal, characteristic, complemented
2#13068636C211yesmaximal, characteristic, complemented
3#13067301C211yesmaximal, characteristic, complemented
4#13067293C211yesmaximal, characteristic, complemented
5#13067111C211yesmaximal, characteristic, complemented
6#13067003C211yesmaximal, characteristic, complemented
7C11×#3511C211yesmaximal, characteristic
8C11×#556C412yescomplemented
9C11×#555—21no—
10C11×#554—21no—
11C11×#553—22no—
12C11×#548—22no—
13C11×#547C412yescomplemented
14C11×#542—22no—
15C11×#537—21no—
16C11×#533—21no—
17C11×#532—21no—
18C11×#532C2211yescharacteristic
19C2×C11×C4⋊Q8C2211yescharacteristic
20C11×#520—21no—
21C4×C11×#41C2211yescharacteristic
22C2×#66901—21no—
23C4×C4⋊Dic11C2211yescharacteristic
24#10622538C2211yescharacteristic
25#10622537C2211yescharacteristic
26C2×C4⋊(C11⋊C8)C2211yescharacteristic
27#10622185—21no—
28#10622185—22no—
29#10622182—21no—
30#10622175—22no—
31Q8⋊(C11⋊C8)—21no—
32D4⋊(C11⋊C8)—21no—
33#10622170—21no—
34#10622167—22no—
35C2×C11×#41—22no—
36C2×C11×#41—21no—
37C2×C11×#41D411yescharacteristic
38C22×Q8×C11—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8C2×C412yes—
42C11×C4⋊Q8D412yes—
43C11×C4⋊Q8D411yescharacteristic
44C11×#127D411yescharacteristic
45C11×#126—24no—
46C11×#125—22no—
47C11×#124—24no—
48C11×#124—22no—
49C11×#124—21no—
50C11×#123—24no—
51C11×C22⋊Q8—22no—
52C11×C22⋊Q8—24no—
53C11×C22⋊Q8—22no—
54C11×C22⋊Q8—22no—
55C11×#121—22no—
56C11×#121—22no—
57C11×#121—24no—
58C11×#121—22no—
59C11×#121—21no—
60C11×#121D412yes—
61C4×Q8×C11—22no—
62C4×Q8×C11—22no—
63C4×Q8×C11C2×C411yescharacteristic
64C4×Q8×C11D411yescharacteristic
65C4×D4×C11—22no—
66C4×D4×C11—24no—
67C4×D4×C11—22no—
68C4×D4×C11—21no—
69C4×D4×C11—21no—
70C4×D4×C11—21no—
71C4×D4×C11C2×C411yescharacteristic
72C4×D4×C11C2×C412yes—
73C4×D4×C11D411yescharacteristic
74C11×#117—22no—
75C11×#117—22no—
76C11×#117—21no—
77C11×#117D411yescharacteristic
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4D412yes—
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83C2×C4⋊Dic11—21no—
84C2×C4×Dic11—21no—
85C2×#4318—21no—
86C22×C11⋊C8—21no—
87#66901—42no—
88C11⋊#95—21no—
89C22⋊(C11⋊C8)—21no—
90C4⋊(C11⋊C8)—21no—
91C4⋊(C11⋊C8)—21no—
92C4⋊(C11⋊C8)—21no—
93C4⋊(C11⋊C8)—21no—
94C4⋊(C11⋊C8)—21no—
95C4×C11⋊C8—21no—
96#8422—111nomaximal, Sylow
97C11×#41—21no—
98C11×#41—21no—
99C11×#41—21no—
100C11×#41—21no—
101C11×#41—41no—
102C11×#41—41no—
103C11×#41—41no—
104C11×#41—41no—
105C11×#41—84no—
106C2×Q8×C11—22no—
107C2×Q8×C11—21no—
108C2×Q8×C11—22no—
109C2×Q8×C11—82no—
110C2×Q8×C11C22⋊C411yescharacteristic
111C2×D4×C11—21no—
112C2×D4×C11—22no—
113C2×D4×C11—24no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11C22⋊C411yescharacteristic
117C2×D4×C11C22⋊C412yes—
118C22×C4×C11—24no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×Dic11—41no—
128C11×C4⋊C4—24no—
129C11×C4⋊C4—24no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4C22⋊C411yescharacteristic
137C11×C4⋊C4C22⋊C414yes—
138C11×C4⋊C4C22⋊C411yescharacteristic
139C11×C4⋊C4C22⋊C412yes—
140C11×C22⋊C4—24no—
141C11×C22⋊C4—24no—
142C11×C22⋊C4—24no—
143C11×C22⋊C4—21no—
144C11×C22⋊C4—21no—
145C11×C22⋊C4—22no—
146C11×C22⋊C4—21no—
147C11×C22⋊C4—22no—
148C42×C11—24no—
149C42×C11—21no—
150C42×C11—21no—
151C42×C11—21no—
152C42×C11C22×C411yescharacteristic
153C42×C11C2×D411yescharacteristic
154C42×C11C2×D411yescharacteristic
155C42×C11C2×D411yescharacteristic
156C4⋊Dic11—22no—
157C4⋊Dic11—41no—
158C4×Dic11—41no—
159C4×Dic11—41no—
160#4318—41no—
161#4318—41no—
162C2×C11⋊C8—42no—
163C2×C11⋊C8—41no—
164C2×C11⋊C8—41no—
165C2×C11⋊C8—41no—
166#3511D1111yescharacteristic
167#1987—111no—
168#1806—111no—
169#1549—111no—
170#1547—111no—
171#1502—111no—
172#1477—111no—
173C23×C11—21no—
174C23×C11—22no—
175C23×C11#12011yescharacteristic
176Q8×C11—21no—
177Q8×C11—21no—
178Q8×C11—44no—
179Q8×C11—41no—
180Q8×C11—41no—
181Q8×C11—82no—
182D4×C11—21no—
183D4×C11—21no—
184D4×C11—42no—
185D4×C11—41no—
186D4×C11—42no—
187D4×C11—41no—
188D4×C11—42no—
189D4×C11—41no—
190D4×C11—41no—
191D4×C11—41no—
192D4×C11—41no—
193D4×C11—84no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—22no—
199C2×C4×C11—21no—
200C2×C4×C11—24no—
201C2×C4×C11—41no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—82no—
210C2×C4×C11—84no—
211C2×C4×C11C2×C22⋊C411yescharacteristic
212C2×C4×C11C2×C22⋊C411yescharacteristic
213C2×C4×C11C2×C22⋊C411yescharacteristic
214C2×C4×C11#12011yescharacteristic
215C2×C4×C11#12011yescharacteristic
216C2×C4×C11#12011yescharacteristic
217C2×C4×C11#13511yescharacteristic
218C2×C4×C11#13511yescharacteristic
219C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
220C2×C4×C11#13711yescharacteristic
221C2×Dic11—42no—
222C2×Dic11—81no—
223C2×Dic11—81no—
224C11⋊C8—81no—
225C11⋊C8—81no—
226C11⋊C8—81no—
227#556Dic1112yescomplemented
228#555—21no—
229#554—21no—
230#553—22no—
231#548—22no—
232#547Dic1112yescomplemented
233#542—22no—
234#537—21no—
235#533—21no—
236#532—21no—
237#532C2×D1111yescharacteristic
238C2×C4⋊Q8C2×D1111yescharacteristic
239#520—21no—
240C4×#41C2×D1111yescharacteristic
241#431—111no—
242#423—111no—
243C2×C4⋊C8—111no—
244C2×#104—221no—
245C4×C4⋊C4—111no—
246#340—222no—
247#339—221no—
248#332—221no—
249#332—222no—
250#331—221no—
251#327—222no—
252Q8⋊C8—221no—
253D4⋊C8—221no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11—41no—
257C22×C11—42no—
258C22×C11—41no—
259C22×C11—42no—
260C22×C11—41no—
261C22×C11—42no—
262C22×C11#37911yescharacteristic
263C22×C11#44911yescharacteristic
264C22×C11#45211yescharacteristic
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—21no—
268C4×C11—41no—
269C4×C11—41no—
270C4×C11—44no—
271C4×C11—41no—
272C4×C11—42no—
273C4×C11#41611yescharacteristic
274C4×C11#41711yescharacteristic
275C4×C11#44911yescharacteristic
276C4×C11#45211yescharacteristic
277C4×C11#45411yescharacteristic
278C4×C11#45611yescharacteristic
279Dic11—82no—
280C2×#41—22no—
281C2×#41—21no—
282C2×#41C22⋊D1111yescharacteristic
283C22×Q8—21no—
284C2×M16—221no—
285C22×C8—221no—
286C4⋊Q8—21no—
287C4⋊Q8—21no—
288C4⋊Q8C2×Dic1112yes—
289C4⋊Q8C22⋊D1112yes—
290C4⋊Q8C22⋊D1111yescharacteristic
291#127C22⋊D1111yescharacteristic
292#126—24no—
293#125—22no—
294#124—24no—
295#124—22no—
296#124—21no—
297#123—24no—
298C22⋊Q8—22no—
299C22⋊Q8—24no—
300C22⋊Q8—22no—
301C22⋊Q8—22no—
302#121—22no—
303#121—22no—
304#121—24no—
305#121—22no—
306#121—21no—
307#121C22⋊D1112yes—
308C4×Q8—22no—
309C4×Q8—22no—
310C4×Q8C2×Dic1111yescharacteristic
311C4×Q8C22⋊D1111yescharacteristic
312C4×D4—22no—
313C4×D4—24no—
314C4×D4—22no—
315C4×D4—21no—
316C4×D4—21no—
317C4×D4—21no—
318C4×D4C2×Dic1111yescharacteristic
319C4×D4C2×Dic1112yes—
320C4×D4C22⋊D1111yescharacteristic
321#117—22no—
322#117—22no—
323#117—21no—
324#117C22⋊D1111yescharacteristic
325C2×C4⋊C4—21no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—221no—
328C2×C4⋊C4C22⋊D1112yes—
329C2×C42—21no—
330C2×C42—221no—
331C2×C42C22×D1111yescharacteristic
332C4⋊C8—221no—
333C4⋊C8—221no—
334C4⋊C8—221no—
335C4⋊C8—221no—
336C4⋊C8—221no—
337#104—442no—
338C22⋊C8—221no—
339C4×C8—221no—
340#95—221no—
341C2×C11—21no—
342C2×C11—21no—
343C2×C11—81no—
344C2×C11—82no—
345C2×C11#178811yescharacteristic
346C2×C11#179311yescharacteristic
347C2×C11#179511yescharacteristic
348#41—21no—
349#41—21no—
350#41—21no—
351#41—21no—
352#41—41no—
353#41—41no—
354#41—41no—
355#41—41no—
356#41—84no—
357C2×Q8—22no—
358C2×Q8—21no—
359C2×Q8—22no—
360C2×Q8—82no—
361C2×Q8C22⋊Dic1111yescharacteristic
362C2×D4—21no—
363C2×D4—22no—
364C2×D4—24no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4C22⋊Dic1111yescharacteristic
368C2×D4C22⋊Dic1112yes—
369C22×C4—24no—
370C22×C4—22no—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—441no—
376C22×C4C2×C22⋊D1111yescharacteristic
377C22×C4C2×C22⋊D1111yescharacteristic
378C22×C4C2×C22⋊D1111yescharacteristic
379M16—441no—
380M16—441no—
381C2×C8—442no—
382C2×C8—441no—
383C2×C8—441no—
384C2×C8—441no—
385C4⋊C4—24no—
386C4⋊C4—24no—
387C4⋊C4—22no—
388C4⋊C4—21no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—222no—
394C4⋊C4—441no—
395C4⋊C4C22⋊Dic1111yescharacteristic
396C4⋊C4C22⋊Dic1114yes—
397C4⋊C4C22⋊Dic1111yescharacteristic
398C4⋊C4C22⋊Dic1112yes—
399C22⋊C4—24no—
400C22⋊C4—24no—
401C22⋊C4—24no—
402C22⋊C4—21no—
403C22⋊C4—21no—
404C22⋊C4—22no—
405C22⋊C4—21no—
406C22⋊C4—22no—
407C42—24no—
408C42—21no—
409C42—21no—
410C42—21no—
411C42—441no—
412C42—441no—
413C42C22×Dic1111yescharacteristic
414C42C2×C22⋊D1111yescharacteristic
415C42C2×C22⋊D1111yescharacteristic
416C42C2×C22⋊D1111yescharacteristic
417C11#842211yescharacteristic, complemented, Sylow
418C23—21no—
419C23—22no—
420C23#6700611yescharacteristic
421Q8—21no—
422Q8—21no—
423Q8—44no—
424Q8—41no—
425Q8—41no—
426Q8—82no—
427D4—21no—
428D4—21no—
429D4—42no—
430D4—41no—
431D4—42no—
432D4—41no—
433D4—42no—
434D4—41no—
435D4—41no—
436D4—41no—
437D4—41no—
438D4—84no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—22no—
444C2×C4—21no—
445C2×C4—24no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—82no—
455C2×C4—84no—
456C2×C4—442no—
457C2×C4—881no—
458C2×C4—881no—
459C2×C4#6700211yescharacteristic
460C2×C4#6700311yescharacteristic
461C2×C4#6700311yescharacteristic
462C2×C4#6700411yescharacteristic
463C2×C4C2×C22⋊Dic1111yescharacteristic
464C2×C4C2×C22⋊Dic1111yescharacteristic
465C2×C4C2×C22⋊Dic1111yescharacteristic
466C2×C4#6700611yescharacteristic
467C2×C4#6700611yescharacteristic
468C2×C4#6700611yescharacteristic
469C8—881no—
470C8—881no—
471C8—881no—
472C22—21no—
473C22—21no—
474C22—41no—
475C22—42no—
476C22—41no—
477C22—42no—
478C22—41no—
479C22—42no—
480C22#1062285111yescharacteristic
481C22#1062285211yescharacteristic
482C22#1062286011yescharacteristic
483C4—21no—
484C4—21no—
485C4—21no—
486C4—41no—
487C4—42no—
488C4—41no—
489C4—41no—
490C4—44no—
491C4—882no—
492C4#1062284511yescharacteristic
493C4#1062284611yescharacteristic
494C4#1062285111yescharacteristic
495C4#1062285211yescharacteristic
496C4#1062285811yescharacteristic
497C4#1062285911yescharacteristic
498C2—21no—
499C2—21no—
500C2—81no—
501C2—82no—
502C2#1306855611yescharacteristic
503C2#1306857511yescharacteristic
504C2#1306858611yescharacteristic
subgroupG/H
centerC22#10622860
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3511C2
socleC22×C11#379
cosocleC2×C42×C11C23
hypercenter#3511D11
hypocenterC11#8422
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3511

Complements

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

NH ≅ G/Ntype
1. #13069565C2semidirect
2. #13068636C2semidirect
3. #13067301C2semidirect
4. #13067293C2semidirect
5. #13067111C2semidirect
6. #13067003C2semidirect
8. C11×#556C4semidirect
13. C11×#547C4semidirect
227. #556Dic11semidirect
232. #547Dic11semidirect
417. C11#8422semidirect

Maximal subgroups

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

subgroupindex
#130695652
#130686362
#130673012
#130672932
#130671112
#130670032
C11×#35112
#842211