Finite Group Databasebeta

← #14645342

Subgroups — #14645342

Order 2816.

710 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069553C211yesmaximal, characteristic, complemented
2#13068612C211yesmaximal, characteristic, complemented
3#13067306C211yesmaximal, characteristic, complemented
4#13067293C211yesmaximal, characteristic
5#13067071C211yesmaximal, characteristic, complemented
6#13067067C211yesmaximal, characteristic
7C11×#3507C211yesmaximal, characteristic
8C11×#559—21no—
9C11×#557—21no—
10C11×#556—21no—
11C11×#556—22no—
12C11×#554—21no—
13C11×#552—22no—
14C11×#539C414yes—
15C11×#536—21no—
16C11×#533C2211yescharacteristic
17C11×#532C2211yescharacteristic
18C11×#529—22no—
19C11×#520—21no—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×#66900—21no—
22#10622537C2211yescharacteristic
23#10622537C2211yescharacteristic
24C2×C4⋊(C11⋊C8)C2211yescharacteristic
25C2×C4×C11⋊C8C2211yescharacteristic
26#10622185—21no—
27#10622185—21no—
28#10622184—21no—
29#10622182—21no—
30Q8⋊(C11⋊C8)—22no—
31D4⋊(C11⋊C8)—22no—
32#10622168—21no—
33#10622162—22no—
34C2×C11×#41—21no—
35C22×Q8×C11D411yescharacteristic
36C11×C4⋊Q8—22no—
37C11×C4⋊Q8D411yescharacteristic
38C11×C4⋊Q8D411yescharacteristic
39C11×C4⋊Q8D411yescharacteristic
40C11×#127D411yescharacteristic
41C11×#126—24no—
42C11×#126—24no—
43C11×#125—22no—
44C11×#125—24no—
45C11×#125—21no—
46C11×#124—22no—
47C11×#124—22no—
48C11×#124—21no—
49C11×#123—24no—
50C11×#123—24no—
51C11×C22⋊Q8—22no—
52C11×C22⋊Q8—22no—
53C11×C22⋊Q8—24no—
54C11×C22⋊Q8—21no—
55C11×C22⋊Q8C2×C412yes—
56C11×#121—21no—
57C11×#121C2×C412yes—
58C4×Q8×C11—22no—
59C4×Q8×C11—22no—
60C4×Q8×C11—21no—
61C4×Q8×C11—21no—
62C4×Q8×C11—21no—
63C4×Q8×C11—21no—
64C4×Q8×C11—21no—
65C4×Q8×C11D412yes—
66C4×D4×C11—22no—
67C4×D4×C11—22no—
68C4×D4×C11—24no—
69C4×D4×C11—21no—
70C4×D4×C11D412yes—
71C11×#117—22no—
72C11×#117—24no—
73C11×#117—21no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4C2×C412yes—
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C42×C11D412yes—
78C2×C42×C11C2311yescharacteristic
79C2×#4318—21no—
80C2×#4318—21no—
81C22×C11⋊C8—21no—
82C22×C11⋊C8—21no—
83#66900—42no—
84C4⋊(C11⋊C8)—21no—
85C4⋊(C11⋊C8)—21no—
86C4⋊(C11⋊C8)—21no—
87C4⋊(C11⋊C8)—21no—
88C4⋊(C11⋊C8)—21no—
89C4⋊(C11⋊C8)—21no—
90C4×C11⋊C8—21no—
91C4×C11⋊C8—21no—
92#8357—111nomaximal, Sylow
93C11×#41—41no—
94C11×#41—41no—
95C11×#41—41no—
96C11×#41—41no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11—21no—
100C2×Q8×C11—21no—
101C2×Q8×C11—21no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×Q8×C11C22⋊C412yes—
106C2×D4×C11—22no—
107C2×D4×C11—21no—
108C2×D4×C11—21no—
109C2×D4×C11C22⋊C412yes—
110C22×C4×C11—24no—
111C22×C4×C11—22no—
112C22×C4×C11C22⋊C412yes—
113C22×C4×C11C22⋊C412yes—
114C22×C4×C11C22×C411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C11×C4⋊C4—24no—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—24no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4C22⋊C412yes—
131C11×C4⋊C4C22⋊C412yes—
132C11×C22⋊C4—24no—
133C11×C22⋊C4—24no—
134C11×C22⋊C4—24no—
135C11×C22⋊C4—22no—
136C11×C22⋊C4—22no—
137C11×C22⋊C4—22no—
138C42×C11—24no—
139C42×C11—22no—
140C42×C11—22no—
141C42×C11—22no—
142C42×C11C2×D411yescharacteristic
143C42×C11C2×D411yescharacteristic
144C42×C11C2×D411yescharacteristic
145C42×C11C2×D411yescharacteristic
146#4318—41no—
147#4318—41no—
148#4318—41no—
149#4318—41no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—41no—
152C2×C11⋊C8—42no—
153C2×C11⋊C8—41no—
154C2×C11⋊C8—41no—
155C2×C11⋊C8—41no—
156C2×C11⋊C8—41no—
157#3507D1111yescharacteristic
158#1984—111no—
159#1801—111no—
160#1550—111no—
161#1547—111no—
162#1493—111no—
163#1492—111no—
164C23×C11—22no—
165C23×C11C2×C22⋊C411yescharacteristic
166Q8×C11—42no—
167Q8×C11—41no—
168Q8×C11—41no—
169Q8×C11—41no—
170Q8×C11—41no—
171Q8×C11—41no—
172Q8×C11—41no—
173Q8×C11—41no—
174Q8×C11—41no—
175D4×C11—42no—
176D4×C11—42no—
177D4×C11—42no—
178D4×C11—41no—
179D4×C11—41no—
180D4×C11—41no—
181D4×C11—41no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—41no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—84no—
196C2×C4×C11C2×C22⋊C411yescharacteristic
197C2×C4×C11C2×C22⋊C411yescharacteristic
198C2×C4×C11#12011yescharacteristic
199C2×C4×C11#12011yescharacteristic
200C2×C4×C11#12011yescharacteristic
201C2×C4×C11#12011yescharacteristic
202C2×C4×C11#13511yescharacteristic
203C2×C4×C11#13511yescharacteristic
204C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
205C2×C4×C11#13711yescharacteristic
206C11⋊C8—42no—
207C11⋊C8—81no—
208C11⋊C8—81no—
209C11⋊C8—81no—
210#559—21no—
211#557—21no—
212#556—21no—
213#556—22no—
214#554—21no—
215#552—22no—
216#539Dic1114yes—
217#536—21no—
218#533C2×D1111yescharacteristic
219#532C2×D1111yescharacteristic
220#529—22no—
221#520—21no—
222C2×C4×Q8C2×D1111yescharacteristic
223#423—111no—
224#423—111no—
225C2×C4⋊C8—111no—
226C2×#101—221no—
227C2×C4×C8—111no—
228#343—221no—
229#336—222no—
230#333—221no—
231#332—221no—
232#332—221no—
233#331—221no—
234Q8⋊C8—222no—
235D4⋊C8—222no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—42no—
239C22×C11—42no—
240C22×C11—42no—
241C22×C11#37911yescharacteristic
242C22×C11#41611yescharacteristic
243C22×C11#41711yescharacteristic
244C4×C11—21no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—42no—
248C4×C11—42no—
249C4×C11—42no—
250C4×C11—42no—
251C4×C11—42no—
252C4×C11#44911yescharacteristic
253C4×C11#44911yescharacteristic
254C4×C11#45211yescharacteristic
255C4×C11#45211yescharacteristic
256C4×C11#45411yescharacteristic
257C4×C11#45611yescharacteristic
258C2×#41—21no—
259C22×Q8C22⋊D1111yescharacteristic
260C2×M16—221no—
261C2×M16—221no—
262C22×C8—221no—
263C22×C8—221no—
264C4⋊Q8—22no—
265C4⋊Q8C22⋊D1111yescharacteristic
266C4⋊Q8C22⋊D1111yescharacteristic
267C4⋊Q8C22⋊D1111yescharacteristic
268#127C22⋊D1111yescharacteristic
269#126—24no—
270#126—24no—
271#125—22no—
272#125—24no—
273#125—21no—
274#124—22no—
275#124—22no—
276#124—21no—
277#123—24no—
278#123—24no—
279C22⋊Q8—22no—
280C22⋊Q8—22no—
281C22⋊Q8—24no—
282C22⋊Q8—21no—
283C22⋊Q8C2×Dic1112yes—
284#121—21no—
285#121C2×Dic1112yes—
286C4×Q8—22no—
287C4×Q8—22no—
288C4×Q8—21no—
289C4×Q8—21no—
290C4×Q8—21no—
291C4×Q8—21no—
292C4×Q8—21no—
293C4×Q8C22⋊D1112yes—
294C4×D4—22no—
295C4×D4—22no—
296C4×D4—24no—
297C4×D4—21no—
298C4×D4C22⋊D1112yes—
299#117—22no—
300#117—24no—
301#117—21no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4C2×Dic1112yes—
304C2×C4⋊C4C22⋊D1111yescharacteristic
305C2×C42C22⋊D1112yes—
306C2×C42C22×D1111yescharacteristic
307C4⋊C8—221no—
308C4⋊C8—221no—
309C4⋊C8—221no—
310C4⋊C8—221no—
311C4⋊C8—221no—
312C4⋊C8—221no—
313#101—442no—
314C4×C8—221no—
315C4×C8—221no—
316C2×C11—21no—
317C2×C11—21no—
318C2×C11—82no—
319C2×C11#178811yescharacteristic
320C2×C11#179111yescharacteristic
321C2×C11#179311yescharacteristic
322#41—41no—
323#41—41no—
324#41—41no—
325#41—41no—
326C2×Q8—21no—
327C2×Q8—21no—
328C2×Q8—21no—
329C2×Q8—21no—
330C2×Q8—21no—
331C2×Q8—21no—
332C2×Q8—21no—
333C2×Q8—21no—
334C2×Q8C22⋊Dic1112yes—
335C2×D4—22no—
336C2×D4—21no—
337C2×D4—21no—
338C2×D4C22⋊Dic1112yes—
339C22×C4—24no—
340C22×C4—22no—
341C22×C4C22⋊Dic1112yes—
342C22×C4C22⋊Dic1112yes—
343C22×C4C22×Dic1111yescharacteristic
344C22×C4C2×C22⋊D1111yescharacteristic
345C22×C4C2×C22⋊D1111yescharacteristic
346M16—441no—
347M16—441no—
348M16—441no—
349M16—441no—
350C2×C8—222no—
351C2×C8—441no—
352C2×C8—441no—
353C2×C8—442no—
354C2×C8—441no—
355C2×C8—441no—
356C2×C8—441no—
357C4⋊C4—24no—
358C4⋊C4—24no—
359C4⋊C4—24no—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—22no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4C22⋊Dic1112yes—
371C4⋊C4C22⋊Dic1112yes—
372C22⋊C4—24no—
373C22⋊C4—24no—
374C22⋊C4—24no—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—22no—
378C42—24no—
379C42—22no—
380C42—22no—
381C42—22no—
382C42C2×C22⋊D1111yescharacteristic
383C42C2×C22⋊D1111yescharacteristic
384C42C2×C22⋊D1111yescharacteristic
385C42C2×C22⋊D1111yescharacteristic
386C11#835711yescharacteristic, complemented, Sylow
387C23—22no—
388C23C2×C22⋊Dic1111yescharacteristic
389Q8—42no—
390Q8—41no—
391Q8—41no—
392Q8—41no—
393Q8—41no—
394Q8—41no—
395Q8—41no—
396Q8—41no—
397Q8—41no—
398D4—42no—
399D4—42no—
400D4—42no—
401D4—41no—
402D4—41no—
403D4—41no—
404D4—41no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—84no—
419C2×C4#6700211yescharacteristic
420C2×C4#6700311yescharacteristic
421C2×C4#6700311yescharacteristic
422C2×C4#6700411yescharacteristic
423C2×C4C2×C22⋊Dic1111yescharacteristic
424C2×C4C2×C22⋊Dic1111yescharacteristic
425C2×C4#6700611yescharacteristic
426C2×C4#6700611yescharacteristic
427C2×C4#6700611yescharacteristic
428C2×C4#6700611yescharacteristic
429C8—442no—
430C8—881no—
431C8—881no—
432C8—881no—
433C22—21no—
434C22—21no—
435C22—42no—
436C22—42no—
437C22—42no—
438C22#1062284511yescharacteristic
439C22#1062284611yescharacteristic
440C22#1062286011yescharacteristic
441C4—21no—
442C4—21no—
443C4—21no—
444C4—42no—
445C4—42no—
446C4—42no—
447C4—42no—
448C4—42no—
449C4#1062285111yescharacteristic
450C4#1062285111yescharacteristic
451C4#1062285211yescharacteristic
452C4#1062285211yescharacteristic
453C4#1062285811yescharacteristic
454C4#1062285911yescharacteristic
455C2—21no—
456C2—21no—
457C2—82no—
458C2#1306855611yescharacteristic
459C2#1306856711yescharacteristic
460C2#1306857511yescharacteristic
subgroupG/H
centerC22#10622860
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#3507C2
socleC22×C11#379
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#3507D11
hypocenterC11#8357
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3507

Complements

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

NH ≅ G/Ntype
1. #13069553C2semidirect
2. #13068612C2semidirect
3. #13067306C2semidirect
5. #13067071C2semidirect
386. C11#8357semidirect

Maximal subgroups

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

subgroupindex
#130695532
#130686122
#130673062
#130672932
#130670712
#130670672
C11×#35072
#835711