Finite Group Databasebeta

← #14763254

Subgroups — #14763254

Order 2816.

1302 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic
2C2×#10622446C211yesmaximal, characteristic
3#13071020C211yesmaximal, characteristic
4#13069575C214yesmaximal, complemented
5#13069569C211yesmaximal, characteristic, complemented
6#13069568C211yesmaximal, characteristic, complemented
7#13069567C211yesmaximal, characteristic, complemented
8#13068701C214yesmaximal
9C11×#1988C211yesmaximal, characteristic, complemented
10C22×Q8×D11—21no—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#66997—21no—
13D11×C4⋊Q8—24no—
14D11×C4⋊Q8C418yescomplemented
15C2×C4⋊C4×D11—21no—
16C2×C4⋊C4×D11C2212yes—
17C2×#66941—21no—
18C2×#66941C2212yes—
19C2×#66925—21no—
20C2×C42×D11C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×(C2×D11)⋊C8C2212yes—
25C2×C8×Dic11C2212yes—
26#10622600C2212yes—
27#10622589C2212yes—
28C4×C4⋊Dic11C2211yescharacteristic
29C4×Dic11⋊C4—21no—
30C2×C4⋊(C11⋊C8)C2211yescharacteristic
31#10622446—24no—
32#10622280—21no—
33#10622263—21no—
34C11×#340C2214yes—
35#10622189C2214yes—
36#10622167C2214yes—
37#10622167C2214yes—
38C22×Q8×C11—21no—
39C2×Q8×D11—28no—
40C2×Q8×D11—44no—
41C2×Q8×D11—44no—
42C22×C4×D11—22no—
43C22×C4×D11D411yescharacteristic
44C22×C4×D11D411yescharacteristic
45C22×C4×D11C2311yescharacteristic
46C22×Dic22—21no—
47C22×Dic22—22no—
48C22×C8×C11C2312yes—
49C11×C4⋊Q8—22no—
50C11×C4⋊Q8C2×C414yes—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4C2312yes—
53C2×C11×C4⋊C4C2312yes—
54C2×C42×C11—21no—
55C2×C42×C11C2311yescharacteristic
56#66997—28no—
57C2×(C2×D11)⋊C4—22no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11C2312yes—
60C2×C4⋊Dic11C2312yes—
61C2×Dic11⋊C4—22no—
62C2×Dic11⋊C4—22no—
63C2×Dic11⋊C4—22no—
64C2×Dic11⋊C4—22no—
65C2×C4×Dic11—21no—
66C2×C4×Dic11D411yescharacteristic
67C2×C4×Dic11D411yescharacteristic
68C2×C4×Dic11C2311yescharacteristic
69C22×C11⋊C8C2312yes—
70C4⋊C4×D11—28no—
71C4⋊C4×D11—24no—
72C4⋊C4×D11C2×C418yes—
73#66941—28no—
74#66941—24no—
75#66941C2×C418yes—
76#66925—44no—
77C42×D11C2×C414yes—
78C42×D11D414yes—
79#66922—22no—
80#66922C2×C414yes—
81C11×C4⋊C8—22no—
82C11×#95—21no—
83C11⋊#95—21no—
84C11⋊#95—22no—
85(C2×D11)⋊C8—24no—
86C8×Dic11—24no—
87C4⋊(C11⋊C8)—22no—
88#21833—111nomaximal, Sylow
89C23×D11C2×D411yescharacteristic
90C2×Q8×C11—24no—
91C2×Q8×C11—42no—
92C2×Q8×C11—42no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2411yescharacteristic
98C22×Dic11—22no—
99C22×Dic11—22no—
100C22×Dic11C2×D411yescharacteristic
101C22×Dic11C2×D411yescharacteristic
102C22×Dic11C2×D411yescharacteristic
103Q8×D11—432no—
104C2×C4×D11—24no—
105C2×C4×D11—28no—
106C2×C4×D11—22no—
107C2×C4×D11—22no—
108C2×C4×D11—44no—
109C2×C4×D11—44no—
110C2×C4×D11C22⋊C414yes—
111C2×C4×D11C22⋊C414yes—
112C2×C4×D11D814yes—
113C2×C4×D11SD1614yes—
114C2×C4×D11C22×C412yes—
115C2×C4×D11C2×D412yes—
116C2×Dic22—28no—
117C2×Dic22—24no—
118C2×Dic22—44no—
119C2×Dic22—44no—
120C2×Dic22—42no—
121C2×Dic22—42no—
122C2×C8×C11—22no—
123C2×C8×C11—24no—
124C11×C4⋊C4—24no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4C22×C414yes—
129C42×C11—42no—
130C42×C11C22×C412yes—
131C42×C11C2×D412yes—
132(C2×D11)⋊C4—44no—
133C4⋊Dic11—24no—
134C4⋊Dic11—22no—
135C4⋊Dic11—22no—
136C4⋊Dic11—22no—
137C4⋊Dic11C22×C414yes—
138Dic11⋊C4—28no—
139Dic11⋊C4—28no—
140Dic11⋊C4—44no—
141Dic11⋊C4—44no—
142C4×Dic11—42no—
143C4×Dic11C22⋊C414yes—
144C4×Dic11C22⋊C414yes—
145C4×Dic11C22×C412yes—
146C4×Dic11C2×D412yes—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—24no—
149C22×C4⋊Q8—111no—
150C2×#431—111no—
151#2285—111no—
152#1990—114no—
153#1988—111no—
154#1988—111no—
155#1988—111no—
156#1988D1111yescharacteristic, complemented
157#1823—114no—
158C23×C11C22×D411yescharacteristic
159C22×D11—22no—
160C22×D11—22no—
161C22×D11C2×C22⋊C412yes—
162C22×D11C2×D812yes—
163C22×D11C2×SD1612yes—
164Q8×C11—48no—
165C2×C4×C11—22no—
166C2×C4×C11—24no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11C2×C22⋊C412yes—
173C2×C4×C11C2×C22⋊C412yes—
174C2×C4×C11C2×D812yes—
175C2×C4×C11C2×SD1612yes—
176C2×C4×C11C23×C411yescharacteristic
177C2×C4×C11C22×D411yescharacteristic
178C2×C4×C112−1+412yes—
179C2×C4×C112−1+412yes—
180C2×Dic11—22no—
181C2×Dic11—24no—
182C2×Dic11—42no—
183C2×Dic11—42no—
184C2×Dic11—42no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11C2×C22⋊C412yes—
188C2×Dic11C2×C22⋊C412yes—
189C2×Dic11C2×C22⋊C412yes—
190C2×Dic11C2×D812yes—
191C2×Dic11C2×SD1612yes—
192C2×Dic11#13714yes—
193C4×D11—24no—
194C4×D11—22no—
195C4×D11—22no—
196C4×D11—28no—
197C4×D11—416no—
198C4×D11#102116yes—
199Dic22—48no—
200Dic22—416no—
201C8×C11—42no—
202C11⋊C8—42no—
203C23×Q8—221no—
204C2×C4⋊Q8—118no—
205C2×C4⋊Q8—112no—
206C2×C4⋊Q8—111no—
207C2×C4⋊Q8—221no—
208C2×C4⋊Q8—224no—
209C2×C4⋊Q8—221no—
210C2×C4⋊Q8C2×D1111yescharacteristic
211C2×#117—221no—
212C22×C4⋊C4—112no—
213C22×C4⋊C4—221no—
214C22×C42—111no—
215#431—224no—
216C2×C4⋊C8—111no—
217C2×C4⋊C8C2×D1111yescharacteristic
218C2×C22⋊C8—112no—
219C2×C4×C8—112no—
220#384—112no—
221#382—221no—
222#380—112no—
223#380—221no—
224C4×C4⋊C4—111no—
225C4×C4⋊C4—221no—
226C4×C4⋊C4C2×D1111yescharacteristic
227#340—114no—
228#340—114no—
229#340—114no—
230#340C2×D1114yes—
231C22×C11C22×C22⋊C411yescharacteristic
232C22×C11#53612yes—
233C22×C11C22×D811yescharacteristic
234C22×C11C22×SD1611yescharacteristic
235C22×C11C2×#13712yes—
236C2×D11—22no—
237C2×D11—22no—
238C2×D11—24no—
239C2×D11—24no—
240C2×D11C2×#10214yes—
241C4×C11—22no—
242C4×C11—44no—
243C4×C11—82no—
244C4×C11C2×#10214yes—
245C4×C11#51912yes—
246C4×C11#53611yescharacteristic
247C4×C11#53611yescharacteristic
248Dic11—22no—
249Dic11—44no—
250Dic11—82no—
251Dic11C2×#10214yes—
252Dic11#41914yes—
253C22×Q8—21no—
254C22×Q8—222no—
255C22×Q8—228no—
256C22×Q8—221no—
257C22×Q8—444no—
258C22×Q8—444no—
259C23×C4—111no—
260C23×C4—111no—
261C23×C4—111no—
262C23×C4—222no—
263C22×C8—112no—
264C22×C8C22×D1112yes—
265C4⋊Q8—22no—
266C4⋊Q8—118no—
267C4⋊Q8—114no—
268C4⋊Q8—228no—
269C4⋊Q8—224no—
270C4⋊Q8—228no—
271C4⋊Q8—222no—
272C4⋊Q8C4×D1114yes—
273#117—444no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—112no—
276C2×C4⋊C4—118no—
277C2×C4⋊C4—112no—
278C2×C4⋊C4—224no—
279C2×C4⋊C4—228no—
280C2×C4⋊C4—222no—
281C2×C4⋊C4—222no—
282C2×C4⋊C4—221no—
283C2×C4⋊C4—222no—
284C2×C4⋊C4—222no—
285C2×C4⋊C4C22×D1112yes—
286C2×C4⋊C4C22×D1112yes—
287C2×C22⋊C4—222no—
288C2×C42—21no—
289C2×C42—111no—
290C2×C42—111no—
291C2×C42—111no—
292C2×C42—114no—
293C2×C42—114no—
294C2×C42—221no—
295C2×C42C22×D1111yescharacteristic
296C4⋊C8—22no—
297C4⋊C8—222no—
298C22⋊C8—224no—
299C4×C8—224no—
300#95—21no—
301#95—222no—
302#95—221no—
303C2×C11#231011yescharacteristic
304C2×C11C22×#10211yescharacteristic
305C2×C11C2×#41911yescharacteristic
306C2×C11#322612yes—
307C2×C11#322912yes—
308D11—24no—
309C24—111no—
310C2×Q8—24no—
311C2×Q8—42no—
312C2×Q8—42no—
313C2×Q8—228no—
314C2×Q8—224no—
315C2×Q8—444no—
316C2×Q8—444no—
317C2×Q8—4432no—
318C2×Q8—442no—
319C2×Q8—442no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—111no—
323C22×C4—111no—
324C22×C4—114no—
325C22×C4—114no—
326C22×C4—114no—
327C22×C4—111no—
328C22×C4—114no—
329C22×C4—112no—
330C22×C4—112no—
331C22×C4—224no—
332C22×C4—228no—
333C22×C4—222no—
334C22×C4—222no—
335C22×C4—222no—
336C22×C4—222no—
337C22×C4—444no—
338C22×C4—444no—
339C22×C4D4×D1111yescharacteristic
340C22×C4D4×D1111yescharacteristic
341C22×C4C23×D1111yescharacteristic
342C2×C8—22no—
343C2×C8—24no—
344C2×C8—222no—
345C2×C8—224no—
346C4⋊C4—24no—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—114no—
351C4⋊C4—228no—
352C4⋊C4—228no—
353C4⋊C4—224no—
354C4⋊C4—222no—
355C4⋊C4—222no—
356C4⋊C4—222no—
357C4⋊C4—444no—
358C4⋊C4—444no—
359C4⋊C4C2×C4×D1114yes—
360C22⋊C4—444no—
361C42—42no—
362C42—114no—
363C42—114no—
364C42—112no—
365C42—112no—
366C42—442no—
367C42C2×C4×D1112yes—
368C42D4×D1112yes—
369C11#2183311yescharacteristic, complemented, Sylow
370C23—112no—
371C23—112no—
372C23—112no—
373C23—222no—
374C23—222no—
375C23C2×D4×D1111yescharacteristic
376Q8—48no—
377Q8—4416no—
378Q8—448no—
379C2×C4—22no—
380C2×C4—24no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—112no—
387C2×C4—112no—
388C2×C4—112no—
389C2×C4—112no—
390C2×C4—114no—
391C2×C4—1116no—
392C2×C4—112no—
393C2×C4—228no—
394C2×C4—222no—
395C2×C4—222no—
396C2×C4—224no—
397C2×C4—222no—
398C2×C4—224no—
399C2×C4—4416no—
400C2×C4—442no—
401C2×C4—442no—
402C2×C4—442no—
403C2×C4—442no—
404C2×C4—442no—
405C2×C4C22⋊C4×D1112yes—
406C2×C4C22⋊C4×D1112yes—
407C2×C4D8×D1112yes—
408C2×C4SD16×D1112yes—
409C2×C4C22×C4×D1111yescharacteristic
410C2×C4C2×D4×D1111yescharacteristic
411C2×C4#6704012yes—
412C2×C4#6704312yes—
413C8—42no—
414C8—442no—
415C22—114no—
416C22—222no—
417C22—222no—
418C22—224no—
419C22—224no—
420C22C2×C22⋊C4×D1111yescharacteristic
421C22#1062315912yes—
422C22C2×D8×D1111yescharacteristic
423C22C2×SD16×D1111yescharacteristic
424C22D11×#13712yes—
425C4—22no—
426C4—44no—
427C4—82no—
428C4—114no—
429C4—114no—
430C4—222no—
431C4—444no—
432C4—882no—
433C4D11×#10214yes—
434C4#1062310312yes—
435C4#1062320611yescharacteristic
436C4#1062325511yescharacteristic
437C2—224no—
438C2#1307119911yescharacteristic
439C2C2×D11×#10211yescharacteristic
440C2D11×#41911yescharacteristic
441C2#1307973612yes—
442C2#1307975912yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1988C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1988D11
hypocenterC11#21833
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1988

Complements

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

NH ≅ G/Ntype
4. #13069575C2semidirect
5. #13069569C2semidirect
6. #13069568C2semidirect
7. #13069567C2semidirect
9. C11×#1988C2semidirect
14. D11×C4⋊Q8C4semidirect
156. #1988D11semidirect
369. C11#21833semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
C2×#106224462
#130710202
#130695752
#130695692
#130695682
#130695672
#130687012
C11×#19882
#2183311