Finite Group Databasebeta

← #14724675

Subgroups — #14724675

Order 2816.

680 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078620C211yesmaximal, characteristic
2#13077565C211yesmaximal, characteristic, complemented
3#13077351C211yesmaximal, characteristic
4#13067503C212yesmaximal, complemented
5#13067456C212yesmaximal, complemented
6#13067455C212yesmaximal, complemented
7#13067413C212yesmaximal, complemented
8#13067388C211yesmaximal, characteristic, complemented
9C2×#10622097C211yesmaximal, characteristic
10C8×#4318C211yesmaximal, characteristic, complemented
11C11×#1493C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×M16×D11—21no—
14C2×C4×D44C2211yescharacteristic
15C11×#423C2211yescharacteristic
16C2×C4×C8×C11C2211yescharacteristic
17#10622739—21no—
18#10622697C411yescharacteristic
19#10622697C411yescharacteristic
20#10622696C411yescharacteristic
21#10622696C411yescharacteristic
22#10622659C412yes—
23#10622656C412yes—
24C4×#4325C2212yes—
25C4×#4325C2212yes—
26#10622637—22no—
27#10622637C2212yescomplemented
28Q8×C11⋊C8C2212yescomplemented
29#10622612—21no—
30#10622610—21no—
31#10622538C2211yescharacteristic
32C2×C4⋊(C11⋊C8)C2211yescharacteristic
33C4×#4318C2211yescharacteristic
34#10622451C2212yes—
35#10622449—22no—
36#10622447C2212yes—
37C11×Q8⋊C8C2212yescomplemented
38C11×Q8⋊C8C2212yescomplemented
39#10622118C2212yescomplemented
40#10622118C2212yescomplemented
41#10622097C2211yescharacteristic
42#10622097C2211yescharacteristic
43#10622097C2211yescharacteristic
44#10622097C2211yescharacteristic
45#10622092C2212yescomplemented
46C8×C11⋊C8C2212yescomplemented
47C22×D44C2×C411yescharacteristic
48C22×C4×D11—21no—
49C2×C11×M16—21no—
50C22×C8×C11—21no—
51C11×C4⋊Q8C2×C411yescharacteristic
52C11×C4⋊Q8C2×C411yescharacteristic
53C11×#125—21no—
54C11×C22⋊Q8—21no—
55C11×C22⋊Q8C2×C412yes—
56C4×Q8×C11—21no—
57C4×Q8×C11C2312yes—
58C11×#117—21no—
59C2×C42×C11C2311yescharacteristic
60C2×#4325C2×C412yes—
61C2×#4325C2×C412yes—
62C2×(C2×D11)⋊C4—21no—
63C2×C4⋊Dic11C2×C411yescharacteristic
64C2×#4318D411yescharacteristic
65C2×#4318D411yescharacteristic
66C22×C11⋊C8—21no—
67M16×D11—44no—
68C2×#4313—22no—
69C2×C8×D11—22no—
70C4×D44—21no—
71C4×D44—21no—
72C4×D44C2×C411yescharacteristic
73C4×D44C2×C411yescharacteristic
74C4×D44C2311yescharacteristic
75C4×D44C2311yescharacteristic
76C11×C4⋊C8—21no—
77C11×C4⋊C8C2312yes—
78C4×C8×C11—21no—
79C4×C8×C11C2311yescharacteristic
80C4×C8×C11C2311yescharacteristic
81#66899C2×C412yes—
82#66899C2×C412yes—
83C22⋊(C11⋊C8)C2×C412yes—
84(C2×D11)⋊C8—22no—
85(C2×D11)⋊C8—22no—
86#66873C2×C412yes—
87#66873C2×C412yes—
88#66872C2×C412yes—
89#66872C2×C412yes—
90C4⋊(C11⋊C8)—21no—
91C4⋊(C11⋊C8)—22no—
92C4⋊(C11⋊C8)—22no—
93C4⋊(C11⋊C8)C2×C411yescharacteristic
94C4⋊(C11⋊C8)C2×C411yescharacteristic
95C4⋊(C11⋊C8)C2311yescharacteristic
96C4⋊(C11⋊C8)C2311yescharacteristic
97#66867—22no—
98#66867D412yes—
99C4×C11⋊C8—22no—
100C4×C11⋊C8C2312yes—
101C4×C11⋊C8C2312yes—
102#17995—111nomaximal, Sylow
103C23×D11—21no—
104C2×Q8×C11—21no—
105C2×Q8×C11C22×C412yes—
106C22×C4×C11C22×C411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11#4111yescharacteristic
109C22×Dic11—21no—
110C2×D44—22no—
111C2×D44—21no—
112C2×D44—41no—
113C2×D44C22×C411yescharacteristic
114C2×D44C22×C411yescharacteristic
115C2×C4×D11—21no—
116C2×C4×D11—21no—
117C2×C4×D11—21no—
118C2×C4×D11—21no—
119C2×C4×D11—42no—
120C2×C4×D11—42no—
121C11×M16—42no—
122C2×C8×C11—22no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11—42no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4C22×C412yes—
132C11×C22⋊C4—22no—
133C42×C11—22no—
134C42×C11C22×C411yescharacteristic
135C42×C11C2×D411yescharacteristic
136C42×C11#4111yescharacteristic
137C42×C11C2411yescharacteristic
138#4325—24no—
139#4325—42no—
140(C2×D11)⋊C4—21no—
141(C2×D11)⋊C4—21no—
142(C2×D11)⋊C4—21no—
143(C2×D11)⋊C4—21no—
144C4⋊Dic11—21no—
145C4⋊Dic11C22×C411yescharacteristic
146C4⋊Dic11C22×C411yescharacteristic
147#4318—22no—
148#4318SD1614yescomplemented
149C2×C11⋊C8—21no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—42no—
152C2×C11⋊C8C22×C412yes—
153C2×C11⋊C8C22×C412yes—
154C2×C11⋊C8C2×D412yes—
155C2×C11⋊C8C2×D412yes—
156#4313—44no—
157C8×D11—44no—
158#3101—111no—
159#2962—111no—
160D4×M16—111no—
161#1590—112no—
162#1583—112no—
163#1582—112no—
164C8×SD16—112no—
165#1570—111no—
166#1493D1111yescharacteristic, complemented
167C2×D4⋊C8—111no—
168C8×M16—111no—
169C23×C11C4×D411yescharacteristic
170C22×D11—21no—
171C22×D11—21no—
172C22×D11—42no—
173C22×D11—42no—
174C22×D11—81no—
175Q8×C11—22no—
176Q8×C11—22no—
177Q8×C11—81no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—41no—
183C2×C4×C11C4×D411yescharacteristic
184C2×C4×C11C4×D411yescharacteristic
185C2×C4×C11C4×D411yescharacteristic
186C2×C4×C11C2×SD1612yes—
187C2×C4×C11#13512yes—
188C2×C4×C11C23×C411yescharacteristic
189C2×C4×C11C22×D411yescharacteristic
190C2×C4×C11C2×#4111yescharacteristic
191C2×Dic11—21no—
192C2×Dic11—21no—
193C2×Dic11—42no—
194D44—21no—
195D44—21no—
196D44—21no—
197D44—42no—
198D44#13112yes—
199C4×D11—41no—
200C4×D11—41no—
201C4×D11—41no—
202C4×D11—41no—
203C4×D11—42no—
204C4×D11—42no—
205C8×C11—22no—
206C8×C11—41no—
207C8×C11—42no—
208C11⋊C8—22no—
209C11⋊C8—22no—
210C11⋊C8—22no—
211C11⋊C8—41no—
212C11⋊C8—41no—
213C11⋊C8C2×SD1614yes—
214C22×M16—221no—
215#533C2×D1111yescharacteristic
216C2×C4×D4—111no—
217#483—112no—
218#476—111no—
219#476—111no—
220#461—111no—
221#461—111no—
222#450—112no—
223#446—112no—
224#446—222no—
225C8×Q8—112no—
226C4×SD16—112no—
227C4×SD16—112no—
228#436—112no—
229#435—222no—
230C8×D4—112no—
231#431—111no—
232#424—221no—
233#423C2×D1111yescharacteristic
234C2×C4⋊C8—111no—
235#407—221no—
236#405—221no—
237C4×M16—111no—
238C2×C4×C8C2×D1111yescharacteristic
239#334—112no—
240#334—112no—
241Q8⋊C8C2×D1112yescomplemented
242Q8⋊C8C2×D1112yescomplemented
243D4⋊C8—111no—
244D4⋊C8—111no—
245D4⋊C8—111no—
246D4⋊C8—111no—
247#322—112no—
248C82—112no—
249C22×C11—21no—
250C22×C11—21no—
251C22×C11C4×SD1612yes—
252C22×C11C2×C4×D411yescharacteristic
253C2×D11—22no—
254C2×D11—41no—
255C2×D11—41no—
256C2×D11—41no—
257C2×D11—41no—
258C2×D11—41no—
259C2×D11—84no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—42no—
264C4×C11—42no—
265C4×C11C4×SD1612yes—
266C4×C11C2×#13111yescharacteristic
267C4×C11#56811yescharacteristic
268C4×C11C22×SD1611yescharacteristic
269C4×C11C2×#13511yescharacteristic
270Dic11—41no—
271Dic11—41no—
272C22×D4—111no—
273C23×C4—221no—
274C2×SD16—112no—
275C2×SD16—112no—
276C2×M16—21no—
277C2×M16—111no—
278C2×M16—111no—
279C2×M16—222no—
280C2×M16—444no—
281C22×C8—21no—
282C22×C8—222no—
283C22×C8—221no—
284C4⋊Q8C4×D1111yescharacteristic
285C4⋊Q8C4×D1111yescharacteristic
286#125—21no—
287C22⋊Q8—21no—
288C22⋊Q8C4×D1112yes—
289C4×Q8—21no—
290C4×Q8C22×D1112yes—
291C4×D4—111no—
292C4×D4—111no—
293C4×D4—111no—
294C4×D4—111no—
295C4×D4—221no—
296C4×D4—221no—
297#117—21no—
298C2×C4⋊C4—111no—
299C2×C22⋊C4—221no—
300C2×C42C22×D1111yescharacteristic
301#106—112no—
302#106—112no—
303C4⋊C8—21no—
304C4⋊C8—111no—
305C4⋊C8—111no—
306C4⋊C8—111no—
307C4⋊C8—111no—
308C4⋊C8—222no—
309C4⋊C8—222no—
310C4⋊C8—221no—
311C4⋊C8C22×D1112yes—
312#103—112no—
313#103—112no—
314#102—112no—
315#102—112no—
316C22⋊C8—112no—
317C22⋊C8—222no—
318C22⋊C8—222no—
319#97—112no—
320#97—222no—
321C4×C8—21no—
322C4×C8—112no—
323C4×C8—112no—
324C4×C8—222no—
325C4×C8C22×D1111yescharacteristic
326C4×C8C22×D1111yescharacteristic
327C2×C11—22no—
328C2×C11#293311yescharacteristic
329C2×C11C2×C4×SD1611yescharacteristic
330C2×C11#295611yescharacteristic
331D11—42no—
332D11—81no—
333C24—221no—
334C2×Q8—21no—
335C2×Q8C2×C4×D1112yes—
336C2×D4—111no—
337C2×D4—111no—
338C2×D4—222no—
339C2×D4—221no—
340C2×D4—441no—
341C22×C4—221no—
342C22×C4—221no—
343C22×C4—221no—
344C22×C4—221no—
345C22×C4—221no—
346C22×C4—442no—
347C22×C4—442no—
348C22×C4C2×C4×D1111yescharacteristic
349C22×C4D4×D1111yescharacteristic
350C22×C4#434111yescharacteristic
351SD16—224no—
352SD16—442no—
353M16—42no—
354M16—114no—
355M16—222no—
356M16—444no—
357C2×C8—21no—
358C2×C8—22no—
359C2×C8—21no—
360C2×C8—42no—
361C2×C8—112no—
362C2×C8—112no—
363C2×C8—112no—
364C2×C8—112no—
365C2×C8—221no—
366C2×C8—221no—
367C2×C8—444no—
368C2×C8—442no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—111no—
375C4⋊C4—111no—
376C4⋊C4—221no—
377C4⋊C4C2×C4×D1112yes—
378C22⋊C4—22no—
379C22⋊C4—221no—
380C22⋊C4—221no—
381C22⋊C4—221no—
382C22⋊C4—221no—
383C42—22no—
384C42C2×C4×D1111yescharacteristic
385C42D4×D1111yescharacteristic
386C42#434111yescharacteristic
387C42C23×D1111yescharacteristic
388C11#1799511yescharacteristic, complemented, Sylow
389C23—221no—
390C23—221no—
391C23—442no—
392C23—442no—
393C23—881no—
394C23(C22⋊D11)⋊C411yescharacteristic
395Q8—22no—
396Q8—22no—
397Q8—81no—
398D4—112no—
399D4—221no—
400D4—221no—
401D4—221no—
402D4—442no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—41no—
408C2×C4—221no—
409C2×C4—221no—
410C2×C4—442no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4—441no—
414C2×C4—441no—
415C2×C4—442no—
416C2×C4—442no—
417C2×C4(C22⋊D11)⋊C411yescharacteristic
418C2×C4(C22⋊D11)⋊C411yescharacteristic
419C2×C4(C22⋊D11)⋊C411yescharacteristic
420C2×C4SD16×D1112yes—
421C2×C4#6697212yes—
422C2×C4C22×C4×D1111yescharacteristic
423C2×C4C2×D4×D1111yescharacteristic
424C2×C4C2×#434111yescharacteristic
425C8—22no—
426C8—41no—
427C8—42no—
428C8—114no—
429C8—222no—
430C8—222no—
431C8—222no—
432C8—441no—
433C8—441no—
434C22—21no—
435C22—21no—
436C22—222no—
437C22—441no—
438C22—441no—
439C22—441no—
440C22—441no—
441C22—441no—
442C22—884no—
443C22#1062240112yes—
444C22C2×(C22⋊D11)⋊C411yescharacteristic
445C4—21no—
446C4—21no—
447C4—21no—
448C4—42no—
449C4—42no—
450C4—441no—
451C4—441no—
452C4#1062240112yes—
453C4D11×#13111yescharacteristic
454C4#1062328111yescharacteristic
455C4C2×SD16×D1111yescharacteristic
456C4C2×#6697211yescharacteristic
457C2—22no—
458C2—442no—
459C2—881no—
460C2#1307734611yescharacteristic
461C2C2×#1062240111yescharacteristic
462C2#1307752211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1493C2
socleC22×C11C2×C4×D4
prime radicalC22×D44C2×C4
cosocleC42×C11C24
hypercenter#1493D11
hypocenterC11#17995
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1493

Complements

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

NH ≅ G/Ntype
2. #13077565C2semidirect
4. #13067503C2semidirect
5. #13067456C2semidirect
6. #13067455C2semidirect
7. #13067413C2semidirect
8. #13067388C2semidirect
10. C8×#4318C2semidirect
11. C11×#1493C2semidirect
27. #10622637C22semidirect
28. Q8×C11⋊C8C22semidirect
37. C11×Q8⋊C8C22semidirect
38. C11×Q8⋊C8C22semidirect
39. #10622118C22semidirect
40. #10622118C22semidirect
45. #10622092C22semidirect
46. C8×C11⋊C8C22semidirect
148. #4318SD16semidirect
166. #1493D11semidirect
241. Q8⋊C8C2×D11semidirect
242. Q8⋊C8C2×D11semidirect
388. C11#17995semidirect

Maximal subgroups

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

subgroupindex
#130786202
#130775652
#130773512
#130675032
#130674562
#130674552
#130674132
#130673882
C2×#106220972
C8×#43182
C11×#14932
#1799511