Finite Group Databasebeta

← #14789992

Subgroups — #14789992

Order 2816.

1170 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#13078409C212yesmaximal, complemented
2C4×#66993C211yesmaximal, characteristic
3#13069958C212yesmaximal, complemented
4#13069769C212yesmaximal, complemented
5#13069594C212yesmaximal, complemented
6#13069014C212yesmaximal
7#13068826C212yesmaximal, complemented
8#13068608C211yesmaximal, characteristic, complemented
9C11×#3501C211yesmaximal, characteristic, complemented
10C11×#554—22no—
11C11×#554—24no—
12D4×Q8×C11—22no—
13C11×#544C2212yes—
14C11×#543—22no—
15C11×#533C2212yes—
16C2×C11×C22⋊Q8—22no—
17C11×#518C2212yes—
18C2×C4×D4×C11C2211yescharacteristic
19C2×#66993C2211yescharacteristic
20C2×C4×C22⋊D11—22no—
21C2×C4×D44C2211yescharacteristic
22#10622834C2211yescharacteristic
23C2×#66897C2212yes—
24#10622700—22no—
25#10622697—22no—
26#10622679—24no—
27#10622614C2214yes—
28#10622608C2214yes—
29#10622601C2211yescharacteristic
30#10622589C2211yescharacteristic
31#10622570—22no—
32C42×Dic11C2211yescharacteristic
33#10622537C2212yes—
34#10622170C2214yes—
35#10622170C2214yes—
36#10622168C2212yes—
37C22×Q8×C11—22no—
38C22×D4×C11C2311yescharacteristic
39C23×C4×C11D412yes—
40C22×C22⋊D11—22no—
41C22×D44C2311yescharacteristic
42C22×C4×D11—21no—
43C11×C4⋊Q8—24no—
44C11×C4⋊Q8D412yescomplemented
45C11×C4⋊Q8D412yescomplemented
46C11×#125—24no—
47C11×#125D414yescomplemented
48C11×C22⋊Q8—24no—
49C11×C22⋊Q8—24no—
50C11×C22⋊Q8—28no—
51C11×C22⋊Q8—28no—
52C11×C22⋊Q8—22no—
53C11×C22⋊Q8—24no—
54C11×C22⋊Q8—22no—
55C4×Q8×C11—22no—
56C4×Q8×C11—22no—
57C4×D4×C11—24no—
58C4×D4×C11—24no—
59C4×D4×C11—22no—
60C4×D4×C11—22no—
61C11×#117C2314yes—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—24no—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C22⋊C4—24no—
66C2×C11×C22⋊C4D412yes—
67C2×C42×C11C2311yescharacteristic
68C2×C22⋊Dic11—22no—
69#66993—22no—
70#66993Q814yescomplemented
71C4×C22⋊D11—48no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—22no—
74C2×C4⋊Dic11C2311yescharacteristic
75C2×Dic11⋊C4—22no—
76C2×C4×Dic11—21no—
77C2×C4×Dic11—21no—
78C2×C4×Dic11C2311yescharacteristic
79C2×C4×Dic11C2311yescharacteristic
80C2×#4318C2314yes—
81C4×D44—22no—
82C4×D44—22no—
83#66897—24no—
84#66873—24no—
85#66873—24no—
86#66872—24no—
87#66871—24no—
88C4⋊(C11⋊C8)—22no—
89C4⋊(C11⋊C8)—22no—
90#24312—111nomaximal, Sylow
91C24×C11C2×D412yes—
92C23×D11—21no—
93C2×Q8×C11—24no—
94C2×Q8×C11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11—84no—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11C2×Q812yes—
100C2×D4×C11#4112yes—
101C22×C4×C11—24no—
102C22×C4×C11—24no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—44no—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2411yescharacteristic
110C2×C22⋊D11—28no—
111C2×C22⋊D11—44no—
112C2×C22⋊D11—44no—
113C22×Dic11—21no—
114C22×Dic11—21no—
115C22×Dic11—21no—
116C2×D44—22no—
117C2×D44—21no—
118C2×D44—22no—
119C2×D44C2×Q812yescomplemented
120C2×C4×D11—44no—
121C2×C4×D11—41no—
122C2×C4×D11—41no—
123C11×C4⋊C4—24no—
124C11×C4⋊C4—28no—
125C11×C4⋊C4—24no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—24no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4C2×D414yes—
131C11×C4⋊C4C2×D414yes—
132C11×C22⋊C4—28no—
133C11×C22⋊C4—24no—
134C11×C22⋊C4—24no—
135C42×C11—24no—
136C42×C11C2×D412yes—
137C42×C11C2×D412yes—
138C22⋊Dic11—44no—
139(C2×D11)⋊C4—44no—
140(C2×D11)⋊C4—42no—
141C4⋊Dic11—22no—
142Dic11⋊C4—44no—
143C4×Dic11—24no—
144C4×Dic11—21no—
145C4×Dic11—22no—
146C4×Dic11—42no—
147C4×Dic11C2×Q812yescomplemented
148#4318—24no—
149#4318—24no—
150C2×C11⋊C8—24no—
151#3501D1111yescharacteristic, complemented
152#3077—112no—
153C4×#127—111no—
154#2060—112no—
155#2027—112no—
156#1994—112no—
157#1887—112no—
158#1856—112no—
159#1800—111no—
160C23×C11—22no—
161C23×C11—22no—
162C23×C11—42no—
163C23×C11—42no—
164C23×C11C22⋊Q814yes—
165C23×C11C22×D411yescharacteristic
166C22×D11—22no—
167C22×D11—42no—
168C22×D11—42no—
169C22×D11—41no—
170C22×D11—41no—
171Q8×C11—44no—
172Q8×C11—82no—
173Q8×C11—84no—
174D4×C11—24no—
175D4×C11—24no—
176C2×C4×C11—22no—
177C2×C4×C11—24no—
178C2×C4×C11—24no—
179C2×C4×C11—22no—
180C2×C4×C11—41no—
181C2×C4×C11—44no—
182C2×C4×C11—42no—
183C2×C4×C11—82no—
184C2×C4×C11—84no—
185C2×C4×C11—84no—
186C2×C4×C11#12012yes—
187C2×C4×C11#12011yescharacteristic
188C2×C4×C11#12011yescharacteristic
189C2×C4×C11C22×D412yes—
190C2×C4×C11C22×Q811yescharacteristic
191C2×C4×C11C2×#4111yescharacteristic
192C2×C4×C112−1+412yes—
193C22⋊D11—416no—
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—42no—
201C2×Dic11—41no—
202D44—24no—
203D44—42no—
204C4×D11—82no—
205C4×D11—82no—
206C11⋊C8—44no—
207#554—22no—
208#554—24no—
209D4×Q8—22no—
210#544C2×D1112yes—
211#543—22no—
212#533C2×D1112yes—
213C2×#127—111no—
214C2×C22⋊Q8—22no—
215#518C2×D1112yes—
216C2×C4×D4—111no—
217C2×C4×D4—222no—
218C2×C4×D4C2×D1111yescharacteristic
219#478—224no—
220#476—222no—
221#474—222no—
222#428—114no—
223#423—112no—
224#418—114no—
225C2×#100—112no—
226#390—111no—
227#390—111no—
228#390—222no—
229#384—111no—
230C43—111no—
231#343—112no—
232#339—114no—
233#339—114no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—24no—
237C22×C11—44no—
238C22×C11—42no—
239C22×C11—42no—
240C22×C11—82no—
241C22×C11C2×#12011yescharacteristic
242C22×C11C2×C22⋊Q811yescharacteristic
243C22×C11#53611yescharacteristic
244C2×D11—44no—
245C2×D11—42no—
246C2×D11—82no—
247C2×D11—81no—
248C2×D11—81no—
249C4×C11—21no—
250C4×C11—22no—
251C4×C11—42no—
252C4×C11—44no—
253C4×C11—44no—
254C4×C11#45312yes—
255C4×C11#54812yes—
256C4×C11D4×Q812yes—
257Dic11—24no—
258Dic11—42no—
259Dic11—81no—
260C22×Q8—22no—
261C22×D4—111no—
262C22×D4—222no—
263C22×D4C22×D1111yescharacteristic
264C23×C4—221no—
265C23×C4C22⋊D1112yes—
266C2×M16—114no—
267C4⋊Q8—24no—
268C4⋊Q8C22⋊D1112yescomplemented
269C4⋊Q8C22⋊D1112yescomplemented
270#127—114no—
271#127—222no—
272#125—24no—
273#125C22⋊D1114yescomplemented
274C22⋊Q8—24no—
275C22⋊Q8—24no—
276C22⋊Q8—28no—
277C22⋊Q8—28no—
278C22⋊Q8—22no—
279C22⋊Q8—24no—
280C22⋊Q8—22no—
281C4×Q8—22no—
282C4×Q8—22no—
283C4×D4—24no—
284C4×D4—24no—
285C4×D4—22no—
286C4×D4—22no—
287C4×D4—222no—
288C4×D4—222no—
289C4×D4—448no—
290#117C22×D1114yes—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—111no—
294C2×C4⋊C4—222no—
295C2×C4⋊C4C22×D1111yescharacteristic
296C2×C22⋊C4—24no—
297C2×C22⋊C4—222no—
298C2×C22⋊C4—221no—
299C2×C22⋊C4—222no—
300C2×C22⋊C4C22⋊D1112yes—
301C2×C42—111no—
302C2×C42—111no—
303C2×C42—221no—
304C2×C42—221no—
305C2×C42C22×D1111yescharacteristic
306#107—224no—
307#106—224no—
308C4⋊C8—222no—
309C4⋊C8—222no—
310#102—224no—
311#102—224no—
312#100—224no—
313C2×C11—21no—
314C2×C11—21no—
315C2×C11—44no—
316C2×C11#240911yescharacteristic
317C2×C11C2×#45311yescharacteristic
318C2×C11#301811yescharacteristic
319D11—82no—
320C24—221no—
321C24C2×C22⋊D1112yes—
322C2×Q8—24no—
323C2×Q8—22no—
324C2×Q8—22no—
325C2×Q8—84no—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4—112no—
329C2×D4—228no—
330C2×D4—221no—
331C2×D4—222no—
332C2×D4—222no—
333C2×D4—444no—
334C2×D4—444no—
335C2×D4Q8×D1112yes—
336C2×D4#434312yes—
337C22×C4—24no—
338C22×C4—24no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—44no—
342C22×C4—221no—
343C22×C4—221no—
344C22×C4—221no—
345C22×C4—444no—
346C22×C4—441no—
347C22×C4—441no—
348C22×C4C2×C22⋊D1111yescharacteristic
349C22×C4C2×C22⋊D1112yes—
350C22×C4C2×C22⋊D1111yescharacteristic
351C22×C4C23×D1111yescharacteristic
352M16—224no—
353M16—224no—
354C2×C8—224no—
355C4⋊C4—24no—
356C4⋊C4—28no—
357C4⋊C4—24no—
358C4⋊C4—22no—
359C4⋊C4—24no—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—222no—
363C4⋊C4—444no—
364C4⋊C4C2×C22⋊D1114yes—
365C4⋊C4C2×C22⋊D1114yes—
366C22⋊C4—28no—
367C22⋊C4—24no—
368C22⋊C4—24no—
369C22⋊C4—444no—
370C22⋊C4—444no—
371C22⋊C4—442no—
372C42—24no—
373C42—112no—
374C42—224no—
375C42—221no—
376C42—222no—
377C42—442no—
378C42C2×C22⋊D1112yes—
379C42C2×C22⋊D1112yes—
380C11#2431211yescharacteristic, complemented, Sylow
381C23—22no—
382C23—22no—
383C23—42no—
384C23—42no—
385C23—222no—
386C23—442no—
387C23—442no—
388C23—441no—
389C23—441no—
390C23#6699914yes—
391C23C22×C22⋊D1111yescharacteristic
392Q8—44no—
393Q8—82no—
394Q8—84no—
395D4—24no—
396D4—24no—
397D4—224no—
398D4—4416no—
399D4—442no—
400C2×C4—22no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—22no—
404C2×C4—41no—
405C2×C4—44no—
406C2×C4—42no—
407C2×C4—82no—
408C2×C4—84no—
409C2×C4—84no—
410C2×C4—222no—
411C2×C4—222no—
412C2×C4—222no—
413C2×C4—222no—
414C2×C4—441no—
415C2×C4—441no—
416C2×C4—442no—
417C2×C4—441no—
418C2×C4—882no—
419C2×C4—882no—
420C2×C4#6700612yes—
421C2×C4#6700611yescharacteristic
422C2×C4#6700611yescharacteristic
423C2×C4C2×Q8×D1111yescharacteristic
424C2×C4C2×#434311yescharacteristic
425C2×C4#6704012yes—
426C2×C4C22×C22⋊D1112yes—
427C8—444no—
428C22—21no—
429C22—21no—
430C22—24no—
431C22—44no—
432C22—42no—
433C22—42no—
434C22—82no—
435C22—444no—
436C22—442no—
437C22—882no—
438C22—881no—
439C22—881no—
440C22C2×#6699911yescharacteristic
441C22#1062334711yescharacteristic
442C22C2×#6700611yescharacteristic
443C4—21no—
444C4—22no—
445C4—42no—
446C4—44no—
447C4—44no—
448C4—224no—
449C4—442no—
450C4—881no—
451C4#1062285412yes—
452C4Q8×C22⋊D1112yes—
453C4#1062334812yes—
454C2—21no—
455C2—21no—
456C2—44no—
457C2—882no—
458C2#1307197511yescharacteristic
459C2C2×#1062285411yescharacteristic
460C2#1307796511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3501C2
socleC22×C11C2×#120
prime radicalC2×#66993C22
hypercenter#3501D11
hypocenterC11#24312
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #13078409C2semidirect
3. #13069958C2semidirect
4. #13069769C2semidirect
5. #13069594C2semidirect
7. #13068826C2semidirect
8. #13068608C2semidirect
9. C11×#3501C2semidirect
44. C11×C4⋊Q8D4semidirect
45. C11×C4⋊Q8D4semidirect
47. C11×#125D4semidirect
70. #66993Q8semidirect
119. C2×D44C2×Q8semidirect
147. C4×Dic11C2×Q8semidirect
151. #3501D11semidirect
268. C4⋊Q8C22⋊D11semidirect
269. C4⋊Q8C22⋊D11semidirect
273. #125C22⋊D11semidirect
380. C11#24312semidirect

Maximal subgroups

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

subgroupindex
#130784092
C4×#669932
#130699582
#130697692
#130695942
#130690142
#130688262
#130686082
C11×#35012
#2431211