Finite Group Databasebeta

← #14754764

Subgroups — #14754764

Order 2816.

1382 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623047C211yesmaximal, characteristic
2C2×#10622733C211yesmaximal, characteristic
3C22×#66874C211yesmaximal, characteristic
4#13071240C211yesmaximal, characteristic
5#13068881C214yesmaximal, complemented
6#13068867C214yesmaximal, complemented
7#13068332C211yesmaximal, characteristic
8#13068314C211yesmaximal, characteristic
9C2×C11×#428C211yesmaximal, characteristic
10C23×Dic22C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C23×C11⋊C8C2211yescharacteristic
17#10623047—24no—
18#10623047—24no—
19C2×#66940C2212yes—
20C2×#66940C2212yes—
21C2×#66930—22no—
22C2×C4×Dic22—21no—
23C2×C4×Dic22—21no—
24C11×#428—24no—
25C2×C11×#107C2212yes—
26C2×C11×#106C2212yes—
27#10622823—22no—
28#10622733C418yescomplemented
29C2×#66880C2214yes—
30#10622590—21no—
31#10622589—21no—
32#10622586C2214yes—
33C2×#66874—24no—
34C2×#66874C2214yes—
35#10622188C2214yes—
36#10622167C2212yes—
37#10622167C2212yes—
38C23×C4×C11—21no—
39C23×C4×C11C2311yescharacteristic
40C23×Dic11—21no—
41C22×Dic22—21no—
42C22×Dic22—22no—
43C22×Dic22—22no—
44C22×Dic22—22no—
45C22×Dic22C2×C414yes—
46C22×Dic22D414yes—
47C22×Dic22Q814yes—
48C22×Dic22C2312yes—
49C2×C11×M16—22no—
50C2×C11×M16—22no—
51C2×C11×M16C2×C414yes—
52C22×C8×C11C2312yes—
53C11×#117—22no—
54C11×#117D414yes—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C22⋊C4—21no—
62C2×C42×C11—21no—
63C2×C22⋊Dic11—21no—
64C2×C22⋊Dic11D412yes—
65#66979—22no—
66#66979—22no—
67#66979—22no—
68#66979C2×C414yes—
69C2×C4⋊Dic11D411yescharacteristic
70C2×C4⋊Dic11D411yescharacteristic
71C2×C4⋊Dic11C2312yes—
72C2×Dic11⋊C4—22no—
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4—24no—
75C2×C4×Dic11—21no—
76C2×C4×Dic11—22no—
77C2×C4×Dic11—22no—
78C2×C4×Dic11C2312yes—
79C22×C11⋊C8—22no—
80C22×C11⋊C8—22no—
81C22×C11⋊C8—22no—
82C22×C11⋊C8C2312yes—
83#66940—24no—
84#66940—24no—
85#66940—24no—
86#66940—24no—
87#66930—216no—
88C4×Dic22—28no—
89C4×Dic22—28no—
90C11×#107—24no—
91C11×#106—24no—
92C11⋊#95—24no—
93#66880C2×C4116yescomplemented
94#66874—28no—
95#20877—111nomaximal, Sylow
96C24×C11C2×D411yescharacteristic
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—42no—
101C22×C4×C11—82no—
102C22×C4×C11C22×C412yes—
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×Q812yes—
107C22×C4×C11#4112yes—
108C22×C4×C11#4112yes—
109C22×C4×C11C2411yescharacteristic
110C22×Dic11—24no—
111C22×Dic11—24no—
112C22×Dic11—24no—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11C2×D412yes—
116C22×Dic11C2×D412yes—
117C2×Dic22—24no—
118C2×Dic22—28no—
119C2×Dic22—24no—
120C2×Dic22—24no—
121C2×Dic22—28no—
122C2×Dic22—28no—
123C2×Dic22—22no—
124C2×Dic22—22no—
125C2×Dic22—22no—
126C2×Dic22C4⋊C4116yescomplemented
127C2×Dic22C22×C414yes—
128C2×Dic22C2×D414yes—
129C2×Dic22C2×Q814yes—
130C11×M16—28no—
131C2×C8×C11—22no—
132C2×C8×C11—22no—
133C2×C8×C11C22×C414yes—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—42no—
139C11×C4⋊C4C2×D412yes—
140C11×C4⋊C4C2×D412yes—
141C11×C22⋊C4—24no—
142C42×C11—24no—
143C22⋊Dic11—24no—
144C22⋊Dic11—24no—
145C4⋊Dic11—22no—
146C4⋊Dic11—22no—
147C4⋊Dic11—22no—
148C4⋊Dic11C22×C414yes—
149Dic11⋊C4—28no—
150Dic11⋊C4—28no—
151Dic11⋊C4—84no—
152C4×Dic11—28no—
153C4×Dic11—28no—
154C4×Dic11—24no—
155C4×Dic11—22no—
156C4×Dic11—22no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—44no—
161C2×#519—111no—
162C2×#428D1111yescharacteristic
163C2×#419—111no—
164C22×#103—111no—
165#2317—111no—
166#1865—114no—
167#1863—114no—
168#1735—111no—
169#1729—111no—
170C23×C11—22no—
171C23×C11—22no—
172C23×C11C4×D412yes—
173C23×C11#12012yes—
174C23×C11C22⋊Q812yes—
175C23×C11C22×D411yescharacteristic
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—44no—
182C2×C4×C11—84no—
183C2×C4×C11C2×C4⋊C414yes—
184C2×C4×C11C4×D412yes—
185C2×C4×C11C4×D414yes—
186C2×C4×C11#12012yes—
187C2×C4×C11C22⋊Q812yes—
188C2×C4×C11C22⋊Q814yes—
189C2×C4×C11#12314yes—
190C2×C4×C11C23×C411yescharacteristic
191C2×C4×C11C22×D411yescharacteristic
192C2×C4×C11C22×D411yescharacteristic
193C2×C4×C11C22×Q811yescharacteristic
194C2×C4×C11C2×#4111yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C2×Dic11—24no—
197C2×Dic11—24no—
198C2×Dic11—24no—
199C2×Dic11—216no—
200C2×Dic11—24no—
201C2×Dic11—22no—
202C2×Dic11—22no—
203C2×Dic11—24no—
204C2×Dic11—24no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207Dic22—24no—
208Dic22—24no—
209Dic22—24no—
210Dic22—216no—
211Dic22C2×C4⋊C418yes—
212C8×C11—24no—
213C11⋊C8—42no—
214C23×Q8—111no—
215C22×M16C2×D1111yescharacteristic
216C23×C8—111no—
217#519—224no—
218#519—224no—
219C2×C4×Q8—112no—
220C2×C4×Q8—112no—
221C2×C4×Q8—221no—
222C2×C4×Q8—221no—
223C2×#117—111no—
224C2×#117—111no—
225C2×#117—222no—
226C2×#117C2×D1111yescharacteristic
227C22×C4⋊C4C2×D1111yescharacteristic
228#428—24no—
229C2×#107C2×D1112yes—
230C2×#106C2×D1112yes—
231#419—118no—
232C2×#103—114no—
233C2×#103—114no—
234C2×#103—224no—
235#389—114no—
236#385—222no—
237#384—221no—
238#382—221no—
239#340—112no—
240#340—112no—
241#336—114no—
242C22×C11—24no—
243C22×C11—24no—
244C22×C11—22no—
245C22×C11—22no—
246C22×C11#38514yes—
247C22×C11C2×C4×D411yescharacteristic
248C22×C11C2×#12011yescharacteristic
249C22×C11C2×C22⋊Q811yescharacteristic
250C22×C11#57712yes—
251C22×C11#57812yes—
252C4×C11—42no—
253C4×C11—42no—
254C4×C11—82no—
255C4×C11#38514yes—
256C4×C11C22×C4⋊C411yescharacteristic
257C4×C11C2×C4×D411yescharacteristic
258C4×C11C2×C22⋊Q811yescharacteristic
259C4×C11C2×#12311yescharacteristic
260Dic11—28no—
261Dic11—44no—
262Dic11—42no—
263Dic11—42no—
264C22×Q8—114no—
265C22×Q8—114no—
266C22×Q8—114no—
267C22×Q8—112no—
268C22×Q8—222no—
269C22×Q8—221no—
270C22×Q8—222no—
271C22×Q8—222no—
272C23×C4—21no—
273C23×C4—221no—
274C23×C4C22×D1111yescharacteristic
275C2×M16—22no—
276C2×M16—22no—
277C2×M16C4×D1114yes—
278C22×C8—112no—
279C22×C8—222no—
280C22×C8—222no—
281C22×C8—222no—
282C22×C8C22×D1112yes—
283C4×Q8—228no—
284C4×Q8—228no—
285C4×Q8—224no—
286C4×Q8—224no—
287C4×Q8—224no—
288C4×Q8—224no—
289#117—22no—
290#117—114no—
291#117—2216no—
292#117—222no—
293#117—222no—
294#117—222no—
295#117C22⋊D1114yes—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—112no—
300C2×C4⋊C4—111no—
301C2×C4⋊C4—111no—
302C2×C4⋊C4—222no—
303C2×C4⋊C4—222no—
304C2×C4⋊C4—224no—
305C2×C4⋊C4C22×D1112yes—
306C2×C4⋊C4C22×D1111yescharacteristic
307C2×C4⋊C4C22×D1111yescharacteristic
308C2×C22⋊C4—21no—
309C2×C22⋊C4—112no—
310C2×C22⋊C4—221no—
311C2×C42—21no—
312C2×C42—112no—
313C2×C42—222no—
314C2×C42—222no—
315C2×C42—221no—
316#107—24no—
317#106—24no—
318#103—1116no—
319#103—228no—
320#95—224no—
321C2×C11—24no—
322C2×C11C2×#38511yescharacteristic
323C2×C11#294712yes—
324C2×C11#301011yescharacteristic
325C2×C11#301111yescharacteristic
326C2×C11#308212yes—
327C24D4×D1111yescharacteristic
328C2×Q8—1116no—
329C2×Q8—114no—
330C2×Q8—114no—
331C2×Q8—114no—
332C2×Q8—224no—
333C2×Q8—228no—
334C2×Q8—224no—
335C2×Q8—228no—
336C2×Q8—224no—
337C2×Q8—228no—
338C2×Q8—222no—
339C2×Q8—222no—
340C2×Q8—222no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—22no—
344C22×C4—42no—
345C22×C4—82no—
346C22×C4—112no—
347C22×C4—112no—
348C22×C4—224no—
349C22×C4—224no—
350C22×C4—224no—
351C22×C4—222no—
352C22×C4—222no—
353C22×C4C2×C4×D1112yes—
354C22×C4#433912yes—
355C22×C4D4×D1112yes—
356C22×C4D4×D1111yescharacteristic
357C22×C4Q8×D1112yes—
358C22×C4#434312yes—
359C22×C4C2×C22⋊D1112yes—
360C22×C4C23×D1111yescharacteristic
361M16—28no—
362C2×C8—22no—
363C2×C8—22no—
364C2×C8—222no—
365C2×C8—222no—
366C2×C8—222no—
367C2×C8—444no—
368C2×C8C2×C4×D1114yes—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—42no—
374C4⋊C4—114no—
375C4⋊C4—228no—
376C4⋊C4—228no—
377C4⋊C4—222no—
378C4⋊C4—222no—
379C4⋊C4—222no—
380C4⋊C4—884no—
381C4⋊C4C2×C22⋊D1112yes—
382C4⋊C4C2×C22⋊D1112yes—
383C22⋊C4—24no—
384C22⋊C4—224no—
385C22⋊C4—224no—
386C42—24no—
387C42—228no—
388C42—228no—
389C42—224no—
390C42—222no—
391C42—222no—
392C11#2087711yescharacteristic, complemented, Sylow
393C23—22no—
394C23—22no—
395C23#6694612yes—
396C23#6694912yes—
397C23#6699012yes—
398C23C2×D4×D1111yescharacteristic
399Q8—118no—
400Q8—224no—
401Q8—224no—
402Q8—224no—
403Q8—2216no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—44no—
409C2×C4—42no—
410C2×C4—84no—
411C2×C4—224no—
412C2×C4—224no—
413C2×C4—224no—
414C2×C4—2216no—
415C2×C4—224no—
416C2×C4—224no—
417C2×C4—224no—
418C2×C4—222no—
419C2×C4—222no—
420C2×C4—442no—
421C2×C4—442no—
422C2×C4C4⋊C4×D1114yes—
423C2×C4#6694612yes—
424C2×C4#6694714yes—
425C2×C4#6694912yes—
426C2×C4C4×C22⋊D1114yes—
427C2×C4#6699012yes—
428C2×C4#6699914yes—
429C2×C4C22×C4×D1111yescharacteristic
430C2×C4C2×#433911yescharacteristic
431C2×C4C2×D4×D1111yescharacteristic
432C2×C4C2×Q8×D1111yescharacteristic
433C2×C4C2×#434311yescharacteristic
434C2×C4C22×C22⋊D1111yescharacteristic
435C8—24no—
436C8—442no—
437C22—22no—
438C22—22no—
439C22—24no—
440C22—24no—
441C22#1062260214yes—
442C22C2×#6694611yescharacteristic
443C22C2×#6694911yescharacteristic
444C22#1062330612yes—
445C22#1062331012yes—
446C22C2×#6699011yescharacteristic
447C4—42no—
448C4—42no—
449C4—82no—
450C4—228no—
451C4—442no—
452C4—442no—
453C4—444no—
454C4#1062260214yes—
455C4C2×C4⋊C4×D1111yescharacteristic
456C4C2×#6694711yescharacteristic
457C4C2×C4×C22⋊D1111yescharacteristic
458C4C2×#6699911yescharacteristic
459C2—24no—
460C2C2×#1062260211yescharacteristic
461C2#1307745712yes—
462C2#1307790111yescharacteristic
463C2#1307791011yescharacteristic
464C2#1307845612yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#428C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×#428D11
hypocenterC11#20877
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
5. #13068881C2semidirect
6. #13068867C2semidirect
28. #10622733C4semidirect
93. #66880C2×C4semidirect
126. C2×Dic22C4⋊C4semidirect
392. C11#20877semidirect

Maximal subgroups

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

subgroupindex
C2×#106230472
C2×#106227332
C22×#668742
#130712402
#130688812
#130688672
#130683322
#130683142
C2×C11×#4282
#2087711