Finite Group Databasebeta

← #14763118

Subgroups — #14763118

Order 2816.

1398 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623256C211yesmaximal, characteristic
2C2×#10622448C211yesmaximal, characteristic, complemented
3#13071020C211yesmaximal, characteristic, complemented
4#13069543C211yesmaximal, characteristic, complemented
5#13069542C211yesmaximal, characteristic, complemented
6#13069540C211yesmaximal, characteristic, complemented
7#13069429C214yesmaximal, complemented
8#13068555C214yesmaximal, complemented
9C11×#1981C211yesmaximal, characteristic, complemented
10C22×#4343C2212yes—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#67000C2212yes—
13#10623256—24no—
14#10623256C418yescomplemented
15C2×#66948—21no—
16C2×#66948—21no—
17C2×#66946—21no—
18C2×#66946—21no—
19C2×#66927C2211yescharacteristic
20C2×#66925—21no—
21C2×C42×D11C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×#103C2214yes—
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×#66899C2214yes—
26C2×#66885C2214yes—
27C2×(C2×D11)⋊C8C2212yes—
28C2×#66879C2212yes—
29#10622600C2212yes—
30#10622589C2212yes—
31C2×#66873C2214yes—
32C4×C4⋊Dic11C2211yescharacteristic
33C4×Dic11⋊C4—21no—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35#10622448—24no—
36#10622280—21no—
37#10622263—21no—
38C22×Q8×C11C2312yes—
39C2×#4343—24no—
40C2×#4343—44no—
41C2×#4343—44no—
42C2×#4343C2×C418yes—
43C22×D44—22no—
44C22×D44—21no—
45C22×D44—21no—
46C22×D44C2312yes—
47C22×C4×D11—22no—
48C22×C4×D11D411yescharacteristic
49C22×C4×D11D411yescharacteristic
50C22×C4×D11C2311yescharacteristic
51C22×C8×C11C2312yes—
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8C2×C414yes—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4C2312yes—
57C2×C42×C11—21no—
58C2×C42×C11C2311yescharacteristic
59#67000—24no—
60#67000C2×C418yes—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—22no—
64C2×C4⋊Dic11C2312yes—
65C2×Dic11⋊C4—22no—
66C2×Dic11⋊C4—22no—
67C2×C4×Dic11—21no—
68C2×C4×Dic11D411yescharacteristic
69C2×C4×Dic11D411yescharacteristic
70C2×C4×Dic11C2311yescharacteristic
71C22×C11⋊C8C2312yes—
72#66948—28no—
73#66948—28no—
74#66946—28no—
75#66946—28no—
76#66927—22no—
77#66927C2×C414yes—
78#66925—44no—
79C42×D11C2×C414yes—
80C42×D11D414yes—
81C11×C4⋊C8—22no—
82C11×#103—44no—
83C11×#95—21no—
84#66899—44no—
85C11⋊#95—21no—
86C11⋊#95—22no—
87#66885—44no—
88(C2×D11)⋊C8—24no—
89#66879—24no—
90#66873—44no—
91C4⋊(C11⋊C8)—22no—
92#21809—111nomaximal, Sylow
93C23×D11—22no—
94C23×D11C2×D411yescharacteristic
95C2×Q8×C11—22no—
96C2×Q8×C11—24no—
97C2×Q8×C11—24no—
98C2×Q8×C11C22×C414yes—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2411yescharacteristic
104C22×Dic11—22no—
105C22×Dic11C2×D411yescharacteristic
106C22×Dic11C2×D411yescharacteristic
107C22×Dic11C2×D411yescharacteristic
108#4343—416no—
109#4343—48no—
110#4343—48no—
111C2×D44—28no—
112C2×D44—24no—
113C2×D44—24no—
114C2×D44—22no—
115C2×D44—24no—
116C2×D44—24no—
117C2×D44—44no—
118C2×D44—48no—
119C2×D44—42no—
120C2×D44—42no—
121C2×D44C22×C414yes—
122C2×C4×D11—28no—
123C2×C4×D11—22no—
124C2×C4×D11—22no—
125C2×C4×D11—22no—
126C2×C4×D11—22no—
127C2×C4×D11—42no—
128C2×C4×D11—48no—
129C2×C4×D11C22⋊C414yes—
130C2×C4×D11C22⋊C414yes—
131C2×C4×D11C22×C412yes—
132C2×C4×D11C2×D412yes—
133C2×C8×C11—22no—
134C2×C8×C11—24no—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C42×C11—42no—
140C42×C11C22×C412yes—
141C42×C11C2×D412yes—
142(C2×D11)⋊C4—28no—
143(C2×D11)⋊C4—28no—
144(C2×D11)⋊C4—44no—
145C4⋊Dic11—22no—
146C4⋊Dic11—22no—
147Dic11⋊C4—44no—
148Dic11⋊C4—44no—
149C4×Dic11—42no—
150C4×Dic11C22⋊C414yes—
151C4×Dic11C22⋊C414yes—
152C4×Dic11C22×C412yes—
153C4×Dic11C2×D412yes—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—24no—
156C2×#532—111no—
157C2×#432—111no—
158#2285—111no—
159#1982—111no—
160#1982—111no—
161#1981—111no—
162#1981D1111yescharacteristic, complemented
163#1959—114no—
164#1788—114no—
165C23×C11C22×D411yescharacteristic
166C22×D11—22no—
167C22×D11—21no—
168C22×D11—21no—
169C22×D11—22no—
170C22×D11—24no—
171C22×D11—44no—
172C22×D11—42no—
173C22×D11—42no—
174C22×D11—44no—
175C22×D11C2×C22⋊C412yes—
176Q8×C11—28no—
177Q8×C11—42no—
178Q8×C11—42no—
179C2×C4×C11—22no—
180C2×C4×C11—24no—
181C2×C4×C11—44no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11C2×C22⋊C412yes—
186C2×C4×C11C2×C22⋊C412yes—
187C2×C4×C11AGL(1,ℤ/8)12yes—
188C2×C4×C11#13712yes—
189C2×C4×C11C23×C411yescharacteristic
190C2×C4×C11C22×D411yescharacteristic
191C2×C4×C11H(5,𝔽2)12yes—
192C2×C4×C11H(5,𝔽2)12yes—
193C2×Dic11—22no—
194C2×Dic11—21no—
195C2×Dic11—21no—
196C2×Dic11—22no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11C2×C22⋊C412yes—
201C2×Dic11C2×C22⋊C412yes—
202C2×Dic11C2×C22⋊C412yes—
203D44—28no—
204D44—48no—
205D44—416no—
206D44—42no—
207D44—42no—
208D44—48no—
209C4×D11—24no—
210C4×D11—22no—
211C4×D11—22no—
212C4×D11—28no—
213C4×D11—44no—
214C4×D11—416no—
215C8×C11—42no—
216C11⋊C8—42no—
217C22×#41—112no—
218#532—118no—
219#532—224no—
220C2×C4⋊Q8C2×D1111yescharacteristic
221C2×#127—111no—
222C2×#124—112no—
223C2×#121—221no—
224C2×#121—221no—
225C2×C4×D4—221no—
226C2×C4×D4—221no—
227C2×#117—221no—
228C22×C42—111no—
229#432—224no—
230C2×C4⋊C8—111no—
231C2×C4⋊C8C2×D1111yescharacteristic
232C2×#103—114no—
233C2×#103C2×D1114yes—
234C2×#102—114no—
235C2×#102—114no—
236C2×C22⋊C8—112no—
237C2×#97—112no—
238#384—112no—
239#382—221no—
240#380—112no—
241#380—221no—
242C4×C4⋊C4—111no—
243C4×C4⋊C4—221no—
244C4×C4⋊C4C2×D1111yescharacteristic
245C22×C11C22×C22⋊C411yescharacteristic
246C22×C11#53512yes—
247C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
248C22×C11C2×#13711yescharacteristic
249C22×C11#57512yes—
250C2×D11—22no—
251C2×D11—22no—
252C2×D11—22no—
253C2×D11—42no—
254C2×D11—42no—
255C2×D11—44no—
256C2×D11—44no—
257C2×D11—44no—
258C2×D11—84no—
259C2×D11—84no—
260C4×C11—22no—
261C4×C11—44no—
262C4×C11—82no—
263C4×C11#41714yes—
264C4×C11#51812yes—
265C4×C11#53511yescharacteristic
266C4×C11#53511yescharacteristic
267Dic11—22no—
268Dic11—22no—
269Dic11—22no—
270Dic11—82no—
271C2×#41—118no—
272C2×#41—224no—
273C2×#41—444no—
274C2×#41—444no—
275C22×Q8C22×D1112yes—
276C22×D4—112no—
277C22×D4—222no—
278C22×D4—221no—
279C22×D4—221no—
280C23×C4—111no—
281C23×C4—111no—
282C23×C4—111no—
283C23×C4—222no—
284C22×C8—112no—
285C22×C8C22×D1112yes—
286C4⋊Q8—22no—
287C4⋊Q8C4×D1114yes—
288#127—114no—
289#127—222no—
290#124—118no—
291#124—224no—
292#121—228no—
293#121—228no—
294C4×D4—228no—
295C4×D4—228no—
296#117—444no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—112no—
300C2×C4⋊C4—222no—
301C2×C4⋊C4—222no—
302C2×C4⋊C4C22×D1112yes—
303C2×C22⋊C4—222no—
304C2×C22⋊C4—222no—
305C2×C22⋊C4—222no—
306C2×C42—21no—
307C2×C42—111no—
308C2×C42—111no—
309C2×C42—111no—
310C2×C42—114no—
311C2×C42—114no—
312C2×C42—221no—
313C2×C42C22×D1111yescharacteristic
314C4⋊C8—22no—
315C4⋊C8—222no—
316#103—44no—
317#103—444no—
318#102—444no—
319#102—444no—
320C22⋊C8—224no—
321#97—224no—
322#95—21no—
323#95—222no—
324#95—221no—
325C2×C11#230911yescharacteristic
326C2×C11C2×#41711yescharacteristic
327C2×C11#289611yescharacteristic
328C2×C11#321412yes—
329C2×C11#321612yes—
330D11—42no—
331D11—84no—
332C24—111no—
333C24—222no—
334#41—4416no—
335#41—448no—
336#41—448no—
337C2×Q8—22no—
338C2×Q8—24no—
339C2×Q8—24no—
340C2×Q8C2×C4×D1114yes—
341C2×D4—114no—
342C2×D4—228no—
343C2×D4—224no—
344C2×D4—224no—
345C2×D4—222no—
346C2×D4—224no—
347C2×D4—224no—
348C2×D4—444no—
349C2×D4—448no—
350C2×D4—442no—
351C2×D4—442no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—111no—
355C22×C4—111no—
356C22×C4—111no—
357C22×C4—114no—
358C22×C4—112no—
359C22×C4—112no—
360C22×C4—114no—
361C22×C4—228no—
362C22×C4—222no—
363C22×C4—222no—
364C22×C4—222no—
365C22×C4—222no—
366C22×C4—222no—
367C22×C4—442no—
368C22×C4—448no—
369C22×C4D4×D1111yescharacteristic
370C22×C4D4×D1111yescharacteristic
371C22×C4C23×D1111yescharacteristic
372C2×C8—22no—
373C2×C8—24no—
374C2×C8—222no—
375C2×C8—224no—
376C4⋊C4—24no—
377C4⋊C4—24no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—222no—
381C4⋊C4—222no—
382C4⋊C4—444no—
383C4⋊C4—444no—
384C22⋊C4—228no—
385C22⋊C4—228no—
386C22⋊C4—444no—
387C42—42no—
388C42—114no—
389C42—114no—
390C42—112no—
391C42—112no—
392C42—442no—
393C42C2×C4×D1112yes—
394C42D4×D1112yes—
395C11#2180911yescharacteristic, complemented, Sylow
396C23—112no—
397C23—221no—
398C23—221no—
399C23—222no—
400C23—222no—
401C23—224no—
402C23—442no—
403C23—442no—
404C23—444no—
405C23—444no—
406C23C2×D4×D1111yescharacteristic
407Q8—28no—
408Q8—42no—
409Q8—42no—
410D4—228no—
411D4—448no—
412D4—4416no—
413D4—442no—
414D4—448no—
415D4—442no—
416C2×C4—22no—
417C2×C4—24no—
418C2×C4—44no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—112no—
423C2×C4—112no—
424C2×C4—112no—
425C2×C4—221no—
426C2×C4—221no—
427C2×C4—222no—
428C2×C4—222no—
429C2×C4—222no—
430C2×C4—224no—
431C2×C4—228no—
432C2×C4—222no—
433C2×C4—444no—
434C2×C4—4416no—
435C2×C4—442no—
436C2×C4—442no—
437C2×C4—442no—
438C2×C4C22⋊C4×D1112yes—
439C2×C4C22⋊C4×D1112yes—
440C2×C4#6696712yes—
441C2×C4#6697112yes—
442C2×C4C22×C4×D1111yescharacteristic
443C2×C4C2×D4×D1111yescharacteristic
444C2×C4#6703712yes—
445C2×C4#6704212yes—
446C8—42no—
447C8—442no—
448C22—222no—
449C22—222no—
450C22—222no—
451C22—442no—
452C22—442no—
453C22—444no—
454C22—444no—
455C22—444no—
456C22—884no—
457C22—884no—
458C22C2×C22⋊C4×D1111yescharacteristic
459C22#1062313812yes—
460C22C2×#6696711yescharacteristic
461C22C2×#6697111yescharacteristic
462C22#1062330812yes—
463C4—22no—
464C4—44no—
465C4—82no—
466C4—222no—
467C4—222no—
468C4—222no—
469C4—882no—
470C4#1062241614yes—
471C4#1062307612yes—
472C4#1062320511yescharacteristic
473C4#1062324611yescharacteristic
474C2—442no—
475C2—884no—
476C2#1307119511yescharacteristic
477C2C2×#1062241611yescharacteristic
478C2#1307713411yescharacteristic
479C2#1307961012yes—
480C2#1307962612yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1981C2
socleC23×C11C22×D4
prime radicalC2×#10623256C2
cosocleC22×C4×C11C24
hypercenter#1981D11
hypocenterC11#21809
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1981

Complements

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

NH ≅ G/Ntype
2. C2×#10622448C2semidirect
3. #13071020C2semidirect
4. #13069543C2semidirect
5. #13069542C2semidirect
6. #13069540C2semidirect
7. #13069429C2semidirect
8. #13068555C2semidirect
9. C11×#1981C2semidirect
14. #10623256C4semidirect
162. #1981D11semidirect
395. C11#21809semidirect

Maximal subgroups

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

subgroupindex
C2×#106232562
C2×#106224482
#130710202
#130695432
#130695422
#130695402
#130694292
#130685552
C11×#19812
#2180911