Finite Group Databasebeta

← #14721606

Subgroups — #14721606

Order 2816.

942 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082481C211yesmaximal, characteristic
2#13077701C211yesmaximal, characteristic, complemented
3#13067179C211yesmaximal, characteristic, complemented
4#13067175C211yesmaximal, characteristic
5#13067152C214yesmaximal, complemented
6#13067139C214yesmaximal, complemented
7#13067114C211yesmaximal, characteristic, complemented
8#13067110C211yesmaximal, characteristic
9C11×#2351C211yesmaximal, characteristic, complemented
10C2×C4×Q8×C11—21no—
11C2×C4×Q8×C11C2211yescharacteristic
12#10623347—21no—
13#10623116C412yescomplemented
14#10623115C412yescomplemented
15#10623112—22no—
16#10623110C412yescomplemented
17#10623099—22no—
18#10623098C412yescomplemented
19#10623046—22no—
20#10623035—21no—
21#10623010C2214yes—
22#10623008C2211yescharacteristic
23#10623001C2211yescharacteristic
24C11×#389—21no—
25C11×#389—22no—
26C11×#382C2212yes—
27C11×#382C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C4×C11×C4⋊C4C2212yes—
30#10622637—22no—
31#10622637—22no—
32#10622539C2214yes—
33#10622538C2211yescharacteristic
34#10622538C2211yescharacteristic
35#10622090C2212yes—
36#10622090C2212yes—
37#10622090C2214yes—
38#10622089C2212yes—
39#10622089C2212yes—
40#10622089C2214yes—
41C22×Q8×C11D411yescharacteristic
42C2×#4339—21no—
43C4×Q8×C11—44no—
44C4×Q8×C11C2×C412yes—
45C4×Q8×C11C2×C412yes—
46C4×Q8×C11D412yes—
47C4×Q8×C11D412yes—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4D411yescharacteristic
53C2×C11×C4⋊C4D412yes—
54C2×C42×C11—22no—
55C2×C42×C11—21no—
56C2×C42×C11C2311yescharacteristic
57C2×C42×C11C2312yes—
58#67000—22no—
59#66999—22no—
60#66999—22no—
61#66997—22no—
62#66983—21no—
63#66983C2312yes—
64#66982—24no—
65C4×C22⋊D11—24no—
66#66979—21no—
67#66977—21no—
68#66977C2312yes—
69#66951—24no—
70#66949—24no—
71#66947—24no—
72#66946—22no—
73#66945—22no—
74C4⋊C4×D11—22no—
75#66942—24no—
76#66940—22no—
77#66929—24no—
78#66928—21no—
79#66928C2×C414yes—
80#66927C2×C411yescharacteristic
81C4×D44—21no—
82C4×D44C2×C412yes—
83C4×D44C2×C414yes—
84#66925—24no—
85#66923—21no—
86#66923C2×C414yes—
87#66922C2×C411yescharacteristic
88#66922C2×C411yescharacteristic
89#66922C2×C411yescharacteristic
90C4×Dic22—21no—
91C4×Dic22C2×C412yes—
92C4×Dic22C2×C414yes—
93C11×#95—21no—
94C11×#95—22no—
95C11×#95C2311yescharacteristic
96C11×#95C2311yescharacteristic
97C11×#95C2312yes—
98C22⋊(C11⋊C8)C2312yes—
99C22⋊(C11⋊C8)C2312yes—
100C4⋊(C11⋊C8)—21no—
101C4⋊(C11⋊C8)—21no—
102C4⋊(C11⋊C8)—24no—
103#66867—24no—
104C4×C11⋊C8—21no—
105C4×C11⋊C8—21no—
106#17628—111nomaximal, Sylow
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11C22⋊C412yes—
110C2×Q8×C11C22⋊C412yes—
111C22×C4×C11—21no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2411yescharacteristic
119C2×C22⋊D11—22no—
120#4339—42no—
121#4339—42no—
122C2×D44—21no—
123C2×D44—21no—
124C2×D44C22×C412yes—
125C2×C4×D11—22no—
126C2×C4×D11—24no—
127C2×Dic22—21no—
128C2×Dic22—21no—
129C2×Dic22C22×C412yes—
130C11×C4⋊C4—42no—
131C11×C4⋊C4—44no—
132C11×C4⋊C4—44no—
133C11×C4⋊C4—42no—
134C11×C4⋊C4C22⋊C412yes—
135C11×C4⋊C4C22⋊C414yes—
136C11×C4⋊C4C22⋊C412yes—
137C11×C4⋊C4C22⋊C414yes—
138C42×C11—44no—
139C42×C11—42no—
140C42×C11C22×C411yescharacteristic
141C42×C11C22×C414yes—
142C42×C11C22×C411yescharacteristic
143C42×C11C2×D411yescharacteristic
144C42×C11C2×D411yescharacteristic
145C42×C11C2×D414yes—
146C22⋊Dic11—22no—
147(C2×D11)⋊C4—24no—
148(C2×D11)⋊C4—22no—
149(C2×D11)⋊C4—24no—
150(C2×D11)⋊C4—24no—
151(C2×D11)⋊C4—22no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11C22×C412yes—
157C4⋊Dic11C22×C412yes—
158Dic11⋊C4—22no—
159Dic11⋊C4—24no—
160Dic11⋊C4—24no—
161Dic11⋊C4—24no—
162Dic11⋊C4—22no—
163C4×Dic11—22no—
164C4×Dic11—24no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167#3507—111no—
168#2983—111no—
169#2351D1111yescharacteristic, complemented
170#1518—111no—
171#1517—111no—
172#1512—114no—
173#1509—114no—
174#1503—111no—
175#1502—111no—
176C23×C11C22×D411yescharacteristic
177C22×D11—22no—
178Q8×C11—24no—
179Q8×C11—24no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—41no—
184C2×C4×C11—42no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—41no—
190C2×C4×C11—42no—
191C2×C4×C11—41no—
192C2×C4×C11—42no—
193C2×C4×C11—41no—
194C2×C4×C11C2×C22⋊C414yes—
195C2×C4×C11C2×C22⋊C411yescharacteristic
196C2×C4×C11C2×C22⋊C414yes—
197C2×C4×C11C2×C22⋊C411yescharacteristic
198C2×C4×C11C2×C22⋊C411yescharacteristic
199C2×C4×C11C2×C22⋊C411yescharacteristic
200C2×C4×C11AGL(1,ℤ/8)12yes—
201C2×C4×C11#13712yes—
202C2×C4×C11C23×C411yescharacteristic
203C2×C4×C11C22×D411yescharacteristic
204C22⋊D11—42no—
205C22⋊D11—42no—
206C2×Dic11—22no—
207C2×Dic11—22no—
208C2×Dic11—22no—
209D44—42no—
210D44—42no—
211D44—81no—
212C4×D11—44no—
213C4×D11—84no—
214Dic22—42no—
215Dic22—42no—
216Dic22—81no—
217C11⋊C8—42no—
218C11⋊C8—42no—
219#559—112no—
220#557—112no—
221#556—112no—
222#556—222no—
223#554—112no—
224#552—222no—
225#539—222no—
226#536—221no—
227#533—111no—
228#532—111no—
229#529—114no—
230#520—221no—
231C2×C4×Q8—21no—
232C2×C4×Q8C2×D1111yescharacteristic
233#446—222no—
234#446—222no—
235#432—114no—
236#431—111no—
237#431—111no—
238#389—21no—
239#389—22no—
240#382C2×D1112yes—
241#382C2×D1111yescharacteristic
242C4×C4⋊C4C2×D1111yescharacteristic
243C4×C4⋊C4C2×D1112yes—
244#328—112no—
245#328—112no—
246#328—114no—
247#327—112no—
248#327—112no—
249#327—114no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11C22×C22⋊C411yescharacteristic
253C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
254C22×C11C2×#13711yescharacteristic
255C2×D11—42no—
256C2×D11—42no—
257C2×D11—42no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—24no—
261C4×C11—21no—
262C4×C11—24no—
263C4×C11—21no—
264C4×C11—42no—
265C4×C11—82no—
266C4×C11—81no—
267C4×C11#41712yes—
268C4×C11#41712yes—
269Dic11—42no—
270Dic11—42no—
271Dic11—42no—
272C2×#41—221no—
273C22×Q8C22⋊D1111yescharacteristic
274C4⋊Q8—111no—
275C4⋊Q8—111no—
276C4⋊Q8—111no—
277C4⋊Q8—222no—
278#127—111no—
279#126—224no—
280#126—224no—
281#125—114no—
282#125—224no—
283#125—221no—
284#124—114no—
285#124—222no—
286#124—221no—
287#123—224no—
288#123—224no—
289C22⋊Q8—112no—
290C22⋊Q8—222no—
291C22⋊Q8—222no—
292C22⋊Q8—221no—
293C22⋊Q8—224no—
294#121—112no—
295#121—221no—
296C4×Q8—44no—
297C4×Q8—114no—
298C4×Q8—112no—
299C4×Q8—222no—
300C4×Q8—221no—
301C4×Q8C4×D1112yes—
302C4×Q8C4×D1112yes—
303C4×Q8D4412yes—
304C4×Q8D4412yes—
305C4×D4—114no—
306C4×D4—112no—
307C4×D4—224no—
308C4×D4—222no—
309C4×D4—221no—
310#117—221no—
311#117—222no—
312#117—224no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—222no—
318C2×C4⋊C4C22⋊D1111yescharacteristic
319C2×C4⋊C4C22⋊D1112yes—
320C2×C42—22no—
321C2×C42—21no—
322C2×C42C22×D1112yes—
323C2×C42C22×D1111yescharacteristic
324C4⋊C8—221no—
325C4⋊C8—221no—
326C4⋊C8—224no—
327C22⋊C8—112no—
328C22⋊C8—112no—
329#97—224no—
330C4×C8—221no—
331C4×C8—221no—
332#95—22no—
333#95—21no—
334#95C22×D1111yescharacteristic
335#95C22×D1111yescharacteristic
336#95C22×D1112yes—
337C2×C11—21no—
338C2×C11—21no—
339C2×C11#288411yescharacteristic
340C2×C11C2×#41711yescharacteristic
341C2×C11#290111yescharacteristic
342D11—82no—
343#41—442no—
344#41—442no—
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8—112no—
348C2×Q8—221no—
349C2×Q8—221no—
350C2×Q8(C2×D11)⋊C412yes—
351C2×Q8(C2×D11)⋊C412yes—
352C2×D4—112no—
353C2×D4—222no—
354C2×D4—221no—
355C2×D4—221no—
356C22×C4—21no—
357C22×C4—22no—
358C22×C4—21no—
359C22×C4—222no—
360C22×C4—224no—
361C22×C4C2×C22⋊D1112yes—
362C22×C4C2×C22⋊D1112yes—
363C22×C4C2×C22⋊D1111yescharacteristic
364C22×C4C2×C22⋊D1111yescharacteristic
365C22×C4C23×D1111yescharacteristic
366C2×C8—222no—
367C2×C8—222no—
368C4⋊C4—44no—
369C4⋊C4—44no—
370C4⋊C4—42no—
371C4⋊C4—42no—
372C4⋊C4—112no—
373C4⋊C4—112no—
374C4⋊C4—221no—
375C4⋊C4—224no—
376C4⋊C4—221no—
377C4⋊C4—224no—
378C4⋊C4—221no—
379C4⋊C4—222no—
380C4⋊C4—224no—
381C4⋊C4—221no—
382C4⋊C4—222no—
383C4⋊C4(C2×D11)⋊C412yes—
384C4⋊C4(C2×D11)⋊C412yes—
385C4⋊C4(C2×D11)⋊C414yes—
386C4⋊C4(C2×D11)⋊C414yes—
387C22⋊C4—222no—
388C22⋊C4—224no—
389C22⋊C4—224no—
390C22⋊C4—222no—
391C22⋊C4—224no—
392C22⋊C4—222no—
393C42—44no—
394C42—42no—
395C42—224no—
396C42—222no—
397C42C2×C4×D1111yescharacteristic
398C42C2×C4×D1114yes—
399C42C2×C4×D1111yescharacteristic
400C42C2×D4411yescharacteristic
401C42C2×D4411yescharacteristic
402C42C2×D4414yes—
403C11#1762811yescharacteristic, complemented, Sylow
404C23—222no—
405C23C22×C22⋊D1111yescharacteristic
406Q8—24no—
407Q8—24no—
408Q8—442no—
409Q8—442no—
410Q8—881no—
411D4—442no—
412D4—442no—
413D4—442no—
414D4—442no—
415D4—881no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—42no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—222no—
431C2×C4—222no—
432C2×C4—222no—
433C2×C4—444no—
434C2×C4—884no—
435C2×C4C2×(C2×D11)⋊C414yes—
436C2×C4C2×(C2×D11)⋊C414yes—
437C2×C4C2×(C2×D11)⋊C411yescharacteristic
438C2×C4C2×(C2×D11)⋊C411yescharacteristic
439C2×C4C2×(C2×D11)⋊C411yescharacteristic
440C2×C4C2×(C2×D11)⋊C411yescharacteristic
441C2×C4#6698512yes—
442C2×C4#6699512yes—
443C2×C4C22×C4×D1111yescharacteristic
444C2×C4C22×D4411yescharacteristic
445C8—442no—
446C8—442no—
447C22—21no—
448C22—21no—
449C22—442no—
450C22—442no—
451C22—442no—
452C22C22×(C2×D11)⋊C411yescharacteristic
453C22C2×#6698511yescharacteristic
454C22C2×#6699511yescharacteristic
455C4—21no—
456C4—21no—
457C4—24no—
458C4—24no—
459C4—21no—
460C4—21no—
461C4—42no—
462C4—82no—
463C4—81no—
464C4—442no—
465C4—442no—
466C4—442no—
467C4#1062257912yes—
468C4#1062257912yes—
469C2—21no—
470C2—21no—
471C2—882no—
472C2#1307707911yescharacteristic
473C2C2×#1062257911yescharacteristic
474C2#1307716411yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2351C2
socleC22×C11C22×C22⋊C4
prime radical#10623008C22
cosocleC22×C4×C11C24
hypercenter#2351D11
hypocenterC11#17628
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ #2351

Complements

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

NH ≅ G/Ntype
2. #13077701C2semidirect
3. #13067179C2semidirect
5. #13067152C2semidirect
6. #13067139C2semidirect
7. #13067114C2semidirect
9. C11×#2351C2semidirect
13. #10623116C4semidirect
14. #10623115C4semidirect
16. #10623110C4semidirect
18. #10623098C4semidirect
169. #2351D11semidirect
403. C11#17628semidirect

Maximal subgroups

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

subgroupindex
#130824812
#130777012
#130671792
#130671752
#130671522
#130671392
#130671142
#130671102
C11×#23512
#1762811