Finite Group Databasebeta

← #14721517

Subgroups — #14721517

Order 2816.

1018 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082470C211yesmaximal, characteristic
2#13077639C211yesmaximal, characteristic, complemented
3#13071591C211yesmaximal, characteristic, complemented
4#13067175C211yesmaximal, characteristic, complemented
5#13067171C214yesmaximal, complemented
6#13067115C211yesmaximal, characteristic, complemented
7#13067112C211yesmaximal, characteristic, complemented
8#13067106C214yesmaximal, complemented
9C11×#1518C211yesmaximal, characteristic, complemented
10C11×#533C2211yescharacteristic
11#10623265C412yescomplemented
12#10623257C412yescomplemented
13#10623226—22no—
14#10623175—22no—
15#10623158C2214yes—
16#10623116—22no—
17#10623115C412yescomplemented
18#10623108C412yescomplemented
19#10623056—21no—
20#10623054—21no—
21#10623008C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C11×#431C2211yescharacteristic
24C11×#382C2211yescharacteristic
25#10622601—21no—
26C4⋊C4×Dic11—21no—
27C4×C4⋊Dic11C2211yescharacteristic
28#10622538C2211yescharacteristic
29#10622447—22no—
30D11×C22⋊C8C2214yes—
31C8×D44—22no—
32#10622283—22no—
33#10622279C2212yes—
34#10622277C2212yes—
35C11×#328C2214yes—
36#10622176C2212yes—
37#10622176C2212yes—
38#10622108C2212yes—
39#10622108C2212yes—
40#10622089C2214yes—
41C2×#4343C2×C414yes—
42C2×#4339—21no—
43C22×D44D411yescharacteristic
44C22×C4×D11C2312yes—
45C11×C4⋊Q8C2×C411yescharacteristic
46C11×C4⋊Q8C2×C411yescharacteristic
47C11×#125—21no—
48C11×C22⋊Q8—21no—
49C11×C22⋊Q8C2312yes—
50C4×Q8×C11—21no—
51C4×Q8×C11C2×C412yes—
52C11×#117—21no—
53C2×C11×C4⋊C4—21no—
54C2×C42×C11C2311yescharacteristic
55#67000—24no—
56#66999C2×C414yes—
57#66983—21no—
58#66983C2312yes—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4D412yes—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11D411yescharacteristic
64C2×C4×Dic11—21no—
65C2×C4×Dic11—22no—
66C2×C8×D11—24no—
67#66951—24no—
68#66948—22no—
69#66948—22no—
70#66948—24no—
71#66948C2×C414yes—
72#66947—24no—
73#66947—24no—
74#66946—24no—
75#66945—22no—
76#66945C2×C414yes—
77C4⋊C4×D11—22no—
78#66935—24no—
79(C22⋊D11)⋊C4—24no—
80#66928—22no—
81#66928—21no—
82#66927—22no—
83#66927C2×C411yescharacteristic
84C4×D44—21no—
85C4×D44—22no—
86C4×D44C2×C412yes—
87C4×D44C2×C412yes—
88C4×D44C2×C412yes—
89C4×D44D412yes—
90C4×D44D412yes—
91#66922C2×C411yescharacteristic
92C4×Dic22—22no—
93C11×C4⋊C8—21no—
94C11×C22⋊C8C2312yes—
95C4×C8×C11—21no—
96C11×#95—21no—
97C11×#95C2312yes—
98C11⋊#95—22no—
99C11⋊#95C2311yescharacteristic
100C11⋊#95C2311yescharacteristic
101C22⋊(C11⋊C8)C2312yes—
102(C2×D11)⋊C8—24no—
103C4⋊(C11⋊C8)—21no—
104C4×C11⋊C8—21no—
105#17617—111nomaximal, Sylow
106C23×D11C2×D412yes—
107C2×Q8×C11—21no—
108C2×Q8×C11C22×C412yes—
109C22×C4×C11—22no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2411yescharacteristic
113C2×C22⋊D11—22no—
114C22×Dic11—21no—
115C22×Dic11—21no—
116C22×Dic11C2×D412yes—
117#4343—84no—
118#4339—42no—
119#4339—42no—
120C2×D44—24no—
121C2×D44—24no—
122C2×D44—21no—
123C2×D44—21no—
124C2×D44—22no—
125C2×D44—22no—
126C2×D44C22⋊C412yes—
127C2×D44C22⋊C412yes—
128C2×D44C22×C412yes—
129C2×C4×D11—24no—
130C2×C4×D11—22no—
131C2×C4×D11—82no—
132C2×C4×D11C22×C414yes—
133C2×C4×D11C2×D414yes—
134C2×Dic22—21no—
135C2×C8×C11—22no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—42no—
142C11×C4⋊C4C22×C412yes—
143C11×C22⋊C4—22no—
144C42×C11—22no—
145C42×C11C22×C411yescharacteristic
146C42×C11C22×C411yescharacteristic
147C42×C11C2×D411yescharacteristic
148C42×C11C2×D411yescharacteristic
149(C2×D11)⋊C4—24no—
150(C2×D11)⋊C4—24no—
151(C2×D11)⋊C4—24no—
152(C2×D11)⋊C4—22no—
153(C2×D11)⋊C4—22no—
154(C2×D11)⋊C4—44no—
155(C2×D11)⋊C4—82no—
156(C2×D11)⋊C4C22⋊C414yes—
157(C2×D11)⋊C4C22⋊C414yes—
158C4⋊Dic11—21no—
159C4⋊Dic11—42no—
160C4⋊Dic11C22⋊C412yes—
161C4⋊Dic11C22⋊C412yes—
162C4⋊Dic11C22×C412yes—
163Dic11⋊C4—24no—
164C4×Dic11—24no—
165C4×Dic11—42no—
166C4×Dic11—82no—
167C2×C11⋊C8—22no—
168C8×D11—84no—
169#3506—111no—
170#2972—111no—
171#2357—111no—
172#1518D1111yescharacteristic, complemented
173#1517—111no—
174#1516—114no—
175#1503—111no—
176#1502—111no—
177#1501—114no—
178C23×C11C22×D411yescharacteristic
179C22×D11—22no—
180C22×D11—22no—
181C22×D11—22no—
182C22×D11—42no—
183C22×D11—42no—
184C22×D11C2×C22⋊C414yes—
185Q8×C11—42no—
186Q8×C11—81no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11C2×C22⋊C411yescharacteristic
195C2×C4×C11C2×C22⋊C411yescharacteristic
196C2×C4×C11C2×C22⋊C411yescharacteristic
197C2×C4×C11C2×C22⋊C411yescharacteristic
198C2×C4×C11#13512yes—
199C2×C4×C11#13512yes—
200C2×C4×C11C23×C411yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C22⋊D11—42no—
203C22⋊D11—42no—
204C2×Dic11—22no—
205C2×Dic11—22no—
206C2×Dic11—42no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11C2×C22⋊C414yes—
213D44—24no—
214D44—24no—
215D44—42no—
216D44—42no—
217D44—81no—
218D44—84no—
219D44—84no—
220C4×D11—44no—
221C4×D11—44no—
222C4×D11—44no—
223C4×D11—84no—
224Dic22—42no—
225C8×C11—42no—
226C11⋊C8—42no—
227#559—222no—
228#556—112no—
229#555—112no—
230#553—222no—
231#550—112no—
232#547—112no—
233#538—222no—
234#535—221no—
235#533C2×D1111yescharacteristic
236#532—111no—
237#525—114no—
238#520—221no—
239C2×C4×D4—111no—
240C8×D4—222no—
241C8×D4—222no—
242#431—111no—
243#431C2×D1111yescharacteristic
244C2×C22⋊C8—114no—
245#390—221no—
246#388—222no—
247#382C2×D1111yescharacteristic
248#381—112no—
249C4×C4⋊C4—111no—
250C4×C4⋊C4—221no—
251C4×C22⋊C4—112no—
252#328—112no—
253#328—112no—
254#328C2×D1114yes—
255#327—112no—
256#327—112no—
257#327—114no—
258C22×C11—21no—
259C22×C11—21no—
260C22×C11C22×C22⋊C411yescharacteristic
261C22×C11C2×#13511yescharacteristic
262C22×C11C2×#13511yescharacteristic
263C2×D11—24no—
264C2×D11—24no—
265C2×D11—24no—
266C2×D11—42no—
267C2×D11—42no—
268C2×D11—42no—
269C2×D11—82no—
270C2×D11—82no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—21no—
274C4×C11—21no—
275C4×C11—42no—
276C4×C11—42no—
277C4×C11—82no—
278C4×C11#41612yes—
279C4×C11#41612yes—
280Dic11—24no—
281Dic11—42no—
282Dic11—42no—
283Dic11—81no—
284C2×#41—114no—
285C2×#41—221no—
286C22×D4—111no—
287C23×C4—112no—
288C22×C8—224no—
289C4⋊Q8—111no—
290C4⋊Q8C4×D1111yescharacteristic
291C4⋊Q8C4×D1111yescharacteristic
292#127—111no—
293#127—222no—
294#126—224no—
295#125—21no—
296#124—222no—
297#124—224no—
298#124—221no—
299#123—224no—
300#123—224no—
301C22⋊Q8—21no—
302C22⋊Q8—114no—
303C22⋊Q8C22×D1112yes—
304#121—112no—
305#121—114no—
306#121—224no—
307#121—222no—
308#121—222no—
309#121—221no—
310#120—224no—
311C4×Q8—21no—
312C4×Q8—222no—
313C4×Q8C4×D1112yes—
314C4×D4—112no—
315C4×D4—112no—
316C4×D4—112no—
317C4×D4—112no—
318C4×D4—112no—
319C4×D4—222no—
320C4×D4—224no—
321C4×D4—224no—
322C4×D4—221no—
323#117—21no—
324#117—114no—
325#117—222no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—111no—
328C2×C4⋊C4—222no—
329C2×C4⋊C4—221no—
330C2×C22⋊C4—112no—
331C2×C22⋊C4—222no—
332C2×C22⋊C4—222no—
333C2×C42—221no—
334C2×C42—222no—
335C2×C42C22×D1111yescharacteristic
336C4⋊C8—21no—
337C4⋊C8—221no—
338C22⋊C8—112no—
339C22⋊C8—224no—
340C22⋊C8C22×D1112yes—
341C4×C8—21no—
342C4×C8—221no—
343#95—21no—
344#95—111no—
345#95—111no—
346#95—222no—
347#95C22×D1112yes—
348C2×C11—21no—
349C2×C11—21no—
350C2×C11#288311yescharacteristic
351C2×C11C2×#41611yescharacteristic
352C2×C11#290111yescharacteristic
353D11—44no—
354D11—82no—
355C24—112no—
356#41—442no—
357#41—442no—
358#41—884no—
359C2×Q8—21no—
360C2×Q8—221no—
361C2×Q8C2×C4×D1112yes—
362C2×D4—112no—
363C2×D4—112no—
364C2×D4—112no—
365C2×D4—224no—
366C2×D4—224no—
367C2×D4—222no—
368C2×D4—221no—
369C2×D4—221no—
370C2×D4—222no—
371C2×D4—222no—
372C22×C4—22no—
373C22×C4—112no—
374C22×C4—114no—
375C22×C4—114no—
376C22×C4—224no—
377C22×C4—221no—
378C22×C4—222no—
379C22×C4—221no—
380C22×C4—882no—
381C22×C4D4×D1111yescharacteristic
382C22×C4D4×D1111yescharacteristic
383C22×C4C23×D1111yescharacteristic
384C2×C8—22no—
385C2×C8—222no—
386C2×C8—884no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—42no—
393C4⋊C4—112no—
394C4⋊C4—112no—
395C4⋊C4—112no—
396C4⋊C4—224no—
397C4⋊C4—221no—
398C4⋊C4—442no—
399C4⋊C4C2×C4×D1112yes—
400C22⋊C4—22no—
401C22⋊C4—114no—
402C22⋊C4—114no—
403C22⋊C4—224no—
404C22⋊C4—224no—
405C22⋊C4—224no—
406C22⋊C4—222no—
407C22⋊C4—222no—
408C22⋊C4—444no—
409C22⋊C4—882no—
410C42—22no—
411C42—224no—
412C42—442no—
413C42—882no—
414C42C2×C4×D1111yescharacteristic
415C42C2×C4×D1111yescharacteristic
416C42D4×D1111yescharacteristic
417C42D4×D1111yescharacteristic
418C11#1761711yescharacteristic, complemented, Sylow
419C23—114no—
420C23—222no—
421C23—222no—
422C23—222no—
423C23—442no—
424C23—442no—
425C23C2×D4×D1111yescharacteristic
426Q8—42no—
427Q8—81no—
428Q8—442no—
429D4—224no—
430D4—224no—
431D4—442no—
432D4—442no—
433D4—442no—
434D4—442no—
435D4—881no—
436D4—884no—
437D4—884no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—114no—
446C2×C4—222no—
447C2×C4—222no—
448C2×C4—444no—
449C2×C4—444no—
450C2×C4—442no—
451C2×C4—441no—
452C2×C4—441no—
453C2×C4—444no—
454C2×C4—441no—
455C2×C4—441no—
456C2×C4—441no—
457C2×C4—884no—
458C2×C4C22⋊C4×D1111yescharacteristic
459C2×C4C22⋊C4×D1111yescharacteristic
460C2×C4C22⋊C4×D1111yescharacteristic
461C2×C4C22⋊C4×D1111yescharacteristic
462C2×C4#6696912yes—
463C2×C4#6697212yes—
464C2×C4C22×C4×D1111yescharacteristic
465C2×C4C2×D4×D1111yescharacteristic
466C8—42no—
467C8—442no—
468C22—21no—
469C22—21no—
470C22—224no—
471C22—224no—
472C22—224no—
473C22—442no—
474C22—442no—
475C22—442no—
476C22—882no—
477C22—882no—
478C22C2×C22⋊C4×D1111yescharacteristic
479C22C2×#6696911yescharacteristic
480C22C2×#6697211yescharacteristic
481C4—21no—
482C4—21no—
483C4—21no—
484C4—21no—
485C4—42no—
486C4—42no—
487C4—82no—
488C4—224no—
489C4—442no—
490C4—442no—
491C4—881no—
492C4#1062241712yes—
493C4#1062241712yes—
494C2—21no—
495C2—21no—
496C2—444no—
497C2—882no—
498C2#1307707511yescharacteristic
499C2C2×#1062241711yescharacteristic
500C2#1307716211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1518C2
socleC22×C11C22×C22⋊C4
prime radical#13082470C2
cosocleC22×C4×C11C24
hypercenter#1518D11
hypocenterC11#17617
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1518

Complements

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

NH ≅ G/Ntype
2. #13077639C2semidirect
3. #13071591C2semidirect
4. #13067175C2semidirect
5. #13067171C2semidirect
6. #13067115C2semidirect
7. #13067112C2semidirect
8. #13067106C2semidirect
9. C11×#1518C2semidirect
11. #10623265C4semidirect
12. #10623257C4semidirect
17. #10623115C4semidirect
18. #10623108C4semidirect
172. #1518D11semidirect
418. C11#17617semidirect

Maximal subgroups

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

subgroupindex
#130824702
#130776392
#130715912
#130671752
#130671712
#130671152
#130671122
#130671062
C11×#15182
#1761711