Finite Group Databasebeta

← #14645877

Subgroups — #14645877

Order 2816.

788 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623115C211yesmaximal, characteristic
2#13069576C211yesmaximal, characteristic, complemented
3#13068613C211yesmaximal, characteristic
4C2×#10622124C211yesmaximal, characteristic, complemented
5C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
6C2×#10622121C211yesmaximal, characteristic
7C11×#1803C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C2×#66999—21no—
10#10623115—22no—
11#10623115—22no—
12#10623115—22no—
13#10623115C414yescomplemented
14C2×#66951—22no—
15C2×#66945—21no—
16C2×#66928—21no—
17C2×C4×D44C2211yescharacteristic
18C2×#66922C2211yescharacteristic
19C2×C4×Dic22—21no—
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×#103—21no—
22C11×#384C2211yescharacteristic
23C2×#66873—21no—
24C2×C4⋊(C11⋊C8)C2211yescharacteristic
25C2×C4×C11⋊C8C2211yescharacteristic
26C11×#340—21no—
27Q8⋊(C11⋊C8)—22no—
28#10622167—22no—
29#10622167—21no—
30#10622124—22no—
31#10622121—22no—
32C22×Q8×C11D411yescharacteristic
33C22×D44D411yescharacteristic
34C22×C4×D11—21no—
35C22×Dic22—21no—
36C22×C8×C11—21no—
37C4×Q8×C11—21no—
38C4×Q8×C11—21no—
39C4×Q8×C11C2×C412yes—
40C4×Q8×C11D412yes—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4D411yescharacteristic
46C2×C42×C11—21no—
47C2×C42×C11C2311yescharacteristic
48#66999—24no—
49#66999—24no—
50C2×(C2×D11)⋊C4—22no—
51C2×(C2×D11)⋊C4—22no—
52C2×(C2×D11)⋊C4—21no—
53C2×C4⋊Dic11—21no—
54C2×C4⋊Dic11D411yescharacteristic
55C2×C4⋊Dic11D412yes—
56C2×Dic11⋊C4—22no—
57C2×C4×Dic11—22no—
58C22×C11⋊C8—21no—
59C22×C11⋊C8—21no—
60#66951—28no—
61#66951—28no—
62#66945—24no—
63#66945—24no—
64#66928—24no—
65#66928—24no—
66C4×D44—21no—
67C4×D44—21no—
68C4×D44C2×C412yes—
69C4×D44D412yes—
70#66922—21no—
71#66922—21no—
72#66922C2×C412yes—
73#66922D412yes—
74C4×Dic22—24no—
75C4×Dic22—24no—
76C11×C4⋊C8—21no—
77C11×C4⋊C8—21no—
78C11×#103—42no—
79#66873—42no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)—21no—
82C4×C11⋊C8—21no—
83C4×C11⋊C8—21no—
84#8449—111nomaximal, Sylow
85C23×D11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11—21no—
89C2×Q8×C11—21no—
90C2×Q8×C11—21no—
91C2×Q8×C11C22⋊C412yes—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—41no—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×Dic11—21no—
99C22×Dic11—22no—
100C2×D44—21no—
101C2×D44—21no—
102C2×D44—21no—
103C2×D44—21no—
104C2×D44—21no—
105C2×D44C22⋊C412yes—
106C2×C4×D11—22no—
107C2×C4×D11—22no—
108C2×C4×D11—41no—
109C2×C4×D11—41no—
110C2×C4×D11—41no—
111C2×C4×D11—41no—
112C2×Dic22—22no—
113C2×Dic22—22no—
114C2×Dic22—41no—
115C2×Dic22—41no—
116C2×Dic22—41no—
117C2×Dic22—41no—
118C2×C8×C11—41no—
119C2×C8×C11—41no—
120C2×C8×C11—41no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—42no—
125C11×C4⋊C4—41no—
126C11×C4⋊C4—41no—
127C11×C4⋊C4—41no—
128C11×C4⋊C4—41no—
129C11×C4⋊C4C22⋊C412yes—
130C42×C11—22no—
131C42×C11—22no—
132C42×C11C22×C411yescharacteristic
133C42×C11C2×D411yescharacteristic
134C42×C11C2×D411yescharacteristic
135C42×C11C2×D411yescharacteristic
136(C2×D11)⋊C4—28no—
137(C2×D11)⋊C4—28no—
138(C2×D11)⋊C4—22no—
139(C2×D11)⋊C4—22no—
140C4⋊Dic11—22no—
141C4⋊Dic11—21no—
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144C4⋊Dic11C22⋊C412yes—
145C4⋊Dic11C22⋊C414yes—
146Dic11⋊C4—28no—
147C4×Dic11—28no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—41no—
150C2×C11⋊C8—41no—
151C2×C11⋊C8—41no—
152C2×C11⋊C8—41no—
153C2×C11⋊C8—41no—
154C2×#556—111no—
155#1990—111no—
156#1803D1111yescharacteristic, complemented
157#1802—111no—
158C2×#332—111no—
159C2×Q8⋊C8—111no—
160C2×D4⋊C8—111no—
161C23×C11#12011yescharacteristic
162C22×D11—22no—
163C22×D11—41no—
164C22×D11—41no—
165C22×D11—41no—
166C22×D11—41no—
167C22×D11—41no—
168C22×D11—41no—
169Q8×C11—22no—
170Q8×C11—22no—
171Q8×C11—41no—
172Q8×C11—41no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—81no—
182C2×C4×C11—81no—
183C2×C4×C11—81no—
184C2×C4×C11C2×C22⋊C411yescharacteristic
185C2×C4×C11C2×C22⋊C411yescharacteristic
186C2×C4×C11C2×C22⋊C411yescharacteristic
187C2×C4×C11#12011yescharacteristic
188C2×C4×C11#12011yescharacteristic
189C2×C4×C11#12011yescharacteristic
190C2×C4×C11#13511yescharacteristic
191C2×C4×C11#13511yescharacteristic
192C2×C4×C11#13511yescharacteristic
193C2×C4×C11#13511yescharacteristic
194C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
195C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
196C2×C4×C11#13711yescharacteristic
197C2×C4×C11#13711yescharacteristic
198C2×Dic11—22no—
199C2×Dic11—24no—
200C2×Dic11—42no—
201C2×Dic11—41no—
202C2×Dic11—42no—
203C2×Dic11—41no—
204D44—22no—
205D44—22no—
206D44—41no—
207D44—41no—
208C4×D11—42no—
209C4×D11—42no—
210C4×D11—42no—
211C4×D11—42no—
212Dic22—42no—
213Dic22—42no—
214Dic22—42no—
215Dic22—42no—
216C8×C11—81no—
217C11⋊C8—42no—
218C11⋊C8—81no—
219#556—114no—
220#556—222no—
221#556—222no—
222#556—222no—
223C2×C4⋊Q8—111no—
224C2×#126—222no—
225C2×#124—221no—
226C2×C22⋊Q8—221no—
227C2×C4×Q8—221no—
228C2×C4×Q8C2×D1111yescharacteristic
229C2×C4×D4—111no—
230C2×#117—221no—
231C2×C4⋊C8—111no—
232C2×C4⋊C8C2×D1111yescharacteristic
233C2×#103—21no—
234C2×#102—221no—
235C2×C4×C8—111no—
236#384C2×D1111yescharacteristic
237#340—21no—
238#340—221no—
239#340—222no—
240#332—222no—
241Q8⋊C8—222no—
242D4⋊C8—222no—
243C22×C11#37911yescharacteristic
244C22×C11#44911yescharacteristic
245C22×C11#44911yescharacteristic
246C22×C11#45211yescharacteristic
247C22×C11#45211yescharacteristic
248C22×C11#45411yescharacteristic
249C22×C11#45611yescharacteristic
250C2×D11—42no—
251C2×D11—42no—
252C2×D11—42no—
253C2×D11—81no—
254C2×D11—81no—
255C2×D11—81no—
256C2×D11—81no—
257C4×C11—21no—
258C4×C11—21no—
259C4×C11—42no—
260C4×C11—42no—
261C4×C11—161no—
262C4×C11#41611yescharacteristic
263C4×C11#41611yescharacteristic
264C4×C11#41711yescharacteristic
265C4×C11#41711yescharacteristic
266C4×C11#44911yescharacteristic
267C4×C11#44911yescharacteristic
268C4×C11#45211yescharacteristic
269C4×C11#45211yescharacteristic
270Dic11—44no—
271Dic11—42no—
272C22×Q8—221no—
273C22×Q8C22⋊D1111yescharacteristic
274C22×D4—111no—
275C23×C4—221no—
276C22×C8—21no—
277C22×C8—221no—
278C22×C8—221no—
279C4⋊Q8—112no—
280C4⋊Q8—112no—
281C4⋊Q8—221no—
282C4⋊Q8—221no—
283#126—228no—
284#126—228no—
285#124—224no—
286#124—224no—
287C22⋊Q8—224no—
288C22⋊Q8—224no—
289C4×Q8—21no—
290C4×Q8—21no—
291C4×Q8—224no—
292C4×Q8—224no—
293C4×Q8C4×D1112yes—
294C4×Q8D4412yes—
295C4×D4—112no—
296C4×D4—112no—
297C4×D4—221no—
298C4×D4—221no—
299#117—224no—
300#117—224no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—111no—
306C2×C4⋊C4—112no—
307C2×C4⋊C4—222no—
308C2×C4⋊C4—221no—
309C2×C4⋊C4C22⋊D1111yescharacteristic
310C2×C22⋊C4—222no—
311C2×C22⋊C4—222no—
312C2×C22⋊C4—221no—
313C2×C42—21no—
314C2×C42—222no—
315C2×C42C22×D1111yescharacteristic
316C4⋊C8—21no—
317C4⋊C8—21no—
318C4⋊C8—221no—
319C4⋊C8—221no—
320#103—42no—
321#102—442no—
322C4×C8—221no—
323C4×C8—221no—
324C2×C11#162811yescharacteristic
325C2×C11#163811yescharacteristic
326C2×C11#165011yescharacteristic
327C2×C11#165211yescharacteristic
328C2×C11#178811yescharacteristic
329C2×C11#178811yescharacteristic
330C2×C11#179311yescharacteristic
331D11—82no—
332C24—221no—
333C2×Q8—21no—
334C2×Q8—21no—
335C2×Q8—21no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8—222no—
339C2×Q8—222no—
340C2×Q8—441no—
341C2×Q8—441no—
342C2×Q8—441no—
343C2×Q8—441no—
344C2×Q8(C2×D11)⋊C412yes—
345C2×D4—112no—
346C2×D4—221no—
347C2×D4—221no—
348C2×D4—221no—
349C2×D4—221no—
350C2×D4—221no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—41no—
354C22×C4—221no—
355C22×C4—222no—
356C22×C4—222no—
357C22×C4—222no—
358C22×C4—441no—
359C22×C4—441no—
360C22×C4—441no—
361C22×C4—441no—
362C22×C4D4×D1111yescharacteristic
363C22×C4D4×D1111yescharacteristic
364C22×C4C2×C22⋊D1111yescharacteristic
365C2×C8—41no—
366C2×C8—41no—
367C2×C8—41no—
368C2×C8—222no—
369C2×C8—441no—
370C2×C8—441no—
371C2×C8—441no—
372C2×C8—441no—
373C2×C8—441no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—21no—
377C4⋊C4—42no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—112no—
383C4⋊C4—114no—
384C4⋊C4—228no—
385C4⋊C4—221no—
386C4⋊C4—222no—
387C4⋊C4—222no—
388C4⋊C4—222no—
389C4⋊C4(C2×D11)⋊C412yes—
390C22⋊C4—228no—
391C22⋊C4—228no—
392C22⋊C4—222no—
393C22⋊C4—222no—
394C42—22no—
395C42—22no—
396C42—228no—
397C42C2×C4×D1111yescharacteristic
398C42C2×D4411yescharacteristic
399C42D4×D1111yescharacteristic
400C42D4×D1111yescharacteristic
401C11#844911yescharacteristic, complemented, Sylow
402C23—222no—
403C23—441no—
404C23—441no—
405C23—441no—
406C23—441no—
407C23—441no—
408C23—441no—
409C23#6699011yescharacteristic
410Q8—22no—
411Q8—22no—
412Q8—41no—
413Q8—41no—
414Q8—442no—
415Q8—442no—
416Q8—442no—
417Q8—442no—
418D4—222no—
419D4—222no—
420D4—441no—
421D4—441no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—81no—
431C2×C4—81no—
432C2×C4—81no—
433C2×C4—222no—
434C2×C4—224no—
435C2×C4—442no—
436C2×C4—442no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4—442no—
440C2×C4—442no—
441C2×C4—442no—
442C2×C4—442no—
443C2×C4C22⋊C4×D1111yescharacteristic
444C2×C4C22⋊C4×D1111yescharacteristic
445C2×C4#6693511yescharacteristic
446C2×C4#6693511yescharacteristic
447C2×C4#6696711yescharacteristic
448C2×C4#6696911yescharacteristic
449C2×C4#6697111yescharacteristic
450C2×C4#6697211yescharacteristic
451C2×C4C2×(C2×D11)⋊C411yescharacteristic
452C2×C4#6698511yescharacteristic
453C2×C4#6699011yescharacteristic
454C2×C4#6699511yescharacteristic
455C2×C4#6700311yescharacteristic
456C2×C4#6700311yescharacteristic
457C8—81no—
458C8—442no—
459C8—881no—
460C22—442no—
461C22—442no—
462C22—442no—
463C22—881no—
464C22—881no—
465C22—881no—
466C22—881no—
467C22#1062256811yescharacteristic
468C22#1062265011yescharacteristic
469C22#1062266011yescharacteristic
470C22#1062278511yescharacteristic
471C22#1062280011yescharacteristic
472C22#1062281411yescharacteristic
473C22#1062281811yescharacteristic
474C4—21no—
475C4—21no—
476C4—42no—
477C4—42no—
478C4—161no—
479C4—442no—
480C4—444no—
481C4#1062241611yescharacteristic
482C4#1062241711yescharacteristic
483C4#1062242311yescharacteristic
484C4#1062242411yescharacteristic
485C4#1062257911yescharacteristic
486C4#1062261511yescharacteristic
487C4#1062265011yescharacteristic
488C4#1062266011yescharacteristic
489C2—882no—
490C2#1306772511yescharacteristic
491C2#1306778711yescharacteristic
492C2#1306787111yescharacteristic
493C2#1306788411yescharacteristic
494C2#1306855411yescharacteristic
495C2#1306855511yescharacteristic
496C2#1306857311yescharacteristic
subgroupG/H
centerC23#66990
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1803C2
socleC23×C11#120
prime radicalC22×D44D4
cosocleC2×C42×C11C23
hypercenter#1803D11
hypocenterC11#8449
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
2. #13069576C2semidirect
4. C2×#10622124C2semidirect
5. C2×Q8⋊(C11⋊C8)C2semidirect
7. C11×#1803C2semidirect
13. #10623115C4semidirect
156. #1803D11semidirect
401. C11#8449semidirect

Maximal subgroups

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

subgroupindex
C2×#106231152
#130695762
#130686132
C2×#106221242
C2×Q8⋊(C11⋊C8)2
C2×#106221212
C11×#18032
#844911