Finite Group Databasebeta

← #14644671

Subgroups — #14644671

Order 2816.

720 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071144C211yesmaximal, characteristic
2#13068380C211yesmaximal, characteristic
3C2×#10622105C211yesmaximal, characteristic
4C2×#10622090C211yesmaximal, characteristic
5#95×Dic11C211yesmaximal, characteristic
6#13066494C211yesmaximal, characteristic
7C11×#1294C211yesmaximal, characteristic
8C2×#66977C2211yescharacteristic
9C22×C4×Dic11—21no—
10C22×C4×Dic11C2211yescharacteristic
11C2×#66940C411yescharacteristic, complemented
12C2×C11×C22⋊C8C2211yescharacteristic
13C11×#380C2211yescharacteristic
14C2×C11×#95C2211yescharacteristic
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2211yescharacteristic
17C2×C22⋊(C11⋊C8)C2211yescharacteristic
18C2×#66879—21no—
19C4⋊C4×Dic11C411yescharacteristic, complemented
20#10622587C411yescharacteristic, complemented
21#10622586C411yescharacteristic, complemented
22#10622559—21no—
23C22⋊C4×Dic11—21no—
24#10622265—21no—
25#10622262—21no—
26#10622188—21no—
27#10622105C414yescomplemented
28#10622090C414yescomplemented
29C23×C4×C11—21no—
30C23×C4×C11C2311yescharacteristic
31C23×Dic11—21no—
32C23×Dic11D411yescharacteristic
33C23×Dic11D411yescharacteristic
34C22×Dic22C2×C411yescharacteristic
35C22×C8×C11—21no—
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C11×C4⋊C4C2×C411yescharacteristic
38C2×C11×C22⋊C4—21no—
39C2×C22⋊Dic11—21no—
40C2×C4⋊Dic11C2×C411yescharacteristic
41#66977—21no—
42#66977—21no—
43#66977C2×C412yes—
44#66977C2×C412yes—
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×C4×Dic11—24no—
49C2×C4×Dic11—21no—
50C2×C4×Dic11—21no—
51C2×C4×Dic11—42no—
52C2×C4×Dic11—42no—
53C2×C4×Dic11—42no—
54C2×C4×Dic11C2×C411yescharacteristic
55C2×C4×Dic11C2×C411yescharacteristic
56C2×C4×Dic11D411yescharacteristic
57C2×C4×Dic11D411yescharacteristic
58C22×C11⋊C8—21no—
59#66940—42no—
60C11×C22⋊C8—21no—
61C11×C22⋊C8C2×C412yes—
62C11×#95—21no—
63C11×#95—21no—
64C11×#95C2×C412yes—
65C11⋊#95—24no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95C2×C412yes—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)C2×C412yes—
74#66879—42no—
75#8219—111nomaximal, Sylow
76C24×C11C2×D411yescharacteristic
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11C22×C411yescharacteristic
89C22×C4×C11C22×C411yescharacteristic
90C22×C4×C11C22×C411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C22×Dic11—22no—
95C22×Dic11—22no—
96C22×Dic11—22no—
97C22×Dic11—22no—
98C22×Dic11—22no—
99C22×Dic11—21no—
100C22×Dic11—21no—
101C22×Dic11—22no—
102C22×Dic11—21no—
103C22×Dic11—21no—
104C22×Dic11—21no—
105C22×Dic11—21no—
106C22×Dic11—41no—
107C22×Dic11—41no—
108C22×Dic11—41no—
109C22×Dic11—41no—
110C22×Dic11—41no—
111C22×Dic11C22⋊C411yescharacteristic
112C22×Dic11C22⋊C411yescharacteristic
113C22×Dic11C22⋊C411yescharacteristic
114C22×Dic11C22⋊C411yescharacteristic
115C2×Dic22—21no—
116C2×Dic22—41no—
117C2×Dic22—41no—
118C2×Dic22C4212yescomplemented
119C2×C8×C11—22no—
120C2×C8×C11—41no—
121C2×C8×C11—41no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C11×C22⋊C4—41no—
125C11×C22⋊C4—41no—
126C22⋊Dic11—22no—
127C22⋊Dic11—22no—
128C4⋊Dic11—21no—
129C4⋊Dic11C4212yescomplemented
130Dic11⋊C4—22no—
131Dic11⋊C4—22no—
132Dic11⋊C4—42no—
133Dic11⋊C4—42no—
134C4×Dic11—22no—
135C4×Dic11—22no—
136C4×Dic11—41no—
137C4×Dic11—41no—
138C4×Dic11—42no—
139C4×Dic11—48no—
140C4×Dic11—42no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—41no—
143C2×C11⋊C8—41no—
144C4×C22⋊Q8—111no—
145#1749—111no—
146C2×#328—111no—
147C2×#328—111no—
148C4×#95—111no—
149#1294—111no—
150#1294D1111yescharacteristic
151C23×C11—21no—
152C23×C11—21no—
153C23×C11—21no—
154C23×C11—21no—
155C23×C11C2×C22⋊C411yescharacteristic
156C23×C11C4×D411yescharacteristic
157C23×C11C4×D411yescharacteristic
158C23×C11AGL(1,ℤ/8)11yescharacteristic
159C23×C11#13711yescharacteristic
160C23×C11#13711yescharacteristic
161C23×C11#13711yescharacteristic
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—24no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11C2×C4211yescharacteristic
184C2×C4×C11#11711yescharacteristic
185C2×C4×C11C4×D411yescharacteristic
186C2×C4×C11C4×D411yescharacteristic
187C2×Dic11—24no—
188C2×Dic11—24no—
189C2×Dic11—21no—
190C2×Dic11—21no—
191C2×Dic11—21no—
192C2×Dic11—21no—
193C2×Dic11—21no—
194C2×Dic11—21no—
195C2×Dic11—24no—
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—21no—
199C2×Dic11—21no—
200C2×Dic11—21no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—42no—
213C2×Dic11#9912yes—
214C2×Dic11#10412yes—
215C2×Dic11#10412yes—
216Dic22—42no—
217Dic22—42no—
218C8×C11—42no—
219C11⋊C8—42no—
220C2×C22⋊Q8—111no—
221C2×C4×Q8—111no—
222C22×C42—111no—
223C22×C42—221no—
224C2×C22⋊C8—111no—
225C2×C22⋊C8C2×D1111yescharacteristic
226C2×#97—221no—
227#391—111no—
228#389—111no—
229#387—221no—
230#385—221no—
231#380C2×D1111yescharacteristic
232C4×C4⋊C4—111no—
233C4×C4⋊C4—221no—
234C4×C22⋊C4—221no—
235C2×#95—111no—
236C2×#95—221no—
237C2×#95C2×D1111yescharacteristic
238#336—221no—
239#328—114no—
240#328—114no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—21no—
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—21no—
247C22×C11—21no—
248C22×C11—21no—
249C22×C11—21no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11C4×C22⋊C411yescharacteristic
254C22×C11C2×#9911yescharacteristic
255C22×C11#41011yescharacteristic
256C22×C11#41711yescharacteristic
257C22×C11#41911yescharacteristic
258C22×C11C2×#10411yescharacteristic
259C22×C11C2×#10411yescharacteristic
260C22×C11#44011yescharacteristic
261C22×C11#44011yescharacteristic
262C22×C11#44111yescharacteristic
263C22×C11#44111yescharacteristic
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—21no—
268C4×C11—44no—
269C4×C11—81no—
270C4×C11—81no—
271Dic11—22no—
272Dic11—22no—
273Dic11—22no—
274Dic11—44no—
275Dic11—42no—
276Dic11—42no—
277Dic11—41no—
278C22×Q8—111no—
279C23×C4—21no—
280C23×C4—111no—
281C23×C4—111no—
282C23×C4—221no—
283C23×C4C22×D1111yescharacteristic
284C22×C8—21no—
285C22×C8—221no—
286C22⋊Q8—112no—
287C22⋊Q8—112no—
288C22⋊Q8—221no—
289C22⋊Q8—221no—
290C4×Q8—442no—
291C2×C4⋊C4—111no—
292C2×C4⋊C4—221no—
293C2×C4⋊C4—221no—
294C2×C4⋊C4—221no—
295C2×C4⋊C4C4×D1111yescharacteristic
296C2×C4⋊C4C4×D1111yescharacteristic
297C2×C22⋊C4—21no—
298C2×C22⋊C4—221no—
299C2×C42—111no—
300C2×C42—111no—
301C2×C42—111no—
302C2×C42—111no—
303C2×C42—221no—
304C2×C42—221no—
305C2×C42—224no—
306C2×C42—442no—
307C2×C42—442no—
308C2×C42—442no—
309C22⋊C8—21no—
310C22⋊C8—112no—
311C22⋊C8—221no—
312C22⋊C8C4×D1112yes—
313#97—442no—
314#95—21no—
315#95—21no—
316#95—112no—
317#95—221no—
318#95—221no—
319#95—221no—
320#95—221no—
321#95—224no—
322#95—221no—
323#95C4×D1112yes—
324C2×C11—21no—
325C2×C11—21no—
326C2×C11—21no—
327C2×C11—21no—
328C2×C11#150411yescharacteristic
329C2×C11#150611yescharacteristic
330C2×C11#150811yescharacteristic
331C2×C11#150911yescharacteristic
332C2×C11C4×#9911yescharacteristic
333C2×C11C4×#10411yescharacteristic
334C2×C11#176311yescharacteristic
335C24D4×D1111yescharacteristic
336C2×Q8—112no—
337C2×Q8—221no—
338C2×Q8—441no—
339C2×Q8—441no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4—111no—
352C22×C4—111no—
353C22×C4—111no—
354C22×C4—111no—
355C22×C4—222no—
356C22×C4—222no—
357C22×C4—222no—
358C22×C4—221no—
359C22×C4—221no—
360C22×C4—222no—
361C22×C4—222no—
362C22×C4—221no—
363C22×C4—221no—
364C22×C4—222no—
365C22×C4—221no—
366C22×C4—221no—
367C22×C4—441no—
368C22×C4—441no—
369C22×C4—441no—
370C22×C4—441no—
371C22×C4—441no—
372C22×C4C2×C4×D1111yescharacteristic
373C22×C4C2×C4×D1111yescharacteristic
374C22×C4C2×C4×D1111yescharacteristic
375C22×C4D4×D1111yescharacteristic
376C22×C4#434111yescharacteristic
377C22×C4#434311yescharacteristic
378C2×C8—22no—
379C2×C8—41no—
380C2×C8—41no—
381C2×C8—222no—
382C2×C8—441no—
383C2×C8—441no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4—112no—
387C4⋊C4—222no—
388C4⋊C4—221no—
389C4⋊C4—222no—
390C4⋊C4—442no—
391C4⋊C4—442no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—222no—
395C22⋊C4—222no—
396C42—222no—
397C42—222no—
398C42—441no—
399C42—441no—
400C42—442no—
401C42—448no—
402C42—442no—
403C11#821911yescharacteristic, complemented, Sylow
404C23—21no—
405C23—21no—
406C23—21no—
407C23—21no—
408C23C22⋊C4×D1111yescharacteristic
409C23(C22⋊D11)⋊C411yescharacteristic
410C23#6694611yescharacteristic
411C23#6696411yescharacteristic
412C23#6696811yescharacteristic
413C23#6696811yescharacteristic
414C23#6697111yescharacteristic
415Q8—442no—
416Q8—442no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—24no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—112no—
439C2×C4—112no—
440C2×C4—112no—
441C2×C4—224no—
442C2×C4—224no—
443C2×C4—221no—
444C2×C4—221no—
445C2×C4—221no—
446C2×C4—221no—
447C2×C4—221no—
448C2×C4—221no—
449C2×C4—224no—
450C2×C4—222no—
451C2×C4—222no—
452C2×C4—221no—
453C2×C4—221no—
454C2×C4—221no—
455C2×C4—442no—
456C2×C4—442no—
457C2×C4—442no—
458C2×C4—442no—
459C2×C4—442no—
460C2×C4—442no—
461C2×C4—442no—
462C2×C4—442no—
463C2×C4—441no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4—441no—
467C2×C4C42×D1111yescharacteristic
468C2×C4(C22⋊D11)⋊C411yescharacteristic
469C2×C4#6694511yescharacteristic
470C2×C4#6694611yescharacteristic
471C8—42no—
472C8—442no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22#1062227911yescharacteristic
486C22#1062235311yescharacteristic
487C22D11×#9911yescharacteristic
488C22#1062237011yescharacteristic
489C22#1062238411yescharacteristic
490C22#1062240211yescharacteristic
491C22#1062241511yescharacteristic
492C22D11×#10411yescharacteristic
493C22D11×#10411yescharacteristic
494C22#1062246611yescharacteristic
495C22#1062250211yescharacteristic
496C4—21no—
497C4—21no—
498C4—21no—
499C4—21no—
500C4—44no—
501C4—81no—
502C4—81no—
503C4—222no—
504C4—222no—
505C4—222no—
506C4—444no—
507C4—442no—
508C4—441no—
509C4—442no—
510C2—21no—
511C2—21no—
512C2—21no—
513C2—21no—
514C2#1306711711yescharacteristic
515C2#1306712611yescharacteristic
516C2#1306713411yescharacteristic
517C2#1306713811yescharacteristic
518C2#1306840311yescharacteristic
519C2#1306842011yescharacteristic
520C2#1306844511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC11×#1294C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1294D11
hypocenterC11#8219
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
11. C2×#66940C4semidirect
19. C4⋊C4×Dic11C4semidirect
20. #10622587C4semidirect
21. #10622586C4semidirect
27. #10622105C4semidirect
28. #10622090C4semidirect
118. C2×Dic22C42semidirect
129. C4⋊Dic11C42semidirect
403. C11#8219semidirect

Maximal subgroups

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

subgroupindex
#130711442
#130683802
C2×#106221052
C2×#106220902
#95×Dic112
#130664942
C11×#12942
#821911