Finite Group Databasebeta

← #14804240

Subgroups — #14804240

Order 2816.

978 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622798C212yesmaximal
2C2×#10622696C211yesmaximal, characteristic
3#13073612C211yesmaximal, characteristic
4#13071676C211yesmaximal, characteristic, complemented
5#13069936C212yesmaximal, complemented
6#13069707C212yesmaximal
7#13069540C211yesmaximal, characteristic, complemented
8#13069334C211yesmaximal, characteristic, complemented
9#13068959C212yesmaximal, complemented
10C4×#66885C211yesmaximal, characteristic
11C2×C11×#494C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2212yes—
13C22×C11×Q16C2212yes—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×#67000C2212yes—
17C2×Q8×Dic11C2212yes—
18C22×#4325C2212yes—
19C2×C4×D44C2211yescharacteristic
20C11×#494—24no—
21C2×C4×C8×C11C2211yescharacteristic
22#10622843C2212yes—
23#10622843C2212yes—
24C2×#66899C2212yes—
25C2×#66899C2212yes—
26C2×#66899C2212yes—
27#10622798—28no—
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×Dic11⋊C8C2212yes—
31#10622696—24no—
32#10622606—22no—
33#10622600—21no—
34#10622600—21no—
35#10622598—21no—
36#10622594—22no—
37C4⋊C4×Dic11—21no—
38C4×C4⋊Dic11C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41#10622189C2211yescharacteristic
42#10622189C2211yescharacteristic
43#10622188C2212yes—
44C22×Q8×C11C2312yes—
45C22×Q8×C11C2312yes—
46C22×D44C2311yescharacteristic
47C22×C4×D11—21no—
48C2×C11×Q16—24no—
49C2×C11×Q16—24no—
50C2×C11×Q16—24no—
51C2×C11×Q16—24no—
52C2×C11×Q16—42no—
53C2×C11×Q16—42no—
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2311yescharacteristic
56C11×C4⋊Q8—22no—
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8—22no—
59C11×C4⋊Q8D414yes—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C42×C11C2311yescharacteristic
65#67000—24no—
66#67000—42no—
67Q8×Dic11—24no—
68Q8×Dic11—42no—
69C2×#4325—24no—
70C2×#4325—24no—
71C2×#4325—42no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4—22no—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11D411yescharacteristic
77C2×C4⋊Dic11D411yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4×Dic11—21no—
82C2×C4×Dic11—22no—
83C2×C4×Dic11C2312yes—
84C22×C11⋊C8C2312yes—
85C4×D44—22no—
86C4×D44—22no—
87C4×C8×C11—22no—
88#66899—24no—
89#66899—24no—
90#66899—42no—
91C11⋊#95—21no—
92C11⋊#95—22no—
93C11⋊#95—22no—
94C11⋊#95—22no—
95C11⋊#95—22no—
96C11⋊#95D412yes—
97#66885—22no—
98#66885D414yes—
99Dic11⋊C8—24no—
100C4⋊(C11⋊C8)—22no—
101#25365—111nomaximal, Sylow
102C23×D11—21no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11C2×D414yes—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2411yescharacteristic
120C22×Dic11—21no—
121C22×Dic11—21no—
122C22×Dic11—21no—
123C22×Dic11C2×D412yes—
124C22×Dic11C2×D412yes—
125C2×D44—21no—
126C2×D44—21no—
127C2×D44—21no—
128C2×D44—21no—
129C2×D44—21no—
130C2×D44C2×D412yes—
131C2×C4×D11—42no—
132C2×C4×D11—42no—
133C2×C4×D11—42no—
134C11×Q16—48no—
135C11×Q16—48no—
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C2×C8×C11—21no—
139C2×C8×C11—21no—
140C2×C8×C11C2×D412yes—
141C2×C8×C11#4112yes—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—42no—
145C11×C4⋊C4—42no—
146C42×C11C2×D412yes—
147C42×C11#4112yes—
148#4325—48no—
149(C2×D11)⋊C4—44no—
150(C2×D11)⋊C4—44no—
151(C2×D11)⋊C4—42no—
152C4⋊Dic11—22no—
153C4⋊Dic11—22no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159C4⋊Dic11—44no—
160C4⋊Dic11C2×D412yes—
161C4×Dic11—22no—
162C4×Dic11—22no—
163C4×Dic11—44no—
164C4×Dic11—42no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×#494D1111yescharacteristic, complemented
169C2×#464—112no—
170C2×#461—111no—
171#2547—111no—
172#2365—111no—
173#2056—112no—
174#2015—112no—
175#1981—111no—
176#1939—111no—
177#1878—112no—
178C4×#102—111no—
179C23×C11C22×D411yescharacteristic
180C22×D11—22no—
181C22×D11—41no—
182C22×D11—41no—
183C22×D11—41no—
184C22×D11—41no—
185C22×D11—41no—
186C22×D11—41no—
187Q8×C11—24no—
188Q8×C11—24no—
189Q8×C11—42no—
190Q8×C11—42no—
191Q8×C11—42no—
192Q8×C11—42no—
193Q8×C11—42no—
194Q8×C11—42no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—24no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11#12112yes—
204C2×C4×C11#12112yes—
205C2×C4×C11#13512yes—
206C2×C4×C11#13712yes—
207C2×C4×C11C22×D411yescharacteristic
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C2×C4×C11H(5,𝔽2)11yescharacteristic
212C2×C4×C11H(5,𝔽2)11yescharacteristic
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228D44—22no—
229D44—22no—
230D44—41no—
231D44—41no—
232C4×D11—84no—
233C8×C11—22no—
234C8×C11—22no—
235C11⋊C8—42no—
236C22×Q16C2×D1112yes—
237C22×Q16C2×D1112yes—
238C22×SD16—112no—
239C2×C4⋊Q8C2×D1111yescharacteristic
240C2×C4⋊Q8C2×D1111yescharacteristic
241C2×#124—112no—
242C2×C4×Q8—112no—
243C2×C4×D4—111no—
244#494—24no—
245#464—228no—
246#461—224no—
247C2×C4⋊C8—112no—
248C2×C4⋊C8—111no—
249C2×#103—112no—
250C2×#103—112no—
251C2×#103—112no—
252C2×#102—111no—
253C2×#102—111no—
254C2×C4×C8C2×D1111yescharacteristic
255#397—222no—
256#391—112no—
257#391—112no—
258#389—221no—
259#387—222no—
260#380—221no—
261#380—221no—
262C4×C4⋊C4—111no—
263C4×C4⋊C4—111no—
264C4×C4⋊C4—221no—
265#340—111no—
266#340—111no—
267#336—112no—
268C22×C11C2×#12111yescharacteristic
269C22×C11D4211yescharacteristic
270C22×C11#55011yescharacteristic
271C22×C11C2×#13511yescharacteristic
272C22×C11C2×#13711yescharacteristic
273C22×C11#57811yescharacteristic
274C22×C11#57811yescharacteristic
275C2×D11—42no—
276C2×D11—42no—
277C2×D11—42no—
278C2×D11—81no—
279C2×D11—81no—
280C2×D11—81no—
281C2×D11—81no—
282C4×C11—22no—
283C4×C11—44no—
284C4×C11—82no—
285C4×C11#46414yescomplemented
286C4×C11#53211yescharacteristic
287C4×C11#54011yescharacteristic
288C4×C11D4211yescharacteristic
289C4×C11#54611yescharacteristic
290Dic11—42no—
291Dic11—42no—
292Dic11—42no—
293Dic11—81no—
294Dic11—81no—
295C22×Q8C22×D1112yes—
296C22×Q8C22×D1112yes—
297C22×D4—111no—
298C23×C4—221no—
299C2×Q16—24no—
300C2×Q16—24no—
301C2×Q16—24no—
302C2×Q16—24no—
303C2×Q16—42no—
304C2×Q16—42no—
305C2×SD16—224no—
306C2×SD16—224no—
307C2×SD16—442no—
308C22×C8—112no—
309C22×C8C22×D1111yescharacteristic
310C22×C8C22×D1111yescharacteristic
311C4⋊Q8—22no—
312C4⋊Q8—22no—
313C4⋊Q8—22no—
314C4⋊Q8C22⋊D1114yes—
315#124—224no—
316#124—442no—
317C4×Q8—224no—
318C4×Q8—442no—
319C4×D4—222no—
320C4×D4—222no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—111no—
326C2×C4⋊C4—111no—
327C2×C4⋊C4—111no—
328C2×C4⋊C4—111no—
329C2×C4⋊C4—111no—
330C2×C4⋊C4—222no—
331C2×C22⋊C4—222no—
332C2×C22⋊C4—222no—
333C2×C22⋊C4—221no—
334C2×C42—112no—
335C2×C42—222no—
336C2×C42—221no—
337C2×C42C22×D1111yescharacteristic
338C4⋊C8—224no—
339C4⋊C8—222no—
340#103—224no—
341#103—224no—
342#103—442no—
343#102—114no—
344#102—222no—
345C4×C8—22no—
346#95—112no—
347#95—222no—
348#95—222no—
349#95—222no—
350#95—222no—
351#95—221no—
352C2×C11#242811yescharacteristic
353C2×C11C2×#46411yescharacteristic
354C2×C11#304411yescharacteristic
355C2×C11#327611yescharacteristic
356C2×C11#328311yescharacteristic
357C2×C11#339311yescharacteristic
358C2×C11#339811yescharacteristic
359D11—82no—
360C24—221no—
361C2×Q8—22no—
362C2×Q8—22no—
363C2×Q8—22no—
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—22no—
369C2×Q8—22no—
370C2×Q8—22no—
371C2×Q8—22no—
372C2×Q8C2×C22⋊D1114yes—
373C2×D4—112no—
374C2×D4—221no—
375C2×D4—221no—
376C2×D4—221no—
377C2×D4—221no—
378C2×D4—221no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—112no—
382C22×C4—112no—
383C22×C4—221no—
384C22×C4—221no—
385C22×C4—221no—
386C22×C4—442no—
387C22×C4—442no—
388C22×C4—442no—
389C22×C4D4×D1111yescharacteristic
390C22×C4D4×D1111yescharacteristic
391C22×C4C23×D1111yescharacteristic
392Q16—48no—
393Q16—48no—
394SD16—448no—
395C2×C8—21no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8—222no—
400C2×C8—222no—
401C2×C8—222no—
402C2×C8D4×D1112yes—
403C2×C8#434112yes—
404C4⋊C4—24no—
405C4⋊C4—24no—
406C4⋊C4—42no—
407C4⋊C4—42no—
408C4⋊C4—112no—
409C4⋊C4—222no—
410C4⋊C4—222no—
411C4⋊C4—221no—
412C4⋊C4—221no—
413C4⋊C4—221no—
414C4⋊C4—221no—
415C4⋊C4—221no—
416C4⋊C4—444no—
417C22⋊C4—444no—
418C22⋊C4—444no—
419C22⋊C4—442no—
420C42—222no—
421C42—222no—
422C42—444no—
423C42—442no—
424C42#434112yes—
425C42C2×C22⋊D1112yes—
426C11#2536511yescharacteristic, complemented, Sylow
427C23—222no—
428C23—441no—
429C23—441no—
430C23—441no—
431C23—441no—
432C23—441no—
433C23—441no—
434C23C2×D4×D1111yescharacteristic
435Q8—24no—
436Q8—24no—
437Q8—42no—
438Q8—42no—
439Q8—42no—
440Q8—42no—
441Q8—42no—
442Q8—42no—
443D4—222no—
444D4—222no—
445D4—441no—
446D4—441no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—24no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—222no—
456C2×C4—222no—
457C2×C4—222no—
458C2×C4—222no—
459C2×C4—222no—
460C2×C4—222no—
461C2×C4—222no—
462C2×C4—441no—
463C2×C4—441no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4—441no—
467C2×C4—441no—
468C2×C4—441no—
469C2×C4—441no—
470C2×C4—884no—
471C2×C4#6697112yes—
472C2×C4#6697212yes—
473C2×C4#6699212yes—
474C2×C4#6699212yes—
475C2×C4C2×D4×D1111yescharacteristic
476C2×C4C2×#434111yescharacteristic
477C2×C4C2×#434111yescharacteristic
478C2×C4#6703711yescharacteristic
479C2×C4#6703711yescharacteristic
480C2×C4C22×C22⋊D1111yescharacteristic
481C8—22no—
482C8—22no—
483C8—442no—
484C22—442no—
485C22—442no—
486C22—442no—
487C22—881no—
488C22—881no—
489C22—881no—
490C22—881no—
491C22#1062324811yescharacteristic
492C22#1062324911yescharacteristic
493C22C2×#6697111yescharacteristic
494C22C2×#6697211yescharacteristic
495C22#1062329711yescharacteristic
496C22#1062329711yescharacteristic
497C22C2×#6699211yescharacteristic
498C4—22no—
499C4—44no—
500C4—82no—
501C4—442no—
502C4—442no—
503C4—442no—
504C4—881no—
505C4—881no—
506C4#1062279814yescomplemented
507C4#1062324711yescharacteristic
508C4#1062325011yescharacteristic
509C4D4×C22⋊D1111yescharacteristic
510C4#1062333711yescharacteristic
511C2—882no—
512C2#1307220711yescharacteristic
513C2C2×#1062279811yescharacteristic
514C2#1307814311yescharacteristic
515C2#1308026111yescharacteristic
516C2#1308033611yescharacteristic
517C2#1308160611yescharacteristic
518C2#1308165211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#494C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenterC2×#494D11
hypocenterC11#25365
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#494

Complements

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

NH ≅ G/Ntype
4. #13071676C2semidirect
5. #13069936C2semidirect
7. #13069540C2semidirect
8. #13069334C2semidirect
9. #13068959C2semidirect
11. C2×C11×#494C2semidirect
168. C2×#494D11semidirect
285. C4×C11#464semidirect
426. C11#25365semidirect
506. C4#10622798semidirect

Maximal subgroups

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

subgroupindex
C2×#106227982
C2×#106226962
#130736122
#130716762
#130699362
#130697072
#130695402
#130693342
#130689592
C4×#668852
C2×C11×#4942
#2536511