Finite Group Databasebeta

← #14914875

Subgroups — #14914875

Order 2816.

2198 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623103C211yesmaximal, characteristic
2#13071583C213yesmaximal, complemented
3#13071571C213yesmaximal, complemented
4Q8×C4⋊Dic11C211yesmaximal, characteristic, complemented
5#13071508C213yesmaximal
6#13071500C213yesmaximal
7Q8×(C2×D11)⋊C4C211yesmaximal, characteristic
8Q8×(C2×D11)⋊C4C211yesmaximal, characteristic
9#13071263C213yesmaximal, complemented
10#13071226C213yesmaximal
11#13071109C213yesmaximal
12#13071087C213yesmaximal, complemented
13#13070981C211yesmaximal, characteristic, complemented
14C4×Q8×Dic11C211yesmaximal, characteristic, complemented
15C11×#2351C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C2×Q8×Dic11C2211yescharacteristic
23#10623103C4116yescomplemented
24C2×#66945C2213yes—
25C2×#66940C2213yes—
26C2×#66925C2213yes—
27C2×C4×Dic22C2213yes—
28C11×#389C2213yes—
29C11×#389C2213yes—
30C11×#382C2213yes—
31C4×C11×C4⋊C4C2213yes—
32#10622603C2213yes—
33#10622603C2213yes—
34#10622600C2213yes—
35#10622600C2213yes—
36#10622598C2213yes—
37#10622598C2213yes—
38#10622591C2213yes—
39#10622591C2213yes—
40#10622590C2216yes—
41C4⋊C4×Dic11C2213yes—
42C4⋊C4×Dic11C2213yes—
43C4⋊C4×Dic11C2213yes—
44C4⋊C4×Dic11C2213yes—
45C4⋊C4×Dic11C2216yes—
46#10622587C2213yes—
47#10622587C2213yes—
48C4×(C2×D11)⋊C4C2213yes—
49C4×(C2×D11)⋊C4C2213yes—
50#10622548C2213yes—
51C4×C4⋊Dic11C2213yes—
52C4×C4⋊Dic11C2213yes—
53C4×C4⋊Dic11C2213yes—
54#10622545C2213yes—
55C42×Dic11C2213yes—
56#10622542C2213yes—
57#10622542C2213yes—
58#10622283C2211yescharacteristic
59#10622283C2213yes—
60#10622283C2216yes—
61#10622268C2213yes—
62#10622268C2213yes—
63#10622268C2216yes—
64#10622268C2216yes—
65#10622264C2216yes—
66#10622261C2216yes—
67C22×Q8×C11C2311yescharacteristic
68C2×Q8×D11—24no—
69C2×Q8×D11—24no—
70C2×Q8×D11C2×C418yes—
71C22×C4×D11C2313yes—
72C22×Dic22C2313yes—
73C4×Q8×C11—24no—
74C4×Q8×C11—24no—
75C4×Q8×C11C2×C418yes—
76C2×C11×C4⋊C4C2313yes—
77C2×C11×C4⋊C4C2313yes—
78C2×C11×C4⋊C4C2313yes—
79C2×C11×C4⋊C4C2313yes—
80C2×C11×C4⋊C4C2313yes—
81C2×C42×C11C2313yes—
82C2×C42×C11C2313yes—
83C2×C42×C11C2313yes—
84Q8×Dic11—24no—
85Q8×Dic11—24no—
86Q8×Dic11C2×C418yes—
87C2×(C2×D11)⋊C4C2311yescharacteristic
88C2×(C2×D11)⋊C4C2311yescharacteristic
89C2×(C2×D11)⋊C4C2313yes—
90C2×(C2×D11)⋊C4C2313yes—
91C2×(C2×D11)⋊C4C2311yescharacteristic
92C2×(C2×D11)⋊C4C2313yes—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2313yes—
95C2×C4⋊Dic11C2313yes—
96C2×C4⋊Dic11C2313yes—
97C2×C4⋊Dic11C2316yes—
98C2×C4⋊Dic11C2313yes—
99C2×Dic11⋊C4C2313yes—
100C2×Dic11⋊C4C2313yes—
101C2×C4×Dic11C2313yes—
102C2×C4×Dic11C2311yescharacteristic
103C2×C4×Dic11C2313yes—
104C2×C4×Dic11C2313yes—
105C2×C4×Dic11C2316yes—
106C2×C4×Dic11C2313yes—
107C2×C4×Dic11C2313yes—
108C2×C4×Dic11C2316yes—
109C2×C4×Dic11C2313yes—
110#66945C2×C4124yes—
111#66940C2×C4124yes—
112#66925C2×C4124yes—
113C4×Dic22C2×C4124yes—
114C11×#95C2316yes—
115C11×#95C2311yescharacteristic
116C11×#95C2313yes—
117C11⋊#95C2313yes—
118C11⋊#95C2313yes—
119C11⋊#95C2316yes—
120C11⋊#95C2313yes—
121C11⋊#95C2313yes—
122C11⋊#95C2313yes—
123C11⋊#95C2316yes—
124C11⋊#95C2316yes—
125C11⋊#95C2313yes—
126C11⋊#95C2313yes—
127C11⋊#95C2313yes—
128C11⋊#95C2313yes—
129C11⋊#95C2311yescharacteristic
130#34262—111nomaximal, Sylow
131C23×D11C2411yescharacteristic
132C2×Q8×C11C22×C414yes—
133C2×Q8×C11#4114yes—
134C2×Q8×C11#4114yes—
135C22×C4×C11C2411yescharacteristic
136C22×C4×C11C2413yes—
137C22×C4×C11C2413yes—
138C22×C4×C11C2413yes—
139C22×C4×C11C2411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C22×C4×C11C2413yes—
142C22×Dic11C2411yescharacteristic
143C22×Dic11C2413yes—
144C22×Dic11C2413yes—
145C22×Dic11C2413yes—
146C22×Dic11C2411yescharacteristic
147C22×Dic11C2413yes—
148C22×Dic11C2411yescharacteristic
149Q8×D11—232no—
150C2×C4×D11—26no—
151C2×C4×D11—26no—
152C2×C4×D11C22×C4112yes—
153C2×Dic22—26no—
154C2×Dic22—26no—
155C2×Dic22C22×C4112yes—
156C11×C4⋊C4—26no—
157C11×C4⋊C4—26no—
158C11×C4⋊C4—26no—
159C11×C4⋊C4—43no—
160C11×C4⋊C4C22×C4112yes—
161C42×C11—26no—
162C42×C11—26no—
163C42×C11C22×C4112yes—
164(C2×D11)⋊C4—22no—
165(C2×D11)⋊C4—22no—
166(C2×D11)⋊C4—43no—
167(C2×D11)⋊C4—43no—
168(C2×D11)⋊C4C22×C414yes—
169(C2×D11)⋊C4C22×C4112yes—
170C4⋊Dic11—22no—
171C4⋊Dic11—26no—
172C4⋊Dic11—26no—
173C4⋊Dic11—43no—
174C4⋊Dic11—46no—
175C4⋊Dic11C22×C4112yes—
176Dic11⋊C4C22×C4112yes—
177Dic11⋊C4C22×C4112yes—
178C4×Dic11—26no—
179C4×Dic11—26no—
180C4×Dic11—26no—
181C4×Dic11—22no—
182C4×Dic11—43no—
183C4×Dic11—46no—
184C4×Dic11—43no—
185C4×Dic11C22×C4124yes—
186C4×Dic11C22×C4112yes—
187C2×#519—111no—
188#2356—113no—
189#2355—113no—
190#2351D1111yescharacteristic, complemented
191Q8×C4⋊C4—111no—
192#2347—113no—
193#2346—113no—
194Q8×C22⋊C4—111no—
195Q8×C22⋊C4—111no—
196#2320—113no—
197#2314—113no—
198#2298—113no—
199#2295—113no—
200#2276—111no—
201C42×Q8—111no—
202C23×C11C2511yescharacteristic
203C22×D11—21no—
204C22×D11—21no—
205C22×D11—21no—
206C22×D11—21no—
207C22×D11—21no—
208C22×D11—21no—
209C22×D11C23×C412yes—
210Q8×C11#117116yes—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—23no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—23no—
217C2×C4×C11—21no—
218C2×C4×C11—23no—
219C2×C4×C11—23no—
220C2×C4×C11—23no—
221C2×C4×C11—21no—
222C2×C4×C11—23no—
223C2×C4×C11—23no—
224C2×C4×C11—23no—
225C2×C4×C11—21no—
226C2×C4×C11C23×C416yes—
227C2×C4×C11C23×C412yes—
228C2×C4×C11C23×C416yes—
229C2×C4×C11C2×#4116yes—
230C2×C4×C11C2×#4116yes—
231C2×C4×C112−1+412yes—
232C2×Dic11—21no—
233C2×Dic11—23no—
234C2×Dic11—23no—
235C2×Dic11—21no—
236C2×Dic11—21no—
237C2×Dic11—23no—
238C2×Dic11—21no—
239C2×Dic11—23no—
240C2×Dic11—21no—
241C2×Dic11—23no—
242C2×Dic11—23no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—23no—
246C2×Dic11—23no—
247C2×Dic11—23no—
248C2×Dic11—23no—
249C2×Dic11C23×C412yes—
250C2×Dic11C23×C416yes—
251C2×Dic11C23×C416yes—
252C2×Dic112−1+412yes—
253C4×D11—224no—
254Dic22—224no—
255C23×Q8—111no—
256#519—1116no—
257C2×C4×Q8—111no—
258C2×C4×Q8—111no—
259C2×C4×Q8—111no—
260C2×C4×Q8—113no—
261C2×C4×Q8—113no—
262C2×C4×Q8C2×D1111yescharacteristic
263C2×C4×Q8C2×D1111yescharacteristic
264C2×C4×Q8C2×D1111yescharacteristic
265C2×#117—113no—
266C2×#117—113no—
267#391—113no—
268#391—113no—
269#391—113no—
270#391—113no—
271#389—113no—
272#389—113no—
273#389C2×D1113yes—
274#389C2×D1113yes—
275#388—113no—
276#388—113no—
277#388—113no—
278#388—116no—
279#388—111no—
280#387—113no—
281#387—113no—
282#387—116no—
283#387—116no—
284#387—113no—
285#387—113no—
286#384—113no—
287#383—116no—
288#382—116no—
289#382C2×D1113yes—
290#380—113no—
291#380—113no—
292C4×C4⋊C4—113no—
293C4×C4⋊C4—113no—
294C4×C4⋊C4—113no—
295C4×C4⋊C4—116no—
296C4×C4⋊C4—113no—
297C4×C4⋊C4—113no—
298C4×C4⋊C4—113no—
299C4×C4⋊C4—113no—
300C4×C4⋊C4C2×D1113yes—
301C4×C22⋊C4—113no—
302C4×C22⋊C4—113no—
303#376—113no—
304#376—116no—
305C43—113no—
306C22×C11C24×C411yescharacteristic
307C22×C11C22×#4111yescharacteristic
308C22×C11C22×#4111yescharacteristic
309C22×C11C2×2−1+411yescharacteristic
310C22×C11C2×2−1+411yescharacteristic
311C22×C11#58511yescharacteristic
312C22×C11#58511yescharacteristic
313C2×D11—22no—
314C2×D11—22no—
315C2×D11—22no—
316C2×D11—41no—
317C2×D11—41no—
318C2×D11—41no—
319C2×D11—41no—
320C4×C11—22no—
321C4×C11—26no—
322C4×C11—22no—
323C4×C11—43no—
324C4×C11—41no—
325C4×C11—43no—
326C4×C11C2×#117112yes—
327Dic11—26no—
328Dic11—26no—
329Dic11—22no—
330Dic11—22no—
331Dic11—41no—
332Dic11—43no—
333Dic11—43no—
334C22×Q8—118no—
335C22×Q8—113no—
336C22×Q8—224no—
337C22×Q8—224no—
338C22×Q8C22×D1111yescharacteristic
339C23×C4—113no—
340C4×Q8—24no—
341C4×Q8—24no—
342C4×Q8—118no—
343C4×Q8—1124no—
344C4×Q8—1124no—
345C4×Q8—224no—
346C4×Q8—224no—
347C4×Q8C4×D1118yes—
348#117—1124no—
349#117—1124no—
350C2×C4⋊C4—113no—
351C2×C4⋊C4—113no—
352C2×C4⋊C4—113no—
353C2×C4⋊C4—113no—
354C2×C4⋊C4—113no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—116no—
357C2×C4⋊C4—113no—
358C2×C4⋊C4C22×D1113yes—
359C2×C4⋊C4C22×D1113yes—
360C2×C4⋊C4C22×D1113yes—
361C2×C4⋊C4C22×D1113yes—
362C2×C4⋊C4C22×D1113yes—
363C2×C22⋊C4—113no—
364C2×C22⋊C4—111no—
365C2×C22⋊C4—111no—
366C2×C22⋊C4—111no—
367C2×C22⋊C4—113no—
368C2×C22⋊C4—113no—
369C2×C42—113no—
370C2×C42—116no—
371C2×C42—113no—
372C2×C42—113no—
373C2×C42—111no—
374C2×C42—113no—
375C2×C42—113no—
376C2×C42—113no—
377C2×C42—116no—
378C2×C42C22×D1113yes—
379C2×C42C22×D1113yes—
380C2×C42C22×D1113yes—
381#95—111no—
382#95—113no—
383#95—113no—
384#95—113no—
385#95—113no—
386#95—113no—
387#95—116no—
388#95—113no—
389#95—113no—
390#95—113no—
391#95—116no—
392#95—116no—
393#95—113no—
394#95C22×D1116yes—
395#95C22×D1111yescharacteristic
396#95C22×D1113yes—
397C2×C11C22×#11711yescharacteristic
398C2×C11C4×2−1+411yescharacteristic
399C2×C11C4×2−1+411yescharacteristic
400C2×C11#351611yescharacteristic
401C2×C11#351811yescharacteristic
402C2×C11#352311yescharacteristic
403C2×C11#352411yescharacteristic
404D11—42no—
405C24—111no—
406C2×Q8—1112no—
407C2×Q8—2232no—
408C2×Q8—226no—
409C2×Q8—226no—
410C2×Q8C2×C4×D1114yes—
411C2×Q8#434114yes—
412C2×Q8#434314yes—
413C22×C4—113no—
414C22×C4—111no—
415C22×C4—111no—
416C22×C4—113no—
417C22×C4—1112no—
418C22×C4—111no—
419C22×C4—113no—
420C22×C4—113no—
421C22×C4—226no—
422C22×C4—226no—
423C22×C4C23×D1111yescharacteristic
424C22×C4C23×D1113yes—
425C22×C4C23×D1113yes—
426C22×C4C23×D1113yes—
427C22×C4C23×D1111yescharacteristic
428C22×C4C23×D1111yescharacteristic
429C22×C4C23×D1113yes—
430C4⋊C4—26no—
431C4⋊C4—26no—
432C4⋊C4—26no—
433C4⋊C4—43no—
434C4⋊C4—1112no—
435C4⋊C4—1112no—
436C4⋊C4—1112no—
437C4⋊C4—222no—
438C4⋊C4—226no—
439C4⋊C4—226no—
440C4⋊C4—446no—
441C4⋊C4—443no—
442C4⋊C4C2×C4×D11112yes—
443C22⋊C4—1112no—
444C22⋊C4—114no—
445C22⋊C4—222no—
446C22⋊C4—222no—
447C22⋊C4—443no—
448C22⋊C4—443no—
449C42—26no—
450C42—26no—
451C42—1112no—
452C42—1124no—
453C42—226no—
454C42—226no—
455C42—226no—
456C42—222no—
457C42—443no—
458C42—443no—
459C42—446no—
460C42C2×C4×D11112yes—
461C11#3426211yescharacteristic, complemented, Sylow
462C23—112no—
463C23—221no—
464C23—221no—
465C23—221no—
466C23—221no—
467C23—221no—
468C23—221no—
469C23C24×D1111yescharacteristic
470Q8—2224no—
471Q8#66945116yes—
472C2×C4—21no—
473C2×C4—23no—
474C2×C4—23no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—23no—
480C2×C4—23no—
481C2×C4—23no—
482C2×C4—23no—
483C2×C4—21no—
484C2×C4—23no—
485C2×C4—21no—
486C2×C4—23no—
487C2×C4—116no—
488C2×C4—112no—
489C2×C4—116no—
490C2×C4—112no—
491C2×C4—223no—
492C2×C4—221no—
493C2×C4—223no—
494C2×C4—221no—
495C2×C4—221no—
496C2×C4—221no—
497C2×C4—223no—
498C2×C4—223no—
499C2×C4—2224no—
500C2×C4—221no—
501C2×C4—223no—
502C2×C4—223no—
503C2×C4—221no—
504C2×C4—223no—
505C2×C4—223no—
506C2×C4—221no—
507C2×C4—223no—
508C2×C4—223no—
509C2×C4C22×C4×D1116yes—
510C2×C4C22×C4×D1112yes—
511C2×C4C22×C4×D1116yes—
512C2×C4C2×#434116yes—
513C2×C4C2×#434316yes—
514C2×C4#6704312yes—
515C22—222no—
516C22—222no—
517C22—222no—
518C22—441no—
519C22—441no—
520C22—441no—
521C22—441no—
522C22C23×C4×D1111yescharacteristic
523C22C22×#434111yescharacteristic
524C22C22×#434311yescharacteristic
525C22C2×#6704311yescharacteristic
526C22#1062345311yescharacteristic
527C22D11×2−1+411yescharacteristic
528C22#1062345711yescharacteristic
529C4—22no—
530C4—26no—
531C4—22no—
532C4—41no—
533C4—43no—
534C4—43no—
535C4—222no—
536C4—226no—
537C4—226no—
538C4—222no—
539C4—441no—
540C4—443no—
541C4—443no—
542C4C2×#66945112yes—
543C2—442no—
544C2C22×#6694511yescharacteristic
545C2#1308182511yescharacteristic
546C2C4×#6704311yescharacteristic
547C2#1308259811yescharacteristic
548C2#1308262411yescharacteristic
549C2#1308271311yescharacteristic
550C2#1308272811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2351C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2351D11
hypocenterC11#34262
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2351

Complements

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

NH ≅ G/Ntype
2. #13071583C2semidirect
3. #13071571C2semidirect
4. Q8×C4⋊Dic11C2semidirect
9. #13071263C2semidirect
12. #13071087C2semidirect
13. #13070981C2semidirect
14. C4×Q8×Dic11C2semidirect
15. C11×#2351C2semidirect
23. #10623103C4semidirect
190. #2351D11semidirect
461. C11#34262semidirect

Maximal subgroups

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

subgroupindex
C2×#106231032
#130715832
#130715712
Q8×C4⋊Dic112
#130715082
#130715002
Q8×(C2×D11)⋊C42
#130712632
#130712262
#130711092
#130710872
#130709812
C4×Q8×Dic112
C11×#23512
#3426211