Finite Group Databasebeta

← #14755027

Subgroups — #14755027

Order 2816.

1778 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623356C211yesmaximal, characteristic
2C2×#10623358C211yesmaximal, characteristic
3C2×#10622733C211yesmaximal, characteristic, complemented
4C22×#66880C211yesmaximal, characteristic, complemented
5#13068926C214yesmaximal, complemented
6#13068921C214yesmaximal, complemented
7#13068336C211yesmaximal, characteristic, complemented
8#13068333C211yesmaximal, characteristic, complemented
9C2×C11×#408C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14#10623358—24no—
15#10623358—24no—
16#10623356—24no—
17#10623356C418yescomplemented
18C2×Q8×Dic11—21no—
19C2×#66997—21no—
20C2×#66989—21no—
21C2×#66988—22no—
22C2×D4×Dic11—22no—
23C2×D4×Dic11—21no—
24C2×#66979C2212yes—
25C2×#66979C2211yescharacteristic
26C2×#66979C2211yescharacteristic
27C22×C4⋊Dic11C2212yes—
28C22×C4⋊Dic11C2211yescharacteristic
29C2×#66977C2214yes—
30C11×#408—24no—
31C2×C11×C22⋊C8C2214yes—
32#10622733—24no—
33C2×#66880—24no—
34C2×#66880C2214yes—
35C2×#66880C2212yes—
36C2×#66880C2212yes—
37#10622189C2212yes—
38#10622189C2212yes—
39#10622189C2214yes—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41C2×C414yes—
45C2×C11×#41D414yes—
46C22×Q8×C11D411yescharacteristic
47C22×D4×C11D412yes—
48C22×D4×C11D411yescharacteristic
49C23×C4×C11C2312yes—
50C23×C4×C11C2311yescharacteristic
51C23×Dic11—21no—
52C23×Dic11—22no—
53C23×Dic11—21no—
54C22×Dic22—22no—
55C22×Dic22—22no—
56C22×Dic22—22no—
57C22×Dic22—22no—
58C22×Dic22—21no—
59C22×Dic22—22no—
60C22×Dic22C2×C414yescomplemented
61C22×Dic22C2312yes—
62C2×C11×M16—22no—
63C2×C11×M16—22no—
64C2×C11×M16—22no—
65C22×C8×C11—22no—
66C22×C8×C11—22no—
67C22×C8×C11—22no—
68C22×C8×C11C2312yes—
69C22×C8×C11C2312yes—
70C2×C22⋊Dic11—24no—
71C2×C22⋊Dic11—22no—
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—21no—
74Q8×Dic11—28no—
75#66997—28no—
76#66989—28no—
77#66988—216no—
78D4×Dic11—216no—
79D4×Dic11—28no—
80#66979—22no—
81#66979—22no—
82#66979—24no—
83#66979—24no—
84#66979C2×C414yescomplemented
85#66979D414yes—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11—24no—
90C2×C4⋊Dic11—24no—
91C2×C4⋊Dic11D414yes—
92C2×C4⋊Dic11C2312yes—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2312yes—
95C2×C4⋊Dic11C2311yescharacteristic
96#66977—28no—
97#66977C2×C4116yescomplemented
98C2×Dic11⋊C4—24no—
99C2×C4×Dic11—22no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C11×C22⋊C8—28no—
103#66880—24no—
104#66880—24no—
105#66880—28no—
106#20913—111nomaximal, Sylow
107C24×C11C2×D412yes—
108C24×C11C2×D411yescharacteristic
109C11×#41—28no—
110C11×#41—28no—
111C11×#41—28no—
112C11×#41—28no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11C22⋊C414yes—
116C2×D4×C11—24no—
117C2×D4×C11—24no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11C22⋊C418yes—
121C2×D4×C11C22⋊C414yes—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11C22×C414yes—
127C22×C4×C11C22×C412yes—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D414yes—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11#4112yes—
135C22×C4×C11#4112yes—
136C22×C4×C11C2411yescharacteristic
137C22×Dic11—28no—
138C22×Dic11—24no—
139C22×Dic11—24no—
140C22×Dic11—21no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—21no—
144C22×Dic11—22no—
145C22×Dic11—42no—
146C22×Dic11—42no—
147C22×Dic11—82no—
148C22×Dic11—84no—
149C2×Dic22—24no—
150C2×Dic22—28no—
151C2×Dic22—28no—
152C2×Dic22—22no—
153C2×Dic22—22no—
154C2×Dic22—22no—
155C2×Dic22—22no—
156C2×Dic22—22no—
157C2×Dic22—42no—
158C2×Dic22—44no—
159C2×Dic22—44no—
160C2×Dic22—42no—
161C2×Dic22C22×C414yes—
162C11×M16—44no—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—44no—
170C22⋊Dic11—28no—
171C22⋊Dic11—216no—
172C22⋊Dic11—24no—
173C22⋊Dic11—24no—
174C4⋊Dic11—28no—
175C4⋊Dic11—24no—
176C4⋊Dic11—22no—
177C4⋊Dic11—22no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11C22×C414yes—
181C4⋊Dic11C2×D412yes—
182C4⋊Dic11C2×D414yes—
183C4⋊Dic11C2×D412yes—
184Dic11⋊C4—216no—
185C4×Dic11—28no—
186C4×Dic11—24no—
187C4×Dic11—24no—
188C2×#536—111no—
189C2×#520—111no—
190C2×#419—111no—
191C22×#103—111no—
192C2×#408D1111yescharacteristic
193#1873—114no—
194#1872—114no—
195#1736—111no—
196#1735—111no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—24no—
202C23×C11—24no—
203C23×C11C2×C22⋊C414yes—
204C23×C11C2×C22⋊C412yes—
205C23×C11#12012yes—
206C23×C11#12312yes—
207C23×C11C22×D411yescharacteristic
208Q8×C11—28no—
209D4×C11—216no—
210D4×C11—28no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11C2×C22⋊C414yes—
218C2×C4×C11C2×C22⋊C412yes—
219C2×C4×C11C4×D414yes—
220C2×C4×C11C4×D414yes—
221C2×C4×C11#12012yes—
222C2×C4×C11#12114yes—
223C2×C4×C11#12114yes—
224C2×C4×C11#12312yes—
225C2×C4×C11C23×C411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C2×#4111yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×Dic11—24no—
232C2×Dic11—24no—
233C2×Dic11—22no—
234C2×Dic11—24no—
235C2×Dic11—22no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—44no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—48no—
244C2×Dic11—84no—
245C2×Dic11—88no—
246Dic22—24no—
247Dic22—24no—
248Dic22—42no—
249Dic22—42no—
250Dic22—48no—
251C8×C11—42no—
252C8×C11—42no—
253C22×#41C2×D1111yescharacteristic
254C23×Q8—111no—
255C22×M16C2×D1111yescharacteristic
256C23×C8C2×D1111yescharacteristic
257#536—118no—
258#536—224no—
259C2×C4⋊Q8—221no—
260C2×#124—221no—
261C2×#123—222no—
262C2×C22⋊Q8—114no—
263#520—224no—
264#520—224no—
265C2×C4×Q8—221no—
266C2×C4×D4—222no—
267C2×C4×D4—221no—
268C2×#117—111no—
269C2×#117—111no—
270C2×#117—112no—
271C22×C4⋊C4—111no—
272C22×C4⋊C4—112no—
273#419—224no—
274C2×#103—114no—
275C2×#103—112no—
276C2×#103—112no—
277C2×#103—224no—
278#408—24no—
279C2×C22⋊C8C2×D1114yes—
280#340—112no—
281#340—114no—
282#340—112no—
283C22×C11—24no—
284C22×C11—24no—
285C22×C11—22no—
286C22×C11—22no—
287C22×C11—28no—
288C22×C11—24no—
289C22×C11—44no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11#38614yes—
293C22×C11C22×C22⋊C411yescharacteristic
294C22×C11C2×#12011yescharacteristic
295C22×C11C2×#12311yescharacteristic
296C22×C11#57712yes—
297C22×C11#57812yes—
298C4×C11—24no—
299C4×C11#38614yes—
300C4×C11C2×C4×D411yescharacteristic
301C4×C11C2×C4×D411yescharacteristic
302C4×C11C2×#12111yescharacteristic
303C4×C11C2×#12111yescharacteristic
304Dic11—44no—
305Dic11—44no—
306Dic11—42no—
307Dic11—42no—
308Dic11—44no—
309C2×#41—22no—
310C2×#41—22no—
311C2×#41—22no—
312C2×#41—22no—
313C2×#41C4×D1114yes—
314C2×#41C22⋊D1114yes—
315C22×Q8—114no—
316C22×Q8—112no—
317C22×Q8—221no—
318C22×Q8—222no—
319C22×Q8—222no—
320C22×Q8—222no—
321C22×Q8—222no—
322C22×Q8—222no—
323C22×Q8D4411yescharacteristic
324C22×D4D4412yes—
325C22×D4D4411yescharacteristic
326C23×C4—221no—
327C23×C4—222no—
328C23×C4—221no—
329C23×C4C22×D1112yes—
330C23×C4C22×D1111yescharacteristic
331C2×M16—22no—
332C2×M16—22no—
333C2×M16—22no—
334C22×C8—22no—
335C22×C8—22no—
336C22×C8—22no—
337C22×C8C22×D1112yes—
338C22×C8C22×D1112yes—
339C4⋊Q8—228no—
340#124—228no—
341#123—2216no—
342C22⋊Q8—1116no—
343C22⋊Q8—228no—
344C4×Q8—228no—
345C4×D4—2216no—
346C4×D4—228no—
347#117—114no—
348#117—114no—
349#117—224no—
350#117—224no—
351#117—222no—
352#117—222no—
353C2×C4⋊C4—114no—
354C2×C4⋊C4—112no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—112no—
358C2×C4⋊C4—224no—
359C2×C4⋊C4—224no—
360C2×C4⋊C4—222no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4—224no—
363C2×C4⋊C4—222no—
364C2×C22⋊C4—222no—
365C2×C22⋊C4—221no—
366C2×C22⋊C4—221no—
367C2×C22⋊C4—224no—
368C2×C42—222no—
369C2×C42—221no—
370C2×C42—221no—
371#103—228no—
372#103—224no—
373#103—224no—
374C22⋊C8—28no—
375C2×C11—24no—
376C2×C11—44no—
377C2×C11C2×#38611yescharacteristic
378C2×C11#289812yes—
379C2×C11#300911yescharacteristic
380C2×C11#301111yescharacteristic
381C2×C11#309712yes—
382C24C2×D4412yes—
383C24C2×D4411yescharacteristic
384#41—28no—
385#41—28no—
386#41—28no—
387#41—28no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—114no—
391C2×Q8—224no—
392C2×Q8—222no—
393C2×Q8—228no—
394C2×Q8—228no—
395C2×Q8—222no—
396C2×Q8—222no—
397C2×Q8—222no—
398C2×Q8—222no—
399C2×Q8—442no—
400C2×Q8—442no—
401C2×Q8—444no—
402C2×Q8—444no—
403C2×Q8(C2×D11)⋊C414yes—
404C2×D4—24no—
405C2×D4—24no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4(C2×D11)⋊C418yes—
409C2×D4(C2×D11)⋊C414yes—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—224no—
415C22×C4—221no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—221no—
419C22×C4—222no—
420C22×C4—228no—
421C22×C4—224no—
422C22×C4—442no—
423C22×C4—442no—
424C22×C4—882no—
425C22×C4—884no—
426C22×C4C2×C4×D1114yes—
427C22×C4C2×C4×D1112yes—
428C22×C4C2×D4412yes—
429C22×C4C2×D4411yescharacteristic
430C22×C4D4×D1112yes—
431C22×C4D4×D1112yes—
432C22×C4#434112yes—
433C22×C4#434112yes—
434C22×C4C2×C22⋊D1114yes—
435C22×C4C2×C22⋊D1112yes—
436C22×C4C23×D1111yescharacteristic
437M16—44no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—44no—
445C4⋊C4—114no—
446C4⋊C4—114no—
447C4⋊C4—112no—
448C4⋊C4—112no—
449C4⋊C4—228no—
450C4⋊C4—224no—
451C4⋊C4—2216no—
452C4⋊C4—221no—
453C4⋊C4—222no—
454C4⋊C4—221no—
455C4⋊C4—222no—
456C22⋊C4—228no—
457C22⋊C4—224no—
458C22⋊C4—224no—
459C22⋊C4—2216no—
460C42—228no—
461C42—224no—
462C42—224no—
463C11#2091311yescharacteristic, complemented, Sylow
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—24no—
469C23—24no—
470C23#6693512yes—
471C23#6693912yes—
472C23C2×(C2×D11)⋊C414yes—
473C23C2×(C2×D11)⋊C412yes—
474C23C22×D4411yescharacteristic
475Q8—28no—
476Q8—224no—
477Q8—224no—
478Q8—442no—
479Q8—442no—
480Q8—448no—
481D4—216no—
482D4—28no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—222no—
490C2×C4—224no—
491C2×C4—222no—
492C2×C4—224no—
493C2×C4—224no—
494C2×C4—442no—
495C2×C4—442no—
496C2×C4—444no—
497C2×C4—442no—
498C2×C4—442no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—448no—
502C2×C4—884no—
503C2×C4—888no—
504C2×C4(C22⋊D11)⋊C414yes—
505C2×C4(C22⋊D11)⋊C414yes—
506C2×C4#6693512yes—
507C2×C4#6693912yes—
508C2×C4C2×(C2×D11)⋊C414yes—
509C2×C4C2×(C2×D11)⋊C412yes—
510C2×C4#6699214yes—
511C2×C4#6699214yes—
512C2×C4C22×C4×D1111yescharacteristic
513C2×C4C2×D4×D1111yescharacteristic
514C2×C4C2×D4×D1111yescharacteristic
515C2×C4C2×#434111yescharacteristic
516C2×C4C2×#434111yescharacteristic
517C2×C4C22×C22⋊D1111yescharacteristic
518C8—42no—
519C8—42no—
520C22—24no—
521C22—22no—
522C22—22no—
523C22—24no—
524C22—28no—
525C22—24no—
526C22—44no—
527C22—42no—
528C22—42no—
529C22#1062257114yes—
530C22C2×#6693511yescharacteristic
531C22C2×#6693911yescharacteristic
532C22#1062328212yes—
533C22#1062328412yes—
534C22C22×(C2×D11)⋊C411yescharacteristic
535C4—24no—
536C4—444no—
537C4—442no—
538C4—442no—
539C4—444no—
540C4—444no—
541C4#1062257114yes—
542C4C2×(C22⋊D11)⋊C411yescharacteristic
543C4C2×(C22⋊D11)⋊C411yescharacteristic
544C4C2×#6699211yescharacteristic
545C4C2×#6699211yescharacteristic
546C2—24no—
547C2—44no—
548C2C2×#1062257111yescharacteristic
549C2#1307715012yes—
550C2#1307789511yescharacteristic
551C2#1307791311yescharacteristic
552C2#1307858612yes—
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#408C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenterC2×#408D11
hypocenterC11#20913
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
3. C2×#10622733C2semidirect
4. C22×#66880C2semidirect
5. #13068926C2semidirect
6. #13068921C2semidirect
7. #13068336C2semidirect
8. #13068333C2semidirect
17. #10623356C4semidirect
60. C22×Dic22C2×C4semidirect
84. #66979C2×C4semidirect
97. #66977C2×C4semidirect
463. C11#20913semidirect

Maximal subgroups

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

subgroupindex
C2×#106233562
C2×#106233582
C2×#106227332
C22×#668802
#130689262
#130689212
#130683362
#130683332
C2×C11×#4082
#2091311