Finite Group Databasebeta

← #14757382

Subgroups — #14757382

Order 2816.

1718 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C211yesmaximal, characteristic
2C2×#10622715C211yesmaximal, characteristic, complemented
3C2×#10622723C211yesmaximal, characteristic, complemented
4C2×#10622723C211yesmaximal, characteristic, complemented
5C2×#10622820C211yesmaximal, characteristic, complemented
6C2×#10622714C211yesmaximal, characteristic, complemented
7#13069412C214yesmaximal, complemented
8#13069408C214yesmaximal, complemented
9C22×C11×C22⋊C8C211yesmaximal, characteristic, complemented
10C24×C4×C11C2211yescharacteristic
11C22×#4339C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×#67006C412yes—
15#10623322—24no—
16#10623322—24no—
17C2×#66983C412yes—
18C2×#66982C412yes—
19C2×C4×C22⋊D11C2214yes—
20C2×#66979C2211yescharacteristic
21C2×#66977C412yes—
22C22×#4318C2211yescharacteristic
23C22×#4318C2211yescharacteristic
24C2×C11×C22⋊C8—24no—
25C2×C11×C22⋊C8C2212yes—
26C2×C11×C22⋊C8C2212yes—
27#10622820—24no—
28C2×C22⋊(C11⋊C8)C2214yes—
29#10622723—24no—
30#10622723—24no—
31C2×(C2×D11)⋊C8C2212yescomplemented
32C2×(C2×D11)⋊C8C2214yescomplemented
33C2×(C2×D11)⋊C8C2212yescomplemented
34#10622715—24no—
35#10622714—24no—
36C2×#66879C2212yescomplemented
37C2×Dic11⋊C8C2214yescomplemented
38C2×C8×Dic11C2212yescomplemented
39C25×C11C2×C411yescharacteristic
40C23×C4×C11—22no—
41C23×C4×C11—22no—
42C23×C4×C11—22no—
43C23×C4×C11—22no—
44C23×C4×C11—22no—
45C23×C4×C11—22no—
46C23×C4×C11C2×C412yes—
47C23×C4×C11C2×C411yescharacteristic
48C23×C4×C11C2312yes—
49C23×C4×C11C2311yescharacteristic
50C22×C22⋊D11C2×C412yes—
51C22×C22⋊D11C2×C414yes—
52C2×#4339—22no—
53C2×#4339—22no—
54C2×#4339—22no—
55C2×#4339—22no—
56C2×#4339—22no—
57C2×#4339—22no—
58C22×D44C2×C411yescharacteristic
59C22×C4×D11C2312yes—
60C22×Dic22C2×C411yescharacteristic
61C22×C8×C11—22no—
62C22×C8×C11—22no—
63C22×C8×C11—22no—
64C22×C8×C11—22no—
65C22×C8×C11—22no—
66C22×C8×C11D414yescomplemented
67C22×C8×C11C2312yes—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70#67006—28no—
71C2×C22⋊Dic11C2×C414yes—
72C2×C22⋊Dic11C2×C412yes—
73#66983—28no—
74#66982—28no—
75C4×C22⋊D11—28no—
76C4×C22⋊D11—28no—
77C2×(C2×D11)⋊C4C2×C414yes—
78#66979D414yes—
79#66979D414yes—
80C2×C4⋊Dic11C2×C412yes—
81#66977—28no—
82C2×Dic11⋊C4C2×C414yes—
83C2×C4×Dic11C2312yes—
84C2×#4318—22no—
85C2×#4318—22no—
86C2×#4318—22no—
87C2×#4318—22no—
88C2×#4318—22no—
89C2×#4318D414yescomplemented
90C22×C11⋊C8C2312yes—
91C22×C11⋊C8C2312yes—
92C11×C22⋊C8—24no—
93C11×C22⋊C8—24no—
94C22⋊(C11⋊C8)—28no—
95(C2×D11)⋊C8—24no—
96(C2×D11)⋊C8—24no—
97(C2×D11)⋊C8—28no—
98#66879—24no—
99Dic11⋊C8—28no—
100C8×Dic11—24no—
101#21191—111nomaximal, Sylow
102C24×C11—22no—
103C24×C11—24no—
104C24×C11—22no—
105C24×C11—22no—
106C24×C11—42no—
107C24×C11C22×C412yes—
108C24×C11C22×C411yescharacteristic
109C23×D11C22×C412yes—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—24no—
114C22×C4×C11—24no—
115C22×C4×C11—24no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—44no—
123C22×C4×C11—44no—
124C22×C4×C11—44no—
125C22×C4×C11—44no—
126C22×C4×C11C22×C412yes—
127C22×C4×C11C22×C411yescharacteristic
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11#4112yes—
133C22×C4×C11#4112yes—
134C22×C4×C11C2411yescharacteristic
135C2×C22⋊D11—28no—
136C2×C22⋊D11—24no—
137C2×C22⋊D11—24no—
138C2×C22⋊D11—24no—
139C2×C22⋊D11—28no—
140C2×C22⋊D11—44no—
141C22×Dic11C22×C412yes—
142C22×Dic11C22×C414yes—
143#4339—44no—
144#4339—44no—
145#4339—44no—
146#4339—44no—
147C2×D44—22no—
148C2×D44—22no—
149C2×D44—22no—
150C2×C4×D11—22no—
151C2×C4×D11—22no—
152C2×C4×D11—22no—
153C2×C4×D11—22no—
154C2×C4×D11—22no—
155C2×C4×D11—22no—
156C2×Dic22—22no—
157C2×Dic22—22no—
158C2×Dic22—22no—
159C2×C8×C11—28no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—44no—
168C2×C8×C11C2×D412yes—
169C2×C8×C11C2×D412yes—
170C22⋊Dic11—28no—
171C22⋊Dic11C22⋊C418yes—
172(C2×D11)⋊C4—28no—
173C4⋊Dic11C22⋊C418yes—
174Dic11⋊C4—28no—
175C4×Dic11C2×D414yes—
176C4×Dic11C2×D414yes—
177#4318—28no—
178#4318—44no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8C2×D414yes—
185C2×#525—111no—
186C2×#424—111no—
187C2×#408—111no—
188C2×#408—111no—
189C2×#407—111no—
190C22×C22⋊C8D1111yescharacteristic, complemented
191C2×#405—111no—
192#1955—114no—
193#1954—114no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—28no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—48no—
204C23×C11—48no—
205C23×C11—44no—
206C23×C11—44no—
207C23×C11C2×C22⋊C412yes—
208C23×C11C4×D412yes—
209C23×C11C4×D412yes—
210C23×C11#13114yes—
211C23×C11C23×C411yescharacteristic
212C22×D11—22no—
213C22×D11—22no—
214C22×D11—22no—
215C22×D11—24no—
216C22×D11—24no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—44no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—48no—
226C2×C4×C11C2×C22⋊C412yes—
227C2×C4×C11C4×D412yes—
228C2×C4×C11C4×D412yes—
229C2×C4×C11#12114yes—
230C2×C4×C11#12114yes—
231C2×C4×C11#12414yes—
232C2×C4×C11#12714yes—
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C22⋊D11—416no—
240C22⋊D11—48no—
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11C2×C22⋊C418yes—
247D44—44no—
248C4×D11—42no—
249C4×D11—42no—
250C4×D11—42no—
251C4×D11—42no—
252Dic22—44no—
253C8×C11—22no—
254C8×C11—22no—
255C8×C11—42no—
256C11⋊C8—24no—
257C11⋊C8—42no—
258C22×#41—111no—
259C24×C4C2×D1111yescharacteristic
260C22×M16—111no—
261C22×M16—111no—
262C23×C8C2×D1111yescharacteristic
263C23×C8C2×D1111yescharacteristic
264#525—224no—
265#525—224no—
266C2×#123—112no—
267C2×C22⋊Q8—112no—
268C2×#121—112no—
269C2×#120—112no—
270C2×C4×D4—114no—
271C2×#117—111no—
272#424—224no—
273C2×C4⋊C8—114no—
274#408—224no—
275#408—224no—
276#407—224no—
277C2×C22⋊C8—24no—
278C2×C22⋊C8—114no—
279C2×C22⋊C8—112no—
280C2×C22⋊C8—114no—
281C2×C22⋊C8—112no—
282C2×C22⋊C8C2×D1112yes—
283C2×C22⋊C8C2×D1112yes—
284#405—224no—
285C2×#97—112no—
286C2×C4×C8—112no—
287C22×C11—24no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—24no—
291C22×C11—24no—
292C22×C11—24no—
293C22×C11—24no—
294C22×C11—416no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11#39014yes—
300C22×C11C22×C22⋊C411yescharacteristic
301C22×C11C2×C4×D411yescharacteristic
302C22×C11C2×C4×D411yescharacteristic
303C22×C11C2×#13112yes—
304C22×C11#56812yes—
305C2×D11—44no—
306C2×D11—42no—
307C2×D11—42no—
308C2×D11—44no—
309C2×D11—42no—
310C4×C11—42no—
311C4×C11#39014yes—
312C4×C11C2×#12111yescharacteristic
313C4×C11C2×#12111yescharacteristic
314C4×C11C2×#12411yescharacteristic
315C4×C11C2×#12711yescharacteristic
316Dic11—28no—
317Dic11—42no—
318C25C4×D1111yescharacteristic
319C2×#41—222no—
320C2×#41—222no—
321C2×#41—222no—
322C2×#41—222no—
323C2×#41—222no—
324C2×#41—222no—
325C22×Q8—111no—
326C22×D4—112no—
327C22×D4—114no—
328C22×D4—111no—
329C23×C4—22no—
330C23×C4—22no—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—112no—
336C23×C4C4×D1112yes—
337C23×C4C4×D1111yescharacteristic
338C23×C4C22×D1112yes—
339C23×C4C22×D1111yescharacteristic
340C2×M16—114no—
341C2×M16—222no—
342C2×M16—222no—
343C2×M16—222no—
344C2×M16—222no—
345C2×M16—222no—
346C22×C8—22no—
347C22×C8—22no—
348C22×C8—22no—
349C22×C8—22no—
350C22×C8—22no—
351C22×C8—112no—
352C22×C8—112no—
353C22×C8C22⋊D1114yescomplemented
354C22×C8C22×D1112yes—
355C22×C8C22×D1111yescharacteristic
356C22×C8C22×D1111yescharacteristic
357#123—228no—
358C22⋊Q8—228no—
359#121—228no—
360#120—228no—
361C4×D4—228no—
362C4×D4—228no—
363#117—114no—
364#117—114no—
365C2×C4⋊C4—112no—
366C2×C4⋊C4—114no—
367C2×C22⋊C4—112no—
368C2×C22⋊C4—114no—
369C2×C22⋊C4—114no—
370C2×C42—112no—
371C4⋊C8—228no—
372C22⋊C8—24no—
373C22⋊C8—24no—
374C22⋊C8—228no—
375C22⋊C8—228no—
376C22⋊C8—224no—
377C22⋊C8—224no—
378#97—224no—
379C4×C8—224no—
380C2×C11—24no—
381C2×C11—44no—
382C2×C11C2×#39011yescharacteristic
383C2×C11#288012yes—
384C2×C11#292911yescharacteristic
385C2×C11#293011yescharacteristic
386C2×C11#293312yes—
387D11—82no—
388C24—24no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—42no—
393C24—112no—
394C24C2×C4×D1112yes—
395C24C2×C4×D1111yescharacteristic
396#41—444no—
397#41—444no—
398#41—444no—
399#41—444no—
400C2×Q8—222no—
401C2×Q8—222no—
402C2×Q8—222no—
403C2×D4—228no—
404C2×D4—224no—
405C2×D4—224no—
406C2×D4—228no—
407C2×D4—224no—
408C2×D4—222no—
409C2×D4—222no—
410C2×D4—222no—
411C2×D4—444no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—44no—
425C22×C4—44no—
426C22×C4—44no—
427C22×C4—44no—
428C22×C4—114no—
429C22×C4—112no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4C2×C4×D1112yes—
437C22×C4C2×C4×D1111yescharacteristic
438C22×C4#433912yes—
439C22×C4D4×D1112yes—
440C22×C4D4×D1112yes—
441C22×C4D4×D1112yes—
442C22×C4#434112yes—
443C22×C4C2×C22⋊D1112yes—
444C22×C4C23×D1111yescharacteristic
445M16—228no—
446M16—444no—
447C2×C8—28no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—22no—
453C2×C8—22no—
454C2×C8—22no—
455C2×C8—44no—
456C2×C8—114no—
457C2×C8—222no—
458C2×C8—222no—
459C2×C8—222no—
460C2×C8—222no—
461C2×C8—222no—
462C2×C8C2×C22⋊D1112yes—
463C2×C8C2×C22⋊D1112yes—
464C4⋊C4—118no—
465C4⋊C4—228no—
466C22⋊C4—118no—
467C22⋊C4—228no—
468C22⋊C4—228no—
469C42—114no—
470C42—114no—
471C11#2119111yescharacteristic, complemented, Sylow
472C23—22no—
473C23—22no—
474C23—28no—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—48no—
482C23—48no—
483C23—44no—
484C23—44no—
485C23—224no—
486C23—222no—
487C23—222no—
488C23—224no—
489C23—222no—
490C23C22⋊C4×D1112yes—
491C23(C22⋊D11)⋊C412yes—
492C23#6695414yes—
493C23C4×C22⋊D1112yes—
494C23C22×C4×D1111yescharacteristic
495Q8—444no—
496D4—4416no—
497D4—448no—
498D4—444no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—44no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—48no—
508C2×C4—118no—
509C2×C4—224no—
510C2×C4—224no—
511C2×C4—222no—
512C2×C4—222no—
513C2×C4—222no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4—442no—
518C2×C4C22⋊C4×D1112yes—
519C2×C4(C22⋊D11)⋊C412yes—
520C2×C4#6693714yes—
521C2×C4#6693814yes—
522C2×C4C4×C22⋊D1112yes—
523C2×C4#6699214yes—
524C2×C4#6699314yes—
525C2×C4C2×#433911yescharacteristic
526C2×C4C2×D4×D1111yescharacteristic
527C2×C4C2×D4×D1111yescharacteristic
528C2×C4C2×D4×D1111yescharacteristic
529C2×C4C2×#434111yescharacteristic
530C2×C4C22×C22⋊D1111yescharacteristic
531C8—22no—
532C8—22no—
533C8—42no—
534C8—224no—
535C8—442no—
536C22—22no—
537C22—24no—
538C22—22no—
539C22—24no—
540C22—24no—
541C22—24no—
542C22—24no—
543C22—416no—
544C22—42no—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—442no—
549C22—444no—
550C22—442no—
551C22—444no—
552C22—442no—
553C22#1062257014yes—
554C22C2×C22⋊C4×D1111yescharacteristic
555C22C2×(C22⋊D11)⋊C411yescharacteristic
556C22C2×#6695412yes—
557C22#1062327612yes—
558C22C2×C4×C22⋊D1111yescharacteristic
559C4—42no—
560C4—228no—
561C4—442no—
562C4#1062257014yes—
563C4C2×#6693711yescharacteristic
564C4C2×#6693811yescharacteristic
565C4C2×#6699211yescharacteristic
566C4C2×#6699311yescharacteristic
567C2—24no—
568C2—44no—
569C2—882no—
570C2C2×#1062257011yescharacteristic
571C2#1307706212yes—
572C2#1307731011yescharacteristic
573C2#1307731911yescharacteristic
574C2#1307733712yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC22×C11×C22⋊C8C2
prime radicalC2×#10623322C2
cosocleC22×C4×C11C24
hypercenterC22×C22⋊C8D11
hypocenterC11#21191
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#10622715C2semidirect
3. C2×#10622723C2semidirect
4. C2×#10622723C2semidirect
5. C2×#10622820C2semidirect
6. C2×#10622714C2semidirect
7. #13069412C2semidirect
8. #13069408C2semidirect
9. C22×C11×C22⋊C8C2semidirect
31. C2×(C2×D11)⋊C8C22semidirect
32. C2×(C2×D11)⋊C8C22semidirect
33. C2×(C2×D11)⋊C8C22semidirect
36. C2×#66879C22semidirect
37. C2×Dic11⋊C8C22semidirect
38. C2×C8×Dic11C22semidirect
66. C22×C8×C11D4semidirect
89. C2×#4318D4semidirect
190. C22×C22⋊C8D11semidirect
353. C22×C8C22⋊D11semidirect
471. C11#21191semidirect

Maximal subgroups

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

subgroupindex
C2×#106233222
C2×#106227152
C2×#106227232
C2×#106228202
C2×#106227142
#130694122
#130694082
C22×C11×C22⋊C82
#2119111