Finite Group Databasebeta

← #14675498

Subgroups — #14675498

Order 2816.

1422 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×C4×Dic11⋊C4C211yesmaximal, characteristic
2C2×#10622545C211yesmaximal, characteristic
3#13066882C212yesmaximal
4#13066876C212yesmaximal
5#13066875C212yesmaximal
6#13066866C212yesmaximal
7C4×C11⋊#95C211yesmaximal, characteristic
8C4×C11⋊#95C211yesmaximal, characteristic
9C4×C11⋊#95C211yesmaximal, characteristic
10C4×C11⋊#95C211yesmaximal, characteristic
11C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
12C22×C11×C4⋊C4C2212yes—
13C22×C42×C11C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×Dic11⋊C4C2211yescharacteristic
17C22×Dic11⋊C4C2211yescharacteristic
18C22×C4×Dic11C2211yescharacteristic
19C22×C4×Dic11C2211yescharacteristic
20C22×C4×Dic11C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C4×C11×C4⋊C4—24no—
23C2×C11×#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2211yescharacteristic
36#10622545—24no—
37C4×Dic11⋊C4C418yescomplemented
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2312yes—
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×Dic11C2311yescharacteristic
44C23×Dic11C2311yescharacteristic
45C23×Dic11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2312yes—
48C23×Dic11C2311yescharacteristic
49C2×C11×C4⋊C4—24no—
50C2×C11×C4⋊C4—24no—
51C2×C11×C4⋊C4—24no—
52C2×C42×C11—22no—
53C2×C42×C11—22no—
54C2×C42×C11—22no—
55C2×C42×C11—22no—
56C2×C42×C11—22no—
57C2×C42×C11—22no—
58C2×C42×C11—22no—
59C2×C42×C11C2×C414yes—
60C2×C42×C11D414yes—
61C2×Dic11⋊C4—24no—
62C2×Dic11⋊C4—24no—
63C2×Dic11⋊C4C2×C414yes—
64C2×Dic11⋊C4C2×C414yes—
65C2×C4×Dic11—22no—
66C2×C4×Dic11—22no—
67C2×C4×Dic11—22no—
68C2×C4×Dic11—22no—
69C2×C4×Dic11—22no—
70C2×C4×Dic11—22no—
71C2×C4×Dic11—22no—
72C2×C4×Dic11—22no—
73C2×C4×Dic11—22no—
74C2×C4×Dic11C2×C414yes—
75C2×C4×Dic11C2×C414yes—
76C2×C4×Dic11Q814yes—
77C11×#95—24no—
78C11⋊#95—24no—
79C11⋊#95—24no—
80C11⋊#95—24no—
81C11⋊#95—24no—
82C11⋊#95—24no—
83C11⋊#95—24no—
84C11⋊#95—24no—
85C11⋊#95—24no—
86C11⋊#95—24no—
87C11⋊#95—24no—
88C11⋊#95C2×C414yes—
89C11⋊#95C2×C414yes—
90#13846—111nomaximal, Sylow
91C24×C11C2411yescharacteristic
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—22no—
95C22×C4×C11—21no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11C22×C412yes—
112C22×C4×C11C22×C412yes—
113C22×C4×C11C22×C412yes—
114C22×C4×C11C2×D414yes—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×Q812yes—
117C22×C4×C11#4114yes—
118C22×C4×C11#4114yes—
119C22×C4×C11#4112yes—
120C22×C4×C11#4112yes—
121C22×C4×C11#4112yes—
122C22×C4×C11#4112yes—
123C22×Dic11—21no—
124C22×Dic11—21no—
125C22×Dic11—22no—
126C22×Dic11—21no—
127C22×Dic11—21no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—22no—
143C22×Dic11—21no—
144C22×Dic11—22no—
145C22×Dic11—21no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11C22×C412yes—
151C22×Dic11C22×C412yes—
152C22×Dic11C22×C412yes—
153C22×Dic11C22×C412yes—
154C22×Dic11C2×Q814yes—
155C22×Dic11#4114yes—
156C22×Dic11#4114yes—
157C11×C4⋊C4—216no—
158C42×C11—28no—
159C42×C11—28no—
160C42×C11—44no—
161Dic11⋊C4—28no—
162Dic11⋊C4—28no—
163C4×Dic11—28no—
164C4×Dic11—28no—
165C4×Dic11—28no—
166C4×Dic11—44no—
167C2×C4×C4⋊C4—111no—
168C2×C4×C4⋊C4D1111yescharacteristic
169C2×#376—111no—
170#1445—112no—
171#1443—112no—
172#1442—112no—
173#1441—112no—
174C4×#95—111no—
175C4×#95—111no—
176C4×#95—111no—
177C4×#95—111no—
178C23×C11C23×C411yescharacteristic
179C23×C11C22×D411yescharacteristic
180C23×C11C22×Q811yescharacteristic
181C23×C11C2×#4112yes—
182C23×C11C2×#4111yescharacteristic
183C23×C11C2×#4112yes—
184C23×C11C2×#4111yescharacteristic
185C23×C11C2×#4111yescharacteristic
186C23×C11C2×#4111yescharacteristic
187C23×C11C2×#4112yes—
188C23×C11C2×#4112yes—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—24no—
192C2×C4×C11—24no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—24no—
197C2×C4×C11—24no—
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11#11714yes—
213C2×C4×C11#11714yes—
214C2×C4×C11C4×D414yes—
215C2×C4×C11C4×Q814yes—
216C2×C4×C11C22⋊Q814yes—
217C2×C4×C11#12314yes—
218C2×C4×C11#12514yes—
219C2×C4×C11#12614yes—
220C2×Dic11—22no—
221C2×Dic11—22no—
222C2×Dic11—24no—
223C2×Dic11—24no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—22no—
227C2×Dic11—22no—
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—24no—
234C2×Dic11—24no—
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—24no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11#11714yes—
254C22×C4⋊C4—111no—
255C22×C4⋊C4—111no—
256C22×C4⋊C4C2×D1112yes—
257C22×C42—111no—
258C22×C42—111no—
259C22×C42—111no—
260C22×C42—111no—
261C22×C42C2×D1111yescharacteristic
262C22×C42C2×D1111yescharacteristic
263C22×C42C2×D1111yescharacteristic
264C4×C4⋊C4—24no—
265C4×C4⋊C4—118no—
266#376—224no—
267C2×#95—111no—
268C2×#95—111no—
269C2×#95—112no—
270C2×#95—112no—
271C2×#95—112no—
272C2×#95—112no—
273C2×#95—112no—
274C2×#95—112no—
275C2×#95—112no—
276C2×#95—112no—
277C2×#95—112no—
278C2×#95—112no—
279C2×#95C2×D1112yes—
280C22×C11C2×#11711yescharacteristic
281C22×C11C2×#11711yescharacteristic
282C22×C11C2×#11711yescharacteristic
283C22×C11C2×C4×D411yescharacteristic
284C22×C11C2×C4×Q811yescharacteristic
285C22×C11C4×#4111yescharacteristic
286C22×C11C4×#4111yescharacteristic
287C22×C11C2×C22⋊Q811yescharacteristic
288C22×C11C2×#12311yescharacteristic
289C22×C11#52512yes—
290C22×C11C2×#12511yescharacteristic
291C22×C11C2×#12611yescharacteristic
292C22×C11#52912yes—
293C22×C11#52912yes—
294C22×C11#52912yes—
295C22×C11#52912yes—
296C22×C11#52912yes—
297C22×C11#52912yes—
298C22×C11#52912yes—
299C22×C11#52912yes—
300C22×C11#53212yes—
301C22×C11#53312yes—
302C22×C11#53312yes—
303C4×C11—24no—
304C4×C11—44no—
305C4×C11—44no—
306C4×C11—42no—
307C4×C11#38718yes—
308Dic11—24no—
309Dic11—44no—
310Dic11—44no—
311Dic11—42no—
312Dic11—42no—
313Dic11—42no—
314C23×C4—111no—
315C23×C4—111no—
316C23×C4—111no—
317C23×C4—111no—
318C23×C4—112no—
319C23×C4—112no—
320C23×C4C22×D1111yescharacteristic
321C23×C4C22×D1112yes—
322C23×C4C22×D1112yes—
323C23×C4C22×D1111yescharacteristic
324C23×C4C22×D1111yescharacteristic
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—114no—
329C2×C4⋊C4—114no—
330C2×C4⋊C4—224no—
331C2×C4⋊C4—224no—
332C2×C42—22no—
333C2×C42—22no—
334C2×C42—22no—
335C2×C42—22no—
336C2×C42—22no—
337C2×C42—22no—
338C2×C42—22no—
339C2×C42—114no—
340C2×C42—114no—
341C2×C42—114no—
342C2×C42—222no—
343C2×C42—222no—
344C2×C42—222no—
345C2×C42—222no—
346C2×C42—222no—
347C2×C42—222no—
348C2×C42—222no—
349C2×C42—222no—
350C2×C42—222no—
351C2×C42C4×D1114yes—
352C2×C42C22⋊D1114yes—
353#95—24no—
354#95—114no—
355#95—114no—
356#95—224no—
357#95—224no—
358#95—224no—
359#95—224no—
360#95—224no—
361#95—224no—
362#95—224no—
363#95—224no—
364#95—224no—
365#95—224no—
366C2×C11#228311yescharacteristic
367C2×C11C2×#38711yescharacteristic
368C2×C11#229011yescharacteristic
369C2×C11#229311yescharacteristic
370C2×C11#229511yescharacteristic
371C2×C11#229511yescharacteristic
372C2×C11#229811yescharacteristic
373C2×C11#239512yes—
374C2×C11#239612yes—
375C2×C11#240112yes—
376C2×C11#240212yes—
377C24C23×D1111yescharacteristic
378C22×C4—21no—
379C22×C4—22no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—112no—
398C22×C4—114no—
399C22×C4—112no—
400C22×C4—112no—
401C22×C4—112no—
402C22×C4—114no—
403C22×C4—114no—
404C22×C4—222no—
405C22×C4—221no—
406C22×C4—221no—
407C22×C4—222no—
408C22×C4—222no—
409C22×C4—222no—
410C22×C4—222no—
411C22×C4—222no—
412C22×C4—222no—
413C22×C4—222no—
414C22×C4—221no—
415C22×C4—221no—
416C22×C4—222no—
417C22×C4—221no—
418C22×C4—222no—
419C22×C4—221no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—222no—
431C22×C4C2×C4×D1112yes—
432C22×C4C2×C4×D1112yes—
433C22×C4C2×C4×D1112yes—
434C22×C4#433914yes—
435C22×C4#433914yes—
436C22×C4#433912yes—
437C22×C4#434112yes—
438C22×C4#434112yes—
439C22×C4Q8×D1112yes—
440C22×C4#434312yes—
441C22×C4C2×C22⋊D1114yes—
442C22×C4C2×C22⋊D1112yes—
443C4⋊C4—216no—
444C4⋊C4—228no—
445C4⋊C4—228no—
446C42—28no—
447C42—28no—
448C42—44no—
449C42—228no—
450C42—228no—
451C42—228no—
452C42—444no—
453C11#1384611yescharacteristic, complemented, Sylow
454C23C22×C4×D1111yescharacteristic
455C23C2×#433912yes—
456C23C2×#433912yes—
457C23C2×#433911yescharacteristic
458C23C2×#434111yescharacteristic
459C23C2×#434111yescharacteristic
460C23C2×Q8×D1111yescharacteristic
461C23C2×#434311yescharacteristic
462C23#41×D1112yes—
463C23#41×D1112yes—
464C23C22×C22⋊D1111yescharacteristic
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—22no—
468C2×C4—24no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—114no—
489C2×C4—222no—
490C2×C4—222no—
491C2×C4—224no—
492C2×C4—224no—
493C2×C4—222no—
494C2×C4—222no—
495C2×C4—222no—
496C2×C4—222no—
497C2×C4—222no—
498C2×C4—222no—
499C2×C4—222no—
500C2×C4—224no—
501C2×C4—222no—
502C2×C4—222no—
503C2×C4—224no—
504C2×C4—224no—
505C2×C4—224no—
506C2×C4—224no—
507C2×C4—224no—
508C2×C4—442no—
509C2×C4—442no—
510C2×C4—442no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4—442no—
518C2×C4—442no—
519C2×C4—442no—
520C2×C4—442no—
521C2×C4—442no—
522C2×C4#6692514yes—
523C2×C4#6694014yes—
524C2×C4#6694214yes—
525C2×C4#6694514yes—
526C2×C4#6695114yes—
527C2×C4C4×C22⋊D1114yes—
528C2×C4#6698814yes—
529C2×C4#6699914yes—
530C22C2×#6692511yescharacteristic
531C22C4×#433911yescharacteristic
532C22#1062301012yes—
533C22C2×#6694011yescharacteristic
534C22C2×#6694211yescharacteristic
535C22C2×#6694511yescharacteristic
536C22C2×#6695111yescharacteristic
537C22D11×#11711yescharacteristic
538C22#1062305311yescharacteristic
539C22#1062305912yes—
540C22#1062306912yes—
541C22#1062306912yes—
542C22#1062308812yes—
543C22#1062308812yes—
544C22#1062310912yes—
545C22#1062310912yes—
546C22#1062311112yes—
547C22#1062311112yes—
548C22C2×C4×C22⋊D1111yescharacteristic
549C22#1062332212yes—
550C22C2×#6698811yescharacteristic
551C22C2×#6699911yescharacteristic
552C22#1062336312yes—
553C4—24no—
554C4—44no—
555C4—44no—
556C4—42no—
557C4—224no—
558C4—442no—
559C4—444no—
560C4—444no—
561C4—442no—
562C4—442no—
563C4#1062259118yes—
564C2#1307101211yescharacteristic
565C2C2×#1062259111yescharacteristic
566C2#1307105911yescharacteristic
567C2#1307107511yescharacteristic
568C2#1307109011yescharacteristic
569C2#1307109211yescharacteristic
570C2#1307110911yescharacteristic
571C2#1307187512yes—
572C2#1307188612yes—
573C2#1307191712yes—
574C2#1307192312yes—
subgroupG/H
centerC23×C4C22×D11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC2×C4×C11×C4⋊C4C2
socle, prime radical, cosocleC24×C11C24
hypercenterC2×C4×C4⋊C4D11
hypocenterC11#13846
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
37. C4×Dic11⋊C4C4semidirect
453. C11#13846semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Dic11⋊C42
C2×#106225452
#130668822
#130668762
#130668752
#130668662
C4×C11⋊#952
C2×C4×C11×C4⋊C42
#1384611