Finite Group Databasebeta

← #14685118

Subgroups — #14685118

Order 2816.

1662 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66942C211yesmaximal, characteristic
2C2×#10622263C211yesmaximal, characteristic
3C2×C42×Dic11C211yesmaximal, characteristic
4#13066851C211yesmaximal, characteristic
5#13066850C212yesmaximal
6#13066849C211yesmaximal, characteristic
7#13066848C211yesmaximal, characteristic
8#13066847C212yesmaximal
9Dic11⋊#95C212yesmaximal
10Dic11⋊#95C212yesmaximal
11C11×#1436C211yesmaximal, characteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C22×Dic11⋊C4C2212yes—
16C22×Dic11⋊C4C2211yescharacteristic
17C22×Dic11⋊C4C2211yescharacteristic
18C22×Dic11⋊C4C2211yescharacteristic
19C22×Dic11⋊C4C2211yescharacteristic
20C22×C4×Dic11C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C22×C4×Dic11C2212yes—
23C22×C4×Dic11C2211yescharacteristic
24C2×#66942—24no—
25C2×#66942—24no—
26C2×#66942C418yescomplemented
27C2×C11×#95C2212yes—
28C2×C11×#95C2212yes—
29C2×C11×#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2211yescharacteristic
38C42×Dic11—24no—
39#10622263—24no—
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2312yes—
45C23×Dic11C2312yes—
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2312yes—
50C23×Dic11C2311yescharacteristic
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4C2×C414yes—
54C2×C42×C11—22no—
55C2×C42×C11—24no—
56C2×C4⋊Dic11—22no—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11C2×C414yes—
59C2×Dic11⋊C4—22no—
60C2×Dic11⋊C4—22no—
61C2×Dic11⋊C4—22no—
62C2×Dic11⋊C4—22no—
63C2×Dic11⋊C4—22no—
64C2×Dic11⋊C4—22no—
65C2×Dic11⋊C4—22no—
66C2×Dic11⋊C4—22no—
67C2×Dic11⋊C4—24no—
68C2×Dic11⋊C4—24no—
69C2×Dic11⋊C4—24no—
70C2×Dic11⋊C4C2×C414yes—
71C2×Dic11⋊C4C2×C414yes—
72C2×Dic11⋊C4C2×C414yes—
73C2×Dic11⋊C4C2×C414yes—
74C2×C4×Dic11—22no—
75C2×C4×Dic11—24no—
76C2×C4×Dic11—24no—
77C2×C4×Dic11—24no—
78C2×C4×Dic11—24no—
79C2×C4×Dic11—24no—
80C2×C4×Dic11—24no—
81C2×C4×Dic11C2×C414yes—
82C2×C4×Dic11D414yes—
83C2×C4×Dic11D414yes—
84C2×C4×Dic11Q818yes—
85#66942—232no—
86C11×#95—22no—
87C11×#95—24no—
88C11×#95—24no—
89C11⋊#95—22no—
90C11⋊#95—24no—
91C11⋊#95—24no—
92C11⋊#95—24no—
93C11⋊#95—24no—
94C11⋊#95—24no—
95C11⋊#95—24no—
96C11⋊#95—24no—
97#14709—111nomaximal, Sylow
98C24×C11C2411yescharacteristic
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11C22×C412yes—
121C22×C4×C11C22×C412yes—
122C22×C4×C11C22×C412yes—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×Q814yes—
126C22×C4×C11#4114yes—
127C22×C4×C11#4114yes—
128C22×Dic11—22no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11C22×C412yes—
150C22×Dic11C22×C412yes—
151C22×Dic11C22×C412yes—
152C22×Dic11C22×C412yes—
153C22×Dic11C2×D412yes—
154C22×Dic11C2×D412yes—
155C22×Dic11C2×D412yes—
156C22×Dic11C2×D412yes—
157C22×Dic11C2×Q814yes—
158C22×Dic11C2×Q814yes—
159C22×Dic11#4114yes—
160C22×Dic11#4114yes—
161C22×Dic11#4114yes—
162C11×C4⋊C4—28no—
163C42×C11—28no—
164C4⋊Dic11—28no—
165Dic11⋊C4—28no—
166Dic11⋊C4—28no—
167Dic11⋊C4—28no—
168Dic11⋊C4—28no—
169Dic11⋊C4—48no—
170C4×Dic11—28no—
171C4×Dic11—216no—
172C4×Dic11—216no—
173C4×Dic11C22⋊C4116yes—
174C22×#125—111no—
175C2×#382—111no—
176C2×C43—111no—
177#1436—111no—
178#1436—112no—
179#1436—112no—
180#1436—111no—
181#1436—111no—
182#1436D1111yescharacteristic
183C4⋊#95—112no—
184C4⋊#95—112no—
185C23×C11C23×C411yescharacteristic
186C23×C11C22×D411yescharacteristic
187C23×C11C22×D411yescharacteristic
188C23×C11C22×Q812yes—
189C23×C11C2×#4112yes—
190C23×C11C2×#4112yes—
191C23×C11C2×#4112yes—
192C23×C11C2×#4112yes—
193C23×C11C2×#4112yes—
194C2×C4×C11—24no—
195C2×C4×C11—24no—
196C2×C4×C11—22no—
197C2×C4×C11—24no—
198C2×C4×C11—22no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—24no—
209C2×C4×C11—42no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11C2×C22⋊C414yes—
222C2×C4×C11#12518yescomplemented
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—24no—
226C2×Dic11—24no—
227C2×Dic11—24no—
228C2×Dic11—24no—
229C2×Dic11—24no—
230C2×Dic11—24no—
231C2×Dic11—24no—
232C2×Dic11—24no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—24no—
238C2×Dic11—42no—
239C2×Dic11—41no—
240C2×Dic11—41no—
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×Dic11C2×C22⋊C414yes—
251C2×Dic11C2×C22⋊C414yes—
252C2×Dic11C4×Q818yes—
253C2×Dic11C22⋊Q818yes—
254C2×Dic11#12414yes—
255C2×Dic11#12518yescomplemented
256C2×Dic11C4⋊Q814yes—
257C2×#125—118no—
258C2×#125—224no—
259C2×#125—224no—
260C22×C4⋊C4—111no—
261C22×C4⋊C4—111no—
262C22×C4⋊C4—111no—
263C22×C4⋊C4—111no—
264C22×C4⋊C4—111no—
265C22×C4⋊C4—112no—
266C22×C4⋊C4C2×D1111yescharacteristic
267C22×C42—111no—
268C22×C42—112no—
269C22×C42—112no—
270C22×C42—111no—
271C22×C42C2×D1111yescharacteristic
272#382—224no—
273C2×#95—112no—
274C2×#95—112no—
275C2×#95—112no—
276C2×#95—112no—
277C2×#95—112no—
278C2×#95—112no—
279C2×#95—112no—
280C2×#95—111no—
281C2×#95C2×D1112yes—
282C2×#95C2×D1112yes—
283C2×#95C2×D1111yescharacteristic
284C43—224no—
285C22×C11C22×C22⋊C411yescharacteristic
286C22×C11C2×C4×Q812yes—
287C22×C11C4×#4111yescharacteristic
288C22×C11C4×#4111yescharacteristic
289C22×C11C4×#4112yes—
290C22×C11C2×C22⋊Q812yes—
291C22×C11#52512yes—
292C22×C11#52511yescharacteristic
293C22×C11#52511yescharacteristic
294C22×C11C2×#12411yescharacteristic
295C22×C11C2×#12512yes—
296C22×C11C2×#12512yes—
297C22×C11#52912yes—
298C22×C11#52912yes—
299C22×C11#52912yes—
300C22×C11#52912yes—
301C22×C11C2×C4⋊Q811yescharacteristic
302C22×C11#53212yes—
303C22×C11#53212yes—
304C22×C11#53312yes—
305C22×C11#53312yes—
306C4×C11—28no—
307C4×C11—24no—
308C4×C11—42no—
309C4×C11—42no—
310C4×C11—82no—
311Dic11—28no—
312Dic11—24no—
313Dic11—42no—
314Dic11—42no—
315Dic11—82no—
316Dic11#39118yes—
317C23×C4—111no—
318C23×C4—111no—
319C23×C4—112no—
320C23×C4—111no—
321C23×C4—111no—
322C23×C4—112no—
323C23×C4C22×D1112yes—
324C23×C4C22×D1111yescharacteristic
325C23×C4C22×D1111yescharacteristic
326C23×C4C22×D1111yescharacteristic
327C23×C4C22×D1112yes—
328#125—2232no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—114no—
332C2×C4⋊C4—114no—
333C2×C4⋊C4—114no—
334C2×C4⋊C4—114no—
335C2×C4⋊C4—114no—
336C2×C4⋊C4—222no—
337C2×C4⋊C4—222no—
338C2×C4⋊C4—222no—
339C2×C4⋊C4—222no—
340C2×C4⋊C4—222no—
341C2×C4⋊C4—222no—
342C2×C4⋊C4—222no—
343C2×C4⋊C4—222no—
344C2×C4⋊C4—222no—
345C2×C4⋊C4—222no—
346C2×C4⋊C4—224no—
347C2×C4⋊C4—224no—
348C2×C4⋊C4—224no—
349C2×C4⋊C4C4×D1114yes—
350C2×C42—22no—
351C2×C42—24no—
352C2×C42—114no—
353C2×C42—114no—
354C2×C42—114no—
355C2×C42—118no—
356C2×C42—224no—
357C2×C42—224no—
358C2×C42—224no—
359C2×C42—224no—
360C2×C42—224no—
361C2×C42—224no—
362C2×C42—222no—
363#95—24no—
364#95—22no—
365#95—24no—
366#95—224no—
367#95—224no—
368#95—224no—
369#95—224no—
370#95—224no—
371#95—224no—
372#95—222no—
373#95—224no—
374C2×C11C2×#39111yescharacteristic
375C2×C11#229711yescharacteristic
376C2×C11#229711yescharacteristic
377C2×C11C4×#12512yes—
378C2×C11C4×#12512yes—
379C2×C11#285112yes—
380C2×C11#285112yes—
381C2×C11#285912yes—
382C2×C11#286112yes—
383C24C23×D1111yescharacteristic
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—112no—
406C22×C4—112no—
407C22×C4—112no—
408C22×C4—114no—
409C22×C4—114no—
410C22×C4—112no—
411C22×C4—112no—
412C22×C4—112no—
413C22×C4—114no—
414C22×C4—114no—
415C22×C4—114no—
416C22×C4—112no—
417C22×C4—112no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—221no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4—221no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—222no—
437C22×C4—222no—
438C22×C4—222no—
439C22×C4C2×C4×D1112yes—
440C22×C4C2×C4×D1112yes—
441C22×C4C2×C4×D1112yes—
442C22×C4#433914yes—
443C22×C4D4×D1112yes—
444C22×C4D4×D1112yes—
445C22×C4#434114yes—
446C22×C4Q8×D1114yes—
447C4⋊C4—28no—
448C4⋊C4—228no—
449C4⋊C4—228no—
450C4⋊C4—228no—
451C4⋊C4—228no—
452C4⋊C4—228no—
453C4⋊C4—448no—
454C42—28no—
455C42—1116no—
456C42—2216no—
457C42—2216no—
458C42—228no—
459C11#1470911yescharacteristic, complemented, Sylow
460C23C22×C4×D1111yescharacteristic
461C23C2×#433912yes—
462C23C2×D4×D1111yescharacteristic
463C23C2×D4×D1111yescharacteristic
464C23C2×#434112yes—
465C23C2×Q8×D1112yes—
466C23#41×D1112yes—
467C23#41×D1112yes—
468C23#41×D1112yes—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—114no—
497C2×C4—114no—
498C2×C4—118no—
499C2×C4—118no—
500C2×C4—114no—
501C2×C4—114no—
502C2×C4—118no—
503C2×C4—224no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—224no—
507C2×C4—224no—
508C2×C4—224no—
509C2×C4—224no—
510C2×C4—224no—
511C2×C4—224no—
512C2×C4—224no—
513C2×C4—222no—
514C2×C4—222no—
515C2×C4—222no—
516C2×C4—222no—
517C2×C4—224no—
518C2×C4—442no—
519C2×C4—442no—
520C2×C4—441no—
521C2×C4—442no—
522C2×C4—441no—
523C2×C4—442no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4—442no—
527C2×C4—442no—
528C2×C4—442no—
529C2×C4—442no—
530C2×C4C22⋊C4×D1114yes—
531C2×C4#6694218yescomplemented
532C22C4×#433911yescharacteristic
533C22C2×C22⋊C4×D1111yescharacteristic
534C22C2×#6694212yes—
535C22#1062305311yescharacteristic
536C22#1062305912yes—
537C22C4×#434112yes—
538C22#1062306912yes—
539C22#1062307812yes—
540C22#1062307912yes—
541C22C4×Q8×D1112yes—
542C22#1062310912yes—
543C22#1062311711yescharacteristic
544C22#1062312712yes—
545C22#1062315312yes—
546C22D11×C22⋊Q812yes—
547C22#1062318012yes—
548C22#1062318711yescharacteristic
549C22D11×#12411yescharacteristic
550C22D11×#12512yes—
551C22#1062323712yes—
552C22D11×C4⋊Q811yescharacteristic
553C4—28no—
554C4—24no—
555C4—42no—
556C4—42no—
557C4—82no—
558C4—118no—
559C4—228no—
560C4—224no—
561C4—442no—
562C4—442no—
563C4—882no—
564C2D11×#39111yescharacteristic
565C2#1307110111yescharacteristic
566C2#1307110211yescharacteristic
567C2C4×#6694212yes—
568C2#1307117312yes—
569C2#1307692212yes—
570C2#1307692312yes—
571C2#1307697512yes—
572C2#1307698512yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1436D11
hypocenterC11#14709
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
26. C2×#66942C4semidirect
222. C2×C4×C11#125semidirect
255. C2×Dic11#125semidirect
459. C11#14709semidirect
531. C2×C4#66942semidirect

Maximal subgroups

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

subgroupindex
C22×#669422
C2×#106222632
C2×C42×Dic112
#130668512
#130668502
#130668492
#130668482
#130668472
Dic11⋊#952
C11×#14362
#1470911