Finite Group Databasebeta

← #14675214

Subgroups — #14675214

Order 2816.

1662 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622263C211yesmaximal, characteristic
2C2×C4×Dic11⋊C4C211yesmaximal, characteristic
3C2×#10622262C212yesmaximal
4C2×#10622262C211yesmaximal, characteristic
5#13066847C212yesmaximal
6#13066847C212yesmaximal
7Dic11⋊#95C212yesmaximal
8#13066841C211yesmaximal, characteristic
9C4×C11⋊#95C211yesmaximal, characteristic
10#95×Dic11C211yesmaximal, characteristic
11C11×#1434C211yesmaximal, characteristic
12C22×C42×C11C2211yescharacteristic
13C22×Dic11⋊C4C2211yescharacteristic
14C22×Dic11⋊C4C2212yes—
15C22×Dic11⋊C4C2212yes—
16C22×Dic11⋊C4C2211yescharacteristic
17C22×C4×Dic11C2212yes—
18C22×C4×Dic11C2212yes—
19C22×C4×Dic11C2212yes—
20C22×C4×Dic11C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C2×C11×#95C2212yes—
23C2×C11×#95C2212yes—
24C2×C11×#95C2211yescharacteristic
25C2×C11×#95C2211yescharacteristic
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C4×Dic11⋊C4C418yescomplemented
36#10622263C418yescomplemented
37#10622262—28no—
38#10622262C418yescomplemented
39C23×C4×C11C2312yes—
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×Dic11C2312yes—
45C23×Dic11C2311yescharacteristic
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2312yes—
49C23×Dic11C2311yescharacteristic
50C2×C42×C11—42no—
51C2×C42×C11C2×C414yes—
52C2×Dic11⋊C4—24no—
53C2×Dic11⋊C4—24no—
54C2×Dic11⋊C4—24no—
55C2×Dic11⋊C4—22no—
56C2×Dic11⋊C4—22no—
57C2×Dic11⋊C4—24no—
58C2×Dic11⋊C4C2×C418yes—
59C2×Dic11⋊C4C2×C418yes—
60C2×Dic11⋊C4C2×C414yes—
61C2×Dic11⋊C4C2×C414yes—
62C2×Dic11⋊C4D414yes—
63C2×Dic11⋊C4Q814yes—
64C2×C4×Dic11—24no—
65C2×C4×Dic11—24no—
66C2×C4×Dic11—24no—
67C2×C4×Dic11—24no—
68C2×C4×Dic11—24no—
69C2×C4×Dic11—24no—
70C2×C4×Dic11—42no—
71C2×C4×Dic11—42no—
72C2×C4×Dic11—42no—
73C2×C4×Dic11C2×C418yes—
74C2×C4×Dic11C2×C414yes—
75C2×C4×Dic11C2×C414yes—
76C2×C4×Dic11C2×C414yes—
77C2×C4×Dic11C2×C414yes—
78C11×#95—24no—
79C11×#95—42no—
80C11×#95C2×C414yes—
81C11×#95C2×C414yes—
82C11⋊#95—24no—
83C11⋊#95—24no—
84C11⋊#95—24no—
85C11⋊#95—42no—
86C11⋊#95C2×C414yes—
87C11⋊#95C2×C414yes—
88C11⋊#95C2×C418yes—
89C11⋊#95C2×C414yes—
90C11⋊#95C2×C414yes—
91#13804—111nomaximal, Sylow
92C24×C11C2411yescharacteristic
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
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—22no—
104C22×C4×C11—22no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11C22×C414yes—
114C22×C4×C11C22×C412yes—
115C22×C4×C11C22×C414yes—
116C22×C4×C11C22×C412yes—
117C22×C4×C11C22×C412yes—
118C22×C4×C11C22×C412yes—
119C22×C4×C11C22×C412yes—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×Q812yes—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—22no—
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×Dic11C22×C414yes—
141C22×Dic11C22×C412yes—
142C22×Dic11C22×C412yes—
143C22×Dic11C22×C412yes—
144C22×Dic11C22×C412yes—
145C22×Dic11C22×C412yes—
146C22×Dic11C22×C414yes—
147C22×Dic11C22×C412yes—
148C22×Dic11C22×C412yes—
149C22×Dic11C22×C412yes—
150C22×Dic11C2×D412yes—
151C22×Dic11C2×D412yes—
152C22×Dic11C2×Q812yes—
153C22×Dic11C2×Q812yes—
154C22×Dic11#4114yes—
155C22×Dic11#4114yes—
156C22×Dic11#4112yes—
157C22×Dic11#4112yes—
158C42×C11—44no—
159Dic11⋊C4—216no—
160Dic11⋊C4—28no—
161Dic11⋊C4—216no—
162Dic11⋊C4C4⋊C4116yescomplemented
163C4×Dic11—216no—
164C4×Dic11—44no—
165C4×Dic11—48no—
166C4×Dic11—48no—
167C4×Dic11C42116yescomplemented
168C2×#382—111no—
169C2×C4×C4⋊C4—111no—
170C2×C4×C4⋊C4—111no—
171C2×C4×C4⋊C4—112no—
172#1436—112no—
173#1436—112no—
174C4⋊#95—112no—
175#1434—111no—
176#1434D1111yescharacteristic
177C4×#95—111no—
178C4×#95—111no—
179C23×C11C23×C411yescharacteristic
180C23×C11C23×C411yescharacteristic
181C23×C11C23×C411yescharacteristic
182C23×C11C22×D411yescharacteristic
183C23×C11C22×Q811yescharacteristic
184C23×C11C2×#4111yescharacteristic
185C23×C11C2×#4111yescharacteristic
186C23×C11C2×#4112yes—
187C23×C11C2×#4112yes—
188C23×C11H(5,𝔽2)12yes—
189C23×C112−1+412yes—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—24no—
195C2×C4×C11—24no—
196C2×C4×C11—24no—
197C2×C4×C11—24no—
198C2×C4×C11—24no—
199C2×C4×C11—22no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—22no—
203C2×C4×C11—24no—
204C2×C4×C11—22no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11C2×C4214yes—
218C2×C4×C11C2×C4⋊C414yes—
219C2×Dic11—24no—
220C2×Dic11—24no—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—22no—
224C2×Dic11—24no—
225C2×Dic11—22no—
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—24no—
235C2×Dic11—22no—
236C2×Dic11—24no—
237C2×Dic11—22no—
238C2×Dic11—24no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11C2×C4214yes—
246C2×Dic11C2×C4214yes—
247C2×Dic11C2×C4⋊C414yes—
248C2×Dic11C2×C4⋊C414yes—
249C2×Dic11#11718yes—
250C2×Dic11#11714yes—
251C2×Dic11C4×D414yes—
252C2×Dic11C4×D414yes—
253C2×Dic11C4×Q814yes—
254C2×Dic11C4×Q814yes—
255C22×C4⋊C4—111no—
256C22×C4⋊C4—111no—
257C22×C4⋊C4—112no—
258C22×C4⋊C4—112no—
259C22×C42—111no—
260C22×C42—112no—
261C22×C42—111no—
262C22×C42—112no—
263C22×C42—112no—
264C22×C42C2×D1111yescharacteristic
265#382—118no—
266C4×C4⋊C4—118no—
267C4×C4⋊C4—118no—
268C4×C4⋊C4—228no—
269C2×#95—111no—
270C2×#95—111no—
271C2×#95—111no—
272C2×#95—111no—
273C2×#95—112no—
274C2×#95—112no—
275C2×#95—112no—
276C2×#95—112no—
277C2×#95—112no—
278C2×#95C2×D1112yes—
279C2×#95C2×D1112yes—
280C2×#95C2×D1111yescharacteristic
281C2×#95C2×D1111yescharacteristic
282C22×C11C22×C4211yescharacteristic
283C22×C11C22×C4⋊C411yescharacteristic
284C22×C11C2×#11712yes—
285C22×C11C2×#11711yescharacteristic
286C22×C11C2×C4×D411yescharacteristic
287C22×C11C2×C4×D411yescharacteristic
288C22×C11C2×C4×Q811yescharacteristic
289C22×C11C2×C4×Q811yescharacteristic
290C22×C11C4×#4111yescharacteristic
291C22×C11C4×#4111yescharacteristic
292C22×C11C4×#4112yes—
293C22×C11#51811yescharacteristic
294C22×C11#51911yescharacteristic
295C22×C11#52012yes—
296C22×C11#52012yes—
297C22×C11#54612yes—
298C22×C11#54812yes—
299C22×C11#55212yes—
300C22×C11#55312yes—
301C22×C11#55412yes—
302C22×C11#55612yes—
303C22×C11#55712yes—
304C22×C11#55912yes—
305C4×C11—24no—
306C4×C11—24no—
307C4×C11—44no—
308C4×C11—42no—
309C4×C11—44no—
310Dic11—24no—
311Dic11—28no—
312Dic11—24no—
313Dic11—42no—
314Dic11—44no—
315Dic11C4×C4⋊C418yes—
316C23×C4—111no—
317C23×C4—111no—
318C23×C4—111no—
319C23×C4—112no—
320C23×C4—112no—
321C23×C4—111no—
322C23×C4C22×D1111yescharacteristic
323C23×C4C22×D1112yes—
324C23×C4C22×D1112yes—
325C23×C4C22×D1111yescharacteristic
326C23×C4C22×D1111yescharacteristic
327C2×C4⋊C4—114no—
328C2×C4⋊C4—114no—
329C2×C4⋊C4—114no—
330C2×C4⋊C4—114no—
331C2×C4⋊C4—118no—
332C2×C4⋊C4—118no—
333C2×C4⋊C4—224no—
334C2×C4⋊C4—222no—
335C2×C4⋊C4—222no—
336C2×C4⋊C4—224no—
337C2×C4⋊C4—224no—
338C2×C4⋊C4—224no—
339C2×C42—42no—
340C2×C42—114no—
341C2×C42—114no—
342C2×C42—114no—
343C2×C42—118no—
344C2×C42—114no—
345C2×C42—224no—
346C2×C42—224no—
347C2×C42—224no—
348C2×C42—224no—
349C2×C42—224no—
350C2×C42—224no—
351C2×C42—442no—
352C2×C42—442no—
353C2×C42—442no—
354C2×C42C4×D1114yes—
355#95—24no—
356#95—42no—
357#95—114no—
358#95—114no—
359#95—114no—
360#95—118no—
361#95—114no—
362#95—224no—
363#95—224no—
364#95—224no—
365#95—442no—
366#95C4×D1114yes—
367#95C4×D1114yes—
368C2×C11C2×C4×C4⋊C411yescharacteristic
369C2×C11C4×#11711yescharacteristic
370C2×C11#227411yescharacteristic
371C2×C11#234911yescharacteristic
372C2×C11#235111yescharacteristic
373C2×C11#235212yes—
374C2×C11#235512yes—
375C2×C11#235611yescharacteristic
376C2×C11#235711yescharacteristic
377C2×C11#236712yes—
378C2×C11#237012yes—
379C24C23×D1111yescharacteristic
380C22×C4—22no—
381C22×C4—22no—
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—21no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—112no—
401C22×C4—112no—
402C22×C4—112no—
403C22×C4—112no—
404C22×C4—112no—
405C22×C4—112no—
406C22×C4—112no—
407C22×C4—112no—
408C22×C4—112no—
409C22×C4—112no—
410C22×C4—114no—
411C22×C4—112no—
412C22×C4—112no—
413C22×C4—112no—
414C22×C4—114no—
415C22×C4—114no—
416C22×C4—114no—
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—222no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4C2×C4×D1114yes—
437C22×C4C2×C4×D1112yes—
438C22×C4C2×C4×D1114yes—
439C22×C4C2×C4×D1112yes—
440C22×C4C2×C4×D1112yes—
441C22×C4C2×C4×D1112yes—
442C22×C4C2×C4×D1112yes—
443C22×C4D4×D1112yes—
444C22×C4Q8×D1112yes—
445C4⋊C4—1116no—
446C4⋊C4—228no—
447C4⋊C4—2216no—
448C4⋊C4—2216no—
449C42—44no—
450C42—1116no—
451C42—2216no—
452C42—444no—
453C42—448no—
454C42—448no—
455C11#1380411yescharacteristic, complemented, Sylow
456C23C22×C4×D1111yescharacteristic
457C23C22×C4×D1111yescharacteristic
458C23C22×C4×D1111yescharacteristic
459C23C2×D4×D1111yescharacteristic
460C23#6703712yes—
461C23C2×Q8×D1111yescharacteristic
462C23#41×D1111yescharacteristic
463C23#41×D1112yes—
464C23#41×D1111yescharacteristic
465C23#41×D1112yes—
466C23#6704312yes—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—22no—
476C2×C4—24no—
477C2×C4—22no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—114no—
495C2×C4—114no—
496C2×C4—114no—
497C2×C4—114no—
498C2×C4—114no—
499C2×C4—114no—
500C2×C4—114no—
501C2×C4—114no—
502C2×C4—114no—
503C2×C4—118no—
504C2×C4—224no—
505C2×C4—222no—
506C2×C4—224no—
507C2×C4—224no—
508C2×C4—222no—
509C2×C4—222no—
510C2×C4—222no—
511C2×C4—224no—
512C2×C4—224no—
513C2×C4—224no—
514C2×C4—224no—
515C2×C4—224no—
516C2×C4—224no—
517C2×C4—224no—
518C2×C4—222no—
519C2×C4—222no—
520C2×C4—224no—
521C2×C4—222no—
522C2×C4—224no—
523C2×C4—224no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4—442no—
527C2×C4—442no—
528C2×C4—442no—
529C2×C4—442no—
530C2×C4C42×D1114yes—
531C2×C4C4⋊C4×D1114yes—
532C22C2×C42×D1111yescharacteristic
533C22#1062301711yescharacteristic
534C22C2×C4⋊C4×D1111yescharacteristic
535C22#1062304711yescharacteristic
536C22D11×#11711yescharacteristic
537C22D11×#11712yes—
538C22#1062305312yes—
539C22#1062305311yescharacteristic
540C22#1062305311yescharacteristic
541C22C4×D4×D1111yescharacteristic
542C22C4×D4×D1111yescharacteristic
543C22#1062307712yes—
544C22#1062307712yes—
545C22C4×Q8×D1111yescharacteristic
546C22C4×Q8×D1111yescharacteristic
547C22#1062314112yes—
548C22#1062316712yes—
549C22#1062319212yes—
550C22#1062319512yes—
551C22#1062320812yes—
552C22#1062321612yes—
553C22#1062323312yes—
554C22#1062323912yes—
555C4—24no—
556C4—24no—
557C4—44no—
558C4—44no—
559C4—42no—
560C4—118no—
561C4—224no—
562C4—224no—
563C4—228no—
564C4—444no—
565C4—442no—
566C2C4×C4⋊C4×D1111yescharacteristic
567C2#1307095511yescharacteristic
568C2#1307097111yescharacteristic
569C2#1307152011yescharacteristic
570C2#1307153311yescharacteristic
571C2#1307154412yes—
572C2#1307157012yes—
573C2#1307157611yescharacteristic
574C2#1307158411yescharacteristic
575C2#1307168212yes—
576C2#1307170712yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC11×#1434C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1434D11
hypocenterC11#13804
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
35. C4×Dic11⋊C4C4semidirect
36. #10622263C4semidirect
38. #10622262C4semidirect
162. Dic11⋊C4C4⋊C4semidirect
167. C4×Dic11C42semidirect
455. C11#13804semidirect

Maximal subgroups

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

subgroupindex
C2×#106222632
C2×C4×Dic11⋊C42
C2×#106222622
#130668472
Dic11⋊#952
#130668412
C4×C11⋊#952
#95×Dic112
C11×#14342
#1380411