Finite Group Databasebeta

← #14676414

Subgroups — #14676414

Order 2816.

1182 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊Dic11C211yesmaximal, characteristic
2#13066883C212yesmaximal
3#13066877C212yesmaximal
4#13066850C212yesmaximal
5#13066843C211yesmaximal, characteristic
6#13066842C212yesmaximal
7#13066842C211yesmaximal, characteristic
8#13066842C211yesmaximal, characteristic
9#13066841C211yesmaximal, characteristic
10#95×Dic11C211yesmaximal, characteristic
11C11×#1434C211yesmaximal, characteristic
12C22×C42×C11C2211yescharacteristic
13C22×C4⋊Dic11C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C22×C4×Dic11C2212yes—
16C22×C4×Dic11C2211yescharacteristic
17C22×C4×Dic11C2211yescharacteristic
18C2×C11×#95C2211yescharacteristic
19C2×C11×#95C2211yescharacteristic
20C2×C11×#95C2212yes—
21C2×C11×#95C2212yes—
22C2×C11⋊#95C2211yescharacteristic
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2211yescharacteristic
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⋊#95C2211yescharacteristic
34C2×C11⋊#95C2211yescharacteristic
35C4×C4⋊Dic11C418yescomplemented
36C23×C4×C11C2312yes—
37C23×C4×C11C2311yescharacteristic
38C23×C4×C11C2312yes—
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C23×Dic11C2312yes—
42C23×Dic11C2311yescharacteristic
43C23×Dic11C2311yescharacteristic
44C23×Dic11C2311yescharacteristic
45C23×Dic11C2312yes—
46C23×Dic11C2311yescharacteristic
47C2×C42×C11—22no—
48C2×C42×C11—22no—
49C2×C42×C11C2×C414yes—
50C2×C4⋊Dic11—22no—
51C2×C4⋊Dic11—22no—
52C2×C4⋊Dic11—22no—
53C2×C4⋊Dic11—22no—
54C2×C4⋊Dic11C2×C414yes—
55C2×C4⋊Dic11C2×C414yes—
56C2×C4×Dic11—24no—
57C2×C4×Dic11—24no—
58C2×C4×Dic11—42no—
59C2×C4×Dic11—42no—
60C2×C4×Dic11—42no—
61C2×C4×Dic11C2×C414yes—
62C2×C4×Dic11C2×C414yes—
63C11×#95—24no—
64C11×#95—22no—
65C11×#95—24no—
66C11×#95—22no—
67C11⋊#95—24no—
68C11⋊#95—24no—
69C11⋊#95—22no—
70C11⋊#95—22no—
71C11⋊#95—24no—
72C11⋊#95—24no—
73C11⋊#95—24no—
74C11⋊#95—24no—
75C11⋊#95—42no—
76C11⋊#95—42no—
77C11⋊#95—42no—
78C11⋊#95C2×C414yes—
79C11⋊#95C2×C414yes—
80#13950—111nomaximal, Sylow
81C24×C11C2411yescharacteristic
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—21no—
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—22no—
104C22×C4×C11—22no—
105C22×C4×C11C22×C412yes—
106C22×C4×C11C22×C412yes—
107C22×C4×C11C22×C412yes—
108C22×C4×C11#4114yes—
109C22×C4×C11#4112yes—
110C22×C4×C11#4112yes—
111C22×C4×C11#4112yes—
112C22×C4×C11#4112yes—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—22no—
116C22×Dic11—22no—
117C22×Dic11—22no—
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—21no—
122C22×Dic11—21no—
123C22×Dic11—21no—
124C22×Dic11—21no—
125C22×Dic11—21no—
126C22×Dic11—21no—
127C22×Dic11—22no—
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×Dic11C22×C412yes—
141C22×Dic11C22×C412yes—
142C22×Dic11C22×C412yes—
143C22×Dic11C22×C412yes—
144C22×Dic11#4114yes—
145C22×Dic11#4112yes—
146C22×Dic11#4112yes—
147C42×C11—28no—
148C4⋊Dic11—28no—
149C4⋊Dic11—28no—
150C4×Dic11—44no—
151C4×Dic11—44no—
152C4×Dic11—48no—
153C2×C4×C4⋊C4—111no—
154#1445—112no—
155#1443—112no—
156#1436—112no—
157#1434—111no—
158#1434—111no—
159#1434—112no—
160#1434—111no—
161#1434—111no—
162#1434D1111yescharacteristic
163C4×#95—111no—
164C23×C11C23×C411yescharacteristic
165C23×C11C2×#4112yes—
166C23×C11C2×#4111yescharacteristic
167C23×C11C2×#4111yescharacteristic
168C23×C11C2×#4111yescharacteristic
169C23×C11C2×#4111yescharacteristic
170C23×C11C2×#4111yescharacteristic
171C23×C11C2×#4111yescharacteristic
172C23×C11C2×#4112yes—
173C23×C11H(5,𝔽2)12yes—
174C23×C112−1+412yes—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—24no—
184C2×C4×C11—24no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—24no—
189C2×C4×C11—24no—
190C2×C4×C11—24no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11#11714yes—
205C2×C4×C11#11714yes—
206C2×Dic11—22no—
207C2×Dic11—22no—
208C2×Dic11—24no—
209C2×Dic11—24no—
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—24no—
220C2×Dic11—24no—
221C2×Dic11—24no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228C2×Dic11—42no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11#11714yes—
240C22×C4⋊C4—111no—
241C22×C4⋊C4—111no—
242C22×C42—111no—
243C22×C42—111no—
244C22×C42—112no—
245C22×C42C2×D1111yescharacteristic
246C4×C4⋊C4—118no—
247C2×#95—111no—
248C2×#95—111no—
249C2×#95—111no—
250C2×#95—112no—
251C2×#95—111no—
252C2×#95—112no—
253C2×#95—112no—
254C2×#95—112no—
255C2×#95—112no—
256C2×#95—112no—
257C2×#95—112no—
258C2×#95—112no—
259C2×#95—112no—
260C2×#95C2×D1111yescharacteristic
261C2×#95C2×D1111yescharacteristic
262C2×#95C2×D1112yes—
263C2×#95C2×D1112yes—
264C22×C11C2×#11711yescharacteristic
265C22×C11C2×#11711yescharacteristic
266C22×C11C2×#11711yescharacteristic
267C22×C11C4×#4111yescharacteristic
268C22×C11C4×#4111yescharacteristic
269C22×C11#51811yescharacteristic
270C22×C11#51911yescharacteristic
271C22×C11#52912yes—
272C22×C11#52912yes—
273C22×C11#52911yescharacteristic
274C22×C11#52911yescharacteristic
275C22×C11#52911yescharacteristic
276C22×C11#52911yescharacteristic
277C22×C11#53912yes—
278C22×C11#53912yes—
279C22×C11#55112yes—
280C22×C11#55212yes—
281C22×C11#55212yes—
282C22×C11#55312yes—
283C22×C11#55312yes—
284C22×C11#55612yes—
285C22×C11#55612yes—
286C22×C11#55912yes—
287C4×C11—24no—
288C4×C11—24no—
289C4×C11—44no—
290C4×C11—42no—
291C4×C11—82no—
292Dic11—24no—
293Dic11—44no—
294Dic11—42no—
295Dic11—42no—
296Dic11—42no—
297Dic11—82no—
298C23×C4—111no—
299C23×C4—111no—
300C23×C4—111no—
301C23×C4—111no—
302C23×C4—112no—
303C23×C4—112no—
304C23×C4C22×D1112yes—
305C23×C4C22×D1111yescharacteristic
306C23×C4C22×D1112yes—
307C23×C4C22×D1111yescharacteristic
308C23×C4C22×D1111yescharacteristic
309C2×C4⋊C4—114no—
310C2×C4⋊C4—114no—
311C2×C4⋊C4—222no—
312C2×C4⋊C4—222no—
313C2×C4⋊C4—222no—
314C2×C4⋊C4—222no—
315C2×C42—22no—
316C2×C42—22no—
317C2×C42—114no—
318C2×C42—114no—
319C2×C42—224no—
320C2×C42—224no—
321C2×C42—442no—
322C2×C42—442no—
323C2×C42—442no—
324C2×C42C4×D1114yes—
325#95—24no—
326#95—22no—
327#95—24no—
328#95—22no—
329#95—114no—
330#95—114no—
331#95—224no—
332#95—224no—
333#95—224no—
334#95—224no—
335#95—224no—
336#95—222no—
337#95—222no—
338#95—224no—
339#95—442no—
340#95—442no—
341#95—442no—
342C2×C11#228311yescharacteristic
343C2×C11#229811yescharacteristic
344C2×C11#231311yescharacteristic
345C2×C11#235311yescharacteristic
346C2×C11#235611yescharacteristic
347C2×C11#235611yescharacteristic
348C2×C11#235711yescharacteristic
349C2×C11#257512yes—
350C2×C11#257712yes—
351C2×C11#259412yes—
352C2×C11#259612yes—
353C24C23×D1111yescharacteristic
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—112no—
378C22×C4—112no—
379C22×C4—112no—
380C22×C4—112no—
381C22×C4—112no—
382C22×C4—112no—
383C22×C4—114no—
384C22×C4—222no—
385C22×C4—222no—
386C22×C4—222no—
387C22×C4—222no—
388C22×C4—222no—
389C22×C4—222no—
390C22×C4—221no—
391C22×C4—221no—
392C22×C4—222no—
393C22×C4—221no—
394C22×C4—221no—
395C22×C4—222no—
396C22×C4—222no—
397C22×C4—221no—
398C22×C4—221no—
399C22×C4—222no—
400C22×C4—222no—
401C22×C4—222no—
402C22×C4—222no—
403C22×C4—222no—
404C22×C4—222no—
405C22×C4—222no—
406C22×C4—222no—
407C22×C4—222no—
408C22×C4—222no—
409C22×C4—222no—
410C22×C4—222no—
411C22×C4C2×C4×D1112yes—
412C22×C4C2×C4×D1112yes—
413C22×C4C2×C4×D1112yes—
414C22×C4#433914yes—
415C22×C4#434112yes—
416C22×C4#434112yes—
417C22×C4#434112yes—
418C22×C4#434312yes—
419C4⋊C4—228no—
420C4⋊C4—228no—
421C42—28no—
422C42—444no—
423C42—444no—
424C42—448no—
425C11#1395011yescharacteristic, complemented, Sylow
426C23C22×C4×D1111yescharacteristic
427C23C2×#433912yes—
428C23C2×#434111yescharacteristic
429C23C2×#434111yescharacteristic
430C23C2×#434111yescharacteristic
431C23C2×#434311yescharacteristic
432C23#41×D1111yescharacteristic
433C23#41×D1112yes—
434C23#41×D1111yescharacteristic
435C23#6704212yes—
436C23#6704312yes—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—114no—
467C2×C4—224no—
468C2×C4—224no—
469C2×C4—222no—
470C2×C4—222no—
471C2×C4—224no—
472C2×C4—222no—
473C2×C4—222no—
474C2×C4—222no—
475C2×C4—222no—
476C2×C4—222no—
477C2×C4—222no—
478C2×C4—222no—
479C2×C4—222no—
480C2×C4—222no—
481C2×C4—224no—
482C2×C4—224no—
483C2×C4—442no—
484C2×C4—442no—
485C2×C4—442no—
486C2×C4—442no—
487C2×C4—442no—
488C2×C4—442no—
489C2×C4—442no—
490C2×C4—442no—
491C2×C4—442no—
492C2×C4—442no—
493C2×C4—442no—
494C2×C4—442no—
495C2×C4—442no—
496C2×C4—442no—
497C2×C4—442no—
498C2×C4—442no—
499C2×C4—442no—
500C2×C4#6693014yes—
501C2×C4#6694514yes—
502C22C4×#433911yescharacteristic
503C22C2×#6693011yescharacteristic
504C22C2×#6694511yescharacteristic
505C22#1062304711yescharacteristic
506C22D11×#11711yescharacteristic
507C22#1062305211yescharacteristic
508C22#1062305311yescharacteristic
509C22#1062306212yes—
510C22#1062306412yes—
511C22#1062306912yes—
512C22#1062308812yes—
513C22#1062309612yes—
514C22#1062311612yes—
515C22#1062313111yescharacteristic
516C22#1062313111yescharacteristic
517C22#1062315511yescharacteristic
518C22#1062315511yescharacteristic
519C22#1062319612yes—
520C22#1062319612yes—
521C22#1062320212yes—
522C22#1062322512yes—
523C22#1062323612yes—
524C22#1062324012yes—
525C4—24no—
526C4—24no—
527C4—42no—
528C4—44no—
529C4—82no—
530C4—224no—
531C4—442no—
532C4—442no—
533C4—442no—
534C4—444no—
535C4—882no—
536C2#1307101111yescharacteristic
537C2#1307111211yescharacteristic
538C2#1307121711yescharacteristic
539C2#1307154911yescharacteristic
540C2#1307158211yescharacteristic
541C2#1307158311yescharacteristic
542C2#1307158711yescharacteristic
543C2#1307390412yes—
544C2#1307393212yes—
545C2#1307412112yes—
546C2#1307414912yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1434D11
hypocenterC11#13950
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
35. C4×C4⋊Dic11C4semidirect
425. C11#13950semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊Dic112
#130668832
#130668772
#130668502
#130668432
#130668422
#130668412
#95×Dic112
C11×#14342
#1395011