Finite Group Databasebeta

← #14676451

Subgroups — #14676451

Order 2816.

1342 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622263C211yesmaximal, characteristic
2C2×C4⋊C4×Dic11C211yesmaximal, characteristic
3C2×#10622262C211yesmaximal, characteristic
4#13066875C211yesmaximal, characteristic
5#13066873C211yesmaximal, characteristic
6#13066872C211yesmaximal, characteristic
7Dic11⋊#95C212yesmaximal
8Dic11⋊#95C212yesmaximal
9#13066841C212yesmaximal
10#13066840C212yesmaximal
11C11×#1442C211yesmaximal, characteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C4⋊Dic11C2211yescharacteristic
14C22×Dic11⋊C4C2211yescharacteristic
15C22×Dic11⋊C4C2211yescharacteristic
16C22×Dic11⋊C4C2212yes—
17C22×C4×Dic11C2212yes—
18C22×C4×Dic11C2212yes—
19C22×C4×Dic11C2211yescharacteristic
20C2×C11×#95C2212yes—
21C2×C11×#95C2211yescharacteristic
22C2×C11×#95C2212yes—
23C2×C11×#95C2211yescharacteristic
24C2×C11⋊#95C2211yescharacteristic
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35C4⋊C4×Dic11—24no—
36#10622263—24no—
37#10622262C418yescomplemented
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2312yes—
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×Dic11C2311yescharacteristic
44C23×Dic11C2311yescharacteristic
45C23×Dic11C2312yes—
46C23×Dic11C2312yes—
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—24no—
51C2×C4⋊Dic11—22no—
52C2×C4⋊Dic11—24no—
53C2×Dic11⋊C4—24no—
54C2×Dic11⋊C4—24no—
55C2×Dic11⋊C4—22no—
56C2×Dic11⋊C4—22no—
57C2×Dic11⋊C4—24no—
58C2×Dic11⋊C4—24no—
59C2×Dic11⋊C4C2×C418yes—
60C2×C4×Dic11—24no—
61C2×C4×Dic11—24no—
62C2×C4×Dic11—24no—
63C2×C4×Dic11—42no—
64C2×C4×Dic11—42no—
65C2×C4×Dic11C2×C418yes—
66C2×C4×Dic11C2×C414yes—
67C2×C4×Dic11D414yes—
68C2×C4×Dic11Q814yes—
69C11×#95—22no—
70C11×#95—24no—
71C11×#95—42no—
72C11×#95C2×C414yes—
73C11⋊#95—22no—
74C11⋊#95—24no—
75C11⋊#95—22no—
76C11⋊#95—22no—
77C11⋊#95—24no—
78C11⋊#95—24no—
79C11⋊#95—24no—
80C11⋊#95—42no—
81C11⋊#95—42no—
82C11⋊#95—42no—
83C11⋊#95C2×C414yes—
84#13955—111nomaximal, Sylow
85C24×C11C2411yescharacteristic
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—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11C22×C414yes—
111C22×C4×C11C22×C412yes—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×Q812yes—
114C22×C4×C11#4114yes—
115C22×Dic11—22no—
116C22×Dic11—21no—
117C22×Dic11—21no—
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—22no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11C22×C414yes—
142C22×Dic11C22×C412yes—
143C22×Dic11C22×C412yes—
144C22×Dic11C2×D412yes—
145C22×Dic11C2×D412yes—
146C22×Dic11C2×Q812yes—
147C22×Dic11C2×Q812yes—
148C22×Dic11#4114yes—
149C22×Dic11#4114yes—
150C22×Dic11#4114yes—
151C11×C4⋊C4—28no—
152C4⋊Dic11—28no—
153Dic11⋊C4—216no—
154Dic11⋊C4—44no—
155Dic11⋊C4—44no—
156C4×Dic11—48no—
157C4×Dic11—48no—
158C4×Dic11C4⋊C4116yes—
159C2×#382—111no—
160C2×C4×C4⋊C4—111no—
161C2×C4×C4⋊C4—111no—
162#1442—111no—
163#1442—111no—
164#1442—111no—
165#1442D1111yescharacteristic
166C4⋊#95—112no—
167C4⋊#95—112no—
168#1434—112no—
169#1434—112no—
170C23×C11C23×C411yescharacteristic
171C23×C11C22×D411yescharacteristic
172C23×C11C22×Q811yescharacteristic
173C23×C11C2×#4112yes—
174C23×C11C2×#4112yes—
175C23×C11C2×#4112yes—
176C23×C11C2×#4112yes—
177C23×C11H(5,𝔽2)11yescharacteristic
178C23×C11H(5,𝔽2)11yescharacteristic
179C23×C112−1+411yescharacteristic
180C23×C112−1+411yescharacteristic
181C2×C4×C11—24no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—24no—
185C2×C4×C11—24no—
186C2×C4×C11—24no—
187C2×C4×C11—24no—
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—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11C2×C4⋊C414yes—
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—24no—
217C2×Dic11—24no—
218C2×Dic11—24no—
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—41no—
231C2×Dic11—41no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11C2×C4⋊C414yes—
241C2×Dic11C2×C4⋊C414yes—
242C2×Dic11#11718yes—
243C2×Dic11#12414yes—
244C2×Dic11#12414yes—
245C2×Dic11#12518yes—
246C22×C4⋊C4—112no—
247C22×C4⋊C4—111no—
248C22×C4⋊C4—111no—
249C22×C4⋊C4—111no—
250C22×C4⋊C4C2×D1111yescharacteristic
251C22×C42—111no—
252C22×C42—112no—
253C22×C42—112no—
254#382—224no—
255C4×C4⋊C4—118no—
256C4×C4⋊C4—224no—
257C2×#95—111no—
258C2×#95—112no—
259C2×#95—111no—
260C2×#95—111no—
261C2×#95—112no—
262C2×#95—112no—
263C2×#95—112no—
264C2×#95—111no—
265C2×#95—112no—
266C2×#95—112no—
267C2×#95—112no—
268C2×#95C2×D1112yes—
269C2×#95C2×D1111yescharacteristic
270C2×#95C2×D1112yes—
271C2×#95C2×D1111yescharacteristic
272C22×C11C22×C4⋊C411yescharacteristic
273C22×C11C2×#11712yes—
274C22×C11C4×#4112yes—
275C22×C11#51811yescharacteristic
276C22×C11#51911yescharacteristic
277C22×C11#52511yescharacteristic
278C22×C11#52511yescharacteristic
279C22×C11C2×#12411yescharacteristic
280C22×C11C2×#12411yescharacteristic
281C22×C11C2×#12512yes—
282C22×C11#53312yes—
283C22×C11#53711yescharacteristic
284C22×C11#53711yescharacteristic
285C22×C11#54411yescharacteristic
286C22×C11#54411yescharacteristic
287C22×C11#55212yes—
288C22×C11#55212yes—
289C22×C11#55312yes—
290C22×C11#55312yes—
291C22×C11#55612yes—
292C22×C11#55612yes—
293C22×C11#55912yes—
294C22×C11#55912yes—
295C4×C11—24no—
296C4×C11—44no—
297C4×C11—44no—
298C4×C11—81no—
299C4×C11—81no—
300Dic11—24no—
301Dic11—44no—
302Dic11—44no—
303Dic11—81no—
304Dic11—81no—
305Dic11#38218yes—
306C23×C4—111no—
307C23×C4—111no—
308C23×C4—112no—
309C23×C4—112no—
310C23×C4—111no—
311C23×C4—111no—
312C23×C4C22×D1111yescharacteristic
313C23×C4C22×D1111yescharacteristic
314C23×C4C22×D1112yes—
315C23×C4C22×D1112yes—
316C23×C4C22×D1111yescharacteristic
317C2×C4⋊C4—22no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—118no—
320C2×C4⋊C4—224no—
321C2×C4⋊C4—224no—
322C2×C4⋊C4—224no—
323C2×C4⋊C4—222no—
324C2×C4⋊C4—222no—
325C2×C4⋊C4—222no—
326C2×C4⋊C4—224no—
327C2×C4⋊C4—224no—
328C2×C42—114no—
329C2×C42—114no—
330C2×C42—114no—
331C2×C42—118no—
332C2×C42—224no—
333C2×C42—224no—
334C2×C42—224no—
335C2×C42—442no—
336C2×C42—442no—
337#95—22no—
338#95—24no—
339#95—42no—
340#95—114no—
341#95—224no—
342#95—224no—
343#95—224no—
344#95—222no—
345#95—222no—
346#95—222no—
347#95—224no—
348#95—442no—
349#95—442no—
350#95—442no—
351#95C4×D1114yes—
352C2×C11C2×#38211yescharacteristic
353C2×C11#229611yescharacteristic
354C2×C11#231611yescharacteristic
355C2×C11#235612yes—
356C2×C11#235712yes—
357C2×C11#256211yescharacteristic
358C2×C11#256211yescharacteristic
359C2×C11#257012yes—
360C2×C11#257012yes—
361C2×C11#259211yescharacteristic
362C2×C11#259211yescharacteristic
363C24C23×D1111yescharacteristic
364C22×C4—22no—
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—22no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—112no—
389C22×C4—112no—
390C22×C4—112no—
391C22×C4—114no—
392C22×C4—114no—
393C22×C4—112no—
394C22×C4—112no—
395C22×C4—112no—
396C22×C4—114no—
397C22×C4—114no—
398C22×C4—221no—
399C22×C4—221no—
400C22×C4—221no—
401C22×C4—221no—
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×C4—222no—
412C22×C4—222no—
413C22×C4—222no—
414C22×C4—221no—
415C22×C4—221no—
416C22×C4—222no—
417C22×C4—221no—
418C22×C4—221no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—221no—
423C22×C4—221no—
424C22×C4C2×C4×D1114yes—
425C22×C4C2×C4×D1112yes—
426C22×C4D4×D1112yes—
427C22×C4#434114yes—
428C22×C4Q8×D1112yes—
429C4⋊C4—28no—
430C4⋊C4—2216no—
431C4⋊C4—228no—
432C4⋊C4—444no—
433C4⋊C4—444no—
434C42—1116no—
435C42—448no—
436C42—448no—
437C11#1395511yescharacteristic, complemented, Sylow
438C23C22×C4×D1111yescharacteristic
439C23C2×D4×D1111yescharacteristic
440C23C2×#434112yes—
441C23#6703711yescharacteristic
442C23C2×Q8×D1111yescharacteristic
443C23#6704011yescharacteristic
444C23#41×D1112yes—
445C23#41×D1112yes—
446C23#41×D1112yes—
447C23#6704211yescharacteristic
448C23#6704311yescharacteristic
449C2×C4—24no—
450C2×C4—22no—
451C2×C4—24no—
452C2×C4—22no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—42no—
477C2×C4—114no—
478C2×C4—118no—
479C2×C4—114no—
480C2×C4—114no—
481C2×C4—118no—
482C2×C4—114no—
483C2×C4—222no—
484C2×C4—222no—
485C2×C4—222no—
486C2×C4—222no—
487C2×C4—222no—
488C2×C4—222no—
489C2×C4—224no—
490C2×C4—224no—
491C2×C4—224no—
492C2×C4—224no—
493C2×C4—224no—
494C2×C4—224no—
495C2×C4—442no—
496C2×C4—442no—
497C2×C4—442no—
498C2×C4—442no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—442no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4—441no—
505C2×C4—441no—
506C2×C4—441no—
507C2×C4—442no—
508C2×C4—441no—
509C2×C4—442no—
510C2×C4—441no—
511C2×C4—441no—
512C2×C4—442no—
513C2×C4C4⋊C4×D1114yes—
514C22C2×C4⋊C4×D1111yescharacteristic
515C22D11×#11712yes—
516C22C4×#434112yes—
517C22#1062307611yescharacteristic
518C22#1062310311yescharacteristic
519C22#1062311711yescharacteristic
520C22#1062313212yes—
521C22#1062313911yescharacteristic
522C22#1062315312yes—
523C22#1062316011yescharacteristic
524C22#1062317212yes—
525C22#1062318112yes—
526C22#1062318711yescharacteristic
527C22#1062319512yes—
528C22D11×#12411yescharacteristic
529C22D11×#12411yescharacteristic
530C22#1062321212yes—
531C22D11×#12512yes—
532C22#1062322011yescharacteristic
533C22#1062322412yes—
534C22#1062323312yes—
535C22#1062324012yes—
536C22#1062326011yescharacteristic
537C4—24no—
538C4—44no—
539C4—44no—
540C4—81no—
541C4—81no—
542C4—118no—
543C4—224no—
544C4—444no—
545C4—444no—
546C4—881no—
547C4—881no—
548C2D11×#38211yescharacteristic
549C2#1307109511yescharacteristic
550C2#1307123111yescharacteristic
551C2#1307157812yes—
552C2#1307158612yes—
553C2#1307377611yescharacteristic
554C2#1307377811yescharacteristic
555C2#1307384312yes—
556C2#1307384512yes—
557C2#1307409811yescharacteristic
558C2#1307410011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1442C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1442D11
hypocenterC11#13955
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
37. #10622262C4semidirect
437. C11#13955semidirect

Maximal subgroups

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

subgroupindex
C2×#106222632
C2×C4⋊C4×Dic112
C2×#106222622
#130668752
#130668732
#130668722
Dic11⋊#952
#130668412
#130668402
C11×#14422
#1395511