Finite Group Databasebeta

← #14680973

Subgroups — #14680973

Order 2816.

2150 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D11C211yesmaximal, characteristic
2C2×#10622825C211yesmaximal, characteristic, complemented
3#13066870C212yesmaximal, complemented
4#13066863C212yesmaximal, complemented
5#13066862C212yesmaximal, complemented
6#13066855C212yesmaximal
7#13066840C212yesmaximal, complemented
8(C2×D11)⋊#95C212yesmaximal, complemented
9C2×C11×#381C211yesmaximal, characteristic, complemented
10C24×C4×C11C2211yescharacteristic
11C23×C22⋊D11C2211yescharacteristic
12C23×C4×D11C2211yescharacteristic
13C22×C11×C22⋊C4C2212yes—
14C22×C22⋊Dic11C2211yescharacteristic
15C22×C22⋊Dic11C2212yes—
16C2×C4×C22⋊D11—24no—
17C2×C4×C22⋊D11—24no—
18C2×C4×C22⋊D11C418yescomplemented
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2214yes—
21C22×C4⋊Dic11C2212yes—
22C22×Dic11⋊C4C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24C11×#381—24no—
25C2×C11×#95C2212yes—
26C2×C11×#95C2212yes—
27#10622825—24no—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2214yes—
30C2×C11⋊#95C2214yes—
31C2×C11⋊#95C2214yes—
32C25×C11C2311yescharacteristic
33C24×D11C2311yescharacteristic
34C23×C4×C11—44no—
35C23×C4×C11C2×C414yes—
36C23×C4×C11D414yes—
37C23×C4×C11D414yes—
38C23×C4×C11C2314yes—
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C22×C22⋊D11—22no—
42C22×C22⋊D11—22no—
43C22×C22⋊D11—24no—
44C22×C22⋊D11—24no—
45C22×C22⋊D11C2×C414yes—
46C23×Dic11C2314yes—
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C22×C4×D11—22no—
51C22×C4×D11—22no—
52C22×C4×D11—44no—
53C22×C4×D11C2×C414yes—
54C2×C11×C22⋊C4—24no—
55C2×C11×C22⋊C4—44no—
56C2×C22⋊Dic11—22no—
57C2×C22⋊Dic11—22no—
58C2×C22⋊Dic11—24no—
59C2×C22⋊Dic11—44no—
60C2×C22⋊Dic11C2×C414yes—
61C4×C22⋊D11—232no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4—28no—
65C2×(C2×D11)⋊C4—44no—
66C2×(C2×D11)⋊C4—44no—
67C2×(C2×D11)⋊C4C2×C414yes—
68C2×C4⋊Dic11—24no—
69C2×C4⋊Dic11—44no—
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4—22no—
72C2×Dic11⋊C4C2×C414yes—
73C2×C4×Dic11—22no—
74C2×C4×Dic11—22no—
75C2×C4×Dic11C2×C414yes—
76C11×#95—24no—
77C11×#95—24no—
78C11⋊#95—24no—
79C11⋊#95—28no—
80C11⋊#95—44no—
81C11⋊#95—44no—
82#14344—111nomaximal, Sylow
83C24×C11—22no—
84C24×C11—22no—
85C24×C11—22no—
86C24×C11—24no—
87C24×C11—22no—
88C24×C11C22×C412yes—
89C24×C11C2×D412yes—
90C24×C11C2×D412yes—
91C24×C11C2411yescharacteristic
92C23×D11—21no—
93C23×D11—21no—
94C23×D11—22no—
95C23×D11—22no—
96C23×D11—24no—
97C23×D11—22no—
98C23×D11C22×C412yes—
99C23×D11#4114yes—
100C22×C4×C11—24no—
101C22×C4×C11—24no—
102C22×C4×C11—24no—
103C22×C4×C11—24no—
104C22×C4×C11—24no—
105C22×C4×C11—24no—
106C22×C4×C11—24no—
107C22×C4×C11—24no—
108C22×C4×C11—24no—
109C22×C4×C11—48no—
110C22×C4×C11—48no—
111C22×C4×C11—48no—
112C22×C4×C11C22⋊C4116yescomplemented
113C22×C4×C11C22×C412yes—
114C22×C4×C11C22×C412yes—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D412yes—
119C2×C22⋊D11—216no—
120C2×C22⋊D11—216no—
121C2×C22⋊D11—28no—
122C2×C22⋊D11—28no—
123C2×C22⋊D11—28no—
124C22×Dic11—21no—
125C22×Dic11—21no—
126C22×Dic11—21no—
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—24no—
131C22×Dic11—22no—
132C22×Dic11—24no—
133C22×Dic11—24no—
134C22×Dic11—22no—
135C22×Dic11—24no—
136C22×Dic11—24no—
137C22×Dic11—24no—
138C22×Dic11—24no—
139C22×Dic11—24no—
140C22×Dic11—22no—
141C22×Dic11C22×C412yes—
142C22×Dic11C22×C412yes—
143C22×Dic11C22×C412yes—
144C22×Dic11#4114yes—
145C2×C4×D11—28no—
146C2×C4×D11—48no—
147C2×C4×D11—48no—
148C2×C4×D11—48no—
149C11×C22⋊C4—48no—
150C22⋊Dic11—28no—
151C22⋊Dic11—48no—
152(C2×D11)⋊C4—28no—
153(C2×D11)⋊C4—416no—
154C4⋊Dic11—48no—
155Dic11⋊C4—28no—
156C4×Dic11—28no—
157C22×C4×D4—111no—
158C2×#381D1111yescharacteristic, complemented
159C2×#380—111no—
160#1441—112no—
161#1440—112no—
162#1439—112no—
163#1438—112no—
164#1434—112no—
165C22⋊#95—112no—
166C23×C11—22no—
167C23×C11—22no—
168C23×C11—24no—
169C23×C11—24no—
170C23×C11—24no—
171C23×C11—24no—
172C23×C11—24no—
173C23×C11—24no—
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—24no—
177C23×C11—44no—
178C23×C11—44no—
179C23×C11—44no—
180C23×C11—44no—
181C23×C11C2×C22⋊C414yes—
182C23×C11C23×C411yescharacteristic
183C23×C11C22×D411yescharacteristic
184C23×C11C22×D411yescharacteristic
185C23×C11C2×#4112yes—
186C23×C11C2×#4112yes—
187C23×C11H(5,𝔽2)14yes—
188C23×C11H(5,𝔽2)12yes—
189C23×C112−1+412yes—
190C22×D11—22no—
191C22×D11—22no—
192C22×D11—24no—
193C22×D11—24no—
194C22×D11—24no—
195C22×D11—24no—
196C22×D11—28no—
197C22×D11—28no—
198C22×D11—42no—
199C22×D11—42no—
200C22×D11—41no—
201C22×D11—41no—
202C22×D11—42no—
203C22×D11—44no—
204C22×D11—44no—
205C22×D11#11714yes—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—416no—
213C2×C4×C11—44no—
214C2×C4×C11—44no—
215C2×C4×C11—44no—
216C2×C4×C11—44no—
217C2×C4×C11—44no—
218C2×C4×C11—44no—
219C2×C4×C11—44no—
220C2×C4×C11C2×C22⋊C414yes—
221C2×C4×C11C2×C22⋊C414yes—
222C22⋊D11—232no—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—24no—
226C2×Dic11—24no—
227C2×Dic11—22no—
228C2×Dic11—22no—
229C2×Dic11—24no—
230C2×Dic11—24no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235C2×Dic11—42no—
236C2×Dic11—44no—
237C2×Dic11—44no—
238C2×Dic11—44no—
239C2×Dic11—44no—
240C2×Dic11—44no—
241C2×Dic11—44no—
242C2×Dic11—44no—
243C2×Dic11#11714yes—
244C4×D11—416no—
245C23×D4—111no—
246C24×C4—111no—
247C24×C4C2×D1111yescharacteristic
248C2×C4×D4—118no—
249C2×C4×D4—224no—
250C2×C4×D4—224no—
251C22×C4⋊C4—111no—
252C22×C4⋊C4—112no—
253C22×C22⋊C4—111no—
254C22×C22⋊C4—111no—
255C22×C22⋊C4—112no—
256C22×C22⋊C4—114no—
257C22×C22⋊C4C2×D1112yes—
258C22×C42—111no—
259#381—24no—
260#380—224no—
261C2×#95—112no—
262C2×#95—114no—
263C2×#95—114no—
264C2×#95—114no—
265C2×#95C2×D1112yes—
266C2×#95C2×D1112yes—
267C22×C11—24no—
268C22×C11—24no—
269C22×C11—24no—
270C22×C11—44no—
271C22×C11—44no—
272C22×C11—48no—
273C22×C11—44no—
274C22×C11—44no—
275C22×C11C22×C22⋊C411yescharacteristic
276C22×C11C2×#11711yescharacteristic
277C22×C11C2×#11711yescharacteristic
278C22×C11#51812yes—
279C22×C11#52012yes—
280C22×C11#52512yes—
281C22×C11#52512yes—
282C22×C11#53412yes—
283C22×C11#53412yes—
284C22×C11#53511yescharacteristic
285C22×C11#53611yescharacteristic
286C22×C11#53712yes—
287C22×C11#53814yes—
288C22×C11#53914yes—
289C22×C11#54014yes—
290C22×C11#54214yes—
291C2×D11—28no—
292C2×D11—24no—
293C2×D11—42no—
294C2×D11—42no—
295C2×D11—44no—
296C2×D11—48no—
297C2×D11—44no—
298C2×D11—44no—
299C4×C11—24no—
300C4×C11—24no—
301C4×C11—84no—
302Dic11—24no—
303Dic11—42no—
304Dic11—42no—
305Dic11—84no—
306C25—111no—
307C25C22×D1111yescharacteristic
308C22×D4—114no—
309C22×D4—224no—
310C22×D4—224no—
311C22×D4—222no—
312C22×D4—222no—
313C23×C4—44no—
314C23×C4—111no—
315C23×C4—111no—
316C23×C4—111no—
317C23×C4—114no—
318C23×C4—114no—
319C23×C4—222no—
320C23×C4—222no—
321C23×C4—444no—
322C23×C4C4×D1114yes—
323C23×C4D4414yes—
324C23×C4C22⋊D1114yes—
325C23×C4C22×D1114yes—
326C23×C4C22×D1111yescharacteristic
327C23×C4C22×D1111yescharacteristic
328C4×D4—2232no—
329C2×C4⋊C4—114no—
330C2×C4⋊C4—222no—
331C2×C4⋊C4—222no—
332C2×C4⋊C4—224no—
333C2×C4⋊C4—444no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—114no—
337C2×C22⋊C4—114no—
338C2×C22⋊C4—222no—
339C2×C22⋊C4—222no—
340C2×C22⋊C4—222no—
341C2×C22⋊C4—222no—
342C2×C22⋊C4—228no—
343C2×C22⋊C4—224no—
344C2×C22⋊C4—444no—
345C2×C22⋊C4—444no—
346C2×C22⋊C4—444no—
347C2×C42—114no—
348C2×C42—222no—
349C2×C42—222no—
350#95—24no—
351#95—24no—
352#95—228no—
353#95—224no—
354#95—444no—
355#95—444no—
356C2×C11—44no—
357C2×C11#228011yescharacteristic
358C2×C11#230811yescharacteristic
359C2×C11#231111yescharacteristic
360C2×C11#231812yes—
361C2×C11#231912yes—
362C2×C11#263014yes—
363C2×C11#263512yes—
364C2×C11#263812yes—
365D11—44no—
366C24—24no—
367C24—22no—
368C24—22no—
369C24—22no—
370C24—22no—
371C24—112no—
372C24—114no—
373C24—221no—
374C24—224no—
375C24—222no—
376C24—222no—
377C24—222no—
378C24—221no—
379C24C2×C4×D1112yes—
380C24C2×D4412yes—
381C24C2×C22⋊D1112yes—
382C24C23×D1111yescharacteristic
383C2×D4—228no—
384C2×D4—228no—
385C2×D4—2216no—
386C2×D4—2216no—
387C2×D4—228no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—24no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—48no—
398C22×C4—48no—
399C22×C4—48no—
400C22×C4—112no—
401C22×C4—114no—
402C22×C4—112no—
403C22×C4—112no—
404C22×C4—221no—
405C22×C4—222no—
406C22×C4—221no—
407C22×C4—221no—
408C22×C4—221no—
409C22×C4—224no—
410C22×C4—222no—
411C22×C4—222no—
412C22×C4—221no—
413C22×C4—221no—
414C22×C4—228no—
415C22×C4—224no—
416C22×C4—224no—
417C22×C4—224no—
418C22×C4—224no—
419C22×C4—224no—
420C22×C4—224no—
421C22×C4—224no—
422C22×C4—448no—
423C22×C4—448no—
424C22×C4—448no—
425C22×C4(C2×D11)⋊C4116yescomplemented
426C22×C4C2×C4×D1112yes—
427C22×C4C2×C4×D1112yes—
428C22×C4C2×D4412yes—
429C22×C4C2×D4412yes—
430C22×C4C2×C22⋊D1112yes—
431C22×C4C2×C22⋊D1112yes—
432C4⋊C4—228no—
433C4⋊C4—448no—
434C22⋊C4—48no—
435C22⋊C4—228no—
436C22⋊C4—228no—
437C22⋊C4—4416no—
438C22⋊C4—448no—
439C42—228no—
440C11#1434411yescharacteristic, complemented, Sylow
441C23—24no—
442C23—24no—
443C23—22no—
444C23—22no—
445C23—24no—
446C23—24no—
447C23—22no—
448C23—22no—
449C23—24no—
450C23—24no—
451C23—24no—
452C23—44no—
453C23—44no—
454C23—44no—
455C23—44no—
456C23—114no—
457C23—224no—
458C23—222no—
459C23—224no—
460C23—224no—
461C23—222no—
462C23—224no—
463C23—228no—
464C23—228no—
465C23—442no—
466C23—441no—
467C23—441no—
468C23—442no—
469C23—442no—
470C23—444no—
471C23—444no—
472C23C2×(C2×D11)⋊C414yes—
473C23C22×C4×D1111yescharacteristic
474C23C22×D4411yescharacteristic
475C23#6703714yes—
476C23#41×D1112yes—
477C23#41×D1112yes—
478C23#6704212yes—
479C23#6704312yes—
480C23C22×C22⋊D1111yescharacteristic
481D4—2232no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—416no—
489C2×C4—44no—
490C2×C4—44no—
491C2×C4—44no—
492C2×C4—44no—
493C2×C4—44no—
494C2×C4—44no—
495C2×C4—44no—
496C2×C4—114no—
497C2×C4—222no—
498C2×C4—224no—
499C2×C4—222no—
500C2×C4—224no—
501C2×C4—224no—
502C2×C4—224no—
503C2×C4—222no—
504C2×C4—222no—
505C2×C4—4416no—
506C2×C4—442no—
507C2×C4—441no—
508C2×C4—441no—
509C2×C4—442no—
510C2×C4—442no—
511C2×C4—444no—
512C2×C4—444no—
513C2×C4—444no—
514C2×C4—444no—
515C2×C4—444no—
516C2×C4—444no—
517C2×C4—444no—
518C2×C4C2×(C2×D11)⋊C414yes—
519C2×C4C2×(C2×D11)⋊C414yes—
520C22—24no—
521C22—24no—
522C22—24no—
523C22—48no—
524C22—44no—
525C22—44no—
526C22—44no—
527C22—44no—
528C22—228no—
529C22—224no—
530C22—448no—
531C22—444no—
532C22—442no—
533C22—442no—
534C22—444no—
535C22—444no—
536C22#1062301712yes—
537C22#1062302412yes—
538C22D11×#11711yescharacteristic
539C22D11×#11711yescharacteristic
540C22#1062305412yes—
541C22#1062305512yes—
542C22#1062305611yescharacteristic
543C22#1062305711yescharacteristic
544C22#1062318814yes—
545C22#1062319114yes—
546C22#1062319314yes—
547C22#1062319414yes—
548C22C22×(C2×D11)⋊C411yescharacteristic
549C22#1062333512yes—
550C22#1062335912yes—
551C22#1062336412yes—
552C4—24no—
553C4—24no—
554C4—84no—
555C4—224no—
556C4—442no—
557C4—442no—
558C4—884no—
559C2—44no—
560C2—444no—
561C2#1307099511yescharacteristic
562C2#1307119111yescharacteristic
563C2#1307120411yescharacteristic
564C2#1307124512yes—
565C2#1307125612yes—
566C2#1307445514yes—
567C2#1307450312yes—
568C2#1307453612yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#381C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#381D11
hypocenterC11#14344
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
2. C2×#10622825C2semidirect
3. #13066870C2semidirect
4. #13066863C2semidirect
5. #13066862C2semidirect
7. #13066840C2semidirect
8. (C2×D11)⋊#95C2semidirect
9. C2×C11×#381C2semidirect
18. C2×C4×C22⋊D11C4semidirect
112. C22×C4×C11C22⋊C4semidirect
158. C2×#381D11semidirect
425. C22×C4(C2×D11)⋊C4semidirect
440. C11#14344semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D112
C2×#106228252
#130668702
#130668632
#130668622
#130668552
#130668402
(C2×D11)⋊#952
C2×C11×#3812
#1434411