Finite Group Databasebeta

← #14760142

Subgroups — #14760142

Order 2816.

980 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622641C211yesmaximal, characteristic
2C2×#10622639C211yesmaximal, characteristic
3C2×C4×#4326C211yesmaximal, characteristic, complemented
4#13071327C211yesmaximal, characteristic
5#13069548C211yesmaximal, characteristic
6#13069374C211yesmaximal, characteristic, complemented
7#13069257C211yesmaximal, characteristic, complemented
8#13069236C211yesmaximal, characteristic
9#13068971C211yesmaximal, characteristic
10#13068957C211yesmaximal, characteristic, complemented
11#13068621C211yesmaximal, characteristic, complemented
12#13068473C211yesmaximal, characteristic, complemented
13#13068449C211yesmaximal, characteristic, complemented
14C4×#66873C211yesmaximal, characteristic
15C11×#2276C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C22×#4325C2211yescharacteristic
21C2×#66928C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C4×C11×C4⋊C4—21no—
25C4×C11×C4⋊C4—21no—
26C4×C11×C4⋊C4—21no—
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C4×C11×C4⋊C4C2211yescharacteristic
30C11×#376—21no—
31C11×#376C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C4×#4326—24no—
35#10622641C418yescomplemented
36#10622639—24no—
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622552C2211yescharacteristic
46#10622548C2211yescharacteristic
47#10622542C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×#66867C2211yescharacteristic
51C2×C4×C11⋊C8C2211yescharacteristic
52#10622283—21no—
53#10622283—21no—
54#10622281—21no—
55#10622281—21no—
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61#10622162C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×Dic22C2311yescharacteristic
66C4×Q8×C11—22no—
67C4×Q8×C11—22no—
68C4×Q8×C11—22no—
69C4×Q8×C11—22no—
70C4×Q8×C11C2×C414yescomplemented
71C4×Q8×C11D414yes—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C42×C11—21no—
79C2×C42×C11—21no—
80C2×C42×C11—21no—
81C2×C42×C11—21no—
82C2×C42×C11—21no—
83C2×C42×C11—21no—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×#4326—22no—
88C2×#4326—22no—
89C2×#4326C2×C414yescomplemented
90C2×#4325—22no—
91C2×#4325—22no—
92C2×#4325C2×C414yes—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×Dic11⋊C4—21no—
103C2×C4×Dic11—21no—
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108#66928—22no—
109#66928C2×C414yes—
110C4×D44—22no—
111C4×D44—22no—
112C4×Dic22—22no—
113C4×Dic22—22no—
114C11×#95—21no—
115C11×#95—21no—
116C11×#95—21no—
117C11×#95D411yescharacteristic
118C11×#95D411yescharacteristic
119C11×#95D411yescharacteristic
120C11×#95D411yescharacteristic
121#66899—22no—
122#66899—22no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125#66874—22no—
126#66874—22no—
127#66874C2×C414yescomplemented
128#66873—22no—
129#66873—22no—
130#66873C2×C414yes—
131#66871—22no—
132#66871—22no—
133C4⋊(C11⋊C8)—22no—
134C4⋊(C11⋊C8)C2×C414yescomplemented
135#66867—22no—
136C4×C11⋊C8—22no—
137#21512—111nomaximal, Sylow
138C23×D11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11C22×C412yes—
143C2×Q8×C11C2×D412yes—
144C2×Q8×C11#4112yes—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2411yescharacteristic
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44C22×C412yes—
165C2×C4×D11—42no—
166C2×C4×D11—81no—
167C2×C4×D11—81no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22C22×C412yes—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—24no—
176C11×C4⋊C4—24no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4C22×C412yes—
181C11×C4⋊C4C2×D412yes—
182C11×C4⋊C4#4112yes—
183C42×C11—24no—
184C42×C11—24no—
185C42×C11—24no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—81no—
189C42×C11—81no—
190C42×C11—81no—
191C42×C11C22×C412yes—
192C42×C11C2×D412yes—
193C42×C11#4112yes—
194C42×C11#4112yes—
195#4326—28no—
196#4325—28no—
197(C2×D11)⋊C4—24no—
198(C2×D11)⋊C4—24no—
199(C2×D11)⋊C4—42no—
200(C2×D11)⋊C4—81no—
201(C2×D11)⋊C4—81no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—81no—
207C4⋊Dic11—81no—
208Dic11⋊C4—42no—
209C4×Dic11—42no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8C22×C412yes—
221C2×C11⋊C8C22×C412yes—
222C2×#464—111no—
223C2×#440—111no—
224C2×C4×Q16—111no—
225#2326—111no—
226#2276D1111yescharacteristic, complemented
227#1983—111no—
228#1947—111no—
229#1928—111no—
230#1925—111no—
231#1880—111no—
232#1878—111no—
233#1803—111no—
234#1768—111no—
235#1763—111no—
236C4×#102—111no—
237C23×C11C22×D411yescharacteristic
238C22×D11—22no—
239C22×D11—41no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—41no—
245Q8×C11—22no—
246Q8×C11—22no—
247Q8×C11—22no—
248Q8×C11C4×D414yes—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11C4×D412yes—
276C2×C4×C11C4×D412yes—
277C2×C4×C11#12112yes—
278C2×C4×C11#12112yes—
279C2×C4×C11C23×C411yescharacteristic
280C2×C4×C11C22×D411yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C2×Dic11—22no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294D44—22no—
295D44—22no—
296D44—41no—
297D44—41no—
298C4×D11—84no—
299Dic22—22no—
300Dic22—22no—
301Dic22—41no—
302Dic22—41no—
303C11⋊C8—22no—
304C11⋊C8—22no—
305C11⋊C8—41no—
306C11⋊C8—41no—
307C22×Q16—111no—
308C22×SD16—111no—
309C2×#124—111no—
310C2×C4×Q8—111no—
311C2×C4×Q8C2×D1111yescharacteristic
312C2×C4×Q8C2×D1111yescharacteristic
313C2×C4×Q8C2×D1111yescharacteristic
314C2×C4×D4—111no—
315#464—118no—
316#440—224no—
317C4×Q16—224no—
318C2×#107—111no—
319C2×#107—111no—
320C2×C4⋊C8—111no—
321C2×C4⋊C8—111no—
322C2×#103—111no—
323C2×#103—111no—
324C2×#103—111no—
325C2×#103—111no—
326C2×#103—111no—
327C2×#102—111no—
328C2×#102—111no—
329C2×#102—111no—
330C2×#97—111no—
331C2×C4×C8—111no—
332#391—111no—
333#390—111no—
334#388—221no—
335#388—221no—
336#385—221no—
337#385—221no—
338#384—111no—
339C4×C4⋊C4—21no—
340C4×C4⋊C4—21no—
341C4×C4⋊C4—21no—
342C4×C4⋊C4C2×D1111yescharacteristic
343C4×C4⋊C4C2×D1111yescharacteristic
344C4×C4⋊C4C2×D1111yescharacteristic
345#376—21no—
346#376C2×D1111yescharacteristic
347#340—111no—
348#340—111no—
349#340—111no—
350#340—111no—
351#336—111no—
352#336—111no—
353C22×C11C2×C4×D411yescharacteristic
354C22×C11C2×#12111yescharacteristic
355C22×C11#52511yescharacteristic
356C22×C11#57611yescharacteristic
357C22×C11#57711yescharacteristic
358C22×C11#57811yescharacteristic
359C22×C11#57811yescharacteristic
360C2×D11—42no—
361C2×D11—42no—
362C2×D11—42no—
363C2×D11—81no—
364C2×D11—81no—
365C2×D11—81no—
366C2×D11—81no—
367C4×C11—22no—
368C4×C11—22no—
369C4×C11—22no—
370C4×C11—22no—
371C4×C11—24no—
372C4×C11—41no—
373C4×C11—41no—
374C4×C11—42no—
375C4×C11—42no—
376C4×C11—42no—
377C4×C11C2×C4×D411yescharacteristic
378C4×C11C4×#4111yescharacteristic
379C4×C11#52911yescharacteristic
380C4×C11#53211yescharacteristic
381Dic11—42no—
382Dic11—81no—
383Dic11—81no—
384C22×Q8—111no—
385C22×Q8C22×D1111yescharacteristic
386C22×D4—111no—
387C23×C4—221no—
388C2×Q16—114no—
389C2×Q16—222no—
390C2×Q16—222no—
391C2×SD16—114no—
392C2×SD16—222no—
393C2×SD16—222no—
394C22×C8—111no—
395C22×C8—111no—
396C22×C8—111no—
397C22×C8—111no—
398#124—114no—
399#124—222no—
400C4×Q8—22no—
401C4×Q8—22no—
402C4×Q8—22no—
403C4×Q8—22no—
404C4×Q8—222no—
405C4×Q8—222no—
406C4×Q8C4×D1114yescomplemented
407C4×Q8D4414yes—
408C4×D4—222no—
409C4×D4—222no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C4⋊C4C22×D1111yescharacteristic
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C42—21no—
427C2×C42—21no—
428C2×C42—21no—
429C2×C42—21no—
430C2×C42—21no—
431C2×C42—21no—
432C2×C42—221no—
433C2×C42C22×D1111yescharacteristic
434C2×C42C22×D1111yescharacteristic
435C2×C42C22×D1111yescharacteristic
436#107—222no—
437#107—222no—
438C4⋊C8—114no—
439C4⋊C8—222no—
440#103—114no—
441#103—222no—
442#103—222no—
443#103—222no—
444#103—222no—
445#102—114no—
446#102—222no—
447#102—222no—
448#97—222no—
449C4×C8—222no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—221no—
454#95—221no—
455#95C22⋊D1111yescharacteristic
456#95C22⋊D1111yescharacteristic
457#95C22⋊D1111yescharacteristic
458#95C22⋊D1111yescharacteristic
459C2×C11C4×#12111yescharacteristic
460C2×C11#294711yescharacteristic
461C2×C11#295111yescharacteristic
462C2×C11#304411yescharacteristic
463C2×C11#304511yescharacteristic
464C2×C11#312111yescharacteristic
465C2×C11#312411yescharacteristic
466D11—82no—
467C24—221no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—112no—
472C2×Q8—221no—
473C2×Q8—221no—
474C2×Q8—221no—
475C2×Q8—221no—
476C2×Q8—221no—
477C2×Q8C2×C4×D1112yes—
478C2×Q8C2×D4412yes—
479C2×Q8#433912yes—
480C2×D4—112no—
481C2×D4—221no—
482C2×D4—221no—
483C2×D4—221no—
484C2×D4—221no—
485C2×D4—221no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—442no—
494C22×C4—881no—
495C22×C4—881no—
496C22×C4C2×C22⋊D1111yescharacteristic
497C22×C4C2×C22⋊D1111yescharacteristic
498C22×C4C2×C22⋊D1111yescharacteristic
499C22×C4C2×C22⋊D1111yescharacteristic
500C22×C4C2×C22⋊D1111yescharacteristic
501C22×C4C2×C22⋊D1111yescharacteristic
502C22×C4C23×D1111yescharacteristic
503Q16—228no—
504SD16—228no—
505C2×C8—112no—
506C2×C8—112no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C4⋊C4—24no—
518C4⋊C4—24no—
519C4⋊C4—24no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—442no—
528C4⋊C4—881no—
529C4⋊C4—881no—
530C4⋊C4C2×C4×D1112yes—
531C4⋊C4C2×D4412yes—
532C4⋊C4#433912yes—
533C22⋊C4—224no—
534C22⋊C4—224no—
535C22⋊C4—442no—
536C22⋊C4—881no—
537C22⋊C4—881no—
538C42—24no—
539C42—24no—
540C42—24no—
541C42—21no—
542C42—21no—
543C42—81no—
544C42—81no—
545C42—81no—
546C42—442no—
547C42C2×C4×D1112yes—
548C42C2×D4412yes—
549C42#433912yes—
550C42#433912yes—
551C11#2151211yescharacteristic, complemented, Sylow
552C23—222no—
553C23—441no—
554C23—441no—
555C23—441no—
556C23—441no—
557C23—441no—
558C23—441no—
559C23C22×C22⋊D1111yescharacteristic
560Q8—22no—
561Q8—22no—
562Q8—22no—
563Q8—222no—
564Q8—222no—
565Q8—441no—
566Q8—441no—
567Q8C4×D4414yes—
568D4—222no—
569D4—222no—
570D4—441no—
571D4—441no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—222no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—884no—
608C2×C4C4×C22⋊D1112yes—
609C2×C4C4×C22⋊D1112yes—
610C2×C4#6698312yes—
611C2×C4#6698312yes—
612C2×C4C22×C4×D1111yescharacteristic
613C2×C4C22×D4411yescharacteristic
614C2×C4C2×#433911yescharacteristic
615C2×C4C2×#433911yescharacteristic
616C2×C4C2×#433911yescharacteristic
617C2×C4C2×#433911yescharacteristic
618C8—222no—
619C8—222no—
620C8—441no—
621C8—441no—
622C22—442no—
623C22—442no—
624C22—442no—
625C22—881no—
626C22—881no—
627C22—881no—
628C22—881no—
629C22C2×C4×C22⋊D1111yescharacteristic
630C22C2×#6698311yescharacteristic
631C22#1062332211yescharacteristic
632C22#1062336611yescharacteristic
633C22#1062336811yescharacteristic
634C22#1062336911yescharacteristic
635C22#1062336911yescharacteristic
636C4—24no—
637C4—22no—
638C4—22no—
639C4—22no—
640C4—22no—
641C4—41no—
642C4—41no—
643C4—42no—
644C4—42no—
645C4—42no—
646C4—442no—
647C4—881no—
648C4—881no—
649C4C2×C4×D4411yescharacteristic
650C4C4×#433911yescharacteristic
651C4#1062300811yescharacteristic
652C4#1062301011yescharacteristic
653C2—882no—
654C2C4×#6698311yescharacteristic
655C2#1307745911yescharacteristic
656C2#1307748911yescharacteristic
657C2#1307814611yescharacteristic
658C2#1307815511yescharacteristic
659C2#1307884511yescharacteristic
660C2#1307887811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2276C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#2276D11
hypocenterC11#21512
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #2276

Complements

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

NH ≅ G/Ntype
3. C2×C4×#4326C2semidirect
6. #13069374C2semidirect
7. #13069257C2semidirect
10. #13068957C2semidirect
11. #13068621C2semidirect
12. #13068473C2semidirect
13. #13068449C2semidirect
15. C11×#2276C2semidirect
35. #10622641C4semidirect
70. C4×Q8×C11C2×C4semidirect
89. C2×#4326C2×C4semidirect
127. #66874C2×C4semidirect
134. C4⋊(C11⋊C8)C2×C4semidirect
226. #2276D11semidirect
406. C4×Q8C4×D11semidirect
551. C11#21512semidirect

Maximal subgroups

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

subgroupindex
C2×#106226412
C2×#106226392
C2×C4×#43262
#130713272
#130695482
#130693742
#130692572
#130692362
#130689712
#130689572
#130686212
#130684732
#130684492
C4×#668732
C11×#22762
#2151211