Finite Group Databasebeta

← #14760143

Subgroups — #14760143

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×#10622777C211yesmaximal, characteristic
2C2×Q16×Dic11C211yesmaximal, characteristic, complemented
3#13071329C211yesmaximal, characteristic
4#13070981C211yesmaximal, characteristic, complemented
5#13069549C211yesmaximal, characteristic
6#13069375C211yesmaximal, characteristic, complemented
7#13069259C211yesmaximal, characteristic, complemented
8#13069238C211yesmaximal, characteristic
9#13068973C211yesmaximal, characteristic
10#13068959C211yesmaximal, characteristic, complemented
11#13068621C211yesmaximal, characteristic, complemented
12#13068475C211yesmaximal, characteristic, complemented
13#13068448C211yesmaximal, characteristic, complemented
14#102×Dic11C211yesmaximal, characteristic
15C2×C11×#464C211yesmaximal, characteristic
16C22×C11×Q16C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C2×C11×#124C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C2×Q8×Dic11C2211yescharacteristic
23C2×D4×Dic11C2211yescharacteristic
24C11×#464C418yescomplemented
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28#10622843C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33#10622834C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36Q16×Dic11—24no—
37#10622777—24no—
38C2×#66882C2211yescharacteristic
39C2×#66882C2211yescharacteristic
40C2×#66879C2211yescharacteristic
41C2×C8×Dic11C2211yescharacteristic
42C4⋊C4×Dic11—21no—
43C4⋊C4×Dic11—21no—
44C4⋊C4×Dic11C2211yescharacteristic
45C4⋊C4×Dic11C2211yescharacteristic
46#10622564—21no—
47#10622564—21no—
48#10622563—21no—
49#10622563—21no—
50#10622548C2211yescharacteristic
51C4×C4⋊Dic11—21no—
52C4×C4⋊Dic11C2211yescharacteristic
53#10622545—21no—
54#10622545C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×D4×C11C2311yescharacteristic
65C23×Dic11—21no—
66C2×C11×Q16—22no—
67C2×C11×Q16—22no—
68C2×C11×Q16C2×C414yescomplemented
69C2×C11×SD16—22no—
70C2×C11×SD16—22no—
71C2×C11×SD16C2×C414yes—
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C11×#124—22no—
75C11×#124C2×C414yes—
76C4×Q8×C11—22no—
77C4×Q8×C11C2×C414yescomplemented
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C42×C11—21no—
83C2×C42×C11C2311yescharacteristic
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—21no—
87Q8×Dic11—22no—
88Q8×Dic11—22no—
89Q8×Dic11—22no—
90Q8×Dic11—22no—
91Q8×Dic11—22no—
92Q8×Dic11D414yes—
93D4×Dic11—22no—
94D4×Dic11—22no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4×Dic11—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11—21no—
108C2×C4×Dic11—21no—
109C2×C4×Dic11—21no—
110C2×C4×Dic11C2311yescharacteristic
111C2×C4×Dic11C2311yescharacteristic
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114C11×C4⋊C8C2×C414yescomplemented
115C11×#103C2×C414yescomplemented
116C11×#102C2×C414yes—
117#66899—22no—
118#66899—22no—
119#66899—22no—
120#66899—22no—
121#66896—22no—
122#66896—22no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95D411yescharacteristic
129C11⋊#95D411yescharacteristic
130C11⋊#95D411yescharacteristic
131C11⋊#95D411yescharacteristic
132#66882—22no—
133#66882—22no—
134#66879—22no—
135C8×Dic11—22no—
136C4⋊(C11⋊C8)—22no—
137#21512—111nomaximal, Sylow
138C24×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11C22×C412yes—
148C2×Q8×C11C22×C412yes—
149C2×Q8×C11C2×D412yes—
150C2×Q8×C11#4112yes—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11C22×C412yes—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2411yescharacteristic
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—42no—
168C22×Dic11—81no—
169C22×Dic11—81no—
170C22×Dic11C2×D411yescharacteristic
171C22×Dic11C2×D411yescharacteristic
172C22×Dic11C2×D411yescharacteristic
173C22×Dic11C2×D411yescharacteristic
174C11×Q16—28no—
175C11×SD16—28no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11C22×C412yes—
181C2×C8×C11C22×C412yes—
182C11×C4⋊C4—24no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4C22×C412yes—
185C11×C22⋊C4—24no—
186C11×C22⋊C4—24no—
187C42×C11—24no—
188C42×C11C22×C412yes—
189C42×C11#4112yes—
190C22⋊Dic11—42no—
191C22⋊Dic11—81no—
192C22⋊Dic11—81no—
193C4⋊Dic11—24no—
194C4⋊Dic11—24no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—42no—
202C4⋊Dic11—81no—
203C4⋊Dic11—81no—
204C4⋊Dic11C2×D412yes—
205C4⋊Dic11#4112yes—
206C4×Dic11—24no—
207C4×Dic11—24no—
208C4×Dic11—21no—
209C4×Dic11—21no—
210C4×Dic11—42no—
211C4×Dic11—81no—
212C4×Dic11—81no—
213C4×Dic11—81no—
214C4×Dic11C2×D412yes—
215C4×Dic11#4112yes—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×#464D1111yescharacteristic
223C2×#440—111no—
224C2×C4×Q16—111no—
225#2326—111no—
226#2276—111no—
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×C11—22no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11C22×D411yescharacteristic
245Q8×C11—22no—
246Q8×C11—22no—
247Q8×C11—22no—
248Q8×C11—22no—
249Q8×C11—22no—
250Q8×C11—41no—
251Q8×C11—41no—
252Q8×C11C4×D414yes—
253D4×C11—22no—
254D4×C11—22no—
255D4×C11—41no—
256D4×C11—41no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11C4×D412yes—
271C2×C4×C11C4×D412yes—
272C2×C4×C11C23×C411yescharacteristic
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—22no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—22no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—84no—
301C2×Dic11#12112yes—
302C2×Dic11#12112yes—
303C8×C11—22no—
304C8×C11—22no—
305C11⋊C8—41no—
306C11⋊C8—41no—
307C22×Q16C2×D1111yescharacteristic
308C22×SD16C2×D1111yescharacteristic
309C2×#124C2×D1111yescharacteristic
310C2×C4×Q8—111no—
311C2×C4×Q8—111no—
312C2×C4×Q8—111no—
313C2×C4×Q8C2×D1111yescharacteristic
314C2×C4×D4—111no—
315#464Dic1118yescomplemented
316#440—224no—
317C4×Q16—224no—
318C2×#107—111no—
319C2×#107—111no—
320C2×C4⋊C8—111no—
321C2×C4⋊C8C2×D1111yescharacteristic
322C2×#103—111no—
323C2×#103—111no—
324C2×#103—111no—
325C2×#103—111no—
326C2×#103C2×D1111yescharacteristic
327C2×#102—111no—
328C2×#102—111no—
329C2×#102C2×D1111yescharacteristic
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—111no—
340C4×C4⋊C4—111no—
341C4×C4⋊C4—111no—
342C4×C4⋊C4—221no—
343C4×C4⋊C4—221no—
344C4×C4⋊C4—221no—
345#376—111no—
346#376—221no—
347#340—111no—
348#340—111no—
349#340—111no—
350#340—111no—
351#336—111no—
352#336—111no—
353C22×C11—42no—
354C22×C11—42no—
355C22×C11—42no—
356C22×C11—81no—
357C22×C11—81no—
358C22×C11—81no—
359C22×C11—81no—
360C22×C11C2×C4×D411yescharacteristic
361C22×C11C2×#12111yescharacteristic
362C22×C11#52511yescharacteristic
363C22×C11#57611yescharacteristic
364C22×C11#57711yescharacteristic
365C22×C11#57811yescharacteristic
366C22×C11#57811yescharacteristic
367C4×C11—22no—
368C4×C11—22no—
369C4×C11—24no—
370C4×C11—42no—
371C4×C11—42no—
372C4×C11C2×C4×D411yescharacteristic
373C4×C11C4×#4111yescharacteristic
374C4×C11#52911yescharacteristic
375C4×C11#53211yescharacteristic
376Dic11—22no—
377Dic11—22no—
378Dic11—41no—
379Dic11—41no—
380Dic11—42no—
381Dic11—42no—
382Dic11—81no—
383Dic11—81no—
384C22×Q8C22×D1111yescharacteristic
385C22×Q8C22×D1111yescharacteristic
386C22×D4C22×D1111yescharacteristic
387C23×C4—221no—
388C2×Q16—22no—
389C2×Q16—22no—
390C2×Q16C2×Dic1114yescomplemented
391C2×SD16—22no—
392C2×SD16—22no—
393C2×SD16C2×Dic1114yes—
394C22×C8—111no—
395C22×C8—111no—
396C22×C8C22×D1111yescharacteristic
397C22×C8C22×D1111yescharacteristic
398#124—22no—
399#124C2×Dic1114yes—
400C4×Q8—22no—
401C4×Q8—114no—
402C4×Q8—222no—
403C4×Q8—222no—
404C4×Q8—222no—
405C4×Q8—222no—
406C4×Q8—222no—
407C4×Q8C2×Dic1114yescomplemented
408C4×D4—222no—
409C4×D4—222no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4C22×D1111yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C42—21no—
427C2×C42—111no—
428C2×C42—111no—
429C2×C42—221no—
430C2×C42—221no—
431C2×C42—221no—
432C2×C42—221no—
433C2×C42—221no—
434C2×C42—221no—
435C2×C42C22×D1111yescharacteristic
436#107—222no—
437#107—222no—
438C4⋊C8—222no—
439C4⋊C8C2×Dic1114yescomplemented
440#103—222no—
441#103—222no—
442#103—222no—
443#103—222no—
444#103C2×Dic1114yescomplemented
445#102—222no—
446#102—222no—
447#102C2×Dic1114yes—
448#97—222no—
449C4×C8—222no—
450#95—111no—
451#95—111no—
452#95—111no—
453#95—111no—
454#95—221no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459C2×C11—82no—
460C2×C11C4×#12111yescharacteristic
461C2×C11#294711yescharacteristic
462C2×C11#295111yescharacteristic
463C2×C11#304411yescharacteristic
464C2×C11#304511yescharacteristic
465C2×C11#312111yescharacteristic
466C2×C11#312411yescharacteristic
467C24—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8D4×D1112yes—
477C2×Q8#434112yes—
478C2×Q8C22×Dic1112yes—
479C2×Q8C22×Dic1112yes—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4C22×Dic1112yes—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—111no—
490C22×C4—111no—
491C22×C4—111no—
492C22×C4—111no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—442no—
498C22×C4—881no—
499C22×C4—881no—
500C22×C4D4×D1111yescharacteristic
501C22×C4D4×D1111yescharacteristic
502C22×C4C23×D1111yescharacteristic
503Q16—28no—
504SD16—28no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8C22×Dic1112yes—
516C2×C8C22×Dic1112yes—
517C4⋊C4—24no—
518C4⋊C4—21no—
519C4⋊C4—112no—
520C4⋊C4—112no—
521C4⋊C4—224no—
522C4⋊C4—224no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—442no—
530C4⋊C4—881no—
531C4⋊C4—881no—
532C4⋊C4C22×Dic1112yes—
533C22⋊C4—24no—
534C22⋊C4—24no—
535C22⋊C4—442no—
536C22⋊C4—881no—
537C22⋊C4—881no—
538C42—24no—
539C42—112no—
540C42—112no—
541C42—224no—
542C42—224no—
543C42—221no—
544C42—221no—
545C42—442no—
546C42—881no—
547C42—881no—
548C42—881no—
549C42#434112yes—
550C42C22×Dic1112yes—
551C11#2151211yescharacteristic, complemented, Sylow
552C23—22no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23C2×D4×D1111yescharacteristic
560Q8—22no—
561Q8—22no—
562Q8—22no—
563Q8—22no—
564Q8—22no—
565Q8—41no—
566Q8—41no—
567Q8D4×Dic1114yes—
568D4—22no—
569D4—22no—
570D4—41no—
571D4—41no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—112no—
586C2×C4—112no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—222no—
596C2×C4—221no—
597C2×C4—222no—
598C2×C4—221no—
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—441no—
608C2×C4—441no—
609C2×C4—884no—
610C2×C4D4×Dic1112yes—
611C2×C4D4×Dic1112yes—
612C2×C4C2×D4×D1111yescharacteristic
613C2×C4C2×#434111yescharacteristic
614C2×C4C2×#434111yescharacteristic
615C2×C4#41×D1111yescharacteristic
616C2×C4#41×D1111yescharacteristic
617C2×C4C23×Dic1111yescharacteristic
618C8—22no—
619C8—22no—
620C8—441no—
621C8—441no—
622C22—42no—
623C22—42no—
624C22—42no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22D11×#12111yescharacteristic
630C22#1062313711yescharacteristic
631C22#1062330011yescharacteristic
632C22#1062330211yescharacteristic
633C22#1062330911yescharacteristic
634C22#1062331011yescharacteristic
635C22C2×D4×Dic1111yescharacteristic
636C4—24no—
637C4—22no—
638C4—22no—
639C4—42no—
640C4—42no—
641C4—222no—
642C4—222no—
643C4—441no—
644C4—441no—
645C4—442no—
646C4—442no—
647C4—881no—
648C4—881no—
649C4#1062312711yescharacteristic
650C4#1062313111yescharacteristic
651C4C2×D4×Dic1111yescharacteristic
652C4#41×Dic1111yescharacteristic
653C2—82no—
654C2#121×Dic1111yescharacteristic
655C2#1307746011yescharacteristic
656C2#1307749211yescharacteristic
657C2#1307814411yescharacteristic
658C2#1307815811yescharacteristic
659C2#1307884411yescharacteristic
660C2#1307887711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#464C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenterC2×#464D11
hypocenterC11#21512
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
2. C2×Q16×Dic11C2semidirect
4. #13070981C2semidirect
6. #13069375C2semidirect
7. #13069259C2semidirect
10. #13068959C2semidirect
11. #13068621C2semidirect
12. #13068475C2semidirect
13. #13068448C2semidirect
24. C11×#464C4semidirect
68. C2×C11×Q16C2×C4semidirect
77. C4×Q8×C11C2×C4semidirect
114. C11×C4⋊C8C2×C4semidirect
115. C11×#103C2×C4semidirect
315. #464Dic11semidirect
390. C2×Q16C2×Dic11semidirect
407. C4×Q8C2×Dic11semidirect
439. C4⋊C8C2×Dic11semidirect
444. #103C2×Dic11semidirect
551. C11#21512semidirect

Maximal subgroups

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

subgroupindex
C2×#106227772
C2×Q16×Dic112
#130713292
#130709812
#130695492
#130693752
#130692592
#130692382
#130689732
#130689592
#130686212
#130684752
#130684482
#102×Dic112
C2×C11×#4642
#2151211