Finite Group Databasebeta

← #14760136

Subgroups — #14760136

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×#10622667C211yesmaximal, characteristic
2C2×#10622631C211yesmaximal, characteristic
3C2×C4×#4326C211yesmaximal, characteristic, complemented
4#13070979C211yesmaximal, characteristic, complemented
5#13069549C211yesmaximal, characteristic
6#13069372C211yesmaximal, characteristic, complemented
7#13069254C211yesmaximal, characteristic, complemented
8#13069233C211yesmaximal, characteristic
9#13068974C211yesmaximal, characteristic
10#13068960C211yesmaximal, characteristic, complemented
11#13068618C211yesmaximal, characteristic, complemented
12#13068473C211yesmaximal, characteristic, complemented
13#13068446C211yesmaximal, characteristic, complemented
14C4×#66896C211yesmaximal, characteristic
15C11×#2326C211yesmaximal, characteristic
16C2×C11×#124C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C22×#4324C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C11×#391C2211yescharacteristic
25C11×#390C2211yescharacteristic
26C11×#388—21no—
27C11×#388—21no—
28C11×#385—21no—
29C11×#385—21no—
30C11×#384C2211yescharacteristic
31C11×#376C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38#10622667C418yescomplemented
39C4×#4326—24no—
40#10622631—24no—
41C2×#66874C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C4×C4⋊Dic11C2211yescharacteristic
46C4×C4⋊Dic11C2211yescharacteristic
47C4×C4⋊Dic11C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×#66867C2211yescharacteristic
51C2×C4×C11⋊C8C2211yescharacteristic
52#10622262—21no—
53#10622262—21no—
54#10622262—21no—
55#10622261—21no—
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61#10622162C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C22×Dic22C2311yescharacteristic
66C11×#124—22no—
67C11×#124C2×C414yes—
68C4×Q8×C11—22no—
69C4×Q8×C11—22no—
70C4×D4×C11—22no—
71C4×D4×C11—22no—
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×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C42×C11—21no—
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×#4326—22no—
87C2×#4326—22no—
88C2×#4326C2×C414yescomplemented
89C2×#4324—22no—
90C2×#4324—22no—
91C2×#4324C2×C414yes—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C4×Dic22—22no—
109C4×Dic22—22no—
110C4×Dic22—22no—
111C4×Dic22—22no—
112C4×Dic22C2×C414yescomplemented
113C4×Dic22D414yes—
114C11×#95—21no—
115C11×#95—21no—
116C11×#95D411yescharacteristic
117C11×#95D411yescharacteristic
118C11×#95D411yescharacteristic
119C11×#95D411yescharacteristic
120#66899—22no—
121#66899—22no—
122#66899C2×C414yescomplemented
123#66896—22no—
124#66896—22no—
125#66896C2×C414yes—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129#66874—22no—
130#66874—22no—
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
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×C11C22×C412yes—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11C22×C412yes—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—42no—
155C22×C4×C11—81no—
156C22×C4×C11—81no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2411yescharacteristic
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22C22×C412yes—
172C2×Dic22C2×D412yes—
173C2×Dic22#4112yes—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—42no—
179C11×C4⋊C4—81no—
180C11×C4⋊C4—81no—
181C11×C22⋊C4—24no—
182C11×C22⋊C4—24no—
183C11×C22⋊C4—42no—
184C11×C22⋊C4—81no—
185C11×C22⋊C4—81no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—42no—
189C42×C11C22×C412yes—
190C42×C11C2×D412yes—
191C42×C11#4112yes—
192C42×C11#4112yes—
193#4326—28no—
194#4324—28no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11C22×C412yes—
199C4⋊Dic11C2×D412yes—
200C4⋊Dic11#4112yes—
201Dic11⋊C4—24no—
202Dic11⋊C4—24no—
203Dic11⋊C4—24no—
204C4×Dic11—24no—
205C4×Dic11—24no—
206C4×Dic11—24no—
207C4×Dic11—81no—
208C4×Dic11—81no—
209C4×Dic11—81no—
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#2326D1111yescharacteristic
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—41no—
248Q8×C11—41no—
249D4×C11—22no—
250D4×C11—22no—
251D4×C11—41no—
252D4×C11—41no—
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—21no—
261C2×C4×C11—22no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—41no—
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×C11—41no—
276C2×C4×C11—84no—
277C2×C4×C11C4×D412yes—
278C2×C4×C11C4×D412yes—
279C2×C4×C11#12112yes—
280C2×C4×C11#12112yes—
281C2×C4×C11C23×C411yescharacteristic
282C2×C4×C11C22×D411yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C2×C4×C11C2×#4111yescharacteristic
286C2×C4×C11C2×#4111yescharacteristic
287C2×Dic11—22no—
288C2×Dic11—22no—
289C2×Dic11—22no—
290C2×Dic11—22no—
291C2×Dic11—22no—
292C2×Dic11—22no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299Dic22—22no—
300Dic22—22no—
301Dic22—22no—
302Dic22C4×D414yes—
303C11⋊C8—22no—
304C11⋊C8—22no—
305C11⋊C8—41no—
306C11⋊C8—41no—
307C22×Q16—111no—
308C22×SD16—111no—
309C2×#124C2×D1111yescharacteristic
310C2×C4×Q8—111no—
311C2×C4×Q8—111no—
312C2×C4×Q8—111no—
313C2×C4×Q8C2×D1111yescharacteristic
314C2×C4×D4C2×D1111yescharacteristic
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#391C2×D1111yescharacteristic
333#390C2×D1111yescharacteristic
334#388—21no—
335#388—21no—
336#385—21no—
337#385—21no—
338#384C2×D1111yescharacteristic
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—221no—
346#376C2×D1111yescharacteristic
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—22no—
370C4×C11—22no—
371C4×C11—41no—
372C4×C11—41no—
373C4×C11—42no—
374C4×C11—81no—
375C4×C11—81no—
376C4×C11C2×C4×D411yescharacteristic
377C4×C11C4×#4111yescharacteristic
378C4×C11#52911yescharacteristic
379C4×C11#53211yescharacteristic
380Dic11—24no—
381Dic11—42no—
382Dic11—42no—
383Dic11—42no—
384C22×Q8—111no—
385C22×Q8C22×D1111yescharacteristic
386C22×D4C22×D1111yescharacteristic
387C23×C4—21no—
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—22no—
399#124C4×D1114yes—
400C4×Q8—22no—
401C4×Q8—22no—
402C4×Q8—114no—
403C4×Q8—114no—
404C4×Q8—222no—
405C4×Q8—222no—
406C4×Q8—222no—
407C4×Q8—222no—
408C4×D4—22no—
409C4×D4—22no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C4⋊C4C22×D1111yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C42—21no—
427C2×C42—221no—
428C2×C42—221no—
429C2×C42—221no—
430C2×C42—221no—
431C2×C42—221no—
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—221no—
453#95—221no—
454#95—221no—
455#95C22⋊D1111yescharacteristic
456#95C22⋊D1111yescharacteristic
457#95C22⋊D1111yescharacteristic
458#95C22⋊D1111yescharacteristic
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—112no—
474C2×Q8—112no—
475C2×Q8—112no—
476C2×Q8—221no—
477C2×Q8—221no—
478C2×Q8—221no—
479C2×Q8C2×C4×D1112yes—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4C2×C4×D1112yes—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—42no—
490C22×C4—81no—
491C22×C4—81no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
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—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—42no—
522C4⋊C4—81no—
523C4⋊C4—81no—
524C4⋊C4—112no—
525C4⋊C4—112no—
526C4⋊C4—112no—
527C4⋊C4—224no—
528C4⋊C4—224no—
529C4⋊C4—224no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C22⋊C4—24no—
534C22⋊C4—24no—
535C22⋊C4—42no—
536C22⋊C4—81no—
537C22⋊C4—81no—
538C42—21no—
539C42—21no—
540C42—42no—
541C42—224no—
542C42—224no—
543C42—224no—
544C42—881no—
545C42—881no—
546C42—881no—
547C42C2×C4×D1112yes—
548C42#433912yes—
549C42D4×D1112yes—
550C42#434112yes—
551C11#2151211yescharacteristic, complemented, Sylow
552C23—22no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23C22×C22⋊D1111yescharacteristic
560Q8—22no—
561Q8—22no—
562Q8—41no—
563Q8—41no—
564Q8—114no—
565Q8—222no—
566Q8—222no—
567Q8—222no—
568D4—22no—
569D4—22no—
570D4—41no—
571D4—41no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—84no—
596C2×C4—222no—
597C2×C4—222no—
598C2×C4—222no—
599C2×C4—222no—
600C2×C4—222no—
601C2×C4—222no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4C4×C22⋊D1112yes—
609C2×C4C4×C22⋊D1112yes—
610C2×C4#6699112yes—
611C2×C4#6699112yes—
612C2×C4C22×C4×D1111yescharacteristic
613C2×C4C2×#433911yescharacteristic
614C2×C4C2×D4×D1111yescharacteristic
615C2×C4C2×#434111yescharacteristic
616C2×C4#41×D1111yescharacteristic
617C2×C4#41×D1111yescharacteristic
618C8—222no—
619C8—222no—
620C8—441no—
621C8—441no—
622C22—42no—
623C22—42no—
624C22—42no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22C2×C4×C22⋊D1111yescharacteristic
630C22C2×#6699111yescharacteristic
631C22#1062335911yescharacteristic
632C22#1062336611yescharacteristic
633C22#1062336711yescharacteristic
634C22#1062336911yescharacteristic
635C22#1062336911yescharacteristic
636C4—22no—
637C4—22no—
638C4—22no—
639C4—22no—
640C4—42no—
641C4—41no—
642C4—41no—
643C4—81no—
644C4—81no—
645C4—224no—
646C4—442no—
647C4—442no—
648C4—442no—
649C4C4×#434111yescharacteristic
650C4C4×D4×D1111yescharacteristic
651C4#1062307911yescharacteristic
652C4#1062308811yescharacteristic
653C2—82no—
654C2C4×#6699111yescharacteristic
655C2#1307745511yescharacteristic
656C2#1307748911yescharacteristic
657C2#1307814211yescharacteristic
658C2#1307815111yescharacteristic
659C2#1307883911yescharacteristic
660C2#1307887211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2326C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#2326D11
hypocenterC11#21512
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #2326

Complements

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

NH ≅ G/Ntype
3. C2×C4×#4326C2semidirect
4. #13070979C2semidirect
6. #13069372C2semidirect
7. #13069254C2semidirect
10. #13068960C2semidirect
11. #13068618C2semidirect
12. #13068473C2semidirect
13. #13068446C2semidirect
38. #10622667C4semidirect
88. C2×#4326C2×C4semidirect
112. C4×Dic22C2×C4semidirect
122. #66899C2×C4semidirect
134. C4⋊(C11⋊C8)C2×C4semidirect
551. C11#21512semidirect

Maximal subgroups

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

subgroupindex
C2×#106226672
C2×#106226312
C2×C4×#43262
#130709792
#130695492
#130693722
#130692542
#130692332
#130689742
#130689602
#130686182
#130684732
#130684462
C4×#668962
C11×#23262
#2151211