Finite Group Databasebeta

← #14770879

Subgroups — #14770879

Order 2816.

962 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×D11×#103C211yesmaximal, characteristic
2#13071492C211yesmaximal, characteristic
3Q8×(C2×D11)⋊C4C211yesmaximal, characteristic
4#13069307C211yesmaximal, characteristic, complemented
5#13069305C211yesmaximal, characteristic, complemented
6#13069251C211yesmaximal, characteristic, complemented
7#13069249C211yesmaximal, characteristic, complemented
8#13068886C211yesmaximal, characteristic, complemented
9#13068705C211yesmaximal, characteristic
10#13068638C211yesmaximal, characteristic
11#13068549C211yesmaximal, characteristic
12#13068448C211yesmaximal, characteristic, complemented
13#13068446C211yesmaximal, characteristic, complemented
14#13068391C211yesmaximal, characteristic
15C11×#1865C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C22×C8×D11C2211yescharacteristic
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×C11×#106C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C2×#66899C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27C2×(C2×D11)⋊C8C2211yescharacteristic
28C2×#66881C2211yescharacteristic
29C2×#66880C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31C2×#66879C2211yescharacteristic
32#10622600—21no—
33#10622600—21no—
34#10622600C2211yescharacteristic
35#10622600C2211yescharacteristic
36#10622598C2211yescharacteristic
37#10622591—21no—
38C4⋊C4×Dic11C2211yescharacteristic
39#10622587—21no—
40#10622587C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C4×(C2×D11)⋊C4—21no—
44C4×(C2×D11)⋊C4C2211yescharacteristic
45C4×C4⋊Dic11C2211yescharacteristic
46#10622542—21no—
47#10622542C2211yescharacteristic
48C2×#66867C2211yescharacteristic
49D11×#103C418yescomplemented
50#10622279—21no—
51#10622268—21no—
52C11×#340C2211yescharacteristic
53C11×#336C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C2×Q8×D11—22no—
62C2×Q8×D11—22no—
63C2×Q8×D11—22no—
64C2×Q8×D11—41no—
65C2×Q8×D11—41no—
66C2×Q8×D11C2×C414yes—
67C22×C4×D11—21no—
68C22×C4×D11—21no—
69C22×C4×D11C2311yescharacteristic
70C22×Dic22—21no—
71C22×Dic22C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C4×Q8×C11—22no—
75C4×Q8×C11—41no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83Q8×Dic11—22no—
84Q8×Dic11—41no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4D411yescharacteristic
88C2×(C2×D11)⋊C4D411yescharacteristic
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C2×C8×D11—41no—
102C2×C8×D11—41no—
103C2×C8×D11C2×C414yes—
104C4⋊C4×D11—22no—
105C4⋊C4×D11C2×C414yes—
106C11×#106—41no—
107C11×#103—22no—
108C11×#103C2×C414yes—
109C11×#95—21no—
110#66899—22no—
111#66899C2×C414yes—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95D411yescharacteristic
122C11⋊#95D411yescharacteristic
123(C2×D11)⋊C8—22no—
124#66881—41no—
125#66880—41no—
126#66880C2×C414yes—
127#66879—41no—
128#66874—41no—
129#66874C2×C414yes—
130#66867—41no—
131#22567—111nomaximal, Sylow
132C23×D11C2×D411yescharacteristic
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11C22×C412yes—
137C2×Q8×C11#4112yes—
138C2×Q8×C11#4112yes—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2411yescharacteristic
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153Q8×D11—28no—
154Q8×D11—44no—
155Q8×D11—44no—
156Q8×D11—44no—
157C2×C4×D11—24no—
158C2×C4×D11—24no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—42no—
164C2×C4×D11—42no—
165C2×C4×D11—81no—
166C2×C4×D11—81no—
167C2×C4×D11C22×C412yes—
168C2×C4×D11#4112yes—
169C2×Dic22—24no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22—42no—
176C2×Dic22—42no—
177C2×Dic22C22×C412yes—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11C22×C412yes—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—42no—
190C11×C4⋊C4—81no—
191C11×C4⋊C4C22×C412yes—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—42no—
195(C2×D11)⋊C4—22no—
196(C2×D11)⋊C4—22no—
197(C2×D11)⋊C4—42no—
198(C2×D11)⋊C4—42no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—42no—
205C4⋊Dic11—81no—
206C4⋊Dic11C22×C412yes—
207Dic11⋊C4—24no—
208C4×Dic11—21no—
209C4×Dic11—21no—
210C4×Dic11—42no—
211C4×Dic11—81no—
212C4×Dic11—81no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8C22×C412yes—
219C8×D11—44no—
220C22×#103—111no—
221#2345—111no—
222Q8×C22⋊C4—111no—
223#1935—111no—
224#1935—111no—
225#1927—111no—
226#1927—111no—
227#1865—111no—
228#1865D1111yescharacteristic, complemented
229#1824—111no—
230#1807—111no—
231#1787—111no—
232#1763—111no—
233#1763—111no—
234#1752—111no—
235C23×C11C22×D411yescharacteristic
236C22×D11—21no—
237C22×D11—21no—
238C22×D11—21no—
239C22×D11—21no—
240C22×D11C4×D412yes—
241C22×D11#13712yes—
242C22×D11#13712yes—
243Q8×C11—22no—
244Q8×C11—22no—
245Q8×C11—22no—
246Q8×C11#11714yes—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11C23×C411yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11H(5,𝔽2)11yescharacteristic
270C2×C4×C11H(5,𝔽2)11yescharacteristic
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11C4×D412yes—
292C4×D11—22no—
293C4×D11—22no—
294C4×D11—22no—
295C4×D11—22no—
296C4×D11—48no—
297C4×D11—84no—
298Dic22—22no—
299Dic22—22no—
300Dic22—48no—
301Dic22—41no—
302Dic22—41no—
303C8×C11—22no—
304C8×C11—41no—
305C11⋊C8—22no—
306C11⋊C8—41no—
307C23×Q8—111no—
308C23×C8—111no—
309C2×C4×Q8—111no—
310C2×C4×Q8C2×D1111yescharacteristic
311C22×C4⋊C4—111no—
312C2×#106—111no—
313C2×#106C2×D1111yescharacteristic
314C2×#103—111no—
315C2×#103—111no—
316C2×#103—111no—
317C2×#103—118no—
318C2×#103—111no—
319C2×#103—111no—
320C2×#103—111no—
321C2×#103C2×D1111yescharacteristic
322C2×#103C2×D1111yescharacteristic
323C2×C22⋊C8—111no—
324C2×#97—111no—
325C2×#97—111no—
326#391—111no—
327#391—111no—
328#391—221no—
329#391—221no—
330#389—111no—
331#389C2×D1111yescharacteristic
332#387—221no—
333#387—221no—
334#380—111no—
335#380—111no—
336#380—221no—
337#380—221no—
338C4×C4⋊C4—111no—
339C4×C4⋊C4—111no—
340C4×C22⋊C4—111no—
341C4×C22⋊C4—221no—
342C4×C22⋊C4—221no—
343#340—111no—
344#340—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340C2×D1111yescharacteristic
349#336—111no—
350#336C2×D1111yescharacteristic
351C22×C11C2×C4×D411yescharacteristic
352C22×C11#54611yescharacteristic
353C22×C11#54611yescharacteristic
354C22×C11C2×#13711yescharacteristic
355C22×C11C2×#13711yescharacteristic
356C22×C11#57711yescharacteristic
357C22×C11#57711yescharacteristic
358C2×D11—22no—
359C2×D11—22no—
360C2×D11—22no—
361C2×D11—22no—
362C2×D11—22no—
363C2×D11—22no—
364C2×D11#44114yes—
365C4×C11—24no—
366C4×C11—42no—
367C4×C11—41no—
368C4×C11—41no—
369C4×C11—81no—
370C4×C11—81no—
371C4×C11C2×#11711yescharacteristic
372C4×C11#51811yescharacteristic
373C4×C11#55111yescharacteristic
374C4×C11#55111yescharacteristic
375Dic11—22no—
376Dic11—42no—
377Dic11—42no—
378Dic11—41no—
379Dic11—41no—
380Dic11—81no—
381Dic11—81no—
382C22×Q8—114no—
383C22×Q8—111no—
384C22×Q8—221no—
385C22×Q8—222no—
386C22×Q8—222no—
387C22×Q8—222no—
388C22×Q8—441no—
389C22×Q8—441no—
390C22×Q8C22×D1111yescharacteristic
391C23×C4—111no—
392C23×C4—221no—
393C23×C4—221no—
394C22×C8—111no—
395C22×C8—114no—
396C22×C8—111no—
397C22×C8—441no—
398C22×C8—441no—
399C22×C8C22×D1111yescharacteristic
400C22×C8C22×D1111yescharacteristic
401C4×Q8—22no—
402C4×Q8—41no—
403C4×Q8—222no—
404C4×Q8—441no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—114no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—222no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C4⋊C4C22×D1111yescharacteristic
417C2×C4⋊C4C22×D1111yescharacteristic
418C2×C22⋊C4—111no—
419C2×C22⋊C4—111no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C42—21no—
423C2×C42—111no—
424C2×C42—221no—
425C2×C42—221no—
426C2×C42—221no—
427C2×C42C22×D1111yescharacteristic
428#106—41no—
429#106—441no—
430#103—22no—
431#103—114no—
432#103—114no—
433#103—114no—
434#103—222no—
435#103—441no—
436#103—441no—
437#103C4×D1114yes—
438C22⋊C8—222no—
439#97—441no—
440#97—441no—
441#95—21no—
442#95—111no—
443#95—111no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95—221no—
451#95—221no—
452#95—221no—
453C2×C11#234211yescharacteristic
454C2×C11C2×#44111yescharacteristic
455C2×C11#294911yescharacteristic
456C2×C11#331611yescharacteristic
457C2×C11#331611yescharacteristic
458C2×C11#332011yescharacteristic
459C2×C11#332011yescharacteristic
460D11—24no—
461C24—111no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—112no—
466C2×Q8—224no—
467C2×Q8—221no—
468C2×Q8—228no—
469C2×Q8—221no—
470C2×Q8—221no—
471C2×Q8—221no—
472C2×Q8—221no—
473C2×Q8—442no—
474C2×Q8—442no—
475C2×Q8—444no—
476C2×Q8—444no—
477C2×Q8—444no—
478C2×Q8C2×C4×D1112yes—
479C2×Q8#434112yes—
480C2×Q8#434312yes—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—111no—
486C22×C4—112no—
487C22×C4—112no—
488C22×C4—111no—
489C22×C4—111no—
490C22×C4—224no—
491C22×C4—224no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—442no—
501C22×C4—442no—
502C22×C4—881no—
503C22×C4—881no—
504C22×C4D4×D1111yescharacteristic
505C22×C4D4×D1111yescharacteristic
506C22×C4C23×D1111yescharacteristic
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—112no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—444no—
519C2×C8C2×C4×D1112yes—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—42no—
526C4⋊C4—81no—
527C4⋊C4—112no—
528C4⋊C4—224no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—442no—
535C4⋊C4—881no—
536C4⋊C4C2×C4×D1112yes—
537C22⋊C4—222no—
538C22⋊C4—222no—
539C22⋊C4—442no—
540C22⋊C4—442no—
541C42—21no—
542C42—21no—
543C42—42no—
544C42—221no—
545C42—221no—
546C42—442no—
547C42—881no—
548C42—881no—
549C11#2256711yescharacteristic, complemented, Sylow
550C23—112no—
551C23—112no—
552C23—112no—
553C23—221no—
554C23—221no—
555C23—221no—
556C23—221no—
557C23C2×D4×D1111yescharacteristic
558Q8—22no—
559Q8—22no—
560Q8—22no—
561Q8—222no—
562Q8—222no—
563Q8—448no—
564Q8—441no—
565Q8—441no—
566Q8#6694514yes—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—112no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—222no—
589C2×C4—222no—
590C2×C4—222no—
591C2×C4—222no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—222no—
597C2×C4—222no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—448no—
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—441no—
610C2×C4—441no—
611C2×C4—884no—
612C2×C4C22×C4×D1111yescharacteristic
613C2×C4C2×#434111yescharacteristic
614C2×C4#6703711yescharacteristic
615C2×C4C2×#434311yescharacteristic
616C2×C4#41×D1111yescharacteristic
617C2×C4#6704211yescharacteristic
618C8—22no—
619C8—41no—
620C8—222no—
621C8—441no—
622C22—114no—
623C22—222no—
624C22—222no—
625C22—222no—
626C22—222no—
627C22—222no—
628C22—222no—
629C22C4×D4×D1111yescharacteristic
630C22#1062312211yescharacteristic
631C22#1062316111yescharacteristic
632C22#1062329311yescharacteristic
633C22#1062330111yescharacteristic
634C22D11×#13711yescharacteristic
635C22D11×#13711yescharacteristic
636C4—24no—
637C4—41no—
638C4—41no—
639C4—42no—
640C4—81no—
641C4—81no—
642C4—222no—
643C4—442no—
644C4—441no—
645C4—441no—
646C4—442no—
647C4—881no—
648C4—881no—
649C4C2×#6694511yescharacteristic
650C4#1062307611yescharacteristic
651C4#1062316811yescharacteristic
652C4#1062318911yescharacteristic
653C2—224no—
654C2#1307146311yescharacteristic
655C2D11×#44111yescharacteristic
656C2#1307747011yescharacteristic
657C2#1308072011yescharacteristic
658C2#1308072411yescharacteristic
659C2#1308078011yescharacteristic
660C2#1308078411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1865C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1865D11
hypocenterC11#22567
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1865

Complements

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

NH ≅ G/Ntype
4. #13069307C2semidirect
5. #13069305C2semidirect
6. #13069251C2semidirect
7. #13069249C2semidirect
8. #13068886C2semidirect
12. #13068448C2semidirect
13. #13068446C2semidirect
15. C11×#1865C2semidirect
49. D11×#103C4semidirect
228. #1865D11semidirect
549. C11#22567semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1032
#130714922
Q8×(C2×D11)⋊C42
#130693072
#130693052
#130692512
#130692492
#130688862
#130687052
#130686382
#130685492
#130684482
#130684462
#130683912
C11×#18652
#2256711