Finite Group Databasebeta

← #14721979

Subgroups — #14721979

Order 2816.

932 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077630C211yesmaximal, characteristic, complemented
2#13077267C211yesmaximal, characteristic, complemented
3#13067251C212yesmaximal, complemented
4#13067247C212yesmaximal, complemented
5#13067236C212yesmaximal, complemented
6#13067227C211yesmaximal, characteristic, complemented
7#13067227C212yesmaximal, complemented
8#13067223C211yesmaximal, characteristic, complemented
9#13067208C211yesmaximal, characteristic, complemented
10#13067204C211yesmaximal, characteristic, complemented
11C11×#3517C211yesmaximal, characteristic
12C11×#557C411yescharacteristic
13C11×#553—21no—
14C11×#553—22no—
15C11×#550—21no—
16C11×#550C411yescharacteristic
17C11×#550C412yes—
18C11×#550C411yescharacteristic
19C11×#547C411yescharacteristic
20C11×#547C412yes—
21C11×#540—21no—
22C11×#540—22no—
23C11×#532C2211yescharacteristic
24C11×#532C2212yes—
25C11×#529C2211yescharacteristic
26C11×#529C2212yes—
27C11×#520—21no—
28C4×C11×#41C2211yescharacteristic
29#10622847—21no—
30#10622637—21no—
31#10622624—22no—
32D4×C11⋊C8—21no—
33#10622613—22no—
34#10622612—21no—
35#10622539C2212yes—
36#10622539C2212yes—
37#10622539C2211yescharacteristic
38#10622539C2212yes—
39C4×#4318C2211yescharacteristic
40C4×#4318C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42C2×#66867C2212yes—
43#10622181C2211yescharacteristic
44#10622181C2211yescharacteristic
45#10622181C2212yes—
46#10622178C2211yescharacteristic
47#10622178C2211yescharacteristic
48#10622178C2212yes—
49#10622178C2212yes—
50#10622178C2212yes—
51#10622178C2212yes—
52#10622178C2212yes—
53C2×C11×#41—21no—
54C2×C11×#41C2×C412yes—
55C2×C11×#41C2×C412yes—
56C2×C11×#41C2×C412yes—
57C2×C11×#41D411yescharacteristic
58C11×C4⋊Q8C2×C411yescharacteristic
59C11×C4⋊Q8C2×C412yes—
60C11×#127—21no—
61C11×#127—22no—
62C11×#127C2×C411yescharacteristic
63C11×#127C2×C412yes—
64C11×#126—21no—
65C11×#126—22no—
66C11×#125—22no—
67C11×#125—21no—
68C11×#125C2311yescharacteristic
69C11×#124C2311yescharacteristic
70C11×#124C2312yes—
71C11×#123—22no—
72C11×#123—21no—
73C11×#123—22no—
74C11×#123—22no—
75C11×#123—22no—
76C11×C22⋊Q8C2×C411yescharacteristic
77C11×C22⋊Q8C2×C412yes—
78C11×#121—21no—
79C11×#121—22no—
80C11×#121—22no—
81C11×#121—21no—
82C11×#121—21no—
83C11×#121—22no—
84C11×#121—22no—
85C11×#121—21no—
86C11×#121—22no—
87C11×#121—22no—
88C11×#121—22no—
89C11×#121C2×C411yescharacteristic
90C11×#121C2×C412yes—
91C4×Q8×C11—21no—
92C4×Q8×C11C2×C411yescharacteristic
93C4×Q8×C11C2×C412yes—
94C4×Q8×C11C2×C411yescharacteristic
95C4×Q8×C11D411yescharacteristic
96C4×D4×C11—21no—
97C4×D4×C11—22no—
98C4×D4×C11—22no—
99C4×D4×C11—21no—
100C4×D4×C11—21no—
101C4×D4×C11—22no—
102C4×D4×C11—21no—
103C4×D4×C11—22no—
104C4×D4×C11C2×C411yescharacteristic
105C4×D4×C11C2×C412yes—
106C4×D4×C11C2×C411yescharacteristic
107C4×D4×C11C2×C412yes—
108C4×D4×C11D411yescharacteristic
109C4×D4×C11D412yes—
110C11×#117—21no—
111C11×#117—22no—
112C11×#117D411yescharacteristic
113C11×#117D412yes—
114C2×C11×C4⋊C4—22no—
115C2×C11×C4⋊C4—21no—
116C2×C42×C11C2311yescharacteristic
117C2×C42×C11C2312yes—
118C2×#4318—21no—
119C2×#4318—21no—
120C22×C11⋊C8—21no—
121C22×C11⋊C8—22no—
122C22⋊(C11⋊C8)—22no—
123C22⋊(C11⋊C8)—22no—
124C22⋊(C11⋊C8)—22no—
125C22⋊(C11⋊C8)—21no—
126C4⋊(C11⋊C8)—22no—
127C4⋊(C11⋊C8)—22no—
128C4⋊(C11⋊C8)—21no—
129C4⋊(C11⋊C8)—22no—
130#66867—21no—
131#66867—22no—
132#66867C2311yescharacteristic
133#66867C2311yescharacteristic
134#66867C2311yescharacteristic
135#66867C2312yes—
136#66867C2312yes—
137#66867C2311yescharacteristic
138C4×C11⋊C8—21no—
139C4×C11⋊C8—21no—
140#17684—111nomaximal, Sylow
141C11×#41—42no—
142C11×#41—44no—
143C11×#41—82no—
144C11×#41—82no—
145C11×#41—82no—
146C2×Q8×C11C22⋊C411yescharacteristic
147C2×Q8×C11C22×C411yescharacteristic
148C2×Q8×C11C22×C412yes—
149C2×D4×C11—21no—
150C2×D4×C11—22no—
151C2×D4×C11—22no—
152C2×D4×C11—22no—
153C2×D4×C11—22no—
154C2×D4×C11—22no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—22no—
158C2×D4×C11C22⋊C411yescharacteristic
159C2×D4×C11C22⋊C412yes—
160C2×D4×C11C22×C411yescharacteristic
161C2×D4×C11C22×C412yes—
162C22×C4×C11—22no—
163C22×C4×C11—21no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11C22×C411yescharacteristic
168C22×C4×C11C22×C412yes—
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D412yes—
171C22×C4×C11C2×D412yes—
172C22×C4×C11C2×D411yescharacteristic
173C11×C4⋊C4—21no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4C22⋊C412yes—
184C11×C4⋊C4C22⋊C411yescharacteristic
185C11×C4⋊C4C22⋊C412yes—
186C11×C4⋊C4C22⋊C411yescharacteristic
187C11×C4⋊C4C22×C411yescharacteristic
188C11×C4⋊C4C22×C411yescharacteristic
189C11×C22⋊C4—21no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—21no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—21no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—21no—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—21no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4C22⋊C412yes—
200C11×C22⋊C4C22⋊C412yes—
201C11×C22⋊C4C22⋊C412yes—
202C42×C11—22no—
203C42×C11—21no—
204C42×C11C22×C412yes—
205C42×C11C22×C411yescharacteristic
206C42×C11C2×D411yescharacteristic
207C42×C11C2×D411yescharacteristic
208C42×C11C2×D412yes—
209C42×C11C2×D412yes—
210C42×C11C2411yescharacteristic
211#4318—42no—
212#4318—42no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—22no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—22no—
219C2×C11⋊C8—42no—
220C2×C11⋊C8—44no—
221#3517D1111yescharacteristic
222#2970—111no—
223#2923—111no—
224#1536—112no—
225#1535—112no—
226#1532—112no—
227#1530—112no—
228#1530—111no—
229#1529—111no—
230#1525—111no—
231#1524—111no—
232C23×C11—22no—
233C23×C11—21no—
234C23×C11C2×C22⋊C411yescharacteristic
235C23×C11C2×C22⋊C412yes—
236Q8×C11—22no—
237Q8×C11—41no—
238Q8×C11—42no—
239D4×C11—22no—
240D4×C11—42no—
241D4×C11—41no—
242D4×C11—42no—
243D4×C11—44no—
244D4×C11—42no—
245D4×C11—82no—
246D4×C11—81no—
247D4×C11—82no—
248D4×C11—81no—
249D4×C11—82no—
250D4×C11—82no—
251D4×C11—82no—
252C2×C4×C11—22no—
253C2×C4×C11—21no—
254C2×C4×C11—22no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—42no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—44no—
263C2×C4×C11—42no—
264C2×C4×C11—82no—
265C2×C4×C11—82no—
266C2×C4×C11—82no—
267C2×C4×C11C2×C22⋊C412yes—
268C2×C4×C11C2×C22⋊C411yescharacteristic
269C2×C4×C11C2×C22⋊C412yes—
270C2×C4×C11C2×C22⋊C411yescharacteristic
271C2×C4×C11C2×C22⋊C412yes—
272C2×C4×C11C2×C22⋊C411yescharacteristic
273C2×C4×C11C23×C411yescharacteristic
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C22×D411yescharacteristic
276C11⋊C8—22no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279C11⋊C8—42no—
280C11⋊C8—42no—
281C11⋊C8—41no—
282#557Dic1111yescharacteristic
283#553—21no—
284#553—22no—
285#550—21no—
286#550Dic1111yescharacteristic
287#550Dic1112yes—
288#550Dic1111yescharacteristic
289#547Dic1111yescharacteristic
290#547Dic1112yes—
291#540—21no—
292#540—22no—
293#532C2×D1112yes—
294#532C2×D1111yescharacteristic
295#529C2×D1111yescharacteristic
296#529C2×D1112yes—
297#520—21no—
298C4×#41C2×D1111yescharacteristic
299#446—221no—
300#435—222no—
301C8×D4—221no—
302#433—222no—
303#432—112no—
304#432—112no—
305#432—112no—
306#432—111no—
307#424—221no—
308#408—221no—
309C4×M16—111no—
310C4×M16—111no—
311C2×#97—111no—
312C2×#97—112no—
313#330—111no—
314#330—111no—
315#330—112no—
316#329—111no—
317#329—112no—
318#329—112no—
319#329—112no—
320#329—111no—
321#329—112no—
322#329—112no—
323C22×C11—21no—
324C22×C11—22no—
325C22×C11—21no—
326C22×C11—22no—
327C22×C11—22no—
328C22×C11—21no—
329C22×C11—42no—
330C22×C11—41no—
331C22×C11—42no—
332C22×C11—41no—
333C22×C11—42no—
334C22×C11—41no—
335C22×C11C22×C22⋊C411yescharacteristic
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—22no—
339C4×C11—21no—
340C4×C11—22no—
341C4×C11—21no—
342C4×C11—22no—
343C4×C11—21no—
344C4×C11—42no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11#42112yes—
349C2×#41—21no—
350C2×#41C2×Dic1112yes—
351C2×#41C2×Dic1112yes—
352C2×#41C2×Dic1112yes—
353C2×#41C22⋊D1111yescharacteristic
354C2×M16—221no—
355C2×M16—221no—
356C22×C8—221no—
357C22×C8—222no—
358C4⋊Q8C2×Dic1112yes—
359C4⋊Q8C2×Dic1111yescharacteristic
360#127—21no—
361#127—22no—
362#127C2×Dic1112yes—
363#127C2×Dic1111yescharacteristic
364#126—21no—
365#126—22no—
366#125—22no—
367#125—21no—
368#125C22×D1111yescharacteristic
369#124C22×D1111yescharacteristic
370#124C22×D1112yes—
371#123—22no—
372#123—21no—
373#123—22no—
374#123—22no—
375#123—22no—
376C22⋊Q8C2×Dic1111yescharacteristic
377C22⋊Q8C2×Dic1112yes—
378#121—21no—
379#121—22no—
380#121—22no—
381#121—21no—
382#121—21no—
383#121—22no—
384#121—22no—
385#121—21no—
386#121—22no—
387#121—22no—
388#121—22no—
389#121C2×Dic1111yescharacteristic
390#121C2×Dic1112yes—
391C4×Q8—21no—
392C4×Q8C2×Dic1111yescharacteristic
393C4×Q8C2×Dic1112yes—
394C4×Q8C2×Dic1111yescharacteristic
395C4×Q8C22⋊D1111yescharacteristic
396C4×D4—21no—
397C4×D4—22no—
398C4×D4—22no—
399C4×D4—21no—
400C4×D4—21no—
401C4×D4—22no—
402C4×D4—21no—
403C4×D4—22no—
404C4×D4C2×Dic1111yescharacteristic
405C4×D4C2×Dic1112yes—
406C4×D4C2×Dic1111yescharacteristic
407C4×D4C2×Dic1112yes—
408C4×D4C22⋊D1111yescharacteristic
409C4×D4C22⋊D1112yes—
410#117—21no—
411#117—22no—
412#117C22⋊D1111yescharacteristic
413#117C22⋊D1112yes—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—21no—
416C2×C42C22×D1111yescharacteristic
417C2×C42C22×D1112yes—
418C4⋊C8—222no—
419C4⋊C8—222no—
420C4⋊C8—221no—
421C4⋊C8—222no—
422C22⋊C8—222no—
423C22⋊C8—222no—
424C22⋊C8—222no—
425C22⋊C8—221no—
426#97—111no—
427#97—111no—
428#97—112no—
429#97—111no—
430#97—111no—
431#97—112no—
432#97—221no—
433#97—222no—
434C4×C8—221no—
435C4×C8—221no—
436C2×C11—41no—
437C2×C11—42no—
438C2×C11—82no—
439C2×C11—81no—
440C2×C11#288811yescharacteristic
441C2×C11C2×#42111yescharacteristic
442C2×C11#290111yescharacteristic
443#41—42no—
444#41—44no—
445#41—82no—
446#41—82no—
447#41—82no—
448C2×Q8C22⋊Dic1111yescharacteristic
449C2×Q8C22×Dic1111yescharacteristic
450C2×Q8C22×Dic1112yes—
451C2×D4—21no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—22no—
460C2×D4C22⋊Dic1111yescharacteristic
461C2×D4C22⋊Dic1112yes—
462C2×D4C22×Dic1111yescharacteristic
463C2×D4C22×Dic1112yes—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4C22×Dic1111yescharacteristic
470C22×C4C22×Dic1112yes—
471C22×C4C2×C22⋊D1111yescharacteristic
472C22×C4C2×C22⋊D1112yes—
473C22×C4C2×C22⋊D1112yes—
474C22×C4C2×C22⋊D1111yescharacteristic
475M16—442no—
476M16—442no—
477C2×C8—221no—
478C2×C8—222no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—222no—
483C2×C8—444no—
484C2×C8—442no—
485C4⋊C4—21no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—22no—
491C4⋊C4—21no—
492C4⋊C4—22no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4C22⋊Dic1112yes—
496C4⋊C4C22⋊Dic1111yescharacteristic
497C4⋊C4C22⋊Dic1112yes—
498C4⋊C4C22⋊Dic1111yescharacteristic
499C4⋊C4C22×Dic1111yescharacteristic
500C4⋊C4C22×Dic1111yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—22no—
503C22⋊C4—21no—
504C22⋊C4—22no—
505C22⋊C4—21no—
506C22⋊C4—22no—
507C22⋊C4—21no—
508C22⋊C4—22no—
509C22⋊C4—21no—
510C22⋊C4—22no—
511C22⋊C4C22⋊Dic1112yes—
512C22⋊C4C22⋊Dic1112yes—
513C22⋊C4C22⋊Dic1112yes—
514C42—22no—
515C42—21no—
516C42C22×Dic1112yes—
517C42C22×Dic1111yescharacteristic
518C42C2×C22⋊D1111yescharacteristic
519C42C2×C22⋊D1111yescharacteristic
520C42C2×C22⋊D1112yes—
521C42C2×C22⋊D1112yes—
522C42C23×D1111yescharacteristic
523C11#1768411yescharacteristic, complemented, Sylow
524C23—22no—
525C23—21no—
526C23C2×C22⋊Dic1111yescharacteristic
527C23C2×C22⋊Dic1112yes—
528Q8—22no—
529Q8—41no—
530Q8—42no—
531D4—22no—
532D4—42no—
533D4—41no—
534D4—42no—
535D4—44no—
536D4—42no—
537D4—82no—
538D4—81no—
539D4—82no—
540D4—81no—
541D4—82no—
542D4—82no—
543D4—82no—
544C2×C4—22no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—42no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—44no—
555C2×C4—42no—
556C2×C4—82no—
557C2×C4—82no—
558C2×C4—82no—
559C2×C4C2×C22⋊Dic1112yes—
560C2×C4C2×C22⋊Dic1111yescharacteristic
561C2×C4C2×C22⋊Dic1112yes—
562C2×C4C2×C22⋊Dic1111yescharacteristic
563C2×C4C2×C22⋊Dic1112yes—
564C2×C4C2×C22⋊Dic1111yescharacteristic
565C2×C4C23×Dic1111yescharacteristic
566C2×C4C22×C22⋊D1111yescharacteristic
567C2×C4C22×C22⋊D1111yescharacteristic
568C8—222no—
569C8—441no—
570C8—441no—
571C8—442no—
572C8—442no—
573C8—441no—
574C22—21no—
575C22—22no—
576C22—21no—
577C22—22no—
578C22—22no—
579C22—21no—
580C22—42no—
581C22—41no—
582C22—42no—
583C22—41no—
584C22—42no—
585C22—41no—
586C22C22×C22⋊Dic1111yescharacteristic
587C4—21no—
588C4—21no—
589C4—22no—
590C4—21no—
591C4—22no—
592C4—21no—
593C4—22no—
594C4—21no—
595C4—42no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4#1062284912yes—
600C2—41no—
601C2—42no—
602C2—82no—
603C2—81no—
604C2#1307709511yescharacteristic
605C2C2×#1062284911yescharacteristic
606C2#1307716311yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
Fitting, prime radicalC11×#3517C2
socleC22×C11C22×C22⋊C4
cosocleC42×C11C24
hypercenter#3517D11
hypocenterC11#17684
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3517

Complements

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

NH ≅ G/Ntype
1. #13077630C2semidirect
2. #13077267C2semidirect
3. #13067251C2semidirect
4. #13067247C2semidirect
5. #13067236C2semidirect
6. #13067227C2semidirect
7. #13067227C2semidirect
8. #13067223C2semidirect
9. #13067208C2semidirect
10. #13067204C2semidirect
523. C11#17684semidirect

Maximal subgroups

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

subgroupindex
#130776302
#130772672
#130672512
#130672472
#130672362
#130672272
#130672232
#130672082
#130672042
C11×#35172
#1768411