Finite Group Databasebeta

← #14816705

Subgroups — #14816705

Order 2816.

804 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622676C211yesmaximal, characteristic, complemented
2C2×#10622577C211yesmaximal, characteristic
3#13071641C211yesmaximal, characteristic
4#13070167C211yesmaximal, characteristic, complemented
5#13070112C211yesmaximal, characteristic, complemented
6#13070008C211yesmaximal, characteristic, complemented
7#13069951C211yesmaximal, characteristic, complemented
8#13069382C211yesmaximal, characteristic, complemented
9#13069191C211yesmaximal, characteristic, complemented
10#13069047C211yesmaximal, characteristic
11#13068923C211yesmaximal, characteristic
12#13068883C211yesmaximal, characteristic, complemented
13#13068813C211yesmaximal, characteristic
14#13068801C211yesmaximal, characteristic
15C11×#2442C211yesmaximal, characteristic
16C2×C11×#125C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C2×#66977C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C11×#400—21no—
23C11×#398—21no—
24C11×#389C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C11×#385—21no—
27C11×#382C2211yescharacteristic
28C11×#380—21no—
29C11×#380C2211yescharacteristic
30C4×C11×C22⋊C4C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32#10622676—24no—
33C2×#66874C2211yescharacteristic
34C2×#66874C2211yescharacteristic
35C2×#66874C2211yescharacteristic
36C2×#66874C2211yescharacteristic
37#10622577—24no—
38C2×#66872C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622558—21no—
45#10622557—21no—
46C4×C4⋊Dic11C2211yescharacteristic
47#10622542C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622265—21no—
52#10622262—21no—
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C11×#125—22no—
65C11×#125—41no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—41no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4D411yescharacteristic
79C2×C11×C22⋊C4D411yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84#66979—22no—
85#66979—41no—
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89#66977—22no—
90#66977Q814yes—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×#4318—22no—
98C2×#4318—22no—
99C2×#4318—22no—
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C4×Dic22—22no—
105C4×Dic22—41no—
106C11×#95—21no—
107C11×#95—21no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95D411yescharacteristic
112C11×#95D411yescharacteristic
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C22⋊(C11⋊C8)—22no—
118#66874—22no—
119#66874—22no—
120#66874—22no—
121#66874—41no—
122#66872—22no—
123#66872—41no—
124#66872D414yes—
125#66871—22no—
126#66871—22no—
127#66871—22no—
128C4⋊(C11⋊C8)—22no—
129C4⋊(C11⋊C8)—22no—
130#26367—111nomaximal, Sylow
131C24×C11C2×D411yescharacteristic
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—42no—
141C22×C4×C11—42no—
142C22×C4×C11—81no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×Q812yes—
149C22×C4×C11#4112yes—
150C22×C4×C11C2411yescharacteristic
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22C2×Q812yes—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—42no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4—42no—
171C11×C4⋊C4—81no—
172C11×C4⋊C4—81no—
173C11×C4⋊C4C2×D412yes—
174C11×C22⋊C4—41no—
175C11×C22⋊C4—41no—
176C11×C22⋊C4—42no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181C22⋊Dic11—24no—
182C22⋊Dic11—42no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11C2×D412yes—
188C4⋊Dic11C2×Q812yes—
189Dic11⋊C4—24no—
190Dic11⋊C4—42no—
191Dic11⋊C4—42no—
192C4×Dic11—42no—
193C4×Dic11—42no—
194C4×Dic11—42no—
195#4318—28no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8C2×D412yes—
207C2×C11⋊C8#4112yes—
208C2×#479—111no—
209C2×#428—111no—
210#2442D1111yescharacteristic
211#2362—111no—
212#2097—111no—
213#2087—111no—
214#2068—111no—
215#2059—111no—
216#1949—111no—
217#1919—111no—
218#1894—111no—
219#1872—111no—
220#1865—111no—
221#1854—111no—
222#1851—111no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11C22⋊Q812yes—
230C23×C11C22×D411yescharacteristic
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—22no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—84no—
262C2×C4×C11C22⋊Q812yes—
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C22×Q811yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11H(5,𝔽2)11yescharacteristic
268C2×C4×C112−1+411yescharacteristic
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281Dic22—22no—
282Dic22—22no—
283Dic22—41no—
284Dic22—41no—
285C11⋊C8—22no—
286C11⋊C8—22no—
287C11⋊C8—41no—
288C11⋊C8—41no—
289C22×M16—111no—
290C2×#125C2×D1111yescharacteristic
291C2×C22⋊Q8—111no—
292C2×C4×Q8—111no—
293C2×#117—111no—
294C22×C4⋊C4C2×D1111yescharacteristic
295#479—224no—
296#428—224no—
297C2×#107—111no—
298C2×#107—111no—
299C2×#107—111no—
300C2×#106—111no—
301C2×#106—111no—
302C2×#106—111no—
303C2×C4⋊C8—111no—
304C2×C4⋊C8—111no—
305C2×#103—111no—
306C2×#103—111no—
307C2×#103—111no—
308C2×#103—111no—
309C2×C22⋊C8—111no—
310#400—21no—
311#398—21no—
312#391—111no—
313#389—111no—
314#389C2×D1111yescharacteristic
315#389C2×D1111yescharacteristic
316#388—221no—
317#388—221no—
318#387—221no—
319#385—21no—
320#382C2×D1111yescharacteristic
321#380—21no—
322#380C2×D1111yescharacteristic
323C4×C4⋊C4—111no—
324C4×C4⋊C4—221no—
325C4×C22⋊C4C2×D1111yescharacteristic
326#340—111no—
327#340—111no—
328#340—111no—
329#340—111no—
330#340—111no—
331#340—111no—
332#336—111no—
333#336—111no—
334C22×C11—22no—
335C22×C11—22no—
336C22×C11—22no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11C2×C22⋊Q811yescharacteristic
342C22×C11D4211yescharacteristic
343C22×C11#54711yescharacteristic
344C22×C11#57511yescharacteristic
345C22×C11#57511yescharacteristic
346C22×C11#57711yescharacteristic
347C22×C11#57811yescharacteristic
348C4×C11—22no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11—41no—
352C4×C11—41no—
353C4×C11—42no—
354C4×C11—81no—
355C4×C11—81no—
356C4×C11—81no—
357C4×C11#52511yescharacteristic
358C4×C11#53911yescharacteristic
359C4×C11D4×Q811yescharacteristic
360C4×C11#55411yescharacteristic
361Dic11—42no—
362Dic11—42no—
363Dic11—42no—
364Dic11—81no—
365C22×Q8—111no—
366C23×C4—21no—
367C23×C4C22×D1111yescharacteristic
368C2×M16—222no—
369C2×M16—222no—
370C2×M16—222no—
371C22×C8—111no—
372C22×C8—111no—
373C22×C8—111no—
374C22×C8—111no—
375#125—22no—
376#125—41no—
377C22⋊Q8—114no—
378C22⋊Q8—222no—
379C4×Q8—222no—
380C4×Q8—441no—
381#117—222no—
382#117—441no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—41no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4C22×D1111yescharacteristic
397C2×C4⋊C4C22×D1111yescharacteristic
398C2×C4⋊C4C22×D1111yescharacteristic
399C2×C4⋊C4C22×D1111yescharacteristic
400C2×C22⋊C4—21no—
401C2×C22⋊C4—221no—
402C2×C22⋊C4—221no—
403C2×C22⋊C4C22⋊D1111yescharacteristic
404C2×C22⋊C4C22⋊D1111yescharacteristic
405C2×C42—221no—
406C2×C42—221no—
407C2×C42—221no—
408C2×C42C22×D1111yescharacteristic
409C2×C42C22×D1111yescharacteristic
410#107—222no—
411#107—222no—
412#107—222no—
413#106—114no—
414#106—222no—
415#106—441no—
416C4⋊C8—222no—
417C4⋊C8—222no—
418#103—222no—
419#103—222no—
420#103—222no—
421#103—441no—
422C22⋊C8—222no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—221no—
429#95—221no—
430#95—221no—
431#95—221no—
432#95C22⋊D1111yescharacteristic
433#95C22⋊D1111yescharacteristic
434C2×C11—42no—
435C2×C11#244911yescharacteristic
436C2×C11#308011yescharacteristic
437C2×C11#308211yescharacteristic
438C2×C11#326911yescharacteristic
439C2×C11#327511yescharacteristic
440C2×C11#334911yescharacteristic
441C2×C11#335111yescharacteristic
442C24C2×C22⋊D1111yescharacteristic
443C2×Q8—112no—
444C2×Q8—221no—
445C2×Q8—221no—
446C2×Q8—221no—
447C2×Q8—221no—
448C2×Q8—221no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—42no—
458C22×C4—42no—
459C22×C4—81no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4Q8×D1112yes—
465C22×C4#434312yes—
466C22×C4C2×C22⋊D1111yescharacteristic
467C22×C4C2×C22⋊D1111yescharacteristic
468C22×C4C2×C22⋊D1111yescharacteristic
469C22×C4C2×C22⋊D1111yescharacteristic
470C22×C4C2×C22⋊D1111yescharacteristic
471C22×C4C23×D1111yescharacteristic
472M16—228no—
473C2×C8—112no—
474C2×C8—112no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—42no—
493C4⋊C4—42no—
494C4⋊C4—42no—
495C4⋊C4—81no—
496C4⋊C4—81no—
497C4⋊C4—112no—
498C4⋊C4—112no—
499C4⋊C4—224no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—442no—
505C4⋊C4—442no—
506C4⋊C4D4×D1112yes—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C22⋊C4—42no—
510C22⋊C4—224no—
511C22⋊C4—442no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—442no—
517C42—442no—
518C42—442no—
519C11#2636711yescharacteristic, complemented, Sylow
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23#6699912yes—
527C23C22×C22⋊D1111yescharacteristic
528Q8—222no—
529Q8—222no—
530Q8—441no—
531Q8—441no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—84no—
563C2×C4—222no—
564C2×C4—222no—
565C2×C4—222no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4#6699912yes—
576C2×C4C2×D4×D1111yescharacteristic
577C2×C4#6703711yescharacteristic
578C2×C4C2×Q8×D1111yescharacteristic
579C2×C4C2×#434311yescharacteristic
580C2×C4#41×D1111yescharacteristic
581C2×C4#6704311yescharacteristic
582C8—222no—
583C8—222no—
584C8—441no—
585C8—441no—
586C22—22no—
587C22—22no—
588C22—22no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22D4×C22⋊D1111yescharacteristic
594C22C2×#6699911yescharacteristic
595C22#1062335311yescharacteristic
596C22#1062335311yescharacteristic
597C22#1062335511yescharacteristic
598C22#1062336711yescharacteristic
599C22#1062336911yescharacteristic
600C4—22no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—42no—
606C4—81no—
607C4—81no—
608C4—81no—
609C4—442no—
610C4—442no—
611C4—442no—
612C4—881no—
613C4#1062315811yescharacteristic
614C4#1062316311yescharacteristic
615C4#1062316711yescharacteristic
616C4#1062317611yescharacteristic
617C2—42no—
618C2#1307242111yescharacteristic
619C2#1307843411yescharacteristic
620C2#1307845211yescharacteristic
621C2#1308017211yescharacteristic
622C2#1308024311yescharacteristic
623C2#1308114611yescharacteristic
624C2#1308117011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2442C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#2442D11
hypocenterC11#26367
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2442

Complements

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

NH ≅ G/Ntype
1. C2×#10622676C2semidirect
4. #13070167C2semidirect
5. #13070112C2semidirect
6. #13070008C2semidirect
7. #13069951C2semidirect
8. #13069382C2semidirect
9. #13069191C2semidirect
12. #13068883C2semidirect
519. C11#26367semidirect

Maximal subgroups

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

subgroupindex
C2×#106226762
C2×#106225772
#130716412
#130701672
#130701122
#130700082
#130699512
#130693822
#130691912
#130690472
#130689232
#130688832
#130688132
#130688012
C11×#24422
#2636711