Finite Group Databasebeta

← #14796458

Subgroups — #14796458

Order 2816.

806 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622407C211yesmaximal, characteristic
2C2×Q16×Dic11C211yesmaximal, characteristic
3#13073826C211yesmaximal, characteristic
4Q8×Dic11⋊C4C211yesmaximal, characteristic
5#13070091C211yesmaximal, characteristic
6#13070089C211yesmaximal, characteristic
7#13070011C211yesmaximal, characteristic
8#13070009C211yesmaximal, characteristic
9#13069575C211yesmaximal, characteristic
10#13069333C211yesmaximal, characteristic
11#13068959C211yesmaximal, characteristic
12#13068621C211yesmaximal, characteristic
13#13068619C211yesmaximal, characteristic
14#13068619C211yesmaximal, characteristic
15C11×#1878C211yesmaximal, characteristic
16C22×C11×Q16C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×#66941C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C11×#391C2211yescharacteristic
25#10622843C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30Q16×Dic11—24no—
31C2×#66882C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36#10622589—21no—
37#10622589C2211yescharacteristic
38#10622589C2211yescharacteristic
39#10622586—21no—
40#10622586C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42#10622548C2211yescharacteristic
43C4×Dic11⋊C4—21no—
44C4×Dic11⋊C4C2211yescharacteristic
45#10622541—21no—
46#10622541C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48#10622407—24no—
49#10622269—21no—
50#10622269—21no—
51#10622260—21no—
52#10622260—21no—
53C11×#340C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×Dic22—21no—
64C2×C11×Q16—22no—
65C2×C11×Q16—22no—
66C2×C11×Q16Q814yescomplemented
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C4×Q8×C11—22no—
70C4×Q8×C11—41no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C42×C11—21no—
75C2×C42×C11C2311yescharacteristic
76Q8×Dic11—22no—
77Q8×Dic11—22no—
78Q8×Dic11—22no—
79Q8×Dic11—22no—
80Q8×Dic11—41no—
81Q8×Dic11D414yes—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4D411yescharacteristic
99C2×Dic11⋊C4D411yescharacteristic
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11C2311yescharacteristic
104C2×C4×Dic11C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107#66941—22no—
108#66941—22no—
109C11×#103—22no—
110C11×#103—41no—
111C11×#95—21no—
112C11×#95—21no—
113#66899—22no—
114#66899—22no—
115#66899—22no—
116#66899—41no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95D411yescharacteristic
122C11⋊#95D411yescharacteristic
123#66882—22no—
124#66882—22no—
125Dic11⋊C8—22no—
126Dic11⋊C8—41no—
127C8×Dic11—22no—
128#66871—22no—
129C4⋊(C11⋊C8)—41no—
130#24817—111nomaximal, Sylow
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11C2×D412yes—
140C2×Q8×C11C2×Q812yes—
141C2×Q8×C11C2×Q812yes—
142C2×Q8×C11#4112yes—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C2×Dic22—42no—
159C2×Dic22—81no—
160C2×Dic22—81no—
161C11×Q16—28no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11C2×Q812yes—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—42no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—42no—
176C4⋊Dic11—24no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—42no—
185C4⋊Dic11—42no—
186C4⋊Dic11—81no—
187C4⋊Dic11—81no—
188C4⋊Dic11C2×D412yes—
189Dic11⋊C4—22no—
190Dic11⋊C4—42no—
191Dic11⋊C4—42no—
192Dic11⋊C4—81no—
193Dic11⋊C4—81no—
194Dic11⋊C4—81no—
195Dic11⋊C4—81no—
196Dic11⋊C4—81no—
197Dic11⋊C4Q1614yescomplemented
198C4×Dic11—24no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11—42no—
202C4×Dic11—42no—
203C4×Dic11C2×D412yes—
204C4×Dic11#4112yes—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×#477—111no—
212C2×C4×Q16—111no—
213#2567—111no—
214Q8×C4⋊C4—111no—
215#2083—111no—
216#2083—111no—
217#2068—111no—
218#2068—111no—
219#1990—111no—
220#1939—111no—
221#1878—111no—
222#1878D1111yescharacteristic
223#1803—111no—
224#1803—111no—
225#1803—111no—
226C23×C11C22×D411yescharacteristic
227Q8×C11—22no—
228Q8×C11—22no—
229Q8×C11—22no—
230Q8×C11—22no—
231Q8×C11—22no—
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11C22⋊Q814yes—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—21no—
238C2×C4×C11—22no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—22no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11C2×Q1612yes—
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C22×Q811yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11H(5,𝔽2)11yescharacteristic
258C2×C4×C112−1+411yescharacteristic
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—22no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11#12112yes—
279C2×Dic11#12112yes—
280C2×Dic11C2×Q1612yes—
281C2×Dic11C2×Q1612yes—
282C2×Dic11#13712yes—
283Dic22—84no—
284C8×C11—22no—
285C8×C11—41no—
286C11⋊C8—41no—
287C11⋊C8—41no—
288C22×Q16C2×D1111yescharacteristic
289C2×C4⋊Q8—111no—
290C2×C4×Q8—111no—
291C2×C4×Q8—111no—
292C2×C4×Q8—111no—
293C2×C4×Q8C2×D1111yescharacteristic
294#477—224no—
295C4×Q16—224no—
296C2×#107—111no—
297C2×#107—111no—
298C2×#107—111no—
299C2×C4⋊C8—111no—
300C2×C4⋊C8—111no—
301C2×C4⋊C8—111no—
302C2×#103—111no—
303C2×#103—111no—
304C2×#103—111no—
305C2×#103—111no—
306C2×#103C2×D1111yescharacteristic
307C2×#103C2×D1111yescharacteristic
308C2×C4×C8—111no—
309#395—221no—
310#395—221no—
311#391—111no—
312#391C2×D1111yescharacteristic
313#389—111no—
314#389—111no—
315#389—221no—
316#389—221no—
317#389—221no—
318#389—221no—
319#384—111no—
320#384—111no—
321#384—111no—
322#384—221no—
323C4×C4⋊C4—111no—
324C4×C4⋊C4—221no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340—111no—
329#340—111no—
330#340C2×D1111yescharacteristic
331#336—111no—
332#336C2×D1111yescharacteristic
333C22×C11C2×#12111yescharacteristic
334C22×C11#54611yescharacteristic
335C22×C11D4×Q811yescharacteristic
336C22×C11C22×Q1611yescharacteristic
337C22×C11C2×#13711yescharacteristic
338C22×C11#57611yescharacteristic
339C22×C11#57711yescharacteristic
340C4×C11—24no—
341C4×C11—22no—
342C4×C11—41no—
343C4×C11—42no—
344C4×C11—81no—
345C4×C11—81no—
346C4×C11C2×C22⋊Q811yescharacteristic
347C4×C11#53711yescharacteristic
348C4×C11#55211yescharacteristic
349C4×C11#55411yescharacteristic
350Dic11—22no—
351Dic11—22no—
352Dic11—41no—
353Dic11—42no—
354Dic11—81no—
355Dic11—81no—
356Dic11—81no—
357Dic11#46214yes—
358C22×Q8—221no—
359C22×Q8C22×D1111yescharacteristic
360C22×Q8C22×D1111yescharacteristic
361C2×Q16—22no—
362C2×Q16—22no—
363C2×Q16Dic2214yescomplemented
364C22×C8—111no—
365C22×C8—111no—
366C22×C8C22×D1111yescharacteristic
367C22×C8C22×D1111yescharacteristic
368C4⋊Q8—222no—
369C4⋊Q8—222no—
370C4×Q8—22no—
371C4×Q8—41no—
372C4×Q8—114no—
373C4×Q8—222no—
374C4×Q8—222no—
375C4×Q8—222no—
376C4×Q8—222no—
377C4×Q8—441no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4C22×D1111yescharacteristic
398C2×C4⋊C4C22×D1111yescharacteristic
399C2×C42—21no—
400C2×C42—111no—
401C2×C42—111no—
402C2×C42—221no—
403C2×C42—221no—
404C2×C42—221no—
405C2×C42C22×D1111yescharacteristic
406#107—222no—
407#107—222no—
408#107—222no—
409C4⋊C8—222no—
410C4⋊C8—441no—
411C4⋊C8—441no—
412#103—22no—
413#103—41no—
414#103—222no—
415#103—222no—
416#103—222no—
417#103—441no—
418C4×C8—222no—
419#95—21no—
420#95—21no—
421#95—111no—
422#95—111no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427C2×C11#241711yescharacteristic
428C2×C11C2×#46211yescharacteristic
429C2×C11#304511yescharacteristic
430C2×C11#329911yescharacteristic
431C2×C11#333311yescharacteristic
432C2×C11Q8×Q1611yescharacteristic
433C2×C11#338711yescharacteristic
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—442no—
443C2×Q8—881no—
444C2×Q8—881no—
445C2×Q8C2×Dic2212yes—
446C2×Q8C2×Dic2212yes—
447C2×Q8D4×D1112yes—
448C2×Q8#434112yes—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—111no—
456C22×C4—111no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4D4×D1111yescharacteristic
462C22×C4D4×D1111yescharacteristic
463C22×C4C23×D1111yescharacteristic
464Q16—28no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8C2×Dic2212yes—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—42no—
482C4⋊C4—114no—
483C4⋊C4—112no—
484C4⋊C4—222no—
485C4⋊C4—224no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—442no—
494C4⋊C4—442no—
495C4⋊C4—442no—
496C4⋊C4—442no—
497C4⋊C4—881no—
498C4⋊C4—881no—
499C4⋊C4—881no—
500C4⋊C4—881no—
501C4⋊C4—881no—
502C4⋊C4—881no—
503C4⋊C4—881no—
504C42—21no—
505C42—21no—
506C42—42no—
507C42—112no—
508C42—112no—
509C42—224no—
510C42—221no—
511C42—221no—
512C42—442no—
513C42—442no—
514C11#2481711yescharacteristic, complemented, Sylow
515C23C2×D4×D1111yescharacteristic
516Q8—22no—
517Q8—22no—
518Q8—22no—
519Q8—22no—
520Q8—22no—
521Q8—41no—
522Q8—41no—
523Q8—884no—
524Q8#6693114yes—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—112no—
543C2×C4—112no—
544C2×C4—112no—
545C2×C4—112no—
546C2×C4—112no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—222no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4Q16×D1112yes—
567C2×C4C22×Dic2211yescharacteristic
568C2×C4C2×D4×D1111yescharacteristic
569C2×C4C2×#434111yescharacteristic
570C2×C4#6703711yescharacteristic
571C2×C4#41×D1111yescharacteristic
572C2×C4#6704311yescharacteristic
573C8—22no—
574C8—41no—
575C8—441no—
576C8—441no—
577C22D4×Dic2211yescharacteristic
578C22#1062312211yescharacteristic
579C22D11×#12111yescharacteristic
580C22C2×Q16×D1111yescharacteristic
581C22#1062330011yescharacteristic
582C22D11×#13711yescharacteristic
583C22#1062330911yescharacteristic
584C4—22no—
585C4—24no—
586C4—41no—
587C4—42no—
588C4—81no—
589C4—81no—
590C4—114no—
591C4—222no—
592C4—222no—
593C4—441no—
594C4—442no—
595C4—881no—
596C4—881no—
597C4—881no—
598C4C2×#6693111yescharacteristic
599C4#1062307011yescharacteristic
600C4#1062312811yescharacteristic
601C4#1062318111yescharacteristic
602C2#1307206411yescharacteristic
603C2D11×#46211yescharacteristic
604C2#1307815811yescharacteristic
605C2#1308048511yescharacteristic
606C2#1308094711yescharacteristic
607C2Q16×Dic2211yescharacteristic
608C2#1308154911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1878C2
socle, prime radicalC23×C11C22×D4
hypercenter#1878D11
hypocenterC11#24817
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1878

Complements

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

NH ≅ G/Ntype
66. C2×C11×Q16Q8semidirect
197. Dic11⋊C4Q16semidirect
363. C2×Q16Dic22semidirect
514. C11#24817semidirect

Maximal subgroups

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

subgroupindex
C2×#106224072
C2×Q16×Dic112
#130738262
Q8×Dic11⋊C42
#130700912
#130700892
#130700112
#130700092
#130695752
#130693332
#130689592
#130686212
#130686192
C11×#18782
#2481711