Finite Group Databasebeta

← #14764302

Subgroups — #14764302

Order 2816.

834 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622446C211yesmaximal, characteristic
2#13071012C211yesmaximal, characteristic
3D11×#382C211yesmaximal, characteristic
4#13069386C211yesmaximal, characteristic, complemented
5#13069384C211yesmaximal, characteristic, complemented
6#13069382C211yesmaximal, characteristic, complemented
7#13068810C211yesmaximal, characteristic
8#13068807C211yesmaximal, characteristic
9#13068805C211yesmaximal, characteristic
10#13068802C211yesmaximal, characteristic
11#13068779C211yesmaximal, characteristic, complemented
12#13068777C211yesmaximal, characteristic, complemented
13#13068745C211yesmaximal, characteristic, complemented
14#13068745C211yesmaximal, characteristic, complemented
15C11×#1949C211yesmaximal, characteristic, complemented
16C2×C4⋊C4×D11C2211yescharacteristic
17C2×C4⋊C4×D11C2211yescharacteristic
18C2×C42×D11C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C11×#382C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×(C2×D11)⋊C8C2211yescharacteristic
25C2×(C2×D11)⋊C8C2211yescharacteristic
26C2×#66882C2211yescharacteristic
27C2×#66881C2211yescharacteristic
28C2×C8×Dic11C2211yescharacteristic
29C2×C8×Dic11C2211yescharacteristic
30#10622600C2211yescharacteristic
31#10622600C2211yescharacteristic
32#10622590C2211yescharacteristic
33#10622590C2211yescharacteristic
34#10622590C2211yescharacteristic
35#10622590C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37C2×#66872C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C4×(C2×D11)⋊C4—21no—
41#10622549C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43#10622545—21no—
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45#10622446C418yescomplemented
46#10622277—21no—
47D11×#95—21no—
48D11×#95—21no—
49#10622264—21no—
50#10622263—21no—
51#10622263—21no—
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×C4×D11—21no—
61C22×C4×D11—21no—
62C22×C4×D11D411yescharacteristic
63C22×C4×D11D411yescharacteristic
64C22×C4×D11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C42×C11—21no—
72C2×C42×C11C2311yescharacteristic
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×C4×Dic11—21no—
82C2×C4×Dic11D411yescharacteristic
83C2×C4×Dic11D411yescharacteristic
84C2×C4×Dic11C2311yescharacteristic
85C22×C11⋊C8C2311yescharacteristic
86C22×C11⋊C8C2311yescharacteristic
87C4⋊C4×D11—41no—
88C4⋊C4×D11—41no—
89C4⋊C4×D11—41no—
90C4⋊C4×D11—41no—
91C42×D11C2×C414yes—
92C42×D11Q814yes—
93C11×#107—41no—
94C11×#106—41no—
95C11×C4⋊C8C2×C414yescomplemented
96C11×#95—21no—
97C11×#95—21no—
98C11×#95—21no—
99C11⋊#95—21no—
100C11⋊#95—21no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112(C2×D11)⋊C8C2×C414yes—
113(C2×D11)⋊C8C2×C414yes—
114#66882—41no—
115#66881—41no—
116C8×Dic11C2×C414yescomplemented
117C8×Dic11C2×C414yescomplemented
118#66872—41no—
119#66872—41no—
120#66871—41no—
121#66871—41no—
122C4⋊(C11⋊C8)C2×C414yescomplemented
123#21983—111nomaximal, Sylow
124C23×D11C2×D411yescharacteristic
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11C2×D411yescharacteristic
137C22×Dic11C2×D411yescharacteristic
138C22×Dic11C2×D411yescharacteristic
139C2×C4×D11—22no—
140C2×C4×D11—22no—
141C2×C4×D11—21no—
142C2×C4×D11—21no—
143C2×C4×D11—21no—
144C2×C4×D11—21no—
145C2×C4×D11—41no—
146C2×C4×D11—41no—
147C2×C4×D11—42no—
148C2×C4×D11—42no—
149C2×C4×D11—42no—
150C2×C4×D11—42no—
151C2×C4×D11—42no—
152C2×C4×D11—42no—
153C2×C4×D11C4⋊C414yes—
154C2×C4×D11C4⋊C414yes—
155C2×C4×D11C22×C412yes—
156C2×C4×D11C2×Q812yes—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11C22×C412yes—
162C2×C8×C11C22×C412yes—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C42×C11—42no—
172C42×C11C22×C412yes—
173C42×C11C2×Q812yes—
174(C2×D11)⋊C4—42no—
175(C2×D11)⋊C4—42no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184Dic11⋊C4—42no—
185Dic11⋊C4—42no—
186C4×Dic11—42no—
187C4×Dic11C4⋊C414yes—
188C4×Dic11C4⋊C414yes—
189C4×Dic11C22×C412yes—
190C4×Dic11C2×Q812yes—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8C22×C412yes—
196C2×C11⋊C8C22×C412yes—
197C2×#431—111no—
198#2283—111no—
199C2×#382—111no—
200#1949—111no—
201#1949—111no—
202#1949—111no—
203#1949D1111yescharacteristic, complemented
204#1853—111no—
205#1853—111no—
206#1852—111no—
207#1852—111no—
208#1846—111no—
209#1846—111no—
210#1835—111no—
211#1835—111no—
212C23×C11C22×D411yescharacteristic
213C22×D11—21no—
214C22×D11—21no—
215C22×D11—21no—
216C22×D11—21no—
217C22×D11C2×C4⋊C412yes—
218C22×D11#13512yes—
219C22×D11#13512yes—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11C2×C4⋊C412yes—
237C2×C4×C11C2×C4⋊C412yes—
238C2×C4×C11C23×C411yescharacteristic
239C2×C4×C11C22×Q811yescharacteristic
240C2×C4×C11H(5,𝔽2)11yescharacteristic
241C2×C4×C11H(5,𝔽2)11yescharacteristic
242C2×C4×C112−1+411yescharacteristic
243C2×C4×C112−1+411yescharacteristic
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11C2×C4⋊C412yes—
263C2×Dic11C2×C4⋊C412yes—
264C2×Dic11C2×C4⋊C412yes—
265C4×D11—28no—
266C4×D11—22no—
267C4×D11—22no—
268C4×D11—22no—
269C4×D11—22no—
270C4×D11—44no—
271C4×D11—84no—
272C4×D11—84no—
273C8×C11—22no—
274C8×C11—22no—
275C11⋊C8—22no—
276C11⋊C8—22no—
277C22×C4⋊C4—111no—
278C22×C4⋊C4—111no—
279C22×C42—111no—
280#431—118no—
281C2×#107—111no—
282C2×#107—111no—
283C2×#107—111no—
284C2×#107C2×D1111yescharacteristic
285C2×#106—111no—
286C2×#106—111no—
287C2×#106—111no—
288C2×#106C2×D1111yescharacteristic
289C2×C4⋊C8—111no—
290C2×C4⋊C8C2×D1111yescharacteristic
291C2×C22⋊C8—111no—
292C2×C22⋊C8—111no—
293C2×C4×C8—111no—
294C2×C4×C8—111no—
295#383—221no—
296#382—111no—
297#382—111no—
298#382—111no—
299#382—111no—
300#382—111no—
301#382—221no—
302#382—221no—
303#382C2×D1111yescharacteristic
304#381—221no—
305#380—111no—
306#380—111no—
307C4×C4⋊C4—111no—
308C4×C4⋊C4C2×D1111yescharacteristic
309C4×C22⋊C4—221no—
310#376—221no—
311C2×#95—221no—
312C2×#95—221no—
313#340—111no—
314#340—111no—
315#340—111no—
316#340—111no—
317#340—111no—
318#340—111no—
319#340C2×D1111yescharacteristic
320#340C2×D1111yescharacteristic
321C22×C11C22×C4⋊C411yescharacteristic
322C22×C11#53511yescharacteristic
323C22×C11#53611yescharacteristic
324C22×C11C2×#13511yescharacteristic
325C22×C11C2×#13511yescharacteristic
326C22×C11#57511yescharacteristic
327C22×C11#57511yescharacteristic
328C2×D11—22no—
329C2×D11—22no—
330C2×D11—22no—
331C2×D11—22no—
332C2×D11—22no—
333C2×D11—22no—
334C2×D11#42714yes—
335C4×C11—22no—
336C4×C11—22no—
337C4×C11—81no—
338C4×C11—81no—
339C4×C11—81no—
340C4×C11—81no—
341C4×C11#52011yescharacteristic
342C4×C11#52011yescharacteristic
343C4×C11#54411yescharacteristic
344C4×C11#54411yescharacteristic
345Dic11—22no—
346Dic11—22no—
347Dic11—22no—
348Dic11—81no—
349Dic11—81no—
350Dic11—81no—
351Dic11—81no—
352C23×C4—111no—
353C23×C4—111no—
354C23×C4—111no—
355C23×C4—221no—
356C23×C4—221no—
357C22×C8—111no—
358C22×C8—111no—
359C22×C8C22×D1111yescharacteristic
360C22×C8C22×D1111yescharacteristic
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—441no—
368C2×C4⋊C4—441no—
369C2×C4⋊C4—441no—
370C2×C4⋊C4—441no—
371C2×C4⋊C4C22×D1111yescharacteristic
372C2×C4⋊C4C22×D1111yescharacteristic
373C2×C4⋊C4C22×D1111yescharacteristic
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C22⋊C4—221no—
376C2×C22⋊C4—221no—
377C2×C42—21no—
378C2×C42—111no—
379C2×C42—111no—
380C2×C42—111no—
381C2×C42—114no—
382C2×C42—114no—
383C2×C42—221no—
384C2×C42C22×D1111yescharacteristic
385#107—41no—
386#107—441no—
387#107—441no—
388#107—441no—
389#106—41no—
390#106—441no—
391#106—441no—
392#106—441no—
393C4⋊C8—114no—
394C4⋊C8C4×D1114yescomplemented
395C22⋊C8—114no—
396C22⋊C8—114no—
397C4×C8—114no—
398C4×C8—114no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—221no—
403#95—221no—
404#95—221no—
405#95—221no—
406#95—221no—
407#95—221no—
408#95—221no—
409#95—221no—
410#95—221no—
411#95—221no—
412#95—221no—
413#95—221no—
414#95—221no—
415C2×C11#231711yescharacteristic
416C2×C11C2×#42711yescharacteristic
417C2×C11#291111yescharacteristic
418C2×C11#321111yescharacteristic
419C2×C11#321111yescharacteristic
420C2×C11#323211yescharacteristic
421C2×C11#323211yescharacteristic
422D11—24no—
423C24—111no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—111no—
429C22×C4—111no—
430C22×C4—111no—
431C22×C4—114no—
432C22×C4—112no—
433C22×C4—112no—
434C22×C4—114no—
435C22×C4—222no—
436C22×C4—222no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4—221no—
441C22×C4—221no—
442C22×C4—221no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—441no—
446C22×C4—441no—
447C22×C4—442no—
448C22×C4—442no—
449C22×C4—442no—
450C22×C4—442no—
451C22×C4—442no—
452C22×C4—442no—
453C22×C4D4×D1111yescharacteristic
454C22×C4D4×D1111yescharacteristic
455C22×C4C23×D1111yescharacteristic
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—112no—
461C2×C8—112no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8C2×C4×D1112yes—
467C2×C8C2×C4×D1112yes—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—442no—
485C4⋊C4—442no—
486C22⋊C4—442no—
487C22⋊C4—442no—
488C42—42no—
489C42—114no—
490C42—114no—
491C42—112no—
492C42—112no—
493C42—442no—
494C42C2×C4×D1112yes—
495C42Q8×D1112yes—
496C11#2198311yescharacteristic, complemented, Sylow
497C23—112no—
498C23—112no—
499C23—112no—
500C23—221no—
501C23—221no—
502C23—221no—
503C23—221no—
504C23C2×D4×D1111yescharacteristic
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—112no—
522C2×C4—112no—
523C2×C4—112no—
524C2×C4—228no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—222no—
532C2×C4—222no—
533C2×C4—222no—
534C2×C4—222no—
535C2×C4—444no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—884no—
549C2×C4—884no—
550C2×C4C4⋊C4×D1112yes—
551C2×C4C4⋊C4×D1112yes—
552C2×C4C22×C4×D1111yescharacteristic
553C2×C4#6703711yescharacteristic
554C2×C4C2×Q8×D1111yescharacteristic
555C2×C4#6704011yescharacteristic
556C2×C4#6704211yescharacteristic
557C2×C4#6704311yescharacteristic
558C8—22no—
559C8—22no—
560C8—222no—
561C8—222no—
562C22—114no—
563C22—222no—
564C22—222no—
565C22—222no—
566C22—222no—
567C22—222no—
568C22—222no—
569C22C2×C4⋊C4×D1111yescharacteristic
570C22#1062313811yescharacteristic
571C22#1062315911yescharacteristic
572C22D11×#13511yescharacteristic
573C22D11×#13511yescharacteristic
574C22#1062330411yescharacteristic
575C22#1062330811yescharacteristic
576C4—22no—
577C4—22no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4—81no—
582C4—222no—
583C4—222no—
584C4—222no—
585C4—881no—
586C4—881no—
587C4—881no—
588C4—881no—
589C4#1062307711yescharacteristic
590C4#1062310511yescharacteristic
591C4#1062322011yescharacteristic
592C4#1062326011yescharacteristic
593C2—224no—
594C2#1307123811yescharacteristic
595C2D11×#42711yescharacteristic
596C2#1307720311yescharacteristic
597C2#1307957911yescharacteristic
598C2#1307958511yescharacteristic
599C2#1307978211yescharacteristic
600C2#1307978811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1949C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1949D11
hypocenterC11#21983
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
4. #13069386C2semidirect
5. #13069384C2semidirect
6. #13069382C2semidirect
11. #13068779C2semidirect
12. #13068777C2semidirect
13. #13068745C2semidirect
14. #13068745C2semidirect
15. C11×#1949C2semidirect
45. #10622446C4semidirect
95. C11×C4⋊C8C2×C4semidirect
116. C8×Dic11C2×C4semidirect
117. C8×Dic11C2×C4semidirect
122. C4⋊(C11⋊C8)C2×C4semidirect
203. #1949D11semidirect
394. C4⋊C8C4×D11semidirect
496. C11#21983semidirect

Maximal subgroups

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

subgroupindex
C2×#106224462
#130710122
D11×#3822
#130693862
#130693842
#130693822
#130688102
#130688072
#130688052
#130688022
#130687792
#130687772
#130687452
C11×#19492
#2198311