Finite Group Databasebeta

← #14816946

Subgroups — #14816946

Order 2816.

772 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622676C211yesmaximal, characteristic
2C2×C4×#4326C211yesmaximal, characteristic
3#13071536C211yesmaximal, characteristic
4#13070164C211yesmaximal, characteristic
5#13070097C211yesmaximal, characteristic
6#13070011C211yesmaximal, characteristic
7#13069951C211yesmaximal, characteristic
8#13069346C211yesmaximal, characteristic
9#13069175C211yesmaximal, characteristic
10#13068960C211yesmaximal, characteristic
11#13068960C211yesmaximal, characteristic
12#13068884C211yesmaximal, characteristic
13#13068883C211yesmaximal, characteristic
14#13068869C211yesmaximal, characteristic
15C11×#2453C211yesmaximal, characteristic
16C2×C11×#125C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C22×#4326C2211yescharacteristic
19C2×C4×Dic22C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C11×#400—21no—
23C11×#398—21no—
24C11×#391C2211yescharacteristic
25C11×#391C2211yescharacteristic
26C11×#389—21no—
27C11×#389C2211yescharacteristic
28C11×#389C2211yescharacteristic
29C11×#387—21no—
30C4×C11×C4⋊C4C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34#10622676—24no—
35C4×#4326—24no—
36#10622585—21no—
37#10622585—21no—
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622549C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622263—21no—
52#10622262—21no—
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Dic22C2311yescharacteristic
63C11×#125—22no—
64C11×#125—41no—
65C4×Q8×C11—22no—
66C4×Q8×C11—41no—
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⋊C4D411yescharacteristic
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C42×C11—21no—
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×#4326—22no—
82C2×#4326—22no—
83C2×#4326Q814yes—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C4×Dic22—22no—
100C4×Dic22—22no—
101C4×Dic22—22no—
102C4×Dic22—22no—
103C4×Dic22—41no—
104C4×Dic22—41no—
105C11×#95—21no—
106C11×#95—21no—
107C11×#95—21no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95D411yescharacteristic
112C11×#95D411yescharacteristic
113#66899—22no—
114#66899—22no—
115#66899—41no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120#66874—22no—
121#66874—22no—
122#66874D414yes—
123#66872—22no—
124#66872—41no—
125#66871—22no—
126#66871—22no—
127#66871—22no—
128C4⋊(C11⋊C8)—22no—
129C4×C11⋊C8—22no—
130#26383—111nomaximal, Sylow
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11C2×Q812yes—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C2×Dic22—21no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22C2×D412yes—
156C2×Dic22C2×Q812yes—
157C2×Dic22#4112yes—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—41no—
165C11×C4⋊C4—42no—
166C11×C4⋊C4—42no—
167C11×C4⋊C4—42no—
168C11×C4⋊C4—42no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4C2×D412yes—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—42no—
178#4326—28no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11#4112yes—
185Dic11⋊C4—24no—
186Dic11⋊C4—42no—
187Dic11⋊C4—42no—
188Dic11⋊C4—42no—
189Dic11⋊C4—42no—
190C4×Dic11—24no—
191C4×Dic11—42no—
192C4×Dic11—42no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
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⋊C8C2×D412yes—
204C2×C11⋊C8C2×Q812yes—
205C2×#479—111no—
206C2×C4×Q16—111no—
207#2453D1111yescharacteristic
208#2351—111no—
209#2097—111no—
210#2085—111no—
211#2068—111no—
212#2059—111no—
213#1942—111no—
214#1916—111no—
215#1878—111no—
216#1878—111no—
217#1865—111no—
218#1865—111no—
219#1863—111no—
220C23×C11C22×D411yescharacteristic
221Q8×C11—22no—
222Q8×C11—22no—
223Q8×C11—41no—
224Q8×C11—41no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
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×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11#13512yes—
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×Q811yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11H(5,𝔽2)11yescharacteristic
260C2×C4×C112−1+411yescharacteristic
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273Dic22—22no—
274Dic22—22no—
275Dic22—22no—
276Dic22C22⋊Q814yes—
277C11⋊C8—22no—
278C11⋊C8—22no—
279C11⋊C8—41no—
280C11⋊C8—41no—
281C22×Q16—111no—
282C2×#125C2×D1111yescharacteristic
283C2×C4×Q8—111no—
284C2×C4×Q8—111no—
285C2×C4×Q8—111no—
286C2×C4×Q8C2×D1111yescharacteristic
287#479—224no—
288C4×Q16—224no—
289C2×#107—111no—
290C2×#107—111no—
291C2×#107—111no—
292C2×#106—111no—
293C2×#106—111no—
294C2×C4⋊C8—111no—
295C2×#103—111no—
296C2×#103—111no—
297C2×#103—111no—
298C2×#103—111no—
299C2×#103—111no—
300C2×#103—111no—
301C2×C4×C8—111no—
302#400—21no—
303#398—21no—
304#391C2×D1111yescharacteristic
305#391C2×D1111yescharacteristic
306#389—21no—
307#389—111no—
308#389—111no—
309#389—221no—
310#389—221no—
311#389C2×D1111yescharacteristic
312#389C2×D1111yescharacteristic
313#387—21no—
314#382—111no—
315#382—221no—
316C4×C4⋊C4—221no—
317C4×C4⋊C4C2×D1111yescharacteristic
318#340—111no—
319#340—111no—
320#340—111no—
321#340—111no—
322#336—111no—
323#336—111no—
324#336—111no—
325#336—111no—
326C22×C11#52511yescharacteristic
327C22×C11D4211yescharacteristic
328C22×C11D4×Q811yescharacteristic
329C22×C11C2×#13511yescharacteristic
330C22×C11#57511yescharacteristic
331C22×C11#57811yescharacteristic
332C22×C11#57811yescharacteristic
333C4×C11—22no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—42no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11—42no—
340C4×C11—41no—
341C4×C11—81no—
342C4×C11—81no—
343C4×C11C2×C22⋊Q811yescharacteristic
344C4×C11#53911yescharacteristic
345C4×C11#54711yescharacteristic
346C4×C11#55411yescharacteristic
347Dic11—24no—
348Dic11—42no—
349Dic11—81no—
350Dic11—81no—
351C22×Q8—111no—
352C22×Q8C22×D1111yescharacteristic
353C2×Q16—114no—
354C2×Q16—222no—
355C2×Q16—222no—
356C22×C8—111no—
357C22×C8—111no—
358C22×C8—111no—
359C22×C8—111no—
360#125—22no—
361#125—41no—
362C4×Q8—22no—
363C4×Q8—41no—
364C4×Q8—222no—
365C4×Q8—222no—
366C4×Q8—222no—
367C4×Q8—222no—
368C4×Q8—441no—
369C4×Q8—441no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4C22⋊D1111yescharacteristic
384C2×C4⋊C4C22⋊D1111yescharacteristic
385C2×C4⋊C4C22×D1111yescharacteristic
386C2×C4⋊C4C22×D1111yescharacteristic
387C2×C4⋊C4C22×D1111yescharacteristic
388C2×C42—21no—
389C2×C42—221no—
390C2×C42—221no—
391C2×C42—221no—
392C2×C42C22×D1111yescharacteristic
393C2×C42C22×D1111yescharacteristic
394C2×C42C22×D1111yescharacteristic
395#107—222no—
396#107—222no—
397#107—222no—
398#106—222no—
399#106—441no—
400C4⋊C8—222no—
401#103—114no—
402#103—222no—
403#103—222no—
404#103—222no—
405#103—222no—
406#103—441no—
407C4×C8—222no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—221no—
415#95—221no—
416#95—221no—
417#95—221no—
418#95C22⋊D1111yescharacteristic
419#95C22⋊D1111yescharacteristic
420C2×C11#244911yescharacteristic
421C2×C11#310211yescharacteristic
422C2×C11#312711yescharacteristic
423C2×C11#326911yescharacteristic
424C2×C11#328511yescharacteristic
425C2×C11#338311yescharacteristic
426C2×C11#339011yescharacteristic
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—112no—
433C2×Q8—112no—
434C2×Q8—112no—
435C2×Q8—221no—
436C2×Q8—221no—
437C2×Q8—221no—
438C2×Q8Q8×D1112yes—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4C2×C22⋊D1111yescharacteristic
448C22×C4C2×C22⋊D1111yescharacteristic
449C22×C4C2×C22⋊D1111yescharacteristic
450C22×C4C2×C22⋊D1111yescharacteristic
451C22×C4C2×C22⋊D1111yescharacteristic
452C22×C4C2×C22⋊D1111yescharacteristic
453C22×C4C23×D1111yescharacteristic
454Q16—228no—
455C2×C8—112no—
456C2×C8—112no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—221no—
467C4⋊C4—22no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—41no—
474C4⋊C4—42no—
475C4⋊C4—42no—
476C4⋊C4—42no—
477C4⋊C4—42no—
478C4⋊C4—42no—
479C4⋊C4—112no—
480C4⋊C4—224no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—442no—
487C4⋊C4—442no—
488C4⋊C4—442no—
489C4⋊C4—442no—
490C4⋊C4D4×D1112yes—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—42no—
498C42—224no—
499C42—442no—
500C42—442no—
501C11#2638311yescharacteristic, complemented, Sylow
502C23C22×C22⋊D1111yescharacteristic
503Q8—22no—
504Q8—22no—
505Q8—41no—
506Q8—41no—
507Q8—114no—
508Q8—222no—
509Q8—222no—
510Q8—222no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—222no—
541C2×C4—222no—
542C2×C4—222no—
543C2×C4—222no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4#6700312yes—
553C2×C4C2×D4×D1111yescharacteristic
554C2×C4#6703711yescharacteristic
555C2×C4C2×Q8×D1111yescharacteristic
556C2×C4#6704011yescharacteristic
557C2×C4#41×D1111yescharacteristic
558C2×C4#41×D1111yescharacteristic
559C8—222no—
560C8—222no—
561C8—441no—
562C8—441no—
563C22D4×C22⋊D1111yescharacteristic
564C22Q8×C22⋊D1111yescharacteristic
565C22C2×#6700311yescharacteristic
566C22#1062335311yescharacteristic
567C22#1062335911yescharacteristic
568C22#1062336911yescharacteristic
569C22#1062336911yescharacteristic
570C4—22no—
571C4—41no—
572C4—42no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—42no—
577C4—41no—
578C4—81no—
579C4—81no—
580C4—224no—
581C4—442no—
582C4—881no—
583C4—881no—
584C4D11×C22⋊Q811yescharacteristic
585C4#1062316211yescharacteristic
586C4#1062316711yescharacteristic
587C4#1062316911yescharacteristic
588C2#1307242211yescharacteristic
589C2#1307862811yescharacteristic
590C2#1307891111yescharacteristic
591C2#1308016711yescharacteristic
592C2#1308035311yescharacteristic
593C2#1308150311yescharacteristic
594C2#1308157911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2453C2
socle, prime radicalC23×C11C22×D4
hypercenter#2453D11
hypocenterC11#26383
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2453

Complements

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

NH ≅ G/Ntype
501. C11#26383semidirect

Maximal subgroups

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

subgroupindex
C2×#106226762
C2×C4×#43262
#130715362
#130701642
#130700972
#130700112
#130699512
#130693462
#130691752
#130689602
#130688842
#130688832
#130688692
C11×#24532
#2638311