Finite Group Databasebeta

← #14816919

Subgroups — #14816919

Order 2816.

796 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622634C211yesmaximal, characteristic
2C2×C4×#4326C211yesmaximal, characteristic
3#13072455C211yesmaximal, characteristic
4#13070155C211yesmaximal, characteristic
5#13070088C211yesmaximal, characteristic
6#13070008C211yesmaximal, characteristic
7#13069944C211yesmaximal, characteristic
8#13069346C211yesmaximal, characteristic
9#13069175C211yesmaximal, characteristic
10#13068957C211yesmaximal, characteristic
11#13068957C211yesmaximal, characteristic
12#13068870C211yesmaximal, characteristic
13#13068870C211yesmaximal, characteristic
14#13068869C211yesmaximal, characteristic
15Q8×C11×C4⋊C4C211yesmaximal, characteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C2×#66922C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C11×#389—21no—
23C11×#389—21no—
24C11×#389C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C11×#384—21no—
27C11×#384C2211yescharacteristic
28C4×C11×C4⋊C4—21no—
29C4×C11×C4⋊C4C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C4×#4326—24no—
34#10622634—24no—
35#10622594—21no—
36#10622592—21no—
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622542C2211yescharacteristic
46#10622542C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622270—21no—
52#10622259—21no—
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Dic22—21no—
63C22×Dic22C2311yescharacteristic
64C4×Q8×C11—22no—
65C4×Q8×C11—22no—
66C4×Q8×C11—22no—
67C4×Q8×C11—22no—
68C4×Q8×C11—41no—
69C4×Q8×C11—41no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C42×C11—21no—
83C2×C42×C11—21no—
84C2×C42×C11—21no—
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×#4326—22no—
89C2×#4326—22no—
90C2×#4326Q814yescomplemented
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×C4×Dic11—21no—
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103#66922—22no—
104#66922—41no—
105C4×Dic22—22no—
106C4×Dic22—41no—
107C11×#95—21no—
108C11×#95—21no—
109C11×#95D411yescharacteristic
110C11×#95D411yescharacteristic
111#66899—22no—
112#66899—22no—
113#66899D414yes—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120#66874—22no—
121#66874—22no—
122#66874—41no—
123#66871—22no—
124#66871—22no—
125#66871—22no—
126#66871—22no—
127#66871—41no—
128C4⋊(C11⋊C8)—22no—
129C4×C11⋊C8—22no—
130#26381—111nomaximal, Sylow
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11C2×D412yes—
135C2×Q8×C11C2×Q812yes—
136C2×Q8×C11#4112yes—
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×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—42no—
158C2×Dic22—42no—
159C2×Dic22—81no—
160C2×Dic22C2×Q812yes—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—41no—
168C11×C4⋊C4—42no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4—42no—
171C11×C4⋊C4—81no—
172C11×C4⋊C4—81no—
173C11×C4⋊C4—81no—
174C11×C4⋊C4Q1614yescomplemented
175C11×C4⋊C4#4112yes—
176C42×C11—24no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—42no—
184C42×C11—42no—
185#4326—28no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—42no—
192C4⋊Dic11C2×D412yes—
193Dic11⋊C4—42no—
194Dic11⋊C4—81no—
195Dic11⋊C4—81no—
196C4×Dic11—42no—
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⋊C8—21no—
207C2×C11⋊C8C2×D412yes—
208C2×C11⋊C8C2×Q812yes—
209C2×#477—111no—
210C2×C4×Q16—111no—
211#2451—111no—
212Q8×C4⋊C4D1111yescharacteristic
213#2095—111no—
214#2083—111no—
215#2068—111no—
216#2057—111no—
217#1942—111no—
218#1916—111no—
219#1878—111no—
220#1878—111no—
221#1863—111no—
222#1863—111no—
223#1863—111no—
224C23×C11C22×D411yescharacteristic
225Q8×C11—22no—
226Q8×C11—22no—
227Q8×C11—22no—
228Q8×C11C22⋊Q814yes—
229C2×C4×C11—21no—
230C2×C4×C11—22no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
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—41no—
249C2×C4×C11—41no—
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×C11C2×Q1612yes—
257C2×C4×C11C2×Q1612yes—
258C2×C4×C11C2×Q1612yes—
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×Q811yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11H(5,𝔽2)11yescharacteristic
264C2×C4×C112−1+411yescharacteristic
265C2×Dic11—22no—
266C2×Dic11—22no—
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—
277Dic22—22no—
278Dic22—22no—
279Dic22—41no—
280Dic22—41no—
281Dic22—84no—
282C11⋊C8—22no—
283C11⋊C8—22no—
284C11⋊C8—41no—
285C11⋊C8—41no—
286C22×Q16—111no—
287C2×C4⋊Q8—111no—
288C2×C4×Q8—111no—
289C2×C4×Q8C2×D1111yescharacteristic
290C2×C4×Q8C2×D1111yescharacteristic
291C2×C4×Q8C2×D1111yescharacteristic
292#477—224no—
293C4×Q16—224no—
294C2×#107—111no—
295C2×#107—111no—
296C2×#107—111no—
297C2×#107—111no—
298C2×#107—111no—
299C2×C4⋊C8—111no—
300C2×#103—111no—
301C2×#103—111no—
302C2×#103—111no—
303C2×#103—111no—
304C2×#103—111no—
305C2×#103—111no—
306C2×C4×C8—111no—
307#398—221no—
308#395—221no—
309#391—111no—
310#391—111no—
311#391—221no—
312#389—21no—
313#389—21no—
314#389—111no—
315#389—111no—
316#389C2×D1111yescharacteristic
317#389C2×D1111yescharacteristic
318#387—221no—
319#384—21no—
320#384C2×D1111yescharacteristic
321C4×C4⋊C4—21no—
322C4×C4⋊C4C2×D1111yescharacteristic
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#336—111no—
328#336—111no—
329#336—111no—
330#336—111no—
331C22×C11#52511yescharacteristic
332C22×C11D4211yescharacteristic
333C22×C11D4×Q811yescharacteristic
334C22×C11C22×Q1611yescharacteristic
335C22×C11#57511yescharacteristic
336C22×C11#57611yescharacteristic
337C22×C11#57811yescharacteristic
338C4×C11—22no—
339C4×C11—24no—
340C4×C11—22no—
341C4×C11—22no—
342C4×C11—41no—
343C4×C11—42no—
344C4×C11—41no—
345C4×C11—41no—
346C4×C11—81no—
347C4×C11—81no—
348C4×C11C2×C22⋊Q811yescharacteristic
349C4×C11#53911yescharacteristic
350C4×C11#54711yescharacteristic
351C4×C11#55411yescharacteristic
352Dic11—42no—
353Dic11—42no—
354Dic11—81no—
355Dic11—81no—
356C22×Q8—111no—
357C22×Q8—221no—
358C22×Q8C22×D1111yescharacteristic
359C2×Q16—114no—
360C2×Q16—222no—
361C2×Q16—222no—
362C22×C8—111no—
363C22×C8—111no—
364C22×C8—111no—
365C22×C8—111no—
366C4⋊Q8—222no—
367C4⋊Q8—441no—
368C4×Q8—22no—
369C4×Q8—22no—
370C4×Q8—22no—
371C4×Q8—22no—
372C4×Q8—41no—
373C4×Q8—41no—
374C4×Q8—222no—
375C4×Q8—441no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4C22⋊D1111yescharacteristic
391C2×C4⋊C4C22⋊D1111yescharacteristic
392C2×C4⋊C4C22×D1111yescharacteristic
393C2×C4⋊C4C22×D1111yescharacteristic
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—221no—
399C2×C42C22×D1111yescharacteristic
400C2×C42C22×D1111yescharacteristic
401C2×C42C22×D1111yescharacteristic
402#107—222no—
403#107—222no—
404#107—222no—
405#107—222no—
406#107—441no—
407C4⋊C8—222no—
408#103—114no—
409#103—222no—
410#103—222no—
411#103—222no—
412#103—222no—
413#103—441no—
414C4×C8—222no—
415#95—21no—
416#95—21no—
417#95—221no—
418#95—221no—
419#95—221no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95C22⋊D1111yescharacteristic
424#95C22⋊D1111yescharacteristic
425C2×C11#244911yescharacteristic
426C2×C11#310411yescharacteristic
427C2×C11#312411yescharacteristic
428C2×C11#326811yescharacteristic
429C2×C11D4×Q1611yescharacteristic
430C2×C11Q8×Q1611yescharacteristic
431C2×C11#339011yescharacteristic
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—112no—
436C2×Q8—221no—
437C2×Q8—221no—
438C2×Q8—221no—
439C2×Q8—221no—
440C2×Q8—221no—
441C2×Q8—442no—
442C2×Q8—442no—
443C2×Q8—881no—
444C2×Q8#433912yes—
445C2×Q8D4×D1112yes—
446C2×Q8Q8×D1112yes—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4C2×C22⋊D1111yescharacteristic
456C22×C4C2×C22⋊D1111yescharacteristic
457C22×C4C2×C22⋊D1111yescharacteristic
458C22×C4C2×C22⋊D1111yescharacteristic
459C22×C4C2×C22⋊D1111yescharacteristic
460C22×C4C2×C22⋊D1111yescharacteristic
461C22×C4C23×D1111yescharacteristic
462Q16—228no—
463C2×C8—112no—
464C2×C8—112no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—221no—
475C4⋊C4—24no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—41no—
482C4⋊C4—42no—
483C4⋊C4—42no—
484C4⋊C4—42no—
485C4⋊C4—81no—
486C4⋊C4—81no—
487C4⋊C4—81no—
488C4⋊C4—112no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—442no—
495C4⋊C4—442no—
496C4⋊C4—881no—
497C4⋊C4—881no—
498C4⋊C4#432614yescomplemented
499C4⋊C4#433912yes—
500C42—24no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—42no—
508C42—42no—
509C42—442no—
510C11#2638111yescharacteristic, complemented, Sylow
511C23C22×C22⋊D1111yescharacteristic
512Q8—22no—
513Q8—22no—
514Q8—22no—
515Q8—222no—
516Q8—222no—
517Q8—441no—
518Q8—441no—
519Q8—884no—
520Q8#6694914yes—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—222no—
549C2×C4—222no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4C2×#432612yes—
561C2×C4C2×#432612yes—
562C2×C4C2×#432612yes—
563C2×C4C2×#433911yescharacteristic
564C2×C4C2×#433911yescharacteristic
565C2×C4C2×D4×D1111yescharacteristic
566C2×C4#6703711yescharacteristic
567C2×C4C2×Q8×D1111yescharacteristic
568C2×C4#6704011yescharacteristic
569C8—222no—
570C8—222no—
571C8—441no—
572C8—441no—
573C22#1062332211yescharacteristic
574C22D4×C22⋊D1111yescharacteristic
575C22C22×#432611yescharacteristic
576C22Q8×C22⋊D1111yescharacteristic
577C22#1062335311yescharacteristic
578C22#1062336611yescharacteristic
579C22#1062336911yescharacteristic
580C4—24no—
581C4—22no—
582C4—22no—
583C4—22no—
584C4—41no—
585C4—41no—
586C4—41no—
587C4—42no—
588C4—81no—
589C4—81no—
590C4—442no—
591C4—442no—
592C4—881no—
593C4—881no—
594C4#1062303811yescharacteristic
595C4C2×#6694911yescharacteristic
596C4#1062304211yescharacteristic
597C4#1062304611yescharacteristic
598C2#1307242511yescharacteristic
599C2#1307865511yescharacteristic
600C2#1307887811yescharacteristic
601C2#1308015711yescharacteristic
602C2D4×#432611yescharacteristic
603C2Q8×#432611yescharacteristic
604C2#1308157911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingQ8×C11×C4⋊C4C2
socle, prime radicalC23×C11C22×D4
hypercenterQ8×C4⋊C4D11
hypocenterC11#26381
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ Q8×C4⋊C4

Complements

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

NH ≅ G/Ntype
90. C2×#4326Q8semidirect
174. C11×C4⋊C4Q16semidirect
498. C4⋊C4#4326semidirect
510. C11#26381semidirect

Maximal subgroups

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

subgroupindex
C2×#106226342
C2×C4×#43262
#130724552
#130701552
#130700882
#130700082
#130699442
#130693462
#130691752
#130689572
#130688702
#130688692
Q8×C11×C4⋊C42
#2638111