Finite Group Databasebeta

← #14816743

Subgroups — #14816743

Order 2816.

788 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×#10622633C211yesmaximal, characteristic
2C2×Q16×Dic11C211yesmaximal, characteristic
3#13072457C211yesmaximal, characteristic
4#13071534C211yesmaximal, characteristic
5#13070162C211yesmaximal, characteristic
6#13070103C211yesmaximal, characteristic
7#13069997C211yesmaximal, characteristic
8#13069945C211yesmaximal, characteristic
9#13069343C211yesmaximal, characteristic
10#13069176C211yesmaximal, characteristic
11#13068959C211yesmaximal, characteristic
12#13068882C211yesmaximal, characteristic
13#13068882C211yesmaximal, characteristic
14#13068872C211yesmaximal, characteristic
15C11×#1878C211yesmaximal, characteristic
16C22×C11×Q16C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×#66922C2211yescharacteristic
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×C8×Dic11C2211yescharacteristic
34#10622633—24no—
35#10622598C2211yescharacteristic
36#10622590—21no—
37#10622590C2211yescharacteristic
38#10622586—21no—
39#10622586C2211yescharacteristic
40#10622586C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C4×Dic11⋊C4—21no—
45C4×Dic11⋊C4C2211yescharacteristic
46#10622541—21no—
47#10622541C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622274—21no—
50#10622269—21no—
51#10622268—21no—
52#10622259—21no—
53C11×#340C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
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×Dic11—41no—
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⋊C4D411yescharacteristic
95C2×Dic11⋊C4D411yescharacteristic
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11C2311yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103#66922—22no—
104#66922—41no—
105C11×#103—22no—
106C11×#103—41no—
107C11×#95—21no—
108C11×#95—21no—
109#66899—22no—
110#66899—22no—
111#66899—22no—
112#66899D414yes—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95D411yescharacteristic
122C11⋊#95D411yescharacteristic
123#66882—22no—
124#66882—41no—
125C8×Dic11—22no—
126#66872—22no—
127#66872—22no—
128#66872—22no—
129C4⋊(C11⋊C8)—22no—
130#26369—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—42no—
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—42no—
184C4⋊Dic11—42no—
185C4⋊Dic11—42no—
186C4⋊Dic11—81no—
187C4⋊Dic11C2×D412yes—
188C4⋊Dic11#4112yes—
189Dic11⋊C4—22no—
190Dic11⋊C4—22no—
191Dic11⋊C4—42no—
192Dic11⋊C4—42no—
193Dic11⋊C4—81no—
194C4×Dic11—24no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199C4×Dic11—42no—
200C4×Dic11—42no—
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×#475—111no—
208C2×C4×Q16—111no—
209#2451—111no—
210#2351—111no—
211#2097—111no—
212#2085—111no—
213#2066—111no—
214#2057—111no—
215#1941—111no—
216#1916—111no—
217#1878—111no—
218#1878D1111yescharacteristic
219#1865—111no—
220#1865—111no—
221#1863—111no—
222C23×C11C22×D411yescharacteristic
223Q8×C11—22no—
224Q8×C11—22no—
225Q8×C11—22no—
226Q8×C11—22no—
227Q8×C11—22no—
228Q8×C11—41no—
229Q8×C11—41no—
230Q8×C11C22⋊Q814yes—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—21no—
234C2×C4×C11—22no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—22no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11#13512yes—
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C22×Q811yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11H(5,𝔽2)11yescharacteristic
254C2×C4×C112−1+411yescharacteristic
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—22no—
260C2×Dic11—21no—
261C2×Dic11—22no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
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#13712yes—
279Dic22—84no—
280C8×C11—22no—
281C8×C11—41no—
282C11⋊C8—22no—
283C11⋊C8—41no—
284C22×Q16C2×D1111yescharacteristic
285C2×C4⋊Q8—111no—
286C2×C4×Q8—111no—
287C2×C4×Q8—111no—
288C2×C4×Q8—111no—
289C2×C4×Q8C2×D1111yescharacteristic
290#475—224no—
291C4×Q16—224no—
292C2×#107—111no—
293C2×#107—111no—
294C2×#106—111no—
295C2×#106—111no—
296C2×#106—111no—
297C2×C4⋊C8—111no—
298C2×#103—111no—
299C2×#103—111no—
300C2×#103—111no—
301C2×#103—111no—
302C2×#103C2×D1111yescharacteristic
303C2×#103C2×D1111yescharacteristic
304C2×C4×C8—111no—
305#398—221no—
306#395—221no—
307#391—111no—
308#391—221no—
309#391C2×D1111yescharacteristic
310#389—111no—
311#389—111no—
312#389—111no—
313#389—111no—
314#389—221no—
315#389—221no—
316#387—221no—
317#382—111no—
318#382—221no—
319C4×C4⋊C4—111no—
320C4×C4⋊C4—221no—
321#340—111no—
322#340—111no—
323#340—111no—
324#340C2×D1111yescharacteristic
325#336—111no—
326#336—111no—
327#336—111no—
328#336C2×D1111yescharacteristic
329C22×C11#52511yescharacteristic
330C22×C11D4211yescharacteristic
331C22×C11D4×Q811yescharacteristic
332C22×C11C2×#13511yescharacteristic
333C22×C11C2×#13711yescharacteristic
334C22×C11#57711yescharacteristic
335C22×C11#57811yescharacteristic
336C4×C11—24no—
337C4×C11—22no—
338C4×C11—42no—
339C4×C11—41no—
340C4×C11—81no—
341C4×C11—81no—
342C4×C11C2×C22⋊Q811yescharacteristic
343C4×C11#53911yescharacteristic
344C4×C11#54711yescharacteristic
345C4×C11#55411yescharacteristic
346Dic11—22no—
347Dic11—41no—
348Dic11—42no—
349Dic11—41no—
350Dic11—42no—
351Dic11—41no—
352Dic11—81no—
353Dic11—81no—
354C22×Q8—221no—
355C22×Q8C22×D1111yescharacteristic
356C22×Q8C22×D1111yescharacteristic
357C2×Q16—22no—
358C2×Q16—22no—
359C2×Q16Dic2214yescomplemented
360C22×C8—111no—
361C22×C8—111no—
362C22×C8C22×D1111yescharacteristic
363C22×C8C22×D1111yescharacteristic
364C4⋊Q8—222no—
365C4⋊Q8—441no—
366C4×Q8—22no—
367C4×Q8—41no—
368C4×Q8—222no—
369C4×Q8—222no—
370C4×Q8—222no—
371C4×Q8—222no—
372C4×Q8—441no—
373C4×Q8—441no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4C22×D1111yescharacteristic
390C2×C4⋊C4C22×D1111yescharacteristic
391C2×C42—21no—
392C2×C42—111no—
393C2×C42—111no—
394C2×C42—221no—
395C2×C42—221no—
396C2×C42—221no—
397C2×C42C22×D1111yescharacteristic
398#107—222no—
399#107—441no—
400#106—222no—
401#106—222no—
402#106—222no—
403C4⋊C8—222no—
404#103—22no—
405#103—41no—
406#103—114no—
407#103—222no—
408#103—222no—
409#103—222no—
410C4×C8—222no—
411#95—21no—
412#95—21no—
413#95—111no—
414#95—111no—
415#95—221no—
416#95—221no—
417#95—221no—
418#95—221no—
419#95—221no—
420#95—221no—
421#95—221no—
422#95—221no—
423C2×C11#244911yescharacteristic
424C2×C11#310711yescharacteristic
425C2×C11#312111yescharacteristic
426C2×C11#327011yescharacteristic
427C2×C11#328211yescharacteristic
428C2×C11#338311yescharacteristic
429C2×C11#338711yescharacteristic
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—442no—
439C2×Q8—442no—
440C2×Q8—881no—
441C2×Q8C2×Dic2212yes—
442C2×Q8C2×Dic2212yes—
443C2×Q8D4×D1112yes—
444C2×Q8#434112yes—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—111no—
450C22×C4—111no—
451C22×C4—111no—
452C22×C4—111no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4D4×D1111yescharacteristic
458C22×C4D4×D1111yescharacteristic
459C22×C4C23×D1111yescharacteristic
460Q16—28no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—112no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8C2×Dic2212yes—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—42no—
478C4⋊C4—112no—
479C4⋊C4—112no—
480C4⋊C4—222no—
481C4⋊C4—224no—
482C4⋊C4—222no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—442no—
490C4⋊C4—442no—
491C4⋊C4—442no—
492C4⋊C4—442no—
493C4⋊C4—442no—
494C4⋊C4—881no—
495C4⋊C4—881no—
496C42—21no—
497C42—21no—
498C42—42no—
499C42—224no—
500C42—221no—
501C42—221no—
502C42—221no—
503C42—221no—
504C42—442no—
505C42—442no—
506C11#2636911yescharacteristic, complemented, Sylow
507C23C2×D4×D1111yescharacteristic
508Q8—22no—
509Q8—22no—
510Q8—22no—
511Q8—22no—
512Q8—22no—
513Q8—41no—
514Q8—41no—
515Q8—884no—
516Q8#6693114yes—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—112no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—222no—
545C2×C4—221no—
546C2×C4—222no—
547C2×C4—221no—
548C2×C4—441no—
549C2×C4—441no—
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#6697212yes—
559C2×C4C22×Dic2211yescharacteristic
560C2×C4C2×D4×D1111yescharacteristic
561C2×C4C2×#434111yescharacteristic
562C2×C4#6703711yescharacteristic
563C2×C4#41×D1111yescharacteristic
564C2×C4#6704311yescharacteristic
565C8—22no—
566C8—41no—
567C8—222no—
568C8—441no—
569C22D4×Dic2211yescharacteristic
570C22#1062312111yescharacteristic
571C22#1062313711yescharacteristic
572C22C2×#6697211yescharacteristic
573C22#1062330211yescharacteristic
574C22D11×#13711yescharacteristic
575C22#1062330911yescharacteristic
576C4—24no—
577C4—22no—
578C4—42no—
579C4—41no—
580C4—81no—
581C4—81no—
582C4—222no—
583C4—441no—
584C4—441no—
585C4—442no—
586C4—441no—
587C4—442no—
588C4—881no—
589C4—881no—
590C4C2×#6693111yescharacteristic
591C4#1062307011yescharacteristic
592C4#1062313311yescharacteristic
593C4#1062318611yescharacteristic
594C2#1307242911yescharacteristic
595C2#1307868611yescharacteristic
596C2#1307884411yescharacteristic
597C2#1308018411yescharacteristic
598C2#1308031611yescharacteristic
599C2#1308150511yescharacteristic
600C2#1308154911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1878C2
socle, prime radicalC23×C11C22×D4
hypercenter#1878D11
hypocenterC11#26369
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
359. C2×Q16Dic22semidirect
506. C11#26369semidirect

Maximal subgroups

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

subgroupindex
C2×#106226332
C2×Q16×Dic112
#130724572
#130715342
#130701622
#130701032
#130699972
#130699452
#130693432
#130691762
#130689592
#130688822
#130688722
C11×#18782
#2636911