Finite Group Databasebeta

← #14816740

Subgroups — #14816740

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×#10622464C211yesmaximal, characteristic
2C2×#10622403C211yesmaximal, characteristic
3#13072457C211yesmaximal, characteristic
4#13071535C211yesmaximal, characteristic
5#13070166C211yesmaximal, characteristic
6#13070102C211yesmaximal, characteristic
7#13069944C211yesmaximal, characteristic
8#13069345C211yesmaximal, characteristic
9#13069170C211yesmaximal, characteristic
10#13068960C211yesmaximal, characteristic
11#13068954C211yesmaximal, characteristic
12#13068886C211yesmaximal, characteristic
13#13068881C211yesmaximal, characteristic
14#13068871C211yesmaximal, characteristic
15C11×#2066C211yesmaximal, characteristic
16C2×Q8×Dic11C2211yescharacteristic
17C22×#4326C2211yescharacteristic
18C2×#66940C2211yescharacteristic
19C2×#66940C2211yescharacteristic
20C2×#66922C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C11×#391C2211yescharacteristic
27C11×#389C2211yescharacteristic
28#10622843C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31C2×#66881C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×C8×Dic11C2211yescharacteristic
35#10622598C2211yescharacteristic
36#10622598C2211yescharacteristic
37#10622590C2211yescharacteristic
38C4⋊C4×Dic11—21no—
39#10622586C2211yescharacteristic
40#10622585—21no—
41C2×#66874C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C4×Dic11⋊C4C2211yescharacteristic
45#10622464—24no—
46#10622403—24no—
47#10622274—21no—
48#10622269—21no—
49#10622268—21no—
50#10622263—21no—
51#10622260—21no—
52#10622259—21no—
53C11×#340C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Dic22—21no—
63C22×Dic22C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71Q8×Dic11—22no—
72Q8×Dic11—41no—
73C2×#4326—22no—
74C2×#4326—22no—
75C2×#4326Q814yescomplemented
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4D411yescharacteristic
88C2×Dic11⋊C4D411yescharacteristic
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11C2311yescharacteristic
94C2×C4×Dic11C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97#66940—22no—
98#66940—22no—
99#66940—22no—
100#66940—41no—
101#66922—22no—
102#66922—41no—
103C4×Dic22—22no—
104C4×Dic22—41no—
105C11×#106—22no—
106C11×C4⋊C8—22no—
107C11×#103—22no—
108C11×#103—22no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95—21no—
112#66899—41no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95D411yescharacteristic
121C11⋊#95D411yescharacteristic
122#66881—22no—
123#66881—22no—
124#66880—22no—
125#66880D414yes—
126C8×Dic11—22no—
127#66874—22no—
128#66871—22no—
129#66871—41no—
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×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×C11C2411yescharacteristic
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C2×Dic22—21no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22—42no—
156C2×Dic22—42no—
157C2×Dic22—81no—
158C2×Dic22C2×D412yes—
159C2×Dic22C2×Q812yes—
160C2×Dic22#4112yes—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11C2×D412yes—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—42no—
173C11×C4⋊C4#4112yes—
174C42×C11—21no—
175C42×C11—21no—
176#4326—28no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—42no—
183C4⋊Dic11—42no—
184C4⋊Dic11—42no—
185C4⋊Dic11—81no—
186C4⋊Dic11C2×D412yes—
187Dic11⋊C4—24no—
188Dic11⋊C4—22no—
189Dic11⋊C4—22no—
190Dic11⋊C4—42no—
191Dic11⋊C4—42no—
192Dic11⋊C4—81no—
193C4×Dic11—24no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—42no—
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×Q812yes—
207C2×#475—111no—
208C2×C4×Q16—111no—
209#2451—111no—
210#2351—111no—
211#2097—111no—
212#2085—111no—
213#2066D1111yescharacteristic
214#2057—111no—
215#1941—111no—
216#1916—111no—
217#1878—111no—
218#1878—111no—
219#1865—111no—
220#1865—111no—
221#1863—111no—
222C23×C11C22×D411yescharacteristic
223Q8×C11—22no—
224Q8×C11—22no—
225Q8×C11—41no—
226Q8×C11—41no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—22no—
230C2×C4×C11—21no—
231C2×C4×C11—22no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11#13512yes—
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×Q811yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11H(5,𝔽2)11yescharacteristic
250C2×C4×C112−1+411yescharacteristic
251C2×Dic11—22no—
252C2×Dic11—21no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—22no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11#13712yes—
275Dic22—22no—
276Dic22—22no—
277Dic22—22no—
278Dic22—84no—
279Dic22C22⋊Q814yes—
280C8×C11—22no—
281C8×C11—41no—
282C11⋊C8—22no—
283C11⋊C8—41no—
284C22×Q16—111no—
285C2×C4⋊Q8—111no—
286C2×C4×Q8—111no—
287C2×C4×Q8—111no—
288C2×C4×Q8—111no—
289C2×C4×Q8—111no—
290#475—224no—
291C4×Q16—224no—
292C2×#107—111no—
293C2×#107—111no—
294C2×#106—111no—
295C2×#106—111no—
296C2×#106C2×D1111yescharacteristic
297C2×C4⋊C8C2×D1111yescharacteristic
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—221no—
314#389—221no—
315#389C2×D1111yescharacteristic
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#336—111no—
329C22×C11#52511yescharacteristic
330C22×C11D4211yescharacteristic
331C22×C11D4×Q811yescharacteristic
332C22×C11C2×#13511yescharacteristic
333C22×C11C2×#13711yescharacteristic
334C22×C11#57711yescharacteristic
335C22×C11#57811yescharacteristic
336C4×C11—22no—
337C4×C11—42no—
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—24no—
347Dic11—22no—
348Dic11—41no—
349Dic11—41no—
350Dic11—42no—
351Dic11—41no—
352Dic11—81no—
353Dic11—81no—
354C22×Q8—111no—
355C22×Q8—221no—
356C22×Q8C22×D1111yescharacteristic
357C2×Q16—114no—
358C2×Q16—222no—
359C2×Q16—222no—
360C22×C8—111no—
361C22×C8—111no—
362C22×C8C22×D1111yescharacteristic
363C22×C8C22×D1111yescharacteristic
364C4⋊Q8—222no—
365C4⋊Q8—441no—
366C4×Q8—222no—
367C4×Q8—222no—
368C4×Q8—222no—
369C4×Q8—222no—
370C4×Q8—222no—
371C4×Q8—441no—
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—221no—
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⋊C4C22×D1111yescharacteristic
389C2×C4⋊C4C22×D1111yescharacteristic
390C2×C4⋊C4C22×D1111yescharacteristic
391C2×C42—111no—
392C2×C42—111no—
393C2×C42—221no—
394C2×C42—221no—
395C2×C42—221no—
396C2×C42—221no—
397C2×C42C22×D1111yescharacteristic
398#107—222no—
399#107—441no—
400#106—22no—
401#106—222no—
402#106—222no—
403C4⋊C8—22no—
404#103—22no—
405#103—22no—
406#103—114no—
407#103—222no—
408#103—222no—
409#103—441no—
410C4×C8—222no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—111no—
415#95—111no—
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—112no—
436C2×Q8—112no—
437C2×Q8—112no—
438C2×Q8—221no—
439C2×Q8—221no—
440C2×Q8—221no—
441C2×Q8—442no—
442C2×Q8—442no—
443C2×Q8—881no—
444C2×Q8Q8×D1112yes—
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—228no—
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×C8D4×D1112yes—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—42no—
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—442no—
489C4⋊C4—442no—
490C4⋊C4—442no—
491C4⋊C4—442no—
492C4⋊C4—442no—
493C4⋊C4—881no—
494C4⋊C4—881no—
495C4⋊C4#434112yes—
496C42—21no—
497C42—21no—
498C42—224no—
499C42—221no—
500C42—221no—
501C42—221no—
502C42—221no—
503C42—442no—
504C42—442no—
505C42—442no—
506C11#2636911yescharacteristic, complemented, Sylow
507C23C2×D4×D1111yescharacteristic
508Q8—22no—
509Q8—22no—
510Q8—41no—
511Q8—41no—
512Q8—114no—
513Q8—222no—
514Q8—222no—
515Q8—222no—
516Q8—884no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—41no—
525C2×C4—41no—
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—222no—
537C2×C4—221no—
538C2×C4—222no—
539C2×C4—222no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—221no—
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#6696912yes—
559C2×C4C2×D4×D1111yescharacteristic
560C2×C4C2×#434111yescharacteristic
561C2×C4C2×Q8×D1111yescharacteristic
562C2×C4#41×D1111yescharacteristic
563C2×C4#6704211yescharacteristic
564C2×C4#6704311yescharacteristic
565C8—22no—
566C8—41no—
567C8—222no—
568C8—441no—
569C22#1062313711yescharacteristic
570C22#1062314011yescharacteristic
571C22#1062316311yescharacteristic
572C22C2×#6696911yescharacteristic
573C22#1062330111yescharacteristic
574C22D11×#13711yescharacteristic
575C22#1062331011yescharacteristic
576C4—22no—
577C4—42no—
578C4—41no—
579C4—42no—
580C4—81no—
581C4—81no—
582C4—224no—
583C4—222no—
584C4—441no—
585C4—442no—
586C4—441no—
587C4—441no—
588C4—881no—
589C4—881no—
590C4#1062314211yescharacteristic
591C4D11×C22⋊Q811yescharacteristic
592C4#1062316611yescharacteristic
593C4#1062323811yescharacteristic
594C2#1307242611yescharacteristic
595C2#1307868411yescharacteristic
596C2#1307884211yescharacteristic
597C2#1308019311yescharacteristic
598C2#1308032011yescharacteristic
599C2#1308150611yescharacteristic
600C2#1308155111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2066C2
socle, prime radicalC23×C11C22×D4
hypercenter#2066D11
hypocenterC11#26369
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2066

Complements

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

NH ≅ G/Ntype
75. C2×#4326Q8semidirect
506. C11#26369semidirect

Maximal subgroups

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

subgroupindex
C2×#106224642
C2×#106224032
#130724572
#130715352
#130701662
#130701022
#130699442
#130693452
#130691702
#130689602
#130689542
#130688862
#130688812
#130688712
C11×#20662
#2636911