Finite Group Databasebeta

← #14775249

Subgroups — #14775249

Order 2816.

802 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071647C211yesmaximal, characteristic
2#13071501C211yesmaximal, characteristic
3#13069360C211yesmaximal, characteristic, complemented
4#13069308C211yesmaximal, characteristic, complemented
5#13069259C211yesmaximal, characteristic, complemented
6#13069210C211yesmaximal, characteristic, complemented
7#13069196C211yesmaximal, characteristic, complemented
8#13069040C211yesmaximal, characteristic
9#13068886C211yesmaximal, characteristic, complemented
10#13068817C211yesmaximal, characteristic
11#13068515C211yesmaximal, characteristic, complemented
12#13068448C211yesmaximal, characteristic, complemented
13#13068395C211yesmaximal, characteristic
14#13068332C211yesmaximal, characteristic
15C2×C11×#485C211yesmaximal, characteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C23×C11⋊C8C2211yescharacteristic
21C11×#485C418yescomplemented
22C2×C11×#107C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27#10622843C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30#10622825C2211yescharacteristic
31C4×C22⋊Dic11C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×#66879C2211yescharacteristic
35C2×#66879C2211yescharacteristic
36#10622598C2211yescharacteristic
37#10622598C2211yescharacteristic
38#10622598C2211yescharacteristic
39#10622594—21no—
40C4⋊C4×Dic11—21no—
41C4⋊C4×Dic11C2211yescharacteristic
42C4⋊C4×Dic11C2211yescharacteristic
43C4⋊C4×Dic11C2211yescharacteristic
44#10622564—21no—
45#10622564—21no—
46#10622564—21no—
47#10622564—21no—
48#10622549—21no—
49#10622545—21no—
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8C2×C414yes—
66C11×#117—22no—
67C11×#117C2×C414yes—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C42×C11—21no—
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11D411yescharacteristic
78C2×C22⋊Dic11D411yescharacteristic
79Q8×Dic11—22no—
80Q8×Dic11—41no—
81#66979—22no—
82#66979—41no—
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×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11C2311yescharacteristic
97C2×C4×Dic11C2311yescharacteristic
98C22×C11⋊C8—22no—
99C22×C11⋊C8—22no—
100C22×C11⋊C8—41no—
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C11×#107C2×C414yes—
104C11×#106C2×C414yes—
105C11×#103C2×C414yes—
106C11×#103C2×C414yes—
107C11×C22⋊C8C2×C414yes—
108#66899—22no—
109#66899—41no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95D411yescharacteristic
120C11⋊#95D411yescharacteristic
121#66882—41no—
122#66881—22no—
123#66879—22no—
124#66879—41no—
125#22939—111nomaximal, Sylow
126C24×C11C2×D411yescharacteristic
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11C22×C412yes—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11C22×C412yes—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11#4112yes—
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11C22×C412yes—
158C2×C8×C11C22×C412yes—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4C22×C412yes—
164C11×C4⋊C4C22×C412yes—
165C11×C4⋊C4C22×C412yes—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—24no—
168C42×C11—24no—
169C22⋊Dic11—41no—
170C22⋊Dic11—41no—
171C22⋊Dic11—42no—
172C22⋊Dic11—81no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—42no—
181C4⋊Dic11—42no—
182C4⋊Dic11—81no—
183C4⋊Dic11—81no—
184C4⋊Dic11#4112yes—
185C4×Dic11—21no—
186C4×Dic11—21no—
187C4×Dic11—21no—
188C4×Dic11—21no—
189C4×Dic11—42no—
190C4×Dic11—42no—
191C4×Dic11—42no—
192C4×Dic11—42no—
193C4×Dic11—42no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—44no—
200C2×C11⋊C8#4112yes—
201C2×#485D1111yescharacteristic
202#2362—111no—
203#2346—111no—
204#1944—111no—
205#1935—111no—
206#1928—111no—
207#1921—111no—
208#1919—111no—
209#1892—111no—
210#1865—111no—
211#1854—111no—
212#1776—111no—
213#1763—111no—
214#1752—111no—
215#1735—111no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11C4×D412yes—
223C23×C11C22×D411yescharacteristic
224Q8×C11—22no—
225Q8×C11—22no—
226Q8×C11—41no—
227Q8×C11—41no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
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—41no—
245C2×C4×C11—41no—
246C2×C4×C11C4×D412yes—
247C2×C4×C11C23×C411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11H(5,𝔽2)11yescharacteristic
252C2×C4×C112−1+411yescharacteristic
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—22no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
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—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C8×C11—22no—
278C8×C11—22no—
279C11⋊C8—22no—
280C11⋊C8—41no—
281C23×C8—111no—
282C2×C22⋊Q8C2×D1111yescharacteristic
283C2×C4×Q8—111no—
284C2×#117—111no—
285C2×#117C2×D1111yescharacteristic
286#485Dic1118yescomplemented
287C2×#107—111no—
288C2×#107C2×D1111yescharacteristic
289C2×#106—111no—
290C2×#106C2×D1111yescharacteristic
291C2×#103—111no—
292C2×#103—111no—
293C2×#103C2×D1111yescharacteristic
294C2×#103C2×D1111yescharacteristic
295C2×C22⋊C8C2×D1111yescharacteristic
296C2×#97—111no—
297C2×#97—111no—
298#391—111no—
299#389—111no—
300#389—111no—
301#389—111no—
302#388—221no—
303#388—221no—
304#388—221no—
305#388—221no—
306#387—221no—
307#382—221no—
308#380—111no—
309C4×C4⋊C4—111no—
310C4×C4⋊C4—111no—
311C4×C4⋊C4—111no—
312C4×C4⋊C4—221no—
313C4×C22⋊C4—111no—
314#376—221no—
315#340—111no—
316#340—111no—
317#340—111no—
318#340—111no—
319#340—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#336—111no—
324#336—111no—
325C22×C11—22no—
326C22×C11—22no—
327C22×C11—22no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11C2×C4×D411yescharacteristic
333C22×C11#54611yescharacteristic
334C22×C11#54711yescharacteristic
335C22×C11#57511yescharacteristic
336C22×C11#57511yescharacteristic
337C22×C11#57711yescharacteristic
338C22×C11#57811yescharacteristic
339C4×C11—22no—
340C4×C11—42no—
341C4×C11—42no—
342C4×C11—42no—
343C4×C11—42no—
344C4×C11C4×#4111yescharacteristic
345C4×C11#52011yescharacteristic
346C4×C11#55111yescharacteristic
347C4×C11#55211yescharacteristic
348Dic11—41no—
349Dic11—41no—
350Dic11—41no—
351Dic11—42no—
352Dic11—41no—
353Dic11—81no—
354Dic11—81no—
355Dic11—81no—
356C22×Q8C22×D1111yescharacteristic
357C23×C4C22×D1111yescharacteristic
358C22×C8—111no—
359C22×C8—111no—
360C22×C8—222no—
361C22×C8—222no—
362C22×C8—441no—
363C22×C8C22×D1111yescharacteristic
364C22×C8C22×D1111yescharacteristic
365C22⋊Q8—22no—
366C22⋊Q8C2×Dic1114yes—
367C4×Q8—222no—
368C4×Q8—441no—
369#117—22no—
370#117—222no—
371#117—441no—
372#117C2×Dic1114yes—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—111no—
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⋊C4C22×D1111yescharacteristic
383C2×C4⋊C4C22×D1111yescharacteristic
384C2×C4⋊C4C22×D1111yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—111no—
388C2×C22⋊C4—111no—
389C2×C22⋊C4—221no—
390C2×C22⋊C4—221no—
391C2×C42—21no—
392C2×C42—111no—
393C2×C42—111no—
394C2×C42—221no—
395C2×C42—221no—
396C2×C42—221no—
397C2×C42—221no—
398C2×C42—221no—
399#107—441no—
400#107C2×Dic1114yes—
401#106—222no—
402#106C2×Dic1114yes—
403#103—222no—
404#103—441no—
405#103C2×Dic1114yes—
406#103C2×Dic1114yes—
407C22⋊C8C2×Dic1114yes—
408#97—222no—
409#97—441no—
410#95—111no—
411#95—111no—
412#95—221no—
413#95—221no—
414#95—221no—
415#95—221no—
416#95—221no—
417#95—221no—
418#95—221no—
419#95—221no—
420#95—221no—
421C2×C11—42no—
422C2×C11#235911yescharacteristic
423C2×C11#294311yescharacteristic
424C2×C11#294711yescharacteristic
425C2×C11#331511yescharacteristic
426C2×C11#332111yescharacteristic
427C2×C11#334811yescharacteristic
428C2×C11#334911yescharacteristic
429C24D4×D1111yescharacteristic
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8C22×Dic1112yes—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—111no—
447C22×C4—111no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4D4×D1111yescharacteristic
453C22×C4#434112yes—
454C22×C4C22×Dic1112yes—
455C22×C4C23×D1111yescharacteristic
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—112no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—444no—
467C2×C8C22×Dic1112yes—
468C2×C8C22×Dic1112yes—
469C4⋊C4—24no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—112no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—442no—
482C4⋊C4—442no—
483C4⋊C4—881no—
484C4⋊C4—881no—
485C4⋊C4C22×Dic1112yes—
486C4⋊C4C22×Dic1112yes—
487C4⋊C4C22×Dic1112yes—
488C22⋊C4—24no—
489C22⋊C4—24no—
490C22⋊C4—441no—
491C22⋊C4—441no—
492C22⋊C4—442no—
493C22⋊C4—881no—
494C42—24no—
495C42—221no—
496C42—221no—
497C42—221no—
498C42—221no—
499C42—442no—
500C42—442no—
501C42—442no—
502C42—442no—
503C42—442no—
504C11#2293911yescharacteristic, complemented, Sylow
505C23—21no—
506C23—21no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23D4×Dic1112yes—
512C23C2×D4×D1111yescharacteristic
513Q8—22no—
514Q8—22no—
515Q8—41no—
516Q8—41no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
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—221no—
545C2×C4—222no—
546C2×C4—221no—
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—441no—
559C2×C4D4×Dic1112yes—
560C2×C4C2×#434111yescharacteristic
561C2×C4#41×D1111yescharacteristic
562C2×C4#41×D1111yescharacteristic
563C2×C4#6704211yescharacteristic
564C2×C4#6704311yescharacteristic
565C2×C4C23×Dic1111yescharacteristic
566C8—22no—
567C8—22no—
568C8—222no—
569C8—441no—
570C22—22no—
571C22—22no—
572C22—22no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22#1062318511yescharacteristic
578C22#1062318611yescharacteristic
579C22#1062329911yescharacteristic
580C22#1062329911yescharacteristic
581C22#1062330911yescharacteristic
582C22#1062331011yescharacteristic
583C22C2×D4×Dic1111yescharacteristic
584C4—22no—
585C4—42no—
586C4—42no—
587C4—42no—
588C4—42no—
589C4—441no—
590C4—441no—
591C4—441no—
592C4—442no—
593C4—441no—
594C4—881no—
595C4—881no—
596C4—881no—
597C4#1062318111yescharacteristic
598C4#1062318911yescharacteristic
599C4#41×Dic1111yescharacteristic
600C4#1062335811yescharacteristic
601C2—42no—
602C2#1307161211yescharacteristic
603C2#1307741711yescharacteristic
604C2#1307746011yescharacteristic
605C2#1308071011yescharacteristic
606C2#1308080011yescharacteristic
607C2#1308113511yescharacteristic
608C2#1308115011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#485C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×#485D11
hypocenterC11#22939
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
3. #13069360C2semidirect
4. #13069308C2semidirect
5. #13069259C2semidirect
6. #13069210C2semidirect
7. #13069196C2semidirect
9. #13068886C2semidirect
11. #13068515C2semidirect
12. #13068448C2semidirect
21. C11×#485C4semidirect
286. #485Dic11semidirect
504. C11#22939semidirect

Maximal subgroups

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

subgroupindex
#130716472
#130715012
#130693602
#130693082
#130692592
#130692102
#130691962
#130690402
#130688862
#130688172
#130685152
#130684482
#130683952
#130683322
C2×C11×#4852
#2293911