Finite Group Databasebeta

← #14775340

Subgroups — #14775340

Order 2816.

818 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622475C211yesmaximal, characteristic
2#13071645C211yesmaximal, characteristic
3#13071489C211yesmaximal, characteristic
4#13069358C211yesmaximal, characteristic, complemented
5#13069292C211yesmaximal, characteristic, complemented
6#13069257C211yesmaximal, characteristic, complemented
7#13069203C211yesmaximal, characteristic, complemented
8#13069201C211yesmaximal, characteristic, complemented
9#13069048C211yesmaximal, characteristic
10#13068881C211yesmaximal, characteristic, complemented
11#13068814C211yesmaximal, characteristic
12#13068445C211yesmaximal, characteristic, complemented
13#13068399C211yesmaximal, characteristic
14#13068334C211yesmaximal, characteristic
15C4×C11×#106C211yesmaximal, characteristic, complemented
16C22×#4313C2211yescharacteristic
17C2×#66950C2211yescharacteristic
18C2×#66945C2211yescharacteristic
19C2×C4⋊C4×D11C2211yescharacteristic
20C2×#66940C2211yescharacteristic
21C2×C11×#106C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26C2×(C2×D11)⋊C8C2211yescharacteristic
27C2×#66880C2211yescharacteristic
28C2×#66880C2211yescharacteristic
29C2×#66879C2211yescharacteristic
30#10622600C2211yescharacteristic
31#10622598C2211yescharacteristic
32C4⋊C4×Dic11C2211yescharacteristic
33#10622586C2211yescharacteristic
34C2×#66874C2211yescharacteristic
35C2×#66874C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37C2×#66871C2211yescharacteristic
38#10622553—21no—
39C4×(C2×D11)⋊C4—21no—
40C4×(C2×D11)⋊C4C2211yescharacteristic
41C4×C4⋊Dic11—21no—
42#10622546—21no—
43#10622542C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622475C418yescomplemented
46#10622283—21no—
47#10622280—21no—
48#10622266—21no—
49#10622265—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×C4×D11—21no—
61C22×C4×D11C2311yescharacteristic
62C22×Dic22C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C42×C11—21no—
70C2×C42×C11—21no—
71C2×C42×C11C2311yescharacteristic
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4D411yescharacteristic
76C2×(C2×D11)⋊C4D411yescharacteristic
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C2×#4313—22no—
93C2×#4313—22no—
94C2×#4313—41no—
95#66950—22no—
96#66950C2×C414yes—
97#66945—22no—
98#66945—41no—
99C4⋊C4×D11—22no—
100C4⋊C4×D11C2×C414yes—
101#66940—22no—
102#66940—41no—
103C11×#106—22no—
104C11×#106C2×C414yes—
105C4×C8×C11—22no—
106C11×#95—21no—
107C11×#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95D411yescharacteristic
116C11⋊#95D411yescharacteristic
117(C2×D11)⋊C8C2×C414yes—
118#66880—22no—
119#66880C2×C414yes—
120#66879—41no—
121#66874—41no—
122#66874C2×C414yes—
123#66872C2×C414yes—
124#66871—41no—
125#22945—111nomaximal, Sylow
126C23×D11C2×D411yescharacteristic
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2411yescharacteristic
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11C2×D411yescharacteristic
139C22×Dic11C2×D411yescharacteristic
140C22×Dic11C2×D411yescharacteristic
141C2×C4×D11—24no—
142C2×C4×D11—21no—
143C2×C4×D11—21no—
144C2×C4×D11—21no—
145C2×C4×D11—21no—
146C2×C4×D11—81no—
147C2×C4×D11—81no—
148C2×C4×D11C22×C412yes—
149C2×C4×D11#4112yes—
150C2×Dic22—21no—
151C2×Dic22—21no—
152C2×Dic22—21no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22C22×C412yes—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11C22×C412yes—
161C2×C8×C11#4112yes—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4C22×C412yes—
168C11×C4⋊C4C22×C412yes—
169C11×C4⋊C4#4112yes—
170C42×C11—21no—
171C42×C11—21no—
172C42×C11—42no—
173C42×C11—81no—
174(C2×D11)⋊C4—24no—
175(C2×D11)⋊C4—22no—
176(C2×D11)⋊C4—41no—
177(C2×D11)⋊C4—42no—
178(C2×D11)⋊C4—42no—
179C4⋊Dic11—24no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—42no—
186C4⋊Dic11C22×C412yes—
187Dic11⋊C4—24no—
188Dic11⋊C4—42no—
189Dic11⋊C4—81no—
190Dic11⋊C4—81no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—42no—
194C4×Dic11—42no—
195C4×Dic11—81no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8C22×C412yes—
202#4313—44no—
203C2×#483—111no—
204#2362—111no—
205#2345—111no—
206#1944—111no—
207#1933—111no—
208#1928—111no—
209#1920—111no—
210#1920—111no—
211#1894—111no—
212#1865—111no—
213#1854—111no—
214C4×#106D1111yescharacteristic, complemented
215#1763—111no—
216#1753—111no—
217#1736—111no—
218C23×C11C22×D411yescharacteristic
219C22×D11—21no—
220C22×D11—21no—
221C22×D11—21no—
222C22×D11—21no—
223C22×D11—21no—
224C22×D11—21no—
225C22×D11C4×D412yes—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—21no—
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#13712yes—
244C2×C4×C11C23×C411yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11H(5,𝔽2)11yescharacteristic
249C2×C4×C112−1+411yescharacteristic
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11C4×D412yes—
271C4×D11—22no—
272C4×D11—22no—
273C4×D11—22no—
274C4×D11—22no—
275C4×D11—84no—
276Dic22—22no—
277Dic22—22no—
278Dic22—41no—
279Dic22—41no—
280C8×C11—22no—
281C8×C11—22no—
282C11⋊C8—22no—
283C11⋊C8—41no—
284C22×M16—111no—
285C2×C22⋊Q8—111no—
286C2×C4×Q8—111no—
287C2×#117—111no—
288C22×C4⋊C4—111no—
289#483—118no—
290C2×#107—111no—
291C2×#106—111no—
292C2×#106C2×D1111yescharacteristic
293C2×#106C2×D1111yescharacteristic
294C2×#103—111no—
295C2×#103—111no—
296C2×#103—111no—
297C2×#103—111no—
298C2×C22⋊C8—111no—
299C2×#97—111no—
300C2×C4×C8C2×D1111yescharacteristic
301#391—111no—
302#389—111no—
303#389—111no—
304#389—111no—
305#388—221no—
306#388—221no—
307#387—221no—
308#387—221no—
309#387—221no—
310#380—111no—
311#380—221no—
312C4×C4⋊C4—111no—
313C4×C4⋊C4—221no—
314C4×C4⋊C4C2×D1111yescharacteristic
315C4×C4⋊C4C2×D1111yescharacteristic
316C4×C22⋊C4—111no—
317C4×C22⋊C4—221no—
318#340—111no—
319#340—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#340—111no—
324#340C2×D1111yescharacteristic
325#340C2×D1111yescharacteristic
326#336—111no—
327#336—111no—
328C22×C11C2×C4×D411yescharacteristic
329C22×C11#54611yescharacteristic
330C22×C11#54711yescharacteristic
331C22×C11C2×#13711yescharacteristic
332C22×C11#57511yescharacteristic
333C22×C11#57711yescharacteristic
334C22×C11#57711yescharacteristic
335C2×D11—22no—
336C2×D11—22no—
337C2×D11—22no—
338C2×D11—41no—
339C2×D11—41no—
340C2×D11—41no—
341C2×D11—41no—
342C4×C11—22no—
343C4×C11—42no—
344C4×C11—41no—
345C4×C11—42no—
346C4×C11—42no—
347C4×C11—81no—
348C4×C11C4×#4111yescharacteristic
349C4×C11#52011yescharacteristic
350C4×C11#55111yescharacteristic
351C4×C11#55211yescharacteristic
352Dic11—22no—
353Dic11—41no—
354Dic11—42no—
355Dic11—42no—
356Dic11—41no—
357Dic11—81no—
358Dic11—81no—
359C22×Q8—111no—
360C23×C4—111no—
361C23×C4—221no—
362C2×M16—222no—
363C2×M16—222no—
364C2×M16—441no—
365C22×C8—111no—
366C22×C8—111no—
367C22×C8C22×D1111yescharacteristic
368C22×C8C22×D1111yescharacteristic
369C22⋊Q8—114no—
370C22⋊Q8—222no—
371C4×Q8—222no—
372C4×Q8—441no—
373#117—222no—
374#117—441no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—114no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—222no—
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⋊C4C22×D1111yescharacteristic
387C2×C4⋊C4C22×D1111yescharacteristic
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C4⋊C4C22×D1111yescharacteristic
390C2×C22⋊C4—111no—
391C2×C22⋊C4—111no—
392C2×C22⋊C4—221no—
393C2×C22⋊C4—221no—
394C2×C22⋊C4—221no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—111no—
398C2×C42—221no—
399C2×C42—221no—
400C2×C42—221no—
401C2×C42C22×D1111yescharacteristic
402#107—441no—
403#106—22no—
404#106—114no—
405#106C4×D1114yes—
406#103—114no—
407#103—114no—
408#103—222no—
409#103—441no—
410C22⋊C8—114no—
411#97—441no—
412C4×C8—22no—
413#95—21no—
414#95—21no—
415#95—111no—
416#95—111no—
417#95—221no—
418#95—221no—
419#95—221no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424C2×C11#235911yescharacteristic
425C2×C11C4×#13711yescharacteristic
426C2×C11#294911yescharacteristic
427C2×C11#332611yescharacteristic
428C2×C11#333111yescharacteristic
429C2×C11#334411yescharacteristic
430C2×C11#335011yescharacteristic
431D11—42no—
432C24—111no—
433C2×Q8—112no—
434C2×Q8—221no—
435C2×Q8—221no—
436C2×Q8—221no—
437C2×Q8—221no—
438C2×Q8—221no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—111no—
444C22×C4—112no—
445C22×C4—112no—
446C22×C4—111no—
447C22×C4—111no—
448C22×C4—224no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—881no—
458C22×C4—881no—
459C22×C4D4×D1111yescharacteristic
460C22×C4D4×D1111yescharacteristic
461C22×C4C23×D1111yescharacteristic
462M16—444no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—112no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8C2×C4×D1112yes—
474C2×C8#433912yes—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—112no—
481C4⋊C4—224no—
482C4⋊C4—224no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—442no—
489C4⋊C4—442no—
490C4⋊C4—881no—
491C4⋊C4—881no—
492C4⋊C4C2×C4×D1112yes—
493C4⋊C4C2×C4×D1112yes—
494C4⋊C4#433912yes—
495C22⋊C4—224no—
496C22⋊C4—222no—
497C22⋊C4—441no—
498C22⋊C4—442no—
499C22⋊C4—442no—
500C42—21no—
501C42—21no—
502C42—42no—
503C42—81no—
504C42—221no—
505C42—221no—
506C42—442no—
507C42—442no—
508C42—881no—
509C11#2294511yescharacteristic, complemented, Sylow
510C23—112no—
511C23—221no—
512C23—221no—
513C23—221no—
514C23—221no—
515C23—221no—
516C23—221no—
517C23C2×D4×D1111yescharacteristic
518Q8—222no—
519Q8—222no—
520Q8—441no—
521Q8—441no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
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—112no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—222no—
543C2×C4—222no—
544C2×C4—222no—
545C2×C4—222no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—222no—
551C2×C4—222no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—884no—
565C2×C4#6696812yes—
566C2×C4C22×C4×D1111yescharacteristic
567C2×C4C2×#433911yescharacteristic
568C2×C4C2×#433911yescharacteristic
569C2×C4#6704011yescharacteristic
570C2×C4#41×D1111yescharacteristic
571C2×C4#6704211yescharacteristic
572C8—22no—
573C8—22no—
574C8—222no—
575C8—441no—
576C22—222no—
577C22—222no—
578C22—222no—
579C22—441no—
580C22—441no—
581C22—441no—
582C22—441no—
583C22#1062303811yescharacteristic
584C22C4×D4×D1111yescharacteristic
585C22#1062308111yescharacteristic
586C22C2×#6696811yescharacteristic
587C22#1062329311yescharacteristic
588C22#1062329911yescharacteristic
589C22#1062330111yescharacteristic
590C4—22no—
591C4—41no—
592C4—42no—
593C4—42no—
594C4—42no—
595C4—81no—
596C4—222no—
597C4—441no—
598C4—441no—
599C4—442no—
600C4—442no—
601C4—881no—
602C4—881no—
603C4C4×#433911yescharacteristic
604C4#1062305811yescharacteristic
605C4#1062310511yescharacteristic
606C4#1062311211yescharacteristic
607C2—442no—
608C2#1307161311yescharacteristic
609C2C4×#6696811yescharacteristic
610C2#1307747011yescharacteristic
611C2#1308087411yescharacteristic
612C2#1308093411yescharacteristic
613C2#1308106711yescharacteristic
614C2#1308115711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#106C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenterC4×#106D11
hypocenterC11#22945
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#106

Complements

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

NH ≅ G/Ntype
4. #13069358C2semidirect
5. #13069292C2semidirect
6. #13069257C2semidirect
7. #13069203C2semidirect
8. #13069201C2semidirect
10. #13068881C2semidirect
12. #13068445C2semidirect
15. C4×C11×#106C2semidirect
45. #10622475C4semidirect
214. C4×#106D11semidirect
509. C11#22945semidirect

Maximal subgroups

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

subgroupindex
C2×#106224752
#130716452
#130714892
#130693582
#130692922
#130692572
#130692032
#130692012
#130690482
#130688812
#130688142
#130684452
#130683992
#130683342
C4×C11×#1062
#2294511