Finite Group Databasebeta

← #14775145

Subgroups — #14775145

Order 2816.

846 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622497C211yesmaximal, characteristic
2#13071623C211yesmaximal, characteristic
3#13071489C211yesmaximal, characteristic
4#13069353C211yesmaximal, characteristic, complemented
5#13069306C211yesmaximal, characteristic, complemented
6#13069250C211yesmaximal, characteristic, complemented
7#13069189C211yesmaximal, characteristic, complemented
8#13069187C211yesmaximal, characteristic, complemented
9#13069038C211yesmaximal, characteristic
10#13068881C211yesmaximal, characteristic, complemented
11#13068807C211yesmaximal, characteristic
12#13068445C211yesmaximal, characteristic, complemented
13#13068393C211yesmaximal, characteristic
14D11×#340C211yesmaximal, characteristic
15C11×#1776C211yesmaximal, characteristic, complemented
16C22×C8×D11C2211yescharacteristic
17C2×#66950C2211yescharacteristic
18C2×C4⋊C4×D11C2211yescharacteristic
19C2×C4⋊C4×D11C2211yescharacteristic
20C2×#66940C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C2×C11×#97C2211yescharacteristic
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
38C4×(C2×D11)⋊C4—21no—
39C4×(C2×D11)⋊C4—21no—
40C4×(C2×D11)⋊C4C2211yescharacteristic
41#10622546—21no—
42#10622542C2211yescharacteristic
43#10622541—21no—
44#10622541C2211yescharacteristic
45#10622497C418yescomplemented
46#10622281—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×D11—21no—
62C22×C4×D11C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C42×C11—21no—
71C2×C42×C11—21no—
72C2×C42×C11C2311yescharacteristic
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×Dic11⋊C4—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C2×C8×D11—22no—
93C2×C8×D11—22no—
94C2×C8×D11—41no—
95#66950—22no—
96#66950C2×C414yes—
97C4⋊C4×D11—22no—
98C4⋊C4×D11—22no—
99C4⋊C4×D11—41no—
100C4⋊C4×D11C2×C414yes—
101#66940—22no—
102#66940—41no—
103C11×#107C2×C414yescomplemented
104C11×#106—22no—
105C11×#97—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×C414yescomplemented
120#66879—41no—
121#66874—41no—
122#66874C2×C414yescomplemented
123#66872—41no—
124#66871C2×C414yescomplemented
125#22932—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—42no—
147C2×C4×D11—42no—
148C2×C4×D11—81no—
149C2×C4×D11—81no—
150C2×C4×D11—81no—
151C2×C4×D11C22×C412yes—
152C2×C4×D11#4112yes—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22C22×C412yes—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11C22×C412yes—
164C2×C8×C11#4112yes—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4C22×C412yes—
171C11×C4⋊C4C22×C412yes—
172C11×C4⋊C4#4112yes—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—81no—
176C42×C11—81no—
177(C2×D11)⋊C4—24no—
178(C2×D11)⋊C4—22no—
179(C2×D11)⋊C4—22no—
180(C2×D11)⋊C4—42no—
181C4⋊Dic11—24no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—81no—
188C4⋊Dic11C22×C412yes—
189Dic11⋊C4—24no—
190Dic11⋊C4—42no—
191Dic11⋊C4—42no—
192Dic11⋊C4—81no—
193Dic11⋊C4—81no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—42no—
197C4×Dic11—81no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8C22×C412yes—
204C8×D11—44no—
205C2×#484—111no—
206#2360—111no—
207#2345—111no—
208#1943—111no—
209#1935—111no—
210#1927—111no—
211#1918—111no—
212#1918—111no—
213#1892—111no—
214#1865—111no—
215#1853—111no—
216#1776D1111yescharacteristic, complemented
217#1763—111no—
218#1752—111no—
219C2×#340—111no—
220C23×C11C22×D411yescharacteristic
221C22×D11—21no—
222C22×D11—21no—
223C22×D11—21no—
224C22×D11—21no—
225C22×D11C4×D412yes—
226C22×D11#13712yes—
227C22×D11#13712yes—
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—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
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—41no—
245C2×C4×C11—41no—
246C2×C4×C11C23×C411yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11H(5,𝔽2)11yescharacteristic
251C2×C4×C112−1+411yescharacteristic
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
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×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11C4×D412yes—
273C4×D11—22no—
274C4×D11—22no—
275C4×D11—22no—
276C4×D11—22no—
277C4×D11—84no—
278C4×D11—84no—
279Dic22—22no—
280Dic22—22no—
281Dic22—41no—
282Dic22—41no—
283C8×C11—22no—
284C8×C11—22no—
285C11⋊C8—22no—
286C11⋊C8—41no—
287C23×C8—111no—
288C2×C22⋊Q8—111no—
289C2×C4×Q8—111no—
290C22×C4⋊C4—111no—
291C22×C4⋊C4—111no—
292#484—118no—
293C2×#107—111no—
294C2×#107C2×D1111yescharacteristic
295C2×#106—111no—
296C2×#106C2×D1111yescharacteristic
297C2×#103—111no—
298C2×#103—111no—
299C2×#103—111no—
300C2×#103—111no—
301C2×C22⋊C8—111no—
302C2×#97—111no—
303C2×#97C2×D1111yescharacteristic
304#391—111no—
305#389—111no—
306#389—111no—
307#389—111no—
308#389—221no—
309#387—221no—
310#387—221no—
311#387—221no—
312#385—221no—
313#380—111no—
314#380—221no—
315C4×C4⋊C4—111no—
316C4×C4⋊C4C2×D1111yescharacteristic
317C4×C4⋊C4C2×D1111yescharacteristic
318C4×C22⋊C4—111no—
319C4×C22⋊C4—221no—
320C4×C22⋊C4—221no—
321#340—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340C2×D1111yescharacteristic
328#340C2×D1111yescharacteristic
329#336—111no—
330#336—111no—
331C22×C11C2×C4×D411yescharacteristic
332C22×C11#54611yescharacteristic
333C22×C11#54711yescharacteristic
334C22×C11C2×#13711yescharacteristic
335C22×C11C2×#13711yescharacteristic
336C22×C11#57611yescharacteristic
337C22×C11#57711yescharacteristic
338C2×D11—22no—
339C2×D11—22no—
340C2×D11—22no—
341C2×D11—22no—
342C2×D11—22no—
343C2×D11—22no—
344C2×D11#44114yes—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11—42no—
348C4×C11—42no—
349C4×C11—42no—
350C4×C11—81no—
351C4×C11C4×#4111yescharacteristic
352C4×C11#52011yescharacteristic
353C4×C11#55111yescharacteristic
354C4×C11#55211yescharacteristic
355Dic11—22no—
356Dic11—42no—
357Dic11—42no—
358Dic11—41no—
359Dic11—41no—
360Dic11—81no—
361Dic11—81no—
362C22×Q8—111no—
363C23×C4—111no—
364C23×C4—221no—
365C23×C4—221no—
366C22×C8—111no—
367C22×C8—111no—
368C22×C8—222no—
369C22×C8—222no—
370C22×C8—441no—
371C22×C8C22×D1111yescharacteristic
372C22×C8C22×D1111yescharacteristic
373C22⋊Q8—114no—
374C22⋊Q8—222no—
375C4×Q8—222no—
376C4×Q8—441no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—114no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—222no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—222no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—441no—
391C2×C4⋊C4C22×D1111yescharacteristic
392C2×C4⋊C4C22×D1111yescharacteristic
393C2×C4⋊C4C22×D1111yescharacteristic
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C22⋊C4—111no—
396C2×C22⋊C4—111no—
397C2×C22⋊C4—221no—
398C2×C22⋊C4—221no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42—111no—
402C2×C42—221no—
403C2×C42—221no—
404C2×C42C22×D1111yescharacteristic
405#107—114no—
406#107C4×D1114yescomplemented
407#106—22no—
408#106—441no—
409#103—114no—
410#103—114no—
411#103—222no—
412#103—441no—
413C22⋊C8—114no—
414#97—22no—
415#97—441no—
416#95—21no—
417#95—21no—
418#95—111no—
419#95—111no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427C2×C11#235911yescharacteristic
428C2×C11C2×#44111yescharacteristic
429C2×C11#294611yescharacteristic
430C2×C11#331411yescharacteristic
431C2×C11#332011yescharacteristic
432C2×C11#334411yescharacteristic
433C2×C11#334611yescharacteristic
434D11—24no—
435C24—111no—
436C2×Q8—112no—
437C2×Q8—221no—
438C2×Q8—221no—
439C2×Q8—221no—
440C2×Q8—221no—
441C2×Q8—221no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—111no—
447C22×C4—112no—
448C22×C4—112no—
449C22×C4—111no—
450C22×C4—111no—
451C22×C4—224no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—442no—
461C22×C4—442no—
462C22×C4—881no—
463C22×C4—881no—
464C22×C4—881no—
465C22×C4D4×D1111yescharacteristic
466C22×C4D4×D1111yescharacteristic
467C22×C4C23×D1111yescharacteristic
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—112no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—444no—
479C2×C8C2×C4×D1112yes—
480C2×C8#433912yes—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—112no—
487C4⋊C4—224no—
488C4⋊C4—224no—
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—881no—
499C4⋊C4C2×C4×D1112yes—
500C4⋊C4C2×C4×D1112yes—
501C4⋊C4#433912yes—
502C22⋊C4—222no—
503C22⋊C4—222no—
504C22⋊C4—224no—
505C22⋊C4—442no—
506C42—21no—
507C42—21no—
508C42—81no—
509C42—81no—
510C42—221no—
511C42—221no—
512C42—442no—
513C42—881no—
514C11#2293211yescharacteristic, complemented, Sylow
515C23—112no—
516C23—112no—
517C23—112no—
518C23—221no—
519C23—221no—
520C23—221no—
521C23—221no—
522C23C2×D4×D1111yescharacteristic
523Q8—222no—
524Q8—222no—
525Q8—441no—
526Q8—441no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—112no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—222no—
549C2×C4—222no—
550C2×C4—222no—
551C2×C4—222no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—222no—
557C2×C4—222no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—884no—
571C2×C4—884no—
572C2×C4C22×C4×D1111yescharacteristic
573C2×C4C2×#433911yescharacteristic
574C2×C4C2×#433911yescharacteristic
575C2×C4#6704011yescharacteristic
576C2×C4#41×D1111yescharacteristic
577C2×C4#6704211yescharacteristic
578C8—22no—
579C8—22no—
580C8—222no—
581C8—441no—
582C22—114no—
583C22—222no—
584C22—222no—
585C22—222no—
586C22—222no—
587C22—222no—
588C22—222no—
589C22#1062303811yescharacteristic
590C22C4×D4×D1111yescharacteristic
591C22#1062308111yescharacteristic
592C22#1062330511yescharacteristic
593C22#1062330611yescharacteristic
594C22D11×#13711yescharacteristic
595C22D11×#13711yescharacteristic
596C4—41no—
597C4—42no—
598C4—42no—
599C4—42no—
600C4—41no—
601C4—81no—
602C4—222no—
603C4—441no—
604C4—442no—
605C4—441no—
606C4—442no—
607C4—881no—
608C4—881no—
609C4C4×#433911yescharacteristic
610C4#1062305811yescharacteristic
611C4#1062310511yescharacteristic
612C4#1062311211yescharacteristic
613C2—224no—
614C2#1307161311yescharacteristic
615C2D11×#44111yescharacteristic
616C2#1307744511yescharacteristic
617C2#1308070211yescharacteristic
618C2#1308079211yescharacteristic
619C2#1308107211yescharacteristic
620C2#1308110211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1776C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1776D11
hypocenterC11#22932
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1776

Complements

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

NH ≅ G/Ntype
4. #13069353C2semidirect
5. #13069306C2semidirect
6. #13069250C2semidirect
7. #13069189C2semidirect
8. #13069187C2semidirect
10. #13068881C2semidirect
12. #13068445C2semidirect
15. C11×#1776C2semidirect
45. #10622497C4semidirect
103. C11×#107C2×C4semidirect
119. #66880C2×C4semidirect
122. #66874C2×C4semidirect
124. #66871C2×C4semidirect
216. #1776D11semidirect
406. #107C4×D11semidirect
514. C11#22932semidirect

Maximal subgroups

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

subgroupindex
C2×#106224972
#130716232
#130714892
#130693532
#130693062
#130692502
#130691892
#130691872
#130690382
#130688812
#130688072
#130684452
#130683932
D11×#3402
C11×#17762
#2293211