Finite Group Databasebeta

← #14645161

Subgroups — #14645161

Order 2816.

868 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623111C211yesmaximal, characteristic
2#13068593C211yesmaximal, characteristic, complemented
3C4×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
4C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
5C2×#10622097C211yesmaximal, characteristic, complemented
6C2×#10622121C211yesmaximal, characteristic, complemented
7C2×C11×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C2×#67000C411yescharacteristic
10C2×#66999C411yescharacteristic
11#10623111—22no—
12#10623111—22no—
13#10623111—22no—
14#10623111—22no—
15C2×#66951—21no—
16C2×#66948C411yescharacteristic
17C2×#66947—21no—
18C2×#66943C411yescharacteristic
19C2×C4×D44—21no—
20C2×C4×D44C2211yescharacteristic
21C2×#66925—21no—
22C2×C42×D11C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C2×(C2×D11)⋊C8—21no—
26C2×(C2×D11)⋊C8—21no—
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28C2×C4×C11⋊C8C2211yescharacteristic
29C11×Q8⋊C8—22no—
30#10622188—21no—
31#10622188—21no—
32Q8⋊(C11⋊C8)—22no—
33#10622121—22no—
34#10622097—22no—
35C22×Q8×C11C2×C411yescharacteristic
36C22×D44—21no—
37C22×D44C2×C411yescharacteristic
38C22×C4×D11—21no—
39C22×C4×D11C2×C411yescharacteristic
40C22×C4×D11D411yescharacteristic
41C22×C4×D11D411yescharacteristic
42C22×C8×C11—21no—
43C22×C8×C11—21no—
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11D412yes—
47C4×Q8×C11D412yes—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4C2×C411yescharacteristic
50C2×C42×C11—21no—
51C2×C42×C11C2311yescharacteristic
52#67000—22no—
53#67000—22no—
54#66999—22no—
55#66999—22no—
56C2×(C2×D11)⋊C4—21no—
57C2×(C2×D11)⋊C4—21no—
58C2×(C2×D11)⋊C4—21no—
59C2×(C2×D11)⋊C4—21no—
60C2×(C2×D11)⋊C4—21no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11C2×C411yescharacteristic
63C2×Dic11⋊C4—21no—
64C2×Dic11⋊C4—21no—
65C2×C4×Dic11C2×C411yescharacteristic
66C2×C4×Dic11D411yescharacteristic
67C2×C4×Dic11D411yescharacteristic
68C22×C11⋊C8—21no—
69C22×C11⋊C8—21no—
70#66951—24no—
71#66951—24no—
72#66948—22no—
73#66948—22no—
74#66947—24no—
75#66947—24no—
76#66943—22no—
77#66943—22no—
78C4×D44—24no—
79C4×D44—24no—
80C4×D44—21no—
81C4×D44—21no—
82C4×D44D412yes—
83C4×D44D412yes—
84#66925—24no—
85#66925—24no—
86C42×D11—21no—
87C42×D11—21no—
88C42×D11—21no—
89C42×D11—21no—
90C11×C4⋊C8—21no—
91C11×C4⋊C8—21no—
92C4×C8×C11—21no—
93C4×C8×C11—21no—
94(C2×D11)⋊C8—24no—
95(C2×D11)⋊C8—42no—
96C4⋊(C11⋊C8)—21no—
97C4⋊(C11⋊C8)—21no—
98C4×C11⋊C8—21no—
99C4×C11⋊C8—21no—
100#8315—111nomaximal, Sylow
101C23×D11—21no—
102C23×D11C22⋊C411yescharacteristic
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11C22⋊C412yes—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11C22×C411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×Dic11—21no—
115C22×Dic11C22⋊C411yescharacteristic
116C22×Dic11C22⋊C411yescharacteristic
117C22×Dic11C22⋊C411yescharacteristic
118C2×D44—24no—
119C2×D44—21no—
120C2×D44—21no—
121C2×D44—21no—
122C2×D44—21no—
123C2×D44—21no—
124C2×D44—42no—
125C2×D44—42no—
126C2×D44C22⋊C412yes—
127C2×C4×D11—22no—
128C2×C4×D11—21no—
129C2×C4×D11—21no—
130C2×C4×D11—21no—
131C2×C4×D11—21no—
132C2×C4×D11—21no—
133C2×C4×D11—21no—
134C2×C4×D11—22no—
135C2×C4×D11—22no—
136C2×C4×D11—21no—
137C2×C4×D11—21no—
138C2×C4×D11—21no—
139C2×C4×D11—21no—
140C2×C4×D11—21no—
141C2×C4×D11—21no—
142C2×C4×D11—21no—
143C2×C4×D11—21no—
144C2×C4×D11—41no—
145C2×C4×D11—41no—
146C2×C4×D11—41no—
147C2×C4×D11—41no—
148C2×C4×D11—41no—
149C2×C8×C11—22no—
150C2×C8×C11—41no—
151C2×C8×C11—41no—
152C2×C8×C11—41no—
153C2×C8×C11—41no—
154C2×C8×C11—41no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4C22⋊C412yes—
159C42×C11—22no—
160C42×C11—22no—
161C42×C11C2×D411yescharacteristic
162C42×C11C2×D411yescharacteristic
163C42×C11C2×D411yescharacteristic
164C42×C11C2×D411yescharacteristic
165(C2×D11)⋊C4—24no—
166(C2×D11)⋊C4—24no—
167(C2×D11)⋊C4—24no—
168(C2×D11)⋊C4—24no—
169(C2×D11)⋊C4—22no—
170(C2×D11)⋊C4—22no—
171C4⋊Dic11—24no—
172C4⋊Dic11—21no—
173C4⋊Dic11C22⋊C412yes—
174Dic11⋊C4—24no—
175Dic11⋊C4—24no—
176C4×Dic11—21no—
177C4×Dic11—21no—
178C4×Dic11—21no—
179C4×Dic11—21no—
180C4×Dic11—21no—
181C4×Dic11—21no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—41no—
184C2×C11⋊C8—41no—
185C2×C11⋊C8—41no—
186C2×C11⋊C8—41no—
187C2×C11⋊C8—41no—
188C2×#529—111no—
189#1797—111no—
190C4×C22⋊C8—111no—
191C2×Q8⋊C8—111no—
192C2×Q8⋊C8D1111yescharacteristic, complemented
193C2×D4⋊C8—111no—
194C2×D4⋊C8—111no—
195C23×C11C2×C22⋊C411yescharacteristic
196C22×D11—21no—
197C22×D11—21no—
198C22×D11—21no—
199C22×D11—21no—
200C22×D11—21no—
201C22×D11—21no—
202C22×D11—22no—
203C22×D11—41no—
204C22×D11—41no—
205C22×D11—41no—
206C22×D11—41no—
207C22×D11—41no—
208C22×D11—41no—
209C22×D11#10412yes—
210Q8×C11—22no—
211Q8×C11—22no—
212Q8×C11—41no—
213Q8×C11—41no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11C2×C22⋊C411yescharacteristic
223C2×C4×C11C2×C22⋊C411yescharacteristic
224C2×C4×C11#12011yescharacteristic
225C2×C4×C11#12011yescharacteristic
226C2×C4×C11#12011yescharacteristic
227C2×C4×C11#12011yescharacteristic
228C2×C4×C11#13111yescharacteristic
229C2×C4×C11#13111yescharacteristic
230C2×C4×C11#13111yescharacteristic
231C2×C4×C11#13111yescharacteristic
232C2×C4×C11#13511yescharacteristic
233C2×C4×C11#13511yescharacteristic
234C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
235C2×C4×C11#13711yescharacteristic
236C2×Dic11—21no—
237C2×Dic11—21no—
238C2×Dic11—21no—
239C2×Dic11—22no—
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248D44—22no—
249D44—22no—
250D44—48no—
251D44—41no—
252D44—41no—
253C4×D11—42no—
254C4×D11—42no—
255C4×D11—41no—
256C4×D11—41no—
257C4×D11—41no—
258C4×D11—41no—
259C4×D11—41no—
260C4×D11—41no—
261C4×D11—42no—
262C4×D11—42no—
263C4×D11—41no—
264C4×D11—41no—
265C4×D11—42no—
266C4×D11—42no—
267C8×C11—42no—
268C8×C11—81no—
269C11⋊C8—42no—
270C11⋊C8—81no—
271#529—222no—
272#529—222no—
273#529—222no—
274#529—222no—
275C2×#126—221no—
276C2×#125—111no—
277C2×#124—111no—
278C2×#123—221no—
279C2×C22⋊Q8—111no—
280C2×#121—111no—
281C2×C4×Q8C2×D1111yescharacteristic
282C2×C4×D4—111no—
283C2×C4×D4—221no—
284C2×#117—221no—
285C22×C42—111no—
286C2×C4⋊C8—111no—
287C2×C4⋊C8C2×D1111yescharacteristic
288C2×C22⋊C8—221no—
289C2×C22⋊C8—221no—
290C2×C4×C8—111no—
291C2×C4×C8C2×D1111yescharacteristic
292#336—221no—
293#336—221no—
294Q8⋊C8—22no—
295Q8⋊C8—222no—
296D4⋊C8—222no—
297D4⋊C8—222no—
298C22×C11#37911yescharacteristic
299C22×C11#40811yescharacteristic
300C22×C11#40811yescharacteristic
301C22×C11#41611yescharacteristic
302C22×C11#41711yescharacteristic
303C22×C11C2×#10411yescharacteristic
304C22×C11#42111yescharacteristic
305C2×D11—22no—
306C2×D11—22no—
307C2×D11—22no—
308C2×D11—41no—
309C2×D11—41no—
310C2×D11—41no—
311C2×D11—41no—
312C2×D11—42no—
313C2×D11—42no—
314C2×D11—42no—
315C2×D11—81no—
316C2×D11—81no—
317C2×D11—81no—
318C2×D11—81no—
319C4×C11—21no—
320C4×C11—21no—
321C4×C11—42no—
322C4×C11—42no—
323C4×C11#40811yescharacteristic
324C4×C11#40811yescharacteristic
325C4×C11#40811yescharacteristic
326C4×C11#40811yescharacteristic
327C4×C11#44911yescharacteristic
328C4×C11#44911yescharacteristic
329C4×C11#45211yescharacteristic
330C4×C11#45211yescharacteristic
331Dic11—41no—
332Dic11—41no—
333Dic11—42no—
334Dic11—41no—
335C22×Q8C4×D1111yescharacteristic
336C22×D4—111no—
337C22×D4—221no—
338C23×C4—111no—
339C23×C4—111no—
340C23×C4—111no—
341C23×C4—221no—
342C22×C8—21no—
343C22×C8—21no—
344C22×C8—221no—
345C22×C8—221no—
346#126—224no—
347#126—224no—
348#125—222no—
349#125—222no—
350#124—222no—
351#124—222no—
352#123—224no—
353#123—224no—
354C22⋊Q8—222no—
355C22⋊Q8—222no—
356#121—222no—
357#121—222no—
358C4×Q8—21no—
359C4×Q8—21no—
360C4×Q8D4412yes—
361C4×Q8C22⋊D1112yes—
362C4×D4—112no—
363C4×D4—112no—
364C4×D4—224no—
365C4×D4—224no—
366C4×D4—221no—
367C4×D4—221no—
368#117—224no—
369#117—224no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4C4×D1111yescharacteristic
376C2×C22⋊C4—221no—
377C2×C22⋊C4—221no—
378C2×C22⋊C4—221no—
379C2×C22⋊C4—221no—
380C2×C22⋊C4—221no—
381C2×C42—21no—
382C2×C42—111no—
383C2×C42—111no—
384C2×C42—111no—
385C2×C42—221no—
386C2×C42—221no—
387C2×C42—221no—
388C2×C42—221no—
389C2×C42C22×D1111yescharacteristic
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C22⋊C8—224no—
395C22⋊C8—442no—
396C4×C8—21no—
397C4×C8—21no—
398C4×C8—221no—
399C4×C8—221no—
400C2×C11#148211yescharacteristic
401C2×C11#148311yescharacteristic
402C2×C11#149411yescharacteristic
403C2×C11#149511yescharacteristic
404C2×C11#178011yescharacteristic
405C2×C11#178811yescharacteristic
406C2×C11#178911yescharacteristic
407D11—42no—
408D11—82no—
409C24—111no—
410C24—221no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8(C2×D11)⋊C412yes—
417C2×D4—112no—
418C2×D4—224no—
419C2×D4—221no—
420C2×D4—221no—
421C2×D4—221no—
422C2×D4—221no—
423C2×D4—221no—
424C2×D4—442no—
425C2×D4—442no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—111no—
429C22×C4—111no—
430C22×C4—111no—
431C22×C4—222no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4—222no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4—221no—
441C22×C4—221no—
442C22×C4—221no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—222no—
449C22×C4—441no—
450C22×C4—441no—
451C22×C4—441no—
452C22×C4—441no—
453C22×C4—441no—
454C22×C4C2×C4×D1111yescharacteristic
455C22×C4D4×D1111yescharacteristic
456C22×C4D4×D1111yescharacteristic
457C2×C8—22no—
458C2×C8—41no—
459C2×C8—41no—
460C2×C8—41no—
461C2×C8—41no—
462C2×C8—41no—
463C2×C8—222no—
464C2×C8—441no—
465C2×C8—441no—
466C2×C8—441no—
467C2×C8—441no—
468C2×C8—441no—
469C4⋊C4—21no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—112no—
473C4⋊C4—224no—
474C4⋊C4—224no—
475C4⋊C4—224no—
476C4⋊C4—221no—
477C4⋊C4(C2×D11)⋊C412yes—
478C22⋊C4—224no—
479C22⋊C4—224no—
480C22⋊C4—224no—
481C22⋊C4—224no—
482C22⋊C4—222no—
483C22⋊C4—222no—
484C42—22no—
485C42—22no—
486C42—221no—
487C42—221no—
488C42—221no—
489C42—221no—
490C42—221no—
491C42—221no—
492C42C2×D4411yescharacteristic
493C42D4×D1111yescharacteristic
494C42D4×D1111yescharacteristic
495C42C2×C22⋊D1111yescharacteristic
496C11#831511yescharacteristic, complemented, Sylow
497C23—112no—
498C23—221no—
499C23—221no—
500C23—221no—
501C23—221no—
502C23—221no—
503C23—221no—
504C23—222no—
505C23—441no—
506C23—441no—
507C23—441no—
508C23—441no—
509C23—441no—
510C23—441no—
511C23C22⋊C4×D1111yescharacteristic
512Q8—22no—
513Q8—22no—
514Q8—41no—
515Q8—41no—
516D4—222no—
517D4—222no—
518D4—448no—
519D4—441no—
520D4—441no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—222no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—442no—
540C2×C4—442no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—442no—
547C2×C4—441no—
548C2×C4—442no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—442no—
553C2×C4—441no—
554C2×C4—442no—
555C2×C4C22⋊C4×D1111yescharacteristic
556C2×C4#6693511yescharacteristic
557C2×C4#6693511yescharacteristic
558C2×C4#6695411yescharacteristic
559C2×C4#6695411yescharacteristic
560C2×C4#6696011yescharacteristic
561C2×C4#6696011yescharacteristic
562C2×C4#6696711yescharacteristic
563C2×C4#6696911yescharacteristic
564C2×C4#6697111yescharacteristic
565C2×C4#6697211yescharacteristic
566C2×C4C2×(C2×D11)⋊C411yescharacteristic
567C2×C4#6699011yescharacteristic
568C2×C4#6699011yescharacteristic
569C8—42no—
570C8—81no—
571C8—442no—
572C8—881no—
573C22—222no—
574C22—222no—
575C22—222no—
576C22—441no—
577C22—441no—
578C22—441no—
579C22—441no—
580C22—442no—
581C22—442no—
582C22—442no—
583C22—881no—
584C22—881no—
585C22—881no—
586C22—881no—
587C22#1062234011yescharacteristic
588C22#1062234011yescharacteristic
589C22#1062241611yescharacteristic
590C22#1062241711yescharacteristic
591C22D11×#10411yescharacteristic
592C22#1062243411yescharacteristic
593C22#1062256811yescharacteristic
594C4—21no—
595C4—21no—
596C4—42no—
597C4—42no—
598C4—441no—
599C4—442no—
600C4—441no—
601C4—441no—
602C4#1062234011yescharacteristic
603C4#1062234011yescharacteristic
604C4#1062242311yescharacteristic
605C4#1062242411yescharacteristic
606C4#1062272311yescharacteristic
607C4#1062274211yescharacteristic
608C4#1062278511yescharacteristic
609C4#1062280011yescharacteristic
610C2—442no—
611C2—882no—
612C2#1306702311yescharacteristic
613C2#1306702811yescharacteristic
614C2#1306707511yescharacteristic
615C2#1306708011yescharacteristic
616C2#1306852711yescharacteristic
617C2#1306855511yescharacteristic
618C2#1306855811yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×Q8⋊C8C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66948C4
cosocleC2×C42×C11C23
hypercenterC2×Q8⋊C8D11
hypocenterC11#8315
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #13068593C2semidirect
3. C4×(C2×D11)⋊C8C2semidirect
4. C2×Q8⋊(C11⋊C8)C2semidirect
5. C2×#10622097C2semidirect
6. C2×#10622121C2semidirect
7. C2×C11×Q8⋊C8C2semidirect
192. C2×Q8⋊C8D11semidirect
496. C11#8315semidirect

Maximal subgroups

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

subgroupindex
C2×#106231112
#130685932
C4×(C2×D11)⋊C82
C2×Q8⋊(C11⋊C8)2
C2×#106220972
C2×#106221212
C2×C11×Q8⋊C82
#831511