Finite Group Databasebeta

← #14752703

Subgroups — #14752703

Order 2816.

1118 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622319C211yesmaximal, characteristic
2C2×#10622449C211yesmaximal, characteristic
3C4×#66946C211yesmaximal, characteristic
4#13068491C211yesmaximal, characteristic, complemented
5C4⋊C8×Dic11C211yesmaximal, characteristic, complemented
6#13068401C211yesmaximal, characteristic, complemented
7#13068398C211yesmaximal, characteristic, complemented
8C8×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
9#13068386C211yesmaximal, characteristic, complemented
10#13068379C211yesmaximal, characteristic, complemented
11C4×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
12#13068364C211yesmaximal, characteristic, complemented
13#13068308C211yesmaximal, characteristic, complemented
14D11×#336C211yesmaximal, characteristic, complemented
15C11×#1771C211yesmaximal, characteristic, complemented
16C22×#4313C2211yescharacteristic
17C22×#4313C2211yescharacteristic
18C22×C8×D11C2211yescharacteristic
19C22×C8×D11C2211yescharacteristic
20C2×#66946C412yes—
21C2×C4×D44C2211yescharacteristic
22C2×C42×D11C2211yescharacteristic
23C2×C42×D11C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×#97C2211yescharacteristic
26C2×C11×#97C2211yescharacteristic
27C2×C4×C8×C11C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34C2×C8×Dic11C2211yescharacteristic
35C4⋊C4×Dic11C412yes—
36C4×(C2×D11)⋊C4C2211yescharacteristic
37C4×(C2×D11)⋊C4C2211yescharacteristic
38C42×Dic11C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40C2×#66867C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622449C418yescomplemented
44#10622319C418yescomplemented
45#10622279C412yes—
46#10622279C412yes—
47C11×#336C2211yescharacteristic
48C11×#336C2211yescharacteristic
49#10622188C2211yescharacteristic
50#10622188C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57C22×D44C2×C411yescharacteristic
58C22×C4×D11C2×C412yes—
59C22×C4×D11C2×C412yes—
60C22×C4×D11C2311yescharacteristic
61C22×C4×D11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C11×C4⋊C4C2×C412yes—
67C2×C42×C11C2311yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×(C2×D11)⋊C4C2×C412yes—
71C2×(C2×D11)⋊C4C2×C411yescharacteristic
72C2×(C2×D11)⋊C4C2×C411yescharacteristic
73C2×(C2×D11)⋊C4C2×C412yes—
74C2×C4⋊Dic11C2×C411yescharacteristic
75C2×C4×Dic11C2×C412yes—
76C2×C4×Dic11C2×C412yes—
77C2×C4×Dic11C2×C412yes—
78C2×C4×Dic11C2×C412yes—
79C2×C4×Dic11C2311yescharacteristic
80C2×C4×Dic11C2311yescharacteristic
81C22×C11⋊C8C2311yescharacteristic
82C22×C11⋊C8C2311yescharacteristic
83C22×C11⋊C8C2311yescharacteristic
84C22×C11⋊C8C2311yescharacteristic
85C2×#4313—41no—
86C2×#4313—41no—
87C2×#4313—41no—
88C2×#4313—41no—
89C2×#4313C2×C414yescomplemented
90C2×#4313C2×C414yescomplemented
91C2×C8×D11—41no—
92C2×C8×D11—41no—
93C2×C8×D11—41no—
94C2×C8×D11—41no—
95C2×C8×D11C2×C414yescomplemented
96C2×C8×D11C2×C414yescomplemented
97#66946—28no—
98C4×D44C2×C414yes—
99C4×D44C2×C414yes—
100C42×D11—41no—
101C42×D11—41no—
102C42×D11—41no—
103C42×D11—41no—
104C11×C4⋊C8C2×C414yescomplemented
105C11×#97—41no—
106C11×#97C2×C414yescomplemented
107C4×C8×C11—41no—
108C11×#95C2×C412yes—
109C11⋊#95C2×C412yes—
110C11⋊#95C2×C412yes—
111(C2×D11)⋊C8C2×C414yescomplemented
112(C2×D11)⋊C8C2×C414yescomplemented
113(C2×D11)⋊C8C2×C414yescomplemented
114(C2×D11)⋊C8C2×C414yescomplemented
115C8×Dic11—41no—
116C8×Dic11—41no—
117C4⋊(C11⋊C8)C2×C414yescomplemented
118#66867—41no—
119#66867C2×C414yescomplemented
120C4×C11⋊C8—41no—
121#20559—111nomaximal, Sylow
122C23×D11C22×C411yescharacteristic
123C23×D11C22×C411yescharacteristic
124C22×C4×C11C22×C412yes—
125C22×C4×C11C22×C411yescharacteristic
126C22×C4×C11C22×C411yescharacteristic
127C22×C4×C11C22×C412yes—
128C22×C4×C11C2411yescharacteristic
129C22×Dic11C22×C411yescharacteristic
130C22×Dic11C22×C411yescharacteristic
131C22×Dic11C22×C412yes—
132C22×Dic11C22×C412yes—
133C2×D44—24no—
134C2×D44C4214yes—
135C2×C4×D11—24no—
136C2×C4×D11—24no—
137C2×C4×D11—24no—
138C2×C4×D11—24no—
139C2×C4×D11—21no—
140C2×C4×D11—21no—
141C2×C4×D11—21no—
142C2×C4×D11—21no—
143C2×C4×D11—21no—
144C2×C4×D11—21no—
145C2×C4×D11—21no—
146C2×C4×D11—21no—
147C2×C4×D11—42no—
148C2×C4×D11—42no—
149C2×C4×D11C22×C412yes—
150C2×C4×D11C22×C412yes—
151C2×C4×D11C22×C412yes—
152C2×C4×D11C22×C412yes—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11C22×C412yes—
162C2×C8×C11C22×C412yes—
163C2×C8×C11C22×C412yes—
164C2×C8×C11C22×C412yes—
165C11×C4⋊C4—24no—
166C42×C11—21no—
167C42×C11—21no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11C22×C412yes—
171C42×C11C22×C412yes—
172(C2×D11)⋊C4—24no—
173(C2×D11)⋊C4C4214yes—
174(C2×D11)⋊C4C4214yes—
175(C2×D11)⋊C4M1618yescomplemented
176C4⋊Dic11C4214yes—
177C4×Dic11—24no—
178C4×Dic11—24no—
179C4×Dic11—21no—
180C4×Dic11—21no—
181C4×Dic11—21no—
182C4×Dic11—21no—
183C4×Dic11—42no—
184C4×Dic11—42no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8C22×C412yes—
194C2×C11⋊C8C22×C412yes—
195C2×C11⋊C8C22×C412yes—
196C2×C11⋊C8C22×C412yes—
197#4313—44no—
198#4313—44no—
199C8×D11—44no—
200C8×D11—44no—
201C2×#435—111no—
202C2×#435—111no—
203C42×D4—111no—
204#1771—111no—
205#1771D1111yescharacteristic, complemented
206C4×C4⋊C8—111no—
207#1753—111no—
208#1753—111no—
209C8×C22⋊C4—111no—
210C8×C22⋊C4—111no—
211#1749—111no—
212C4×C22⋊C8—111no—
213#1745—111no—
214#1728—111no—
215C2×#336—111no—
216C23×C11C23×C411yescharacteristic
217C22×D11—21no—
218C22×D11—21no—
219C22×D11—22no—
220C22×D11—21no—
221C22×D11—21no—
222C22×D11—22no—
223C22×D11—22no—
224C22×D11C2×C4212yes—
225C22×D11C2×C4212yes—
226C22×D11C2×M1614yes—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11C2×C4212yes—
235C2×C4×C11C2×C4212yes—
236C2×C4×C11C2×M1614yes—
237C2×C4×C11C23×C411yescharacteristic
238C2×C4×C11C23×C411yescharacteristic
239C2×C4×C11H(5,𝔽2)11yescharacteristic
240C2×C4×C11H(5,𝔽2)11yescharacteristic
241C2×C4×C11H(5,𝔽2)11yescharacteristic
242C2×C4×C112−1+411yescharacteristic
243C2×Dic11—22no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—22no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11C2×C4212yes—
252C2×Dic11C2×C4212yes—
253C2×Dic11C2×M1614yes—
254C2×Dic11#13114yes—
255D44—28no—
256C4×D11—22no—
257C4×D11—22no—
258C4×D11—22no—
259C4×D11—22no—
260C4×D11—22no—
261C4×D11—22no—
262C4×D11—22no—
263C4×D11—22no—
264C4×D11—48no—
265C4×D11—48no—
266C8×C11—22no—
267C8×C11—22no—
268C8×C11—22no—
269C8×C11—22no—
270C11⋊C8—22no—
271C11⋊C8—22no—
272C11⋊C8—22no—
273C11⋊C8—22no—
274C22×M16—111no—
275C22×M16—111no—
276C23×C8—111no—
277C23×C8—111no—
278C2×C4×D4—112no—
279C2×C4×D4—111no—
280C22×C42—111no—
281C22×C42—111no—
282#435—118no—
283#435—118no—
284C2×C4⋊C8—111no—
285C2×C4⋊C8C2×D1111yescharacteristic
286C2×C22⋊C8—111no—
287C2×C22⋊C8—111no—
288C2×C22⋊C8—111no—
289C2×C22⋊C8—111no—
290C2×#97—111no—
291C2×#97—111no—
292C2×#97C2×D1111yescharacteristic
293C2×#97C2×D1111yescharacteristic
294C2×C4×C8—111no—
295C2×C4×C8—111no—
296C2×C4×C8—111no—
297C2×C4×C8C2×D1111yescharacteristic
298C4×C4⋊C4—112no—
299C4×C4⋊C4C2×D1111yescharacteristic
300C4×C22⋊C4—111no—
301C4×C22⋊C4—111no—
302C4×C22⋊C4—112no—
303C4×C22⋊C4—112no—
304C43—111no—
305#336—111no—
306#336—111no—
307#336—111no—
308#336—111no—
309#336—111no—
310#336—111no—
311#336—111no—
312#336—111no—
313#336C2×D1111yescharacteristic
314#336C2×D1111yescharacteristic
315C22×C11C22×C4211yescharacteristic
316C22×C11#51811yescharacteristic
317C22×C11#52011yescharacteristic
318C22×C11C22×M1612yes—
319C22×C11C2×#13112yes—
320C2×D11—22no—
321C2×D11—24no—
322C2×D11—24no—
323C2×D11—22no—
324C2×D11—22no—
325C2×D11—22no—
326C2×D11—22no—
327C2×D11—42no—
328C2×D11—42no—
329C2×D11C4×M1614yes—
330C4×C11—22no—
331C4×C11—22no—
332C4×C11—24no—
333C4×C11—42no—
334C4×C11#51811yescharacteristic
335C4×C11#51811yescharacteristic
336C4×C11#52011yescharacteristic
337C4×C11#52011yescharacteristic
338Dic11—24no—
339Dic11—24no—
340Dic11—22no—
341Dic11—22no—
342C22×D4—111no—
343C23×C4—111no—
344C23×C4—111no—
345C23×C4—112no—
346C23×C4—112no—
347C2×M16—114no—
348C2×M16—114no—
349C2×M16—441no—
350C2×M16—441no—
351C2×M16—441no—
352C2×M16—441no—
353C22×C8—111no—
354C22×C8—111no—
355C22×C8—111no—
356C22×C8—111no—
357C22×C8—114no—
358C22×C8—114no—
359C22×C8—441no—
360C22×C8—441no—
361C22×C8—441no—
362C22×C8—441no—
363C22×C8C22×D1111yescharacteristic
364C22×C8C22×D1111yescharacteristic
365C22×C8C22×D1111yescharacteristic
366C22×C8C22×D1111yescharacteristic
367C4×D4—114no—
368C4×D4—114no—
369C4×D4—228no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4C4×D1112yes—
372C2×C22⋊C4—111no—
373C2×C22⋊C4—111no—
374C2×C22⋊C4—112no—
375C2×C22⋊C4—112no—
376C2×C42—112no—
377C2×C42—112no—
378C2×C42—111no—
379C2×C42—111no—
380C2×C42—112no—
381C2×C42—112no—
382C2×C42—441no—
383C2×C42—441no—
384C2×C42—441no—
385C2×C42—441no—
386C2×C42C22×D1111yescharacteristic
387C2×C42C22×D1111yescharacteristic
388C2×C42C22×D1111yescharacteristic
389C4⋊C8—114no—
390C4⋊C8C4×D1114yescomplemented
391C22⋊C8—114no—
392C22⋊C8—114no—
393C22⋊C8—114no—
394C22⋊C8—114no—
395#97—41no—
396#97—114no—
397#97—441no—
398#97C4×D1114yescomplemented
399C4×C8—41no—
400C4×C8—441no—
401C4×C8—441no—
402C4×C8—441no—
403#95—112no—
404#95—112no—
405#95C4×D1112yes—
406C2×C11#227511yescharacteristic
407C2×C11C2×C4×M1611yescharacteristic
408C2×C11C4×#13111yescharacteristic
409C2×C11#297412yes—
410C2×C11#299012yes—
411D11—24no—
412D11—42no—
413C24—111no—
414C24—111no—
415C2×D4—114no—
416C2×D4—224no—
417C22×C4—112no—
418C22×C4—111no—
419C22×C4—111no—
420C22×C4—112no—
421C22×C4—112no—
422C22×C4—112no—
423C22×C4—112no—
424C22×C4—112no—
425C22×C4—224no—
426C22×C4—224no—
427C22×C4—224no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—221no—
431C22×C4—221no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4—224no—
437C22×C4—442no—
438C22×C4—442no—
439C22×C4C2×C4×D1112yes—
440C22×C4C2×C4×D1111yescharacteristic
441C22×C4C2×C4×D1111yescharacteristic
442C22×C4C2×C4×D1112yes—
443C22×C4C23×D1111yescharacteristic
444M16—444no—
445M16—444no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—112no—
455C2×C8—112no—
456C2×C8—112no—
457C2×C8—112no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—444no—
467C2×C8—444no—
468C2×C8C2×C4×D1112yes—
469C2×C8C2×C4×D1112yes—
470C2×C8C2×C4×D1112yes—
471C2×C8C2×C4×D1112yes—
472C4⋊C4—24no—
473C4⋊C4—114no—
474C22⋊C4—114no—
475C22⋊C4—114no—
476C22⋊C4—118no—
477C22⋊C4—224no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—224no—
483C42—224no—
484C42—221no—
485C42—221no—
486C42—221no—
487C42—221no—
488C42—442no—
489C42—442no—
490C42C2×C4×D1112yes—
491C42C2×C4×D1112yes—
492C11#2055911yescharacteristic, complemented, Sylow
493C23—112no—
494C23—114no—
495C23—112no—
496C23—222no—
497C23—221no—
498C23—221no—
499C23—222no—
500C23—222no—
501C23—221no—
502C23—221no—
503C23C22×C4×D1111yescharacteristic
504D4—228no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—112no—
513C2×C4—112no—
514C2×C4—114no—
515C2×C4—114no—
516C2×C4—222no—
517C2×C4—222no—
518C2×C4—222no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—222no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—222no—
525C2×C4—222no—
526C2×C4—222no—
527C2×C4—222no—
528C2×C4—222no—
529C2×C4—222no—
530C2×C4—222no—
531C2×C4—222no—
532C2×C4—448no—
533C2×C4—448no—
534C2×C4C42×D1112yes—
535C2×C4C42×D1112yes—
536C2×C4M16×D1114yes—
537C2×C4C22×C4×D1111yescharacteristic
538C2×C4C22×C4×D1111yescharacteristic
539C2×C4#6703711yescharacteristic
540C2×C4#6704011yescharacteristic
541C2×C4#6704211yescharacteristic
542C2×C4#6704211yescharacteristic
543C8—22no—
544C8—22no—
545C8—22no—
546C8—22no—
547C8—222no—
548C8—222no—
549C8—222no—
550C8—222no—
551C22—114no—
552C22—222no—
553C22—222no—
554C22—224no—
555C22—224no—
556C22—222no—
557C22—222no—
558C22—222no—
559C22—442no—
560C22—442no—
561C22C2×C42×D1111yescharacteristic
562C22#1062307611yescharacteristic
563C22#1062310511yescharacteristic
564C22C2×M16×D1112yes—
565C22D11×#13112yes—
566C4—22no—
567C4—22no—
568C4—24no—
569C4—42no—
570C4—222no—
571C4—222no—
572C4—224no—
573C4—224no—
574C4#1062303511yescharacteristic
575C4#1062305211yescharacteristic
576C4#1062307611yescharacteristic
577C4#1062310511yescharacteristic
578C2—224no—
579C2—442no—
580C2#1307097611yescharacteristic
581C2C4×M16×D1111yescharacteristic
582C2#1307703811yescharacteristic
583C2#1307764612yes—
584C2#1307774012yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C22×C42
FittingC11×#1771C2
socleC23×C11C23×C4
prime radicalC22×D44C2×C4
cosocleC22×C4×C11C24
hypercenter#1771D11
hypocenterC11#20559
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1771

Complements

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

NH ≅ G/Ntype
4. #13068491C2semidirect
5. C4⋊C8×Dic11C2semidirect
6. #13068401C2semidirect
7. #13068398C2semidirect
8. C8×(C2×D11)⋊C4C2semidirect
9. #13068386C2semidirect
10. #13068379C2semidirect
11. C4×(C2×D11)⋊C8C2semidirect
12. #13068364C2semidirect
13. #13068308C2semidirect
14. D11×#336C2semidirect
15. C11×#1771C2semidirect
43. #10622449C4semidirect
44. #10622319C4semidirect
89. C2×#4313C2×C4semidirect
90. C2×#4313C2×C4semidirect
95. C2×C8×D11C2×C4semidirect
96. C2×C8×D11C2×C4semidirect
104. C11×C4⋊C8C2×C4semidirect
106. C11×#97C2×C4semidirect
111. (C2×D11)⋊C8C2×C4semidirect
112. (C2×D11)⋊C8C2×C4semidirect
113. (C2×D11)⋊C8C2×C4semidirect
114. (C2×D11)⋊C8C2×C4semidirect
117. C4⋊(C11⋊C8)C2×C4semidirect
119. #66867C2×C4semidirect
175. (C2×D11)⋊C4M16semidirect
205. #1771D11semidirect
390. C4⋊C8C4×D11semidirect
398. #97C4×D11semidirect
492. C11#20559semidirect

Maximal subgroups

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

subgroupindex
C2×#106223192
C2×#106224492
C4×#669462
#130684912
C4⋊C8×Dic112
#130684012
#130683982
C8×(C2×D11)⋊C42
#130683862
#130683792
C4×(C2×D11)⋊C82
#130683642
#130683082
D11×#3362
C11×#17712
#2055911