Finite Group Databasebeta

← #14754544

Subgroups — #14754544

Order 2816.

1462 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623358C211yesmaximal, characteristic
2C2×#10622608C211yesmaximal, characteristic, complemented
3C2×#10622611C211yesmaximal, characteristic, complemented
4C2×#10622847C211yesmaximal, characteristic
5#13068813C212yesmaximal, complemented
6#13068813C212yesmaximal, complemented
7#13068808C212yesmaximal, complemented
8#13068803C212yesmaximal, complemented
9#13068335C211yesmaximal, characteristic, complemented
10C2×#10622167C211yesmaximal, characteristic, complemented
11C11×#2311C211yesmaximal, characteristic
12C22×C11×#41C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15#10623358—24no—
16#10623358—24no—
17C2×Q8×Dic11—21no—
18C2×D4×Dic11—22no—
19C2×D4×Dic11—21no—
20C2×#66979C2212yes—
21C2×#66979C2211yescharacteristic
22C22×C4⋊Dic11C2212yes—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×#4318C2211yescharacteristic
25C23×C11⋊C8C2211yescharacteristic
26C11×#391—21no—
27C11×#390—21no—
28C11×#386—22no—
29C11×#380C2212yes—
30C11×#380C2212yes—
31#10622847C418yescomplemented
32C2×C22⋊(C11⋊C8)C2212yes—
33C2×C22⋊(C11⋊C8)C2212yes—
34#10622611—24no—
35#10622608—24no—
36C2×#66872C2211yescharacteristic
37C2×#66872C2212yes—
38C2×#66872C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C2×#66871C2212yes—
41C2×#66871C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41C2×C414yes—
51C2×C11×#41Q814yes—
52C22×Q8×C11D411yescharacteristic
53C22×D4×C11D412yes—
54C22×D4×C11D411yescharacteristic
55C23×C4×C11—21no—
56C23×C4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C23×Dic11—22no—
59C23×Dic11—21no—
60C11×#117—22no—
61C11×#117—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C42×C11—21no—
72C2×C22⋊Dic11—22no—
73C2×C22⋊Dic11—21no—
74Q8×Dic11—28no—
75D4×Dic11—216no—
76D4×Dic11—28no—
77#66979—22no—
78#66979—24no—
79#66979—24no—
80#66979D414yes—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11—24no—
85C2×C4⋊Dic11—24no—
86C2×C4⋊Dic11D414yes—
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2312yes—
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4×Dic11—22no—
91C2×C4×Dic11—21no—
92C2×#4318—22no—
93C2×#4318—22no—
94C2×#4318C2×C414yescomplemented
95C22×C11⋊C8—22no—
96C22×C11⋊C8—22no—
97C22×C11⋊C8C2×C414yescomplemented
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2312yes—
101C11×#95—22no—
102C11×#95—22no—
103C22⋊(C11⋊C8)C2×C418yescomplemented
104C22⋊(C11⋊C8)C2×C418yescomplemented
105#66872—24no—
106#66872—22no—
107#66872—22no—
108#66871—24no—
109#66871—22no—
110#66871—22no—
111#20849—111nomaximal, Sylow
112C24×C11C2×D412yes—
113C24×C11C2×D411yescharacteristic
114C11×#41—28no—
115C11×#41—28no—
116C11×#41—28no—
117C11×#41—28no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11C4⋊C414yes—
121C2×D4×C11—24no—
122C2×D4×C11—24no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11C4⋊C418yes—
126C2×D4×C11C4⋊C414yes—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11—42no—
135C22×C4×C11—81no—
136C22×C4×C11—81no—
137C22×C4×C11C22×C414yes—
138C22×C4×C11C22×C412yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×Q814yes—
144C22×C4×C11C2×Q812yes—
145C22×C4×C11#4112yes—
146C22×C4×C11#4112yes—
147C22×C4×C11C2411yescharacteristic
148C22×Dic11—28no—
149C22×Dic11—24no—
150C22×Dic11—21no—
151C22×Dic11—22no—
152C22×Dic11—21no—
153C22×Dic11—81no—
154C22×Dic11—81no—
155C22×Dic11—82no—
156C22×Dic11—82no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—42no—
164C11×C22⋊C4—42no—
165C11×C22⋊C4—82no—
166C11×C22⋊C4—82no—
167C42×C11—42no—
168C22⋊Dic11—28no—
169C22⋊Dic11—24no—
170C4⋊Dic11—28no—
171C4⋊Dic11—24no—
172C4⋊Dic11—22no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11C2×D412yes—
176C4⋊Dic11C2×D414yes—
177C4⋊Dic11C2×D412yes—
178C4×Dic11—28no—
179C4×Dic11—24no—
180#4318—28no—
181C2×C11⋊C8—28no—
182C2×C11⋊C8—21no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8C22×C412yes—
189C2×C11⋊C8C22×C412yes—
190C2×C11⋊C8C22×C414yes—
191C2×#520—111no—
192C2×#428—111no—
193C2×#427—111no—
194C2×#408—111no—
195#2311D1111yescharacteristic
196#1854—112no—
197#1854—112no—
198#1853—112no—
199#1852—112no—
200#1736—111no—
201C2×#340—111no—
202C23×C11—21no—
203C23×C11—21no—
204C23×C11—21no—
205C23×C11—21no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—22no—
212C23×C11C2×C4⋊C414yes—
213C23×C11C2×C4⋊C412yes—
214C23×C11#12012yes—
215C23×C11#12312yes—
216C23×C11C22×D411yescharacteristic
217Q8×C11—28no—
218D4×C11—216no—
219D4×C11—28no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—42no—
229C2×C4×C11—41no—
230C2×C4×C11—42no—
231C2×C4×C11—41no—
232C2×C4×C11—42no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—84no—
236C2×C4×C11C2×C4⋊C414yes—
237C2×C4×C11C2×C4⋊C412yes—
238C2×C4×C11C4×D414yes—
239C2×C4×C11C4×D414yes—
240C2×C4×C11#12012yes—
241C2×C4×C11C22⋊Q814yes—
242C2×C4×C11C22⋊Q814yes—
243C2×C4×C11#12312yes—
244C2×C4×C11C23×C411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×Q811yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×Dic11—22no—
251C2×Dic11—24no—
252C2×Dic11—22no—
253C2×Dic11—42no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—42no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—84no—
260C2×Dic11—88no—
261C11⋊C8—22no—
262C11⋊C8—22no—
263C11⋊C8—24no—
264C22×#41C2×D1111yescharacteristic
265C22×M16—111no—
266C23×C8—111no—
267#520—224no—
268#520—224no—
269C2×C4×Q8—221no—
270C2×C4×D4—222no—
271C2×C4×D4—221no—
272C2×#117—111no—
273C2×#117—112no—
274C2×#117C2×D1111yescharacteristic
275C22×C4⋊C4—111no—
276C22×C4⋊C4—112no—
277C22×C4⋊C4C2×D1111yescharacteristic
278#428—224no—
279#427—224no—
280C2×#107—111no—
281C2×#107—112no—
282C2×#107—111no—
283C2×#106—111no—
284C2×#106—112no—
285C2×#106—111no—
286#408—118no—
287C2×C22⋊C8—112no—
288C2×C22⋊C8—112no—
289#391—21no—
290#390—21no—
291#386—22no—
292#380C2×D1112yes—
293#380C2×D1112yes—
294#340—112no—
295#340—112no—
296#340—112no—
297#340—112no—
298C22×C11—22no—
299C22×C11—22no—
300C22×C11—22no—
301C22×C11—22no—
302C22×C11—22no—
303C22×C11—22no—
304C22×C11—24no—
305C22×C11—24no—
306C22×C11—24no—
307C22×C11—42no—
308C22×C11—42no—
309C22×C11—42no—
310C22×C11—42no—
311C22×C11#38514yes—
312C22×C11C22×C4⋊C411yescharacteristic
313C22×C11C2×#12011yescharacteristic
314C22×C11C2×#12311yescharacteristic
315C22×C11#57611yescharacteristic
316C22×C11#57711yescharacteristic
317C22×C11#57711yescharacteristic
318C22×C11#57811yescharacteristic
319C4×C11—24no—
320C4×C11—82no—
321C4×C11—81no—
322C4×C11—81no—
323C4×C11#38514yes—
324C4×C11C2×C4×D411yescharacteristic
325C4×C11C2×C4×D411yescharacteristic
326C4×C11C2×C22⋊Q811yescharacteristic
327C4×C11C2×C22⋊Q811yescharacteristic
328Dic11—44no—
329Dic11—42no—
330Dic11—42no—
331C2×#41—22no—
332C2×#41—22no—
333C2×#41—22no—
334C2×#41—22no—
335C2×#41Dic2214yes—
336C2×#41C4×D1114yes—
337C22×Q8C22⋊D1111yescharacteristic
338C22×D4C22⋊D1112yes—
339C22×D4C22⋊D1111yescharacteristic
340C23×C4—21no—
341C23×C4—222no—
342C23×C4—221no—
343C23×C4C22×D1112yes—
344C23×C4C22×D1111yescharacteristic
345C2×M16—114no—
346C2×M16—222no—
347C2×M16—222no—
348C22×C8—114no—
349C22×C8—111no—
350C22×C8—111no—
351C22×C8—112no—
352C22×C8—222no—
353C22×C8—222no—
354C4×Q8—228no—
355C4×D4—2216no—
356C4×D4—228no—
357#117—22no—
358#117—22no—
359#117—114no—
360#117—224no—
361#117—224no—
362#117—222no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—114no—
367C2×C4⋊C4—112no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—224no—
371C2×C4⋊C4—224no—
372C2×C4⋊C4—222no—
373C2×C4⋊C4—222no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4C22×D1112yes—
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C4⋊C4C22×D1111yescharacteristic
378C2×C22⋊C4—21no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—222no—
382C2×C22⋊C4—221no—
383C2×C42—21no—
384C2×C42—222no—
385C2×C42—221no—
386#107—222no—
387#107—222no—
388#107—224no—
389#106—222no—
390#106—222no—
391#106—224no—
392C22⋊C8—118no—
393C22⋊C8—118no—
394#95—22no—
395#95—22no—
396C2×C11—24no—
397C2×C11—44no—
398C2×C11C2×#38511yescharacteristic
399C2×C11#291211yescharacteristic
400C2×C11#291311yescharacteristic
401C2×C11#301211yescharacteristic
402C2×C11#301311yescharacteristic
403C2×C11#309611yescharacteristic
404C2×C11#309711yescharacteristic
405C24C2×C22⋊D1112yes—
406C24C2×C22⋊D1111yescharacteristic
407#41—28no—
408#41—28no—
409#41—28no—
410#41—28no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8Dic11⋊C414yes—
414C2×D4—24no—
415C2×D4—24no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4Dic11⋊C418yes—
419C2×D4Dic11⋊C414yes—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—42no—
428C22×C4—81no—
429C22×C4—81no—
430C22×C4—221no—
431C22×C4—222no—
432C22×C4—221no—
433C22×C4—228no—
434C22×C4—224no—
435C22×C4—881no—
436C22×C4—882no—
437C22×C4—881no—
438C22×C4—882no—
439C22×C4C2×Dic2214yes—
440C22×C4C2×Dic2212yes—
441C22×C4C2×C4×D1114yes—
442C22×C4C2×C4×D1112yes—
443C22×C4D4×D1112yes—
444C22×C4D4×D1112yes—
445C22×C4#434112yes—
446C22×C4#434112yes—
447C22×C4C2×C22⋊D1112yes—
448C22×C4C2×C22⋊D1111yescharacteristic
449C22×C4C23×D1111yescharacteristic
450M16—228no—
451C2×C8—112no—
452C2×C8—112no—
453C2×C8—114no—
454C2×C8—228no—
455C2×C8—221no—
456C2×C8—222no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—222no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—42no—
468C4⋊C4—114no—
469C4⋊C4—112no—
470C4⋊C4—112no—
471C4⋊C4—228no—
472C4⋊C4—224no—
473C4⋊C4—221no—
474C4⋊C4—222no—
475C4⋊C4—221no—
476C22⋊C4—42no—
477C22⋊C4—82no—
478C22⋊C4—82no—
479C22⋊C4—228no—
480C22⋊C4—224no—
481C42—42no—
482C42—228no—
483C42—224no—
484C11#2084911yescharacteristic, complemented, Sylow
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—22no—
495C23C2×Dic11⋊C414yes—
496C23C2×Dic11⋊C412yes—
497C23#6698812yes—
498C23#6699012yes—
499C23C22×C22⋊D1111yescharacteristic
500Q8—28no—
501D4—216no—
502D4—28no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—42no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—42no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—84no—
519C2×C4—222no—
520C2×C4—224no—
521C2×C4—222no—
522C2×C4—442no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4—442no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4—884no—
529C2×C4—888no—
530C2×C4#6693114yes—
531C2×C4#6693114yes—
532C2×C4(C22⋊D11)⋊C414yes—
533C2×C4(C22⋊D11)⋊C414yes—
534C2×C4C2×Dic11⋊C414yes—
535C2×C4C2×Dic11⋊C412yes—
536C2×C4#6698812yes—
537C2×C4#6699012yes—
538C2×C4C22×Dic2211yescharacteristic
539C2×C4C22×C4×D1111yescharacteristic
540C2×C4C2×D4×D1111yescharacteristic
541C2×C4C2×D4×D1111yescharacteristic
542C2×C4C2×#434111yescharacteristic
543C2×C4C2×#434111yescharacteristic
544C8—222no—
545C8—222no—
546C8—224no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—24no—
554C22—24no—
555C22—24no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22#1062255914yes—
561C22C22×Dic11⋊C411yescharacteristic
562C22C2×#6698811yescharacteristic
563C22C2×#6699011yescharacteristic
564C22#1062336611yescharacteristic
565C22#1062336711yescharacteristic
566C22#1062336811yescharacteristic
567C22#1062336911yescharacteristic
568C4—24no—
569C4—82no—
570C4—81no—
571C4—81no—
572C4—444no—
573C4—442no—
574C4—442no—
575C4#1062255914yes—
576C4C2×#6693111yescharacteristic
577C4C2×#6693111yescharacteristic
578C4C2×(C22⋊D11)⋊C411yescharacteristic
579C4C2×(C22⋊D11)⋊C411yescharacteristic
580C2—24no—
581C2—44no—
582C2C2×#1062255911yescharacteristic
583C2#1307720911yescharacteristic
584C2#1307721411yescharacteristic
585C2#1307791711yescharacteristic
586C2#1307792811yescharacteristic
587C2#1307856811yescharacteristic
588C2#1307857911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2311C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenter#2311D11
hypocenterC11#20849
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. C2×#10622608C2semidirect
3. C2×#10622611C2semidirect
5. #13068813C2semidirect
6. #13068813C2semidirect
7. #13068808C2semidirect
8. #13068803C2semidirect
9. #13068335C2semidirect
10. C2×#10622167C2semidirect
31. #10622847C4semidirect
94. C2×#4318C2×C4semidirect
97. C22×C11⋊C8C2×C4semidirect
103. C22⋊(C11⋊C8)C2×C4semidirect
104. C22⋊(C11⋊C8)C2×C4semidirect
484. C11#20849semidirect

Maximal subgroups

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

subgroupindex
C2×#106233582
C2×#106226082
C2×#106226112
C2×#106228472
#130688132
#130688082
#130688032
#130683352
C2×#106221672
C11×#23112
#2084911