Finite Group Databasebeta

← #14660223

Subgroups — #14660223

Order 2816.

1014 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622838C211yesmaximal, characteristic
2C2×#10622843C211yesmaximal, characteristic
3#13070972C211yesmaximal, characteristic
4C2×#10622192C211yesmaximal, characteristic
5C2×#10622193C211yesmaximal, characteristic
6C2×#10622170C211yesmaximal, characteristic
7C2×C11×#419C211yesmaximal, characteristic
8C23×Q8×C11C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C2×C11×#117C2211yescharacteristic
11C2×#66979C2211yescharacteristic
12C22×C4⋊Dic11C2211yescharacteristic
13C22×C4×Dic11C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C11×#419—22no—
16C11×#419C414yescomplemented
17C2×C11×#103—22no—
18#10622843—22no—
19#10622843C414yescomplemented
20#10622838—22no—
21#10622838C414yescomplemented
22C2×#66899—22no—
23C2×C11⋊#95—22no—
24C4⋊C4×Dic11—22no—
25C22⋊C4×Dic11—22no—
26C4×C4⋊Dic11—22no—
27#10622193—22no—
28#10622192—22no—
29#10622170—22no—
30C22×Q8×C11—21no—
31C22×Q8×C11—21no—
32C22×Q8×C11—21no—
33C22×Q8×C11—21no—
34C22×Q8×C11—21no—
35C22×Q8×C11—21no—
36C22×Q8×C11—21no—
37C22×Q8×C11—21no—
38C22×Q8×C11—21no—
39C22×Q8×C11—21no—
40C22×Q8×C11—21no—
41C22×Q8×C11C2×C412yes—
42C22×Q8×C11C2×C412yes—
43C22×Q8×C11C2×C412yes—
44C23×C4×C11—21no—
45C23×C4×C11C2311yescharacteristic
46C23×Dic11—21no—
47C23×Dic11D412yes—
48C2×C11×M16—21no—
49C2×C11×M16—21no—
50C2×C11×M16—21no—
51C2×C11×M16—21no—
52C2×C11×M16—21no—
53C2×C11×M16C2×C412yes—
54C22×C8×C11—21no—
55C11×#117—21no—
56C11×#117—21no—
57C11×#117C2×C412yes—
58C11×#117D412yes—
59C2×C11×C4⋊C4D412yes—
60C2×C11×C22⋊C4—21no—
61C2×C42×C11—21no—
62C2×C22⋊Dic11—21no—
63#66979—21no—
64#66979—21no—
65#66979C2×C412yes—
66#66979D412yes—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11C2×C412yes—
72C2×C4⋊Dic11D412yes—
73C2×C4⋊Dic11D412yes—
74C2×C4×Dic11—21no—
75C2×C4×Dic11—21no—
76C2×C4×Dic11—21no—
77C2×C4×Dic11—21no—
78C2×C4×Dic11—21no—
79C2×C4×Dic11—21no—
80C2×C4×Dic11—24no—
81C2×C4×Dic11C2×C412yes—
82C2×#4318—21no—
83C2×#4318—21no—
84C2×#4318—21no—
85C2×#4318—21no—
86C2×#4318—21no—
87C2×#4318C2×C412yes—
88C22×C11⋊C8—21no—
89C11×#103—28no—
90#66899—28no—
91C11⋊#95—24no—
92C11⋊#95—28no—
93#10957—111nomaximal, Sylow
94C24×C11C2×D411yescharacteristic
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×Q8×C11—22no—
101C2×Q8×C11—22no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—41no—
111C2×Q8×C11—41no—
112C2×Q8×C11—41no—
113C2×Q8×C11—41no—
114C2×Q8×C11—41no—
115C2×Q8×C11—41no—
116C2×Q8×C11—41no—
117C2×Q8×C11—41no—
118C2×Q8×C11—41no—
119C2×Q8×C11—41no—
120C2×Q8×C11—41no—
121C2×Q8×C11—41no—
122C2×Q8×C11C4214yescomplemented
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—41no—
128C22×C4×C11—41no—
129C22×C4×C11—41no—
130C22×C4×C11—41no—
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C22×C411yescharacteristic
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11#4111yescharacteristic
140C22×C4×C11#4111yescharacteristic
141C22×C4×C11#4111yescharacteristic
142C22×C4×C11#4111yescharacteristic
143C22×C4×C11#4111yescharacteristic
144C22×C4×C11#4111yescharacteristic
145C22×Dic11—24no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—42no—
151C22×Dic11—44no—
152C22×Dic11—41no—
153C22×Dic11—41no—
154C22×Dic11C22⋊C414yes—
155C11×M16—22no—
156C11×M16—22no—
157C11×M16—41no—
158C11×M16—41no—
159C2×C8×C11—22no—
160C2×C8×C11—41no—
161C2×C8×C11—41no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4C22⋊C414yes—
164C11×C22⋊C4—22no—
165C11×C22⋊C4—22no—
166C42×C11—22no—
167C42×C11—22no—
168C22⋊Dic11—22no—
169C22⋊Dic11—22no—
170C4⋊Dic11—22no—
171C4⋊Dic11—22no—
172C4⋊Dic11—22no—
173C4⋊Dic11—22no—
174C4⋊Dic11—22no—
175C4⋊Dic11C22⋊C414yes—
176C4×Dic11—22no—
177C4×Dic11—22no—
178C4×Dic11—22no—
179C4×Dic11—22no—
180C4×Dic11—41no—
181C4×Dic11—41no—
182C4×Dic11—84no—
183#4318—22no—
184#4318—22no—
185#4318—41no—
186#4318—41no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—41no—
189C2×C11⋊C8—41no—
190C2×#419—111no—
191C2×#419D1111yescharacteristic
192C2×#391—111no—
193#2274—111no—
194C2×#343—111no—
195C2×#339—111no—
196C2×#339—111no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11C2×C22⋊C411yescharacteristic
200C23×C11C4×D411yescharacteristic
201C23×C11C4×D411yescharacteristic
202C23×C11#12011yescharacteristic
203C23×C11#12111yescharacteristic
204C23×C11#12111yescharacteristic
205C23×C11#12311yescharacteristic
206Q8×C11—24no—
207Q8×C11—24no—
208Q8×C11—42no—
209Q8×C11—42no—
210Q8×C11—42no—
211Q8×C11—42no—
212Q8×C11—42no—
213Q8×C11—42no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11C2×C4211yescharacteristic
225C2×C4×C11C2×C22⋊C411yescharacteristic
226C2×C4×C11C2×C22⋊C411yescharacteristic
227C2×C4×C11#11711yescharacteristic
228C2×C4×C11#11711yescharacteristic
229C2×C4×C11#11711yescharacteristic
230C2×C4×C11C4×D411yescharacteristic
231C2×C4×C11C4×D411yescharacteristic
232C2×C4×C11C4×D411yescharacteristic
233C2×C4×C11C4×D411yescharacteristic
234C2×C4×C11C4×D411yescharacteristic
235C2×C4×C11C4×D411yescharacteristic
236C2×C4×C11C4×D411yescharacteristic
237C2×C4×C11C4×D411yescharacteristic
238C2×C4×C11C4×D411yescharacteristic
239C2×C4×C11C4×D411yescharacteristic
240C2×C4×C11#12111yescharacteristic
241C2×C4×C11#12111yescharacteristic
242C2×C4×C11#12111yescharacteristic
243C2×C4×C11#12111yescharacteristic
244C2×C4×C11#12311yescharacteristic
245C2×C4×C11#12311yescharacteristic
246C2×C4×C11#12411yescharacteristic
247C2×C4×C11#12411yescharacteristic
248C2×C4×C11#12411yescharacteristic
249C2×C4×C11#12611yescharacteristic
250C2×C4×C11#12611yescharacteristic
251C2×C4×C11#12711yescharacteristic
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—44no—
256C2×Dic11—44no—
257C2×Dic11—42no—
258C2×Dic11—42no—
259C2×Dic11—42no—
260C2×Dic11—44no—
261C2×Dic11—42no—
262C2×Dic11—44no—
263C2×Dic11—82no—
264C8×C11—42no—
265C11⋊C8—42no—
266C23×Q8C2×D1111yescharacteristic
267C22×M16—111no—
268C22×M16C2×D1111yescharacteristic
269C2×#117—111no—
270C2×#117C2×D1111yescharacteristic
271C22×C4⋊C4—111no—
272C22×C42—111no—
273#419—22no—
274#419—114no—
275#419—222no—
276#419Dic1114yescomplemented
277C2×#103—22no—
278C2×#103—222no—
279#391—114no—
280#391—222no—
281C4×C4⋊C4—222no—
282C4×C4⋊C4—222no—
283C4×C22⋊C4—222no—
284C2×#95—222no—
285#343—222no—
286#339—222no—
287#339—222no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—22no—
291C22×C11—22no—
292C22×C11—21no—
293C22×C11—21no—
294C22×C11—21no—
295C22×C11—21no—
296C22×C11C4×C22⋊C411yescharacteristic
297C22×C11#38611yescharacteristic
298C22×C11#38611yescharacteristic
299C22×C11#38611yescharacteristic
300C22×C11#38811yescharacteristic
301C22×C11#38811yescharacteristic
302C22×C11#39011yescharacteristic
303C22×C11#45512yes—
304C22×C11#45612yes—
305C4×C11—44no—
306C4×C11—44no—
307C4×C11C4×C22⋊C411yescharacteristic
308C4×C11C4×C22⋊C411yescharacteristic
309C4×C11#38811yescharacteristic
310C4×C11#38811yescharacteristic
311C4×C11#38811yescharacteristic
312C4×C11#38811yescharacteristic
313C4×C11#39011yescharacteristic
314C4×C11#39011yescharacteristic
315Dic11—44no—
316Dic11—44no—
317Dic11—44no—
318C22×Q8—21no—
319C22×Q8—21no—
320C22×Q8—21no—
321C22×Q8—21no—
322C22×Q8—21no—
323C22×Q8—21no—
324C22×Q8—21no—
325C22×Q8—21no—
326C22×Q8—21no—
327C22×Q8—21no—
328C22×Q8—21no—
329C22×Q8C4×D1112yes—
330C22×Q8C4×D1112yes—
331C22×Q8C2×Dic1112yes—
332C23×C4—21no—
333C23×C4—112no—
334C23×C4—221no—
335C23×C4C22×D1111yescharacteristic
336C2×M16—21no—
337C2×M16—21no—
338C2×M16—21no—
339C2×M16—21no—
340C2×M16—21no—
341C2×M16—112no—
342C2×M16—221no—
343C2×M16—221no—
344C2×M16—221no—
345C2×M16—221no—
346C2×M16—221no—
347C2×M16C2×Dic1112yes—
348C22×C8—21no—
349C22×C8—221no—
350#117—21no—
351#117—21no—
352#117—112no—
353#117—112no—
354#117—221no—
355#117—221no—
356#117C2×Dic1112yes—
357#117C22⋊D1112yes—
358C2×C4⋊C4—112no—
359C2×C4⋊C4—112no—
360C2×C4⋊C4—112no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4C22⋊D1112yes—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—221no—
368C2×C42—21no—
369C2×C42—112no—
370C2×C42—221no—
371C2×C42—221no—
372C2×C42—221no—
373C2×C42—221no—
374C2×C42—221no—
375C2×C42—221no—
376C2×C42—224no—
377#103—28no—
378#103—228no—
379#95—228no—
380#95—224no—
381C2×C11—21no—
382C2×C11—21no—
383C2×C11—21no—
384C2×C11—21no—
385C2×C11#143711yescharacteristic
386C2×C11#188212yes—
387C2×C11#188212yes—
388C2×C11#188511yescharacteristic
389C2×C11#188611yescharacteristic
390C24D4×D1111yescharacteristic
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—41no—
407C2×Q8—41no—
408C2×Q8—41no—
409C2×Q8—41no—
410C2×Q8—41no—
411C2×Q8—41no—
412C2×Q8—41no—
413C2×Q8—41no—
414C2×Q8—41no—
415C2×Q8—41no—
416C2×Q8—41no—
417C2×Q8—41no—
418C2×Q8C4×Dic1114yescomplemented
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—114no—
428C22×C4—224no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4—442no—
434C22×C4—441no—
435C22×C4—441no—
436C22×C4—444no—
437C22×C4C2×C4×D1111yescharacteristic
438C22×C4C2×C4×D1111yescharacteristic
439C22×C4#433911yescharacteristic
440C22×C4#433911yescharacteristic
441C22×C4D4×D1111yescharacteristic
442C22×C4D4×D1111yescharacteristic
443C22×C4D4×D1111yescharacteristic
444C22×C4#434111yescharacteristic
445C22×C4#434111yescharacteristic
446C22×C4#434111yescharacteristic
447C22×C4#434111yescharacteristic
448C22×C4C22×Dic1111yescharacteristic
449C22×C4C2×C22⋊D1111yescharacteristic
450C22×C4C2×C22⋊D1111yescharacteristic
451M16—22no—
452M16—22no—
453M16—41no—
454M16—41no—
455M16—222no—
456M16—222no—
457M16—441no—
458M16—441no—
459C2×C8—22no—
460C2×C8—41no—
461C2×C8—41no—
462C2×C8—222no—
463C2×C8—441no—
464C2×C8—441no—
465C4⋊C4—22no—
466C4⋊C4—114no—
467C4⋊C4—222no—
468C4⋊C4—222no—
469C4⋊C4—222no—
470C4⋊C4—222no—
471C4⋊C4—222no—
472C4⋊C4C22⋊Dic1114yes—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—222no—
476C22⋊C4—222no—
477C42—22no—
478C42—22no—
479C42—222no—
480C42—222no—
481C42—222no—
482C42—222no—
483C42—441no—
484C42—441no—
485C42—884no—
486C11#1095711yescharacteristic, complemented, Sylow
487C23—22no—
488C23—22no—
489C23C22⋊C4×D1111yescharacteristic
490C23(C22⋊D11)⋊C411yescharacteristic
491C23#6693611yescharacteristic
492C23#6693711yescharacteristic
493C23D4×Dic1111yescharacteristic
494C23#6699011yescharacteristic
495C23#6699211yescharacteristic
496Q8—24no—
497Q8—24no—
498Q8—42no—
499Q8—42no—
500Q8—42no—
501Q8—42no—
502Q8—42no—
503Q8—42no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—224no—
515C2×C4—224no—
516C2×C4—224no—
517C2×C4—444no—
518C2×C4—444no—
519C2×C4—442no—
520C2×C4—442no—
521C2×C4—444no—
522C2×C4—442no—
523C2×C4—442no—
524C2×C4—444no—
525C2×C4—882no—
526C2×C4#6693011yescharacteristic
527C2×C4#6693011yescharacteristic
528C2×C4#6693211yescharacteristic
529C2×C4#6693211yescharacteristic
530C2×C4C22⋊C4×D1111yescharacteristic
531C2×C4(C22⋊D11)⋊C411yescharacteristic
532C2×C4(C22⋊D11)⋊C411yescharacteristic
533C2×C4(C22⋊D11)⋊C411yescharacteristic
534C2×C4#6693611yescharacteristic
535C2×C4#6693711yescharacteristic
536C2×C4#6693811yescharacteristic
537C2×C4#6693811yescharacteristic
538C2×C4C2×C4×Dic1111yescharacteristic
539C2×C4#6697911yescharacteristic
540C2×C4C4×C22⋊D1111yescharacteristic
541C2×C4C4×C22⋊D1111yescharacteristic
542C2×C4C4×C22⋊D1111yescharacteristic
543C2×C4C4×C22⋊D1111yescharacteristic
544C2×C4D4×Dic1111yescharacteristic
545C2×C4D4×Dic1111yescharacteristic
546C2×C4D4×Dic1111yescharacteristic
547C2×C4#6698811yescharacteristic
548C2×C4#6698911yescharacteristic
549C2×C4#6699111yescharacteristic
550C2×C4#6699111yescharacteristic
551C2×C4#6699211yescharacteristic
552C2×C4#6699311yescharacteristic
553C2×C4C2×C22⋊Dic1111yescharacteristic
554C8—42no—
555C8—442no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22C22⋊C4×Dic1111yescharacteristic
565C22#1062255811yescharacteristic
566C22#1062256411yescharacteristic
567C22#1062256911yescharacteristic
568C22#1062256911yescharacteristic
569C22#1062257011yescharacteristic
570C22#1062281512yes—
571C22#1062281812yes—
572C22#1062283311yescharacteristic
573C4—44no—
574C4—44no—
575C4—444no—
576C4—444no—
577C4—444no—
578C4C22⋊C4×Dic1111yescharacteristic
579C4#1062255711yescharacteristic
580C4#1062255711yescharacteristic
581C4#1062255811yescharacteristic
582C4#1062256411yescharacteristic
583C4#1062257011yescharacteristic
584C4C4×C22⋊Dic1111yescharacteristic
585C4#1062283411yescharacteristic
586C2—21no—
587C2—21no—
588C2—21no—
589C2—21no—
590C2#1306685311yescharacteristic
591C2#1306898212yes—
592C2#1306898712yes—
593C2#1306900111yescharacteristic
594C2#1306900611yescharacteristic
subgroupG/H
centerC23#66990
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC2×C11×#419C2
socleC23×C11#120
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenterC2×#419D11
hypocenterC11#10957
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
16. C11×#419C4semidirect
19. #10622843C4semidirect
21. #10622838C4semidirect
122. C2×Q8×C11C42semidirect
276. #419Dic11semidirect
418. C2×Q8C4×Dic11semidirect
486. C11#10957semidirect

Maximal subgroups

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

subgroupindex
C2×#106228382
C2×#106228432
#130709722
C2×#106221922
C2×#106221932
C2×#106221702
C2×C11×#4192
#1095711