Finite Group Databasebeta

← #14771976

Subgroups — #14771976

Order 2816.

970 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622724C211yesmaximal, characteristic
2C2×#10622474C211yesmaximal, characteristic, complemented
3C2×#10622719C211yesmaximal, characteristic, complemented
4#13071560C211yesmaximal, characteristic
5#13071538C211yesmaximal, characteristic
6#13069383C211yesmaximal, characteristic, complemented
7#13069378C211yesmaximal, characteristic, complemented
8#13068816C211yesmaximal, characteristic, complemented
9#13068813C211yesmaximal, characteristic, complemented
10#13068813C211yesmaximal, characteristic, complemented
11#13068810C211yesmaximal, characteristic, complemented
12#13068781C211yesmaximal, characteristic, complemented
13#13068646C211yesmaximal, characteristic, complemented
14#13068516C211yesmaximal, characteristic, complemented
15C11×#1807C211yesmaximal, characteristic, complemented
16C23×C8×C11C2211yescharacteristic
17C2×C4×C22⋊D11C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C22×#4313C2211yescharacteristic
21C2×#66945C2211yescharacteristic
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C11×#380C2211yescharacteristic
26C11×#380C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28#10622724C418yescomplemented
29C2×(C2×D11)⋊C8C2211yescharacteristic
30#10622719—24no—
31C2×#66882C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35C2×#66879C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37#10622600C2211yescharacteristic
38#10622600C2211yescharacteristic
39#10622590C2211yescharacteristic
40#10622589C2211yescharacteristic
41C4⋊C4×Dic11C2211yescharacteristic
42C4⋊C4×Dic11C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47#10622570—21no—
48#10622569—21no—
49#10622558—21no—
50#10622557—21no—
51#10622474—24no—
52#10622282—21no—
53#10622279—21no—
54#10622265—21no—
55#10622262—21no—
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11D411yescharacteristic
64C22×C4×D11—21no—
65C22×C4×D11C2311yescharacteristic
66C22×C8×C11—22no—
67C22×C8×C11—22no—
68C22×C8×C11C2×C414yescomplemented
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11D411yescharacteristic
80C4×C22⋊D11C2×C414yes—
81C4×C22⋊D11Q814yes—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4D411yescharacteristic
86#66979—22no—
87#66979—22no—
88#66979—41no—
89#66979—41no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4D411yescharacteristic
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C2×#4313—22no—
107C2×#4313—22no—
108C2×#4313C2×C414yes—
109#66945—22no—
110#66945—41no—
111C4⋊C4×D11—22no—
112C4⋊C4×D11—41no—
113C11×#106—22no—
114C11×#106—22no—
115C11×#95—21no—
116C11×#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C22⋊(C11⋊C8)C2×C414yescomplemented
124(C2×D11)⋊C8C2×C414yes—
125#66882—22no—
126#66882D414yescomplemented
127#66881—22no—
128#66881—22no—
129#66879C2×C414yescomplemented
130Dic11⋊C8C2×C414yescomplemented
131#66872—22no—
132#66872—41no—
133#66871—22no—
134#66871—41no—
135#22662—111nomaximal, Sylow
136C24×C11C2×D411yescharacteristic
137C23×D11C2×D411yescharacteristic
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11C22×C412yes—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×Q812yes—
149C22×C4×C11C2411yescharacteristic
150C2×C22⋊D11—41no—
151C2×C22⋊D11—41no—
152C2×C22⋊D11C4⋊C414yes—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—42no—
165C2×C4×D11—42no—
166C2×C4×D11—81no—
167C2×C4×D11C22×C412yes—
168C2×C4×D11C2×Q812yes—
169C2×C8×C11—28no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11C22×C412yes—
173C2×C8×C11C22×C412yes—
174C2×C8×C11C2×D412yes—
175C2×C8×C11#4112yes—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C22⋊C4—81no—
185C11×C22⋊C4—81no—
186C22⋊Dic11—42no—
187C22⋊Dic11—42no—
188C22⋊Dic11C4⋊C414yes—
189(C2×D11)⋊C4—42no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—81no—
192(C2×D11)⋊C4C4⋊C414yes—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11C2×D412yes—
200C4⋊Dic11C2×D412yes—
201Dic11⋊C4—42no—
202Dic11⋊C4—42no—
203Dic11⋊C4—81no—
204Dic11⋊C4C4⋊C414yes—
205C4×Dic11—42no—
206C4×Dic11—42no—
207C4×Dic11—42no—
208C4×Dic11—42no—
209C4×Dic11—81no—
210C4×Dic11C22×C412yes—
211C4×Dic11C2×Q812yes—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8C22×C412yes—
217C2×C11⋊C8C22×C412yes—
218#4313—28no—
219C2×#435—111no—
220C2×#428—111no—
221C2×#427—111no—
222#2354—111no—
223#2352—111no—
224#1949—111no—
225#1948—111no—
226#1854—111no—
227#1854—111no—
228#1854—111no—
229#1853—111no—
230#1847—111no—
231#1809—111no—
232#1807D1111yescharacteristic, complemented
233#1776—111no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11C2×C4⋊C412yes—
241C23×C11C22×D411yescharacteristic
242C22×D11—21no—
243C22×D11—21no—
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—21no—
248C22×D11C2×C4⋊C412yes—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11C2×C4⋊C412yes—
268C2×C4×C11C23×C411yescharacteristic
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×Q811yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11H(5,𝔽2)11yescharacteristic
273C2×C4×C112−1+411yescharacteristic
274C22⋊D11—44no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—22no—
282C2×Dic11—22no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11C2×C4⋊C412yes—
294C2×Dic11C2×C4⋊C412yes—
295C2×Dic11C2×C4⋊C412yes—
296C4×D11—22no—
297C4×D11—22no—
298C4×D11—22no—
299C4×D11—22no—
300C4×D11—84no—
301C8×C11—22no—
302C8×C11C4×D414yes—
303C11⋊C8—22no—
304C11⋊C8—22no—
305C22×M16—111no—
306C23×C8C2×D1111yescharacteristic
307C2×C4×D4—111no—
308C2×#117—111no—
309C2×#117—111no—
310C2×#117—111no—
311C22×C4⋊C4—111no—
312#435—118no—
313#428—224no—
314#427—224no—
315C2×#107—111no—
316C2×#107—111no—
317C2×#107—111no—
318C2×#107—111no—
319C2×#106—111no—
320C2×#106—111no—
321C2×#106—111no—
322C2×#106—111no—
323C2×#106C2×D1111yescharacteristic
324C2×#106C2×D1111yescharacteristic
325C2×C4⋊C8—111no—
326C2×C22⋊C8—111no—
327C2×C22⋊C8—111no—
328C2×#97—111no—
329#390—221no—
330#388—221no—
331#388—221no—
332#388—221no—
333#387—221no—
334#386—221no—
335#384—111no—
336#382—111no—
337#380—111no—
338#380—111no—
339#380C2×D1111yescharacteristic
340#380C2×D1111yescharacteristic
341C4×C4⋊C4—111no—
342C4×C4⋊C4—111no—
343C4×C4⋊C4—221no—
344C4×C22⋊C4—221no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340C2×D1111yescharacteristic
350#340C2×D1111yescharacteristic
351C22×C11—22no—
352C22×C11—22no—
353C22×C11—22no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11C22×C4⋊C411yescharacteristic
359C22×C11D4211yescharacteristic
360C22×C11#54711yescharacteristic
361C22×C11#57511yescharacteristic
362C22×C11#57511yescharacteristic
363C22×C11#57711yescharacteristic
364C22×C11#57711yescharacteristic
365C2×D11—22no—
366C2×D11—22no—
367C2×D11—22no—
368C2×D11—41no—
369C2×D11—41no—
370C2×D11—41no—
371C2×D11—41no—
372C4×C11—22no—
373C4×C11—81no—
374C4×C11—81no—
375C4×C11—81no—
376C4×C11—81no—
377C4×C11C2×C4×D411yescharacteristic
378C4×C11#52011yescharacteristic
379C4×C11D4×Q811yescharacteristic
380C4×C11#55411yescharacteristic
381Dic11—22no—
382Dic11—22no—
383Dic11—22no—
384Dic11—42no—
385Dic11—42no—
386Dic11—81no—
387Dic11—81no—
388C22×D4—111no—
389C23×C4—111no—
390C23×C4—221no—
391C23×C4C22×D1111yescharacteristic
392C2×M16—114no—
393C2×M16—222no—
394C2×M16—222no—
395C22×C8—22no—
396C22×C8—22no—
397C22×C8—111no—
398C22×C8—111no—
399C22×C8C4×D1114yescomplemented
400C22×C8C22×D1111yescharacteristic
401C22×C8C22×D1111yescharacteristic
402C4×D4—114no—
403C4×D4—114no—
404#117—222no—
405#117—222no—
406#117—222no—
407#117—441no—
408#117—441no—
409#117—441no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—222no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—441no—
420C2×C4⋊C4C22×D1111yescharacteristic
421C2×C4⋊C4C22×D1111yescharacteristic
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C4⋊C4C22×D1111yescharacteristic
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—111no—
427C2×C22⋊C4—111no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C42—111no—
434C2×C42—221no—
435C2×C42—221no—
436C2×C42—221no—
437C2×C42—221no—
438C2×C42—221no—
439#107—114no—
440#107—222no—
441#107—222no—
442#107—441no—
443#106—22no—
444#106—22no—
445#106—222no—
446#106—222no—
447#106—222no—
448#106—441no—
449C4⋊C8—114no—
450C22⋊C8—114no—
451C22⋊C8—114no—
452#97—114no—
453#95—21no—
454#95—21no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461C2×C11—42no—
462C2×C11D4×C4⋊C411yescharacteristic
463C2×C11#291111yescharacteristic
464C2×C11#291211yescharacteristic
465C2×C11#326711yescharacteristic
466C2×C11#327111yescharacteristic
467C2×C11#334811yescharacteristic
468C2×C11#335011yescharacteristic
469D11—42no—
470C24—111no—
471C24D4×D1111yescharacteristic
472C2×D4—114no—
473C2×D4—441no—
474C2×D4—441no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—111no—
484C22×C4—111no—
485C22×C4—111no—
486C22×C4—112no—
487C22×C4—112no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—442no—
497C22×C4—442no—
498C22×C4—881no—
499C22×C4C2×C4×D1112yes—
500C22×C4D4×D1111yescharacteristic
501C22×C4Q8×D1112yes—
502C22×C4C23×D1111yescharacteristic
503M16—228no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—28no—
507C2×C8—112no—
508C2×C8—112no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8C2×C4×D1112yes—
514C2×C8C2×C4×D1112yes—
515C2×C8D4×D1112yes—
516C2×C8#434112yes—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—114no—
526C4⋊C4—112no—
527C4⋊C4—112no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—442no—
535C4⋊C4—442no—
536C4⋊C4—881no—
537C22⋊C4—81no—
538C22⋊C4—81no—
539C22⋊C4—114no—
540C22⋊C4—114no—
541C22⋊C4—442no—
542C22⋊C4—442no—
543C22⋊C4—442no—
544C22⋊C4—442no—
545C22⋊C4—881no—
546C42—112no—
547C42—112no—
548C42—442no—
549C42—442no—
550C42—442no—
551C42—442no—
552C42—881no—
553C11#2266211yescharacteristic, complemented, Sylow
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—112no—
561C23—221no—
562C23—221no—
563C23—221no—
564C23—221no—
565C23—221no—
566C23—221no—
567C23C4⋊C4×D1112yes—
568C23C2×D4×D1111yescharacteristic
569D4—444no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—112no—
589C2×C4—112no—
590C2×C4—112no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—222no—
598C2×C4—222no—
599C2×C4—222no—
600C2×C4—222no—
601C2×C4—222no—
602C2×C4—222no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—884no—
614C2×C4C4⋊C4×D1112yes—
615C2×C4C22×C4×D1111yescharacteristic
616C2×C4C2×D4×D1111yescharacteristic
617C2×C4C2×#434111yescharacteristic
618C2×C4C2×Q8×D1111yescharacteristic
619C2×C4#6704211yescharacteristic
620C2×C4#6704311yescharacteristic
621C8—22no—
622C8—222no—
623C8—222no—
624C8(C22⋊D11)⋊C414yes—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—222no—
633C22—222no—
634C22—222no—
635C22—441no—
636C22—441no—
637C22—441no—
638C22—441no—
639C22C2×C4⋊C4×D1111yescharacteristic
640C22#1062314011yescharacteristic
641C22#1062314211yescharacteristic
642C22#1062329311yescharacteristic
643C22#1062329311yescharacteristic
644C22#1062329911yescharacteristic
645C22#1062329911yescharacteristic
646C4—22no—
647C4—81no—
648C4—81no—
649C4—81no—
650C4—81no—
651C4—222no—
652C4—222no—
653C4—222no—
654C4—442no—
655C4—442no—
656C4—881no—
657C4—881no—
658C4C2×(C22⋊D11)⋊C411yescharacteristic
659C4#1062305411yescharacteristic
660C4#1062316311yescharacteristic
661C4#1062316611yescharacteristic
662C2—42no—
663C2—442no—
664C2#1307151211yescharacteristic
665C2#1307720411yescharacteristic
666C2#1307720711yescharacteristic
667C2#1308013811yescharacteristic
668C2#1308019811yescharacteristic
669C2#1308113711yescharacteristic
670C2#1308116711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1807C2
socleC23×C11C22×D4
prime radicalC22×C22⋊D11D4
cosocleC22×C4×C11C24
hypercenter#1807D11
hypocenterC11#22662
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1807

Complements

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

NH ≅ G/Ntype
2. C2×#10622474C2semidirect
3. C2×#10622719C2semidirect
6. #13069383C2semidirect
7. #13069378C2semidirect
8. #13068816C2semidirect
9. #13068813C2semidirect
10. #13068813C2semidirect
11. #13068810C2semidirect
12. #13068781C2semidirect
13. #13068646C2semidirect
14. #13068516C2semidirect
15. C11×#1807C2semidirect
28. #10622724C4semidirect
68. C22×C8×C11C2×C4semidirect
123. C22⋊(C11⋊C8)C2×C4semidirect
126. #66882D4semidirect
129. #66879C2×C4semidirect
130. Dic11⋊C8C2×C4semidirect
232. #1807D11semidirect
399. C22×C8C4×D11semidirect
553. C11#22662semidirect

Maximal subgroups

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

subgroupindex
C2×#106227242
C2×#106224742
C2×#106227192
#130715602
#130715382
#130693832
#130693782
#130688162
#130688132
#130688102
#130687812
#130686462
#130685162
C11×#18072
#2266211