Finite Group Databasebeta

← #14803947

Subgroups — #14803947

Order 2816.

850 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622635C211yesmaximal, characteristic, complemented
2C2×D4×C11⋊C8C211yesmaximal, characteristic
3#13073782C211yesmaximal, characteristic
4#13070052C211yesmaximal, characteristic, complemented
5#13070042C211yesmaximal, characteristic, complemented
6#13069816C211yesmaximal, characteristic, complemented
7#13069809C211yesmaximal, characteristic, complemented
8#13069580C211yesmaximal, characteristic, complemented
9#13069382C211yesmaximal, characteristic, complemented
10#13069040C211yesmaximal, characteristic, complemented
11#13069040C211yesmaximal, characteristic, complemented
12#13068643C211yesmaximal, characteristic, complemented
13#13068639C211yesmaximal, characteristic, complemented
14C4×#66899C211yesmaximal, characteristic, complemented
15C11×#2536C211yesmaximal, characteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C23×C11⋊C8C2211yescharacteristic
21C23×C11⋊C8C2211yescharacteristic
22C2×#66923C2211yescharacteristic
23C11×#398—21no—
24C11×#394—21no—
25C11×#388—21no—
26C11×#388—21no—
27C11×#382C2211yescharacteristic
28C11×#380C2211yescharacteristic
29C11×#380C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34#10622835—21no—
35#10622825C2211yescharacteristic
36#10622825C2211yescharacteristic
37#10622825C2211yescharacteristic
38#10622825C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41#10622635—24no—
42D4×C11⋊C8—24no—
43#10622595—21no—
44C2×#66872C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47C2×#66871C2211yescharacteristic
48#10622558—21no—
49#10622558—21no—
50C4×C4⋊Dic11C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4×C11⋊C8C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11D411yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C11×C22⋊Q8—22no—
66C11×C22⋊Q8—22no—
67C11×C22⋊Q8—41no—
68C11×C22⋊Q8—41no—
69C4×Q8×C11—22no—
70C4×Q8×C11—22no—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4D411yescharacteristic
85C2×C11×C22⋊C4D411yescharacteristic
86C2×C42×C11—21no—
87C2×C42×C11C2311yescharacteristic
88C2×C22⋊Dic11—21no—
89C2×C22⋊Dic11—21no—
90C2×C22⋊Dic11—21no—
91C2×C22⋊Dic11—21no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×C4×Dic11—21no—
99C22×C11⋊C8—22no—
100C22×C11⋊C8—22no—
101C22×C11⋊C8—22no—
102C22×C11⋊C8—22no—
103C22×C11⋊C8—41no—
104C22×C11⋊C8—41no—
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109#66923—22no—
110#66923—22no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95—21no—
115#66899—22no—
116#66899—22no—
117#66899—22no—
118#66899—22no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C22⋊(C11⋊C8)—22no—
125C22⋊(C11⋊C8)—22no—
126#66872—22no—
127#66872—41no—
128#66871—22no—
129#66871—41no—
130C4⋊(C11⋊C8)D414yes—
131C4×C11⋊C8—22no—
132#25343—111nomaximal, Sylow
133C24×C11C2×D411yescharacteristic
134C24×C11C2×D411yescharacteristic
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11#4112yes—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2411yescharacteristic
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—42no—
177C11×C4⋊C4—42no—
178C11×C4⋊C4—42no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—42no—
182C11×C22⋊C4—42no—
183C11×C22⋊C4—42no—
184C11×C22⋊C4—42no—
185C42×C11—42no—
186C42×C11C2×D412yes—
187C42×C11#4112yes—
188C22⋊Dic11—42no—
189C22⋊Dic11—42no—
190C22⋊Dic11—81no—
191C22⋊Dic11—81no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200Dic11⋊C4—42no—
201Dic11⋊C4—42no—
202C4×Dic11—81no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—44no—
213C2×C11⋊C8—44no—
214C2×C11⋊C8C2×D412yes—
215C2×C11⋊C8C2×D412yes—
216C2×C11⋊C8#4112yes—
217C2×#479—111no—
218C2×C8×D4—111no—
219#2562—111no—
220#2536D1111yescharacteristic
221#2077—111no—
222#2075—111no—
223#2036—111no—
224#2035—111no—
225#1991—111no—
226#1949—111no—
227#1892—111no—
228#1892—111no—
229#1808—111no—
230#1807—111no—
231C4×#103—111no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11#13512yes—
245C23×C11#13512yes—
246C23×C11C22×D411yescharacteristic
247Q8×C11—22no—
248Q8×C11—22no—
249Q8×C11—41no—
250Q8×C11—41no—
251D4×C11—28no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—22no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11#12112yes—
283C2×C4×C11#12112yes—
284C2×C4×C11C22×D411yescharacteristic
285C2×C4×C11C2×#4111yescharacteristic
286C2×C4×C11C2×#4111yescharacteristic
287C2×C4×C11C2×#4111yescharacteristic
288C2×C4×C11H(5,𝔽2)11yescharacteristic
289C2×C4×C112−1+411yescharacteristic
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C11⋊C8—22no—
303C11⋊C8—22no—
304C11⋊C8—22no—
305C11⋊C8—41no—
306C23×C8—111no—
307C23×C8—111no—
308C2×#125—111no—
309C2×C22⋊Q8C2×D1111yescharacteristic
310C2×C22⋊Q8C2×D1111yescharacteristic
311C2×C4×Q8C2×D1111yescharacteristic
312C2×C4×D4C2×D1111yescharacteristic
313#479—224no—
314C8×D4—224no—
315C2×#107—111no—
316C2×#107—111no—
317C2×#106—111no—
318C2×#106—111no—
319C2×C4⋊C8—111no—
320C2×#103—111no—
321C2×#103—111no—
322C2×#103—111no—
323C2×#103—111no—
324C2×C22⋊C8—111no—
325C2×C22⋊C8—111no—
326C2×C4×C8—111no—
327#400—221no—
328#398—21no—
329#394—21no—
330#394—221no—
331#388—21no—
332#388—21no—
333#388—221no—
334#388—221no—
335#382C2×D1111yescharacteristic
336#380—111no—
337#380—111no—
338#380—111no—
339#380—111no—
340#380C2×D1111yescharacteristic
341#380C2×D1111yescharacteristic
342C4×C4⋊C4—111no—
343#340—111no—
344#340—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340—111no—
350#340—111no—
351C22×C11—22no—
352C22×C11—22no—
353C22×C11—22no—
354C22×C11—22no—
355C22×C11—22no—
356C22×C11—22no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11C2×#12111yescharacteristic
366C22×C11#54611yescharacteristic
367C22×C11#54711yescharacteristic
368C22×C11C2×#13511yescharacteristic
369C22×C11C2×#13511yescharacteristic
370C22×C11#57711yescharacteristic
371C22×C11#57811yescharacteristic
372C4×C11—22no—
373C4×C11—22no—
374C4×C11—41no—
375C4×C11—41no—
376C4×C11—42no—
377C4×C11—81no—
378C4×C11—81no—
379C4×C11—81no—
380C4×C11#52911yescharacteristic
381C4×C11#54211yescharacteristic
382C4×C11#54611yescharacteristic
383C4×C11#54811yescharacteristic
384Dic11—81no—
385Dic11—81no—
386Dic11—81no—
387Dic11—81no—
388C22×Q8C22×D1111yescharacteristic
389C22×D4C22⋊D1111yescharacteristic
390C23×C4C22×D1111yescharacteristic
391C23×C4C22×D1111yescharacteristic
392C22×C8—111no—
393C22×C8—111no—
394C22×C8—111no—
395C22×C8—111no—
396C22×C8—222no—
397C22×C8—222no—
398C22×C8—222no—
399C22×C8—222no—
400C22×C8—441no—
401C22×C8—441no—
402#125—222no—
403#125—222no—
404C22⋊Q8—22no—
405C22⋊Q8—22no—
406C22⋊Q8—41no—
407C22⋊Q8—41no—
408C4×Q8—22no—
409C4×Q8—22no—
410C4×D4—22no—
411C4×D4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4C22⋊D1111yescharacteristic
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C4⋊C4C22×D1111yescharacteristic
424C2×C4⋊C4C22×D1111yescharacteristic
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4C22⋊D1111yescharacteristic
434C2×C22⋊C4C22⋊D1111yescharacteristic
435C2×C42—21no—
436C2×C42—221no—
437C2×C42C22×D1111yescharacteristic
438#107—222no—
439#107—441no—
440#106—222no—
441#106—441no—
442C4⋊C8—114no—
443#103—222no—
444#103—222no—
445#103—222no—
446#103—222no—
447C22⋊C8—222no—
448C22⋊C8—222no—
449C4×C8—222no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—221no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459C2×C11—42no—
460C2×C11—42no—
461C2×C11#242711yescharacteristic
462C2×C11#305011yescharacteristic
463C2×C11#306311yescharacteristic
464C2×C11#330011yescharacteristic
465C2×C11#330111yescharacteristic
466C2×C11#333611yescharacteristic
467C2×C11#333711yescharacteristic
468C24C2×C22⋊D1111yescharacteristic
469C24C2×C22⋊D1111yescharacteristic
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8#434112yes—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4C2×C22⋊D1111yescharacteristic
500C22×C4C2×C22⋊D1111yescharacteristic
501C22×C4C2×C22⋊D1111yescharacteristic
502C22×C4C2×C22⋊D1111yescharacteristic
503C22×C4C23×D1111yescharacteristic
504C2×C8—112no—
505C2×C8—112no—
506C2×C8—112no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—444no—
517C2×C8—444no—
518C4⋊C4—22no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—42no—
526C4⋊C4—42no—
527C4⋊C4—42no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—442no—
537C4⋊C4—442no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—42no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C22⋊C4—442no—
545C22⋊C4—442no—
546C22⋊C4—881no—
547C22⋊C4—881no—
548C42—42no—
549C42—881no—
550C42D4×D1112yes—
551C42#434112yes—
552C11#2534311yescharacteristic, complemented, Sylow
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23#6700312yes—
566C23#6700312yes—
567C23C22×C22⋊D1111yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—41no—
571Q8—41no—
572D4—28no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
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—441no—
614C2×C4—441no—
615C2×C4#6699212yes—
616C2×C4#6699212yes—
617C2×C4C2×D4×D1111yescharacteristic
618C2×C4C2×#434111yescharacteristic
619C2×C4C2×#434111yescharacteristic
620C2×C4#6703711yescharacteristic
621C2×C4#41×D1111yescharacteristic
622C2×C4#6704311yescharacteristic
623C8—222no—
624C8—222no—
625C8—222no—
626C8—441no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22C2×#6699211yescharacteristic
642C22#1062333711yescharacteristic
643C22C2×#6700311yescharacteristic
644C22C2×#6700311yescharacteristic
645C22#1062335511yescharacteristic
646C22#1062336811yescharacteristic
647C22#1062336911yescharacteristic
648C4—22no—
649C4—22no—
650C4—41no—
651C4—41no—
652C4—42no—
653C4—81no—
654C4—81no—
655C4—81no—
656C4—881no—
657C4—881no—
658C4—881no—
659C4—881no—
660C4#1062312911yescharacteristic
661C4#1062313111yescharacteristic
662C4#1062313411yescharacteristic
663C4#1062314311yescharacteristic
664C2—42no—
665C2—42no—
666C2#1307219511yescharacteristic
667C2#1307819411yescharacteristic
668C2#1307830311yescharacteristic
669C2#1308050311yescharacteristic
670C2#1308051811yescharacteristic
671C2#1308097811yescharacteristic
672C2#1308099511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2536C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenter#2536D11
hypocenterC11#25343
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2536

Complements

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

NH ≅ G/Ntype
1. C2×#10622635C2semidirect
4. #13070052C2semidirect
5. #13070042C2semidirect
6. #13069816C2semidirect
7. #13069809C2semidirect
8. #13069580C2semidirect
9. #13069382C2semidirect
10. #13069040C2semidirect
11. #13069040C2semidirect
12. #13068643C2semidirect
13. #13068639C2semidirect
14. C4×#66899C2semidirect
552. C11#25343semidirect

Maximal subgroups

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

subgroupindex
C2×#106226352
C2×D4×C11⋊C82
#130737822
#130700522
#130700422
#130698162
#130698092
#130695802
#130693822
#130690402
#130686432
#130686392
C4×#668992
C11×#25362
#2534311