Finite Group Databasebeta

← #14772201

Subgroups — #14772201

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4326C211yesmaximal, characteristic
2C2×#10622403C211yesmaximal, characteristic
3C2×#10622403C211yesmaximal, characteristic
4#13071530C211yesmaximal, characteristic
5Q8×Dic11⋊C4C211yesmaximal, characteristic
6#13069348C211yesmaximal, characteristic
7#13069346C211yesmaximal, characteristic
8#13068873C211yesmaximal, characteristic
9#13068872C211yesmaximal, characteristic
10#13068867C211yesmaximal, characteristic
11#13068774C211yesmaximal, characteristic
12#13068620C211yesmaximal, characteristic
13#13068619C211yesmaximal, characteristic
14#13068477C211yesmaximal, characteristic
15C11×#1863C211yesmaximal, characteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C2×#66940C2211yescharacteristic
21C2×#66940C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×#66880C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34C4×#4326—24no—
35#10622598C2211yescharacteristic
36#10622589—21no—
37#10622589—21no—
38#10622589C2211yescharacteristic
39#10622589C2211yescharacteristic
40#10622586—21no—
41#10622586C2211yescharacteristic
42#10622585—21no—
43C2×#66874C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47C4×Dic11⋊C4—21no—
48C4×Dic11⋊C4C2211yescharacteristic
49#10622541—21no—
50#10622541C2211yescharacteristic
51C2×C4×C11⋊C8C2211yescharacteristic
52#10622403—24no—
53#10622403C418yescomplemented
54#10622262—21no—
55#10622260—21no—
56C11×#340C2211yescharacteristic
57C11×#336C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C4×Q8×C11—22no—
67C4×Q8×C11—41no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C42×C11—21no—
74C2×C42×C11C2311yescharacteristic
75Q8×Dic11—22no—
76Q8×Dic11—22no—
77Q8×Dic11—41no—
78Q8×Dic11C2×C414yes—
79C2×#4326C2×C414yes—
80C2×#4326D414yes—
81C2×#4326Q814yes—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4D411yescharacteristic
98C2×Dic11⋊C4D411yescharacteristic
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11C2311yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108#66940—22no—
109#66940—22no—
110#66940—41no—
111#66940C2×C414yes—
112C4×Dic22—22no—
113C4×Dic22—41no—
114C11×#107—41no—
115C11×#103—22no—
116C11×#103C2×C414yes—
117C11×#95—21no—
118#66899—22no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95D411yescharacteristic
123C11⋊#95D411yescharacteristic
124#66882—41no—
125#66880—22no—
126#66880C2×C414yes—
127Dic11⋊C8—22no—
128C8×Dic11—22no—
129C8×Dic11C2×C414yes—
130#66874—22no—
131#66871—22no—
132#66871—22no—
133#66871C2×C414yes—
134C4×C11⋊C8—22no—
135C4⋊C4×Q16—111nomaximal, Sylow
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11C22×C412yes—
140C2×Q8×C11C2×D412yes—
141C2×Q8×C11C2×Q812yes—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2411yescharacteristic
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22C22×C412yes—
161C2×Dic22C2×D412yes—
162C2×Dic22C2×Q812yes—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11C22×C412yes—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—42no—
175C11×C4⋊C4—81no—
176C11×C4⋊C4C22×C412yes—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—42no—
180#4326C4⋊C4116yescomplemented
181C4⋊Dic11—24no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—42no—
188C4⋊Dic11—81no—
189C4⋊Dic11C22×C412yes—
190Dic11⋊C4—24no—
191Dic11⋊C4—22no—
192Dic11⋊C4—42no—
193Dic11⋊C4—42no—
194Dic11⋊C4—42no—
195Dic11⋊C4—42no—
196Dic11⋊C4—81no—
197Dic11⋊C4—81no—
198Dic11⋊C4—81no—
199Dic11⋊C4—81no—
200Dic11⋊C4Q1614yescomplemented
201C4×Dic11—24no—
202C4×Dic11—24no—
203C4×Dic11—21no—
204C4×Dic11—21no—
205C4×Dic11—42no—
206C4×Dic11—42no—
207C4×Dic11—42no—
208C4×Dic11C22×C412yes—
209C4×Dic11#4112yes—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8C22×C412yes—
214C2×C11⋊C8C2×D412yes—
215C2×C11⋊C8C2×Q812yes—
216C2×C4×Q16—111no—
217C2×C4×Q16—111no—
218C2×C4×Q16—111no—
219Q8×C4⋊C4—111no—
220Q8×C4⋊C4—111no—
221#1942—111no—
222#1942—111no—
223#1863—111no—
224#1863—111no—
225#1863—111no—
226#1863D1111yescharacteristic
227#1845—111no—
228#1803—111no—
229#1803—111no—
230C8×C4⋊C4—111no—
231C23×C11C22×D411yescharacteristic
232Q8×C11—22no—
233Q8×C11—22no—
234Q8×C11—22no—
235Q8×C11C2×C4⋊C414yes—
236C2×C4×C11—22no—
237C2×C4×C11—21no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—21no—
241C2×C4×C11—22no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11C2×Q1612yes—
254C2×C4×C11C23×C411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×Q811yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11H(5,𝔽2)11yescharacteristic
259C2×C4×C112−1+411yescharacteristic
260C2×Dic11—22no—
261C2×Dic11—21no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—22no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11C4×D412yes—
280C2×Dic11C4×D412yes—
281C2×Dic11C2×Q1612yes—
282C2×Dic11C2×Q1612yes—
283C2×Dic11#13512yes—
284Dic22—22no—
285Dic22—22no—
286Dic22—22no—
287Dic22C2×C4⋊C414yes—
288C8×C11—22no—
289C8×C11—41no—
290C11⋊C8—41no—
291C11⋊C8C2×C4⋊C414yes—
292C22×Q16—111no—
293C2×C4×Q8—111no—
294C2×C4×Q8—111no—
295C2×C4×Q8—111no—
296C2×C4×Q8—111no—
297C2×C4×Q8—111no—
298C2×C4×Q8C2×D1111yescharacteristic
299C4×Q16—118no—
300C4×Q16—224no—
301C4×Q16—224no—
302C2×#107—111no—
303C2×#107—111no—
304C2×#107—111no—
305C2×#107—111no—
306C2×#107C2×D1111yescharacteristic
307C2×C4⋊C8—111no—
308C2×#103—111no—
309C2×#103—111no—
310C2×#103—111no—
311C2×#103—111no—
312C2×#103C2×D1111yescharacteristic
313C2×#103C2×D1111yescharacteristic
314C2×C4×C8—111no—
315C2×C4×C8—111no—
316C2×C4×C8—111no—
317#389—111no—
318#389—111no—
319#389—111no—
320#389—221no—
321#389—221no—
322#389—221no—
323#389—221no—
324#389C2×D1111yescharacteristic
325#384—111no—
326#384—111no—
327#384—221no—
328#384—221no—
329C4×C4⋊C4—111no—
330C4×C4⋊C4—221no—
331C4×C4⋊C4—221no—
332#340—111no—
333#340—111no—
334#340—111no—
335#340C2×D1111yescharacteristic
336#336—111no—
337#336C2×D1111yescharacteristic
338C22×C11C2×C4×D411yescharacteristic
339C22×C11D4211yescharacteristic
340C22×C11D4×Q811yescharacteristic
341C22×C11C22×Q1611yescharacteristic
342C22×C11C2×#13511yescharacteristic
343C22×C11#57611yescharacteristic
344C22×C11#57811yescharacteristic
345C4×C11—24no—
346C4×C11—22no—
347C4×C11—42no—
348C4×C11—41no—
349C4×C11—81no—
350C4×C11—81no—
351C4×C11C22×C4⋊C411yescharacteristic
352C4×C11#52011yescharacteristic
353C4×C11#54711yescharacteristic
354C4×C11#55411yescharacteristic
355Dic11—24no—
356Dic11—22no—
357Dic11—22no—
358Dic11—42no—
359Dic11—41no—
360Dic11—81no—
361Dic11—81no—
362Dic11C4×Q1614yescomplemented
363C22×Q8—111no—
364C22×Q8C22×D1111yescharacteristic
365C2×Q16—114no—
366C2×Q16—114no—
367C2×Q16—114no—
368C22×C8—111no—
369C22×C8—111no—
370C22×C8C22×D1111yescharacteristic
371C22×C8C22×D1111yescharacteristic
372C4×Q8—22no—
373C4×Q8—41no—
374C4×Q8—114no—
375C4×Q8—114no—
376C4×Q8—222no—
377C4×Q8—222no—
378C4×Q8—222no—
379C4×Q8—222no—
380C4×Q8—222no—
381C4×Q8—441no—
382C4×Q8—441no—
383C4×Q8—441no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4C22×D1111yescharacteristic
404C2×C4⋊C4C22×D1111yescharacteristic
405C2×C4⋊C4C22×D1111yescharacteristic
406C2×C42—21no—
407C2×C42—111no—
408C2×C42—111no—
409C2×C42—221no—
410C2×C42—221no—
411C2×C42—221no—
412C2×C42—221no—
413C2×C42—221no—
414C2×C42C22×D1111yescharacteristic
415#107—41no—
416#107—114no—
417#107—222no—
418#107—222no—
419#107—441no—
420C4⋊C8—222no—
421#103—22no—
422#103—114no—
423#103—222no—
424#103—222no—
425#103—222no—
426#103C4×D1114yes—
427C4×C8—114no—
428C4×C8—222no—
429C4×C8—222no—
430#95—21no—
431#95—111no—
432#95—111no—
433#95—221no—
434#95—221no—
435#95—221no—
436C2×C11D4×C4⋊C411yescharacteristic
437C2×C11C2×C4×Q1611yescharacteristic
438C2×C11#295111yescharacteristic
439C2×C11D4×Q1611yescharacteristic
440C2×C11#328711yescharacteristic
441C2×C11Q8×Q1611yescharacteristic
442C2×C11#338311yescharacteristic
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—112no—
447C2×Q8—112no—
448C2×Q8—112no—
449C2×Q8—221no—
450C2×Q8—221no—
451C2×Q8—221no—
452C2×Q8C2×C4×D1112yes—
453C2×Q8D4×D1112yes—
454C2×Q8Q8×D1112yes—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—111no—
460C22×C4—111no—
461C22×C4—111no—
462C22×C4—111no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4D4×D1111yescharacteristic
468C22×C4D4×D1111yescharacteristic
469C22×C4C23×D1111yescharacteristic
470Q16—1116no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—112no—
477C2×C8—112no—
478C2×C8—112no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8C2×C4×D1112yes—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—42no—
489C4⋊C4—81no—
490C4⋊C4—114no—
491C4⋊C4—112no—
492C4⋊C4—222no—
493C4⋊C4—224no—
494C4⋊C4—224no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—442no—
501C4⋊C4—442no—
502C4⋊C4—442no—
503C4⋊C4—442no—
504C4⋊C4—442no—
505C4⋊C4—881no—
506C4⋊C4—881no—
507C4⋊C4—881no—
508C4⋊C4—881no—
509C4⋊C4—881no—
510C4⋊C4C2×C4×D1112yes—
511C42—21no—
512C42—21no—
513C42—42no—
514C42—112no—
515C42—112no—
516C42—224no—
517C42—224no—
518C42—221no—
519C42—221no—
520C42—442no—
521C42—442no—
522C42—442no—
523C11C4⋊C4×Q1611yescharacteristic, complemented, Sylow
524C23C2×D4×D1111yescharacteristic
525Q8—22no—
526Q8—22no—
527Q8—22no—
528Q8—114no—
529Q8—222no—
530Q8—222no—
531Q8—222no—
532Q8C4⋊C4×D1114yes—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—112no—
551C2×C4—112no—
552C2×C4—112no—
553C2×C4—112no—
554C2×C4—112no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—222no—
559C2×C4—221no—
560C2×C4—222no—
561C2×C4—222no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—222no—
565C2×C4—221no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4Q16×D1112yes—
575C2×C4C22×C4×D1111yescharacteristic
576C2×C4C2×D4×D1111yescharacteristic
577C2×C4#6703711yescharacteristic
578C2×C4C2×Q8×D1111yescharacteristic
579C2×C4#41×D1111yescharacteristic
580C2×C4#6704311yescharacteristic
581C8—22no—
582C8—41no—
583C8—114no—
584C8—441no—
585C22C4×D4×D1111yescharacteristic
586C22#1062312111yescharacteristic
587C22#1062316311yescharacteristic
588C22C2×Q16×D1111yescharacteristic
589C22D11×#13511yescharacteristic
590C22#1062330511yescharacteristic
591C22#1062331011yescharacteristic
592C4—22no—
593C4—24no—
594C4—41no—
595C4—42no—
596C4—81no—
597C4—81no—
598C4—114no—
599C4—222no—
600C4—224no—
601C4—222no—
602C4—441no—
603C4—442no—
604C4—881no—
605C4—881no—
606C4C2×C4⋊C4×D1111yescharacteristic
607C4#1062307711yescharacteristic
608C4#1062316711yescharacteristic
609C4#1062318611yescharacteristic
610C2#1307151411yescharacteristic
611C2C4×Q16×D1111yescharacteristic
612C2#1307748811yescharacteristic
613C2#1308036111yescharacteristic
614C2#1308036911yescharacteristic
615C2#1308149711yescharacteristic
616C2#1308150211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1863C2
socle, prime radicalC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenter#1863D11
hypocenterC11C4⋊C4×Q16
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1863

Complements

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

NH ≅ G/Ntype
53. #10622403C4semidirect
180. #4326C4⋊C4semidirect
200. Dic11⋊C4Q16semidirect
362. Dic11C4×Q16semidirect
523. C11C4⋊C4×Q16semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43262
C2×#106224032
#130715302
Q8×Dic11⋊C42
#130693482
#130693462
#130688732
#130688722
#130688672
#130687742
#130686202
#130686192
#130684772
C11×#18632
C4⋊C4×Q1611