Finite Group Databasebeta

← #14770432

Subgroups — #14770432

Order 2816.

1022 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×Q8×Dic22C211yesmaximal, characteristic
2C2×#10622314C211yesmaximal, characteristic
3#13071574C211yesmaximal, characteristic
4#13069589C211yesmaximal, characteristic
5#13069587C211yesmaximal, characteristic
6#13069575C211yesmaximal, characteristic
7#13069568C211yesmaximal, characteristic
8#13069566C211yesmaximal, characteristic
9#13069562C211yesmaximal, characteristic
10#13068631C211yesmaximal, characteristic
11#13068629C211yesmaximal, characteristic
12#13068619C211yesmaximal, characteristic
13#13068448C211yesmaximal, characteristic
14#103×Dic11C211yesmaximal, characteristic
15C11×#1763C211yesmaximal, characteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19Q8×Dic22—24no—
20Q8×Dic22C418yescomplemented
21C2×#66941—21no—
22C2×#66941—21no—
23C2×#66941C2211yescharacteristic
24C2×#66941C2211yescharacteristic
25C2×#66922—21no—
26C2×#66922C2211yescharacteristic
27C2×C4×Dic22—21no—
28C2×C4×Dic22C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#97C2211yescharacteristic
32C4×C11×C4⋊C4C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66879C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38C2×C8×Dic11C2211yescharacteristic
39#10622590C2211yescharacteristic
40#10622589C2211yescharacteristic
41C4⋊C4×Dic11C2211yescharacteristic
42C4⋊C4×Dic11C2211yescharacteristic
43#10622549C2211yescharacteristic
44#10622546—21no—
45C4×Dic11⋊C4—21no—
46C2×C4⋊(C11⋊C8)C2211yescharacteristic
47#10622314—24no—
48#10622267—21no—
49#10622259—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×Dic22—21no—
64C22×Dic22—21no—
65C22×Dic22—21no—
66C22×Dic22D411yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C4×Q8×C11—22no—
70C4×Q8×C11C2×C414yes—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C42×C11—21no—
76C2×C42×C11—21no—
77C2×C42×C11C2311yescharacteristic
78Q8×Dic11—22no—
79Q8×Dic11—22no—
80Q8×Dic11C2×C414yes—
81Q8×Dic11C2×C414yes—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11D411yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4D411yescharacteristic
95C2×Dic11⋊C4D411yescharacteristic
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11C2311yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104#66941—28no—
105#66941—28no—
106#66941—22no—
107#66941—22no—
108#66941C2×C414yes—
109#66941C2×C414yes—
110#66922—22no—
111#66922—28no—
112#66922C2×C414yes—
113C4×Dic22—28no—
114C4×Dic22C2×C414yes—
115C4×Dic22D414yes—
116C11×#103—22no—
117C11×#103Q814yescomplemented
118C11×#97—22no—
119C11×#95—21no—
120#66899—22no—
121#66899—22no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128#66879—22no—
129Dic11⋊C8—22no—
130Dic11⋊C8—22no—
131C8×Dic11—22no—
132C4⋊(C11⋊C8)—22no—
133#22525—111nomaximal, Sylow
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11C22×C412yes—
138C2×Q8×C11C2×Q812yes—
139C2×Q8×C11#4112yes—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C2×Dic22—22no—
156C2×Dic22—22no—
157C2×Dic22—24no—
158C2×Dic22—24no—
159C2×Dic22—24no—
160C2×Dic22—81no—
161C2×Dic22—81no—
162C2×Dic22—81no—
163C2×Dic22—81no—
164C2×Dic22—81no—
165C2×Dic22—81no—
166C2×Dic22C22⋊C414yes—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11C2×Q812yes—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4C22×C412yes—
179C11×C4⋊C4C2×Q812yes—
180C42×C11—24no—
181C42×C11—81no—
182C42×C11C22×C412yes—
183C42×C11C2×D412yes—
184C4⋊Dic11—24no—
185C4⋊Dic11—24no—
186C4⋊Dic11—24no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11C22⋊C414yes—
194C4⋊Dic11C22×C412yes—
195C4⋊Dic11C22×C412yes—
196Dic11⋊C4—24no—
197Dic11⋊C4—24no—
198Dic11⋊C4—42no—
199Dic11⋊C4—81no—
200Dic11⋊C4C22⋊C414yes—
201Dic11⋊C4C22⋊C414yes—
202C4×Dic11—24no—
203C4×Dic11—24no—
204C4×Dic11—42no—
205C4×Dic11—81no—
206C4×Dic11C22×C412yes—
207C4×Dic11C22×C412yes—
208C4×Dic11C2×D412yes—
209C4×Dic11C2×D412yes—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×Q82—111no—
217C2×#446—111no—
218#2355—111no—
219#1993—111no—
220#1993—111no—
221#1990—111no—
222#1988—111no—
223#1988—111no—
224#1987—111no—
225#1805—111no—
226#1805—111no—
227#1803—111no—
228#1763—111no—
229#1763D1111yescharacteristic
230C4×#103—111no—
231C23×C11C22×D411yescharacteristic
232Q8×C11—22no—
233Q8×C11—22no—
234Q8×C11—22no—
235Q8×C11C4×Q814yes—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
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×C11C2×C22⋊C412yes—
253C2×C4×C11C2×C22⋊C412yes—
254C2×C4×C11C23×C411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×Q811yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C112−1+411yescharacteristic
259C2×C4×C112−1+411yescharacteristic
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11C2×C22⋊C412yes—
279C2×Dic11C2×C22⋊C412yes—
280C2×Dic11C2×C22⋊C412yes—
281C2×Dic11C2×C22⋊C412yes—
282C2×Dic11#13712yes—
283C2×Dic11#13712yes—
284Dic22—28no—
285Dic22—84no—
286Dic22—84no—
287Dic22—84no—
288C8×C11—22no—
289C8×C11—41no—
290C11⋊C8—41no—
291C11⋊C8—41no—
292Q82—118no—
293Q82—224no—
294C2×C4⋊Q8—111no—
295C2×C4⋊Q8—111no—
296C2×C4⋊Q8—111no—
297C2×C4⋊Q8—221no—
298C2×C4⋊Q8—221no—
299C2×C4⋊Q8—221no—
300C2×C4×Q8—111no—
301C2×C4×Q8—111no—
302C2×C4×Q8—111no—
303C2×C4×Q8—221no—
304C2×C4×Q8C2×D1111yescharacteristic
305#446—224no—
306C2×C4⋊C8—111no—
307C2×C4⋊C8—111no—
308C2×C4⋊C8—111no—
309C2×#103—111no—
310C2×#103—111no—
311C2×#103C2×D1111yescharacteristic
312C2×#103C2×D1111yescharacteristic
313C2×#97—111no—
314C2×#97C2×D1111yescharacteristic
315C2×C4×C8—111no—
316#391—221no—
317#387—221no—
318#387—221no—
319#384—111no—
320#382—111no—
321#382—111no—
322C4×C4⋊C4—111no—
323C4×C4⋊C4—111no—
324C4×C4⋊C4—221no—
325C4×C4⋊C4C2×D1111yescharacteristic
326#340—111no—
327#340—111no—
328#340—111no—
329#340—111no—
330#340—111no—
331#340—111no—
332#340—111no—
333#340—111no—
334#340—111no—
335#340—111no—
336#340C2×D1111yescharacteristic
337#340C2×D1111yescharacteristic
338C22×C11C22×C22⋊C411yescharacteristic
339C22×C11#54811yescharacteristic
340C22×C11D4×Q811yescharacteristic
341C22×C11C2×#13711yescharacteristic
342C22×C11C2×#13711yescharacteristic
343C22×C11#57611yescharacteristic
344C22×C11#57711yescharacteristic
345C4×C11—24no—
346C4×C11—22no—
347C4×C11—22no—
348C4×C11—42no—
349C4×C11—42no—
350C4×C11—81no—
351C4×C11C2×C4×Q811yescharacteristic
352C4×C11#51911yescharacteristic
353C4×C11#54811yescharacteristic
354C4×C11D4×Q811yescharacteristic
355Dic11—22no—
356Dic11—22no—
357Dic11—22no—
358Dic11—42no—
359Dic11—42no—
360Dic11—81no—
361Dic11—81no—
362Dic11#41914yes—
363C22×Q8—111no—
364C22×Q8—221no—
365C22×Q8—221no—
366C22×Q8—221no—
367C22×Q8C22×D1111yescharacteristic
368C22×C8—111no—
369C22×C8—111no—
370C22×C8C22×D1111yescharacteristic
371C22×C8C22×D1111yescharacteristic
372C4⋊Q8—114no—
373C4⋊Q8—114no—
374C4⋊Q8—114no—
375C4⋊Q8—228no—
376C4⋊Q8—222no—
377C4⋊Q8—222no—
378C4⋊Q8—228no—
379C4⋊Q8—228no—
380C4⋊Q8—222no—
381C4×Q8—22no—
382C4×Q8—114no—
383C4×Q8—114no—
384C4×Q8—114no—
385C4×Q8—114no—
386C4×Q8—228no—
387C4×Q8—222no—
388C4×Q8—222no—
389C4×Q8C4×D1114yes—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4C22×D1111yescharacteristic
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—111no—
411C2×C42—111no—
412C2×C42—221no—
413C2×C42—221no—
414C2×C42—221no—
415C2×C42—221no—
416C2×C42C22×D1111yescharacteristic
417C4⋊C8—222no—
418C4⋊C8—222no—
419C4⋊C8—222no—
420#103—22no—
421#103—222no—
422#103—222no—
423#103Dic2214yescomplemented
424#97—22no—
425#97—222no—
426C4×C8—222no—
427#95—21no—
428#95—221no—
429#95—221no—
430#95—221no—
431#95—221no—
432#95—221no—
433#95—221no—
434C2×C11Q8×C22⋊C411yescharacteristic
435C2×C11C2×#41911yescharacteristic
436C2×C11#289711yescharacteristic
437C2×C11#336911yescharacteristic
438C2×C11#337511yescharacteristic
439C2×C11#338511yescharacteristic
440C2×C11#338711yescharacteristic
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—114no—
445C2×Q8—222no—
446C2×Q8—222no—
447C2×Q8—224no—
448C2×Q8—224no—
449C2×Q8—224no—
450C2×Q8—881no—
451C2×Q8—881no—
452C2×Q8—881no—
453C2×Q8—881no—
454C2×Q8—881no—
455C2×Q8—881no—
456C2×Q8C2×Dic2212yes—
457C2×Q8C2×C4×D1112yes—
458C2×Q8#433912yes—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—111no—
464C22×C4—111no—
465C22×C4—111no—
466C22×C4—111no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4D4×D1111yescharacteristic
472C22×C4D4×D1111yescharacteristic
473C22×C4C23×D1111yescharacteristic
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8C2×Dic2212yes—
486C4⋊C4—24no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—114no—
492C4⋊C4—114no—
493C4⋊C4—114no—
494C4⋊C4—112no—
495C4⋊C4—112no—
496C4⋊C4—224no—
497C4⋊C4—224no—
498C4⋊C4—224no—
499C4⋊C4—224no—
500C4⋊C4—224no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—442no—
508C4⋊C4—881no—
509C4⋊C4C2×Dic2212yes—
510C4⋊C4C2×C4×D1112yes—
511C42—24no—
512C42—81no—
513C42—112no—
514C42—112no—
515C42—112no—
516C42—112no—
517C42—224no—
518C42—224no—
519C42—442no—
520C42—881no—
521C42C2×C4×D1112yes—
522C42D4×D1112yes—
523C11#2252511yescharacteristic, complemented, Sylow
524C23C2×D4×D1111yescharacteristic
525Q8—22no—
526Q8—22no—
527Q8—22no—
528Q8—228no—
529Q8—884no—
530Q8—884no—
531Q8—884no—
532Q8C4×Dic2214yes—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—112no—
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—221no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—222no—
562C2×C4—222no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4C22⋊C4×D1112yes—
574C2×C4C22⋊C4×D1112yes—
575C2×C4C22×Dic2211yescharacteristic
576C2×C4C22×C4×D1111yescharacteristic
577C2×C4C2×#433911yescharacteristic
578C2×C4C2×D4×D1111yescharacteristic
579C2×C4#6704311yescharacteristic
580C2×C4#6704311yescharacteristic
581C8—22no—
582C8—41no—
583C8—441no—
584C8—441no—
585C22C2×C22⋊C4×D1111yescharacteristic
586C22D4×Dic2211yescharacteristic
587C22#1062308311yescharacteristic
588C22#1062330511yescharacteristic
589C22D11×#13711yescharacteristic
590C22D11×#13711yescharacteristic
591C22#1062330911yescharacteristic
592C4—24no—
593C4—22no—
594C4—22no—
595C4—42no—
596C4—42no—
597C4—81no—
598C4—114no—
599C4—222no—
600C4—222no—
601C4—222no—
602C4—442no—
603C4—442no—
604C4—881no—
605C4—881no—
606C4C2×C4×Dic2211yescharacteristic
607C4#1062304711yescharacteristic
608C4D4×Dic2211yescharacteristic
609C4#1062308311yescharacteristic
610C2C22⋊C4×Dic2211yescharacteristic
611C2D11×#41911yescharacteristic
612C2#1307714011yescharacteristic
613C2#1308135711yescharacteristic
614C2#1308143111yescharacteristic
615C2#1308152711yescharacteristic
616C2#1308154911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1763C2
socle, prime radicalC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenter#1763D11
hypocenterC11#22525
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
20. Q8×Dic22C4semidirect
117. C11×#103Q8semidirect
423. #103Dic22semidirect
523. C11#22525semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic222
C2×#106223142
#130715742
#130695892
#130695872
#130695752
#130695682
#130695662
#130695622
#130686312
#130686292
#130686192
#130684482
#103×Dic112
C11×#17632
#2252511