Finite Group Databasebeta

← #14809902

Subgroups — #14809902

Order 2816.

1056 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623070C211yesmaximal, characteristic
2C2×#10622489C211yesmaximal, characteristic, complemented
3C2×#10622372C211yesmaximal, characteristic
4#13073823C211yesmaximal, characteristic, complemented
5#13069955C211yesmaximal, characteristic, complemented
6#13069954C211yesmaximal, characteristic, complemented
7#13069943C211yesmaximal, characteristic, complemented
8#13069942C211yesmaximal, characteristic, complemented
9#13069572C211yesmaximal, characteristic, complemented
10#13069554C211yesmaximal, characteristic, complemented
11#13068879C211yesmaximal, characteristic
12#13068875C211yesmaximal, characteristic
13#13068863C211yesmaximal, characteristic
14#13068443C211yesmaximal, characteristic
15C11×#1862C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×D4×Dic11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C2×#66977—21no—
20C22×Dic11⋊C4—21no—
21#10623070—24no—
22#10623070—24no—
23C2×#66943C2211yescharacteristic
24C2×#66941C2211yescharacteristic
25C2×#66941C2211yescharacteristic
26C2×#66931—21no—
27C2×#66931—21no—
28C2×#66923C2211yescharacteristic
29C2×C4×Dic22C2211yescharacteristic
30C2×C11×#107C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C11×#389C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66882C2211yescharacteristic
37C2×#66881C2211yescharacteristic
38C2×#66879C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40#10622598C2211yescharacteristic
41#10622592—21no—
42#10622589—21no—
43C4⋊C4×Dic11C2211yescharacteristic
44#10622586C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47C2×#66871C2211yescharacteristic
48#10622541C2211yescharacteristic
49#10622489—24no—
50#10622372—24no—
51#10622269—21no—
52#10622259—21no—
53C11×#340C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C23×Dic11—21no—
66C23×Dic11—21no—
67C22×Dic22—21no—
68C22×Dic22—21no—
69C22×Dic22D411yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C42×C11C2311yescharacteristic
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82D4×Dic11—22no—
83D4×Dic11—22no—
84D4×Dic11—22no—
85D4×Dic11D414yes—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11D411yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93#66977—28no—
94C2×Dic11⋊C4—28no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4D411yescharacteristic
103C2×Dic11⋊C4D411yescharacteristic
104C2×C4×Dic11—21no—
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109#66943—22no—
110#66943D414yes—
111#66941—22no—
112#66941—22no—
113#66941—22no—
114#66941—22no—
115#66931—28no—
116#66931—28no—
117#66923—22no—
118#66923—22no—
119C4×Dic22—22no—
120C4×Dic22—22no—
121C11×#107—22no—
122C11×#102—22no—
123C11×#102Q814yescomplemented
124C11×#95—21no—
125#66896—22no—
126#66896Q814yescomplemented
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131#66882—22no—
132#66881—22no—
133#66879—22no—
134Dic11⋊C8—22no—
135#66872—22no—
136#66871—22no—
137#66871—22no—
138#25850—111nomaximal, Sylow
139C24×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11C2×D412yes—
144C2×D4×C11C2×Q812yes—
145C2×D4×C11C2×Q812yes—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—24no—
149C22×C4×C11—21no—
150C22×C4×C11—81no—
151C22×C4×C11—81no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2411yescharacteristic
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—42no—
162C22×Dic11—42no—
163C22×Dic11—81no—
164C22×Dic11—81no—
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168C22×Dic11C2×D411yescharacteristic
169C2×Dic22—22no—
170C2×Dic22—22no—
171C2×Dic22—24no—
172C2×Dic22—41no—
173C2×Dic22—42no—
174C2×Dic22—81no—
175C2×Dic22—81no—
176C2×Dic22—81no—
177C2×Dic22—81no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11C2×Q812yes—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—81no—
189C11×C4⋊C4C2×D412yes—
190C11×C4⋊C4C2×Q812yes—
191C11×C22⋊C4—24no—
192C42×C11—21no—
193C42×C11—21no—
194C22⋊Dic11—24no—
195C22⋊Dic11—24no—
196C4⋊Dic11—22no—
197C4⋊Dic11—24no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—81no—
204C4⋊Dic11C2×D412yes—
205C4⋊Dic11C2×D412yes—
206C4⋊Dic11C2×Q812yes—
207Dic11⋊C4—24no—
208Dic11⋊C4—24no—
209Dic11⋊C4—24no—
210Dic11⋊C4—22no—
211Dic11⋊C4—22no—
212Dic11⋊C4—24no—
213Dic11⋊C4—42no—
214Dic11⋊C4—81no—
215Dic11⋊C4—81no—
216C4×Dic11—21no—
217C4×Dic11—21no—
218C4×Dic11—42no—
219C4×Dic11C2×D412yes—
220C4×Dic11C2×D412yes—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8C2×Q812yes—
227C2×#554—111no—
228C2×#501—111no—
229C2×#474—111no—
230#2567—111no—
231#2059—111no—
232#2059—111no—
233#2057—111no—
234#2057—111no—
235#1989—111no—
236#1985—111no—
237#1864—111no—
238#1864—111no—
239#1862—111no—
240#1862D1111yescharacteristic
241#1762—111no—
242C23×C11—22no—
243C23×C11—22no—
244C23×C11—22no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11C22×D411yescharacteristic
250D4×C11—22no—
251D4×C11—22no—
252D4×C11—22no—
253D4×C11C4⋊Q814yes—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—41no—
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—84no—
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×Q811yescharacteristic
273C2×C4×C11C22×Q811yescharacteristic
274C2×C4×C112−1+411yescharacteristic
275C2×C4×C112−1+411yescharacteristic
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—22no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—48no—
289C2×Dic11—41no—
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—84no—
299C2×Dic11#12012yes—
300C2×Dic11#12012yes—
301C2×Dic11#13712yes—
302Dic22—44no—
303Dic22—84no—
304Dic22—84no—
305C8×C11—22no—
306C8×C11—41no—
307C11⋊C8—22no—
308C11⋊C8—41no—
309#554—224no—
310#554—224no—
311C2×C4⋊Q8—111no—
312C2×C4⋊Q8—111no—
313C2×#125—111no—
314C2×#125—111no—
315C2×C22⋊Q8—221no—
316C2×C22⋊Q8—221no—
317C2×C22⋊Q8—221no—
318C2×C4×Q8—111no—
319C2×C4×D4—111no—
320C2×C4×D4—111no—
321C2×C4×D4C2×D1111yescharacteristic
322C22×C4⋊C4—221no—
323#501—224no—
324#474—224no—
325C2×#107—111no—
326C2×#107—111no—
327C2×#107—111no—
328C2×#107C2×D1111yescharacteristic
329C2×#106—111no—
330C2×#106—111no—
331C2×C4⋊C8—111no—
332C2×#102—111no—
333C2×#102—111no—
334C2×#102C2×D1111yescharacteristic
335C2×#102C2×D1111yescharacteristic
336C2×#97—111no—
337#395—221no—
338#395—221no—
339#391—221no—
340#389—111no—
341#389—111no—
342#389—111no—
343#389C2×D1111yescharacteristic
344#384—221no—
345C4×C4⋊C4—111no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340—111no—
350#340—111no—
351#340C2×D1111yescharacteristic
352#336—111no—
353#336—111no—
354#336—111no—
355#336C2×D1111yescharacteristic
356C22×C11—24no—
357C22×C11—42no—
358C22×C11—42no—
359C22×C11—42no—
360C22×C11—42no—
361C22×C11—42no—
362C22×C11—42no—
363C22×C11C2×#12011yescharacteristic
364C22×C11D4×Q811yescharacteristic
365C22×C11D4×Q811yescharacteristic
366C22×C11C2×#13711yescharacteristic
367C22×C11#57511yescharacteristic
368C22×C11#57611yescharacteristic
369C22×C11#57611yescharacteristic
370C4×C11—42no—
371C4×C11—41no—
372C4×C11—41no—
373C4×C11—42no—
374C4×C11—81no—
375C4×C11C2×C4⋊Q811yescharacteristic
376C4×C11#53611yescharacteristic
377C4×C11D4×Q811yescharacteristic
378C4×C11D4×Q811yescharacteristic
379Dic11—22no—
380Dic11—22no—
381Dic11—22no—
382Dic11—42no—
383Dic11—42no—
384Dic11—41no—
385Dic11—42no—
386Dic11—81no—
387C22×Q8—111no—
388C22×Q8—221no—
389C22×Q8—221no—
390C22×D4C22×D1111yescharacteristic
391C23×C4—21no—
392C23×C4—221no—
393C23×C4—221no—
394C22×C8—111no—
395C22×C8—111no—
396C22×C8C22×D1111yescharacteristic
397C22×C8C22×D1111yescharacteristic
398C4⋊Q8—222no—
399C4⋊Q8—222no—
400C4⋊Q8—222no—
401C4⋊Q8—222no—
402#125—114no—
403#125—222no—
404#125—222no—
405#125—222no—
406C22⋊Q8—228no—
407C22⋊Q8—228no—
408C22⋊Q8—228no—
409C4×Q8—222no—
410C4×Q8—222no—
411C4×D4—22no—
412C4×D4—22no—
413C4×D4—114no—
414C4×D4—222no—
415C4×D4—222no—
416C4×D4—222no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—228no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4C22×D1111yescharacteristic
436C2×C4⋊C4C22×D1111yescharacteristic
437C2×C4⋊C4C22×D1111yescharacteristic
438C2×C22⋊C4—21no—
439C2×C22⋊C4—221no—
440C2×C22⋊C4—221no—
441C2×C42—111no—
442C2×C42—111no—
443C2×C42—221no—
444C2×C42C22×D1111yescharacteristic
445#107—22no—
446#107—222no—
447#107—222no—
448#107—222no—
449#106—222no—
450#106—222no—
451C4⋊C8—222no—
452#102—22no—
453#102—114no—
454#102—222no—
455#102Dic2214yescomplemented
456#97—222no—
457#95—21no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95—221no—
462C2×C11—44no—
463C2×C11#243411yescharacteristic
464C2×C11#300711yescharacteristic
465C2×C11#300811yescharacteristic
466C2×C11#338511yescharacteristic
467C2×C11#338511yescharacteristic
468C2×C11#338911yescharacteristic
469C2×C11#338911yescharacteristic
470C24—21no—
471C2×Q8—222no—
472C2×Q8—222no—
473C2×Q8—224no—
474C2×Q8—441no—
475C2×Q8—442no—
476C2×Q8—881no—
477C2×Q8—881no—
478C2×Q8—881no—
479C2×Q8—881no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4C2×Dic2212yes—
484C2×D4D4×D1112yes—
485C2×D4Q8×D1112yes—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—24no—
489C22×C4—21no—
490C22×C4—81no—
491C22×C4—81no—
492C22×C4—111no—
493C22×C4—111no—
494C22×C4—111no—
495C22×C4—111no—
496C22×C4—224no—
497C22×C4—224no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—442no—
503C22×C4—442no—
504C22×C4—881no—
505C22×C4—881no—
506C22×C4D4×D1111yescharacteristic
507C22×C4D4×D1111yescharacteristic
508C22×C4C23×D1111yescharacteristic
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—112no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8C2×Dic2212yes—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—81no—
526C4⋊C4—112no—
527C4⋊C4—112no—
528C4⋊C4—112no—
529C4⋊C4—222no—
530C4⋊C4—222no—
531C4⋊C4—222no—
532C4⋊C4—224no—
533C4⋊C4—224no—
534C4⋊C4—224no—
535C4⋊C4—224no—
536C4⋊C4—224no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C4⋊C4—221no—
542C4⋊C4—442no—
543C4⋊C4—881no—
544C4⋊C4—881no—
545C4⋊C4—881no—
546C4⋊C4C2×Dic2212yes—
547C4⋊C4D4×D1112yes—
548C22⋊C4—24no—
549C22⋊C4—224no—
550C22⋊C4—224no—
551C42—21no—
552C42—21no—
553C42—112no—
554C42—112no—
555C42—221no—
556C42—221no—
557C42—442no—
558C11#2585011yescharacteristic, complemented, Sylow
559C23—22no—
560C23—22no—
561C23—22no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23C2×D4×D1111yescharacteristic
567Q8—444no—
568Q8—884no—
569Q8—884no—
570D4—22no—
571D4—22no—
572D4—22no—
573D4#6694114yes—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—84no—
590C2×C4—112no—
591C2×C4—112no—
592C2×C4—112no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—222no—
603C2×C4—222no—
604C2×C4—222no—
605C2×C4—448no—
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—884no—
616C2×C4C22×Dic2211yescharacteristic
617C2×C4C2×D4×D1111yescharacteristic
618C2×C4C2×D4×D1111yescharacteristic
619C2×C4C2×Q8×D1111yescharacteristic
620C2×C4#6704311yescharacteristic
621C2×C4#6704311yescharacteristic
622C8—22no—
623C8—41no—
624C8—222no—
625C8—441no—
626C22—24no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—42no—
633C22D4×Dic2211yescharacteristic
634C22D11×#12011yescharacteristic
635C22#1062316311yescharacteristic
636C22#1062328811yescharacteristic
637C22#1062329911yescharacteristic
638C22#1062330511yescharacteristic
639C22D11×#13711yescharacteristic
640C4—41no—
641C4—41no—
642C4—42no—
643C4—42no—
644C4—81no—
645C4—222no—
646C4—222no—
647C4—222no—
648C4—442no—
649C4—441no—
650C4—442no—
651C4—442no—
652C4—881no—
653C4C2×#6694111yescharacteristic
654C4D4×Dic2211yescharacteristic
655C4#1062316311yescharacteristic
656C4#1062317911yescharacteristic
657C2—44no—
658C2#1307225811yescharacteristic
659C2#1307787311yescharacteristic
660C2#1307787911yescharacteristic
661C2#1308152111yescharacteristic
662C2#1308152711yescharacteristic
663C2#1308157211yescharacteristic
664C2#1308157411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1862C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#1862D11
hypocenterC11#25850
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1862

Complements

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

NH ≅ G/Ntype
2. C2×#10622489C2semidirect
4. #13073823C2semidirect
5. #13069955C2semidirect
6. #13069954C2semidirect
7. #13069943C2semidirect
8. #13069942C2semidirect
9. #13069572C2semidirect
10. #13069554C2semidirect
123. C11×#102Q8semidirect
126. #66896Q8semidirect
455. #102Dic22semidirect
558. C11#25850semidirect

Maximal subgroups

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

subgroupindex
C2×#106230702
C2×#106224892
C2×#106223722
#130738232
#130699552
#130699542
#130699432
#130699422
#130695722
#130695542
#130688792
#130688752
#130688632
#130684432
C11×#18622
#2585011