Finite Group Databasebeta

← #14776254

Subgroups — #14776254

Order 2816.

954 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×#10622380C211yesmaximal, characteristic
2C2×#10622466C211yesmaximal, characteristic, complemented
3C2×C4×#4324C211yesmaximal, characteristic
4#13071689C211yesmaximal, characteristic
5#13071530C211yesmaximal, characteristic, complemented
6#13069431C211yesmaximal, characteristic
7#13069376C211yesmaximal, characteristic, complemented
8#13069315C211yesmaximal, characteristic
9#13069291C211yesmaximal, characteristic, complemented
10#13068968C211yesmaximal, characteristic
11#13068956C211yesmaximal, characteristic, complemented
12#13068885C211yesmaximal, characteristic, complemented
13#13068487C211yesmaximal, characteristic, complemented
14#13068445C211yesmaximal, characteristic, complemented
15C11×#1864C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66989C2211yescharacteristic
18C22×#4324C2211yescharacteristic
19C22×Dic44C2211yescharacteristic
20C2×#66940C2211yescharacteristic
21C2×#66940C2211yescharacteristic
22C2×#66940C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C11×#389C2211yescharacteristic
28#10622834C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30#10622823—21no—
31C4×C22⋊Dic11—21no—
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66879C2211yescharacteristic
35C2×#66879C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37C4×#4324—24no—
38#10622598C2211yescharacteristic
39#10622589—21no—
40#10622589C2211yescharacteristic
41C4⋊C4×Dic11C2211yescharacteristic
42#10622585—21no—
43C2×#66874C2211yescharacteristic
44C2×#66874C2211yescharacteristic
45C2×#66874C2211yescharacteristic
46C2×#66872C2211yescharacteristic
47#10622558—21no—
48#10622557—21no—
49C4×Dic11⋊C4C2211yescharacteristic
50#10622542C2211yescharacteristic
51C2×C4×C11⋊C8C2211yescharacteristic
52#10622466—24no—
53#10622380C418yescomplemented
54#10622262—21no—
55#10622260—21no—
56C11×#340C2211yescharacteristic
57C11×#336C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C22×Dic22C2311yescharacteristic
65C22×Dic22C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C4×D4×C11—22no—
69C4×D4×C11—41no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C42×C11C2311yescharacteristic
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80#66989—22no—
81#66989C2×C414yes—
82C2×#4324—22no—
83C2×#4324—22no—
84C2×#4324C2×C414yes—
85C2×C4⋊Dic11—21no—
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⋊C4D411yescharacteristic
95C2×Dic11⋊C4D411yescharacteristic
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11C2311yescharacteristic
102C2×C4×Dic11C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C2×Dic44—22no—
106C2×Dic44—22no—
107C2×Dic44C2×C414yescomplemented
108#66940—22no—
109#66940—22no—
110#66940—22no—
111#66940—41no—
112#66940—41no—
113#66940C2×C414yescomplemented
114C4×Dic22—22no—
115C4×Dic22—41no—
116C11×#106—22no—
117C11×#102—41no—
118C11×#102C2×C414yes—
119C11×#95—21no—
120#66896—22no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95D411yescharacteristic
126C11⋊#95D411yescharacteristic
127#66880—22no—
128#66880—41no—
129#66879—22no—
130#66879—22no—
131Dic11⋊C8C2×C414yescomplemented
132#66874—22no—
133#66874C2×C414yescomplemented
134#66874D414yes—
135#66872—22no—
136C4×C11⋊C8—22no—
137#23013—111nomaximal, Sylow
138C24×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11C22×C412yes—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—42no—
149C22×C4×C11—42no—
150C22×C4×C11—81no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22C22×C412yes—
171C2×Dic22C22×C412yes—
172C2×Dic22C2×D412yes—
173C2×Dic22#4112yes—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11C22×C412yes—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—81no—
185C11×C4⋊C4C22×C412yes—
186C11×C4⋊C4C2×D412yes—
187C11×C22⋊C4—42no—
188C42×C11—21no—
189C42×C11—21no—
190C22⋊Dic11—24no—
191C22⋊Dic11—24no—
192C22⋊Dic11—42no—
193C22⋊Dic11—81no—
194#4324—28no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—81no—
200Dic11⋊C4—24no—
201Dic11⋊C4—22no—
202Dic11⋊C4—41no—
203Dic11⋊C4—42no—
204Dic11⋊C4—42no—
205Dic11⋊C4—42no—
206Dic11⋊C4—42no—
207Dic11⋊C4—81no—
208C4×Dic11—24no—
209C4×Dic11—21no—
210C4×Dic11—21no—
211C4×Dic11—42no—
212C4×Dic11—42no—
213C4×Dic11—42no—
214C4×Dic11—81no—
215C4×Dic11C22×C412yes—
216C4×Dic11#4112yes—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8C22×C412yes—
222C2×C11⋊C8C2×D412yes—
223Dic44—28no—
224C2×#464—111no—
225C2×#441—111no—
226C2×C4×SD16—111no—
227#2367—111no—
228Q8×C4⋊C4—111no—
229#1959—111no—
230#1948—111no—
231#1936—111no—
232#1933—111no—
233#1880—111no—
234#1878—111no—
235#1865—111no—
236#1864D1111yescharacteristic
237#1771—111no—
238#1763—111no—
239C23×C11—22no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11C22×D411yescharacteristic
247D4×C11—22no—
248D4×C11—22no—
249D4×C11—41no—
250D4×C11—41no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
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—84no—
266C2×C4×C11#13712yes—
267C2×C4×C11C23×C411yescharacteristic
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11H(5,𝔽2)11yescharacteristic
272C2×C4×C112−1+411yescharacteristic
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—22no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11C4×D412yes—
296C2×Dic11C4×D412yes—
297Dic22—22no—
298Dic22—22no—
299Dic22—22no—
300Dic22—22no—
301Dic22—22no—
302Dic22—41no—
303Dic22—41no—
304Dic22C4×D414yes—
305C8×C11—22no—
306C8×C11—41no—
307C11⋊C8—22no—
308C11⋊C8—22no—
309C22×Q16—111no—
310C22×SD16—111no—
311C2×#124—111no—
312C2×C4×Q8—111no—
313C2×C4×Q8—111no—
314C2×C4×Q8—111no—
315C2×C4×Q8—111no—
316C2×C4×D4C2×D1111yescharacteristic
317#464—118no—
318#441—224no—
319C4×SD16—224no—
320C2×#106—111no—
321C2×#106C2×D1111yescharacteristic
322C2×C4⋊C8—111no—
323C2×#103—111no—
324C2×#103—111no—
325C2×#103—111no—
326C2×#103—111no—
327C2×#103—111no—
328C2×#102—111no—
329C2×#102C2×D1111yescharacteristic
330C2×#102C2×D1111yescharacteristic
331C2×#97—111no—
332C2×#97—111no—
333C2×C4×C8—111no—
334#391—111no—
335#390—111no—
336#389—111no—
337#389—221no—
338#389—221no—
339#389C2×D1111yescharacteristic
340#388—221no—
341#388—221no—
342#385—221no—
343#384—111no—
344#384—221no—
345C4×C4⋊C4—111no—
346C4×C4⋊C4—111no—
347C4×C4⋊C4—221no—
348C4×C22⋊C4—221no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340C2×D1111yescharacteristic
353#336—111no—
354#336C2×D1111yescharacteristic
355C22×C11—42no—
356C22×C11—42no—
357C22×C11—42no—
358C22×C11—81no—
359C22×C11—81no—
360C22×C11—81no—
361C22×C11—81no—
362C22×C11C2×C4×D411yescharacteristic
363C22×C11D4211yescharacteristic
364C22×C11#54811yescharacteristic
365C22×C11C2×#13711yescharacteristic
366C22×C11#57511yescharacteristic
367C22×C11#57711yescharacteristic
368C22×C11#57711yescharacteristic
369C4×C11—22no—
370C4×C11—42no—
371C4×C11—42no—
372C4×C11—41no—
373C4×C11—81no—
374C4×C11C2×C4×D411yescharacteristic
375C4×C11#52011yescharacteristic
376C4×C11#54711yescharacteristic
377C4×C11#55311yescharacteristic
378Dic11—24no—
379Dic11—22no—
380Dic11—22no—
381Dic11—42no—
382Dic11—41no—
383Dic11—41no—
384Dic11—81no—
385Dic11—81no—
386C22×Q8—111no—
387C22×Q8—111no—
388C22×D4C22×D1111yescharacteristic
389C23×C4—21no—
390C2×Q16—114no—
391C2×Q16—222no—
392C2×Q16—222no—
393C2×SD16—114no—
394C2×SD16—222no—
395C2×SD16—222no—
396C22×C8—111no—
397C22×C8—111no—
398C22×C8C22×D1111yescharacteristic
399C22×C8C22×D1111yescharacteristic
400#124—114no—
401#124—222no—
402C4×Q8—114no—
403C4×Q8—222no—
404C4×Q8—222no—
405C4×Q8—222no—
406C4×Q8—222no—
407C4×Q8—441no—
408C4×Q8—441no—
409C4×Q8—441no—
410C4×D4—22no—
411C4×D4—41no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4C22×D1111yescharacteristic
425C2×C4⋊C4C22×D1111yescharacteristic
426C2×C4⋊C4C22×D1111yescharacteristic
427C2×C22⋊C4—21no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C42—111no—
433C2×C42—111no—
434C2×C42—221no—
435C2×C42—221no—
436C2×C42—221no—
437C2×C42—221no—
438C2×C42—221no—
439C2×C42C22×D1111yescharacteristic
440#106—22no—
441#106—222no—
442C4⋊C8—114no—
443#103—114no—
444#103—114no—
445#103—222no—
446#103—222no—
447#103—441no—
448#102—41no—
449#102—222no—
450#102C4×D1114yes—
451#97—222no—
452#97—222no—
453C4×C8—222no—
454#95—21no—
455#95—111no—
456#95—111no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461C2×C11—82no—
462C2×C11#236111yescharacteristic
463C2×C11C4×#13711yescharacteristic
464C2×C11#295211yescharacteristic
465C2×C11#326611yescharacteristic
466C2×C11#327111yescharacteristic
467C2×C11#336911yescharacteristic
468C2×C11#337111yescharacteristic
469C24—21no—
470C2×Q8—112no—
471C2×Q8—112no—
472C2×Q8—112no—
473C2×Q8—112no—
474C2×Q8—221no—
475C2×Q8—221no—
476C2×Q8—221no—
477C2×Q8—221no—
478C2×Q8—221no—
479C2×Q8—221no—
480C2×Q8—221no—
481C2×Q8—221no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4C2×C4×D1112yes—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—81no—
494C22×C4—111no—
495C22×C4—111no—
496C22×C4—111no—
497C22×C4—111no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4D4×D1111yescharacteristic
503C22×C4D4×D1111yescharacteristic
504C22×C4C23×D1111yescharacteristic
505Q16—228no—
506SD16—228no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—112no—
513C2×C8—112no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8C2×C4×D1112yes—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—81no—
524C4⋊C4—224no—
525C4⋊C4—222no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—441no—
531C4⋊C4—442no—
532C4⋊C4—442no—
533C4⋊C4—442no—
534C4⋊C4—442no—
535C4⋊C4—881no—
536C4⋊C4—881no—
537C4⋊C4C2×C4×D1112yes—
538C4⋊C4D4×D1112yes—
539C22⋊C4—42no—
540C22⋊C4—224no—
541C22⋊C4—224no—
542C22⋊C4—442no—
543C22⋊C4—881no—
544C42—21no—
545C42—21no—
546C42—112no—
547C42—112no—
548C42—224no—
549C42—221no—
550C42—221no—
551C42—442no—
552C42—442no—
553C42—442no—
554C42—881no—
555C11#2301311yescharacteristic, complemented, Sylow
556C23—22no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23C2×D4×D1111yescharacteristic
564Q8—114no—
565Q8—222no—
566Q8—222no—
567Q8—222no—
568Q8—222no—
569Q8—222no—
570Q8—441no—
571Q8—441no—
572D4—22no—
573D4—22no—
574D4—41no—
575D4—41no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—84no—
591C2×C4—112no—
592C2×C4—112no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—222no—
598C2×C4—222no—
599C2×C4—222no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—222no—
605C2×C4—221no—
606C2×C4—221no—
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#6696812yes—
616C2×C4C22×C4×D1111yescharacteristic
617C2×C4C2×D4×D1111yescharacteristic
618C2×C4#6703711yescharacteristic
619C2×C4#6704011yescharacteristic
620C2×C4#41×D1111yescharacteristic
621C2×C4#41×D1111yescharacteristic
622C8—22no—
623C8—41no—
624C8—222no—
625C8—222no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22—81no—
633C22C4×D4×D1111yescharacteristic
634C22#1062312111yescharacteristic
635C22#1062316411yescharacteristic
636C22C2×#6696811yescharacteristic
637C22#1062329911yescharacteristic
638C22#1062330611yescharacteristic
639C22#1062330611yescharacteristic
640C4—22no—
641C4—42no—
642C4—41no—
643C4—42no—
644C4—81no—
645C4—224no—
646C4—222no—
647C4—222no—
648C4—442no—
649C4—441no—
650C4—441no—
651C4—881no—
652C4—881no—
653C4#1062303511yescharacteristic
654C4C4×D4×D1111yescharacteristic
655C4#1062316211yescharacteristic
656C4#1062319211yescharacteristic
657C2—82no—
658C2#1307163511yescharacteristic
659C2C4×#6696811yescharacteristic
660C2#1307749811yescharacteristic
661C2#1308013011yescharacteristic
662C2#1308019411yescharacteristic
663C2#1308135511yescharacteristic
664C2#1308138211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1864C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#1864D11
hypocenterC11#23013
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1864

Complements

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

NH ≅ G/Ntype
2. C2×#10622466C2semidirect
5. #13071530C2semidirect
7. #13069376C2semidirect
9. #13069291C2semidirect
11. #13068956C2semidirect
12. #13068885C2semidirect
13. #13068487C2semidirect
14. #13068445C2semidirect
53. #10622380C4semidirect
107. C2×Dic44C2×C4semidirect
113. #66940C2×C4semidirect
131. Dic11⋊C8C2×C4semidirect
133. #66874C2×C4semidirect
555. C11#23013semidirect

Maximal subgroups

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

subgroupindex
C2×#106223802
C2×#106224662
C2×C4×#43242
#130716892
#130715302
#130694312
#130693762
#130693152
#130692912
#130689682
#130689562
#130688852
#130684872
#130684452
C11×#18642
#2301311