Finite Group Databasebeta

← #14926868

Subgroups — #14926868

Order 2816.

1690 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076968C211yesmaximal, characteristic
2#13076968C211yesmaximal, characteristic
3#13076955C212yesmaximal
4#13074586C212yesmaximal
5#13074429C212yesmaximal
6#13074076C214yesmaximal, complemented
7#13074046C214yesmaximal, complemented
8#13073191C212yesmaximal, complemented
9#13073143C212yesmaximal, complemented
10#13072455C212yesmaximal, complemented
11#13072392C212yesmaximal, complemented
12#13071349C212yesmaximal
13#13071219C212yesmaximal
14C4×#66977C212yesmaximal
15C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C2×#66977C2212yes—
22C2×#66977C2212yes—
23C2×#66922C2211yescharacteristic
24C2×#66922C2211yescharacteristic
25C2×C4×Dic22C2212yes—
26C4×C11×C4⋊C4C2212yes—
27C4×C11×C4⋊C4C2212yes—
28C4×C11×C4⋊C4C2212yes—
29C4×C11×C4⋊C4C2212yes—
30C2×C11×#95C2211yescharacteristic
31C2×C11×#95C2211yescharacteristic
32#10622825C2212yes—
33#10622825C2212yes—
34#10622825C2212yes—
35#10622825C2212yes—
36#10622824C2214yes—
37#10622823C2214yes—
38#10622823C2214yes—
39C4×C22⋊Dic11C2214yes—
40#10622599C2214yes—
41#10622597C2214yes—
42#10622597C2214yes—
43#10622594C2214yes—
44#10622594C2214yes—
45#10622594C2214yes—
46#10622594C2214yes—
47#10622592C2214yes—
48#10622548C2211yescharacteristic
49#10622548C2211yescharacteristic
50C4×C4⋊Dic11C2212yes—
51#10622546C2214yes—
52#10622546C2214yes—
53#10622546C2214yes—
54C4×Dic11⋊C4C2214yes—
55#10622542C2212yes—
56#10622542C2212yes—
57#10622542C2212yes—
58#10622542C2212yes—
59#10622542C2212yes—
60#10622541C2212yes—
61#10622541C2212yes—
62#10622541C2212yes—
63#10622541C2212yes—
64#10622541C2212yes—
65#10622541C2212yes—
66#10622541C2212yes—
67#10622273C2214yes—
68#10622273C2214yes—
69#10622270C2214yes—
70#10622270C2214yes—
71#10622268C2214yes—
72#10622267C2214yes—
73#10622260C2214yes—
74#10622259C2214yes—
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C22×Dic22C2312yes—
83C22×Dic22C2312yes—
84C2×C11×C4⋊C4—24no—
85C2×C11×C4⋊C4Q818yescomplemented
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C4⋊C4C2312yes—
90C2×C42×C11—24no—
91C2×C42×C11—42no—
92C2×C42×C11—42no—
93C2×C42×C11C2312yes—
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2312yes—
97C2×C42×C11C2312yes—
98C2×C42×C11C2311yescharacteristic
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2312yes—
101C2×C22⋊Dic11C2314yes—
102C2×C22⋊Dic11C2314yes—
103C2×C4⋊Dic11C2312yes—
104C2×C4⋊Dic11C2312yes—
105C2×C4⋊Dic11C2312yes—
106C2×C4⋊Dic11C2312yes—
107C2×C4⋊Dic11C2312yes—
108C2×C4⋊Dic11C2312yes—
109C2×C4⋊Dic11C2312yes—
110C2×C4⋊Dic11C2312yes—
111C2×C4⋊Dic11C2312yes—
112C2×C4⋊Dic11C2312yes—
113#66977—28no—
114#66977—28no—
115C2×Dic11⋊C4C2314yes—
116C2×Dic11⋊C4C2314yes—
117C2×Dic11⋊C4C2314yes—
118C2×Dic11⋊C4C2314yes—
119C2×Dic11⋊C4C2314yes—
120C2×Dic11⋊C4C2314yes—
121C2×C4×Dic11C2314yes—
122C2×C4×Dic11C2314yes—
123#66922—42no—
124#66922—42no—
125C4×Dic22—44no—
126C11×#95C2312yes—
127C11×#95C2312yes—
128C11×#95C2312yes—
129C11×#95C2312yes—
130C11⋊#95C2314yes—
131C11⋊#95C2314yes—
132C11⋊#95C2314yes—
133C11⋊#95C2314yes—
134C11⋊#95C2314yes—
135C11⋊#95C2314yes—
136C11⋊#95C2314yes—
137C11⋊#95C2314yes—
138C11⋊#95C2314yes—
139C11⋊#95C2314yes—
140C11⋊#95C2314yes—
141C11⋊#95C2314yes—
142C11⋊#95C2314yes—
143C11⋊#95C2314yes—
144#35015—111nomaximal, Sylow
145C24×C11C2411yescharacteristic
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—41no—
153C22×C4×C11—41no—
154C22×C4×C11—41no—
155C22×C4×C11—41no—
156C22×C4×C11—41no—
157C22×C4×C11—41no—
158C22×C4×C11—41no—
159C22×C4×C11—41no—
160C22×C4×C11—41no—
161C22×C4×C11—41no—
162C22×C4×C11C2×Q814yes—
163C22×C4×C11C2×Q814yes—
164C22×C4×C11C2×Q814yes—
165C22×C4×C11#4114yes—
166C22×C4×C11#4114yes—
167C22×C4×C11C2412yes—
168C22×C4×C11C2412yes—
169C22×C4×C11C2412yes—
170C22×C4×C11C2412yes—
171C22×C4×C11C2411yescharacteristic
172C22×C4×C11C2411yescharacteristic
173C22×C4×C11C2411yescharacteristic
174C22×C4×C11C2411yescharacteristic
175C22×C4×C11C2411yescharacteristic
176C22×C4×C11C2411yescharacteristic
177C22×Dic11C2414yes—
178C22×Dic11C2414yes—
179C22×Dic11C2414yes—
180C22×Dic11C2414yes—
181C2×Dic22—24no—
182C2×Dic22—24no—
183C2×Dic22—24no—
184C2×Dic22—24no—
185C2×Dic22—42no—
186C2×Dic22—42no—
187C11×C4⋊C4—24no—
188C11×C4⋊C4—24no—
189C11×C4⋊C4C2×Q818yes—
190C11×C4⋊C4C2×Q818yes—
191C42×C11—24no—
192C42×C11—24no—
193C42×C11—24no—
194C42×C11—22no—
195C42×C11—22no—
196C42×C11—42no—
197C42×C11—41no—
198C42×C11—41no—
199C22⋊Dic11—28no—
200C22⋊Dic11—28no—
201C4⋊Dic11—24no—
202C4⋊Dic11—24no—
203C4⋊Dic11—24no—
204C4⋊Dic11—24no—
205C4⋊Dic11—42no—
206C4⋊Dic11—42no—
207C4⋊Dic11—42no—
208C4⋊Dic11—42no—
209C4⋊Dic11—42no—
210C4⋊Dic11—42no—
211Dic11⋊C4—28no—
212Dic11⋊C4—28no—
213Dic11⋊C4—44no—
214Dic11⋊C4—44no—
215Dic11⋊C4—44no—
216Dic11⋊C4—44no—
217C4×Dic11—44no—
218C4×Dic11—44no—
219#2857—111no—
220#2857—111no—
221#2855—112no—
222#2646—112no—
223#2627—112no—
224#2590—114no—
225#2588—114no—
226#2511—112no—
227#2507—112no—
228#2451—112no—
229#2446—112no—
230#2329—112no—
231#2313—112no—
232C4×C22⋊Q8—112no—
233C2×C4×C4⋊C4D1111yescharacteristic
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11C22×Q812yes—
239C23×C11C2×#4112yes—
240C23×C11C2×#4112yes—
241C23×C11C2511yescharacteristic
242C2×C4×C11—28no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—22no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—28no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—44no—
265C2×C4×C11—44no—
266C2×C4×C11—44no—
267C2×C4×C11—44no—
268C2×C4×C11—44no—
269C2×C4×C11C22×Q814yes—
270C2×C4×C11C22×Q814yes—
271C2×C4×C11C22×Q812yes—
272C2×C4×C11C22×Q812yes—
273C2×C4×C11C2×#4112yes—
274C2×C4×C11C2×#4112yes—
275C2×C4×C11C2×#4112yes—
276C2×C4×C11C2×#4112yes—
277C2×C4×C11H(5,𝔽2)12yes—
278C2×C4×C112−1+412yes—
279C2×Dic11—24no—
280C2×Dic11—24no—
281C2×Dic11—24no—
282C2×Dic11—24no—
283C2×Dic11—24no—
284C2×Dic11—24no—
285C2×Dic11—24no—
286C2×Dic11—24no—
287C2×Dic11—24no—
288C2×Dic11—24no—
289C2×Dic11—24no—
290C2×Dic11—24no—
291Dic22—48no—
292Dic22—84no—
293C2×C4⋊Q8—111no—
294C2×C4⋊Q8—111no—
295C2×C22⋊Q8—112no—
296C2×C22⋊Q8—112no—
297C2×C4×Q8—112no—
298C22×C4⋊C4C2×D1111yescharacteristic
299C22×C4⋊C4C2×D1111yescharacteristic
300C22×C42C2×D1111yescharacteristic
301C22×C42C2×D1111yescharacteristic
302C22×C42C2×D1111yescharacteristic
303#400—114no—
304#400—114no—
305#400—114no—
306#398—114no—
307#398—114no—
308#398—114no—
309#398—114no—
310#395—114no—
311#391—112no—
312#391—112no—
313#391—112no—
314#391—112no—
315#391—112no—
316#391—114no—
317#389—112no—
318#389—112no—
319#389—112no—
320#389—112no—
321#389—112no—
322#389—112no—
323#389—112no—
324#389—114no—
325#387—114no—
326#387—114no—
327#387—114no—
328#387—114no—
329#387—114no—
330#387—114no—
331#387—114no—
332#387—114no—
333#387—114no—
334#385—114no—
335#385—114no—
336#384—111no—
337#384—111no—
338#381—114no—
339#380—112no—
340#380—112no—
341#380—112no—
342#380—112no—
343C4×C4⋊C4—114no—
344C4×C4⋊C4—112no—
345C4×C4⋊C4C2×D1112yes—
346C4×C4⋊C4C2×D1112yes—
347C4×C4⋊C4C2×D1112yes—
348C4×C4⋊C4C2×D1112yes—
349C4×C22⋊C4—114no—
350C2×#95C2×D1111yescharacteristic
351C2×#95C2×D1111yescharacteristic
352C22×C11—22no—
353C22×C11—22no—
354C22×C11—22no—
355C22×C11—22no—
356C22×C11—22no—
357C22×C11—22no—
358C22×C11#53314yes—
359C22×C11C23×Q811yescharacteristic
360C22×C11C22×#4111yescharacteristic
361C22×C11C22×#4111yescharacteristic
362C22×C11C2×H(5,𝔽2)11yescharacteristic
363C22×C11C2×2−1+411yescharacteristic
364C22×C11#58511yescharacteristic
365C22×C11#58511yescharacteristic
366C4×C11—24no—
367C4×C11—22no—
368C4×C11—24no—
369C4×C11—22no—
370C4×C11—22no—
371C4×C11—22no—
372C4×C11—22no—
373C4×C11—42no—
374C4×C11—42no—
375C4×C11#53914yes—
376Dic11—44no—
377Dic11—44no—
378Dic11—44no—
379Dic11—44no—
380C22×Q8—112no—
381C22×Q8—112no—
382C23×C4C22×D1111yescharacteristic
383C23×C4C22×D1111yescharacteristic
384C23×C4C22×D1111yescharacteristic
385C23×C4C22×D1111yescharacteristic
386C23×C4C22×D1111yescharacteristic
387C23×C4C22×D1111yescharacteristic
388C23×C4C22×D1111yescharacteristic
389C4⋊Q8—442no—
390C4⋊Q8—442no—
391C22⋊Q8—228no—
392C22⋊Q8—228no—
393C4×Q8—444no—
394C2×C4⋊C4—24no—
395C2×C4⋊C4—112no—
396C2×C4⋊C4—112no—
397C2×C4⋊C4—114no—
398C2×C4⋊C4—112no—
399C2×C4⋊C4—114no—
400C2×C4⋊C4—112no—
401C2×C4⋊C4—114no—
402C2×C4⋊C4—112no—
403C2×C4⋊C4—112no—
404C2×C4⋊C4—112no—
405C2×C4⋊C4—114no—
406C2×C4⋊C4—112no—
407C2×C4⋊C4—112no—
408C2×C4⋊C4—112no—
409C2×C4⋊C4—114no—
410C2×C4⋊C4—114no—
411C2×C4⋊C4Dic2218yescomplemented
412C2×C4⋊C4C22×D1112yes—
413C2×C4⋊C4C22×D1112yes—
414C2×C4⋊C4C22×D1112yes—
415C2×C4⋊C4C22×D1112yes—
416C2×C22⋊C4—114no—
417C2×C22⋊C4—114no—
418C2×C42—24no—
419C2×C42—42no—
420C2×C42—42no—
421C2×C42—114no—
422C2×C42—114no—
423C2×C42C22×D1112yes—
424C2×C42C22×D1111yescharacteristic
425C2×C42C22×D1111yescharacteristic
426C2×C42C22×D1112yes—
427C2×C42C22×D1112yes—
428C2×C42C22×D1112yes—
429C2×C42C22×D1111yescharacteristic
430C2×C42C22×D1111yescharacteristic
431#95—114no—
432#95—114no—
433#95—114no—
434#95—114no—
435#95—114no—
436#95—114no—
437#95—114no—
438#95—114no—
439#95—114no—
440#95—114no—
441#95—114no—
442#95—114no—
443#95—114no—
444#95—114no—
445#95C22×D1112yes—
446#95C22×D1112yes—
447#95C22×D1112yes—
448#95C22×D1112yes—
449C2×C11—24no—
450C2×C11C2×#53311yescharacteristic
451C2×C11C2×#53911yescharacteristic
452C2×C11#345511yescharacteristic
453C2×C11#350111yescharacteristic
454C2×C11#350211yescharacteristic
455C2×C11#350511yescharacteristic
456C2×C11#350711yescharacteristic
457C24C23×D1111yescharacteristic
458C2×Q8—224no—
459C2×Q8—224no—
460C2×Q8—224no—
461C2×Q8—224no—
462C2×Q8—442no—
463C2×Q8—442no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—114no—
481C22×C4—114no—
482C22×C4—114no—
483C22×C4—114no—
484C22×C4C2×Dic2214yes—
485C22×C4C2×Dic2214yes—
486C22×C4C2×Dic2214yes—
487C22×C4#433914yes—
488C22×C4#433914yes—
489C22×C4C23×D1112yes—
490C22×C4C23×D1112yes—
491C22×C4C23×D1112yes—
492C22×C4C23×D1112yes—
493C22×C4C23×D1111yescharacteristic
494C22×C4C23×D1111yescharacteristic
495C22×C4C23×D1111yescharacteristic
496C22×C4C23×D1111yescharacteristic
497C22×C4C23×D1111yescharacteristic
498C22×C4C23×D1111yescharacteristic
499C4⋊C4—24no—
500C4⋊C4—24no—
501C4⋊C4—228no—
502C4⋊C4—228no—
503C4⋊C4—224no—
504C4⋊C4—224no—
505C4⋊C4—224no—
506C4⋊C4—224no—
507C4⋊C4—444no—
508C4⋊C4—442no—
509C4⋊C4—442no—
510C4⋊C4—442no—
511C4⋊C4—444no—
512C4⋊C4—444no—
513C4⋊C4—444no—
514C4⋊C4—442no—
515C4⋊C4—442no—
516C4⋊C4—442no—
517C4⋊C4C2×Dic2218yes—
518C4⋊C4C2×Dic2218yes—
519C22⋊C4—228no—
520C22⋊C4—228no—
521C42—24no—
522C42—24no—
523C42—24no—
524C42—22no—
525C42—22no—
526C42—42no—
527C42—41no—
528C42—41no—
529C42—444no—
530C42—444no—
531C11#3501511yescharacteristic, complemented, Sylow
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23C22×Dic2212yes—
537C23C2×#433912yes—
538C23C2×#433912yes—
539C23C24×D1111yescharacteristic
540Q8—448no—
541Q8—884no—
542C2×C4—28no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—28no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—44no—
565C2×C4—44no—
566C2×C4—44no—
567C2×C4—44no—
568C2×C4—44no—
569C2×C4—224no—
570C2×C4—224no—
571C2×C4—224no—
572C2×C4—224no—
573C2×C4—224no—
574C2×C4—224no—
575C2×C4—224no—
576C2×C4—224no—
577C2×C4—224no—
578C2×C4—224no—
579C2×C4—224no—
580C2×C4—224no—
581C2×C4C22×Dic2214yes—
582C2×C4C22×Dic2214yes—
583C2×C4C22×Dic2212yes—
584C2×C4C22×Dic2212yes—
585C2×C4C2×#433912yes—
586C2×C4C2×#433912yes—
587C2×C4C2×#433912yes—
588C2×C4C2×#433912yes—
589C2×C4#6703712yes—
590C2×C4#6704012yes—
591C22—22no—
592C22—22no—
593C22—22no—
594C22—22no—
595C22—22no—
596C22—22no—
597C22#1062300114yes—
598C22C23×Dic2211yescharacteristic
599C22C22×#433911yescharacteristic
600C22C22×#433911yescharacteristic
601C22C2×#6703711yescharacteristic
602C22C2×#6704011yescharacteristic
603C22#1062345311yescharacteristic
604C22#1062345311yescharacteristic
605C4—24no—
606C4—24no—
607C4—22no—
608C4—22no—
609C4—22no—
610C4—22no—
611C4—22no—
612C4—42no—
613C4—42no—
614C4—444no—
615C4—444no—
616C4—444no—
617C4—444no—
618C4#1062304614yes—
619C2—24no—
620C2C2×#1062300111yescharacteristic
621C2C2×#1062304611yescharacteristic
622C2#1308200611yescharacteristic
623C2#1308241911yescharacteristic
624C2#1308242611yescharacteristic
625C2#1308245511yescharacteristic
626C2#1308248111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C4×C11×C4⋊C4C2
prime radicalC24×C11C24
hypercenterC2×C4×C4⋊C4D11
hypocenterC11#35015
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
6. #13074076C2semidirect
7. #13074046C2semidirect
8. #13073191C2semidirect
9. #13073143C2semidirect
10. #13072455C2semidirect
11. #13072392C2semidirect
85. C2×C11×C4⋊C4Q8semidirect
411. C2×C4⋊C4Dic22semidirect
531. C11#35015semidirect

Maximal subgroups

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

subgroupindex
#130769682
#130769552
#130745862
#130744292
#130740762
#130740462
#130731912
#130731432
#130724552
#130723922
#130713492
#130712192
C4×#669772
C2×C4×C11×C4⋊C42
#3501511