Finite Group Databasebeta

← #14915063

Subgroups — #14915063

Order 2816.

2930 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623347C211yesmaximal, characteristic
2C2×#10623035C211yesmaximal, characteristic
3C2×#10623343C211yesmaximal, characteristic, complemented
4#13071648C214yesmaximal, complemented
5#13071626C214yesmaximal, complemented
6#13071604C218yesmaximal, complemented
7#13071334C212yesmaximal, complemented
8#13071330C212yesmaximal, complemented
9#13071240C211yesmaximal, characteristic, complemented
10#13071185C212yesmaximal, complemented
11#13071159C212yesmaximal, complemented
12#13071106C211yesmaximal, characteristic
13C4×#66979C211yesmaximal, characteristic, complemented
14C2×C11×#391C211yesmaximal, characteristic, complemented
15C23×Q8×C11C2211yescharacteristic
16C22×#4339C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19#10623347C4116yescomplemented
20C2×#67000C2212yes—
21C2×#66999C2214yes—
22#10623343—28no—
23C2×Q8×Dic11C2212yes—
24C2×Q8×Dic11C2212yes—
25C2×Q8×Dic11C2212yes—
26C2×Q8×Dic11C2212yes—
27C2×#66997C2212yes—
28C2×#66982C2214yes—
29C2×C4×C22⋊D11C2214yes—
30C2×#66979C2211yescharacteristic
31C2×#66979C2214yes—
32C2×#66979C2211yescharacteristic
33C2×#66979C2211yescharacteristic
34#10623035—28no—
35C2×#66946C2212yes—
36C2×#66945C2212yes—
37C2×C4⋊C4×D11C2212yes—
38C2×#66940C2212yes—
39C11×#391C2214yes—
40C11×#391C2212yes—
41C11×#391C2212yes—
42C2×C11×#95C2214yes—
43#10622826C2214yes—
44#10622823C2214yes—
45C4×C22⋊Dic11C2214yes—
46#10622590C2212yes—
47#10622589C2212yes—
48#10622586C2214yes—
49#10622552C2211yescharacteristic
50#10622552C2211yescharacteristic
51C4×(C2×D11)⋊C4C2214yes—
52C4×C4⋊Dic11C2212yes—
53C4×C4⋊Dic11C2212yes—
54#10622545C2212yes—
55C42×Dic11C2212yes—
56#10622542C2211yescharacteristic
57#10622542C2211yescharacteristic
58#10622283C2218yes—
59#10622282C2218yes—
60#10622281C2218yes—
61#10622279C2218yes—
62#10622268C2218yes—
63#10622265C2218yes—
64#10622262C2218yes—
65#10622260C2218yes—
66C22×Q8×C11—24no—
67C22×Q8×C11—24no—
68C22×Q8×C11C2×C418yescomplemented
69C22×Q8×C11C2312yes—
70C22×Q8×C11C2312yes—
71C23×C4×C11C2312yes—
72C23×C4×C11C2312yes—
73C23×C4×C11C2312yes—
74C23×C4×C11C2311yescharacteristic
75C22×C22⋊D11C2312yes—
76C2×#4339—24no—
77C2×#4339—24no—
78C2×#4339C2×C418yes—
79C22×D44C2311yescharacteristic
80C22×C4×D11C2312yes—
81C22×C4×D11C2314yes—
82C22×Dic22C2311yescharacteristic
83C2×C11×C4⋊C4—24no—
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C4⋊C4C2312yes—
86C2×C42×C11—24no—
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×C42×C11C2312yes—
90C2×C22⋊Dic11C2312yes—
91C2×C22⋊Dic11C2312yes—
92C2×C22⋊Dic11C2312yes—
93#67000C2×C4116yescomplemented
94#66999C2×C4132yescomplemented
95Q8×Dic11—28no—
96Q8×Dic11—28no—
97Q8×Dic11—28no—
98Q8×Dic11—28no—
99#66997C2×C4116yescomplemented
100#66982C2×C4132yescomplemented
101C4×C22⋊D11—216no—
102C2×(C2×D11)⋊C4C2314yes—
103C2×(C2×D11)⋊C4C2314yes—
104C2×(C2×D11)⋊C4C2314yes—
105C2×(C2×D11)⋊C4C2318yes—
106#66979—24no—
107#66979—216no—
108#66979C2×C418yescomplemented
109#66979D418yes—
110C2×C4⋊Dic11C2314yes—
111C2×C4⋊Dic11C2314yes—
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2311yescharacteristic
114C2×C4⋊Dic11C2312yes—
115C2×C4⋊Dic11C2311yescharacteristic
116C2×C4⋊Dic11C2311yescharacteristic
117C2×Dic11⋊C4C2314yes—
118C2×Dic11⋊C4C2318yes—
119C2×Dic11⋊C4C2318yes—
120C2×C4×Dic11C2314yes—
121C2×C4×Dic11C2314yes—
122C2×C4×Dic11C2314yes—
123C2×C4×Dic11C2314yes—
124C2×C4×Dic11C2312yes—
125C2×C4×Dic11C2314yes—
126C2×C4×Dic11C2312yes—
127C2×C4×Dic11C2312yes—
128#66946—28no—
129#66945—28no—
130C4⋊C4×D11—28no—
131#66940—28no—
132C11×#95C2318yes—
133C11×#95C2318yes—
134C11⋊#95C2314yes—
135C11⋊#95C2314yes—
136C11⋊#95C2314yes—
137C11⋊#95C2318yes—
138C11⋊#95C2314yes—
139#34276—111nomaximal, Sylow
140C24×C11C2411yescharacteristic
141C23×D11C2412yes—
142C2×Q8×C11—232no—
143C2×Q8×C11—24no—
144C2×Q8×C11—24no—
145C2×Q8×C11—24no—
146C2×Q8×C11—24no—
147C2×Q8×C11C22×C418yes—
148C2×Q8×C11C22×C418yes—
149C22×C4×C11—24no—
150C22×C4×C11—24no—
151C22×C4×C11—24no—
152C22×C4×C11—24no—
153C22×C4×C11—24no—
154C22×C4×C11—42no—
155C22×C4×C11—44no—
156C22×C4×C11C22×C418yes—
157C22×C4×C11C22×C414yes—
158C22×C4×C11C2×D414yes—
159C22×C4×C11#4114yes—
160C22×C4×C11C2412yes—
161C22×C4×C11C2414yes—
162C22×C4×C11C2414yes—
163C22×C4×C11C2412yes—
164C22×C4×C11C2411yescharacteristic
165C22×C4×C11C2411yescharacteristic
166C2×C22⋊D11—24no—
167C2×C22⋊D11—24no—
168C2×C22⋊D11C22×C418yes—
169C22×Dic11C2412yes—
170C22×Dic11C2412yes—
171C22×Dic11C2414yes—
172C22×Dic11C2412yes—
173C22×Dic11C2412yes—
174C22×Dic11C2412yes—
175#4339—232no—
176C2×D44—22no—
177C2×D44—22no—
178C2×D44C22×C414yes—
179C2×C4×D11—28no—
180C2×C4×D11—24no—
181C2×C4×D11—24no—
182C2×C4×D11—48no—
183C2×C4×D11C22×C418yes—
184C2×Dic22—22no—
185C2×Dic22—22no—
186C2×Dic22C22×C414yes—
187C11×C4⋊C4—24no—
188C11×C4⋊C4—24no—
189C42×C11—22no—
190C42×C11—24no—
191C42×C11—22no—
192C22⋊Dic11—24no—
193C22⋊Dic11C22×C418yes—
194C22⋊Dic11C2×D418yes—
195(C2×D11)⋊C4—28no—
196(C2×D11)⋊C4—28no—
197(C2×D11)⋊C4—44no—
198(C2×D11)⋊C4C22×C4132yes—
199C4⋊Dic11—28no—
200C4⋊Dic11—28no—
201C4⋊Dic11—22no—
202C4⋊Dic11—22no—
203C4⋊Dic11C22×C418yes—
204C4⋊Dic11C2×D414yes—
205C4⋊Dic11C2×D414yes—
206Dic11⋊C4—28no—
207Dic11⋊C4—48no—
208Dic11⋊C4C22×C4132yes—
209C4×Dic11—28no—
210C4×Dic11—28no—
211C4×Dic11—28no—
212C4×Dic11—24no—
213C4×Dic11—28no—
214C4×Dic11—44no—
215C4×Dic11C22×C418yes—
216C4×Dic11C2×D418yes—
217C2×#536—111no—
218C2×#520—111no—
219C2×#519—111no—
220#2362—114no—
221#2360—114no—
222#2359—118no—
223#2327—112no—
224#2326—112no—
225#2317—111no—
226C4×C4⋊Q8—112no—
227C4×#124—112no—
228#2297—111no—
229C2×#391D1111yescharacteristic, complemented
230C4×#117—111no—
231C23×C11—22no—
232C23×C11—22no—
233C23×C11C23×C412yes—
234C23×C11C22×D412yes—
235C23×C11C2×#4112yes—
236C23×C11C2511yescharacteristic
237C22×D11—22no—
238C22×D11—22no—
239C22×D11—24no—
240C22×D11—24no—
241C22×D11C23×C414yes—
242Q8×C11—216no—
243Q8×C11—216no—
244C2×C4×C11—216no—
245C2×C4×C11—24no—
246C2×C4×C11—22no—
247C2×C4×C11—24no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—28no—
253C2×C4×C11—22no—
254C2×C4×C11—48no—
255C2×C4×C11—84no—
256C2×C4×C11C4×D4116yes—
257C2×C4×C11C23×C418yes—
258C2×C4×C11C23×C412yes—
259C2×C4×C11C23×C412yes—
260C2×C4×C11C22×D412yes—
261C2×C4×C11C22×D412yes—
262C2×C4×C11C2×#4112yes—
263C2×C4×C11C2×#4112yes—
264C2×C4×C112−1+414yes—
265C22⋊D11—216no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—24no—
275C2×Dic11—24no—
276C2×Dic11C23×C418yes—
277C2×Dic11C23×C414yes—
278C2×Dic11C22×D414yes—
279C2×Dic11C22×D414yes—
280D44—28no—
281C4×D11—216no—
282C4×D11—88no—
283Dic22—28no—
284C22×#41—111no—
285C23×Q8C2×D1111yescharacteristic
286#536—1116no—
287C2×C4⋊Q8—112no—
288C2×#124—112no—
289C2×#123—114no—
290C2×C22⋊Q8—114no—
291#520—228no—
292#519—228no—
293C2×C4×Q8—112no—
294C2×C4×Q8—112no—
295C2×C4×Q8—112no—
296C2×C4×Q8—112no—
297C2×C4×Q8—112no—
298C2×C4×D4—114no—
299C2×C4×D4—112no—
300C2×#117—111no—
301C2×#117—111no—
302C2×#117—111no—
303C2×#117—114no—
304C2×#117—112no—
305C22×C4⋊C4—112no—
306C22×C4⋊C4C2×D1111yescharacteristic
307C22×C42C2×D1111yescharacteristic
308#391—111no—
309#391—111no—
310#391C2×D1112yes—
311#391C2×D1112yes—
312#391C2×D1114yes—
313#390—111no—
314#390—111no—
315#389—114no—
316#389—118no—
317#388—118no—
318#388—118no—
319#387—118no—
320#387—118no—
321#386—114no—
322#385—114no—
323#385—118no—
324#384—112no—
325#382—112no—
326C4×C4⋊C4—112no—
327C4×C4⋊C4—112no—
328C4×C4⋊C4—118no—
329C4×C22⋊C4—114no—
330C4×C22⋊C4—114no—
331C4×C22⋊C4—118no—
332#376—112no—
333C2×#95C2×D1114yes—
334C43—112no—
335C22×C11—24no—
336C22×C11—24no—
337C22×C11—22no—
338C22×C11—22no—
339C22×C11C2×C4×D414yes—
340C22×C11C24×C411yescharacteristic
341C22×C11C23×D411yescharacteristic
342C22×C11C22×#4111yescharacteristic
343C22×C11C2×2−1+412yes—
344C22×C11#58512yes—
345C2×D11—24no—
346C2×D11—28no—
347C2×D11—44no—
348C2×D11—42no—
349C2×D11—42no—
350C4×C11—28no—
351C4×C11—24no—
352C4×C11—42no—
353C4×C11—44no—
354C4×C11C2×C4×D414yes—
355C4×C11C2×C4×D414yes—
356Dic11—24no—
357Dic11—28no—
358Dic11—24no—
359Dic11—24no—
360Dic11—42no—
361Dic11—42no—
362C2×#41—118no—
363C2×#41—224no—
364C2×#41—224no—
365C22×Q8—24no—
366C22×Q8—24no—
367C22×Q8—111no—
368C22×Q8C4×D1118yescomplemented
369C22×Q8C22×D1112yes—
370C22×Q8C22×D1112yes—
371C22×D4—112no—
372C22×D4—111no—
373C23×C4—112no—
374C23×C4—114no—
375C23×C4C22×D1112yes—
376C23×C4C22×D1112yes—
377C23×C4C22×D1112yes—
378C23×C4C22×D1111yescharacteristic
379C4⋊Q8—1116no—
380#124—1116no—
381#123—1132no—
382C22⋊Q8—1132no—
383C4×Q8—228no—
384C4×Q8—228no—
385C4×Q8—228no—
386C4×Q8—228no—
387C4×Q8—228no—
388C4×D4—228no—
389C4×D4—2216no—
390#117—118no—
391#117—118no—
392#117—2216no—
393#117—228no—
394#117—224no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—112no—
399C2×C4⋊C4—118no—
400C2×C4⋊C4—114no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—114no—
404C2×C4⋊C4—114no—
405C2×C4⋊C4—118no—
406C2×C4⋊C4—228no—
407C2×C4⋊C4C22×D1112yes—
408C2×C4⋊C4C22×D1112yes—
409C2×C22⋊C4—112no—
410C2×C22⋊C4—112no—
411C2×C22⋊C4—118no—
412C2×C22⋊C4—112no—
413C2×C22⋊C4—114no—
414C2×C22⋊C4—114no—
415C2×C22⋊C4—114no—
416C2×C42—24no—
417C2×C42—112no—
418C2×C42—112no—
419C2×C42—114no—
420C2×C42—114no—
421C2×C42—112no—
422C2×C42—114no—
423C2×C42—114no—
424C2×C42—114no—
425C2×C42C22×D1111yescharacteristic
426C2×C42C22×D1111yescharacteristic
427C2×C42C22×D1112yes—
428#95—114no—
429#95—114no—
430#95—114no—
431#95—118no—
432#95—114no—
433#95C22×D1118yes—
434#95C22×D1118yes—
435C2×C11—24no—
436C2×C11C22×C4×D411yescharacteristic
437C2×C11C4×2−1+412yes—
438C2×C11#349512yes—
439C2×C11#349911yescharacteristic
440C2×C11#350011yescharacteristic
441D11—44no—
442C24—112no—
443C24C23×D1111yescharacteristic
444#41—2232no—
445C2×Q8—232no—
446C2×Q8—24no—
447C2×Q8—24no—
448C2×Q8—24no—
449C2×Q8—24no—
450C2×Q8—114no—
451C2×Q8—222no—
452C2×Q8—222no—
453C2×Q8C2×C4×D1118yes—
454C2×Q8C2×C4×D1118yes—
455C2×D4—118no—
456C2×D4—114no—
457C2×D4—224no—
458C2×D4—224no—
459C2×D4—222no—
460C2×D4—222no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—42no—
467C22×C4—44no—
468C22×C4—114no—
469C22×C4—112no—
470C22×C4—112no—
471C22×C4—112no—
472C22×C4—118no—
473C22×C4—112no—
474C22×C4—112no—
475C22×C4—228no—
476C22×C4—224no—
477C22×C4—224no—
478C22×C4—448no—
479C22×C4C2×C4×D1118yes—
480C22×C4C2×C4×D1114yes—
481C22×C4D4×D1114yes—
482C22×C4#434114yes—
483C22×C4C23×D1112yes—
484C22×C4C23×D1114yes—
485C22×C4C23×D1114yes—
486C22×C4C23×D1112yes—
487C22×C4C23×D1111yescharacteristic
488C22×C4C23×D1111yescharacteristic
489C4⋊C4—24no—
490C4⋊C4—24no—
491C4⋊C4—118no—
492C4⋊C4—1132no—
493C4⋊C4—114no—
494C4⋊C4—114no—
495C4⋊C4—228no—
496C4⋊C4—228no—
497C4⋊C4—228no—
498C4⋊C4—222no—
499C4⋊C4—222no—
500C4⋊C4—448no—
501C22⋊C4—118no—
502C22⋊C4—118no—
503C22⋊C4—1132no—
504C22⋊C4—228no—
505C22⋊C4—224no—
506C22⋊C4—228no—
507C22⋊C4—444no—
508C42—22no—
509C42—24no—
510C42—22no—
511C42—118no—
512C42—118no—
513C42—228no—
514C42—228no—
515C42—228no—
516C42—224no—
517C42—228no—
518C42—444no—
519C11#3427611yescharacteristic, complemented, Sylow
520C23—22no—
521C23—22no—
522C23—114no—
523C23—222no—
524C23—222no—
525C23—224no—
526C23—224no—
527C23C22×C4×D1112yes—
528C23C2×D4×D1112yes—
529C23C2×#434112yes—
530C23C24×D1111yescharacteristic
531Q8—216no—
532Q8—216no—
533Q8—228no—
534D4—2216no—
535D4—228no—
536C2×C4—216no—
537C2×C4—24no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—28no—
546C2×C4—48no—
547C2×C4—84no—
548C2×C4—118no—
549C2×C4—114no—
550C2×C4—114no—
551C2×C4—114no—
552C2×C4—222no—
553C2×C4—222no—
554C2×C4—224no—
555C2×C4—224no—
556C2×C4—224no—
557C2×C4—224no—
558C2×C4—2216no—
559C2×C4—222no—
560C2×C4—222no—
561C2×C4—224no—
562C2×C4—224no—
563C2×C4—888no—
564C2×C4(C22⋊D11)⋊C4116yes—
565C2×C4C22×C4×D1118yes—
566C2×C4C22×C4×D1112yes—
567C2×C4C22×C4×D1112yes—
568C2×C4C2×D4×D1112yes—
569C2×C4C2×D4×D1112yes—
570C2×C4C2×#434112yes—
571C2×C4C2×#434112yes—
572C2×C4#6704014yes—
573C22—22no—
574C22—22no—
575C22—24no—
576C22—24no—
577C22—224no—
578C22—228no—
579C22—442no—
580C22—442no—
581C22—444no—
582C22C2×(C22⋊D11)⋊C414yes—
583C22C23×C4×D1111yescharacteristic
584C22C22×D4×D1111yescharacteristic
585C22C22×#434111yescharacteristic
586C22C2×#6704012yes—
587C22#1062345312yes—
588C4—28no—
589C4—24no—
590C4—44no—
591C4—42no—
592C4—224no—
593C4—224no—
594C4—224no—
595C4—228no—
596C4—442no—
597C4—442no—
598C4C2×(C22⋊D11)⋊C414yes—
599C4C2×(C22⋊D11)⋊C414yes—
600C2—24no—
601C2—444no—
602C2C22×(C22⋊D11)⋊C411yescharacteristic
603C2C4×#6704012yes—
604C2#1308236212yes—
605C2#1308239911yescharacteristic
606C2#1308240611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC2×C11×#391C2
socle, cosocleC23×C11C25
prime radicalC22×#4339C22
hypercenterC2×#391D11
hypocenterC11#34276
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
3. C2×#10623343C2semidirect
4. #13071648C2semidirect
5. #13071626C2semidirect
6. #13071604C2semidirect
7. #13071334C2semidirect
8. #13071330C2semidirect
9. #13071240C2semidirect
10. #13071185C2semidirect
11. #13071159C2semidirect
13. C4×#66979C2semidirect
14. C2×C11×#391C2semidirect
19. #10623347C4semidirect
68. C22×Q8×C11C2×C4semidirect
93. #67000C2×C4semidirect
94. #66999C2×C4semidirect
99. #66997C2×C4semidirect
100. #66982C2×C4semidirect
108. #66979C2×C4semidirect
229. C2×#391D11semidirect
368. C22×Q8C4×D11semidirect
519. C11#34276semidirect

Maximal subgroups

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

subgroupindex
C2×#106233472
C2×#106230352
C2×#106233432
#130716482
#130716262
#130716042
#130713342
#130713302
#130712402
#130711852
#130711592
#130711062
C4×#669792
C2×C11×#3912
#3427611