Finite Group Databasebeta

← #14915066

Subgroups — #14915066

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×#10623057C211yesmaximal, characteristic
2C2×#10623035C211yesmaximal, characteristic
3C2×#10623047C211yesmaximal, characteristic, complemented
4#13071642C214yesmaximal, complemented
5#13071620C214yesmaximal, complemented
6#13071606C218yesmaximal, complemented
7#13071333C212yesmaximal, complemented
8#13071324C212yesmaximal, complemented
9#13071183C212yesmaximal, complemented
10#13071155C212yesmaximal, complemented
11#13071104C211yesmaximal, characteristic
12C2×#10622587C211yesmaximal, characteristic, complemented
13#117×Dic11C211yesmaximal, characteristic, complemented
14C11×#2317C211yesmaximal, characteristic, complemented
15C22×#4339C2211yescharacteristic
16C23×Dic22C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C2×C4×C22⋊D11C2214yes—
21C2×#66979C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23#10623057C4116yescomplemented
24#10623047—28no—
25C2×#66950C2214yes—
26#10623035—28no—
27C2×#66946C2212yes—
28C2×#66945C2212yes—
29C2×C4⋊C4×D11C2212yes—
30C2×#66940C2212yes—
31C2×#66940C2212yes—
32C2×#66940C2212yes—
33C2×#66939C2214yes—
34C2×#66930C2214yes—
35C2×#66928C2212yes—
36C2×#66922C2212yes—
37C2×C4×Dic22C2212yes—
38C2×C4×Dic22C2212yes—
39C11×#389C2214yes—
40C11×#385C2214yes—
41C11×#384C2212yes—
42C11×#382C2212yes—
43C2×C11⋊#95C2214yes—
44#10622603C2218yes—
45#10622602C2218yes—
46#10622601C2211yescharacteristic
47#10622601C2211yescharacteristic
48C4⋊C4×Dic11C2212yes—
49C4⋊C4×Dic11C2212yes—
50C4⋊C4×Dic11C2218yes—
51#10622587C2211yescharacteristic
52#10622587C2211yescharacteristic
53#10622587C2214yes—
54#10622587C2212yes—
55#10622587C2212yes—
56#10622586C2218yes—
57#10622571C2214yes—
58C22⋊C4×Dic11C2214yes—
59C4×(C2×D11)⋊C4C2214yes—
60#10622545C2212yes—
61C42×Dic11C2212yes—
62#10622282C2218yes—
63#10622279C2218yes—
64#10622267C2218yes—
65#10622267C2218yes—
66C23×C4×C11C2312yes—
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11C2312yes—
69C23×Dic11C2312yes—
70C23×Dic11C2312yes—
71C2×#4339—24no—
72C2×#4339—24no—
73C2×#4339C2×C418yes—
74C22×D44C2311yescharacteristic
75C22×C4×D11C2312yes—
76C22×C4×D11C2314yes—
77C22×Dic22—24no—
78C22×Dic22—24no—
79C22×Dic22C2×C418yescomplemented
80C22×Dic22C2312yes—
81C22×Dic22C2311yescharacteristic
82C22×Dic22C2312yes—
83C11×#117—24no—
84C11×#117C2×C418yescomplemented
85C2×C11×C4⋊C4—24no—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C4⋊C4C2312yes—
90C2×C11×C4⋊C4C2318yes—
91C2×C11×C4⋊C4C2312yes—
92C2×C11×C22⋊C4C2312yes—
93C2×C11×C22⋊C4C2312yes—
94C2×C42×C11C2312yes—
95C2×C42×C11C2312yes—
96C2×C22⋊Dic11C2312yes—
97C4×C22⋊D11—216no—
98C2×(C2×D11)⋊C4C2314yes—
99C2×(C2×D11)⋊C4C2314yes—
100C2×(C2×D11)⋊C4C2314yes—
101C2×(C2×D11)⋊C4C2318yes—
102#66979D418yes—
103C2×C4⋊Dic11C2318yes—
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4⋊Dic11C2311yescharacteristic
106C2×Dic11⋊C4C2314yes—
107C2×Dic11⋊C4C2314yes—
108C2×Dic11⋊C4C2314yes—
109C2×C4×Dic11—24no—
110C2×C4×Dic11C2314yes—
111C2×C4×Dic11C2314yes—
112C2×C4×Dic11C2314yes—
113C2×C4×Dic11C2314yes—
114C2×C4×Dic11C2311yescharacteristic
115C2×C4×Dic11C2311yescharacteristic
116C2×C4×Dic11C2312yes—
117C2×C4×Dic11C2314yes—
118C2×C4×Dic11C2312yes—
119#66950C2×C4132yescomplemented
120#66946—28no—
121#66945—28no—
122C4⋊C4×D11—28no—
123#66940—28no—
124#66940—28no—
125#66940—28no—
126#66939C2×C4132yescomplemented
127#66930—216no—
128#66928C2×C4116yescomplemented
129#66922C2×C4116yescomplemented
130C4×Dic22—28no—
131C4×Dic22—28no—
132C11×#95C2318yes—
133C11⋊#95C2314yes—
134C11⋊#95C2314yes—
135C11⋊#95C2314yes—
136C11⋊#95C2318yes—
137C11⋊#95C2318yes—
138C11⋊#95C2314yes—
139#34276—111nomaximal, Sylow
140C24×C11C2411yescharacteristic
141C23×D11C2412yes—
142C22×C4×C11—24no—
143C22×C4×C11—44no—
144C22×C4×C11C22×C414yes—
145C22×C4×C11C2×D414yes—
146C22×C4×C11#4114yes—
147C22×C4×C11C2414yes—
148C22×C4×C11C2412yes—
149C22×C4×C11C2412yes—
150C22×C4×C11C2414yes—
151C22×C4×C11C2411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C2×C22⋊D11—24no—
154C2×C22⋊D11—24no—
155C2×C22⋊D11C22×C418yes—
156C22×Dic11—24no—
157C22×Dic11—24no—
158C22×Dic11—24no—
159C22×Dic11—24no—
160C22×Dic11—42no—
161C22×Dic11C22×C418yes—
162C22×Dic11C2412yes—
163C22×Dic11C2412yes—
164C22×Dic11C2414yes—
165C22×Dic11C2412yes—
166C22×Dic11C2412yes—
167C22×Dic11C2412yes—
168#4339—232no—
169C2×D44—22no—
170C2×D44—22no—
171C2×D44C22×C414yes—
172C2×C4×D11—28no—
173C2×C4×D11—24no—
174C2×C4×D11—24no—
175C2×C4×D11—48no—
176C2×C4×D11C22×C418yes—
177C2×Dic22—232no—
178C2×Dic22—24no—
179C2×Dic22—24no—
180C2×Dic22—22no—
181C2×Dic22—24no—
182C2×Dic22—24no—
183C2×Dic22—22no—
184C2×Dic22C22×C414yes—
185C2×Dic22C22×C418yes—
186C2×Dic22C22×C418yes—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—24no—
190C11×C4⋊C4—24no—
191C11×C4⋊C4—48no—
192C11×C4⋊C4C22×C418yes—
193C11×C22⋊C4—24no—
194C11×C22⋊C4C22×C418yes—
195C42×C11—24no—
196C42×C11C22×C418yes—
197C22⋊Dic11C2×D418yes—
198(C2×D11)⋊C4—28no—
199(C2×D11)⋊C4—28no—
200(C2×D11)⋊C4—44no—
201(C2×D11)⋊C4C22×C4132yes—
202C4⋊Dic11C22×C4132yes—
203C4⋊Dic11C2×D414yes—
204C4⋊Dic11C2×D414yes—
205Dic11⋊C4—28no—
206Dic11⋊C4—28no—
207Dic11⋊C4—28no—
208C4×Dic11—28no—
209C4×Dic11—28no—
210C4×Dic11—28no—
211C4×Dic11—28no—
212C4×Dic11—22no—
213C4×Dic11—22no—
214C4×Dic11—24no—
215C4×Dic11—44no—
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#2317D1111yescharacteristic, complemented
226C4×C4⋊Q8—112no—
227C4×#124—112no—
228#2297—111no—
229C2×#391—111no—
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—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—28no—
250C2×C4×C11—84no—
251C2×C4×C11C4×D4116yes—
252C2×C4×C11C23×C418yes—
253C2×C4×C11C23×C412yes—
254C2×C4×C11C23×C412yes—
255C2×C4×C11C22×D412yes—
256C2×C4×C11C22×D412yes—
257C2×C4×C11C2×#4112yes—
258C2×C4×C11C2×#4112yes—
259C22⋊D11—216no—
260C2×Dic11—216no—
261C2×Dic11—24no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—24no—
265C2×Dic11—22no—
266C2×Dic11—24no—
267C2×Dic11—22no—
268C2×Dic11—24no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—48no—
273C2×Dic11C23×C414yes—
274C2×Dic11C23×C418yes—
275C2×Dic11C22×D414yes—
276C2×Dic11C22×D414yes—
277C2×Dic112−1+414yes—
278D44—28no—
279C4×D11—216no—
280C4×D11—88no—
281Dic22—216no—
282Dic22—216no—
283Dic22—28no—
284C22×#41—111no—
285C23×Q8—111no—
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—112no—
302C2×#117—114no—
303C2×#117C2×D1111yescharacteristic
304C2×#117C2×D1111yescharacteristic
305C22×C4⋊C4—112no—
306C22×C4⋊C4C2×D1111yescharacteristic
307C22×C42—111no—
308#391—111no—
309#391—112no—
310#391—112no—
311#391—111no—
312#391—114no—
313#390—111no—
314#390—111no—
315#389—118no—
316#389C2×D1114yes—
317#388—118no—
318#388—118no—
319#387—118no—
320#387—118no—
321#386—114no—
322#385—118no—
323#385C2×D1114yes—
324#384C2×D1112yes—
325#382C2×D1112yes—
326C4×C4⋊C4—118no—
327C4×C4⋊C4—112no—
328C4×C4⋊C4—112no—
329C4×C22⋊C4—114no—
330C4×C22⋊C4—114no—
331C4×C22⋊C4—118no—
332#376—112no—
333C2×#95—114no—
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—42no—
352C4×C11—42no—
353C4×C11—44no—
354C4×C11C2×C4×D414yes—
355C4×C11C2×C4×D414yes—
356Dic11—28no—
357Dic11—24no—
358Dic11—24no—
359Dic11—24no—
360Dic11—24no—
361Dic11—42no—
362C2×#41—118no—
363C2×#41—224no—
364C2×#41—224no—
365C22×Q8—118no—
366C22×Q8—112no—
367C22×Q8—112no—
368C22×Q8—111no—
369C22×Q8—224no—
370C22×Q8—224no—
371C22×D4—112no—
372C22×D4—111no—
373C23×C4—112no—
374C23×C4—112no—
375C23×C4—112no—
376C23×C4—114no—
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—24no—
391#117—118no—
392#117—2216no—
393#117—228no—
394#117C4×D1118yescomplemented
395C2×C4⋊C4—24no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—118no—
399C2×C4⋊C4—114no—
400C2×C4⋊C4—114no—
401C2×C4⋊C4—114no—
402C2×C4⋊C4—228no—
403C2×C4⋊C4C22×D1112yes—
404C2×C4⋊C4C22×D1112yes—
405C2×C4⋊C4C22×D1111yescharacteristic
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C4⋊C4C22×D1118yes—
408C2×C4⋊C4C22×D1112yes—
409C2×C22⋊C4—112no—
410C2×C22⋊C4—118no—
411C2×C22⋊C4—114no—
412C2×C22⋊C4—114no—
413C2×C22⋊C4—114no—
414C2×C22⋊C4C22×D1112yes—
415C2×C22⋊C4C22×D1112yes—
416C2×C42—112no—
417C2×C42—114no—
418C2×C42—114no—
419C2×C42—114no—
420C2×C42—111no—
421C2×C42—114no—
422C2×C42—111no—
423C2×C42—112no—
424C2×C42—114no—
425C2×C42—224no—
426C2×C42C22×D1112yes—
427C2×C42C22×D1112yes—
428#95—118no—
429#95—118no—
430#95—114no—
431#95—114no—
432#95—114no—
433#95—114no—
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—118no—
446C2×Q8—118no—
447C2×Q8—114no—
448C2×Q8—2232no—
449C2×Q8—224no—
450C2×Q8—224no—
451C2×Q8—222no—
452C2×Q8—224no—
453C2×Q8—224no—
454C2×Q8—222no—
455C2×D4—118no—
456C2×D4—114no—
457C2×D4—224no—
458C2×D4—224no—
459C2×D4—222no—
460C2×D4—222no—
461C22×C4—24no—
462C22×C4—44no—
463C22×C4—118no—
464C22×C4—112no—
465C22×C4—114no—
466C22×C4—112no—
467C22×C4—112no—
468C22×C4—112no—
469C22×C4—118no—
470C22×C4—112no—
471C22×C4—228no—
472C22×C4—224no—
473C22×C4—224no—
474C22×C4—224no—
475C22×C4—224no—
476C22×C4—224no—
477C22×C4—224no—
478C22×C4—448no—
479C22×C4—442no—
480C22×C4C2×C4×D1114yes—
481C22×C4D4×D1114yes—
482C22×C4#434314yes—
483C22×C4C23×D1114yes—
484C22×C4C23×D1112yes—
485C22×C4C23×D1112yes—
486C22×C4C23×D1114yes—
487C22×C4C23×D1111yescharacteristic
488C22×C4C23×D1111yescharacteristic
489C4⋊C4—24no—
490C4⋊C4—24no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—48no—
494C4⋊C4—1132no—
495C4⋊C4—114no—
496C4⋊C4—114no—
497C4⋊C4—228no—
498C4⋊C4—228no—
499C4⋊C4—228no—
500C4⋊C4C2×C4×D1118yes—
501C22⋊C4—24no—
502C22⋊C4—118no—
503C22⋊C4—1132no—
504C22⋊C4—228no—
505C22⋊C4—228no—
506C22⋊C4—444no—
507C22⋊C4C2×C4×D1118yes—
508C42—24no—
509C42—118no—
510C42—228no—
511C42—228no—
512C42—228no—
513C42—228no—
514C42—222no—
515C42—224no—
516C42—222no—
517C42—444no—
518C42C2×C4×D1118yes—
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×#434312yes—
530C23C24×D1111yescharacteristic
531Q8—2216no—
532Q8—2216no—
533Q8—228no—
534D4—2216no—
535D4—228no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—28no—
543C2×C4—24no—
544C2×C4—84no—
545C2×C4—118no—
546C2×C4—114no—
547C2×C4—114no—
548C2×C4—114no—
549C2×C4—114no—
550C2×C4—2216no—
551C2×C4—222no—
552C2×C4—224no—
553C2×C4—222no—
554C2×C4—222no—
555C2×C4—224no—
556C2×C4—222no—
557C2×C4—224no—
558C2×C4—224no—
559C2×C4—2216no—
560C2×C4—222no—
561C2×C4—222no—
562C2×C4—222no—
563C2×C4—448no—
564C2×C4—888no—
565C2×C4#66946116yes—
566C2×C4C22×C4×D1118yes—
567C2×C4C22×C4×D1112yes—
568C2×C4C22×C4×D1112yes—
569C2×C4C2×D4×D1112yes—
570C2×C4C2×D4×D1112yes—
571C2×C4C2×#434312yes—
572C2×C4C2×#434312yes—
573C22—24no—
574C22—22no—
575C22—22no—
576C22—24no—
577C22—224no—
578C22—228no—
579C22—444no—
580C22—442no—
581C22—442no—
582C22C2×#6694614yes—
583C22C23×C4×D1111yescharacteristic
584C22C22×D4×D1111yescharacteristic
585C22C22×#434311yescharacteristic
586C22#1062345512yes—
587C22D11×2−1+412yes—
588C4—28no—
589C4—42no—
590C4—44no—
591C4—42no—
592C4—224no—
593C4—224no—
594C4—224no—
595C4—224no—
596C4—228no—
597C4—442no—
598C4C2×#6694614yes—
599C4C2×#6694614yes—
600C2—24no—
601C2—444no—
602C2C22×#6694611yescharacteristic
603C2#1308182712yes—
604C2#1308237112yes—
605C2#1308239811yescharacteristic
606C2#1308240811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2317C2
socle, cosocleC23×C11C25
prime radicalC22×#4339C22
hypercenter#2317D11
hypocenterC11#34276
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2317

Complements

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

NH ≅ G/Ntype
3. C2×#10623047C2semidirect
4. #13071642C2semidirect
5. #13071620C2semidirect
6. #13071606C2semidirect
7. #13071333C2semidirect
8. #13071324C2semidirect
9. #13071183C2semidirect
10. #13071155C2semidirect
12. C2×#10622587C2semidirect
13. #117×Dic11C2semidirect
14. C11×#2317C2semidirect
23. #10623057C4semidirect
79. C22×Dic22C2×C4semidirect
84. C11×#117C2×C4semidirect
119. #66950C2×C4semidirect
126. #66939C2×C4semidirect
128. #66928C2×C4semidirect
129. #66922C2×C4semidirect
225. #2317D11semidirect
394. #117C4×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×#106230572
C2×#106230352
C2×#106230472
#130716422
#130716202
#130716062
#130713332
#130713242
#130711832
#130711552
#130711042
C2×#106225872
#117×Dic112
C11×#23172
#3427611