Finite Group Databasebeta

← #14914984

Subgroups — #14914984

Order 2816.

3426 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623056C211yesmaximal, characteristic
2C2×#10623052C211yesmaximal, characteristic, complemented
3C2×#10623053C211yesmaximal, characteristic, complemented
4#13071687C214yesmaximal, complemented
5#13071680C214yesmaximal, complemented
6#13071598C218yesmaximal, complemented
7#13071310C214yesmaximal, complemented
8#13071209C211yesmaximal, characteristic, complemented
9C4×#66948C214yesmaximal, complemented
10#13071100C211yesmaximal, characteristic, complemented
11C2×#10622601C211yesmaximal, characteristic, complemented
12C11×#2274C211yesmaximal, characteristic, complemented
13C22×#4339C2211yescharacteristic
14C23×D44C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×(C2×D11)⋊C4C2214yes—
19C2×#66979C2211yescharacteristic
20C22×C4×Dic11C2211yescharacteristic
21#10623056C4116yescomplemented
22#10623053—28no—
23#10623052—28no—
24C2×#66948C2214yes—
25C2×#66946C2214yes—
26C2×#66946C2212yescomplemented
27C2×#66940C2212yescomplemented
28C2×#66935C2214yes—
29C2×(C22⋊D11)⋊C4C2214yes—
30C2×C22⋊C4×D11C2214yes—
31C2×#66928C2212yes—
32C2×#66927C2212yes—
33C2×C4×D44C2214yes—
34C2×C4×D44C2218yescomplemented
35C2×#66925C2212yescomplemented
36C2×C42×D11C2212yescomplemented
37C4×C11×C4⋊C4C2214yescomplemented
38C4×C11×C4⋊C4C2214yescomplemented
39C4×C11×C22⋊C4C2214yes—
40#10622826C2214yes—
41#10622601C2212yes—
42#10622601C2214yes—
43#10622601C2212yes—
44#10622601C2212yescomplemented
45#10622600C2214yescomplemented
46#10622598C2212yescomplemented
47#10622598C2212yescomplemented
48#10622587C2212yescomplemented
49#10622563C2214yes—
50#10622553C2218yescomplemented
51#10622552C2218yescomplemented
52C4×(C2×D11)⋊C4C2218yescomplemented
53C4×C4⋊Dic11C2214yescomplemented
54#10622283C2218yescomplemented
55#10622281C2218yescomplemented
56#10622278C2218yescomplemented
57#10622278C2218yescomplemented
58C24×D11C2312yes—
59C23×C4×C11C2312yes—
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11C2312yes—
62C23×Dic11C2312yes—
63C2×#4339—24no—
64C2×#4339—24no—
65C2×#4339C2×C418yescomplemented
66C22×D44—24no—
67C22×D44—24no—
68C22×D44C2×C418yescomplemented
69C22×D44C2312yes—
70C22×D44C2311yescharacteristic
71C22×D44C2312yes—
72C22×D44C2318yes—
73C22×C4×D11C2314yes—
74C22×C4×D11C2312yes—
75C22×C4×D11C2318yes—
76C22×Dic22C2311yescharacteristic
77C11×#117C2×C418yescomplemented
78C11×#117D418yescomplemented
79C2×C11×C4⋊C4—24no—
80C2×C11×C4⋊C4C2312yes—
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C22⋊C4C2312yes—
85C2×C11×C22⋊C4C2312yes—
86C2×C42×C11C2318yes—
87C2×C42×C11C2312yes—
88C2×C42×C11C2312yes—
89C2×C22⋊Dic11C2312yes—
90C2×(C2×D11)⋊C4—48no—
91C2×(C2×D11)⋊C4C2314yes—
92C2×(C2×D11)⋊C4C2318yes—
93C2×(C2×D11)⋊C4C2318yes—
94C2×(C2×D11)⋊C4C2318yes—
95C2×(C2×D11)⋊C4C2318yes—
96C2×(C2×D11)⋊C4C2318yes—
97#66979—24no—
98C2×C4⋊Dic11C2312yes—
99C2×C4⋊Dic11C2314yes—
100C2×C4⋊Dic11C2314yes—
101C2×Dic11⋊C4C2314yes—
102C2×C4×Dic11—24no—
103C2×C4×Dic11C2311yescharacteristic
104C2×C4×Dic11C2314yes—
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2312yes—
107C2×C4×Dic11C2312yes—
108#66948C2×C4132yescomplemented
109#66946—216no—
110#66946—28no—
111#66940—28no—
112#66935C2×C4132yescomplemented
113(C22⋊D11)⋊C4—216no—
114C22⋊C4×D11—216no—
115#66928C2×C4116yescomplemented
116#66927C2×C4116yescomplemented
117C4×D44—216no—
118C4×D44—416no—
119#66925—28no—
120C42×D11—28no—
121C11×#95C2318yes—
122C11⋊#95C2314yes—
123C11⋊#95C2314yes—
124C11⋊#95C2318yes—
125#34269—111nomaximal, Sylow
126C24×C11C2411yescharacteristic
127C23×D11—24no—
128C23×D11—24no—
129C23×D11—44no—
130C23×D11—44no—
131C23×D11C22×C418yes—
132C23×D11C2414yes—
133C23×D11C2412yes—
134C22×C4×C11—24no—
135C22×C4×C11—44no—
136C22×C4×C11C22×C414yes—
137C22×C4×C11C2×D414yes—
138C22×C4×C11#4114yes—
139C22×C4×C11C2414yes—
140C22×C4×C11C2414yes—
141C22×C4×C11C2414yes—
142C22×C4×C11C2411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C2×C22⋊D11—24no—
145C2×C22⋊D11—24no—
146C2×C22⋊D11C22×C418yes—
147C22×Dic11—24no—
148C22×Dic11—24no—
149C22×Dic11—42no—
150C22×Dic11C2414yes—
151C22×Dic11C2412yes—
152C22×Dic11C2412yes—
153C22×Dic11C2412yes—
154#4339—232no—
155C2×D44—232no—
156C2×D44—24no—
157C2×D44—24no—
158C2×D44—22no—
159C2×D44—24no—
160C2×D44—24no—
161C2×D44—22no—
162C2×D44—48no—
163C2×D44—48no—
164C2×D44C22×C414yes—
165C2×D44C22×C418yes—
166C2×D44C22×C418yes—
167C2×D44C22×C4132yes—
168C2×C4×D11—28no—
169C2×C4×D11—24no—
170C2×C4×D11—28no—
171C2×C4×D11—216no—
172C2×C4×D11—24no—
173C2×C4×D11—44no—
174C2×C4×D11—48no—
175C2×C4×D11—48no—
176C2×C4×D11C22×C418yes—
177C2×Dic22—22no—
178C2×Dic22—22no—
179C2×Dic22C22×C414yes—
180C11×C4⋊C4—24no—
181C11×C4⋊C4—24no—
182C11×C4⋊C4C22×C418yes—
183C11×C4⋊C4C2×D418yes—
184C11×C22⋊C4C22×C418yes—
185C11×C22⋊C4C2×D418yes—
186C42×C11—48no—
187C42×C11C22×C418yes—
188C42×C11C2×D418yes—
189C22⋊Dic11—24no—
190(C2×D11)⋊C4—216no—
191(C2×D11)⋊C4—28no—
192(C2×D11)⋊C4—216no—
193(C2×D11)⋊C4—48no—
194(C2×D11)⋊C4—48no—
195(C2×D11)⋊C4C22×C4132yes—
196C4⋊Dic11—28no—
197C4⋊Dic11—24no—
198C4⋊Dic11—44no—
199Dic11⋊C4—28no—
200C4×Dic11—22no—
201C4×Dic11—28no—
202C4×Dic11—22no—
203C4×Dic11—24no—
204C4×Dic11—24no—
205C2×#535—111no—
206C2×#518—111no—
207C2×C4×#41—111no—
208#2367—114no—
209#2366—114no—
210#2358—118no—
211#2324—114no—
212#2311—111no—
213C4×#121—114no—
214#2296—111no—
215C2×#390—111no—
216#2274D1111yescharacteristic, complemented
217C23×C11—22no—
218C23×C11—22no—
219C23×C11C23×C412yes—
220C23×C11C22×D412yes—
221C23×C11C2×#4112yes—
222C23×C11C2511yescharacteristic
223C22×D11—22no—
224C22×D11—24no—
225C22×D11—22no—
226C22×D11—24no—
227C22×D11—28no—
228C22×D11—24no—
229C22×D11—24no—
230C22×D11—28no—
231C22×D11—216no—
232C22×D11—416no—
233C22×D11—88no—
234C22×D11—84no—
235C22×D11—84no—
236C22×D11C23×C418yes—
237C22×D11C23×C414yes—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—28no—
244C2×C4×C11—84no—
245C2×C4×C11C4×D4116yescomplemented
246C2×C4×C11C23×C418yes—
247C2×C4×C11C23×C412yes—
248C2×C4×C11C23×C412yes—
249C2×C4×C11C22×D418yes—
250C2×C4×C11C22×D412yes—
251C2×C4×C11C22×D412yes—
252C2×C4×C11C2×#4112yes—
253C2×C4×C11C2×#4112yes—
254C22⋊D11—216no—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—24no—
265C2×Dic11—48no—
266C2×Dic11C23×C414yes—
267C2×Dic11H(5,𝔽2)14yes—
268D44—216no—
269D44—216no—
270D44—28no—
271D44—432no—
272C4×D11—216no—
273C4×D11—416no—
274C4×D11—816no—
275Dic22—28no—
276C22×#41—111no—
277C23×D4—111no—
278#535—1116no—
279C2×#127—112no—
280C2×#124—112no—
281C2×#121—114no—
282C2×#120—114no—
283#518—228no—
284C4×#41—228no—
285C2×C4×Q8—112no—
286C2×C4×D4—114no—
287C2×C4×D4—112no—
288C2×C4×D4—114no—
289C2×C4×D4—114no—
290C2×C4×D4—118no—
291C2×#117—111no—
292C2×#117—112no—
293C2×#117C2×D1111yescharacteristic
294C2×#117C2×D1111yescharacteristic
295C22×C4⋊C4C2×D1111yescharacteristic
296C22×C22⋊C4—114no—
297C22×C22⋊C4—114no—
298C22×C42—111no—
299C22×C42—112no—
300#391—112no—
301#390—112no—
302#390—112no—
303#390—114no—
304#390—112no—
305#390—118no—
306#389—112no—
307#389—112no—
308#388—118no—
309#388—118no—
310#386—114no—
311#386—118no—
312#386—118no—
313#385—114no—
314#385—118no—
315#380—114no—
316C4×C4⋊C4—114no—
317C4×C4⋊C4C2×D1114yescomplemented
318C4×C4⋊C4C2×D1114yescomplemented
319C4×C22⋊C4—118no—
320C4×C22⋊C4C2×D1114yes—
321C22×C11—24no—
322C22×C11—24no—
323C22×C11—22no—
324C22×C11—22no—
325C22×C11C2×C4×D414yes—
326C22×C11C24×C411yescharacteristic
327C22×C11C23×D411yescharacteristic
328C22×C11C22×#4111yescharacteristic
329C22×C11C2×H(5,𝔽2)12yes—
330C22×C11#58512yes—
331C2×D11—28no—
332C2×D11—24no—
333C2×D11—216no—
334C2×D11—28no—
335C2×D11—48no—
336C2×D11—44no—
337C2×D11—42no—
338C2×D11—44no—
339C2×D11—42no—
340C2×D11—44no—
341C2×D11—816no—
342C4×C11—28no—
343C4×C11—28no—
344C4×C11—44no—
345C4×C11C2×C4×D414yes—
346C4×C11C2×C4×D414yes—
347Dic11—24no—
348Dic11—24no—
349Dic11—44no—
350Dic11—42no—
351C25—112no—
352C2×#41—118no—
353C2×#41—224no—
354C2×#41—224no—
355C22×Q8—111no—
356C22×D4—112no—
357C22×D4—118no—
358C22×D4—112no—
359C22×D4—112no—
360C22×D4—111no—
361C22×D4—118no—
362C22×D4—224no—
363C22×D4—224no—
364C23×C4—112no—
365C23×C4—112no—
366C23×C4—114no—
367C23×C4—118no—
368C23×C4C22×D1112yes—
369C23×C4C22×D1111yescharacteristic
370#127—1116no—
371#124—1116no—
372#121—1132no—
373#120—1132no—
374C4×Q8—228no—
375C4×D4—228no—
376C4×D4—2216no—
377C4×D4—2216no—
378C4×D4—2216no—
379C4×D4—4416no—
380#117—224no—
381#117—228no—
382#117C4×D1118yescomplemented
383#117D4418yescomplemented
384C2×C4⋊C4—24no—
385C2×C4⋊C4—112no—
386C2×C4⋊C4—114no—
387C2×C4⋊C4—114no—
388C2×C4⋊C4—114no—
389C2×C4⋊C4C22×D1112yes—
390C2×C4⋊C4C22×D1112yes—
391C2×C4⋊C4C22×D1112yes—
392C2×C4⋊C4C22×D1112yes—
393C2×C22⋊C4—118no—
394C2×C22⋊C4—112no—
395C2×C22⋊C4—118no—
396C2×C22⋊C4—118no—
397C2×C22⋊C4—114no—
398C2×C22⋊C4—118no—
399C2×C22⋊C4—118no—
400C2×C22⋊C4—2216no—
401C2×C22⋊C4—448no—
402C2×C22⋊C4C22×D1112yes—
403C2×C22⋊C4C22×D1112yes—
404C2×C42—111no—
405C2×C42—112no—
406C2×C42—114no—
407C2×C42—112no—
408C2×C42—111no—
409C2×C42—224no—
410C2×C42—228no—
411C2×C42C22×D1118yes—
412C2×C42C22×D1112yes—
413C2×C42C22×D1112yes—
414#95—114no—
415#95—118no—
416#95—114no—
417#95C22×D1118yes—
418C2×C11—24no—
419C2×C11C22×C4×D411yescharacteristic
420C2×C11C4×H(5,𝔽2)12yes—
421C2×C11#348812yes—
422C2×C11#350811yescharacteristic
423C2×C11#351011yescharacteristic
424D11—44no—
425D11—48no—
426C24—114no—
427C24—112no—
428C24—118no—
429C24—224no—
430C24—224no—
431C24—444no—
432C24—444no—
433C24C23×D1111yescharacteristic
434#41—2232no—
435C2×Q8—114no—
436C2×Q8—222no—
437C2×Q8—222no—
438C2×D4—118no—
439C2×D4—118no—
440C2×D4—118no—
441C2×D4—114no—
442C2×D4—1132no—
443C2×D4—224no—
444C2×D4—224no—
445C2×D4—2232no—
446C2×D4—224no—
447C2×D4—224no—
448C2×D4—222no—
449C2×D4—224no—
450C2×D4—224no—
451C2×D4—222no—
452C2×D4—448no—
453C2×D4—448no—
454C22×C4—24no—
455C22×C4—44no—
456C22×C4—112no—
457C22×C4—112no—
458C22×C4—118no—
459C22×C4—114no—
460C22×C4—112no—
461C22×C4—228no—
462C22×C4—224no—
463C22×C4—224no—
464C22×C4—224no—
465C22×C4—224no—
466C22×C4—228no—
467C22×C4—2216no—
468C22×C4—444no—
469C22×C4—448no—
470C22×C4—448no—
471C22×C4—442no—
472C22×C4C2×C4×D1114yes—
473C22×C4C2×D4414yes—
474C22×C4#433914yes—
475C22×C4C23×D1114yes—
476C22×C4C23×D1114yes—
477C22×C4C23×D1114yes—
478C22×C4C23×D1111yescharacteristic
479C22×C4C23×D1111yescharacteristic
480C4⋊C4—24no—
481C4⋊C4—24no—
482C4⋊C4—228no—
483C4⋊C4—224no—
484C4⋊C4—228no—
485C4⋊C4—444no—
486C4⋊C4C2×C4×D1118yes—
487C4⋊C4C2×D4418yes—
488C22⋊C4—1132no—
489C22⋊C4—2216no—
490C22⋊C4—224no—
491C22⋊C4—2216no—
492C22⋊C4—228no—
493C22⋊C4—448no—
494C22⋊C4—448no—
495C22⋊C4C2×C4×D1118yes—
496C22⋊C4C2×D4418yes—
497C42—48no—
498C42—222no—
499C42—222no—
500C42—228no—
501C42—224no—
502C42—224no—
503C42C2×C4×D1118yes—
504C42C2×D4418yes—
505C11#3426911yescharacteristic, complemented, Sylow
506C23—22no—
507C23—22no—
508C23—118no—
509C23—114no—
510C23—222no—
511C23—224no—
512C23—222no—
513C23—224no—
514C23—228no—
515C23—224no—
516C23—224no—
517C23—228no—
518C23—2216no—
519C23—4416no—
520C23—884no—
521C23—884no—
522C23—888no—
523C23C22×C4×D1112yes—
524C23C22×D4412yes—
525C23C2×#433912yes—
526C23C24×D1111yescharacteristic
527Q8—228no—
528D4—2216no—
529D4—2216no—
530D4—2216no—
531D4—228no—
532D4—4432no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—28no—
539C2×C4—84no—
540C2×C4—114no—
541C2×C4—114no—
542C2×C4—222no—
543C2×C4—222no—
544C2×C4—222no—
545C2×C4—222no—
546C2×C4—2216no—
547C2×C4—222no—
548C2×C4—224no—
549C2×C4—222no—
550C2×C4—224no—
551C2×C4—222no—
552C2×C4—224no—
553C2×C4—4416no—
554C2×C4—448no—
555C2×C4—8816no—
556C2×C4C4×D44116yescomplemented
557C2×C4C22×C4×D1118yes—
558C2×C4C22×C4×D1112yes—
559C2×C4C22×C4×D1112yes—
560C2×C4C22×D4418yes—
561C2×C4C22×D4412yes—
562C2×C4C22×D4412yes—
563C2×C4C2×#433912yes—
564C2×C4C2×#433912yes—
565C22—22no—
566C22—22no—
567C22—24no—
568C22—24no—
569C22—224no—
570C22—228no—
571C22—228no—
572C22—2216no—
573C22—444no—
574C22—442no—
575C22—444no—
576C22—442no—
577C22—444no—
578C22—448no—
579C22—8816no—
580C22C2×C4×D4414yes—
581C22C23×C4×D1111yescharacteristic
582C22C23×D4411yescharacteristic
583C22C22×#433911yescharacteristic
584C22D11×H(5,𝔽2)12yes—
585C22#1062345712yes—
586C4—28no—
587C4—28no—
588C4—44no—
589C4—224no—
590C4—224no—
591C4—442no—
592C4—444no—
593C4C2×C4×D4414yes—
594C4C2×C4×D4414yes—
595C2—24no—
596C2—448no—
597C2—444no—
598C2C22×C4×D4411yescharacteristic
599C2#1308182212yes—
600C2#1308228612yes—
601C2#1308248711yescharacteristic
602C2#1308251311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2274C2
socle, cosocleC23×C11C25
prime radicalC2×#10623056C2
hypercenter#2274D11
hypocenterC11#34269
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2274

Complements

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

NH ≅ G/Ntype
2. C2×#10623052C2semidirect
3. C2×#10623053C2semidirect
4. #13071687C2semidirect
5. #13071680C2semidirect
6. #13071598C2semidirect
7. #13071310C2semidirect
8. #13071209C2semidirect
9. C4×#66948C2semidirect
10. #13071100C2semidirect
11. C2×#10622601C2semidirect
12. C11×#2274C2semidirect
21. #10623056C4semidirect
26. C2×#66946C22semidirect
27. C2×#66940C22semidirect
34. C2×C4×D44C22semidirect
35. C2×#66925C22semidirect
36. C2×C42×D11C22semidirect
37. C4×C11×C4⋊C4C22semidirect
38. C4×C11×C4⋊C4C22semidirect
44. #10622601C22semidirect
45. #10622600C22semidirect
46. #10622598C22semidirect
47. #10622598C22semidirect
48. #10622587C22semidirect
50. #10622553C22semidirect
51. #10622552C22semidirect
52. C4×(C2×D11)⋊C4C22semidirect
53. C4×C4⋊Dic11C22semidirect
54. #10622283C22semidirect
55. #10622281C22semidirect
56. #10622278C22semidirect
57. #10622278C22semidirect
65. C2×#4339C2×C4semidirect
68. C22×D44C2×C4semidirect
77. C11×#117C2×C4semidirect
78. C11×#117D4semidirect
108. #66948C2×C4semidirect
112. #66935C2×C4semidirect
115. #66928C2×C4semidirect
116. #66927C2×C4semidirect
216. #2274D11semidirect
245. C2×C4×C11C4×D4semidirect
317. C4×C4⋊C4C2×D11semidirect
318. C4×C4⋊C4C2×D11semidirect
382. #117C4×D11semidirect
383. #117D44semidirect
505. C11#34269semidirect
556. C2×C4C4×D44semidirect

Maximal subgroups

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

subgroupindex
C2×#106230562
C2×#106230522
C2×#106230532
#130716872
#130716802
#130715982
#130713102
#130712092
C4×#669482
#130711002
C2×#106226012
C11×#22742
#3426911