Finite Group Databasebeta

← #14914983

Subgroups — #14914983

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×#10623361C211yesmaximal, characteristic
2C2×#10623052C211yesmaximal, characteristic, complemented
3#13071683C214yesmaximal, complemented
4#13071678C214yesmaximal, complemented
5#13071593C218yesmaximal, complemented
6#13071309C214yesmaximal, complemented
7#13071208C211yesmaximal, characteristic, complemented
8C4×#66983C214yesmaximal, complemented
9#13071099C211yesmaximal, characteristic, complemented
10C2×#10622552C211yesmaximal, characteristic, complemented
11#13070972C211yesmaximal, characteristic, complemented
12C2×C4×C11×#41C211yesmaximal, characteristic, complemented
13C22×C11×#41C2211yescharacteristic
14C23×D44C2211yescharacteristic
15C4×C11×#41—28no—
16C2×C4×Q8×C11C2212yescomplemented
17C2×C4×D4×C11C2214yes—
18C2×C4×D4×C11C2212yescomplemented
19C2×C11×#117C2211yescharacteristic
20C2×C11×#117C2212yescomplemented
21C22×C42×C11C2211yescharacteristic
22C22×C42×C11C2212yescomplemented
23#10623361C4116yescomplemented
24C2×#67000C2212yes—
25C2×#66993C2212yes—
26C2×#66990C2214yes—
27C2×#66983C2214yes—
28C2×C4×C22⋊D11C2218yescomplemented
29C22×(C2×D11)⋊C4C2214yes—
30C2×#66979C2211yescharacteristic
31C2×#66979C2211yescharacteristic
32C22×C4⋊Dic11C2211yescharacteristic
33#10623052—28no—
34C2×#66946C2214yes—
35C2×C22⋊C4×D11C2214yes—
36C2×C4×D44C2214yes—
37#10622843C2212yescomplemented
38#10622834C2212yescomplemented
39#10622833C2214yes—
40#10622826C2218yescomplemented
41#10622825C2214yescomplemented
42#10622823C2214yes—
43#10622603C2218yescomplemented
44#10622602C2218yescomplemented
45C4⋊C4×Dic11C2214yescomplemented
46#10622570C2218yescomplemented
47#10622569C2218yescomplemented
48C22⋊C4×Dic11C2214yes—
49#10622553C2218yescomplemented
50#10622552C2212yes—
51#10622552C2214yes—
52#10622552C2212yes—
53C4×(C2×D11)⋊C4C2218yescomplemented
54C4×C4⋊Dic11C2214yescomplemented
55C4×Dic11⋊C4C2214yescomplemented
56#10622541C2212yescomplemented
57#10622541C2212yescomplemented
58C24×D11C2312yes—
59C2×C11×#41—24no—
60C2×C11×#41—24no—
61C2×C11×#41C2×C418yescomplemented
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11C2312yes—
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11C2312yes—
66C23×C4×C11C2314yes—
67C23×C4×C11C2312yes—
68C23×C4×C11C2311yescharacteristic
69C22×C22⋊D11C2318yes—
70C23×Dic11C2312yes—
71C22×D44—24no—
72C22×D44—24no—
73C22×D44C2×C418yescomplemented
74C22×D44C2312yes—
75C22×D44C2312yes—
76C22×C4×D11C2318yes—
77C4×Q8×C11—28no—
78C4×D4×C11—28no—
79C4×D4×C11—216no—
80C11×#117—28no—
81C11×#117D418yescomplemented
82C2×C11×C4⋊C4C2314yes—
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C22⋊C4C2314yes—
85C2×C11×C22⋊C4C2312yes—
86C2×C42×C11—24no—
87C2×C42×C11—28no—
88C2×C42×C11C2311yescharacteristic
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2312yes—
91C2×C42×C11C2314yes—
92C2×C42×C11C2312yes—
93C2×C22⋊Dic11C2312yes—
94C2×C22⋊Dic11C2318yes—
95C2×C22⋊Dic11C2312yes—
96#67000C2×C4116yescomplemented
97#66993C2×C4116yescomplemented
98#66990C2×C4132yescomplemented
99#66983C2×C4132yescomplemented
100C4×C22⋊D11—416no—
101C2×(C2×D11)⋊C4—48no—
102C2×(C2×D11)⋊C4C2318yes—
103C2×(C2×D11)⋊C4C2318yes—
104C2×(C2×D11)⋊C4C2318yes—
105C2×(C2×D11)⋊C4C2318yes—
106#66979—24no—
107#66979C2×C418yescomplemented
108C2×C4⋊Dic11—24no—
109C2×C4⋊Dic11C2312yes—
110C2×C4⋊Dic11C2312yes—
111C2×C4⋊Dic11C2312yes—
112C2×C4⋊Dic11C2312yes—
113C2×Dic11⋊C4C2314yes—
114C2×Dic11⋊C4C2314yes—
115C2×C4×Dic11C2312yes—
116C2×C4×Dic11C2318yes—
117C2×C4×Dic11C2312yes—
118#66946—216no—
119C22⋊C4×D11—216no—
120C4×D44—216no—
121C11⋊#95C2314yes—
122C11⋊#95C2314yes—
123C11⋊#95C2318yes—
124C11⋊#95C2318yes—
125#34269—111nomaximal, Sylow
126C24×C11C2412yes—
127C24×C11C2411yescharacteristic
128C23×D11—24no—
129C23×D11—24no—
130C23×D11—44no—
131C23×D11—44no—
132C23×D11C22×C418yes—
133C23×D11C2414yes—
134C11×#41—232no—
135C2×Q8×C11—22no—
136C2×Q8×C11—22no—
137C2×Q8×C11C22×C414yes—
138C2×D4×C11—24no—
139C2×D4×C11—24no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11C22×C418yes—
143C2×D4×C11C22×C414yes—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—28no—
148C22×C4×C11—24no—
149C22×C4×C11—28no—
150C22×C4×C11—44no—
151C22×C4×C11—42no—
152C22×C4×C11C22×C418yes—
153C22×C4×C11C22×C414yes—
154C22×C4×C11C2×D414yes—
155C22×C4×C11#4114yes—
156C22×C4×C11C2412yes—
157C22×C4×C11C2412yes—
158C22×C4×C11C2414yes—
159C22×C4×C11C2412yes—
160C22×C4×C11C2411yescharacteristic
161C22×C4×C11C2411yescharacteristic
162C2×C22⋊D11—48no—
163C2×C22⋊D11—48no—
164C2×C22⋊D11C22×C4132yes—
165C22×Dic11—24no—
166C22×Dic11—44no—
167C22×Dic11C2414yes—
168C22×Dic11C2414yes—
169C22×Dic11C2414yes—
170C2×D44—232no—
171C2×D44—24no—
172C2×D44—24no—
173C2×D44—24no—
174C2×D44—24no—
175C2×D44C22×C418yes—
176C2×D44C22×C418yes—
177C2×C4×D11—216no—
178C2×C4×D11—48no—
179C2×C4×D11—48no—
180C11×C4⋊C4—28no—
181C11×C4⋊C4C2×D418yes—
182C11×C22⋊C4—28no—
183C11×C22⋊C4C2×D418yes—
184C42×C11—22no—
185C42×C11—22no—
186C42×C11—28no—
187C42×C11—24no—
188C42×C11C2×D418yes—
189C22⋊Dic11—24no—
190C22⋊Dic11—48no—
191C22⋊Dic11C22×C418yes—
192(C2×D11)⋊C4—216no—
193(C2×D11)⋊C4—216no—
194(C2×D11)⋊C4—48no—
195(C2×D11)⋊C4C22×C4132yes—
196C4⋊Dic11—24no—
197C4⋊Dic11—24no—
198C4⋊Dic11—24no—
199C4⋊Dic11C22×C418yes—
200Dic11⋊C4—28no—
201Dic11⋊C4—44no—
202C4×Dic11—24no—
203C4×Dic11—48no—
204C4×Dic11C22×C418yes—
205C2×#535—111no—
206C2×#518—111no—
207C2×C4×#41D1111yescharacteristic, complemented
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#2274—111no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—24no—
222C23×C11—24no—
223C23×C11C23×C414yes—
224C23×C11C23×C412yes—
225C23×C11C22×D412yes—
226C23×C11C2×#4112yes—
227C23×C11C2511yescharacteristic
228C22×D11—24no—
229C22×D11—24no—
230C22×D11—28no—
231C22×D11—28no—
232C22×D11—216no—
233C22×D11—416no—
234C22×D11—88no—
235C22×D11—84no—
236C22×D11—84no—
237C22×D11C23×C418yes—
238Q8×C11—28no—
239D4×C11—216no—
240D4×C11—28no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—22no—
247C2×C4×C11—216no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—416no—
252C2×C4×C11—48no—
253C2×C4×C11C4×D4116yescomplemented
254C2×C4×C11C23×C414yes—
255C2×C4×C11C23×C412yes—
256C2×C4×C11C23×C412yes—
257C2×C4×C11C22×D418yes—
258C2×C4×C11C22×D412yes—
259C2×C4×C11C22×D412yes—
260C2×C4×C11C2×#4112yes—
261C2×C4×C11C2×#4112yes—
262C2×C4×C11H(5,𝔽2)14yes—
263C22⋊D11—432no—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—28no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—84no—
272C2×Dic11C23×C418yes—
273D44—216no—
274D44—216no—
275C4×D11—816no—
276C22×#41C2×D1111yescharacteristic
277C23×D4—111no—
278#535—1116no—
279C2×#127—112no—
280C2×#124—112no—
281C2×#121—114no—
282C2×#120—114no—
283#518—228no—
284C4×#41—28no—
285C2×C4×Q8C2×D1112yescomplemented
286C2×C4×D4—118no—
287C2×C4×D4—114no—
288C2×C4×D4—114no—
289C2×C4×D4C2×D1114yes—
290C2×C4×D4C2×D1112yescomplemented
291C2×#117—111no—
292C2×#117—111no—
293C2×#117C2×D1111yescharacteristic
294C2×#117C2×D1112yescomplemented
295C22×C4⋊C4—111no—
296C22×C22⋊C4—114no—
297C22×C22⋊C4—114no—
298C22×C42C2×D1111yescharacteristic
299C22×C42C2×D1112yescomplemented
300#391—112no—
301#390—112no—
302#390—118no—
303#390—112no—
304#390—114no—
305#390—112no—
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⋊C4—114no—
318C4×C4⋊C4—114no—
319C4×C22⋊C4—114no—
320C4×C22⋊C4—118no—
321C22×C11—24no—
322C22×C11—24no—
323C22×C11—22no—
324C22×C11—22no—
325C22×C11—24no—
326C22×C11—28no—
327C22×C11—44no—
328C22×C11—42no—
329C22×C11—42no—
330C22×C11C2×C4×D414yes—
331C22×C11C24×C411yescharacteristic
332C22×C11C23×D411yescharacteristic
333C22×C11C22×#4111yescharacteristic
334C22×C11C2×H(5,𝔽2)12yes—
335C22×C11#58512yes—
336C2×D11—28no—
337C2×D11—216no—
338C2×D11—48no—
339C2×D11—44no—
340C2×D11—44no—
341C2×D11—816no—
342C4×C11—24no—
343C4×C11—24no—
344C4×C11—28no—
345C4×C11—42no—
346C4×C11C2×C4×D414yes—
347C4×C11C2×C4×D414yes—
348Dic11—28no—
349Dic11—44no—
350Dic11—44no—
351C25—112no—
352C2×#41—24no—
353C2×#41—24no—
354C2×#41C4×D1118yescomplemented
355C22×Q8C22×D1111yescharacteristic
356C22×D4—118no—
357C22×D4—118no—
358C22×D4—112no—
359C22×D4—112no—
360C22×D4—224no—
361C22×D4—224no—
362C22×D4C22×D1112yes—
363C22×D4C22×D1111yescharacteristic
364C23×C4—112no—
365C23×C4—118no—
366C23×C4C22×D1112yes—
367C23×C4C22×D1114yes—
368C23×C4C22×D1112yes—
369C23×C4C22×D1111yescharacteristic
370#127—1116no—
371#124—1116no—
372#121—1132no—
373#120—1132no—
374C4×Q8—28no—
375C4×D4—28no—
376C4×D4—216no—
377C4×D4—2216no—
378C4×D4—2216no—
379C4×D4—4416no—
380#117—28no—
381#117—118no—
382#117—224no—
383#117C22⋊D1118yescomplemented
384C2×C4⋊C4—112no—
385C2×C4⋊C4—112no—
386C2×C4⋊C4—112no—
387C2×C4⋊C4—112no—
388C2×C4⋊C4—114no—
389C2×C4⋊C4—114no—
390C2×C4⋊C4—224no—
391C2×C4⋊C4C22×D1114yes—
392C2×C4⋊C4C22×D1112yes—
393C2×C22⋊C4—112no—
394C2×C22⋊C4—118no—
395C2×C22⋊C4—112no—
396C2×C22⋊C4—118no—
397C2×C22⋊C4—118no—
398C2×C22⋊C4—118no—
399C2×C22⋊C4—118no—
400C2×C22⋊C4—2216no—
401C2×C22⋊C4—448no—
402C2×C22⋊C4C22×D1114yes—
403C2×C22⋊C4C22×D1112yes—
404C2×C42—24no—
405C2×C42—28no—
406C2×C42—112no—
407C2×C42—112no—
408C2×C42—118no—
409C2×C42C22×D1111yescharacteristic
410C2×C42C22×D1114yes—
411C2×C42C22×D1112yes—
412C2×C42C22×D1111yescharacteristic
413C2×C42C22×D1112yes—
414#95—114no—
415#95—118no—
416#95—118no—
417#95—114no—
418C2×C11—24no—
419C2×C11—44no—
420C2×C11C22×C4×D411yescharacteristic
421C2×C11C4×H(5,𝔽2)12yes—
422C2×C11#348812yes—
423C2×C11#350811yescharacteristic
424C2×C11#351011yescharacteristic
425D11—48no—
426C24—114no—
427C24—118no—
428C24—224no—
429C24—224no—
430C24—444no—
431C24—444no—
432C24C23×D1112yes—
433C24C23×D1111yescharacteristic
434#41—232no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8C2×C4×D1114yes—
438C2×D4—24no—
439C2×D4—24no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—1132no—
443C2×D4—118no—
444C2×D4—118no—
445C2×D4—2232no—
446C2×D4—224no—
447C2×D4—224no—
448C2×D4—224no—
449C2×D4—224no—
450C2×D4—448no—
451C2×D4—448no—
452C2×D4C2×C4×D1118yes—
453C2×D4C2×C4×D1114yes—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—28no—
459C22×C4—28no—
460C22×C4—44no—
461C22×C4—42no—
462C22×C4—114no—
463C22×C4—114no—
464C22×C4—114no—
465C22×C4—224no—
466C22×C4—2216no—
467C22×C4—448no—
468C22×C4—448no—
469C22×C4—444no—
470C22×C4C2×C4×D1118yes—
471C22×C4C2×C4×D1114yes—
472C22×C4#433914yes—
473C22×C4C2×C22⋊D1114yes—
474C22×C4C23×D1112yes—
475C22×C4C23×D1112yes—
476C22×C4C23×D1112yes—
477C22×C4C23×D1114yes—
478C22×C4C23×D1111yescharacteristic
479C22×C4C23×D1111yescharacteristic
480C4⋊C4—28no—
481C4⋊C4—118no—
482C4⋊C4—224no—
483C4⋊C4—224no—
484C4⋊C4—228no—
485C4⋊C4—224no—
486C4⋊C4—444no—
487C4⋊C4C2×C22⋊D1118yes—
488C22⋊C4—28no—
489C22⋊C4—118no—
490C22⋊C4—1132no—
491C22⋊C4—224no—
492C22⋊C4—2216no—
493C22⋊C4—2216no—
494C22⋊C4—448no—
495C22⋊C4—448no—
496C22⋊C4C2×C22⋊D1118yes—
497C42—22no—
498C42—22no—
499C42—28no—
500C42—24no—
501C42—118no—
502C42—224no—
503C42—448no—
504C42C2×C22⋊D1118yes—
505C11#3426911yescharacteristic, complemented, Sylow
506C23—22no—
507C23—22no—
508C23—22no—
509C23—24no—
510C23—24no—
511C23—22no—
512C23—118no—
513C23—224no—
514C23—228no—
515C23—228no—
516C23—224no—
517C23—2216no—
518C23—4416no—
519C23—884no—
520C23—884no—
521C23—888no—
522C23C22×C4×D1114yes—
523C23C22×C4×D1112yes—
524C23C2×#433912yes—
525C23C22×C22⋊D1112yes—
526C23C24×D1111yescharacteristic
527Q8—28no—
528D4—216no—
529D4—28no—
530D4—2216no—
531D4—2216no—
532D4—4432no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—22no—
536C2×C4—24no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—216no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—416no—
544C2×C4—48no—
545C2×C4—118no—
546C2×C4—224no—
547C2×C4—224no—
548C2×C4—224no—
549C2×C4—228no—
550C2×C4—224no—
551C2×C4—224no—
552C2×C4—224no—
553C2×C4—8816no—
554C2×C4—884no—
555C2×C4C4×C22⋊D11116yescomplemented
556C2×C4C22×C4×D1114yes—
557C2×C4C22×C4×D1112yes—
558C2×C4C22×C4×D1112yes—
559C2×C4C2×#433912yes—
560C2×C4C2×#433912yes—
561C2×C4#6704214yes—
562C2×C4C22×C22⋊D1118yes—
563C2×C4C22×C22⋊D1112yes—
564C2×C4C22×C22⋊D1112yes—
565C22—22no—
566C22—22no—
567C22—24no—
568C22—24no—
569C22—24no—
570C22—28no—
571C22—42no—
572C22—42no—
573C22—44no—
574C22—228no—
575C22—2216no—
576C22—444no—
577C22—444no—
578C22—448no—
579C22—8816no—
580C22C2×C4×C22⋊D1114yes—
581C22C23×C4×D1111yescharacteristic
582C22C22×#433911yescharacteristic
583C22C2×#6704212yes—
584C22#1062345312yes—
585C22C23×C22⋊D1111yescharacteristic
586C4—24no—
587C4—28no—
588C4—24no—
589C4—42no—
590C4—228no—
591C4—444no—
592C4—444no—
593C4C2×C4×C22⋊D1114yes—
594C4C2×C4×C22⋊D1114yes—
595C2—24no—
596C2—44no—
597C2—448no—
598C2C22×C4×C22⋊D1111yescharacteristic
599C2C4×#6704212yes—
600C2#1308228512yes—
601C2#1308249211yescharacteristic
602C2#1308251211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC2×C4×C11×#41C2
socle, cosocleC23×C11C25
prime radicalC2×#10623361C2
hypercenterC2×C4×#41D11
hypocenterC11#34269
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
2. C2×#10623052C2semidirect
3. #13071683C2semidirect
4. #13071678C2semidirect
5. #13071593C2semidirect
6. #13071309C2semidirect
7. #13071208C2semidirect
8. C4×#66983C2semidirect
9. #13071099C2semidirect
10. C2×#10622552C2semidirect
11. #13070972C2semidirect
12. C2×C4×C11×#41C2semidirect
16. C2×C4×Q8×C11C22semidirect
18. C2×C4×D4×C11C22semidirect
20. C2×C11×#117C22semidirect
22. C22×C42×C11C22semidirect
23. #10623361C4semidirect
28. C2×C4×C22⋊D11C22semidirect
37. #10622843C22semidirect
38. #10622834C22semidirect
40. #10622826C22semidirect
41. #10622825C22semidirect
43. #10622603C22semidirect
44. #10622602C22semidirect
45. C4⋊C4×Dic11C22semidirect
46. #10622570C22semidirect
47. #10622569C22semidirect
49. #10622553C22semidirect
53. C4×(C2×D11)⋊C4C22semidirect
54. C4×C4⋊Dic11C22semidirect
55. C4×Dic11⋊C4C22semidirect
56. #10622541C22semidirect
57. #10622541C22semidirect
61. C2×C11×#41C2×C4semidirect
73. C22×D44C2×C4semidirect
81. C11×#117D4semidirect
96. #67000C2×C4semidirect
97. #66993C2×C4semidirect
98. #66990C2×C4semidirect
99. #66983C2×C4semidirect
107. #66979C2×C4semidirect
207. C2×C4×#41D11semidirect
253. C2×C4×C11C4×D4semidirect
285. C2×C4×Q8C2×D11semidirect
290. C2×C4×D4C2×D11semidirect
294. C2×#117C2×D11semidirect
299. C22×C42C2×D11semidirect
354. C2×#41C4×D11semidirect
383. #117C22⋊D11semidirect
505. C11#34269semidirect
555. C2×C4C4×C22⋊D11semidirect

Maximal subgroups

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

subgroupindex
C2×#106233612
C2×#106230522
#130716832
#130716782
#130715932
#130713092
#130712082
C4×#669832
#130710992
C2×#106225522
#130709722
C2×C4×C11×#412
#3426911