Finite Group Databasebeta

← #14914978

Subgroups — #14914978

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×#10623336C211yesmaximal, characteristic
2C2×#10623053C211yesmaximal, characteristic, complemented
3#13071689C214yesmaximal, complemented
4#13071678C214yesmaximal, complemented
5#13071595C218yesmaximal, complemented
6#13071303C214yesmaximal, complemented
7#13071204C211yesmaximal, characteristic, complemented
8C4×#66991C214yesmaximal, complemented
9#13071098C211yesmaximal, characteristic, complemented
10C2×#10622834C211yesmaximal, characteristic, complemented
11#13070972C211yesmaximal, characteristic, complemented
12C2×C11×#518C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C22×#4339C2211yescharacteristic
15C11×#518—28no—
16C2×C4×D4×C11C2214yes—
17C2×C4×D4×C11C2214yes—
18C2×C11×#117C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C22×C11×C22⋊C4C2214yes—
21C2×#67006C2214yes—
22C22×C22⋊Dic11C2214yes—
23#10623336C4116yescomplemented
24C2×#66993C2212yes—
25C2×#66991C2214yes—
26C2×#66989C2212yes—
27C2×C4×C22⋊D11C2218yescomplemented
28C2×#66979C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31#10623053—28no—
32C2×#66946C2212yescomplemented
33C2×#66940C2212yescomplemented
34C2×(C22⋊D11)⋊C4C2214yes—
35C2×#66925C2212yescomplemented
36C2×C42×D11C2212yescomplemented
37#10622834C2212yes—
38#10622834C2214yes—
39#10622834C2212yes—
40#10622826C2218yescomplemented
41#10622823C2218yescomplemented
42C4×C22⋊Dic11C2218yescomplemented
43#10622600C2214yescomplemented
44C4⋊C4×Dic11C2214yescomplemented
45#10622586C2212yescomplemented
46#10622586C2212yescomplemented
47#10622571C2214yes—
48#10622570C2218yescomplemented
49#10622569C2218yescomplemented
50#10622559C2214yes—
51#10622558C2218yescomplemented
52#10622557C2218yescomplemented
53C22⋊C4×Dic11C2214yes—
54#10622552C2212yescomplemented
55C4×C4⋊Dic11C2214yescomplemented
56C4×Dic11⋊C4C2214yescomplemented
57#10622542C2212yescomplemented
58C25×C11C2312yes—
59C22×D4×C11—24no—
60C22×D4×C11—24no—
61C22×D4×C11C2×C418yescomplemented
62C22×D4×C11C2312yes—
63C22×D4×C11C2312yes—
64C23×C4×C11C2318yes—
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11C2312yes—
67C22×C22⋊D11C2318yes—
68C23×Dic11C2312yes—
69C23×Dic11C2312yes—
70C2×#4339—24no—
71C2×#4339—24no—
72C2×#4339C2×C418yescomplemented
73C22×D44C2311yescharacteristic
74C22×C4×D11C2314yes—
75C22×C4×D11C2312yes—
76C22×Dic22C2311yescharacteristic
77C4×D4×C11—216no—
78C4×D4×C11—216no—
79C11×#117—24no—
80C11×#117D418yescomplemented
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C22⋊C4—216no—
84C2×C11×C22⋊C4C2318yes—
85C2×C11×C22⋊C4C2312yes—
86C2×C11×C22⋊C4C2312yes—
87C2×C42×C11C2312yes—
88C2×C42×C11C2312yes—
89#67006C2×C4132yescomplemented
90C2×C22⋊Dic11—48no—
91C2×C22⋊Dic11C2318yes—
92C2×C22⋊Dic11C2318yes—
93C2×C22⋊Dic11C2312yes—
94C2×C22⋊Dic11C2318yes—
95#66993C2×C4116yescomplemented
96#66991C2×C4132yescomplemented
97#66989C2×C4116yescomplemented
98C4×C22⋊D11—416no—
99C2×(C2×D11)⋊C4C2314yes—
100C2×(C2×D11)⋊C4C2318yes—
101#66979C2×C418yescomplemented
102C2×C4⋊Dic11—24no—
103C2×C4⋊Dic11C2312yes—
104C2×C4⋊Dic11C2312yes—
105C2×C4⋊Dic11C2312yes—
106C2×Dic11⋊C4C2314yes—
107C2×Dic11⋊C4C2314yes—
108C2×Dic11⋊C4C2314yes—
109C2×C4×Dic11—24no—
110C2×C4×Dic11C2311yescharacteristic
111C2×C4×Dic11C2314yes—
112C2×C4×Dic11C2311yescharacteristic
113C2×C4×Dic11C2312yes—
114C2×C4×Dic11C2318yes—
115C2×C4×Dic11C2312yes—
116#66946—28no—
117#66940—28no—
118(C22⋊D11)⋊C4—216no—
119#66925—28no—
120C42×D11—28no—
121C11⋊#95C2318yes—
122C11⋊#95C2314yes—
123C11⋊#95C2314yes—
124C11⋊#95C2318yes—
125#34269—111nomaximal, Sylow
126C24×C11—24no—
127C24×C11—24no—
128C24×C11—44no—
129C24×C11—44no—
130C24×C11C22×C418yes—
131C24×C11C2414yes—
132C24×C11C2411yescharacteristic
133C23×D11C2412yes—
134C2×D4×C11—232no—
135C2×D4×C11—24no—
136C2×D4×C11—24no—
137C2×D4×C11—24no—
138C2×D4×C11—24no—
139C2×D4×C11C22×C418yes—
140C2×D4×C11C22×C418yes—
141C22×C4×C11—216no—
142C22×C4×C11—48no—
143C22×C4×C11—48no—
144C22×C4×C11C22×C414yes—
145C22×C4×C11C2×D414yes—
146C22×C4×C11#4114yes—
147C22×C4×C11C2414yes—
148C22×C4×C11C2414yes—
149C22×C4×C11C2411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C2×C22⋊D11—24no—
152C2×C22⋊D11—24no—
153C2×C22⋊D11—48no—
154C2×C22⋊D11—48no—
155C2×C22⋊D11C22×C418yes—
156C2×C22⋊D11C22×C4132yes—
157C22×Dic11—24no—
158C22×Dic11—24no—
159C22×Dic11—24no—
160C22×Dic11—42no—
161C22×Dic11—44no—
162C22×Dic11C2414yes—
163C22×Dic11C2412yes—
164C22×Dic11C2414yes—
165C22×Dic11C2412yes—
166C22×Dic11C2412yes—
167#4339—232no—
168C2×D44—22no—
169C2×D44—22no—
170C2×D44C22×C414yes—
171C2×C4×D11—28no—
172C2×C4×D11—24no—
173C2×C4×D11—28no—
174C2×C4×D11—24no—
175C2×C4×D11—44no—
176C2×C4×D11C22×C418yes—
177C2×Dic22—22no—
178C2×Dic22—22no—
179C2×Dic22C22×C414yes—
180C11×C4⋊C4—24no—
181C11×C4⋊C4C2×D418yes—
182C11×C22⋊C4—24no—
183C11×C22⋊C4—216no—
184C11×C22⋊C4C2×D418yes—
185C42×C11—24no—
186C42×C11C2×D418yes—
187C22⋊Dic11—216no—
188C22⋊Dic11—48no—
189C22⋊Dic11C22×C418yes—
190C22⋊Dic11C22×C4132yes—
191(C2×D11)⋊C4—28no—
192(C2×D11)⋊C4—48no—
193C4⋊Dic11—24no—
194C4⋊Dic11—24no—
195C4⋊Dic11C22×C418yes—
196Dic11⋊C4—28no—
197Dic11⋊C4—28no—
198Dic11⋊C4—44no—
199C4×Dic11—22no—
200C4×Dic11—28no—
201C4×Dic11—22no—
202C4×Dic11—24no—
203C4×Dic11—48no—
204C4×Dic11C22×C418yes—
205C2×#535—111no—
206C2×#518D1111yescharacteristic, complemented
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#2274—111no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—24no—
220C23×C11—24no—
221C23×C11—28no—
222C23×C11—28no—
223C23×C11—216no—
224C23×C11—416no—
225C23×C11—88no—
226C23×C11—84no—
227C23×C11—84no—
228C23×C11C23×C418yes—
229C23×C11C23×C412yes—
230C23×C11C22×D412yes—
231C23×C11C2×#4112yes—
232C23×C11C2511yescharacteristic
233C22×D11—22no—
234C22×D11—22no—
235C22×D11—24no—
236C22×D11—24no—
237C22×D11C23×C414yes—
238D4×C11—216no—
239D4×C11—216no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—816no—
246C2×C4×C11C4×D4116yescomplemented
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—
255C22⋊D11—432no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—24no—
264C2×Dic11—28no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—48no—
268C2×Dic11—84no—
269C2×Dic11C23×C418yes—
270C2×Dic11C23×C414yes—
271C2×Dic11H(5,𝔽2)14yes—
272D44—28no—
273C4×D11—216no—
274C4×D11—416no—
275Dic22—28no—
276C22×#41—111no—
277C23×D4C2×D1111yescharacteristic
278#535—1116no—
279C2×#127—112no—
280C2×#124—112no—
281C2×#121—114no—
282C2×#120—114no—
283#518—28no—
284C4×#41—228no—
285C2×C4×Q8—112no—
286C2×C4×D4—118no—
287C2×C4×D4—112no—
288C2×C4×D4—114no—
289C2×C4×D4C2×D1114yes—
290C2×C4×D4C2×D1114yes—
291C2×#117—111no—
292C2×#117—112no—
293C2×#117C2×D1111yescharacteristic
294C2×#117C2×D1111yescharacteristic
295C22×C4⋊C4—111no—
296C22×C22⋊C4—114no—
297C22×C22⋊C4C2×D1114yes—
298C22×C42—111no—
299C22×C42—112no—
300#391—112no—
301#390—112no—
302#390—114no—
303#390—112no—
304#390—118no—
305#390—112no—
306#389—112no—
307#389—112no—
308#388—118no—
309#388—118no—
310#386—118no—
311#386—114no—
312#386—118no—
313#385—118no—
314#385—114no—
315#380—114no—
316C4×C4⋊C4—114no—
317C4×C4⋊C4—114no—
318C4×C4⋊C4—114no—
319C4×C22⋊C4—118no—
320C4×C22⋊C4—114no—
321C22×C11—24no—
322C22×C11—24no—
323C22×C11—22no—
324C22×C11—22no—
325C22×C11—28no—
326C22×C11—216no—
327C22×C11—48no—
328C22×C11—44no—
329C22×C11—44no—
330C22×C11—816no—
331C22×C11C2×C4×D414yes—
332C22×C11C24×C411yescharacteristic
333C22×C11C23×D411yescharacteristic
334C22×C11C22×#4111yescharacteristic
335C22×C11C2×H(5,𝔽2)12yes—
336C22×C11#58512yes—
337C2×D11—24no—
338C2×D11—28no—
339C2×D11—44no—
340C2×D11—42no—
341C2×D11—42no—
342C4×C11—28no—
343C4×C11—44no—
344C4×C11C2×C4×D414yes—
345C4×C11C2×C4×D414yes—
346Dic11—24no—
347Dic11—28no—
348Dic11—24no—
349Dic11—42no—
350Dic11—44no—
351C25C22×D1112yes—
352C2×#41—118no—
353C2×#41—224no—
354C2×#41—224no—
355C22×Q8—111no—
356C22×D4—24no—
357C22×D4—24no—
358C22×D4—112no—
359C22×D4—118no—
360C22×D4—111no—
361C22×D4C4×D1118yescomplemented
362C22×D4C22×D1112yes—
363C22×D4C22×D1112yes—
364C23×C4—112no—
365C23×C4—112no—
366C23×C4—112no—
367C23×C4—114no—
368C23×C4C22×D1118yes—
369C23×C4C22×D1111yescharacteristic
370#127—1116no—
371#124—1116no—
372#121—1132no—
373#120—1132no—
374C4×Q8—228no—
375C4×D4—216no—
376C4×D4—216no—
377C4×D4—228no—
378C4×D4—2216no—
379C4×D4—4416no—
380#117—24no—
381#117—118no—
382#117—228no—
383#117C22⋊D1118yescomplemented
384C2×C4⋊C4—112no—
385C2×C4⋊C4—112no—
386C2×C4⋊C4—112no—
387C2×C4⋊C4—114no—
388C2×C4⋊C4—114no—
389C2×C4⋊C4—114no—
390C2×C4⋊C4—224no—
391C2×C4⋊C4C22×D1112yes—
392C2×C4⋊C4C22×D1112yes—
393C2×C22⋊C4—216no—
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—448no—
401C2×C22⋊C4C22×D1112yes—
402C2×C22⋊C4C22×D1118yes—
403C2×C22⋊C4C22×D1112yes—
404C2×C42—112no—
405C2×C42—111no—
406C2×C42—114no—
407C2×C42—112no—
408C2×C42—111no—
409C2×C42—118no—
410C2×C42—224no—
411C2×C42—228no—
412C2×C42C22×D1112yes—
413C2×C42C22×D1112yes—
414#95—114no—
415#95—118no—
416#95—118no—
417#95—114no—
418C2×C11—24no—
419C2×C11—48no—
420C2×C11C22×C4×D411yescharacteristic
421C2×C11C4×H(5,𝔽2)12yes—
422C2×C11#348812yes—
423C2×C11#350811yescharacteristic
424C2×C11#351011yescharacteristic
425D11—44no—
426C24—24no—
427C24—24no—
428C24—44no—
429C24—44no—
430C24—112no—
431C24C2×C4×D1118yes—
432C24C23×D1114yes—
433C24C23×D1111yescharacteristic
434#41—2232no—
435C2×Q8—114no—
436C2×Q8—222no—
437C2×Q8—222no—
438C2×D4—232no—
439C2×D4—24no—
440C2×D4—24no—
441C2×D4—24no—
442C2×D4—24no—
443C2×D4—118no—
444C2×D4—1132no—
445C2×D4—114no—
446C2×D4—224no—
447C2×D4—224no—
448C2×D4—222no—
449C2×D4—222no—
450C2×D4—448no—
451C2×D4—448no—
452C2×D4C2×C4×D1118yes—
453C2×D4C2×C4×D1118yes—
454C22×C4—216no—
455C22×C4—48no—
456C22×C4—48no—
457C22×C4—114no—
458C22×C4—112no—
459C22×C4—112no—
460C22×C4—118no—
461C22×C4—114no—
462C22×C4—112no—
463C22×C4—228no—
464C22×C4—224no—
465C22×C4—224no—
466C22×C4—224no—
467C22×C4—224no—
468C22×C4—224no—
469C22×C4—228no—
470C22×C4—444no—
471C22×C4—442no—
472C22×C4—444no—
473C22×C4C2×C4×D1114yes—
474C22×C4#433914yes—
475C22×C4C2×C22⋊D1114yes—
476C22×C4C23×D1114yes—
477C22×C4C23×D1114yes—
478C22×C4C23×D1111yescharacteristic
479C22×C4C23×D1111yescharacteristic
480C4⋊C4—24no—
481C4⋊C4—118no—
482C4⋊C4—228no—
483C4⋊C4—224no—
484C4⋊C4—224no—
485C4⋊C4—228no—
486C4⋊C4—444no—
487C4⋊C4C2×C22⋊D1118yes—
488C22⋊C4—24no—
489C22⋊C4—216no—
490C22⋊C4—118no—
491C22⋊C4—1132no—
492C22⋊C4—2216no—
493C22⋊C4—228no—
494C22⋊C4—448no—
495C22⋊C4—448no—
496C22⋊C4C2×C22⋊D1118yes—
497C42—24no—
498C42—118no—
499C42—222no—
500C42—222no—
501C42—228no—
502C42—224no—
503C42—448no—
504C42C2×C22⋊D1118yes—
505C11#3426911yescharacteristic, complemented, Sylow
506C23—22no—
507C23—22no—
508C23—24no—
509C23—28no—
510C23—28no—
511C23—24no—
512C23—216no—
513C23—416no—
514C23—84no—
515C23—84no—
516C23—88no—
517C23—114no—
518C23—222no—
519C23—224no—
520C23—224no—
521C23—222no—
522C23C22×C4×D1118yes—
523C23C22×C4×D1112yes—
524C23C2×#433912yes—
525C23C22×C22⋊D1112yes—
526C23C24×D1111yescharacteristic
527Q8—228no—
528D4—216no—
529D4—216no—
530D4—2216no—
531D4—228no—
532D4—4432no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—816no—
539C2×C4—118no—
540C2×C4—114no—
541C2×C4—114no—
542C2×C4—222no—
543C2×C4—224no—
544C2×C4—224no—
545C2×C4—222no—
546C2×C4—222no—
547C2×C4—222no—
548C2×C4—2216no—
549C2×C4—224no—
550C2×C4—228no—
551C2×C4—222no—
552C2×C4—222no—
553C2×C4—222no—
554C2×C4—4416no—
555C2×C4—448no—
556C2×C4—884no—
557C2×C4C4×C22⋊D11116yescomplemented
558C2×C4C22×C4×D1112yes—
559C2×C4C22×C4×D1112yes—
560C2×C4C2×#433912yes—
561C2×C4C2×#433912yes—
562C2×C4C22×C22⋊D1118yes—
563C2×C4C22×C22⋊D1112yes—
564C2×C4C22×C22⋊D1112yes—
565C22—22no—
566C22—22no—
567C22—24no—
568C22—24no—
569C22—28no—
570C22—216no—
571C22—44no—
572C22—44no—
573C22—48no—
574C22—816no—
575C22—224no—
576C22—228no—
577C22—442no—
578C22—442no—
579C22—444no—
580C22C2×C4×C22⋊D1114yes—
581C22C23×C4×D1111yescharacteristic
582C22C22×#433911yescharacteristic
583C22D11×H(5,𝔽2)12yes—
584C22#1062345512yes—
585C22C23×C22⋊D1111yescharacteristic
586C4—28no—
587C4—44no—
588C4—224no—
589C4—224no—
590C4—228no—
591C4—444no—
592C4—442no—
593C4C2×C4×C22⋊D1114yes—
594C4C2×C4×C22⋊D1114yes—
595C2—24no—
596C2—48no—
597C2—444no—
598C2C22×C4×C22⋊D1111yescharacteristic
599C2#1308182012yes—
600C2#1308227812yes—
601C2#1308248711yescharacteristic
602C2#1308250711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC2×C11×#518C2
socle, cosocleC23×C11C25
prime radicalC2×#10623336C2
hypercenterC2×#518D11
hypocenterC11#34269
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#518

Complements

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

NH ≅ G/Ntype
2. C2×#10623053C2semidirect
3. #13071689C2semidirect
4. #13071678C2semidirect
5. #13071595C2semidirect
6. #13071303C2semidirect
7. #13071204C2semidirect
8. C4×#66991C2semidirect
9. #13071098C2semidirect
10. C2×#10622834C2semidirect
11. #13070972C2semidirect
12. C2×C11×#518C2semidirect
23. #10623336C4semidirect
27. C2×C4×C22⋊D11C22semidirect
32. C2×#66946C22semidirect
33. C2×#66940C22semidirect
35. C2×#66925C22semidirect
36. C2×C42×D11C22semidirect
40. #10622826C22semidirect
41. #10622823C22semidirect
42. C4×C22⋊Dic11C22semidirect
43. #10622600C22semidirect
44. C4⋊C4×Dic11C22semidirect
45. #10622586C22semidirect
46. #10622586C22semidirect
48. #10622570C22semidirect
49. #10622569C22semidirect
51. #10622558C22semidirect
52. #10622557C22semidirect
54. #10622552C22semidirect
55. C4×C4⋊Dic11C22semidirect
56. C4×Dic11⋊C4C22semidirect
57. #10622542C22semidirect
61. C22×D4×C11C2×C4semidirect
72. C2×#4339C2×C4semidirect
80. C11×#117D4semidirect
89. #67006C2×C4semidirect
95. #66993C2×C4semidirect
96. #66991C2×C4semidirect
97. #66989C2×C4semidirect
101. #66979C2×C4semidirect
206. C2×#518D11semidirect
246. C2×C4×C11C4×D4semidirect
361. C22×D4C4×D11semidirect
383. #117C22⋊D11semidirect
505. C11#34269semidirect
557. 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×#106233362
C2×#106230532
#130716892
#130716782
#130715952
#130713032
#130712042
C4×#669912
#130710982
C2×#106228342
#130709722
C2×C11×#5182
#3426911