Finite Group Databasebeta

← #14914982

Subgroups — #14914982

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
3C2×#41×Dic11C211yesmaximal, characteristic, complemented
4#13071692C214yesmaximal, complemented
5#13071677C214yesmaximal, complemented
6#13071596C218yesmaximal, complemented
7#13071305C214yesmaximal, complemented
8#13071122C214yesmaximal, complemented
9#13071098C211yesmaximal, characteristic, complemented
10C2×#10622601C211yesmaximal, characteristic, complemented
11#13070973C211yesmaximal, characteristic, complemented
12C11×#2311C211yesmaximal, characteristic, complemented
13C22×C11×#41C2211yescharacteristic
14C23×D44C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17#10623361C4116yescomplemented
18#41×Dic11—28no—
19C2×#67000C2212yes—
20C2×Q8×Dic11C2212yescomplemented
21C2×#66993C2212yes—
22C2×#66990C2214yes—
23C2×D4×Dic11C2214yes—
24C2×D4×Dic11C2212yescomplemented
25C2×#66983C2214yes—
26C22×(C2×D11)⋊C4C2214yes—
27C2×#66979C2211yescharacteristic
28C2×#66979C2211yescharacteristic
29C2×#66979C2212yescomplemented
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2212yescomplemented
32#10623052—28no—
33C2×#66946C2214yes—
34C2×(C22⋊D11)⋊C4C2218yescomplemented
35C2×C22⋊C4×D11C2214yes—
36C2×C4×D44C2214yes—
37C11×#391C2212yescomplemented
38C11×#390C2212yescomplemented
39C11×#386C2214yes—
40C11×#380C2214yescomplemented
41C4×C22⋊Dic11C2214yes—
42#10622601C2212yes—
43#10622601C2214yes—
44#10622601C2212yes—
45C4⋊C4×Dic11C2214yescomplemented
46C4⋊C4×Dic11C2214yescomplemented
47#10622586C2212yescomplemented
48#10622586C2212yescomplemented
49#10622571C2218yescomplemented
50#10622570C2218yescomplemented
51#10622569C2218yescomplemented
52#10622559C2214yes—
53C4×Dic11⋊C4C2214yescomplemented
54#10622283C2218yescomplemented
55#10622282C2218yescomplemented
56#10622281C2218yescomplemented
57#10622279C2218yescomplemented
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×C11C2312yes—
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11C2318yes—
69C23×Dic11C2314yes—
70C23×Dic11C2312yes—
71C22×D44—24no—
72C22×D44—24no—
73C22×D44C2×C418yescomplemented
74C22×D44C2312yes—
75C22×D44C2312yes—
76C22×C4×D11C2318yes—
77C11×#117—24no—
78C2×C11×C4⋊C4—24no—
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2312yes—
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C22⋊C4C2312yes—
83C2×C11×C22⋊C4C2318yes—
84C2×C42×C11C2312yes—
85C2×C22⋊Dic11C2314yes—
86C2×C22⋊Dic11C2312yes—
87C2×C22⋊Dic11C2312yes—
88#67000C2×C4116yescomplemented
89Q8×Dic11—28no—
90#66993C2×C4116yescomplemented
91#66990C2×C4132yescomplemented
92D4×Dic11—216no—
93D4×Dic11—28no—
94#66983C2×C4132yescomplemented
95C2×(C2×D11)⋊C4—48no—
96C2×(C2×D11)⋊C4C2318yes—
97C2×(C2×D11)⋊C4C2318yes—
98C2×(C2×D11)⋊C4C2318yes—
99C2×(C2×D11)⋊C4C2318yes—
100#66979—28no—
101#66979C2×C418yescomplemented
102#66979D418yescomplemented
103C2×C4⋊Dic11C2314yes—
104C2×C4⋊Dic11C2312yes—
105C2×C4⋊Dic11C2312yes—
106C2×Dic11⋊C4C2314yes—
107C2×Dic11⋊C4C2314yes—
108C2×C4×Dic11—24no—
109C2×C4×Dic11—28no—
110C2×C4×Dic11C2314yes—
111C2×C4×Dic11C2312yes—
112C2×C4×Dic11C2311yescharacteristic
113C2×C4×Dic11C2311yescharacteristic
114C2×C4×Dic11C2318yes—
115C2×C4×Dic11C2312yes—
116C2×C4×Dic11C2312yes—
117#66946—216no—
118(C22⋊D11)⋊C4—416no—
119C22⋊C4×D11—216no—
120C4×D44—216no—
121C11×#95C2318yes—
122C11⋊#95C2314yes—
123C11⋊#95C2318yes—
124C11⋊#95C2314yes—
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—44no—
148C22×C4×C11C22×C418yes—
149C22×C4×C11C22×C414yes—
150C22×C4×C11C2×D414yes—
151C22×C4×C11#4114yes—
152C22×C4×C11C2414yes—
153C22×C4×C11C2414yes—
154C22×C4×C11C2412yes—
155C22×C4×C11C2411yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C2×C22⋊D11—48no—
158C2×C22⋊D11—48no—
159C2×C22⋊D11C22×C4132yes—
160C22×Dic11—28no—
161C22×Dic11—28no—
162C22×Dic11—24no—
163C22×Dic11—24no—
164C22×Dic11—42no—
165C22×Dic11—44no—
166C22×Dic11C2412yes—
167C22×Dic11C2414yes—
168C22×Dic11C2414yes—
169C22×Dic11C2412yes—
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—24no—
181C11×C4⋊C4—24no—
182C11×C4⋊C4—24no—
183C11×C22⋊C4—24no—
184C11×C22⋊C4—48no—
185C42×C11—24no—
186C22⋊Dic11—28no—
187C22⋊Dic11C22×C418yes—
188C22⋊Dic11C2×D418yes—
189(C2×D11)⋊C4—216no—
190(C2×D11)⋊C4—216no—
191(C2×D11)⋊C4—48no—
192(C2×D11)⋊C4C22×C4132yes—
193C4⋊Dic11—28no—
194C4⋊Dic11C22×C418yes—
195C4⋊Dic11C2×D418yes—
196Dic11⋊C4—28no—
197Dic11⋊C4—44no—
198C4×Dic11—28no—
199C4×Dic11—22no—
200C4×Dic11—22no—
201C4×Dic11—24no—
202C4×Dic11—48no—
203C4×Dic11C22×C418yes—
204C4×Dic11C2×D418yes—
205C2×#535—111no—
206C2×#518—111no—
207C2×C4×#41—111no—
208#2367—114no—
209#2366—114no—
210#2358—118no—
211#2324—114no—
212#2311D1111yescharacteristic, complemented
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—216no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—28no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—84no—
250C2×C4×C11C4×D4116yescomplemented
251C2×C4×C11C23×C414yes—
252C2×C4×C11C23×C412yes—
253C2×C4×C11C23×C412yes—
254C2×C4×C11C22×D412yes—
255C2×C4×C11C22×D412yes—
256C2×C4×C11C2×#4112yes—
257C2×C4×C11C2×#4112yes—
258C22⋊D11—432no—
259C2×Dic11—22no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—416no—
269C2×Dic11—48no—
270C2×Dic11C23×C418yes—
271C2×Dic11C22×D418yes—
272C2×Dic11H(5,𝔽2)14yes—
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—228no—
285C2×C4×Q8—112no—
286C2×C4×D4—114no—
287C2×C4×D4—112no—
288C2×C4×D4—114no—
289C2×C4×D4—118no—
290C2×C4×D4—114no—
291C2×#117—111no—
292C2×#117—111no—
293C2×#117—112no—
294C2×#117C2×D1111yescharacteristic
295C22×C4⋊C4C2×D1111yescharacteristic
296C22×C22⋊C4—114no—
297C22×C22⋊C4—114no—
298C22×C42—111no—
299C22×C42—112no—
300#391C2×D1112yescomplemented
301#390—112no—
302#390—114no—
303#390—112no—
304#390—118no—
305#390C2×D1112yescomplemented
306#389—112no—
307#389—112no—
308#388—118no—
309#388—118no—
310#386—118no—
311#386—118no—
312#386C2×D1114yes—
313#385—114no—
314#385—118no—
315#380C2×D1114yescomplemented
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—44no—
344C4×C11—44no—
345C4×C11C2×C4×D414yes—
346C4×C11C2×C4×D414yes—
347Dic11—28no—
348Dic11—28no—
349Dic11—24no—
350Dic11—42no—
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—114no—
366C23×C4—118no—
367C23×C4C22×D1112yes—
368C23×C4C22×D1112yes—
369C23×C4C22×D1111yescharacteristic
370#127—1116no—
371#124—1116no—
372#121—1132no—
373#120—1132no—
374C4×Q8—228no—
375C4×D4—2216no—
376C4×D4—2216no—
377C4×D4—2216no—
378C4×D4—228no—
379C4×D4—4416no—
380#117—24no—
381#117—118no—
382#117—118no—
383#117—228no—
384C2×C4⋊C4—24no—
385C2×C4⋊C4—112no—
386C2×C4⋊C4—112no—
387C2×C4⋊C4—114no—
388C2×C4⋊C4—114no—
389C2×C4⋊C4—114no—
390C2×C4⋊C4C22×D1112yes—
391C2×C4⋊C4C22×D1112yes—
392C2×C4⋊C4C22×D1112yes—
393C2×C22⋊C4—112no—
394C2×C22⋊C4—112no—
395C2×C22⋊C4—118no—
396C2×C22⋊C4—114no—
397C2×C22⋊C4—118no—
398C2×C22⋊C4—118no—
399C2×C22⋊C4—118no—
400C2×C22⋊C4—2216no—
401C2×C22⋊C4—448no—
402C2×C22⋊C4C22×D1112yes—
403C2×C22⋊C4C22×D1118yes—
404C2×C42—112no—
405C2×C42—112no—
406C2×C42—111no—
407C2×C42—114no—
408C2×C42—112no—
409C2×C42—111no—
410C2×C42—118no—
411C2×C42—228no—
412C2×C42—224no—
413C2×C42C22×D1112yes—
414#95—114no—
415#95—118no—
416#95—114no—
417#95C22×D1118yes—
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—44no—
458C22×C4—114no—
459C22×C4—114no—
460C22×C4—112no—
461C22×C4—112no—
462C22×C4—2216no—
463C22×C4—228no—
464C22×C4—224no—
465C22×C4—228no—
466C22×C4—224no—
467C22×C4—448no—
468C22×C4—448no—
469C22×C4—444no—
470C22×C4—442no—
471C22×C4C2×C4×D1118yes—
472C22×C4C2×C4×D1114yes—
473C22×C4D4×D1114yes—
474C22×C4#434114yes—
475C22×C4C23×D1114yes—
476C22×C4C23×D1114yes—
477C22×C4C23×D1112yes—
478C22×C4C23×D1111yescharacteristic
479C22×C4C23×D1111yescharacteristic
480C4⋊C4—24no—
481C4⋊C4—24no—
482C4⋊C4—24no—
483C4⋊C4—118no—
484C4⋊C4—118no—
485C4⋊C4—228no—
486C4⋊C4—228no—
487C4⋊C4—444no—
488C22⋊C4—24no—
489C22⋊C4—48no—
490C22⋊C4—118no—
491C22⋊C4—118no—
492C22⋊C4—1132no—
493C22⋊C4—2216no—
494C22⋊C4—2216no—
495C22⋊C4—228no—
496C22⋊C4—448no—
497C42—24no—
498C42—118no—
499C42—118no—
500C42—228no—
501C42—222no—
502C42—222no—
503C42—224no—
504C42—448no—
505C11#3426911yescharacteristic, complemented, Sylow
506C23—22no—
507C23—22no—
508C23—22no—
509C23—22no—
510C23—24no—
511C23—24no—
512C23—118no—
513C23—224no—
514C23—224no—
515C23—228no—
516C23—228no—
517C23—2216no—
518C23—4416no—
519C23—884no—
520C23—884no—
521C23—888no—
522C23C22×C4×D1114yes—
523C23C22×C4×D1112yes—
524C23C2×D4×D1112yes—
525C23C2×#434112yes—
526C23C24×D1111yescharacteristic
527Q8—28no—
528D4—216no—
529D4—28no—
530D4—2216no—
531D4—2216no—
532D4—4432no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—216no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—28no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—84no—
542C2×C4—118no—
543C2×C4—118no—
544C2×C4—114no—
545C2×C4—222no—
546C2×C4—224no—
547C2×C4—224no—
548C2×C4—224no—
549C2×C4—222no—
550C2×C4—224no—
551C2×C4—222no—
552C2×C4—222no—
553C2×C4—222no—
554C2×C4—4416no—
555C2×C4—448no—
556C2×C4—8816no—
557C2×C4(C22⋊D11)⋊C4116yescomplemented
558C2×C4C22×C4×D1114yes—
559C2×C4C22×C4×D1112yes—
560C2×C4C22×C4×D1112yes—
561C2×C4C2×D4×D1112yes—
562C2×C4C2×D4×D1112yes—
563C2×C4C2×#434112yes—
564C2×C4C2×#434112yes—
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×(C22⋊D11)⋊C414yes—
581C22C23×C4×D1111yescharacteristic
582C22C22×D4×D1111yescharacteristic
583C22C22×#434111yescharacteristic
584C22D11×H(5,𝔽2)12yes—
585C22#1062345712yes—
586C4—24no—
587C4—44no—
588C4—44no—
589C4—224no—
590C4—228no—
591C4—228no—
592C4—442no—
593C4C2×(C22⋊D11)⋊C414yes—
594C4C2×(C22⋊D11)⋊C414yes—
595C2—24no—
596C2—44no—
597C2—448no—
598C2C22×(C22⋊D11)⋊C411yescharacteristic
599C2#1308182212yes—
600C2#1308228012yes—
601C2#1308249111yescharacteristic
602C2#1308251511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2311C2
socle, cosocleC23×C11C25
prime radicalC2×#10623361C2
hypercenter#2311D11
hypocenterC11#34269
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. C2×#10623052C2semidirect
3. C2×#41×Dic11C2semidirect
4. #13071692C2semidirect
5. #13071677C2semidirect
6. #13071596C2semidirect
7. #13071305C2semidirect
8. #13071122C2semidirect
9. #13071098C2semidirect
10. C2×#10622601C2semidirect
11. #13070973C2semidirect
12. C11×#2311C2semidirect
17. #10623361C4semidirect
20. C2×Q8×Dic11C22semidirect
24. C2×D4×Dic11C22semidirect
29. C2×#66979C22semidirect
31. C22×C4×Dic11C22semidirect
34. C2×(C22⋊D11)⋊C4C22semidirect
37. C11×#391C22semidirect
38. C11×#390C22semidirect
40. C11×#380C22semidirect
45. C4⋊C4×Dic11C22semidirect
46. C4⋊C4×Dic11C22semidirect
47. #10622586C22semidirect
48. #10622586C22semidirect
49. #10622571C22semidirect
50. #10622570C22semidirect
51. #10622569C22semidirect
53. C4×Dic11⋊C4C22semidirect
54. #10622283C22semidirect
55. #10622282C22semidirect
56. #10622281C22semidirect
57. #10622279C22semidirect
61. C2×C11×#41C2×C4semidirect
73. C22×D44C2×C4semidirect
88. #67000C2×C4semidirect
90. #66993C2×C4semidirect
91. #66990C2×C4semidirect
94. #66983C2×C4semidirect
101. #66979C2×C4semidirect
102. #66979D4semidirect
212. #2311D11semidirect
250. C2×C4×C11C4×D4semidirect
300. #391C2×D11semidirect
305. #390C2×D11semidirect
315. #380C2×D11semidirect
354. C2×#41C4×D11semidirect
505. C11#34269semidirect
557. C2×C4(C22⋊D11)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#106233612
C2×#106230522
C2×#41×Dic112
#130716922
#130716772
#130715962
#130713052
#130711222
#130710982
C2×#106226012
#130709732
C11×#23112
#3426911