Finite Group Databasebeta

← #15638500

Subgroups — #15638500

Order 2816.

2090 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082417C211yesmaximal, characteristic
2C2×Q8×D44C211yesmaximal, characteristic
3#13080494C214yesmaximal, complemented
4#13080489C214yesmaximal, complemented
5Q16×D44C214yesmaximal, complemented
6#13080363C214yesmaximal, complemented
7#13079566C211yesmaximal, characteristic, complemented
8#13079561C211yesmaximal, characteristic, complemented
9#13079390C214yesmaximal, complemented
10#13078655C211yesmaximal, characteristic, complemented
11D11×#451C214yesmaximal, complemented
12#13077639C211yesmaximal, characteristic
13C11×#3104C211yesmaximal, characteristic, complemented
14C22×Q8×D11C2212yes—
15C11×#533C2211yescharacteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×Q16×D11C2218yescomplemented
18#10623261C2212yes—
19#10623258C2212yes—
20#10623221—22no—
21#10623165—22no—
22D11×C22⋊Q8C2214yes—
23#10623110—22no—
24#10623110C2212yes—
25Q8×D44—22no—
26Q8×D44—22no—
27Q8×D44C2214yes—
28Q8×D44C2212yes—
29Q8×D44C2214yes—
30#10623052—21no—
31#10623050—21no—
32C2×#66950—22no—
33C2×#66950C2212yes—
34C2×C4×D44—21no—
35C2×C4×D44C2211yescharacteristic
36#10623001C2211yescharacteristic
37C2×#66922—21no—
38C2×#66922C2211yescharacteristic
39C11×#484C2212yes—
40C11×#477C2212yescomplemented
41C11×#462C2212yescomplemented
42C11×#451C2212yes—
43C4×C11×Q16C2214yescomplemented
44C11×#431C2211yescharacteristic
45#10622841C2212yes—
46#10622799C2218yescomplemented
47#10622706C2212yescomplemented
48#10622705C2212yescomplemented
49#10622663C2214yes—
50#10622644C2214yescomplemented
51#10622644C2212yescomplemented
52C4×#4326C2214yescomplemented
53#10622634C2212yescomplemented
54#10622583C2212yes—
55#10622538C2211yescharacteristic
56#10622500C2218yescomplemented
57#10622497C2218yescomplemented
58#10622462C2214yescomplemented
59#10622447C2214yes—
60#10622426C2218yescomplemented
61#10622421C2218yescomplemented
62#10622421C2218yescomplemented
63D11×#103C2218yescomplemented
64#10622352C2214yes—
65D11×C22⋊C8C2214yes—
66#10622312C2212yescomplemented
67C8×D44C2214yes—
68#10622294C2212yescomplemented
69C22×Q8×C11C2311yescharacteristic
70C2×Q8×D11—24no—
71C2×Q8×D11—48no—
72C2×Q8×D11C2318yes—
73C2×Q8×D11C2314yes—
74C22×D44D411yescharacteristic
75C22×C4×D11—22no—
76C22×C4×D11C2312yes—
77C22×Dic22—22no—
78C22×Dic22C2312yes—
79C2×C11×Q16C2314yes—
80C11×C4⋊Q8C2311yescharacteristic
81C11×C4⋊Q8C2311yescharacteristic
82C11×#125—21no—
83C11×C22⋊Q8—21no—
84C11×C22⋊Q8C2312yes—
85C4×Q8×C11—21no—
86C4×Q8×C11—21no—
87C4×Q8×C11—21no—
88C4×Q8×C11C2312yes—
89C4×Q8×C11C2312yes—
90C4×Q8×C11C2312yes—
91C11×#117—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C42×C11—21no—
95C2×C42×C11C2311yescharacteristic
96#66999—24no—
97#66999C2314yes—
98C2×#4326C2314yes—
99C2×#4326C2318yes—
100C2×(C2×D11)⋊C4—22no—
101C2×(C2×D11)⋊C4D412yes—
102#66979—21no—
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11—21no—
105C2×C4⋊Dic11—22no—
106C2×C4⋊Dic11D411yescharacteristic
107#66977—21no—
108#66977C2312yes—
109Q16×D11—416no—
110C2×Dic44C2318yes—
111C2×C8×D11C2318yes—
112#66950—24no—
113#66950—28no—
114#66950—28no—
115#66950—24no—
116#66950C2314yes—
117#66950C2318yes—
118#66949—24no—
119#66949—24no—
120#66949—24no—
121#66946—22no—
122#66946—22no—
123C4⋊C4×D11—24no—
124C4⋊C4×D11C2314yes—
125#66943—22no—
126#66941—22no—
127C22⋊C4×D11—24no—
128#66931—24no—
129C4×D44—24no—
130C4×D44—24no—
131C4×D44—22no—
132C4×D44—22no—
133C4×D44D412yes—
134C4×D44D412yes—
135C4×D44C2312yes—
136C4×D44C2312yes—
137#66923—21no—
138#66923—22no—
139#66922—21no—
140#66922—21no—
141#66922—24no—
142#66922—24no—
143#66922—22no—
144#66922C2312yes—
145#66922C2312yes—
146#66922C2311yescharacteristic
147#66922C2311yescharacteristic
148C4×Dic22—21no—
149C4×Dic22C2312yes—
150C11×#107C2314yes—
151C11×C4⋊C8C2312yes—
152C11×#103C2314yes—
153C11×#103C2314yes—
154C11×C22⋊C8C2312yes—
155C4×C8×C11C2312yes—
156#66899C2314yes—
157C22⋊(C11⋊C8)C2312yes—
158(C2×D11)⋊C8C2318yes—
159#66880C2318yes—
160#66874C2318yes—
161#66874C2314yes—
162#66871C2314yes—
163C4⋊(C11⋊C8)C2312yes—
164C4×C11⋊C8C2312yes—
165#61563—111nomaximal, Sylow
166C23×D11C2×D412yes—
167C2×Q8×C11—24no—
168C2×Q8×C11—21no—
169C2×Q8×C11—21no—
170C2×Q8×C11C2412yes—
171C2×Q8×C11C2412yes—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2411yescharacteristic
177C22×Dic11—22no—
178C22×Dic11C2×D412yes—
179Q8×D11—216no—
180Q8×D11—48no—
181Q8×D11—48no—
182Q8×D11—416no—
183C2×D44Q1618yescomplemented
184C2×D44C2×D412yes—
185C2×D44C2×D412yes—
186C2×C4×D11—28no—
187C2×C4×D11—24no—
188C2×C4×D11—24no—
189C2×C4×D11—44no—
190C2×C4×D11—48no—
191C2×C4×D11C2×D414yes—
192C2×C4×D11C2414yes—
193C2×Dic22—28no—
194C2×Dic22—24no—
195C2×Dic22—22no—
196C2×Dic22—21no—
197C2×Dic22—44no—
198C2×Dic22—48no—
199C2×Dic22C2414yes—
200C2×Dic22C2412yes—
201C11×Q16—28no—
202C2×C8×C11C2414yes—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—22no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—22no—
208C11×C4⋊C4—22no—
209C11×C4⋊C4—22no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4C2412yes—
212C11×C4⋊C4C2412yes—
213C11×C22⋊C4—22no—
214C42×C11—22no—
215C42×C11—22no—
216C42×C11—22no—
217C42×C11C2×D411yescharacteristic
218C42×C11C2×D411yescharacteristic
219C42×C11C2411yescharacteristic
220C42×C11C2411yescharacteristic
221C22⋊Dic11—22no—
222#4326—28no—
223#4326—48no—
224(C2×D11)⋊C4—28no—
225(C2×D11)⋊C4—24no—
226(C2×D11)⋊C4—24no—
227(C2×D11)⋊C4C2×D414yes—
228(C2×D11)⋊C4C2×D414yes—
229C4⋊Dic11—28no—
230C4⋊Dic11—24no—
231C4⋊Dic11—21no—
232C4⋊Dic11—22no—
233C4⋊Dic11—22no—
234C4⋊Dic11—21no—
235C4⋊Dic11—22no—
236C4⋊Dic11—22no—
237C4⋊Dic11—21no—
238C4⋊Dic11C2×D412yes—
239C4⋊Dic11C2×D412yes—
240C4⋊Dic11C2412yes—
241Dic11⋊C4—24no—
242Dic11⋊C4—24no—
243Dic11⋊C4—22no—
244Dic11⋊C4—22no—
245C4×Dic11—22no—
246C2×C11⋊C8C2414yes—
247Dic44—48no—
248C8×D11—48no—
249#3501—111no—
250C2×D4×Q8—111no—
251#3299—114no—
252#3299—114no—
253D4×Q16—114no—
254D4×Q16—114no—
255#3209—111no—
256#3209—111no—
257#3189—114no—
258#3104—111no—
259#3104D1111yescharacteristic, complemented
260C2×#451—114no—
261#2972—111no—
262C23×C11C22×D411yescharacteristic
263C22×D11—42no—
264C22×D11—42no—
265C22×D11C2×Q1618yescomplemented
266C22×D11C22×D414yes—
267Q8×C11—24no—
268Q8×C11—22no—
269Q8×C11—24no—
270Q8×C11—81no—
271Q8×C11H(5,𝔽2)14yes—
272C2×C4×C11—24no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—41no—
279C2×C4×C11—42no—
280C2×C4×C11C2×Q1614yescomplemented
281C2×C4×C11C22×D411yescharacteristic
282C2×C4×C11C22×D411yescharacteristic
283C2×C4×C11C22×D411yescharacteristic
284C2×C4×C11C22×D411yescharacteristic
285C2×C4×C11C22×D411yescharacteristic
286C2×C4×C11C2511yescharacteristic
287C2×Dic11—22no—
288C2×Dic11—22no—
289C2×Dic11—24no—
290C2×Dic11—42no—
291C2×Dic11—44no—
292C2×Dic11C22×D414yes—
293D44C2×Q1618yescomplemented
294D44C2×Q1618yescomplemented
295C4×D11—28no—
296C4×D11—44no—
297C4×D11—416no—
298C4×D11—84no—
299C4×D11—84no—
300Dic22—24no—
301Dic22—28no—
302Dic22—416no—
303Dic22—44no—
304Dic22—84no—
305Dic22—81no—
306C8×C11—24no—
307C11⋊C8—24no—
308C23×Q8—112no—
309C22×Q16—118no—
310#554—112no—
311#554—112no—
312#554—222no—
313#554—222no—
314D4×Q8—112no—
315D4×Q8—114no—
316D4×Q8—114no—
317D4×Q8—112no—
318D4×Q8—222no—
319D4×Q8—222no—
320#544—221no—
321#543—222no—
322#533—111no—
323#533C2×D1111yescharacteristic
324C2×C4⋊Q8—111no—
325C2×C4⋊Q8—221no—
326C2×C22⋊Q8—114no—
327C2×C22⋊Q8—112no—
328C2×C22⋊Q8—222no—
329#518—221no—
330C2×C4×Q8C2×D1111yescharacteristic
331C2×C4×D4—111no—
332C2×C4×D4—221no—
333#494—112no—
334#494—112no—
335#487—112no—
336#487—112no—
337#484—112no—
338#484—118no—
339#484C2×D1112yes—
340#477—112no—
341#477C2×D1112yescomplemented
342#467—118no—
343#467—118no—
344#462—112no—
345#462—114no—
346#462—114no—
347#462C2×D1112yescomplemented
348#451—112no—
349#451—118no—
350#451—114no—
351#451—118no—
352#451—118no—
353#451—114no—
354#451C2×D1112yes—
355C4×Q16—114no—
356C4×Q16C2×D1114yescomplemented
357C8×D4—114no—
358C8×D4—114no—
359#431—111no—
360#431C2×D1111yescharacteristic
361C2×#103—118no—
362C2×C22⋊C8—114no—
363C22×C11—21no—
364C22×C11—21no—
365C22×C11C22×Q1612yes—
366C22×C11C23×D411yescharacteristic
367C2×D11—24no—
368C2×D11—24no—
369C2×D11—48no—
370C2×D11C22×Q1618yes—
371C4×C11—21no—
372C4×C11—21no—
373C4×C11—24no—
374C4×C11—21no—
375C4×C11—42no—
376C4×C11—42no—
377C4×C11—42no—
378C4×C11C22×Q1612yes—
379C4×C11C22×Q1612yes—
380C4×C11C2×H(5,𝔽2)12yes—
381Dic11—24no—
382Dic11—42no—
383Dic11—44no—
384Dic11—42no—
385C22×Q8—118no—
386C22×Q8—114no—
387C22×Q8—112no—
388C22×Q8—222no—
389C22×Q8—224no—
390C22×Q8—448no—
391C22×Q8C22×D1111yescharacteristic
392C22×D4—111no—
393C23×C4—112no—
394C23×C4—222no—
395C2×Q16—114no—
396C2×Q16—118no—
397C2×Q16—118no—
398C2×Q16—4416no—
399C2×Q16C22×D1114yes—
400C22×C8—118no—
401C4⋊Q8—111no—
402C4⋊Q8—112no—
403C4⋊Q8—112no—
404C4⋊Q8—111no—
405C4⋊Q8—224no—
406C4⋊Q8—224no—
407C4⋊Q8—222no—
408C4⋊Q8—222no—
409C4⋊Q8—221no—
410C4⋊Q8—221no—
411C4⋊Q8C22×D1111yescharacteristic
412C4⋊Q8C22×D1111yescharacteristic
413#125—21no—
414#125—222no—
415#125—222no—
416#125—221no—
417C22⋊Q8—21no—
418C22⋊Q8—114no—
419C22⋊Q8—112no—
420C22⋊Q8—118no—
421C22⋊Q8—114no—
422C22⋊Q8—224no—
423C22⋊Q8—228no—
424C22⋊Q8—228no—
425C22⋊Q8—224no—
426C22⋊Q8—224no—
427C22⋊Q8—224no—
428C22⋊Q8—224no—
429C22⋊Q8—224no—
430C22⋊Q8—224no—
431C22⋊Q8—221no—
432C22⋊Q8C22×D1112yes—
433C4×Q8—21no—
434C4×Q8—21no—
435C4×Q8—21no—
436C4×Q8—112no—
437C4×Q8—221no—
438C4×Q8C22×D1112yes—
439C4×Q8C22×D1112yes—
440C4×Q8C22×D1112yes—
441C4×D4—112no—
442C4×D4—112no—
443C4×D4—112no—
444C4×D4—112no—
445C4×D4—224no—
446C4×D4—224no—
447C4×D4—222no—
448C4×D4—222no—
449C4×D4—222no—
450C4×D4—222no—
451#117—21no—
452#117—221no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—111no—
455C2×C4⋊C4—114no—
456C2×C4⋊C4—224no—
457C2×C4⋊C4—222no—
458C2×C4⋊C4—221no—
459C2×C4⋊C4—221no—
460C2×C4⋊C4C22×D1111yescharacteristic
461C2×C22⋊C4—112no—
462C2×C22⋊C4—224no—
463C2×C22⋊C4—222no—
464C2×C42—21no—
465C2×C42C22×D1111yescharacteristic
466#107—114no—
467#107C22×D1114yes—
468C4⋊C8—112no—
469C4⋊C8C22×D1112yes—
470#103—114no—
471#103—118no—
472#103—118no—
473#103—114no—
474#103C22×D1114yes—
475#103C22×D1114yes—
476C22⋊C8—112no—
477C22⋊C8—118no—
478C22⋊C8C22×D1112yes—
479C4×C8—112no—
480C4×C8C22×D1112yes—
481C2×C11—22no—
482C2×C11#348411yescharacteristic
483C2×C11C23×Q1611yescharacteristic
484C2×C11#358611yescharacteristic
485D11—28no—
486C24—112no—
487C2×Q8—24no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—114no—
491C2×Q8—112no—
492C2×Q8—228no—
493C2×Q8—224no—
494C2×Q8—222no—
495C2×Q8—221no—
496C2×Q8—2216no—
497C2×Q8—444no—
498C2×Q8—448no—
499C2×Q8—448no—
500C2×Q8—448no—
501C2×Q8—4416no—
502C2×Q8C23×D1112yes—
503C2×Q8C23×D1112yes—
504C2×D4—118no—
505C2×D4—112no—
506C2×D4—112no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—112no—
510C22×C4—114no—
511C22×C4—114no—
512C22×C4—228no—
513C22×C4—224no—
514C22×C4—224no—
515C22×C4—222no—
516C22×C4—444no—
517C22×C4—448no—
518C22×C4D4×D1111yescharacteristic
519C22×C4D4×D1111yescharacteristic
520C22×C4C23×D1111yescharacteristic
521Q16—28no—
522Q16—228no—
523Q16—448no—
524Q16—448no—
525C2×C8—114no—
526C2×C8—448no—
527C2×C8C23×D1114yes—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—22no—
536C4⋊C4—112no—
537C4⋊C4—112no—
538C4⋊C4—112no—
539C4⋊C4—224no—
540C4⋊C4—224no—
541C4⋊C4—224no—
542C4⋊C4—228no—
543C4⋊C4—222no—
544C4⋊C4—222no—
545C4⋊C4—222no—
546C4⋊C4—222no—
547C4⋊C4—222no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—222no—
551C4⋊C4—221no—
552C4⋊C4C23×D1112yes—
553C4⋊C4C23×D1112yes—
554C22⋊C4—22no—
555C22⋊C4—114no—
556C22⋊C4—114no—
557C22⋊C4—228no—
558C22⋊C4—224no—
559C22⋊C4—224no—
560C22⋊C4—222no—
561C42—22no—
562C42—22no—
563C42—22no—
564C42—222no—
565C42D4×D1111yescharacteristic
566C42D4×D1111yescharacteristic
567C42C23×D1111yescharacteristic
568C42C23×D1111yescharacteristic
569C11#6156311yescharacteristic, complemented, Sylow
570C23—114no—
571C23—118no—
572C23—442no—
573C23—442no—
574C23C2×D4×D1111yescharacteristic
575Q8—24no—
576Q8—22no—
577Q8—24no—
578Q8—81no—
579Q8—224no—
580Q8—228no—
581Q8—4416no—
582Q8—444no—
583Q8—881no—
584Q8—884no—
585Q8#6704214yes—
586D4—118no—
587D4—118no—
588C2×C4—24no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—41no—
595C2×C4—42no—
596C2×C4—114no—
597C2×C4—228no—
598C2×C4—222no—
599C2×C4—222no—
600C2×C4—224no—
601C2×C4—444no—
602C2×C4—4416no—
603C2×C4—442no—
604C2×C4—444no—
605C2×C4—884no—
606C2×C4—884no—
607C2×C4Q16×D1114yescomplemented
608C2×C4C2×D4×D1111yescharacteristic
609C2×C4C2×D4×D1111yescharacteristic
610C2×C4C2×D4×D1111yescharacteristic
611C2×C4C2×D4×D1111yescharacteristic
612C2×C4C2×D4×D1111yescharacteristic
613C2×C4C24×D1111yescharacteristic
614C8—24no—
615C8—224no—
616C22—21no—
617C22—21no—
618C22—118no—
619C22—224no—
620C22—224no—
621C22—448no—
622C22C2×Q16×D1112yes—
623C22C22×D4×D1111yescharacteristic
624C4—21no—
625C4—21no—
626C4—24no—
627C4—21no—
628C4—42no—
629C4—42no—
630C4—42no—
631C4—224no—
632C4—442no—
633C4—444no—
634C4—442no—
635C4C2×Q16×D1112yes—
636C4C2×Q16×D1112yes—
637C4C2×#6704212yes—
638C2—22no—
639C2—228no—
640C2#1308224911yescharacteristic
641C2C22×Q16×D1111yescharacteristic
642C2#1308340011yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3104C2
socleC22×C11C23×D4
prime radicalC22×D44D4
hypercenter#3104D11
hypocenterC11#61563
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3104

Complements

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

NH ≅ G/Ntype
3. #13080494C2semidirect
4. #13080489C2semidirect
5. Q16×D44C2semidirect
6. #13080363C2semidirect
7. #13079566C2semidirect
8. #13079561C2semidirect
9. #13079390C2semidirect
10. #13078655C2semidirect
11. D11×#451C2semidirect
13. C11×#3104C2semidirect
17. C2×Q16×D11C22semidirect
40. C11×#477C22semidirect
41. C11×#462C22semidirect
43. C4×C11×Q16C22semidirect
46. #10622799C22semidirect
47. #10622706C22semidirect
48. #10622705C22semidirect
50. #10622644C22semidirect
51. #10622644C22semidirect
52. C4×#4326C22semidirect
53. #10622634C22semidirect
56. #10622500C22semidirect
57. #10622497C22semidirect
58. #10622462C22semidirect
60. #10622426C22semidirect
61. #10622421C22semidirect
62. #10622421C22semidirect
63. D11×#103C22semidirect
66. #10622312C22semidirect
68. #10622294C22semidirect
183. C2×D44Q16semidirect
259. #3104D11semidirect
265. C22×D11C2×Q16semidirect
280. C2×C4×C11C2×Q16semidirect
293. D44C2×Q16semidirect
294. D44C2×Q16semidirect
341. #477C2×D11semidirect
347. #462C2×D11semidirect
356. C4×Q16C2×D11semidirect
569. C11#61563semidirect
607. C2×C4Q16×D11semidirect

Maximal subgroups

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

subgroupindex
#130824172
C2×Q8×D442
#130804942
#130804892
Q16×D442
#130803632
#130795662
#130795612
#130793902
#130786552
D11×#4512
#130776392
C11×#31042
#6156311