Finite Group Databasebeta

← #14925859

Subgroups — #14925859

Order 2816.

2402 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×#10623259C211yesmaximal, characteristic
2C2×C4×Q8×D11C211yesmaximal, characteristic
3#13074001C214yesmaximal, complemented
4#13073990C214yesmaximal
5#13073824C211yesmaximal, characteristic, complemented
6#13073821C211yesmaximal, characteristic, complemented
7#13073605C211yesmaximal, characteristic, complemented
8#13073093C212yesmaximal
9#13072257C212yesmaximal
10#13071908C214yesmaximal, complemented
11C4⋊Q8×Dic11C212yesmaximal, complemented
12#13071185C212yesmaximal, complemented
13#13071097C214yesmaximal
14C4×#66945C211yesmaximal, characteristic
15C11×#2546C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2211yescharacteristic
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×C4⋊Q8C2212yes—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×#66999C2212yes—
21C2×Q8×Dic11C2212yes—
22C2×Q8×Dic11C2211yescharacteristic
23C2×#66997C2212yes—
24#10623259—28no—
25C4×Q8×D11—28no—
26C2×#66950C2212yes—
27C2×#66945C2212yes—
28C2×#66945C2212yes—
29C2×C4⋊C4×D11C2212yes—
30C2×C4⋊C4×D11C2211yescharacteristic
31C2×#66943C2212yes—
32C2×#66940C2212yes—
33C2×#66940C2212yes—
34C2×#66940C2211yescharacteristic
35C2×C42×D11C2212yes—
36C2×C42×D11C2211yescharacteristic
37C2×#66922C2211yescharacteristic
38C2×C4×Dic22C2212yes—
39C2×C4×Dic22C2211yescharacteristic
40C11×#398C2214yes—
41C11×#391C2212yes—
42C11×#389C2214yes—
43C4×C11×C4⋊C4C2211yescharacteristic
44#10622843C2212yes—
45#10622843C2212yes—
46#10622602C2218yes—
47#10622598C2218yes—
48#10622598C2214yes—
49#10622593C2214yes—
50#10622592C2214yes—
51#10622592C2218yes—
52#10622589C2212yes—
53C4⋊C4×Dic11C2218yes—
54C4⋊C4×Dic11C2212yes—
55#10622586C2214yes—
56C4×(C2×D11)⋊C4C2212yes—
57#10622548C2212yes—
58C4×C4⋊Dic11C2211yescharacteristic
59C42×Dic11C2212yes—
60#10622542C2212yes—
61#10622541C2214yes—
62#10622281C2218yes—
63#10622279C2212yes—
64#10622270C2218yes—
65#10622269C2214yes—
66#10622262C2218yes—
67#10622261C2212yes—
68#10622260C2218yes—
69C22×Q8×C11C2312yes—
70C22×Q8×C11C2311yescharacteristic
71C2×Q8×D11—24no—
72C2×Q8×D11—24no—
73C2×Q8×D11—24no—
74C22×C4×D11C2312yes—
75C22×C4×D11C2311yescharacteristic
76C22×C4×D11C2312yes—
77C22×C4×D11C2311yescharacteristic
78C22×C4×D11C2311yescharacteristic
79C22×Dic22C2312yes—
80C22×Dic22C2311yescharacteristic
81C22×Dic22C2312yes—
82C11×C4⋊Q8—28no—
83C11×C4⋊Q8—24no—
84C4×Q8×C11—24no—
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C4⋊C4C2318yes—
90C2×C11×C4⋊C4C2312yes—
91C2×C42×C11C2312yes—
92C2×C42×C11C2312yes—
93C2×C42×C11C2311yescharacteristic
94#66999—28no—
95Q8×Dic11—28no—
96Q8×Dic11—24no—
97#66997—28no—
98C2×(C2×D11)⋊C4C2314yes—
99C2×(C2×D11)⋊C4C2314yes—
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2312yes—
102C2×C4⋊Dic11C2312yes—
103C2×C4⋊Dic11C2312yes—
104C2×C4⋊Dic11C2314yes—
105C2×C4⋊Dic11C2318yes—
106C2×C4⋊Dic11C2312yes—
107C2×Dic11⋊C4C2312yes—
108C2×Dic11⋊C4C2312yes—
109C2×Dic11⋊C4C2312yes—
110C2×Dic11⋊C4C2314yes—
111C2×Dic11⋊C4C2318yes—
112C2×Dic11⋊C4C2318yes—
113C2×C4×Dic11C2312yes—
114C2×C4×Dic11C2312yes—
115C2×C4×Dic11C2312yes—
116C2×C4×Dic11C2314yes—
117C2×C4×Dic11C2312yes—
118C2×C4×Dic11C2314yes—
119C2×C4×Dic11C2311yescharacteristic
120C2×C4×Dic11C2311yescharacteristic
121C2×C4×Dic11C2311yescharacteristic
122C2×C4×Dic11C2314yes—
123#66950—28no—
124#66945—28no—
125#66945Q8116yescomplemented
126C4⋊C4×D11—24no—
127C4⋊C4×D11—28no—
128#66943—28no—
129#66940—28no—
130#66940—24no—
131#66940—28no—
132C42×D11—28no—
133C42×D11D418yes—
134#66922—24no—
135C4×Dic22—24no—
136C4×Dic22—28no—
137C11×#95C2318yes—
138C11×#95C2312yes—
139C11⋊#95C2318yes—
140C11⋊#95C2314yes—
141C11⋊#95C2312yes—
142C11⋊#95C2318yes—
143C11⋊#95C2318yes—
144#34953—111nomaximal, Sylow
145C23×D11C2411yescharacteristic
146C2×Q8×C11—22no—
147C2×Q8×C11—24no—
148C2×Q8×C11—22no—
149C2×Q8×C11—24no—
150C2×Q8×C11—24no—
151C2×Q8×C11#4114yes—
152C22×C4×C11C2414yes—
153C22×C4×C11C2412yes—
154C22×C4×C11C2411yescharacteristic
155C22×C4×C11C2414yes—
156C22×C4×C11C2412yes—
157C22×C4×C11C2411yescharacteristic
158C22×C4×C11C2411yescharacteristic
159C22×Dic11C2412yes—
160C22×Dic11C2414yes—
161C22×Dic11C2411yescharacteristic
162C22×Dic11C2411yescharacteristic
163C22×Dic11C2414yes—
164C22×Dic11C2412yes—
165C22×Dic11C2411yescharacteristic
166Q8×D11—232no—
167C2×C4×D11—24no—
168C2×C4×D11—24no—
169C2×C4×D11—24no—
170C2×C4×D11—24no—
171C2×C4×D11—22no—
172C2×C4×D11—22no—
173C2×C4×D11—42no—
174C2×C4×D11—44no—
175C2×C4×D11C2×D414yes—
176C2×C4×D11C2×D414yes—
177C2×C4×D11C2×D414yes—
178C2×C4×D11C2×Q818yes—
179C2×Dic22—24no—
180C2×Dic22—24no—
181C2×Dic22—22no—
182C2×Dic22—24no—
183C2×Dic22—24no—
184C2×Dic22—22no—
185C2×Dic22—44no—
186C2×Dic22#4114yes—
187C11×C4⋊C4—24no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—24no—
190C11×C4⋊C4—24no—
191C11×C4⋊C4—216no—
192C11×C4⋊C4C2×Q818yescomplemented
193C42×C11—24no—
194C42×C11—24no—
195C42×C11C2×D414yes—
196(C2×D11)⋊C4—28no—
197(C2×D11)⋊C4C2×Q8116yes—
198C4⋊Dic11—24no—
199C4⋊Dic11—28no—
200C4⋊Dic11—22no—
201C4⋊Dic11—24no—
202C4⋊Dic11—24no—
203C4⋊Dic11—48no—
204C4⋊Dic11C2×Q818yescomplemented
205Dic11⋊C4—24no—
206Dic11⋊C4—24no—
207Dic11⋊C4—28no—
208Dic11⋊C4—216no—
209Dic11⋊C4—24no—
210Dic11⋊C4—48no—
211C4×Dic11—24no—
212C4×Dic11—24no—
213C4×Dic11—28no—
214C4×Dic11—24no—
215C4×Dic11—24no—
216C4×Dic11—44no—
217C4×Dic11C2×D414yes—
218C4×Dic11C2×D414yes—
219C4×Dic11C2×D414yes—
220C4×Dic11C2×Q8116yescomplemented
221C2×#533—111no—
222C22×C4×Q8—111no—
223#2584—114no—
224#2583—114no—
225#2567—111no—
226#2567—111no—
227#2546—111no—
228#2546D1111yescharacteristic, complemented
229#2502—112no—
230#2434—112no—
231#2399—114no—
232C4×C4⋊Q8—112no—
233C4×C4⋊Q8—112no—
234#2296—114no—
235C4×#117—111no—
236C23×C11C2511yescharacteristic
237C22×D11—21no—
238C22×D11—21no—
239C22×D11—22no—
240C22×D11C22×D412yes—
241C22×D11C22×Q814yes—
242Q8×C11—28no—
243Q8×C11—48no—
244C2×C4×C11—22no—
245C2×C4×C11—24no—
246C2×C4×C11—22no—
247C2×C4×C11—24no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11C22×D412yes—
255C2×C4×C11C22×D412yes—
256C2×C4×C11C22×D412yes—
257C2×C4×C11C22×Q818yes—
258C2×C4×C11C22×Q814yes—
259C2×C4×C11C2×#4114yes—
260C2×C4×C11C2×#4112yes—
261C2×C4×C11C2×#4112yes—
262C2×Dic11—22no—
263C2×Dic11—24no—
264C2×Dic11—21no—
265C2×Dic11—22no—
266C2×Dic11—21no—
267C2×Dic11—22no—
268C2×Dic11—24no—
269C2×Dic11—22no—
270C2×Dic11—24no—
271C2×Dic11—28no—
272C2×Dic11—24no—
273C2×Dic11C22×D412yes—
274C2×Dic11C22×D412yes—
275C2×Dic11C22×D412yes—
276C2×Dic11C22×Q818yes—
277C2×Dic11C22×Q814yes—
278C2×Dic11C2×#4114yes—
279C4×D11—216no—
280C4×D11—28no—
281C4×D11—44no—
282C4×D11—48no—
283C4×D11C4⋊Q8116yescomplemented
284Dic22—216no—
285Dic22—28no—
286Dic22—48no—
287C23×Q8—111no—
288#533—228no—
289C2×C4⋊Q8—112no—
290C2×C4⋊Q8—111no—
291C2×C4⋊Q8C2×D1112yes—
292C2×C4⋊Q8C2×D1111yescharacteristic
293C2×#125—112no—
294C2×C22⋊Q8—112no—
295C2×C22⋊Q8—112no—
296C2×C4×Q8—111no—
297C2×C4×Q8—112no—
298C2×C4×Q8—111no—
299C2×C4×Q8—112no—
300C2×C4×Q8—112no—
301C2×C4×Q8—111no—
302C2×C4×Q8—112no—
303C2×C4×Q8—228no—
304C2×C4×Q8C2×D1111yescharacteristic
305C2×#117—112no—
306C2×#117—112no—
307C22×C4⋊C4—112no—
308C22×C4⋊C4—111no—
309C22×C42—111no—
310C22×C42—112no—
311#398—114no—
312#398—118no—
313#398C2×D1114yes—
314#395—114no—
315#395—118no—
316#395—114no—
317#391—112no—
318#391—112no—
319#391—112no—
320#391C2×D1112yes—
321#389—118no—
322#389—114no—
323#389—114no—
324#389—114no—
325#389—118no—
326#389C2×D1114yes—
327#385—118no—
328#385—118no—
329#384—112no—
330#384—112no—
331C4×C4⋊C4—118no—
332C4×C4⋊C4—112no—
333C4×C4⋊C4—111no—
334C4×C4⋊C4—118no—
335C4×C4⋊C4C2×D1111yescharacteristic
336C4×C22⋊C4—112no—
337C4×C22⋊C4—112no—
338#376—112no—
339C43—112no—
340C22×C11C23×D411yescharacteristic
341C22×C11C23×Q812yes—
342C22×C11C22×#4111yescharacteristic
343C22×C11C22×#4111yescharacteristic
344C22×C11#58512yes—
345C2×D11—22no—
346C2×D11—22no—
347C2×D11—24no—
348C2×D11—24no—
349C2×D11C2×C4⋊Q814yes—
350C4×C11—24no—
351C4×C11—22no—
352C4×C11—28no—
353C4×C11—44no—
354C4×C11—42no—
355C4×C11#52514yes—
356C4×C11C2×C4⋊Q814yes—
357Dic11—22no—
358Dic11—24no—
359Dic11—22no—
360Dic11—28no—
361Dic11—44no—
362Dic11—42no—
363Dic11C2×C4⋊Q814yes—
364C22×Q8—111no—
365C22×Q8—112no—
366C22×Q8—112no—
367C22×Q8—224no—
368C22×Q8—224no—
369C22×Q8—224no—
370C22×Q8C22×D1112yes—
371C22×Q8C22×D1111yescharacteristic
372C23×C4—111no—
373C23×C4—111no—
374C23×C4—111no—
375C23×C4—112no—
376C23×C4—112no—
377C4⋊Q8—28no—
378C4⋊Q8—24no—
379C4⋊Q8—228no—
380C4⋊Q8—224no—
381#125—228no—
382C22⋊Q8—228no—
383C22⋊Q8—228no—
384C4×Q8—24no—
385C4×Q8—228no—
386C4×Q8—224no—
387C4×Q8—228no—
388C4×Q8—228no—
389C4×Q8—224no—
390C4×Q8—228no—
391C4×Q8—224no—
392#117—1116no—
393#117—228no—
394C2×C4⋊C4—112no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—112no—
397C2×C4⋊C4—112no—
398C2×C4⋊C4—112no—
399C2×C4⋊C4—112no—
400C2×C4⋊C4—112no—
401C2×C4⋊C4—114no—
402C2×C4⋊C4—114no—
403C2×C4⋊C4—112no—
404C2×C4⋊C4—118no—
405C2×C4⋊C4—118no—
406C2×C4⋊C4—118no—
407C2×C4⋊C4—224no—
408C2×C4⋊C4—228no—
409C2×C4⋊C4C22×D1111yescharacteristic
410C2×C4⋊C4C22×D1112yes—
411C2×C4⋊C4C22×D1112yes—
412C2×C4⋊C4C22×D1112yes—
413C2×C4⋊C4C22×D1118yes—
414C2×C4⋊C4C22×D1112yes—
415C2×C22⋊C4—114no—
416C2×C22⋊C4—114no—
417C2×C42—114no—
418C2×C42—111no—
419C2×C42—111no—
420C2×C42—111no—
421C2×C42—118no—
422C2×C42—114no—
423C2×C42—112no—
424C2×C42—112no—
425C2×C42—112no—
426C2×C42—112no—
427C2×C42—114no—
428C2×C42—228no—
429C2×C42C22×D1112yes—
430C2×C42C22×D1112yes—
431C2×C42C22×D1111yescharacteristic
432#95—112no—
433#95—114no—
434#95—118no—
435#95—118no—
436#95—118no—
437#95C22×D1112yes—
438#95C22×D1118yes—
439C2×C11C2×#52511yescharacteristic
440C2×C11C22×C4⋊Q811yescharacteristic
441C2×C11#344911yescharacteristic
442C2×C11Q8×#4112yes—
443C2×C11Q8×#4112yes—
444D11—24no—
445C24—111no—
446C2×Q8—22no—
447C2×Q8—24no—
448C2×Q8—24no—
449C2×Q8—22no—
450C2×Q8—24no—
451C2×Q8—114no—
452C2×Q8—224no—
453C2×Q8—224no—
454C2×Q8—2232no—
455C2×Q8—222no—
456C2×Q8—224no—
457C2×Q8—224no—
458C2×Q8—222no—
459C2×Q8—444no—
460C2×Q8#434114yes—
461C22×C4—111no—
462C22×C4—114no—
463C22×C4—118no—
464C22×C4—114no—
465C22×C4—111no—
466C22×C4—112no—
467C22×C4—111no—
468C22×C4—114no—
469C22×C4—114no—
470C22×C4—112no—
471C22×C4—114no—
472C22×C4—224no—
473C22×C4—224no—
474C22×C4—224no—
475C22×C4—224no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—442no—
479C22×C4—444no—
480C22×C4C23×D1114yes—
481C22×C4C23×D1112yes—
482C22×C4C23×D1111yescharacteristic
483C22×C4C23×D1112yes—
484C22×C4C23×D1114yes—
485C22×C4C23×D1111yescharacteristic
486C22×C4C23×D1111yescharacteristic
487C4⋊C4—24no—
488C4⋊C4—22no—
489C4⋊C4—24no—
490C4⋊C4—24no—
491C4⋊C4—216no—
492C4⋊C4—118no—
493C4⋊C4—224no—
494C4⋊C4—224no—
495C4⋊C4—224no—
496C4⋊C4—228no—
497C4⋊C4—228no—
498C4⋊C4—2216no—
499C4⋊C4—224no—
500C4⋊C4—222no—
501C4⋊C4—224no—
502C4⋊C4—224no—
503C4⋊C4—448no—
504C4⋊C4—448no—
505C4⋊C4Q8×D1118yescomplemented
506C22⋊C4—1116no—
507C22⋊C4—228no—
508C42—24no—
509C42—24no—
510C42—114no—
511C42—114no—
512C42—114no—
513C42—1116no—
514C42—224no—
515C42—224no—
516C42—228no—
517C42—224no—
518C42—224no—
519C42—444no—
520C42D4×D1114yes—
521C11#3495311yescharacteristic, complemented, Sylow
522C23—112no—
523C23—114no—
524C23—221no—
525C23—221no—
526C23—222no—
527C23C24×D1111yescharacteristic
528Q8—28no—
529Q8—48no—
530Q8—2216no—
531Q8—228no—
532Q8—448no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—22no—
536C2×C4—24no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—112no—
544C2×C4—114no—
545C2×C4—1116no—
546C2×C4—112no—
547C2×C4—112no—
548C2×C4—118no—
549C2×C4—114no—
550C2×C4—2216no—
551C2×C4—222no—
552C2×C4—221no—
553C2×C4—222no—
554C2×C4—224no—
555C2×C4—221no—
556C2×C4—222no—
557C2×C4—224no—
558C2×C4—228no—
559C2×C4—222no—
560C2×C4—224no—
561C2×C4—224no—
562C2×C4—228no—
563C2×C4—444no—
564C2×C4—448no—
565C2×C4C2×D4×D1112yes—
566C2×C4C2×D4×D1112yes—
567C2×C4C2×D4×D1112yes—
568C2×C4C2×#434114yes—
569C2×C4C2×#434112yes—
570C2×C4C2×Q8×D1118yes—
571C2×C4C2×Q8×D1114yes—
572C2×C4#41×D1112yes—
573C22—114no—
574C22—222no—
575C22—224no—
576C22—224no—
577C22—222no—
578C22C22×D4×D1111yescharacteristic
579C22C22×#434111yescharacteristic
580C22C22×Q8×D1112yes—
581C22C2×#41×D1111yescharacteristic
582C22#1062345712yes—
583C4—24no—
584C4—28no—
585C4—22no—
586C4—44no—
587C4—42no—
588C4—114no—
589C4—222no—
590C4—224no—
591C4—228no—
592C4—222no—
593C4—442no—
594C4—444no—
595C4#1062313714yes—
596C4D11×C4⋊Q814yes—
597C2—224no—
598C2C2×#1062313711yescharacteristic
599C2C2×D11×C4⋊Q811yescharacteristic
600C2#1308194811yescharacteristic
601C2Q8×#434112yes—
602C2#1308219812yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2546C2
prime radicalC23×D11C24
hypercenter#2546D11
hypocenterC11#34953
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2546

Complements

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

NH ≅ G/Ntype
3. #13074001C2semidirect
5. #13073824C2semidirect
6. #13073821C2semidirect
7. #13073605C2semidirect
10. #13071908C2semidirect
11. C4⋊Q8×Dic11C2semidirect
12. #13071185C2semidirect
15. C11×#2546C2semidirect
125. #66945Q8semidirect
192. C11×C4⋊C4C2×Q8semidirect
204. C4⋊Dic11C2×Q8semidirect
220. C4×Dic11C2×Q8semidirect
228. #2546D11semidirect
283. C4×D11C4⋊Q8semidirect
505. C4⋊C4Q8×D11semidirect
521. C11#34953semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×C4×Q8×D112
#130740012
#130739902
#130738242
#130738212
#130736052
#130730932
#130722572
#130719082
C4⋊Q8×Dic112
#130711852
#130710972
C4×#669452
C11×#25462
#3495311