Finite Group Databasebeta

← #14913965

Subgroups — #14913965

Order 2816.

2250 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D11C211yesmaximal, characteristic
2#13071582C212yesmaximal, complemented
3#13071581C211yesmaximal, characteristic, complemented
4#13071576C212yesmaximal, complemented
5#13071536C211yesmaximal, characteristic, complemented
6#13071533C211yesmaximal, characteristic, complemented
7#13071490C214yesmaximal
8#13071489C212yesmaximal
9#13071450C212yesmaximal
10#13071265C214yesmaximal, complemented
11#13071261C212yesmaximal, complemented
12#13071013C212yesmaximal
13#13071012C211yesmaximal, characteristic
14#13071009C211yesmaximal, characteristic
15#13071008C212yesmaximal
16#13070980C212yesmaximal, complemented
17C11×#2356C211yesmaximal, characteristic, complemented
18C22×Q8×D11C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C4×Q8×D11C4116yescomplemented
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×C4⋊C4×D11C2212yes—
24C2×#66940C2212yes—
25C2×#66940C2211yescharacteristic
26C2×#66940C2212yes—
27C2×C42×D11C2212yes—
28C2×C42×D11C2211yescharacteristic
29C2×C4×Dic22C2212yes—
30C2×C4×Dic22C2211yescharacteristic
31C2×C4×Dic22C2212yes—
32C11×#391C2212yes—
33C11×#387C2214yes—
34C11×#383C2212yes—
35C11×#382C2211yescharacteristic
36C4×C11×C4⋊C4C2212yes—
37C4×C11×C4⋊C4C2211yescharacteristic
38C11×#376C2212yes—
39#10622843C2212yes—
40#10622600C2212yes—
41#10622600C2212yes—
42#10622594C2214yes—
43#10622590C2212yes—
44C4⋊C4×Dic11C2212yes—
45C4⋊C4×Dic11C2212yes—
46#10622586C2212yes—
47#10622585C2214yes—
48C4×(C2×D11)⋊C4C2212yes—
49C4×(C2×D11)⋊C4C2214yes—
50#10622550C2212yes—
51#10622549C2211yescharacteristic
52C4×C4⋊Dic11C2211yescharacteristic
53#10622546C2214yes—
54#10622545C2212yes—
55#10622545C2212yes—
56C4×Dic11⋊C4C2214yes—
57C4×Dic11⋊C4C2214yes—
58#10622541C2212yes—
59#10622280C2214yes—
60#10622280C2214yes—
61#10622279C2214yes—
62#10622279C2212yes—
63#10622277C2211yescharacteristic
64#10622277C2212yes—
65#10622277C2211yescharacteristic
66#10622267C2214yes—
67#10622266C2214yes—
68#10622265C2214yes—
69#10622264C2214yes—
70#10622264C2212yes—
71#10622264C2211yescharacteristic
72#10622264C2211yescharacteristic
73#10622263C2214yes—
74#10622263C2212yes—
75#10622263C2212yes—
76#10622262C2214yes—
77#10622262C2212yes—
78#10622262C2212yes—
79#10622261C2214yes—
80#10622261C2212yes—
81#10622260C2214yes—
82#10622259C2214yes—
83#10622259C2214yes—
84C22×Q8×C11C2311yescharacteristic
85C2×Q8×D11—24no—
86C2×Q8×D11—24no—
87C2×Q8×D11C2×C418yes—
88C22×C4×D11C2311yescharacteristic
89C22×C4×D11C2312yes—
90C22×C4×D11C2311yescharacteristic
91C22×C4×D11C2311yescharacteristic
92C22×C4×D11C2312yes—
93C22×Dic22C2312yes—
94C22×Dic22C2311yescharacteristic
95C4×Q8×C11C2×C418yes—
96C2×C11×C4⋊C4C2312yes—
97C2×C11×C4⋊C4C2312yes—
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2312yes—
100C2×C42×C11C2312yes—
101C2×C42×C11C2314yes—
102C2×C42×C11C2312yes—
103C2×C42×C11C2311yescharacteristic
104Q8×Dic11C2×C418yes—
105C2×(C2×D11)⋊C4C2314yes—
106C2×(C2×D11)⋊C4C2312yes—
107C2×(C2×D11)⋊C4C2312yes—
108C2×C4⋊Dic11C2312yes—
109C2×C4⋊Dic11C2312yes—
110C2×C4⋊Dic11C2312yes—
111C2×C4⋊Dic11C2311yescharacteristic
112C2×Dic11⋊C4C2314yes—
113C2×Dic11⋊C4C2314yes—
114C2×Dic11⋊C4C2314yes—
115C2×Dic11⋊C4C2314yes—
116C2×Dic11⋊C4C2312yes—
117C2×Dic11⋊C4C2312yes—
118C2×Dic11⋊C4C2312yes—
119C2×C4×Dic11C2314yes—
120C2×C4×Dic11C2314yes—
121C2×C4×Dic11C2312yes—
122C2×C4×Dic11C2314yes—
123C2×C4×Dic11C2314yes—
124C2×C4×Dic11C2311yescharacteristic
125C2×C4×Dic11C2312yes—
126C2×C4×Dic11C2312yes—
127C2×C4×Dic11C2311yescharacteristic
128C2×C4×Dic11C2312yes—
129C2×C4×Dic11C2311yescharacteristic
130C4⋊C4×D11C2×C418yes—
131C4⋊C4×D11C2×C4116yes—
132#66940—28no—
133#66940C2×C4116yes—
134#66940C2×C418yes—
135C42×D11C2×C4116yes—
136C42×D11C2×C418yes—
137C4×Dic22—28no—
138C4×Dic22C2×C4116yes—
139C4×Dic22C2×C418yes—
140C11×#95C2314yes—
141C11×#95C2314yes—
142C11×#95C2312yes—
143C11×#95C2312yes—
144C11×#95C2314yes—
145C11×#95C2311yescharacteristic
146C11×#95C2311yescharacteristic
147C11⋊#95C2314yes—
148C11⋊#95C2312yes—
149C11⋊#95C2312yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2312yes—
154C11⋊#95C2312yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2312yes—
158C11⋊#95C2311yescharacteristic
159C11⋊#95C2311yescharacteristic
160C11⋊#95C2314yes—
161C11⋊#95C2312yes—
162C11⋊#95C2312yes—
163C11⋊#95C2312yes—
164#34192—111nomaximal, Sylow
165C23×D11C2411yescharacteristic
166C2×Q8×C11—22no—
167C2×Q8×C11—22no—
168C2×Q8×C11C22×C414yes—
169C22×C4×C11C2412yes—
170C22×C4×C11C2412yes—
171C22×C4×C11C2414yes—
172C22×C4×C11C2411yescharacteristic
173C22×C4×C11C2412yes—
174C22×C4×C11C2412yes—
175C22×C4×C11C2411yescharacteristic
176C22×C4×C11C2411yescharacteristic
177C22×Dic11C2412yes—
178C22×Dic11C2412yes—
179C22×Dic11C2414yes—
180C22×Dic11C2411yescharacteristic
181C22×Dic11C2411yescharacteristic
182C22×Dic11C2411yescharacteristic
183C22×Dic11C2412yes—
184C22×Dic11C2412yes—
185Q8×D11—232no—
186C2×C4×D11—24no—
187C2×C4×D11—24no—
188C2×C4×D11—24no—
189C2×C4×D11—22no—
190C2×C4×D11—22no—
191C2×C4×D11—44no—
192C2×C4×D11—42no—
193C2×C4×D11C22×C414yes—
194C2×C4×D11C22×C418yes—
195C2×C4×D11C22×C414yes—
196C2×C4×D11C22×C414yes—
197C2×C4×D11C22×C418yes—
198C2×Dic22—24no—
199C2×Dic22—24no—
200C2×Dic22C22×C418yes—
201C2×Dic22C22×C414yes—
202C2×Dic22#4114yes—
203C2×Dic22#4114yes—
204C11×C4⋊C4—24no—
205C11×C4⋊C4—42no—
206C11×C4⋊C4C22×C418yes—
207C11×C4⋊C4C22×C414yes—
208C42×C11—24no—
209C42×C11—44no—
210C42×C11C22×C418yes—
211C42×C11C22×C414yes—
212(C2×D11)⋊C4—28no—
213(C2×D11)⋊C4—24no—
214(C2×D11)⋊C4—24no—
215C4⋊Dic11—24no—
216C4⋊Dic11—42no—
217C4⋊Dic11C22×C418yes—
218C4⋊Dic11C22×C414yes—
219Dic11⋊C4—28no—
220Dic11⋊C4—28no—
221Dic11⋊C4—44no—
222Dic11⋊C4—44no—
223Dic11⋊C4C22×C418yes—
224Dic11⋊C4C22×C418yes—
225Dic11⋊C4C22×C418yes—
226C4×Dic11—28no—
227C4×Dic11—28no—
228C4×Dic11—24no—
229C4×Dic11—44no—
230C4×Dic11—44no—
231C4×Dic11C22×C414yes—
232C4×Dic11C22×C418yes—
233C4×Dic11C22×C414yes—
234C4×Dic11C22×C418yes—
235C4×Dic11C22×C418yes—
236C4×Dic11C22×C414yes—
237C22×C4×Q8—111no—
238#2356—112no—
239#2356—112no—
240#2356—111no—
241#2356D1111yescharacteristic, complemented
242#2351—111no—
243#2351—111no—
244#2345—114no—
245#2345—112no—
246Q8×C22⋊C4—112no—
247#2320—112no—
248#2320—114no—
249#2283—112no—
250#2283—111no—
251#2283—111no—
252#2283—112no—
253#2276—112no—
254C23×C11C2511yescharacteristic
255C22×D11—21no—
256C22×D11—21no—
257C22×D11—22no—
258C22×D11C23×C412yes—
259C22×D112−1+414yes—
260Q8×C11—28no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—24no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—24no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—24no—
271C2×C4×C11—22no—
272C2×C4×C11—24no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11C23×C412yes—
276C2×C4×C11C23×C414yes—
277C2×C4×C11C23×C412yes—
278C2×C4×C11C23×C414yes—
279C2×C4×C11C23×C412yes—
280C2×C4×C11C2×#4112yes—
281C2×C4×C11C2×#4112yes—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—22no—
285C2×Dic11—22no—
286C2×Dic11—24no—
287C2×Dic11—22no—
288C2×Dic11—22no—
289C2×Dic11—24no—
290C2×Dic11—22no—
291C2×Dic11—22no—
292C2×Dic11—24no—
293C2×Dic11—24no—
294C2×Dic11—22no—
295C2×Dic11—22no—
296C2×Dic11C23×C412yes—
297C2×Dic11C23×C412yes—
298C2×Dic11C23×C414yes—
299C2×Dic11C23×C412yes—
300C2×Dic11C23×C414yes—
301C2×Dic11C2×#4114yes—
302C2×Dic11C2×#4114yes—
303C4×D11—28no—
304C4×D11—28no—
305C4×D11—216no—
306C4×D11—44no—
307C4×D11—48no—
308Dic22—216no—
309Dic22#117116yes—
310C23×Q8—111no—
311C2×C4×Q8—111no—
312C2×C4×Q8—1116no—
313C2×C4×Q8—112no—
314C2×C4×Q8—111no—
315C2×C4×Q8—112no—
316C2×C4×Q8—111no—
317C2×C4×Q8—112no—
318C2×C4×Q8—112no—
319C2×C4×Q8C2×D1111yescharacteristic
320C22×C4⋊C4—112no—
321C22×C4⋊C4—111no—
322C22×C42—111no—
323C22×C42—112no—
324#391—112no—
325#391—114no—
326#391—114no—
327#391C2×D1112yes—
328#389—114no—
329#389—112no—
330#389—112no—
331#389—114no—
332#387—114no—
333#387—114no—
334#387—114no—
335#387—114no—
336#387—114no—
337#387C2×D1114yes—
338#383—112no—
339#383—112no—
340#383—114no—
341#383—111no—
342#383—111no—
343#383C2×D1112yes—
344#382—112no—
345#382—111no—
346#382—114no—
347#382—112no—
348#382—112no—
349#382C2×D1111yescharacteristic
350#381—111no—
351#381—112no—
352#381—111no—
353#380—112no—
354#380—112no—
355#380—114no—
356#380—114no—
357C4×C4⋊C4—112no—
358C4×C4⋊C4—112no—
359C4×C4⋊C4—114no—
360C4×C4⋊C4—114no—
361C4×C4⋊C4—111no—
362C4×C4⋊C4—114no—
363C4×C4⋊C4—112no—
364C4×C4⋊C4—112no—
365C4×C4⋊C4C2×D1112yes—
366C4×C4⋊C4C2×D1111yescharacteristic
367C4×C22⋊C4—112no—
368C4×C22⋊C4—114no—
369C4×C22⋊C4—114no—
370C4×C22⋊C4—112no—
371#376—112no—
372#376—112no—
373#376—114no—
374#376—112no—
375#376C2×D1112yes—
376C22×C11C24×C411yescharacteristic
377C22×C11C22×#4111yescharacteristic
378C22×C11C22×#4111yescharacteristic
379C22×C11C2×2−1+412yes—
380C22×C11#58512yes—
381C2×D11—22no—
382C2×D11—22no—
383C2×D11—24no—
384C2×D11—24no—
385C2×D11#51914yes—
386C4×C11—24no—
387C4×C11—22no—
388C4×C11—24no—
389C4×C11—22no—
390C4×C11—44no—
391C4×C11—42no—
392C4×C11—42no—
393C4×C11C2×#11714yes—
394Dic11—22no—
395Dic11—22no—
396Dic11—22no—
397Dic11—24no—
398Dic11—42no—
399Dic11—42no—
400Dic11—44no—
401Dic11C2×#11718yes—
402C22×Q8—118no—
403C22×Q8—111no—
404C22×Q8—112no—
405C22×Q8—224no—
406C22×Q8—224no—
407C22×Q8C22×D1111yescharacteristic
408C23×C4—112no—
409C23×C4—111no—
410C23×C4—111no—
411C23×C4—111no—
412C23×C4—112no—
413C4×Q8—118no—
414C4×Q8—118no—
415C4×Q8—1116no—
416C4×Q8—118no—
417C4×Q8—1116no—
418C4×Q8—228no—
419C4×Q8—228no—
420C4×Q8C4×D1118yes—
421C2×C4⋊C4—112no—
422C2×C4⋊C4—112no—
423C2×C4⋊C4—112no—
424C2×C4⋊C4—112no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—1116no—
427C2×C4⋊C4—118no—
428C2×C4⋊C4—114no—
429C2×C4⋊C4—114no—
430C2×C4⋊C4—112no—
431C2×C4⋊C4—114no—
432C2×C4⋊C4—114no—
433C2×C4⋊C4—112no—
434C2×C4⋊C4C22×D1112yes—
435C2×C4⋊C4C22×D1112yes—
436C2×C4⋊C4C22×D1111yescharacteristic
437C2×C4⋊C4C22×D1112yes—
438C2×C22⋊C4—112no—
439C2×C22⋊C4—112no—
440C2×C22⋊C4—114no—
441C2×C42—112no—
442C2×C42—111no—
443C2×C42—111no—
444C2×C42—112no—
445C2×C42—111no—
446C2×C42—112no—
447C2×C42—1116no—
448C2×C42—118no—
449C2×C42—114no—
450C2×C42—114no—
451C2×C42—112no—
452C2×C42—114no—
453C2×C42—114no—
454C2×C42C22×D1112yes—
455C2×C42C22×D1114yes—
456C2×C42C22×D1112yes—
457C2×C42C22×D1111yescharacteristic
458#95—112no—
459#95—112no—
460#95—111no—
461#95—112no—
462#95—112no—
463#95—114no—
464#95—112no—
465#95—114no—
466#95—114no—
467#95—114no—
468#95—114no—
469#95—114no—
470#95—112no—
471#95—112no—
472#95—112no—
473#95—114no—
474#95—111no—
475#95C22×D1112yes—
476#95C22×D1114yes—
477#95C22×D1111yescharacteristic
478#95C22×D1114yes—
479#95C22×D1114yes—
480#95C22×D1112yes—
481#95C22×D1111yescharacteristic
482C2×C11C22×#11711yescharacteristic
483C2×C11C2×#51911yescharacteristic
484C2×C11#342811yescharacteristic
485C2×C11#351612yes—
486C2×C11#351612yes—
487D11—24no—
488C24—111no—
489C2×Q8—22no—
490C2×Q8—22no—
491C2×Q8—114no—
492C2×Q8—118no—
493C2×Q8—114no—
494C2×Q8—114no—
495C2×Q8—224no—
496C2×Q8—224no—
497C2×Q8—2232no—
498C2×Q8C2×C4×D1114yes—
499C22×C4—112no—
500C22×C4—111no—
501C22×C4—111no—
502C22×C4—111no—
503C22×C4—112no—
504C22×C4—114no—
505C22×C4—118no—
506C22×C4—114no—
507C22×C4—114no—
508C22×C4—118no—
509C22×C4—112no—
510C22×C4—112no—
511C22×C4—114no—
512C22×C4—224no—
513C22×C4—224no—
514C22×C4—224no—
515C22×C4—222no—
516C22×C4—222no—
517C22×C4—444no—
518C22×C4—442no—
519C22×C4C23×D1112yes—
520C22×C4C23×D1112yes—
521C22×C4C23×D1114yes—
522C22×C4C23×D1111yescharacteristic
523C22×C4C23×D1112yes—
524C22×C4C23×D1112yes—
525C22×C4C23×D1111yescharacteristic
526C22×C4C23×D1111yescharacteristic
527C4⋊C4—24no—
528C4⋊C4—42no—
529C4⋊C4—118no—
530C4⋊C4—118no—
531C4⋊C4—118no—
532C4⋊C4—118no—
533C4⋊C4—114no—
534C4⋊C4—228no—
535C4⋊C4—228no—
536C4⋊C4—224no—
537C4⋊C4—444no—
538C4⋊C4—444no—
539C4⋊C4—442no—
540C4⋊C4C2×C4×D1118yes—
541C4⋊C4C2×C4×D1114yes—
542C22⋊C4—228no—
543C22⋊C4—224no—
544C22⋊C4—224no—
545C42—24no—
546C42—44no—
547C42—118no—
548C42—118no—
549C42—118no—
550C42—114no—
551C42—114no—
552C42—114no—
553C42—228no—
554C42—228no—
555C42—224no—
556C42—444no—
557C42—444no—
558C42C2×C4×D1118yes—
559C42C2×C4×D1114yes—
560C11#3419211yescharacteristic, complemented, Sylow
561C23—112no—
562C23—114no—
563C23—221no—
564C23—221no—
565C23—222no—
566C23C24×D1111yescharacteristic
567Q8—28no—
568Q8—1116no—
569Q8—2216no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—24no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—114no—
585C2×C4—114no—
586C2×C4—114no—
587C2×C4—112no—
588C2×C4—112no—
589C2×C4—114no—
590C2×C4—112no—
591C2×C4—2216no—
592C2×C4—228no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—222no—
596C2×C4—224no—
597C2×C4—222no—
598C2×C4—228no—
599C2×C4—222no—
600C2×C4—222no—
601C2×C4—224no—
602C2×C4—222no—
603C2×C4—224no—
604C2×C4—222no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—224no—
608C2×C4—448no—
609C2×C4—444no—
610C2×C4C22×C4×D1112yes—
611C2×C4C22×C4×D1114yes—
612C2×C4C22×C4×D1112yes—
613C2×C4C22×C4×D1114yes—
614C2×C4C22×C4×D1112yes—
615C2×C4#41×D1112yes—
616C2×C4#41×D1112yes—
617C22—114no—
618C22—222no—
619C22—222no—
620C22—224no—
621C22—224no—
622C22C23×C4×D1111yescharacteristic
623C22C2×#41×D1111yescharacteristic
624C22C2×#41×D1111yescharacteristic
625C22#1062345312yes—
626C22D11×2−1+412yes—
627C4—24no—
628C4—22no—
629C4—24no—
630C4—22no—
631C4—44no—
632C4—42no—
633C4—42no—
634C4—118no—
635C4—222no—
636C4—222no—
637C4—222no—
638C4—224no—
639C4—442no—
640C4—442no—
641C4—444no—
642C4D11×#11714yes—
643C2—224no—
644C2C2×D11×#11711yescharacteristic
645C2D11×#51911yescharacteristic
646C2#1308181511yescharacteristic
647C2#1308260412yes—
648C2#1308260812yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2356C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2356D11
hypocenterC11#34192
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2356

Complements

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

NH ≅ G/Ntype
2. #13071582C2semidirect
3. #13071581C2semidirect
4. #13071576C2semidirect
5. #13071536C2semidirect
6. #13071533C2semidirect
10. #13071265C2semidirect
11. #13071261C2semidirect
16. #13070980C2semidirect
17. C11×#2356C2semidirect
21. C4×Q8×D11C4semidirect
241. #2356D11semidirect
560. C11#34192semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D112
#130715822
#130715812
#130715762
#130715362
#130715332
#130714902
#130714892
#130714502
#130712652
#130712612
#130710132
#130710122
#130710092
#130710082
#130709802
C11×#23562
#3419211