Finite Group Databasebeta

← #14913964

Subgroups — #14913964

Order 2816.

2250 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
1C2×C4×Q8×D11C211yesmaximal, characteristic
2#13071580C212yesmaximal, complemented
3#13071578C214yesmaximal, complemented
4#13071535C212yesmaximal, complemented
5#13071492C212yesmaximal
6#13071490C214yesmaximal
7#13071450C212yesmaximal
8#13071267C211yesmaximal, characteristic, complemented
9#13071266C212yesmaximal, complemented
10#13071264C212yesmaximal, complemented
11#13071013C212yesmaximal
12#13071012C211yesmaximal, characteristic
13#13071009C212yesmaximal
14#13071008C211yesmaximal, characteristic
15#13070980C211yesmaximal, characteristic, complemented
16#13070979C211yesmaximal, characteristic, complemented
17C11×#2320C211yesmaximal, characteristic, complemented
18C22×Q8×D11C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C4×Q8×D11C4116yescomplemented
22C2×C4⋊C4×D11C2212yes—
23C2×C4⋊C4×D11C2211yescharacteristic
24C2×#66940C2212yes—
25C2×#66940C2211yescharacteristic
26C2×#66940C2212yes—
27C2×C42×D11C2211yescharacteristic
28C2×C42×D11C2212yes—
29C2×C4×Dic22C2212yes—
30C2×C4×Dic22C2211yescharacteristic
31C2×C4×Dic22C2212yes—
32C11×#391C2212yes—
33C11×#389C2212yes—
34C11×#387C2214yes—
35C11×#383C2212yes—
36C11×#382C2212yes—
37C4×C11×C4⋊C4C2211yescharacteristic
38C11×#376C2211yescharacteristic
39#10622843C2212yes—
40#10622600C2212yes—
41#10622600C2214yes—
42#10622598C2212yes—
43#10622594C2214yes—
44#10622591C2214yes—
45#10622590C2212yes—
46C4⋊C4×Dic11C2212yes—
47C4⋊C4×Dic11C2214yes—
48#10622585C2214yes—
49C4×(C2×D11)⋊C4C2212yes—
50C4×(C2×D11)⋊C4C2212yes—
51#10622550C2212yes—
52#10622549C2212yes—
53C4×C4⋊Dic11C2212yes—
54C4×C4⋊Dic11C2211yescharacteristic
55#10622545C2211yescharacteristic
56#10622545C2212yes—
57C4×Dic11⋊C4C2214yes—
58C4×Dic11⋊C4C2212yes—
59#10622280C2214yes—
60#10622280C2212yes—
61#10622279C2214yes—
62#10622279C2214yes—
63#10622277C2211yescharacteristic
64#10622277C2211yescharacteristic
65#10622277C2212yes—
66#10622268C2214yes—
67#10622267C2214yes—
68#10622266C2214yes—
69#10622264C2212yes—
70#10622264C2212yes—
71#10622264C2214yes—
72#10622263C2211yescharacteristic
73#10622263C2211yescharacteristic
74#10622263C2214yes—
75#10622262C2214yes—
76#10622262C2212yes—
77#10622262C2212yes—
78#10622261C2212yes—
79#10622261C2212yes—
80#10622261C2214yes—
81#10622260C2214yes—
82#10622259C2214yes—
83#10622259C2214yes—
84C22×Q8×C11C2311yescharacteristic
85C2×Q8×D11—28no—
86C2×Q8×D11C2×C418yes—
87C22×C4×D11C2311yescharacteristic
88C22×C4×D11C2312yes—
89C22×C4×D11C2311yescharacteristic
90C22×C4×D11C2312yes—
91C22×C4×D11C2311yescharacteristic
92C22×Dic22C2312yes—
93C22×Dic22C2311yescharacteristic
94C4×Q8×C11C2×C418yes—
95C2×C11×C4⋊C4C2312yes—
96C2×C11×C4⋊C4C2314yes—
97C2×C11×C4⋊C4C2312yes—
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C42×C11C2312yes—
100C2×C42×C11C2312yes—
101C2×C42×C11C2311yescharacteristic
102C2×C42×C11C2312yes—
103Q8×Dic11C2×C418yes—
104C2×(C2×D11)⋊C4C2312yes—
105C2×(C2×D11)⋊C4C2312yes—
106C2×(C2×D11)⋊C4C2314yes—
107C2×C4⋊Dic11C2312yes—
108C2×C4⋊Dic11C2314yes—
109C2×C4⋊Dic11C2312yes—
110C2×C4⋊Dic11C2311yescharacteristic
111C2×Dic11⋊C4C2314yes—
112C2×Dic11⋊C4C2314yes—
113C2×Dic11⋊C4C2312yes—
114C2×Dic11⋊C4C2312yes—
115C2×Dic11⋊C4C2312yes—
116C2×Dic11⋊C4C2312yes—
117C2×Dic11⋊C4C2312yes—
118C2×C4×Dic11C2314yes—
119C2×C4×Dic11C2314yes—
120C2×C4×Dic11C2312yes—
121C2×C4×Dic11C2314yes—
122C2×C4×Dic11C2314yes—
123C2×C4×Dic11C2312yes—
124C2×C4×Dic11C2312yes—
125C2×C4×Dic11C2311yescharacteristic
126C2×C4×Dic11C2312yes—
127C2×C4×Dic11C2311yescharacteristic
128C2×C4×Dic11C2312yes—
129C2×C4×Dic11C2311yescharacteristic
130C4⋊C4×D11C2×C4116yes—
131C4⋊C4×D11C2×C418yes—
132#66940—28no—
133#66940C2×C4116yes—
134#66940C2×C418yes—
135C42×D11C2×C418yes—
136C42×D11C2×C4116yes—
137C4×Dic22—28no—
138C4×Dic22C2×C4116yes—
139C4×Dic22C2×C418yes—
140C11×#95C2314yes—
141C11×#95C2314yes—
142C11×#95C2314yes—
143C11×#95C2311yescharacteristic
144C11×#95C2312yes—
145C11×#95C2311yescharacteristic
146C11×#95C2312yes—
147C11⋊#95C2312yes—
148C11⋊#95C2312yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2312yes—
154C11⋊#95C2311yescharacteristic
155C11⋊#95C2314yes—
156C11⋊#95C2312yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2311yescharacteristic
160C11⋊#95C2314yes—
161C11⋊#95C2312yes—
162C11⋊#95C2312yes—
163#34192—111nomaximal, Sylow
164C23×D11C2411yescharacteristic
165C2×Q8×C11—24no—
166C2×Q8×C11C22×C414yes—
167C22×C4×C11C2412yes—
168C22×C4×C11C2414yes—
169C22×C4×C11C2412yes—
170C22×C4×C11C2411yescharacteristic
171C22×C4×C11C2412yes—
172C22×C4×C11C2411yescharacteristic
173C22×C4×C11C2412yes—
174C22×C4×C11C2411yescharacteristic
175C22×Dic11C2412yes—
176C22×Dic11C2412yes—
177C22×Dic11C2414yes—
178C22×Dic11C2411yescharacteristic
179C22×Dic11C2411yescharacteristic
180C22×Dic11C2412yes—
181C22×Dic11C2411yescharacteristic
182C22×Dic11C2412yes—
183Q8×D11—232no—
184C2×C4×D11—28no—
185C2×C4×D11—24no—
186C2×C4×D11—24no—
187C2×C4×D11—41no—
188C2×C4×D11—42no—
189C2×C4×D11—41no—
190C2×C4×D11—42no—
191C2×C4×D11C22×C414yes—
192C2×C4×D11C22×C418yes—
193C2×C4×D11C22×C414yes—
194C2×C4×D11C22×C418yes—
195C2×C4×D11C22×C414yes—
196C2×Dic22—28no—
197C2×Dic22C22×C418yes—
198C2×Dic22C22×C414yes—
199C2×Dic22#4118yes—
200C11×C4⋊C4—24no—
201C11×C4⋊C4—44no—
202C11×C4⋊C4C22×C418yes—
203C11×C4⋊C4C22×C414yes—
204C42×C11—24no—
205C42×C11—42no—
206C42×C11C22×C418yes—
207C42×C11C22×C414yes—
208(C2×D11)⋊C4—24no—
209(C2×D11)⋊C4—24no—
210(C2×D11)⋊C4—28no—
211C4⋊Dic11—24no—
212C4⋊Dic11—44no—
213C4⋊Dic11C22×C418yes—
214C4⋊Dic11C22×C414yes—
215Dic11⋊C4—28no—
216Dic11⋊C4—28no—
217Dic11⋊C4—42no—
218Dic11⋊C4—42no—
219Dic11⋊C4C22×C418yes—
220Dic11⋊C4C22×C418yes—
221Dic11⋊C4C22×C418yes—
222C4×Dic11—28no—
223C4×Dic11—28no—
224C4×Dic11—24no—
225C4×Dic11—42no—
226C4×Dic11—44no—
227C4×Dic11—44no—
228C4×Dic11C22×C414yes—
229C4×Dic11C22×C418yes—
230C4×Dic11C22×C414yes—
231C4×Dic11C22×C418yes—
232C4×Dic11C22×C418yes—
233C4×Dic11C22×C414yes—
234C22×C4×Q8—111no—
235#2356—112no—
236#2356—114no—
237#2351—112no—
238#2345—112no—
239#2345—114no—
240Q8×C22⋊C4—112no—
241#2320—112no—
242#2320—112no—
243#2320—111no—
244#2320D1111yescharacteristic, complemented
245#2283—112no—
246#2283—112no—
247#2283—111no—
248#2283—111no—
249#2276—111no—
250#2276—111no—
251C23×C11C2511yescharacteristic
252C22×D11—22no—
253C22×D11—21no—
254C22×D11—21no—
255C22×D11C23×C412yes—
256C22×D112−1+414yes—
257Q8×C11—28no—
258C2×C4×C11—24no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
262C2×C4×C11—21no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—24no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—24no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—24no—
272C2×C4×C11—22no—
273C2×C4×C11C23×C412yes—
274C2×C4×C11C23×C412yes—
275C2×C4×C11C23×C414yes—
276C2×C4×C11C23×C414yes—
277C2×C4×C11C23×C412yes—
278C2×C4×C11C2×#4114yes—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—22no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—22no—
286C2×Dic11—22no—
287C2×Dic11—24no—
288C2×Dic11—22no—
289C2×Dic11—22no—
290C2×Dic11—24no—
291C2×Dic11—22no—
292C2×Dic11—24no—
293C2×Dic11—22no—
294C2×Dic11C23×C412yes—
295C2×Dic11C23×C414yes—
296C2×Dic11C23×C412yes—
297C2×Dic11C23×C412yes—
298C2×Dic11C23×C414yes—
299C2×Dic11C2×#4118yes—
300C4×D11—28no—
301C4×D11—28no—
302C4×D11—216no—
303C4×D11—48no—
304C4×D11—44no—
305Dic22—216no—
306Dic22#117116yes—
307C23×Q8—111no—
308C2×C4×Q8—111no—
309C2×C4×Q8—1116no—
310C2×C4×Q8—111no—
311C2×C4×Q8—112no—
312C2×C4×Q8—112no—
313C2×C4×Q8—112no—
314C2×C4×Q8—111no—
315C2×C4×Q8—112no—
316C2×C4×Q8C2×D1111yescharacteristic
317C22×C4⋊C4—112no—
318C22×C4⋊C4—111no—
319C22×C42—112no—
320C22×C42—111no—
321#391—112no—
322#391—114no—
323#391—114no—
324#391C2×D1112yes—
325#389—114no—
326#389—112no—
327#389—114no—
328#389C2×D1112yes—
329#387—114no—
330#387—114no—
331#387—114no—
332#387—114no—
333#387—114no—
334#387C2×D1114yes—
335#383—112no—
336#383—112no—
337#383—114no—
338#383—112no—
339#383C2×D1112yes—
340#382—112no—
341#382—112no—
342#382—111no—
343#382—111no—
344#382—114no—
345#382C2×D1112yes—
346#381—111no—
347#381—112no—
348#381—111no—
349#380—112no—
350#380—114no—
351#380—114no—
352#380—112no—
353C4×C4⋊C4—112no—
354C4×C4⋊C4—114no—
355C4×C4⋊C4—111no—
356C4×C4⋊C4—114no—
357C4×C4⋊C4—112no—
358C4×C4⋊C4—112no—
359C4×C4⋊C4—112no—
360C4×C4⋊C4—112no—
361C4×C4⋊C4—114no—
362C4×C4⋊C4C2×D1111yescharacteristic
363C4×C22⋊C4—112no—
364C4×C22⋊C4—112no—
365C4×C22⋊C4—114no—
366C4×C22⋊C4—114no—
367#376—111no—
368#376—112no—
369#376—112no—
370#376—112no—
371#376—114no—
372#376C2×D1111yescharacteristic
373C22×C11C24×C411yescharacteristic
374C22×C11C22×#4112yes—
375C22×C11C2×2−1+412yes—
376C22×C11#58511yescharacteristic
377C22×C11#58511yescharacteristic
378C2×D11—22no—
379C2×D11—22no—
380C2×D11—24no—
381C2×D11—24no—
382C2×D11#51914yes—
383C4×C11—24no—
384C4×C11—22no—
385C4×C11—22no—
386C4×C11—24no—
387C4×C11—42no—
388C4×C11—44no—
389C4×C11—42no—
390C4×C11C2×#11714yes—
391Dic11—22no—
392Dic11—22no—
393Dic11—24no—
394Dic11—22no—
395Dic11—42no—
396Dic11—42no—
397Dic11—44no—
398Dic11C2×#11718yes—
399C22×Q8—118no—
400C22×Q8—111no—
401C22×Q8—112no—
402C22×Q8—228no—
403C22×Q8C22×D1111yescharacteristic
404C23×C4—112no—
405C23×C4—111no—
406C23×C4—111no—
407C23×C4—112no—
408C23×C4—111no—
409C4×Q8—118no—
410C4×Q8—118no—
411C4×Q8—1116no—
412C4×Q8—118no—
413C4×Q8—1116no—
414C4×Q8—228no—
415C4×Q8—228no—
416C4×Q8C4×D1118yes—
417C2×C4⋊C4—112no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—112no—
420C2×C4⋊C4—112no—
421C2×C4⋊C4—112no—
422C2×C4⋊C4—1116no—
423C2×C4⋊C4—118no—
424C2×C4⋊C4—114no—
425C2×C4⋊C4—114no—
426C2×C4⋊C4—112no—
427C2×C4⋊C4—112no—
428C2×C4⋊C4—112no—
429C2×C4⋊C4—114no—
430C2×C4⋊C4C22×D1112yes—
431C2×C4⋊C4C22×D1114yes—
432C2×C4⋊C4C22×D1112yes—
433C2×C4⋊C4C22×D1111yescharacteristic
434C2×C22⋊C4—112no—
435C2×C22⋊C4—114no—
436C2×C22⋊C4—112no—
437C2×C42—112no—
438C2×C42—111no—
439C2×C42—112no—
440C2×C42—112no—
441C2×C42—111no—
442C2×C42—111no—
443C2×C42—1116no—
444C2×C42—118no—
445C2×C42—114no—
446C2×C42—114no—
447C2×C42—112no—
448C2×C42—114no—
449C2×C42—114no—
450C2×C42—112no—
451C2×C42C22×D1112yes—
452C2×C42C22×D1112yes—
453C2×C42C22×D1111yescharacteristic
454C2×C42C22×D1112yes—
455#95—111no—
456#95—114no—
457#95—112no—
458#95—114no—
459#95—114no—
460#95—112no—
461#95—112no—
462#95—111no—
463#95—114no—
464#95—114no—
465#95—114no—
466#95—114no—
467#95—112no—
468#95—112no—
469#95—114no—
470#95—112no—
471#95C22×D1111yescharacteristic
472#95C22×D1112yes—
473#95C22×D1114yes—
474#95C22×D1112yes—
475#95C22×D1111yescharacteristic
476#95C22×D1114yes—
477#95C22×D1114yes—
478C2×C11C22×#11711yescharacteristic
479C2×C11C2×#51911yescharacteristic
480C2×C11#342811yescharacteristic
481C2×C11#351612yes—
482C2×C11#351612yes—
483D11—24no—
484C24—111no—
485C2×Q8—24no—
486C2×Q8—114no—
487C2×Q8—118no—
488C2×Q8—118no—
489C2×Q8—228no—
490C2×Q8—2232no—
491C2×Q8C2×C4×D1114yes—
492C22×C4—112no—
493C22×C4—111no—
494C22×C4—111no—
495C22×C4—112no—
496C22×C4—111no—
497C22×C4—114no—
498C22×C4—118no—
499C22×C4—114no—
500C22×C4—118no—
501C22×C4—114no—
502C22×C4—112no—
503C22×C4—112no—
504C22×C4—114no—
505C22×C4—228no—
506C22×C4—224no—
507C22×C4—224no—
508C22×C4—441no—
509C22×C4—442no—
510C22×C4—441no—
511C22×C4—442no—
512C22×C4C23×D1112yes—
513C22×C4C23×D1114yes—
514C22×C4C23×D1112yes—
515C22×C4C23×D1111yescharacteristic
516C22×C4C23×D1112yes—
517C22×C4C23×D1111yescharacteristic
518C22×C4C23×D1112yes—
519C22×C4C23×D1111yescharacteristic
520C4⋊C4—24no—
521C4⋊C4—44no—
522C4⋊C4—118no—
523C4⋊C4—118no—
524C4⋊C4—118no—
525C4⋊C4—118no—
526C4⋊C4—114no—
527C4⋊C4—228no—
528C4⋊C4—228no—
529C4⋊C4—224no—
530C4⋊C4—442no—
531C4⋊C4—442no—
532C4⋊C4—444no—
533C4⋊C4C2×C4×D1118yes—
534C4⋊C4C2×C4×D1114yes—
535C22⋊C4—224no—
536C22⋊C4—228no—
537C22⋊C4—224no—
538C42—24no—
539C42—42no—
540C42—118no—
541C42—118no—
542C42—118no—
543C42—114no—
544C42—114no—
545C42—114no—
546C42—228no—
547C42—228no—
548C42—224no—
549C42—442no—
550C42—444no—
551C42—444no—
552C42C2×C4×D1118yes—
553C42C2×C4×D1114yes—
554C11#3419211yescharacteristic, complemented, Sylow
555C23—112no—
556C23—114no—
557C23—222no—
558C23—221no—
559C23—221no—
560C23C24×D1111yescharacteristic
561Q8—28no—
562Q8—1116no—
563Q8—2216no—
564C2×C4—24no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—114no—
580C2×C4—118no—
581C2×C4—112no—
582C2×C4—114no—
583C2×C4—112no—
584C2×C4—112no—
585C2×C4—2216no—
586C2×C4—228no—
587C2×C4—222no—
588C2×C4—222no—
589C2×C4—221no—
590C2×C4—222no—
591C2×C4—222no—
592C2×C4—221no—
593C2×C4—228no—
594C2×C4—222no—
595C2×C4—222no—
596C2×C4—224no—
597C2×C4—222no—
598C2×C4—222no—
599C2×C4—222no—
600C2×C4—224no—
601C2×C4—224no—
602C2×C4—222no—
603C2×C4—444no—
604C2×C4—448no—
605C2×C4C22×C4×D1112yes—
606C2×C4C22×C4×D1112yes—
607C2×C4C22×C4×D1114yes—
608C2×C4C22×C4×D1114yes—
609C2×C4C22×C4×D1112yes—
610C2×C4#41×D1114yes—
611C22—114no—
612C22—222no—
613C22—222no—
614C22—224no—
615C22—224no—
616C22C23×C4×D1111yescharacteristic
617C22C2×#41×D1112yes—
618C22#1062345511yescharacteristic
619C22D11×2−1+412yes—
620C22#1062345711yescharacteristic
621C4—24no—
622C4—22no—
623C4—22no—
624C4—24no—
625C4—42no—
626C4—44no—
627C4—42no—
628C4—118no—
629C4—222no—
630C4—222no—
631C4—224no—
632C4—222no—
633C4—442no—
634C4—442no—
635C4—444no—
636C4D11×#11714yes—
637C2—224no—
638C2C2×D11×#11711yescharacteristic
639C2D11×#51911yescharacteristic
640C2#1308181611yescharacteristic
641C2#1308260312yes—
642C2#1308260712yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2320C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2320D11
hypocenterC11#34192
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2320

Complements

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

NH ≅ G/Ntype
2. #13071580C2semidirect
3. #13071578C2semidirect
4. #13071535C2semidirect
8. #13071267C2semidirect
9. #13071266C2semidirect
10. #13071264C2semidirect
15. #13070980C2semidirect
16. #13070979C2semidirect
17. C11×#2320C2semidirect
21. C4×Q8×D11C4semidirect
244. #2320D11semidirect
554. 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
#130715802
#130715782
#130715352
#130714922
#130714902
#130714502
#130712672
#130712662
#130712642
#130710132
#130710122
#130710092
#130710082
#130709802
#130709792
C11×#23202
#3419211