Finite Group Databasebeta

← #14914462

Subgroups — #14914462

Order 2816.

2094 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623109C211yesmaximal, characteristic
2#13071702C212yesmaximal, complemented
3#13071673C212yesmaximal, complemented
4#13071648C212yesmaximal
5#13071642C212yesmaximal
6#13071583C212yesmaximal, complemented
7#13071576C212yesmaximal, complemented
8#13071504C212yesmaximal
9#13071496C212yesmaximal
10#13071370C214yesmaximal
11#13071262C211yesmaximal, characteristic, complemented
12#13071173C214yesmaximal, complemented
13#13071008C211yesmaximal, characteristic
14#13070981C211yesmaximal, characteristic, complemented
15#13070979C211yesmaximal, characteristic, complemented
16C4×#66945C211yesmaximal, characteristic
17C11×#2320C211yesmaximal, characteristic, complemented
18C2×C4×Q8×C11C2211yescharacteristic
19C2×#66999C2211yescharacteristic
20C2×Q8×Dic11C2212yes—
21C2×#66997C2211yescharacteristic
22#10623109C4116yescomplemented
23C2×#66950C2211yescharacteristic
24C2×#66949C2212yes—
25C2×#66945C2212yes—
26C2×#66942C2212yes—
27C2×#66941C2211yescharacteristic
28C2×#66925C2212yes—
29C2×C42×D11C2211yescharacteristic
30C2×C4×Dic22C2212yes—
31C2×C4×Dic22C2211yescharacteristic
32C2×C4×Dic22C2212yes—
33C11×#391C2212yes—
34C11×#389C2212yes—
35C11×#387C2214yes—
36C11×#383C2212yes—
37C11×#382C2212yes—
38C4×C11×C4⋊C4C2211yescharacteristic
39C11×#376C2211yescharacteristic
40#10622603C2214yes—
41C4⋊C4×Dic11C2214yes—
42C4⋊C4×Dic11C2214yes—
43C4⋊C4×Dic11C2212yes—
44C4⋊C4×Dic11C2212yes—
45#10622587C2214yes—
46#10622587C2212yes—
47#10622586C2212yes—
48#10622585C2214yes—
49C4×(C2×D11)⋊C4C2212yes—
50C4×(C2×D11)⋊C4C2212yes—
51C4×C4⋊Dic11C2212yes—
52C4×C4⋊Dic11C2211yescharacteristic
53C4×C4⋊Dic11C2212yes—
54#10622546C2214yes—
55#10622545C2212yes—
56#10622545C2211yescharacteristic
57C4×Dic11⋊C4C2212yes—
58C42×Dic11C2212yes—
59#10622283C2214yes—
60#10622282C2214yes—
61#10622282C2214yes—
62#10622280C2211yescharacteristic
63#10622280C2211yescharacteristic
64#10622279C2212yes—
65#10622277C2212yes—
66#10622268C2214yes—
67#10622268C2214yes—
68#10622267C2214yes—
69#10622265C2214yes—
70#10622264C2212yes—
71#10622264C2211yescharacteristic
72#10622264C2211yescharacteristic
73#10622263C2212yes—
74#10622263C2212yes—
75#10622262C2214yes—
76#10622262C2214yes—
77#10622262C2214yes—
78#10622262C2214yes—
79#10622262C2212yes—
80#10622261C2212yes—
81#10622261C2212yes—
82#10622260C2214yes—
83#10622259C2214yes—
84C22×Q8×C11C2311yescharacteristic
85C22×C4×D11C2311yescharacteristic
86C22×C4×D11C2311yescharacteristic
87C22×C4×D11C2311yescharacteristic
88C22×Dic22C2311yescharacteristic
89C22×Dic22C2312yes—
90C4×Q8×C11C2×C418yes—
91C2×C11×C4⋊C4C2312yes—
92C2×C11×C4⋊C4C2314yes—
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2312yes—
95C2×C42×C11C2312yes—
96C2×C42×C11C2312yes—
97C2×C42×C11C2311yescharacteristic
98C2×C42×C11C2312yes—
99#66999C2×C418yes—
100Q8×Dic11—28no—
101#66997C2×C418yes—
102C2×(C2×D11)⋊C4C2314yes—
103C2×(C2×D11)⋊C4C2312yes—
104C2×(C2×D11)⋊C4C2312yes—
105C2×(C2×D11)⋊C4C2312yes—
106C2×(C2×D11)⋊C4C2312yes—
107C2×C4⋊Dic11C2314yes—
108C2×C4⋊Dic11C2311yescharacteristic
109C2×C4⋊Dic11C2312yes—
110C2×C4⋊Dic11C2312yes—
111C2×Dic11⋊C4C2314yes—
112C2×Dic11⋊C4C2312yes—
113C2×Dic11⋊C4C2312yes—
114C2×Dic11⋊C4C2314yes—
115C2×Dic11⋊C4C2312yes—
116C2×Dic11⋊C4C2312yes—
117C2×Dic11⋊C4C2312yes—
118C2×Dic11⋊C4C2312yes—
119C2×Dic11⋊C4C2312yes—
120C2×C4×Dic11C2314yes—
121C2×C4×Dic11C2314yes—
122C2×C4×Dic11C2314yes—
123C2×C4×Dic11C2314yes—
124C2×C4×Dic11C2312yes—
125C2×C4×Dic11C2314yes—
126C2×C4×Dic11C2312yes—
127C2×C4×Dic11C2314yes—
128C2×C4×Dic11C2311yescharacteristic
129C2×C4×Dic11C2312yes—
130C2×C4×Dic11C2311yescharacteristic
131C2×C4×Dic11C2311yescharacteristic
132#66950C2×C418yes—
133#66949C2×C4116yes—
134#66945—28no—
135#66942C2×C4116yes—
136#66941C2×C418yes—
137#66925C2×C4116yes—
138C42×D11C2×C418yes—
139C4×Dic22—28no—
140C4×Dic22C2×C4116yes—
141C4×Dic22C2×C418yes—
142C11×#95C2314yes—
143C11×#95C2314yes—
144C11×#95C2311yescharacteristic
145C11×#95C2312yes—
146C11×#95C2312yes—
147C11×#95C2311yescharacteristic
148C11×#95C2314yes—
149C11⋊#95C2312yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2312yes—
154C11⋊#95C2314yes—
155C11⋊#95C2312yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2311yescharacteristic
159C11⋊#95C2312yes—
160C11⋊#95C2312yes—
161C11⋊#95C2311yescharacteristic
162C11⋊#95C2312yes—
163#34231—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×C11C2411yescharacteristic
172C22×C4×C11C2412yes—
173C22×C4×C11C2412yes—
174C22×C4×C11C2411yescharacteristic
175C22×Dic11C2412yes—
176C22×Dic11C2412yes—
177C22×Dic11C2411yescharacteristic
178C22×Dic11C2411yescharacteristic
179C22×Dic11C2412yes—
180C22×Dic11C2412yes—
181C22×Dic11C2414yes—
182C22×Dic11C2411yescharacteristic
183C2×C4×D11—24no—
184C2×C4×D11—24no—
185C2×C4×D11—41no—
186C2×C4×D11—41no—
187C2×C4×D11C22×C414yes—
188C2×C4×D11C22×C414yes—
189C2×C4×D11C22×C414yes—
190C2×Dic22—24no—
191C2×Dic22—42no—
192C2×Dic22—42no—
193C2×Dic22C22×C414yes—
194C2×Dic22C22×C418yes—
195C11×C4⋊C4—24no—
196C11×C4⋊C4—44no—
197C11×C4⋊C4C22×C414yes—
198C11×C4⋊C4C22×C418yes—
199C42×C11—24no—
200C42×C11—42no—
201C42×C11C22×C414yes—
202C42×C11C22×C418yes—
203(C2×D11)⋊C4—28no—
204(C2×D11)⋊C4—42no—
205(C2×D11)⋊C4—42no—
206(C2×D11)⋊C4C22×C418yes—
207(C2×D11)⋊C4C22×C418yes—
208C4⋊Dic11—28no—
209C4⋊Dic11C22×C414yes—
210C4⋊Dic11C22×C418yes—
211C4⋊Dic11#4118yes—
212Dic11⋊C4—28no—
213Dic11⋊C4—24no—
214Dic11⋊C4—24no—
215Dic11⋊C4—44no—
216Dic11⋊C4C22×C418yes—
217Dic11⋊C4C22×C418yes—
218Dic11⋊C4C22×C418yes—
219Dic11⋊C4C22×C418yes—
220Dic11⋊C4C22×C418yes—
221C4×Dic11—28no—
222C4×Dic11—28no—
223C4×Dic11—28no—
224C4×Dic11—28no—
225C4×Dic11—24no—
226C4×Dic11—44no—
227C4×Dic11—42no—
228C4×Dic11—44no—
229C4×Dic11C22×C414yes—
230C4×Dic11C22×C418yes—
231C4×Dic11C22×C414yes—
232C4×Dic11C22×C414yes—
233C2×#533—111no—
234#2369—112no—
235#2365—112no—
236#2362—112no—
237#2362—112no—
238#2356—112no—
239#2356—112no—
240#2347—112no—
241#2346—112no—
242#2332—114no—
243#2320—111no—
244#2320D1111yescharacteristic, complemented
245C4×#125—114no—
246#2283—111no—
247#2276—111no—
248#2276—111no—
249C4×#117—111no—
250C23×C11C2511yescharacteristic
251C22×D11—22no—
252C22×D11—22no—
253C22×D11—21no—
254C22×D11—21no—
255C22×D11C23×C412yes—
256Q8×C11—28no—
257C2×C4×C11—24no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—24no—
265C2×C4×C11—22no—
266C2×C4×C11—24no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—24no—
271C2×C4×C11—22no—
272C2×C4×C11C23×C412yes—
273C2×C4×C11C23×C412yes—
274C2×C4×C11C23×C414yes—
275C2×C4×C11C23×C414yes—
276C2×C4×C11C23×C412yes—
277C2×C4×C11C2×#4114yes—
278C2×Dic11—22no—
279C2×Dic11—24no—
280C2×Dic11—24no—
281C2×Dic11—24no—
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—22no—
287C2×Dic11—22no—
288C2×Dic11—22no—
289C2×Dic11—22no—
290C2×Dic11—22no—
291C2×Dic11—22no—
292C2×Dic11C23×C412yes—
293C2×Dic11C23×C412yes—
294C2×Dic11C23×C414yes—
295C2×Dic11C23×C414yes—
296C2×Dic11C23×C412yes—
297C2×Dic11C2×#4118yes—
298C2×Dic112−1+414yes—
299C4×D11—28no—
300C4×D11—28no—
301C4×D11—44no—
302Dic22—28no—
303Dic22—48no—
304#533—1116no—
305C2×C4⋊Q8—111no—
306C2×C4⋊Q8—111no—
307C2×#125—112no—
308C2×C22⋊Q8—111no—
309C2×C22⋊Q8—112no—
310C2×C22⋊Q8—111no—
311C2×C4×Q8—112no—
312C2×C4×Q8—111no—
313C2×C4×Q8—112no—
314C2×C4×Q8—112no—
315C2×C4×Q8C2×D1111yescharacteristic
316C2×#117—112no—
317C2×#117—112no—
318C22×C42—111no—
319#391—112no—
320#391—114no—
321#391—114no—
322#391C2×D1112yes—
323#389—114no—
324#389—112no—
325#389—114no—
326#389C2×D1112yes—
327#388—114no—
328#388—114no—
329#388—114no—
330#388—114no—
331#387—114no—
332#387—114no—
333#387—114no—
334#387—114no—
335#387—114no—
336#387C2×D1114yes—
337#383—112no—
338#383—111no—
339#383—111no—
340#383C2×D1112yes—
341#382—112no—
342#382—112no—
343#382C2×D1112yes—
344#381—112no—
345#380—111no—
346#380—111no—
347C4×C4⋊C4—114no—
348C4×C4⋊C4—114no—
349C4×C4⋊C4—112no—
350C4×C4⋊C4—112no—
351C4×C4⋊C4—112no—
352C4×C4⋊C4—112no—
353C4×C4⋊C4—112no—
354C4×C4⋊C4—111no—
355C4×C4⋊C4—114no—
356C4×C4⋊C4—114no—
357C4×C4⋊C4—114no—
358C4×C4⋊C4—114no—
359C4×C4⋊C4—112no—
360C4×C4⋊C4C2×D1111yescharacteristic
361C4×C22⋊C4—112no—
362C4×C22⋊C4—112no—
363C4×C22⋊C4—112no—
364#376—111no—
365#376—112no—
366#376—112no—
367#376—112no—
368#376C2×D1111yescharacteristic
369C43—112no—
370C22×C11C24×C411yescharacteristic
371C22×C11C22×#4112yes—
372C22×C11C2×2−1+412yes—
373C22×C11#58511yescharacteristic
374C22×C11#58511yescharacteristic
375C2×D11—22no—
376C2×D11—22no—
377C2×D11—22no—
378C2×D11—42no—
379C2×D11—42no—
380C4×C11—24no—
381C4×C11—22no—
382C4×C11—24no—
383C4×C11—22no—
384C4×C11—42no—
385C4×C11—42no—
386C4×C11—44no—
387C4×C11C4×#4114yes—
388Dic11—24no—
389Dic11—22no—
390Dic11—22no—
391Dic11—24no—
392Dic11—28no—
393Dic11—42no—
394Dic11—42no—
395Dic11#51914yes—
396C22×Q8—111no—
397C22×Q8—112no—
398C22×Q8C22×D1111yescharacteristic
399C23×C4—111no—
400C23×C4—111no—
401C23×C4—111no—
402C4⋊Q8—118no—
403C4⋊Q8—118no—
404#125—1116no—
405C22⋊Q8—118no—
406C22⋊Q8—1116no—
407C22⋊Q8—118no—
408C4×Q8—1116no—
409C4×Q8—118no—
410C4×Q8—228no—
411C4×Q8—228no—
412C4×Q8C4×D1118yes—
413#117—1116no—
414#117—228no—
415C2×C4⋊C4—112no—
416C2×C4⋊C4—112no—
417C2×C4⋊C4—112no—
418C2×C4⋊C4—112no—
419C2×C4⋊C4—112no—
420C2×C4⋊C4—112no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—112no—
423C2×C4⋊C4—114no—
424C2×C4⋊C4—114no—
425C2×C4⋊C4—112no—
426C2×C4⋊C4—112no—
427C2×C4⋊C4—114no—
428C2×C4⋊C4C22×D1112yes—
429C2×C4⋊C4C22×D1114yes—
430C2×C4⋊C4C22×D1112yes—
431C2×C4⋊C4C22×D1111yescharacteristic
432C2×C22⋊C4—112no—
433C2×C22⋊C4—112no—
434C2×C22⋊C4—114no—
435C2×C22⋊C4—112no—
436C2×C22⋊C4—112no—
437C2×C42—112no—
438C2×C42—111no—
439C2×C42—111no—
440C2×C42—111no—
441C2×C42—118no—
442C2×C42—114no—
443C2×C42—112no—
444C2×C42—114no—
445C2×C42—114no—
446C2×C42—114no—
447C2×C42—112no—
448C2×C42—114no—
449C2×C42—114no—
450C2×C42C22×D1112yes—
451C2×C42C22×D1112yes—
452C2×C42C22×D1112yes—
453C2×C42C22×D1111yescharacteristic
454#95—112no—
455#95—111no—
456#95—114no—
457#95—111no—
458#95—112no—
459#95—114no—
460#95—114no—
461#95—112no—
462#95—112no—
463#95—112no—
464#95—112no—
465#95—114no—
466#95—114no—
467#95—114no—
468#95C22×D1111yescharacteristic
469#95C22×D1112yes—
470#95C22×D1111yescharacteristic
471#95C22×D1112yes—
472#95C22×D1114yes—
473#95C22×D1114yes—
474#95C22×D1114yes—
475C2×C11C2×C4×#4111yescharacteristic
476C2×C11C2×#51911yescharacteristic
477C2×C11#342811yescharacteristic
478C2×C11#351512yes—
479C2×C11#351812yes—
480D11—42no—
481C24—111no—
482C2×Q8—24no—
483C2×Q8—114no—
484C2×Q8—118no—
485C2×Q8—224no—
486C2×Q8—442no—
487C2×Q8—442no—
488C2×Q8C2×C4×D1114yes—
489C22×C4—111no—
490C22×C4—111no—
491C22×C4—114no—
492C22×C4—111no—
493C22×C4—112no—
494C22×C4—112no—
495C22×C4—114no—
496C22×C4—114no—
497C22×C4—114no—
498C22×C4—112no—
499C22×C4—112no—
500C22×C4—224no—
501C22×C4—224no—
502C22×C4—441no—
503C22×C4—441no—
504C22×C4C23×D1112yes—
505C22×C4C23×D1114yes—
506C22×C4C23×D1112yes—
507C22×C4C23×D1111yescharacteristic
508C22×C4C23×D1111yescharacteristic
509C22×C4C23×D1112yes—
510C22×C4C23×D1112yes—
511C22×C4C23×D1111yescharacteristic
512C4⋊C4—24no—
513C4⋊C4—44no—
514C4⋊C4—118no—
515C4⋊C4—118no—
516C4⋊C4—118no—
517C4⋊C4—118no—
518C4⋊C4—118no—
519C4⋊C4—118no—
520C4⋊C4—114no—
521C4⋊C4—118no—
522C4⋊C4—228no—
523C4⋊C4—228no—
524C4⋊C4—224no—
525C4⋊C4—224no—
526C4⋊C4—444no—
527C4⋊C4C2×C4×D1118yes—
528C4⋊C4C2×C4×D1114yes—
529C22⋊C4—118no—
530C22⋊C4—118no—
531C22⋊C4—228no—
532C22⋊C4—442no—
533C22⋊C4—442no—
534C42—24no—
535C42—42no—
536C42—114no—
537C42—114no—
538C42—114no—
539C42—118no—
540C42—228no—
541C42—228no—
542C42—228no—
543C42—228no—
544C42—224no—
545C42—442no—
546C42—444no—
547C42—444no—
548C42C2×C4×D1114yes—
549C42C2×C4×D1118yes—
550C11#3423111yescharacteristic, complemented, Sylow
551C23—112no—
552C23—222no—
553C23—221no—
554C23—222no—
555C23—221no—
556C23C24×D1111yescharacteristic
557Q8—28no—
558Q8—228no—
559Q8—448no—
560C2×C4—24no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—22no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—112no—
576C2×C4—114no—
577C2×C4—112no—
578C2×C4—112no—
579C2×C4—114no—
580C2×C4—114no—
581C2×C4—118no—
582C2×C4—228no—
583C2×C4—222no—
584C2×C4—224no—
585C2×C4—222no—
586C2×C4—221no—
587C2×C4—224no—
588C2×C4—224no—
589C2×C4—222no—
590C2×C4—221no—
591C2×C4—228no—
592C2×C4—222no—
593C2×C4—222no—
594C2×C4—222no—
595C2×C4—222no—
596C2×C4—222no—
597C2×C4—222no—
598C2×C4—444no—
599C2×C4C22×C4×D1112yes—
600C2×C4C22×C4×D1112yes—
601C2×C4C22×C4×D1114yes—
602C2×C4C22×C4×D1114yes—
603C2×C4C22×C4×D1112yes—
604C2×C4#41×D1114yes—
605C22—222no—
606C22—222no—
607C22—222no—
608C22—442no—
609C22—442no—
610C22C23×C4×D1111yescharacteristic
611C22C2×#41×D1112yes—
612C22#1062345511yescharacteristic
613C22D11×2−1+412yes—
614C22#1062345711yescharacteristic
615C4—24no—
616C4—22no—
617C4—22no—
618C4—24no—
619C4—42no—
620C4—44no—
621C4—42no—
622C4—114no—
623C4—222no—
624C4—224no—
625C4—222no—
626C4—224no—
627C4—228no—
628C4—442no—
629C4—442no—
630C4#1062305314yes—
631C2—442no—
632C2C2×#1062305311yescharacteristic
633C2D11×#51911yescharacteristic
634C2#1308181611yescharacteristic
635C2#1308259212yes—
636C2#1308262912yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2320C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2320D11
hypocenterC11#34231
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2320

Complements

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

NH ≅ G/Ntype
2. #13071702C2semidirect
3. #13071673C2semidirect
6. #13071583C2semidirect
7. #13071576C2semidirect
11. #13071262C2semidirect
12. #13071173C2semidirect
14. #13070981C2semidirect
15. #13070979C2semidirect
17. C11×#2320C2semidirect
22. #10623109C4semidirect
244. #2320D11semidirect
550. C11#34231semidirect

Maximal subgroups

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

subgroupindex
C2×#106231092
#130717022
#130716732
#130716482
#130716422
#130715832
#130715762
#130715042
#130714962
#130713702
#130712622
#130711732
#130710082
#130709812
#130709792
C4×#669452
C11×#23202
#3423111