Finite Group Databasebeta

← #14914523

Subgroups — #14914523

Order 2816.

2238 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623109C211yesmaximal, characteristic
2#13071675C212yesmaximal, complemented
3#13071673C212yesmaximal, complemented
4#13071624C214yesmaximal
5#13071583C211yesmaximal, characteristic, complemented
6#13071537C211yesmaximal, characteristic, complemented
7#13071536C211yesmaximal, characteristic, complemented
8#13071477C212yesmaximal
9#13071473C212yesmaximal
10#13071421C214yesmaximal, complemented
11#13071266C212yesmaximal, complemented
12#13071154C212yesmaximal
13C4×#66950C212yesmaximal
14#13071009C211yesmaximal, characteristic
15#13070979C212yesmaximal, complemented
16C4×C4⋊C4×D11C211yesmaximal, characteristic
17C11×#2356C211yesmaximal, characteristic, complemented
18C2×C4×Q8×C11C2211yescharacteristic
19C2×#66999C2211yescharacteristic
20C2×Q8×Dic11C2212yes—
21C2×#66997C2211yescharacteristic
22#10623109C4116yescomplemented
23C2×#66950C2211yescharacteristic
24C2×#66949C2212yes—
25C2×C4⋊C4×D11C2212yes—
26C2×#66942C2212yes—
27C2×#66941C2211yescharacteristic
28C2×#66925C2212yes—
29C2×C42×D11C2212yes—
30C2×C42×D11C2211yescharacteristic
31C2×C4×Dic22C2214yes—
32C2×C4×Dic22C2212yes—
33C2×C4×Dic22C2212yes—
34C2×C4×Dic22C2211yescharacteristic
35C11×#391C2212yes—
36C11×#387C2214yes—
37C11×#383C2212yes—
38C11×#382C2211yescharacteristic
39C4×C11×C4⋊C4C2212yes—
40C4×C11×C4⋊C4C2211yescharacteristic
41C11×#376C2212yes—
42#10622600C2212yes—
43#10622598C2214yes—
44#10622598C2212yes—
45C4⋊C4×Dic11C2212yes—
46C4⋊C4×Dic11C2212yes—
47C4⋊C4×Dic11C2212yes—
48#10622587C2212yes—
49#10622585C2214yes—
50C4×(C2×D11)⋊C4C2214yes—
51#10622549C2212yes—
52#10622549C2211yescharacteristic
53C4×C4⋊Dic11C2214yes—
54C4×C4⋊Dic11C2211yescharacteristic
55C4×C4⋊Dic11C2212yes—
56#10622546C2214yes—
57C4×Dic11⋊C4C2212yes—
58#10622541C2212yes—
59#10622281C2214yes—
60#10622281C2214yes—
61#10622279C2212yes—
62#10622279C2214yes—
63#10622277C2212yes—
64D11×#95C2211yescharacteristic
65D11×#95C2211yescharacteristic
66#10622268C2214yes—
67#10622268C2214yes—
68#10622268C2214yes—
69#10622268C2214yes—
70#10622266C2214yes—
71#10622265C2214yes—
72#10622264C2212yes—
73#10622264C2212yes—
74#10622263C2212yes—
75#10622262C2214yes—
76#10622262C2214yes—
77#10622262C2211yescharacteristic
78#10622262C2211yescharacteristic
79#10622262C2212yes—
80#10622261C2212yes—
81#10622261C2212yes—
82#10622260C2214yes—
83#10622259C2214yes—
84C22×Q8×C11C2311yescharacteristic
85C22×C4×D11C2312yes—
86C22×C4×D11C2312yes—
87C22×C4×D11C2311yescharacteristic
88C22×C4×D11C2311yescharacteristic
89C22×C4×D11C2311yescharacteristic
90C22×Dic22C2312yes—
91C22×Dic22C2311yescharacteristic
92C4×Q8×C11C2×C418yescomplemented
93C2×C11×C4⋊C4C2312yes—
94C2×C11×C4⋊C4C2312yes—
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2312yes—
97C2×C42×C11C2312yes—
98C2×C42×C11C2314yes—
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2312yes—
101#66999C2×C418yes—
102Q8×Dic11—44no—
103#66997C2×C418yescomplemented
104C2×(C2×D11)⋊C4C2314yes—
105C2×(C2×D11)⋊C4C2312yes—
106C2×(C2×D11)⋊C4C2312yes—
107C2×C4⋊Dic11C2314yes—
108C2×C4⋊Dic11C2312yes—
109C2×C4⋊Dic11C2312yes—
110C2×C4⋊Dic11C2314yes—
111C2×C4⋊Dic11C2311yescharacteristic
112C2×C4⋊Dic11C2312yes—
113C2×Dic11⋊C4C2314yes—
114C2×Dic11⋊C4C2312yes—
115C2×Dic11⋊C4C2314yes—
116C2×Dic11⋊C4C2312yes—
117C2×Dic11⋊C4C2312yes—
118C2×Dic11⋊C4C2312yes—
119C2×Dic11⋊C4C2312yes—
120C2×Dic11⋊C4C2312yes—
121C2×Dic11⋊C4C2312yes—
122C2×C4×Dic11C2314yes—
123C2×C4×Dic11C2314yes—
124C2×C4×Dic11C2312yes—
125C2×C4×Dic11C2314yes—
126C2×C4×Dic11C2312yes—
127C2×C4×Dic11C2312yes—
128C2×C4×Dic11C2314yes—
129C2×C4×Dic11C2311yescharacteristic
130C2×C4×Dic11C2312yes—
131C2×C4×Dic11C2311yescharacteristic
132C2×C4×Dic11C2311yescharacteristic
133#66950C2×C418yes—
134#66949C2×C4116yes—
135C4⋊C4×D11—28no—
136#66942C2×C4116yescomplemented
137#66941C2×C418yescomplemented
138#66925C2×C4116yes—
139C42×D11—44no—
140C42×D11C2×C418yes—
141C4×Dic22—216no—
142C4×Dic22—44no—
143C4×Dic22C2×C4116yescomplemented
144C4×Dic22C2×C418yescomplemented
145C11×#95C2314yes—
146C11×#95C2314yes—
147C11×#95C2312yes—
148C11×#95C2311yescharacteristic
149C11×#95C2314yes—
150C11×#95C2311yescharacteristic
151C11×#95C2312yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2311yescharacteristic
157C11⋊#95C2312yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2311yescharacteristic
161C11⋊#95C2314yes—
162C11⋊#95C2312yes—
163C11⋊#95C2312yes—
164C11⋊#95C2312yes—
165#34235—111nomaximal, Sylow
166C23×D11C2411yescharacteristic
167C2×Q8×C11—22no—
168C2×Q8×C11—22no—
169C2×Q8×C11C22×C414yes—
170C22×C4×C11C2414yes—
171C22×C4×C11C2412yes—
172C22×C4×C11C2411yescharacteristic
173C22×C4×C11C2411yescharacteristic
174C22×C4×C11C2412yes—
175C22×C4×C11C2412yes—
176C22×C4×C11C2412yes—
177C22×C4×C11C2411yescharacteristic
178C22×Dic11C2412yes—
179C22×Dic11C2414yes—
180C22×Dic11C2411yescharacteristic
181C22×Dic11C2411yescharacteristic
182C22×Dic11C2412yes—
183C22×Dic11C2412yes—
184C22×Dic11C2412yes—
185C22×Dic11C2411yescharacteristic
186C2×C4×D11—24no—
187C2×C4×D11—24no—
188C2×C4×D11—24no—
189C2×C4×D11—24no—
190C2×C4×D11—24no—
191C2×C4×D11—24no—
192C2×C4×D11—22no—
193C2×C4×D11—22no—
194C2×C4×D11—42no—
195C2×C4×D11—42no—
196C2×C4×D11C22×C414yes—
197C2×C4×D11C22×C414yes—
198C2×C4×D11C22×C414yes—
199C2×Dic22—28no—
200C2×Dic22—22no—
201C2×Dic22—22no—
202C2×Dic22C22×C418yes—
203C2×Dic22C22×C414yes—
204C11×C4⋊C4—24no—
205C11×C4⋊C4—24no—
206C11×C4⋊C4C22×C414yes—
207C11×C4⋊C4C22×C418yes—
208C42×C11—28no—
209C42×C11—24no—
210C42×C11C22×C414yes—
211C42×C11C22×C418yes—
212(C2×D11)⋊C4—28no—
213(C2×D11)⋊C4C22×C418yes—
214(C2×D11)⋊C4C22×C418yes—
215C4⋊Dic11—28no—
216C4⋊Dic11—24no—
217C4⋊Dic11—24no—
218C4⋊Dic11—44no—
219C4⋊Dic11C22×C414yes—
220C4⋊Dic11C22×C418yes—
221Dic11⋊C4—24no—
222Dic11⋊C4—28no—
223Dic11⋊C4—44no—
224Dic11⋊C4C22×C418yes—
225Dic11⋊C4C22×C418yes—
226Dic11⋊C4C22×C418yes—
227Dic11⋊C4C22×C418yes—
228Dic11⋊C4C22×C418yes—
229Dic11⋊C4#4118yes—
230C4×Dic11—28no—
231C4×Dic11—28no—
232C4×Dic11—24no—
233C4×Dic11—44no—
234C4×Dic11—42no—
235C4×Dic11—42no—
236C4×Dic11—44no—
237C4×Dic11C22×C414yes—
238C4×Dic11C22×C418yes—
239C4×Dic11C22×C414yes—
240C4×Dic11C22×C414yes—
241C2×#533—111no—
242#2365—112no—
243#2365—112no—
244#2360—114no—
245#2356—111no—
246#2356D1111yescharacteristic, complemented
247#2351—111no—
248#2351—111no—
249#2343—112no—
250#2343—112no—
251#2336—114no—
252#2320—112no—
253C4×C22⋊Q8—112no—
254C4×C22⋊Q8—112no—
255#2283—111no—
256#2276—112no—
257C2×C4×C4⋊C4—111no—
258C23×C11C2511yescharacteristic
259C22×D11—22no—
260C22×D11—21no—
261C22×D11—21no—
262C22×D11C23×C412yes—
263C22×D112−1+414yes—
264Q8×C11—28no—
265C2×C4×C11—24no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—24no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—24no—
276C2×C4×C11—24no—
277C2×C4×C11—22no—
278C2×C4×C11C23×C412yes—
279C2×C4×C11C23×C412yes—
280C2×C4×C11C23×C414yes—
281C2×C4×C11C23×C414yes—
282C2×C4×C11C23×C412yes—
283C2×C4×C11C2×#4114yes—
284C2×C4×C11H(5,𝔽2)12yes—
285C2×C4×C112−1+412yes—
286C2×Dic11—24no—
287C2×Dic11—22no—
288C2×Dic11—21no—
289C2×Dic11—22no—
290C2×Dic11—22no—
291C2×Dic11—21no—
292C2×Dic11—22no—
293C2×Dic11—22no—
294C2×Dic11—24no—
295C2×Dic11—22no—
296C2×Dic11—22no—
297C2×Dic11—24no—
298C2×Dic11—24no—
299C2×Dic11—22no—
300C2×Dic11C23×C412yes—
301C2×Dic11C23×C412yes—
302C2×Dic11C23×C414yes—
303C2×Dic11C23×C414yes—
304C2×Dic11C23×C412yes—
305C2×Dic11C2×#4114yes—
306C2×Dic11C2×#4114yes—
307C4×D11—28no—
308C4×D11—28no—
309C4×D11—28no—
310C4×D11—48no—
311C4×D11—48no—
312Dic22—28no—
313Dic22—216no—
314#533—1116no—
315C2×C4⋊Q8—111no—
316C2×C4⋊Q8—111no—
317C2×#125—112no—
318C2×C22⋊Q8—111no—
319C2×C22⋊Q8—112no—
320C2×C22⋊Q8—111no—
321C2×C4×Q8—112no—
322C2×C4×Q8—112no—
323C2×C4×Q8—111no—
324C2×C4×Q8—114no—
325C2×C4×Q8—112no—
326C2×C4×Q8C2×D1111yescharacteristic
327C2×#117—112no—
328C22×C4⋊C4—112no—
329C22×C42—111no—
330C22×C42—112no—
331#391—112no—
332#391—114no—
333#391C2×D1112yes—
334#389—114no—
335#389—114no—
336#389—112no—
337#389—112no—
338#389—114no—
339#387—114no—
340#387—114no—
341#387—114no—
342#387—114no—
343#387—114no—
344#387—114no—
345#387—114no—
346#387C2×D1114yes—
347#385—114no—
348#385—114no—
349#383—112no—
350#383—112no—
351#383C2×D1112yes—
352#382—112no—
353#382—111no—
354#382—112no—
355#382C2×D1111yescharacteristic
356#381—112no—
357#380—112no—
358C4×C4⋊C4—112no—
359C4×C4⋊C4—112no—
360C4×C4⋊C4—112no—
361C4×C4⋊C4—114no—
362C4×C4⋊C4—112no—
363C4×C4⋊C4—111no—
364C4×C4⋊C4—112no—
365C4×C4⋊C4—111no—
366C4×C4⋊C4—114no—
367C4×C4⋊C4—112no—
368C4×C4⋊C4—114no—
369C4×C4⋊C4—111no—
370C4×C4⋊C4C2×D1111yescharacteristic
371C4×C4⋊C4C2×D1112yes—
372C4×C22⋊C4—114no—
373C4×C22⋊C4—114no—
374C4×C22⋊C4—112no—
375#376—112no—
376#376—112no—
377#376C2×D1112yes—
378C2×#95—111no—
379C2×#95—111no—
380C22×C11C24×C411yescharacteristic
381C22×C11C22×#4112yes—
382C22×C11C2×H(5,𝔽2)11yescharacteristic
383C22×C11C2×2−1+411yescharacteristic
384C22×C11C2×2−1+412yes—
385C2×D11—22no—
386C2×D11—22no—
387C2×D11—24no—
388C2×D11—24no—
389C2×D11#51914yes—
390C4×C11—24no—
391C4×C11—22no—
392C4×C11—22no—
393C4×C11—24no—
394C4×C11—24no—
395C4×C11—42no—
396C4×C11—44no—
397C4×C11#52014yes—
398Dic11—24no—
399Dic11—22no—
400Dic11—24no—
401Dic11—22no—
402Dic11—24no—
403Dic11—42no—
404Dic11—44no—
405Dic11C4×#4114yes—
406C22×Q8—112no—
407C22×Q8—111no—
408C22×Q8C22×D1111yescharacteristic
409C23×C4—111no—
410C23×C4—111no—
411C23×C4—111no—
412C23×C4—112no—
413C23×C4—112no—
414C4⋊Q8—118no—
415C4⋊Q8—118no—
416#125—1116no—
417C22⋊Q8—118no—
418C22⋊Q8—1116no—
419C22⋊Q8—118no—
420C4×Q8—1116no—
421C4×Q8—118no—
422C4×Q8—2216no—
423C4×Q8—444no—
424C4×Q8—444no—
425C4×Q8C4×D1118yescomplemented
426#117—1116no—
427C2×C4⋊C4—112no—
428C2×C4⋊C4—112no—
429C2×C4⋊C4—112no—
430C2×C4⋊C4—112no—
431C2×C4⋊C4—112no—
432C2×C4⋊C4—112no—
433C2×C4⋊C4—112no—
434C2×C4⋊C4—111no—
435C2×C4⋊C4—112no—
436C2×C4⋊C4—112no—
437C2×C4⋊C4—112no—
438C2×C4⋊C4—114no—
439C2×C4⋊C4—114no—
440C2×C4⋊C4—114no—
441C2×C4⋊C4—114no—
442C2×C4⋊C4—228no—
443C2×C4⋊C4C22×D1112yes—
444C2×C4⋊C4C22×D1112yes—
445C2×C4⋊C4C22×D1112yes—
446C2×C4⋊C4C22×D1111yescharacteristic
447C2×C22⋊C4—112no—
448C2×C22⋊C4—112no—
449C2×C22⋊C4—114no—
450C2×C42—112no—
451C2×C42—111no—
452C2×C42—111no—
453C2×C42—111no—
454C2×C42—118no—
455C2×C42—114no—
456C2×C42—114no—
457C2×C42—112no—
458C2×C42—114no—
459C2×C42—114no—
460C2×C42—112no—
461C2×C42—112no—
462C2×C42—444no—
463C2×C42C22×D1114yes—
464C2×C42C22×D1112yes—
465C2×C42C22×D1112yes—
466C2×C42C22×D1111yescharacteristic
467#95—111no—
468#95—111no—
469#95—112no—
470#95—112no—
471#95—114no—
472#95—112no—
473#95—114no—
474#95—112no—
475#95—114no—
476#95—114no—
477#95—114no—
478#95—114no—
479#95—114no—
480#95C22×D1111yescharacteristic
481#95C22×D1111yescharacteristic
482#95C22×D1112yes—
483#95C22×D1114yes—
484#95C22×D1112yes—
485#95C22×D1114yes—
486#95C22×D1114yes—
487C2×C11C2×C4×#4111yescharacteristic
488C2×C11C2×#51911yescharacteristic
489C2×C11C2×#52011yescharacteristic
490C2×C11#352012yes—
491C2×C11#352312yes—
492D11—24no—
493C24—111no—
494C2×Q8—22no—
495C2×Q8—22no—
496C2×Q8—118no—
497C2×Q8—114no—
498C2×Q8—228no—
499C2×Q8—222no—
500C2×Q8—222no—
501C2×Q8C2×C4×D1114yes—
502C22×C4—111no—
503C22×C4—111no—
504C22×C4—111no—
505C22×C4—112no—
506C22×C4—112no—
507C22×C4—112no—
508C22×C4—114no—
509C22×C4—114no—
510C22×C4—114no—
511C22×C4—112no—
512C22×C4—114no—
513C22×C4—224no—
514C22×C4—224no—
515C22×C4—224no—
516C22×C4—224no—
517C22×C4—224no—
518C22×C4—222no—
519C22×C4—222no—
520C22×C4—224no—
521C22×C4—442no—
522C22×C4—442no—
523C22×C4C23×D1114yes—
524C22×C4C23×D1112yes—
525C22×C4C23×D1111yescharacteristic
526C22×C4C23×D1111yescharacteristic
527C22×C4C23×D1112yes—
528C22×C4C23×D1112yes—
529C22×C4C23×D1112yes—
530C22×C4C23×D1111yescharacteristic
531C4⋊C4—24no—
532C4⋊C4—24no—
533C4⋊C4—118no—
534C4⋊C4—118no—
535C4⋊C4—118no—
536C4⋊C4—118no—
537C4⋊C4—118no—
538C4⋊C4—118no—
539C4⋊C4—114no—
540C4⋊C4—118no—
541C4⋊C4—224no—
542C4⋊C4—224no—
543C4⋊C4—228no—
544C4⋊C4—228no—
545C4⋊C4—224no—
546C4⋊C4—444no—
547C4⋊C4—444no—
548C4⋊C4C2×C4×D1118yes—
549C4⋊C4C2×C4×D1114yes—
550C22⋊C4—118no—
551C22⋊C4—118no—
552C22⋊C4—228no—
553C42—28no—
554C42—24no—
555C42—114no—
556C42—114no—
557C42—114no—
558C42—118no—
559C42—228no—
560C42—228no—
561C42—224no—
562C42—442no—
563C42—442no—
564C42—444no—
565C42—444no—
566C42C2×C4×D1114yes—
567C42C2×C4×D1118yes—
568C11#3423511yescharacteristic, complemented, Sylow
569C23—112no—
570C23—114no—
571C23—222no—
572C23—221no—
573C23—221no—
574C23C24×D1111yescharacteristic
575Q8—28no—
576Q8—2216no—
577Q8—228no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—22no—
591C2×C4—112no—
592C2×C4—114no—
593C2×C4—112no—
594C2×C4—112no—
595C2×C4—114no—
596C2×C4—114no—
597C2×C4—114no—
598C2×C4—228no—
599C2×C4—228no—
600C2×C4—224no—
601C2×C4—222no—
602C2×C4—221no—
603C2×C4—222no—
604C2×C4—221no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—222no—
608C2×C4—228no—
609C2×C4—224no—
610C2×C4—222no—
611C2×C4—222no—
612C2×C4—224no—
613C2×C4—224no—
614C2×C4—222no—
615C2×C4—448no—
616C2×C4—448no—
617C2×C4C22×C4×D1112yes—
618C2×C4C22×C4×D1112yes—
619C2×C4C22×C4×D1114yes—
620C2×C4C22×C4×D1114yes—
621C2×C4C22×C4×D1112yes—
622C2×C4#41×D1114yes—
623C2×C4#6704212yes—
624C2×C4#6704312yes—
625C22—114no—
626C22—224no—
627C22—224no—
628C22—222no—
629C22—222no—
630C22C23×C4×D1111yescharacteristic
631C22C2×#41×D1112yes—
632C22C2×#6704211yescharacteristic
633C22C2×#6704311yescharacteristic
634C22D11×2−1+412yes—
635C4—24no—
636C4—22no—
637C4—24no—
638C4—22no—
639C4—24no—
640C4—42no—
641C4—44no—
642C4—114no—
643C4—224no—
644C4—224no—
645C4—222no—
646C4—222no—
647C4—224no—
648C4—442no—
649C4—444no—
650C4#1062305414yes—
651C2—224no—
652C2C4×#41×D1111yescharacteristic
653C2D11×#51911yescharacteristic
654C2C2×#1062305411yescharacteristic
655C2#1308266212yes—
656C2#1308271112yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2356C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2356D11
hypocenterC11#34235
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2356

Complements

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

NH ≅ G/Ntype
2. #13071675C2semidirect
3. #13071673C2semidirect
5. #13071583C2semidirect
6. #13071537C2semidirect
7. #13071536C2semidirect
10. #13071421C2semidirect
11. #13071266C2semidirect
15. #13070979C2semidirect
17. C11×#2356C2semidirect
22. #10623109C4semidirect
92. C4×Q8×C11C2×C4semidirect
103. #66997C2×C4semidirect
136. #66942C2×C4semidirect
137. #66941C2×C4semidirect
143. C4×Dic22C2×C4semidirect
144. C4×Dic22C2×C4semidirect
246. #2356D11semidirect
425. C4×Q8C4×D11semidirect
568. C11#34235semidirect

Maximal subgroups

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

subgroupindex
C2×#106231092
#130716752
#130716732
#130716242
#130715832
#130715372
#130715362
#130714772
#130714732
#130714212
#130712662
#130711542
C4×#669502
#130710092
#130709792
C4×C4⋊C4×D112
C11×#23562
#3423511