Finite Group Databasebeta

← #14914369

Subgroups — #14914369

Order 2816.

2194 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×#10623109C211yesmaximal, characteristic
2#13071709C214yesmaximal, complemented
3#13071648C212yesmaximal
4#13071645C212yesmaximal
5#13071579C211yesmaximal, characteristic, complemented
6#13071537C211yesmaximal, characteristic, complemented
7#13071533C211yesmaximal, characteristic, complemented
8#13071504C212yesmaximal
9#13071502C212yesmaximal
10#13071297C214yesmaximal
11#13071266C212yesmaximal, complemented
12C4×#66941C212yesmaximal, complemented
13#13071185C212yesmaximal, complemented
14#13071022C211yesmaximal, characteristic
15#13070979C212yesmaximal, complemented
16C4×#66945C211yesmaximal, characteristic
17C11×#2356C211yesmaximal, characteristic, complemented
18C2×C4×Q8×C11C2211yescharacteristic
19C2×#66999C2211yescharacteristic
20C2×Q8×Dic11C2212yes—
21C2×#66997C2211yescharacteristic
22#10623109C4116yescomplemented
23C2×#66950C2211yescharacteristic
24C2×#66949C2212yes—
25C2×#66945C2212yes—
26C2×#66945C2212yes—
27C2×#66942C2212yes—
28C2×#66941C2211yescharacteristic
29C2×#66940C2212yes—
30C2×#66925C2212yes—
31C2×C42×D11C2211yescharacteristic
32C2×C4×Dic22C2214yes—
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#10622598C2212yes—
43#10622598C2214yes—
44#10622591C2214yes—
45#10622589C2212yes—
46C4⋊C4×Dic11C2212yes—
47#10622586C2212yes—
48#10622553C2214yes—
49C4×(C2×D11)⋊C4C2212yes—
50#10622549C2212yes—
51#10622549C2211yescharacteristic
52C4×C4⋊Dic11C2214yes—
53C4×C4⋊Dic11C2212yes—
54C4×C4⋊Dic11C2211yescharacteristic
55C4×C4⋊Dic11C2212yes—
56C4×Dic11⋊C4C2214yes—
57C42×Dic11C2212yes—
58#10622542C2212yes—
59#10622283C2214yes—
60#10622283C2214yes—
61#10622282C2214yes—
62#10622280C2212yes—
63#10622280C2212yes—
64#10622279C2211yescharacteristic
65#10622279C2211yescharacteristic
66#10622268C2214yes—
67#10622266C2214yes—
68#10622264C2212yes—
69#10622263C2212yes—
70#10622262C2214yes—
71#10622262C2214yes—
72#10622262C2214yes—
73#10622262C2212yes—
74#10622262C2212yes—
75#10622262C2212yes—
76#10622261C2211yescharacteristic
77#10622261C2211yescharacteristic
78#10622261C2212yes—
79#10622260C2214yes—
80#10622260C2214yes—
81#10622260C2214yes—
82#10622260C2214yes—
83#10622259C2214yes—
84C22×Q8×C11C2311yescharacteristic
85C22×C4×D11C2311yescharacteristic
86C22×C4×D11C2311yescharacteristic
87C22×C4×D11C2311yescharacteristic
88C22×Dic22C2312yes—
89C22×Dic22C2311yescharacteristic
90C4×Q8×C11C2×C418yes—
91C2×C11×C4⋊C4C2312yes—
92C2×C11×C4⋊C4C2312yes—
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2312yes—
95C2×C42×C11C2314yes—
96C2×C42×C11C2312yes—
97C2×C42×C11C2311yescharacteristic
98C2×C42×C11C2312yes—
99#66999C2×C418yes—
100Q8×Dic11—44no—
101#66997C2×C418yes—
102C2×(C2×D11)⋊C4C2312yes—
103C2×(C2×D11)⋊C4C2312yes—
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⋊C4C2314yes—
115C2×Dic11⋊C4C2314yes—
116C2×Dic11⋊C4C2314yes—
117C2×Dic11⋊C4C2312yes—
118C2×Dic11⋊C4C2312yes—
119C2×Dic11⋊C4C2312yes—
120C2×Dic11⋊C4C2312yes—
121C2×Dic11⋊C4C2312yes—
122C2×C4×Dic11C2314yes—
123C2×C4×Dic11C2312yes—
124C2×C4×Dic11C2312yes—
125C2×C4×Dic11C2312yes—
126C2×C4×Dic11C2312yes—
127C2×C4×Dic11C2314yes—
128C2×C4×Dic11C2314yes—
129C2×C4×Dic11C2314yes—
130C2×C4×Dic11C2311yescharacteristic
131C2×C4×Dic11C2312yes—
132C2×C4×Dic11C2311yescharacteristic
133C2×C4×Dic11C2311yescharacteristic
134C2×C4×Dic11C2312yes—
135#66950C2×C418yes—
136#66949C2×C4116yes—
137#66945—28no—
138#66945—44no—
139#66942C2×C4116yes—
140#66941C2×C418yes—
141#66940—44no—
142#66925C2×C4116yes—
143C42×D11C2×C418yes—
144C4×Dic22—216no—
145C4×Dic22C2×C4116yes—
146C4×Dic22C2×C418yes—
147C11×#95C2314yes—
148C11×#95C2312yes—
149C11×#95C2314yes—
150C11×#95C2314yes—
151C11×#95C2311yescharacteristic
152C11×#95C2311yescharacteristic
153C11×#95C2312yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2311yescharacteristic
160C11⋊#95C2312yes—
161C11⋊#95C2312yes—
162C11⋊#95C2311yescharacteristic
163C11⋊#95C2312yes—
164C11⋊#95C2312yes—
165#34225—111nomaximal, Sylow
166C23×D11C2411yescharacteristic
167C2×Q8×C11—22no—
168C2×Q8×C11—22no—
169C2×Q8×C11C22×C414yes—
170C22×C4×C11C2412yes—
171C22×C4×C11C2414yes—
172C22×C4×C11C2411yescharacteristic
173C22×C4×C11C2411yescharacteristic
174C22×C4×C11C2412yes—
175C22×C4×C11C2412yes—
176C22×C4×C11C2412yes—
177C22×C4×C11C2411yescharacteristic
178C22×Dic11C2414yes—
179C22×Dic11C2412yes—
180C22×Dic11C2411yescharacteristic
181C22×Dic11C2412yes—
182C22×Dic11C2412yes—
183C22×Dic11C2412yes—
184C22×Dic11C2411yescharacteristic
185C22×Dic11C2411yescharacteristic
186C2×C4×D11—24no—
187C2×C4×D11—24no—
188C2×C4×D11—22no—
189C2×C4×D11—22no—
190C2×C4×D11C22×C414yes—
191C2×C4×D11C22×C414yes—
192C2×C4×D11C22×C414yes—
193C2×Dic22—28no—
194C2×Dic22—22no—
195C2×Dic22—22no—
196C2×Dic22C22×C418yes—
197C2×Dic22C22×C414yes—
198C11×C4⋊C4—24no—
199C11×C4⋊C4—24no—
200C11×C4⋊C4C22×C414yes—
201C11×C4⋊C4C22×C418yes—
202C42×C11—28no—
203C42×C11—24no—
204C42×C11C22×C414yes—
205C42×C11C22×C418yes—
206(C2×D11)⋊C4—24no—
207(C2×D11)⋊C4—24no—
208(C2×D11)⋊C4—44no—
209(C2×D11)⋊C4C22×C418yes—
210(C2×D11)⋊C4C22×C418yes—
211C4⋊Dic11—28no—
212C4⋊Dic11—24no—
213C4⋊Dic11—24no—
214C4⋊Dic11—44no—
215C4⋊Dic11C22×C414yes—
216C4⋊Dic11C22×C418yes—
217Dic11⋊C4—28no—
218Dic11⋊C4—28no—
219Dic11⋊C4—28no—
220Dic11⋊C4—44no—
221Dic11⋊C4C22×C418yes—
222Dic11⋊C4C22×C418yes—
223Dic11⋊C4C22×C418yes—
224Dic11⋊C4C22×C418yes—
225Dic11⋊C4C22×C418yes—
226C4×Dic11—24no—
227C4×Dic11—24no—
228C4×Dic11—24no—
229C4×Dic11—28no—
230C4×Dic11—24no—
231C4×Dic11—44no—
232C4×Dic11—44no—
233C4×Dic11—44no—
234C4×Dic11C22×C414yes—
235C4×Dic11C22×C418yes—
236C4×Dic11C22×C414yes—
237C4×Dic11C22×C414yes—
238C4×Dic11#4118yes—
239C2×#533—111no—
240#2370—114no—
241#2362—112no—
242#2362—112no—
243#2356—111no—
244#2356D1111yescharacteristic, complemented
245#2351—111no—
246#2351—111no—
247#2347—112no—
248#2346—112no—
249#2323—114no—
250#2320—112no—
251C4×C4⋊Q8—112no—
252C4×C4⋊Q8—112no—
253#2285—111no—
254#2276—112no—
255C4×#117—111no—
256C23×C11C2511yescharacteristic
257C22×D11—22no—
258C22×D11—21no—
259C22×D11—21no—
260C22×D11—22no—
261C22×D11C23×C412yes—
262Q8×C11—28no—
263C2×C4×C11—24no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—24no—
272C2×C4×C11—24no—
273C2×C4×C11—22no—
274C2×C4×C11—24no—
275C2×C4×C11—22no—
276C2×C4×C11C23×C412yes—
277C2×C4×C11C23×C412yes—
278C2×C4×C11C23×C414yes—
279C2×C4×C11C23×C414yes—
280C2×C4×C11C23×C412yes—
281C2×C4×C11C2×#4114yes—
282C2×C4×C11H(5,𝔽2)12yes—
283C2×C4×C112−1+412yes—
284C2×Dic11—24no—
285C2×Dic11—22no—
286C2×Dic11—21no—
287C2×Dic11—22no—
288C2×Dic11—22no—
289C2×Dic11—22no—
290C2×Dic11—21no—
291C2×Dic11—24no—
292C2×Dic11—22no—
293C2×Dic11—22no—
294C2×Dic11—24no—
295C2×Dic11—22no—
296C2×Dic11—24no—
297C2×Dic11C23×C412yes—
298C2×Dic11C23×C414yes—
299C2×Dic11C23×C414yes—
300C2×Dic11C23×C412yes—
301C2×Dic11C23×C412yes—
302C2×Dic11C2×#4114yes—
303C2×Dic11C2×#4114yes—
304C2×Dic112−1+414yes—
305C4×D11—28no—
306C4×D11—28no—
307C4×D11—28no—
308Dic22—28no—
309Dic22—216no—
310#533—1116no—
311C2×C4⋊Q8—111no—
312C2×C4⋊Q8—111no—
313C2×#125—112no—
314C2×C22⋊Q8—111no—
315C2×C22⋊Q8—112no—
316C2×C22⋊Q8—111no—
317C2×C4×Q8—112no—
318C2×C4×Q8—112no—
319C2×C4×Q8—112no—
320C2×C4×Q8—111no—
321C2×C4×Q8—114no—
322C2×C4×Q8C2×D1111yescharacteristic
323C2×#117—112no—
324C2×#117—112no—
325C2×#117—112no—
326C22×C42—111no—
327#391—112no—
328#391—114no—
329#391C2×D1112yes—
330#389—112no—
331#389—112no—
332#389—114no—
333#389—114no—
334#389—114no—
335#389—114no—
336#389—114no—
337#388—114no—
338#388—114no—
339#388—114no—
340#388—114no—
341#387—114no—
342#387—114no—
343#387—114no—
344#387C2×D1114yes—
345#384—112no—
346#383—112no—
347#383C2×D1112yes—
348#382—112no—
349#382—111no—
350#382—112no—
351#382C2×D1111yescharacteristic
352#380—112no—
353#380—112no—
354C4×C4⋊C4—112no—
355C4×C4⋊C4—114no—
356C4×C4⋊C4—112no—
357C4×C4⋊C4—112no—
358C4×C4⋊C4—111no—
359C4×C4⋊C4—114no—
360C4×C4⋊C4—114no—
361C4×C4⋊C4—114no—
362C4×C4⋊C4—112no—
363C4×C4⋊C4—112no—
364C4×C4⋊C4—114no—
365C4×C4⋊C4—112no—
366C4×C4⋊C4C2×D1112yes—
367C4×C4⋊C4C2×D1111yescharacteristic
368C4×C22⋊C4—112no—
369C4×C22⋊C4—111no—
370C4×C22⋊C4—111no—
371#376—111no—
372#376—112no—
373#376—111no—
374#376C2×D1112yes—
375C43—112no—
376C22×C11C24×C411yescharacteristic
377C22×C11C22×#4112yes—
378C22×C11C2×H(5,𝔽2)11yescharacteristic
379C22×C11C2×2−1+411yescharacteristic
380C22×C11C2×2−1+412yes—
381C2×D11—22no—
382C2×D11—22no—
383C2×D11—22no—
384C2×D11—42no—
385C2×D11—42no—
386C4×C11—24no—
387C4×C11—22no—
388C4×C11—22no—
389C4×C11—24no—
390C4×C11—24no—
391C4×C11—42no—
392C4×C11—44no—
393C4×C11#52014yes—
394Dic11—24no—
395Dic11—24no—
396Dic11—22no—
397Dic11—24no—
398Dic11—44no—
399Dic11—42no—
400Dic11C4×#4114yes—
401Dic11#51914yes—
402C22×Q8—112no—
403C22×Q8—111no—
404C22×Q8C22×D1111yescharacteristic
405C23×C4—111no—
406C23×C4—111no—
407C23×C4—111no—
408C4⋊Q8—118no—
409C4⋊Q8—118no—
410#125—1116no—
411C22⋊Q8—118no—
412C22⋊Q8—1116no—
413C22⋊Q8—118no—
414C4×Q8—1116no—
415C4×Q8—118no—
416C4×Q8—2216no—
417C4×Q8—444no—
418C4×Q8—444no—
419C4×Q8C4×D1118yes—
420#117—1116no—
421#117—228no—
422#117—444no—
423C2×C4⋊C4—112no—
424C2×C4⋊C4—112no—
425C2×C4⋊C4—112no—
426C2×C4⋊C4—112no—
427C2×C4⋊C4—112no—
428C2×C4⋊C4—112no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—112no—
431C2×C4⋊C4—112no—
432C2×C4⋊C4—114no—
433C2×C4⋊C4—114no—
434C2×C4⋊C4—114no—
435C2×C4⋊C4—114no—
436C2×C4⋊C4—114no—
437C2×C4⋊C4—114no—
438C2×C4⋊C4C22×D1112yes—
439C2×C4⋊C4C22×D1112yes—
440C2×C4⋊C4C22×D1112yes—
441C2×C4⋊C4C22×D1111yescharacteristic
442C2×C22⋊C4—112no—
443C2×C22⋊C4—112no—
444C2×C22⋊C4—112no—
445C2×C22⋊C4—112no—
446C2×C22⋊C4—114no—
447C2×C42—112no—
448C2×C42—112no—
449C2×C42—111no—
450C2×C42—111no—
451C2×C42—111no—
452C2×C42—118no—
453C2×C42—112no—
454C2×C42—112no—
455C2×C42—114no—
456C2×C42—112no—
457C2×C42—112no—
458C2×C42—114no—
459C2×C42—114no—
460C2×C42—114no—
461C2×C42C22×D1114yes—
462C2×C42C22×D1112yes—
463C2×C42C22×D1112yes—
464C2×C42C22×D1111yescharacteristic
465#95—112no—
466#95—111no—
467#95—111no—
468#95—112no—
469#95—112no—
470#95—114no—
471#95—112no—
472#95—114no—
473#95—114no—
474#95—114no—
475#95—114no—
476#95C22×D1111yescharacteristic
477#95C22×D1111yescharacteristic
478#95C22×D1112yes—
479#95C22×D1114yes—
480#95C22×D1112yes—
481#95C22×D1114yes—
482#95C22×D1114yes—
483C2×C11C2×C4×#4111yescharacteristic
484C2×C11C2×#51911yescharacteristic
485C2×C11C2×#52011yescharacteristic
486C2×C11#350912yes—
487C2×C11#351112yes—
488D11—42no—
489C24—111no—
490C2×Q8—22no—
491C2×Q8—22no—
492C2×Q8—118no—
493C2×Q8—114no—
494C2×Q8—228no—
495C2×Q8—222no—
496C2×Q8—222no—
497C2×Q8C2×C4×D1114yes—
498C22×C4—111no—
499C22×C4—111no—
500C22×C4—111no—
501C22×C4—112no—
502C22×C4—112no—
503C22×C4—112no—
504C22×C4—114no—
505C22×C4—114no—
506C22×C4—114no—
507C22×C4—112no—
508C22×C4—114no—
509C22×C4—224no—
510C22×C4—224no—
511C22×C4—222no—
512C22×C4—222no—
513C22×C4C23×D1112yes—
514C22×C4C23×D1114yes—
515C22×C4C23×D1111yescharacteristic
516C22×C4C23×D1111yescharacteristic
517C22×C4C23×D1112yes—
518C22×C4C23×D1112yes—
519C22×C4C23×D1112yes—
520C22×C4C23×D1111yescharacteristic
521C4⋊C4—24no—
522C4⋊C4—24no—
523C4⋊C4—118no—
524C4⋊C4—118no—
525C4⋊C4—118no—
526C4⋊C4—118no—
527C4⋊C4—118no—
528C4⋊C4—118no—
529C4⋊C4—114no—
530C4⋊C4—224no—
531C4⋊C4—228no—
532C4⋊C4—228no—
533C4⋊C4—228no—
534C4⋊C4—228no—
535C4⋊C4—224no—
536C4⋊C4—444no—
537C4⋊C4—444no—
538C4⋊C4C2×C4×D1118yes—
539C4⋊C4C2×C4×D1114yes—
540C22⋊C4—118no—
541C22⋊C4—118no—
542C22⋊C4—224no—
543C22⋊C4—224no—
544C22⋊C4—444no—
545C42—28no—
546C42—24no—
547C42—114no—
548C42—114no—
549C42—114no—
550C42—118no—
551C42—118no—
552C42—224no—
553C42—224no—
554C42—224no—
555C42—228no—
556C42—224no—
557C42—444no—
558C42—444no—
559C42—444no—
560C42C2×C4×D1114yes—
561C42C2×C4×D1118yes—
562C11#3422511yescharacteristic, complemented, Sylow
563C23—112no—
564C23—222no—
565C23—221no—
566C23—221no—
567C23—222no—
568C23C24×D1111yescharacteristic
569Q8—28no—
570Q8—2216no—
571Q8—228no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—24no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—24no—
585C2×C4—112no—
586C2×C4—112no—
587C2×C4—114no—
588C2×C4—114no—
589C2×C4—112no—
590C2×C4—114no—
591C2×C4—114no—
592C2×C4—114no—
593C2×C4—228no—
594C2×C4—228no—
595C2×C4—224no—
596C2×C4—222no—
597C2×C4—221no—
598C2×C4—222no—
599C2×C4—221no—
600C2×C4—222no—
601C2×C4—222no—
602C2×C4—228no—
603C2×C4—222no—
604C2×C4—224no—
605C2×C4—222no—
606C2×C4—224no—
607C2×C4—222no—
608C2×C4—224no—
609C2×C4C22×C4×D1112yes—
610C2×C4C22×C4×D1112yes—
611C2×C4C22×C4×D1114yes—
612C2×C4C22×C4×D1114yes—
613C2×C4C22×C4×D1112yes—
614C2×C4#41×D1114yes—
615C2×C4#6704212yes—
616C2×C4#6704312yes—
617C22—222no—
618C22—222no—
619C22—222no—
620C22—442no—
621C22—442no—
622C22C23×C4×D1111yescharacteristic
623C22C2×#41×D1112yes—
624C22C2×#6704211yescharacteristic
625C22C2×#6704311yescharacteristic
626C22D11×2−1+412yes—
627C4—24no—
628C4—22no—
629C4—24no—
630C4—22no—
631C4—24no—
632C4—42no—
633C4—44no—
634C4—114no—
635C4—114no—
636C4—224no—
637C4—224no—
638C4—222no—
639C4—224no—
640C4—442no—
641C4—444no—
642C4#1062305414yes—
643C2—442no—
644C2C4×#41×D1111yescharacteristic
645C2D11×#51911yescharacteristic
646C2C2×#1062305411yescharacteristic
647C2#1308249412yes—
648C2#1308252012yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2356C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2356D11
hypocenterC11#34225
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2356

Complements

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

NH ≅ G/Ntype
2. #13071709C2semidirect
5. #13071579C2semidirect
6. #13071537C2semidirect
7. #13071533C2semidirect
11. #13071266C2semidirect
12. C4×#66941C2semidirect
13. #13071185C2semidirect
15. #13070979C2semidirect
17. C11×#2356C2semidirect
22. #10623109C4semidirect
244. #2356D11semidirect
562. C11#34225semidirect

Maximal subgroups

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

subgroupindex
C2×#106231092
#130717092
#130716482
#130716452
#130715792
#130715372
#130715332
#130715042
#130715022
#130712972
#130712662
C4×#669412
#130711852
#130710222
#130709792
C4×#669452
C11×#23562
#3422511