Finite Group Databasebeta

← #14914458

Subgroups — #14914458

Order 2816.

2094 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic
2#13071705C211yesmaximal, characteristic, complemented
3#13071705C211yesmaximal, characteristic, complemented
4#13071676C211yesmaximal, characteristic, complemented
5#13071648C212yesmaximal
6#13071639C212yesmaximal
7#13071578C214yesmaximal, complemented
8#13071508C212yesmaximal
9#13071497C212yesmaximal
10#13071368C214yesmaximal
11#13071261C212yesmaximal, complemented
12#13071175C212yesmaximal, complemented
13C4×#66943C212yesmaximal, complemented
14#13071012C211yesmaximal, characteristic
15#13070981C212yesmaximal, complemented
16C4×#66945C211yesmaximal, characteristic
17C11×#2365C211yesmaximal, characteristic, complemented
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C4×Q8×C11C2212yes—
20C2×#66999C2212yes—
21C2×Q8×Dic11C2212yes—
22C2×Q8×Dic11C2212yes—
23#10623259C4116yescomplemented
24C2×#66950C2212yes—
25C2×#66945C2211yescharacteristic
26C2×#66945C2211yescharacteristic
27C2×#66945C2212yes—
28C2×#66943C2212yes—
29C2×#66940C2212yes—
30C2×C42×D11C2211yescharacteristic
31C2×#66922C2211yescharacteristic
32C11×#391C2212yes—
33C11×#389C2212yes—
34C11×#387C2214yes—
35C4×C11×C4⋊C4C2212yes—
36C4×C11×C4⋊C4C2211yescharacteristic
37C4×C11×C4⋊C4C2211yescharacteristic
38#10622843C2212yes—
39#10622603C2214yes—
40#10622600C2211yescharacteristic
41#10622600C2211yescharacteristic
42#10622598C2212yes—
43#10622594C2214yes—
44#10622591C2214yes—
45#10622590C2211yescharacteristic
46#10622590C2211yescharacteristic
47C4⋊C4×Dic11C2214yes—
48C4⋊C4×Dic11C2212yes—
49C4⋊C4×Dic11C2212yes—
50C4⋊C4×Dic11C2212yes—
51C4⋊C4×Dic11C2211yescharacteristic
52C4⋊C4×Dic11C2211yescharacteristic
53C4⋊C4×Dic11C2214yes—
54#10622586C2212yes—
55#10622586C2212yes—
56#10622553C2214yes—
57C4×(C2×D11)⋊C4C2212yes—
58C4×(C2×D11)⋊C4C2212yes—
59C4×C4⋊Dic11C2214yes—
60C4×C4⋊Dic11C2212yes—
61C4×C4⋊Dic11C2211yescharacteristic
62C4×C4⋊Dic11C2211yescharacteristic
63C4×C4⋊Dic11C2212yes—
64#10622545C2214yes—
65#10622545C2212yes—
66C4×Dic11⋊C4C2214yes—
67C42×Dic11C2212yes—
68#10622541C2212yes—
69#10622541C2212yes—
70#10622283C2214yes—
71#10622282C2214yes—
72#10622279C2212yes—
73#10622277C2212yes—
74#10622268C2214yes—
75#10622267C2214yes—
76#10622266C2214yes—
77#10622264C2214yes—
78#10622264C2212yes—
79#10622263C2214yes—
80#10622262C2214yes—
81#10622261C2212yes—
82#10622259C2214yes—
83#10622259C2214yes—
84C22×Q8×C11C2312yes—
85C22×C4×D11C2311yescharacteristic
86C22×C4×D11C2311yescharacteristic
87C22×C4×D11C2311yescharacteristic
88C22×Dic22C2312yes—
89C11×C4⋊Q8C2×C418yes—
90C4×Q8×C11—28no—
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2314yes—
95C2×C11×C4⋊C4C2312yes—
96C2×C11×C4⋊C4C2312yes—
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C42×C11C2312yes—
99C2×C42×C11C2312yes—
100C2×C42×C11C2314yes—
101C2×C42×C11C2311yescharacteristic
102#66999C2×C4116yes—
103Q8×Dic11—28no—
104Q8×Dic11C2×C4116yes—
105C2×(C2×D11)⋊C4C2312yes—
106C2×(C2×D11)⋊C4C2312yes—
107C2×(C2×D11)⋊C4C2312yes—
108C2×(C2×D11)⋊C4C2312yes—
109C2×(C2×D11)⋊C4C2314yes—
110C2×C4⋊Dic11C2311yescharacteristic
111C2×C4⋊Dic11C2314yes—
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2311yescharacteristic
114C2×C4⋊Dic11C2312yes—
115C2×C4⋊Dic11C2312yes—
116C2×C4⋊Dic11C2314yes—
117C2×C4⋊Dic11C2311yescharacteristic
118C2×Dic11⋊C4C2314yes—
119C2×Dic11⋊C4C2314yes—
120C2×Dic11⋊C4C2314yes—
121C2×C4×Dic11C2312yes—
122C2×C4×Dic11C2312yes—
123C2×C4×Dic11C2314yes—
124C2×C4×Dic11C2312yes—
125C2×C4×Dic11C2312yes—
126C2×C4×Dic11C2314yes—
127C2×C4×Dic11C2314yes—
128C2×C4×Dic11C2312yes—
129C2×C4×Dic11C2312yes—
130C2×C4×Dic11C2311yescharacteristic
131C2×C4×Dic11C2311yescharacteristic
132C2×C4×Dic11C2311yescharacteristic
133C2×C4×Dic11C2314yes—
134#66950C2×C4116yes—
135#66945—24no—
136#66945—24no—
137#66945C2×C4116yes—
138#66943C2×C4116yes—
139#66940C2×C4116yes—
140C42×D11C2×C418yes—
141#66922C2×C418yes—
142C11×#95C2312yes—
143C11×#95C2312yes—
144C11×#95C2314yes—
145C11×#95C2314yes—
146C11⋊#95C2312yes—
147C11⋊#95C2312yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2312yes—
153C11⋊#95C2312yes—
154C11⋊#95C2312yes—
155C11⋊#95C2312yes—
156C11⋊#95C2314yes—
157C11⋊#95C2312yes—
158C11⋊#95C2314yes—
159C11⋊#95C2312yes—
160C11⋊#95C2312yes—
161C11⋊#95C2312yes—
162#34231—111nomaximal, Sylow
163C23×D11C2411yescharacteristic
164C2×Q8×C11—24no—
165C2×Q8×C11—24no—
166C2×Q8×C11C22×C418yes—
167C22×C4×C11C2412yes—
168C22×C4×C11C2412yes—
169C22×C4×C11C2412yes—
170C22×C4×C11C2411yescharacteristic
171C22×C4×C11C2414yes—
172C22×C4×C11C2412yes—
173C22×C4×C11C2411yescharacteristic
174C22×C4×C11C2411yescharacteristic
175C22×Dic11C2412yes—
176C22×Dic11C2412yes—
177C22×Dic11C2412yes—
178C22×Dic11C2411yescharacteristic
179C22×Dic11C2411yescharacteristic
180C22×Dic11C2411yescharacteristic
181C22×Dic11C2414yes—
182C22×Dic11C2412yes—
183C2×C4×D11—22no—
184C2×C4×D11—22no—
185C2×C4×D11—22no—
186C2×C4×D11—22no—
187C2×C4×D11—41no—
188C2×C4×D11—41no—
189C2×C4×D11C22×C414yes—
190C2×C4×D11C22×C414yes—
191C2×C4×D11C22×C414yes—
192C2×Dic22—42no—
193C2×Dic22—42no—
194C2×Dic22C22×C418yes—
195C11×C4⋊C4—22no—
196C11×C4⋊C4—28no—
197C11×C4⋊C4—22no—
198C11×C4⋊C4—22no—
199C11×C4⋊C4C22×C418yes—
200C11×C4⋊C4C22×C418yes—
201C11×C4⋊C4#4114yes—
202C42×C11—28no—
203C42×C11—24no—
204C42×C11—24no—
205C42×C11C22×C414yes—
206(C2×D11)⋊C4—24no—
207(C2×D11)⋊C4—24no—
208(C2×D11)⋊C4—42no—
209(C2×D11)⋊C4—42no—
210(C2×D11)⋊C4C22×C4116yes—
211C4⋊Dic11—28no—
212C4⋊Dic11—22no—
213C4⋊Dic11—22no—
214C4⋊Dic11—22no—
215C4⋊Dic11C22×C418yes—
216C4⋊Dic11C22×C418yes—
217C4⋊Dic11C22×C4116yes—
218C4⋊Dic11#4114yes—
219Dic11⋊C4—44no—
220Dic11⋊C4—44no—
221Dic11⋊C4C22×C4116yes—
222C4×Dic11—24no—
223C4×Dic11—28no—
224C4×Dic11—24no—
225C4×Dic11—24no—
226C4×Dic11—24no—
227C4×Dic11—42no—
228C4×Dic11—44no—
229C4×Dic11—44no—
230C4×Dic11—42no—
231C4×Dic11C22×C414yes—
232C4×Dic11C22×C414yes—
233C4×Dic11C22×C414yes—
234C4×Dic11C22×C4116yes—
235C2×#533—111no—
236#2369—111no—
237#2369—111no—
238#2365—111no—
239#2365D1111yescharacteristic, complemented
240#2362—112no—
241#2362—112no—
242#2356—114no—
243#2347—112no—
244#2346—112no—
245#2332—114no—
246#2320—112no—
247C4×#125—112no—
248C4×#125—112no—
249#2283—111no—
250#2276—112no—
251C4×#117—111no—
252C23×C11C2511yescharacteristic
253C22×D11—21no—
254C22×D11—21no—
255C22×D11—21no—
256C22×D11—21no—
257C22×D11—21no—
258C22×D11—21no—
259C22×D11C23×C412yes—
260Q8×C11—216no—
261C2×C4×C11—24no—
262C2×C4×C11—24no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11C23×C418yes—
277C2×C4×C11C23×C412yes—
278C2×C4×C11C23×C412yes—
279C2×C4×C11C23×C412yes—
280C2×C4×C11C2×#4114yes—
281C2×C4×C11C2×#4112yes—
282C2×C4×C11C2×#4112yes—
283C2×C4×C112−1+412yes—
284C2×C4×C112−1+412yes—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—22no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—22no—
291C2×Dic11—24no—
292C2×Dic11—21no—
293C2×Dic11—21no—
294C2×Dic11—24no—
295C2×Dic11—22no—
296C2×Dic11—22no—
297C2×Dic11—22no—
298C2×Dic11—22no—
299C2×Dic11—22no—
300C2×Dic11—22no—
301C2×Dic11—22no—
302C2×Dic11—22no—
303C2×Dic11—22no—
304C2×Dic11C23×C412yes—
305C2×Dic11C23×C412yes—
306C2×Dic11C23×C412yes—
307C2×Dic11C23×C418yes—
308C2×Dic11C2×#4114yes—
309C4×D11—28no—
310C4×D11—28no—
311C4×D11—44no—
312Dic22—48no—
313#533—1116no—
314C2×C4⋊Q8—111no—
315C2×C4⋊Q8C2×D1111yescharacteristic
316C2×#125—112no—
317C2×C22⋊Q8—112no—
318C2×C22⋊Q8—112no—
319C2×C4×Q8—112no—
320C2×C4×Q8—112no—
321C2×C4×Q8—112no—
322C2×C4×Q8C2×D1112yes—
323C2×#117—112no—
324C2×#117—111no—
325C2×#117—111no—
326C22×C42—111no—
327#391—112no—
328#391—114no—
329#391—114no—
330#391C2×D1112yes—
331#389—112no—
332#389—112no—
333#389—112no—
334#389—112no—
335#389—112no—
336#389C2×D1112yes—
337#388—114no—
338#388—114no—
339#388—114no—
340#388—114no—
341#387—114no—
342#387—114no—
343#387—114no—
344#387—114no—
345#387—114no—
346#387C2×D1114yes—
347#383—114no—
348#383—112no—
349#382—111no—
350#382—111no—
351#382—114no—
352#381—112no—
353#380—111no—
354#380—111no—
355C4×C4⋊C4—114no—
356C4×C4⋊C4—112no—
357C4×C4⋊C4—112no—
358C4×C4⋊C4—111no—
359C4×C4⋊C4—114no—
360C4×C4⋊C4—112no—
361C4×C4⋊C4—111no—
362C4×C4⋊C4—114no—
363C4×C4⋊C4—112no—
364C4×C4⋊C4—114no—
365C4×C4⋊C4—112no—
366C4×C4⋊C4—111no—
367C4×C4⋊C4—111no—
368C4×C4⋊C4—114no—
369C4×C4⋊C4C2×D1112yes—
370C4×C4⋊C4C2×D1111yescharacteristic
371C4×C4⋊C4C2×D1111yescharacteristic
372C4×C22⋊C4—112no—
373C4×C22⋊C4—112no—
374C4×C22⋊C4—112no—
375#376—112no—
376#376—114no—
377#376—112no—
378C43—112no—
379C22×C11C24×C411yescharacteristic
380C22×C11C22×#4111yescharacteristic
381C22×C11C22×#4111yescharacteristic
382C22×C11C2×2−1+411yescharacteristic
383C22×C11C2×2−1+411yescharacteristic
384C22×C11#58511yescharacteristic
385C22×C11#58511yescharacteristic
386C2×D11—22no—
387C2×D11—22no—
388C2×D11—22no—
389C2×D11—41no—
390C2×D11—41no—
391C2×D11—41no—
392C2×D11—41no—
393C4×C11—28no—
394C4×C11—22no—
395C4×C11—24no—
396C4×C11—42no—
397C4×C11—42no—
398C4×C11—42no—
399C4×C11C4×#4114yes—
400C4×C11#51914yes—
401Dic11—22no—
402Dic11—22no—
403Dic11—28no—
404Dic11—22no—
405Dic11—24no—
406Dic11—42no—
407Dic11—42no—
408Dic11—42no—
409C22×Q8—112no—
410C22×Q8C22×D1112yes—
411C23×C4—111no—
412C23×C4—111no—
413C23×C4—111no—
414C4⋊Q8—118no—
415C4⋊Q8C4×D1118yes—
416#125—1116no—
417C22⋊Q8—1116no—
418C22⋊Q8—1116no—
419C4×Q8—28no—
420C4×Q8—1116no—
421C4×Q8—1116no—
422C4×Q8—228no—
423#117—1116no—
424#117—224no—
425#117—224no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—112no—
428C2×C4⋊C4—114no—
429C2×C4⋊C4—114no—
430C2×C4⋊C4—112no—
431C2×C4⋊C4—111no—
432C2×C4⋊C4—114no—
433C2×C4⋊C4—111no—
434C2×C4⋊C4—111no—
435C2×C4⋊C4—114no—
436C2×C4⋊C4—114no—
437C2×C4⋊C4C22×D1111yescharacteristic
438C2×C4⋊C4C22×D1114yes—
439C2×C4⋊C4C22×D1111yescharacteristic
440C2×C4⋊C4C22×D1111yescharacteristic
441C2×C4⋊C4C22×D1112yes—
442C2×C4⋊C4C22×D1112yes—
443C2×C4⋊C4C22×D1111yescharacteristic
444C2×C22⋊C4—114no—
445C2×C22⋊C4—112no—
446C2×C22⋊C4—112no—
447C2×C22⋊C4—112no—
448C2×C22⋊C4—112no—
449C2×C42—114no—
450C2×C42—111no—
451C2×C42—111no—
452C2×C42—111no—
453C2×C42—118no—
454C2×C42—112no—
455C2×C42—112no—
456C2×C42—112no—
457C2×C42—114no—
458C2×C42—112no—
459C2×C42—112no—
460C2×C42—112no—
461C2×C42—114no—
462C2×C42—114no—
463C2×C42C22×D1112yes—
464C2×C42C22×D1114yes—
465C2×C42C22×D1112yes—
466C2×C42C22×D1111yescharacteristic
467#95—112no—
468#95—112no—
469#95—112no—
470#95—112no—
471#95—112no—
472#95—112no—
473#95—112no—
474#95—114no—
475#95—114no—
476#95—112no—
477#95—112no—
478#95—112no—
479#95—114no—
480#95—114no—
481#95—114no—
482#95—114no—
483#95C22×D1112yes—
484#95C22×D1114yes—
485#95C22×D1112yes—
486#95C22×D1114yes—
487C2×C11C2×C4×#4111yescharacteristic
488C2×C11C2×#51911yescharacteristic
489C2×C11#342811yescharacteristic
490C2×C11#351511yescharacteristic
491C2×C11#351511yescharacteristic
492C2×C11#351811yescharacteristic
493C2×C11#351811yescharacteristic
494D11—42no—
495C24—111no—
496C2×Q8—24no—
497C2×Q8—24no—
498C2×Q8—118no—
499C2×Q8—442no—
500C2×Q8—442no—
501C2×Q8C2×C4×D1118yes—
502C22×C4—111no—
503C22×C4—112no—
504C22×C4—111no—
505C22×C4—111no—
506C22×C4—114no—
507C22×C4—114no—
508C22×C4—114no—
509C22×C4—114no—
510C22×C4—112no—
511C22×C4—112no—
512C22×C4—112no—
513C22×C4—222no—
514C22×C4—222no—
515C22×C4—222no—
516C22×C4—222no—
517C22×C4—441no—
518C22×C4—441no—
519C22×C4C23×D1112yes—
520C22×C4C23×D1112yes—
521C22×C4C23×D1112yes—
522C22×C4C23×D1111yescharacteristic
523C22×C4C23×D1114yes—
524C22×C4C23×D1112yes—
525C22×C4C23×D1111yescharacteristic
526C22×C4C23×D1111yescharacteristic
527C4⋊C4—28no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—118no—
532C4⋊C4—1116no—
533C4⋊C4—1116no—
534C4⋊C4—118no—
535C4⋊C4—114no—
536C4⋊C4—228no—
537C4⋊C4—222no—
538C4⋊C4—222no—
539C4⋊C4—222no—
540C4⋊C4—444no—
541C4⋊C4—444no—
542C4⋊C4C2×C4×D1118yes—
543C4⋊C4C2×C4×D1118yes—
544C4⋊C4#434114yes—
545C22⋊C4—1116no—
546C22⋊C4—224no—
547C22⋊C4—224no—
548C22⋊C4—442no—
549C22⋊C4—442no—
550C42—28no—
551C42—24no—
552C42—24no—
553C42—114no—
554C42—114no—
555C42—114no—
556C42—1116no—
557C42—224no—
558C42—228no—
559C42—224no—
560C42—224no—
561C42—224no—
562C42—442no—
563C42—444no—
564C42—444no—
565C42—442no—
566C42C2×C4×D1114yes—
567C11#3423111yescharacteristic, complemented, Sylow
568C23—112no—
569C23—221no—
570C23—221no—
571C23—221no—
572C23—221no—
573C23—221no—
574C23—221no—
575C23C24×D1111yescharacteristic
576Q8—216no—
577Q8—448no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—112no—
594C2×C4—112no—
595C2×C4—112no—
596C2×C4—118no—
597C2×C4—114no—
598C2×C4—221no—
599C2×C4—222no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—222no—
604C2×C4—221no—
605C2×C4—221no—
606C2×C4—224no—
607C2×C4—224no—
608C2×C4—228no—
609C2×C4—228no—
610C2×C4—222no—
611C2×C4—222no—
612C2×C4—222no—
613C2×C4—222no—
614C2×C4—222no—
615C2×C4—222no—
616C2×C4—222no—
617C2×C4—222no—
618C2×C4—222no—
619C2×C4—444no—
620C2×C4C22×C4×D1112yes—
621C2×C4C22×C4×D1118yes—
622C2×C4C22×C4×D1112yes—
623C2×C4C22×C4×D1112yes—
624C2×C4C2×#434114yes—
625C2×C4C2×#434112yes—
626C2×C4#6704012yes—
627C2×C4#41×D1112yes—
628C2×C4#6704312yes—
629C22—222no—
630C22—222no—
631C22—222no—
632C22—441no—
633C22—441no—
634C22—441no—
635C22—441no—
636C22C23×C4×D1111yescharacteristic
637C22C22×#434111yescharacteristic
638C22C2×#6704011yescharacteristic
639C22C2×#41×D1111yescharacteristic
640C22C2×#6704311yescharacteristic
641C22#1062345711yescharacteristic
642C22#1062345711yescharacteristic
643C4—28no—
644C4—24no—
645C4—22no—
646C4—42no—
647C4—42no—
648C4—42no—
649C4—222no—
650C4—222no—
651C4—222no—
652C4—228no—
653C4—224no—
654C4—442no—
655C4—442no—
656C4—442no—
657C4C4×#434114yes—
658C4#1062310314yes—
659C2—442no—
660C2C2×C4×#434111yescharacteristic
661C2C2×#1062310311yescharacteristic
662C2#1308181811yescharacteristic
663C2#1308258511yescharacteristic
664C2#1308259311yescharacteristic
665C2#1308262811yescharacteristic
666C2#1308263011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2365C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2365D11
hypocenterC11#34231
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2365

Complements

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

NH ≅ G/Ntype
2. #13071705C2semidirect
3. #13071705C2semidirect
4. #13071676C2semidirect
7. #13071578C2semidirect
11. #13071261C2semidirect
12. #13071175C2semidirect
13. C4×#66943C2semidirect
15. #13070981C2semidirect
17. C11×#2365C2semidirect
23. #10623259C4semidirect
239. #2365D11semidirect
567. C11#34231semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
#130717052
#130716762
#130716482
#130716392
#130715782
#130715082
#130714972
#130713682
#130712612
#130711752
C4×#669432
#130710122
#130709812
C4×#669452
C11×#23652
#3423111