Finite Group Databasebeta

← #14925721

Subgroups — #14925721

Order 2816.

1900 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073891C214yesmaximal, complemented
2#13073825C211yesmaximal, characteristic, complemented
3#13073651C211yesmaximal, characteristic, complemented
4#13073538C211yesmaximal, characteristic
5#13073150C212yesmaximal, complemented
6#13073045C212yesmaximal, complemented
7#13072490C212yesmaximal
8#13072143C212yesmaximal, complemented
9#13071883C214yesmaximal, complemented
10C4⋊Q8×Dic11C211yesmaximal, characteristic, complemented
11#13071171C212yesmaximal, complemented
12#13071144C212yesmaximal, complemented
13#13071078C212yesmaximal
14#13071018C212yesmaximal, complemented
15C4×#66940C211yesmaximal, characteristic, complemented
16C4×D4×Dic11C211yesmaximal, characteristic
17C11×#2563C211yesmaximal, characteristic
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×Q8×Dic11C2212yes—
21C2×D4×Dic11C2211yescharacteristic
22C2×D4×Dic11C2211yescharacteristic
23C2×#66977C2212yes—
24C22×C4×Dic11C2212yes—
25C2×#66940C2211yescharacteristic
26C2×#66940C2211yescharacteristic
27C2×#66930C2214yes—
28C2×#66923C2212yes—
29C2×C4×Dic22C2211yescharacteristic
30C11×#393C2214yes—
31C11×#390C2212yes—
32C11×#382C2212yes—
33C11×#380C2212yes—
34C11×#380C2212yes—
35C4×C11×C4⋊C4C2211yescharacteristic
36#10622843C2212yes—
37#10622842C2214yes—
38#10622834C2212yes—
39#10622825C2212yes—
40C4×C22⋊Dic11C2212yes—
41#10622598C2212yes—
42#10622598C2212yes—
43#10622589C2212yes—
44#10622589C2212yes—
45C4⋊C4×Dic11C2212yes—
46C4⋊C4×Dic11C2211yescharacteristic
47C4⋊C4×Dic11C2212yes—
48C4⋊C4×Dic11C2211yescharacteristic
49C4⋊C4×Dic11C2211yescharacteristic
50C4⋊C4×Dic11C2211yescharacteristic
51#10622587C2212yes—
52#10622586C2212yes—
53#10622586C2212yes—
54#10622586C2212yes—
55#10622586C2212yes—
56#10622562C2214yes—
57#10622561C2214yes—
58#10622561C2214yes—
59#10622559C2214yes—
60#10622558C2214yes—
61#10622557C2214yes—
62#10622555C2214yes—
63C22⋊C4×Dic11C2212yes—
64C22⋊C4×Dic11C2214yes—
65C22⋊C4×Dic11C2212yes—
66#10622548C2211yescharacteristic
67C4×C4⋊Dic11C2211yescharacteristic
68C4×Dic11⋊C4C2212yes—
69C42×Dic11C2212yes—
70C42×Dic11C2211yescharacteristic
71#10622541C2212yes—
72#10622272C2214yes—
73#10622270C2214yes—
74#10622270C2214yes—
75#10622265C2214yes—
76#10622265C2214yes—
77#10622265C2214yes—
78#10622263C2214yes—
79#10622262C2212yes—
80#10622262C2214yes—
81#10622262C2214yes—
82#10622262C2212yes—
83C22×Q8×C11C2312yes—
84C22×D4×C11C2311yescharacteristic
85C23×C4×C11C2312yes—
86C23×Dic11C2312yes—
87C23×Dic11C2312yes—
88C22×Dic22C2311yescharacteristic
89C11×C4⋊Q8—24no—
90C4×D4×C11—24no—
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2312yes—
95C2×C11×C4⋊C4C2312yes—
96C2×C11×C22⋊C4C2312yes—
97C2×C11×C22⋊C4C2314yes—
98C2×C11×C22⋊C4C2314yes—
99C2×C42×C11C2312yes—
100C2×C42×C11C2311yescharacteristic
101C2×C22⋊Dic11C2314yes—
102C2×C22⋊Dic11C2312yes—
103C2×C22⋊Dic11C2314yes—
104C2×C22⋊Dic11C2312yes—
105Q8×Dic11—44no—
106D4×Dic11—24no—
107D4×Dic11Q818yescomplemented
108C2×C4⋊Dic11C2311yescharacteristic
109C2×C4⋊Dic11C2312yes—
110C2×C4⋊Dic11C2312yes—
111C2×C4⋊Dic11C2312yes—
112C2×C4⋊Dic11C2314yes—
113C2×C4⋊Dic11C2311yescharacteristic
114C2×C4⋊Dic11C2311yescharacteristic
115#66977—28no—
116C2×Dic11⋊C4C2312yes—
117C2×Dic11⋊C4C2314yes—
118C2×Dic11⋊C4C2314yes—
119C2×Dic11⋊C4C2312yes—
120C2×Dic11⋊C4C2312yes—
121C2×Dic11⋊C4C2314yes—
122C2×Dic11⋊C4C2314yes—
123C2×Dic11⋊C4C2314yes—
124C2×Dic11⋊C4C2314yes—
125C2×C4×Dic11—28no—
126C2×C4×Dic11C2312yes—
127C2×C4×Dic11C2312yes—
128C2×C4×Dic11C2314yes—
129C2×C4×Dic11C2312yes—
130C2×C4×Dic11C2312yes—
131C2×C4×Dic11C2311yescharacteristic
132C2×C4×Dic11C2312yes—
133C2×C4×Dic11C2311yescharacteristic
134C2×C4×Dic11C2312yes—
135C2×C4×Dic11C2311yescharacteristic
136C2×C4×Dic11C2312yes—
137C2×C4×Dic11C2311yescharacteristic
138C2×C4×Dic11C2312yes—
139C2×C4×Dic11C2311yescharacteristic
140C2×C4×Dic11C2311yescharacteristic
141#66940—24no—
142#66940—24no—
143#66930—48no—
144#66923—28no—
145C4×Dic22—24no—
146C11×#95C2312yes—
147C11×#95C2314yes—
148C11×#95C2314yes—
149C11⋊#95C2312yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2312yes—
153C11⋊#95C2314yes—
154C11⋊#95C2312yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2312yes—
159C11⋊#95C2312yes—
160#34941—111nomaximal, Sylow
161C24×C11C2412yes—
162C2×Q8×C11—24no—
163C2×Q8×C11—42no—
164C2×Q8×C11—42no—
165C2×D4×C11—22no—
166C2×D4×C11—22no—
167C2×D4×C11C2×Q814yes—
168C22×C4×C11—24no—
169C22×C4×C11—24no—
170C22×C4×C11—24no—
171C22×C4×C11C2412yes—
172C22×C4×C11C2414yes—
173C22×C4×C11C2412yes—
174C22×C4×C11C2412yes—
175C22×C4×C11C2411yescharacteristic
176C22×C4×C11C2411yescharacteristic
177C22×C4×C11C2411yescharacteristic
178C22×Dic11—24no—
179C22×Dic11—24no—
180C22×Dic11—24no—
181C22×Dic11—24no—
182C22×Dic11—42no—
183C22×Dic11C2×Q818yes—
184C22×Dic11C2412yes—
185C22×Dic11C2411yescharacteristic
186C22×Dic11C2414yes—
187C22×Dic11C2411yescharacteristic
188C22×Dic11C2412yes—
189C22×Dic11C2411yescharacteristic
190C22×Dic11C2412yes—
191C22×Dic11C2412yes—
192C22×Dic11C2411yescharacteristic
193C2×Dic22—22no—
194C2×Dic22—22no—
195C2×Dic22#4114yes—
196C11×C4⋊C4—22no—
197C11×C4⋊C4—22no—
198C11×C4⋊C4—22no—
199C11×C4⋊C4—24no—
200C11×C4⋊C4—24no—
201C11×C22⋊C4—24no—
202C11×C22⋊C4—44no—
203C11×C22⋊C4—44no—
204C42×C11—24no—
205C42×C11#4114yes—
206C22⋊Dic11—28no—
207C22⋊Dic11—24no—
208C22⋊Dic11—44no—
209C22⋊Dic11C2×Q818yes—
210C4⋊Dic11—22no—
211C4⋊Dic11—24no—
212C4⋊Dic11—24no—
213C4⋊Dic11—42no—
214C4⋊Dic11—44no—
215C4⋊Dic11C2×Q814yes—
216C4⋊Dic11#4114yes—
217Dic11⋊C4—28no—
218Dic11⋊C4—28no—
219Dic11⋊C4—24no—
220Dic11⋊C4—24no—
221Dic11⋊C4—28no—
222Dic11⋊C4—24no—
223Dic11⋊C4—44no—
224Dic11⋊C4—44no—
225Dic11⋊C4—44no—
226C4×Dic11—24no—
227C4×Dic11—24no—
228C4×Dic11—24no—
229C4×Dic11—24no—
230C4×Dic11—24no—
231C4×Dic11—28no—
232C4×Dic11—22no—
233C4×Dic11—24no—
234C4×Dic11—22no—
235C4×Dic11—24no—
236C4×Dic11—22no—
237C4×Dic11—41no—
238C4×Dic11—42no—
239C4×Dic11C2×Q814yes—
240C4×Dic11#4114yes—
241#2574—114no—
242#2567—111no—
243#2563D1111yescharacteristic
244#2552—111no—
245#2538—111no—
246#2508—112no—
247#2497—112no—
248#2454—112no—
249#2423—112no—
250#2396—114no—
251C4×C4⋊Q8—111no—
252C4×#125—112no—
253C4×C22⋊Q8—112no—
254#2293—112no—
255#2285—112no—
256C42×Q8—111no—
257C42×D4—111no—
258C23×C11—22no—
259C23×C11—22no—
260C23×C11—22no—
261C23×C11—22no—
262C23×C11—22no—
263C23×C11—22no—
264C23×C11C22×Q814yes—
265C23×C11C2511yescharacteristic
266Q8×C11—48no—
267D4×C11—28no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
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×C11—22no—
277C2×C4×C11—24no—
278C2×C4×C11—22no—
279C2×C4×C11—24no—
280C2×C4×C11—22no—
281C2×C4×C11—24no—
282C2×C4×C11—48no—
283C2×C4×C11C22×Q812yes—
284C2×C4×C11C2×#4112yes—
285C2×C4×C11C2×#4112yes—
286C2×C4×C11C2×#4112yes—
287C2×C4×C11C2×#4112yes—
288C2×C4×C11C2×#4112yes—
289C2×C4×C11C2×#4112yes—
290C2×Dic11—21no—
291C2×Dic11—22no—
292C2×Dic11—22no—
293C2×Dic11—22no—
294C2×Dic11—22no—
295C2×Dic11—21no—
296C2×Dic11—22no—
297C2×Dic11—21no—
298C2×Dic11—21no—
299C2×Dic11—22no—
300C2×Dic11—216no—
301C2×Dic11—21no—
302C2×Dic11—22no—
303C2×Dic11—21no—
304C2×Dic11—24no—
305C2×Dic11—24no—
306C2×Dic11—22no—
307C2×Dic11—24no—
308C2×Dic11—21no—
309C2×Dic11—22no—
310C2×Dic11—48no—
311C2×Dic11C22×Q812yes—
312C2×Dic11C22×Q814yes—
313C2×Dic11C22×Q812yes—
314C2×Dic11C2×#4112yes—
315C2×Dic11C2×#4114yes—
316C2×Dic11C2×#4114yes—
317C2×Dic11C2×#4112yes—
318C2×Dic11H(5,𝔽2)12yes—
319Dic22—28no—
320C2×C4⋊Q8C2×D1111yescharacteristic
321C2×#125—112no—
322C2×C22⋊Q8—112no—
323C2×C4×Q8—112no—
324C2×C4×Q8—111no—
325C2×C4×Q8—111no—
326C2×C4×Q8—111no—
327C2×C4×D4—111no—
328C2×C4×D4—111no—
329C2×C4×D4C2×D1111yescharacteristic
330C2×#117—114no—
331C22×C42—112no—
332#400—114no—
333#399—114no—
334#398—114no—
335#398—114no—
336#396—114no—
337#396—114no—
338#395—114no—
339#393C2×D1114yes—
340#391—112no—
341#391—112no—
342#390—112no—
343#390C2×D1112yes—
344#389—112no—
345#389—112no—
346#389—112no—
347#389—112no—
348#389—112no—
349#389—112no—
350#389—112no—
351#388—114no—
352#388—114no—
353#387—114no—
354#387—114no—
355#387—114no—
356#385—114no—
357#384—112no—
358#384—112no—
359#384—111no—
360#382—114no—
361#382C2×D1112yes—
362#380—112no—
363#380—114no—
364#380C2×D1112yes—
365#380C2×D1112yes—
366C4×C4⋊C4—111no—
367C4×C4⋊C4—112no—
368C4×C4⋊C4—112no—
369C4×C4⋊C4—111no—
370C4×C4⋊C4—111no—
371C4×C4⋊C4—111no—
372C4×C4⋊C4—111no—
373C4×C4⋊C4—112no—
374C4×C4⋊C4—114no—
375C4×C4⋊C4—114no—
376C4×C4⋊C4—112no—
377C4×C4⋊C4—112no—
378C4×C4⋊C4C2×D1111yescharacteristic
379C4×C22⋊C4—112no—
380C4×C22⋊C4—112no—
381C4×C22⋊C4—112no—
382C4×C22⋊C4—114no—
383C43—112no—
384C43—111no—
385C22×C11—24no—
386C22×C11—24no—
387C22×C11—24no—
388C22×C11—42no—
389C22×C11—42no—
390C22×C11—42no—
391C22×C11—42no—
392C22×C11C23×Q811yescharacteristic
393C22×C11C22×#4111yescharacteristic
394C22×C11C22×#4111yescharacteristic
395C22×C11C22×#4111yescharacteristic
396C22×C11C22×#4111yescharacteristic
397C22×C11C2×H(5,𝔽2)11yescharacteristic
398C22×C11#58511yescharacteristic
399C4×C11—22no—
400C4×C11—42no—
401C4×C11—44no—
402C4×C11—42no—
403C4×C11—42no—
404C4×C11#52914yes—
405C4×C11#53314yes—
406Dic11—24no—
407Dic11—24no—
408Dic11—22no—
409Dic11—24no—
410Dic11—22no—
411Dic11—42no—
412Dic11—41no—
413Dic11—44no—
414Dic11#55414yes—
415C22×Q8—111no—
416C22×Q8C22×D1112yes—
417C22×D4C22×D1111yescharacteristic
418C23×C4—112no—
419C23×C4—112no—
420C23×C4C22×D1112yes—
421C4⋊Q8—24no—
422#125—228no—
423C22⋊Q8—228no—
424C4×Q8—224no—
425C4×Q8—224no—
426C4×Q8—224no—
427C4×Q8—444no—
428C4×D4—24no—
429C4×D4—118no—
430C4×D4—224no—
431#117—448no—
432C2×C4⋊C4—111no—
433C2×C4⋊C4—111no—
434C2×C4⋊C4—111no—
435C2×C4⋊C4—112no—
436C2×C4⋊C4—112no—
437C2×C4⋊C4—112no—
438C2×C4⋊C4—112no—
439C2×C4⋊C4—114no—
440C2×C4⋊C4—114no—
441C2×C4⋊C4—112no—
442C2×C4⋊C4—114no—
443C2×C4⋊C4—114no—
444C2×C4⋊C4—114no—
445C2×C4⋊C4—112no—
446C2×C4⋊C4—114no—
447C2×C4⋊C4—114no—
448C2×C4⋊C4C22×D1111yescharacteristic
449C2×C4⋊C4C22×D1111yescharacteristic
450C2×C4⋊C4C22×D1111yescharacteristic
451C2×C4⋊C4C22×D1112yes—
452C2×C4⋊C4C22×D1112yes—
453C2×C22⋊C4—112no—
454C2×C22⋊C4—112no—
455C2×C22⋊C4—114no—
456C2×C22⋊C4—114no—
457C2×C22⋊C4C22×D1112yes—
458C2×C22⋊C4C22×D1114yes—
459C2×C22⋊C4C22×D1114yes—
460C2×C42—111no—
461C2×C42—111no—
462C2×C42—112no—
463C2×C42—114no—
464C2×C42—111no—
465C2×C42—111no—
466C2×C42—112no—
467C2×C42—111no—
468C2×C42—112no—
469C2×C42—112no—
470C2×C42—112no—
471C2×C42—112no—
472C2×C42—112no—
473C2×C42—111no—
474C2×C42—112no—
475C2×C42—228no—
476C2×C42C22×D1112yes—
477C2×C42C22×D1111yescharacteristic
478#95—112no—
479#95—112no—
480#95—112no—
481#95—114no—
482#95—114no—
483#95—112no—
484#95—112no—
485#95—114no—
486#95—114no—
487#95—114no—
488#95—114no—
489#95C22×D1112yes—
490#95C22×D1114yes—
491#95C22×D1114yes—
492C2×C11—44no—
493C2×C11C2×#52911yescharacteristic
494C2×C11C2×#53311yescharacteristic
495C2×C11#346011yescharacteristic
496C2×C11C2×#55411yescharacteristic
497C2×C11#347511yescharacteristic
498C2×C11Q8×#4111yescharacteristic
499C2×C11#348311yescharacteristic
500C24C23×D1112yes—
501C2×Q8—24no—
502C2×Q8—42no—
503C2×Q8—42no—
504C2×Q8—114no—
505C2×Q8—222no—
506C2×Q8—222no—
507C2×D4—22no—
508C2×D4—22no—
509C2×D4Q8×D1114yes—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—111no—
514C22×C4—118no—
515C22×C4—111no—
516C22×C4—111no—
517C22×C4—112no—
518C22×C4—112no—
519C22×C4—112no—
520C22×C4—112no—
521C22×C4—111no—
522C22×C4—114no—
523C22×C4—224no—
524C22×C4—224no—
525C22×C4—224no—
526C22×C4—224no—
527C22×C4—442no—
528C22×C4C23×D1112yes—
529C22×C4C23×D1114yes—
530C22×C4C23×D1112yes—
531C22×C4C23×D1112yes—
532C22×C4C23×D1111yescharacteristic
533C22×C4C23×D1111yescharacteristic
534C22×C4C23×D1111yescharacteristic
535C4⋊C4—22no—
536C4⋊C4—24no—
537C4⋊C4—24no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—114no—
541C4⋊C4—114no—
542C4⋊C4—224no—
543C4⋊C4—224no—
544C4⋊C4—228no—
545C4⋊C4—228no—
546C4⋊C4—228no—
547C4⋊C4—224no—
548C4⋊C4—222no—
549C4⋊C4—224no—
550C4⋊C4—224no—
551C4⋊C4—444no—
552C4⋊C4—444no—
553C4⋊C4—442no—
554C4⋊C4—444no—
555C4⋊C4—444no—
556C22⋊C4—24no—
557C22⋊C4—44no—
558C22⋊C4—44no—
559C22⋊C4—118no—
560C22⋊C4—224no—
561C22⋊C4—228no—
562C22⋊C4—444no—
563C42—24no—
564C42—114no—
565C42—114no—
566C42—224no—
567C42—224no—
568C42—224no—
569C42—228no—
570C42—224no—
571C42—224no—
572C42—222no—
573C42—224no—
574C42—224no—
575C42—222no—
576C42—222no—
577C42—441no—
578C42—442no—
579C42#434114yes—
580C11#3494111yescharacteristic, complemented, Sylow
581C23—22no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23C2×Q8×D1114yes—
588C23C24×D1111yescharacteristic
589Q8—48no—
590Q8—228no—
591D4—28no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—24no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—24no—
604C2×C4—22no—
605C2×C4—24no—
606C2×C4—48no—
607C2×C4—112no—
608C2×C4—112no—
609C2×C4—112no—
610C2×C4—112no—
611C2×C4—114no—
612C2×C4—112no—
613C2×C4—114no—
614C2×C4—114no—
615C2×C4—2216no—
616C2×C4—222no—
617C2×C4—221no—
618C2×C4—222no—
619C2×C4—222no—
620C2×C4—222no—
621C2×C4—221no—
622C2×C4—222no—
623C2×C4—221no—
624C2×C4—221no—
625C2×C4—222no—
626C2×C4—222no—
627C2×C4—221no—
628C2×C4—221no—
629C2×C4—224no—
630C2×C4—224no—
631C2×C4—222no—
632C2×C4—224no—
633C2×C4—221no—
634C2×C4—222no—
635C2×C4—448no—
636C2×C4C2×#434112yes—
637C2×C4C2×#434112yes—
638C2×C4C2×#434112yes—
639C2×C4C2×Q8×D1112yes—
640C2×C4#41×D1112yes—
641C2×C4#41×D1112yes—
642C2×C4#41×D1112yes—
643C22—24no—
644C22—24no—
645C22—24no—
646C22—42no—
647C22—42no—
648C22—42no—
649C22—42no—
650C22C22×#434111yescharacteristic
651C22C22×Q8×D1111yescharacteristic
652C22C2×#41×D1111yescharacteristic
653C22C2×#41×D1111yescharacteristic
654C22C2×#41×D1111yescharacteristic
655C22D11×H(5,𝔽2)11yescharacteristic
656C22#1062345511yescharacteristic
657C4—22no—
658C4—42no—
659C4—42no—
660C4—42no—
661C4—44no—
662C4—114no—
663C4—224no—
664C4—224no—
665C4—222no—
666C4—224no—
667C4—222no—
668C4—441no—
669C4—444no—
670C4—442no—
671C4#1062315314yes—
672C4#1062321114yes—
673C2—44no—
674C2C2×#1062321111yescharacteristic
675C2C2×#1062315311yescharacteristic
676C2#1308202911yescharacteristic
677C2D11×#55411yescharacteristic
678C2#1308217311yescharacteristic
679C2#1308219511yescharacteristic
680C2#1308224111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2563C2
prime radicalC22×D4×C11C23
hypercenter#2563D11
hypocenterC11#34941
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2563

Complements

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

NH ≅ G/Ntype
1. #13073891C2semidirect
2. #13073825C2semidirect
3. #13073651C2semidirect
5. #13073150C2semidirect
6. #13073045C2semidirect
8. #13072143C2semidirect
9. #13071883C2semidirect
10. C4⋊Q8×Dic11C2semidirect
11. #13071171C2semidirect
12. #13071144C2semidirect
14. #13071018C2semidirect
15. C4×#66940C2semidirect
107. D4×Dic11Q8semidirect
580. C11#34941semidirect

Maximal subgroups

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

subgroupindex
#130738912
#130738252
#130736512
#130735382
#130731502
#130730452
#130724902
#130721432
#130718832
C4⋊Q8×Dic112
#130711712
#130711442
#130710782
#130710182
C4×#669402
C4×D4×Dic112
C11×#25632
#3494111