Finite Group Databasebeta

← #14925762

Subgroups — #14925762

Order 2816.

1812 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073875C214yesmaximal, complemented
2#13073855C211yesmaximal, characteristic, complemented
3#13073831C211yesmaximal, characteristic, complemented
4#13073608C211yesmaximal, characteristic
5#13073538C211yesmaximal, characteristic
6#13073218C212yesmaximal, complemented
7#13073016C212yesmaximal, complemented
8#13072397C212yesmaximal
9#13072119C212yesmaximal, complemented
10#13071916C214yesmaximal, complemented
11C4×#66922C211yesmaximal, characteristic, complemented
12C4×#66989C212yesmaximal
13C4×#66977C212yesmaximal, complemented
14#13071090C212yesmaximal, complemented
15#13071014C212yesmaximal, complemented
16C42×Dic22C211yesmaximal, characteristic, complemented
17C42×D4×C11C211yesmaximal, characteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C22×C42×C11C2212yes—
22C2×#66989C2212yes—
23C2×#66977C2212yes—
24C2×#66922C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic
26C2×C4×Dic22C2212yes—
27C2×C4×Dic22C2211yescharacteristic
28C2×C4×Dic22C2211yescharacteristic
29C4×C11×C4⋊C4C2211yescharacteristic
30C4×C11×C4⋊C4C2211yescharacteristic
31C4×C11×C4⋊C4C2211yescharacteristic
32C4×C11×C22⋊C4C2212yes—
33C4×C11×C22⋊C4C2212yes—
34C4×C11×C22⋊C4C2212yes—
35C43×C11C2211yescharacteristic
36#10622834C2212yes—
37#10622825C2212yes—
38#10622825C2212yes—
39#10622825C2212yes—
40#10622824C2214yes—
41#10622823C2214yes—
42C4×C22⋊Dic11C2214yes—
43C4×C22⋊Dic11C2214yes—
44#10622590C2212yes—
45#10622587C2212yes—
46#10622587C2212yes—
47#10622587C2212yes—
48#10622586C2212yes—
49#10622586C2212yes—
50#10622566C2214yes—
51#10622565C2214yes—
52#10622565C2214yes—
53#10622561C2214yes—
54#10622558C2214yes—
55#10622558C2214yes—
56#10622550C2214yes—
57#10622549C2212yes—
58#10622549C2212yes—
59#10622548C2211yescharacteristic
60C4×C4⋊Dic11C2212yes—
61C4×C4⋊Dic11C2212yes—
62C4×C4⋊Dic11C2211yescharacteristic
63C4×C4⋊Dic11C2211yescharacteristic
64C4×C4⋊Dic11C2211yescharacteristic
65#10622546C2214yes—
66#10622545C2214yes—
67C4×Dic11⋊C4C2212yes—
68C4×Dic11⋊C4C2212yes—
69C4×Dic11⋊C4C2214yes—
70C4×Dic11⋊C4C2212yes—
71C42×Dic11C2212yes—
72#10622542C2212yes—
73#10622542C2212yes—
74#10622541C2212yes—
75#10622541C2212yes—
76#10622541C2212yes—
77C11⋊#401C2214yes—
78#10622273C2214yes—
79#10622272C2214yes—
80#10622271C2214yes—
81#10622265C2214yes—
82#10622265C2214yes—
83C22×D4×C11C2311yescharacteristic
84C23×C4×C11C2312yes—
85C23×C4×C11C2312yes—
86C23×C4×C11C2312yes—
87C22×Dic22C2312yes—
88C22×Dic22C2311yescharacteristic
89C4×D4×C11—24no—
90C4×D4×C11—24no—
91C4×D4×C11—24no—
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C22⋊C4C2312yes—
96C2×C11×C22⋊C4C2312yes—
97C2×C11×C22⋊C4C2312yes—
98C2×C42×C11—28no—
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2312yes—
101C2×C42×C11C2311yescharacteristic
102C2×C42×C11C2312yes—
103C2×C42×C11C2311yescharacteristic
104C2×C42×C11C2312yes—
105C2×C42×C11C2311yescharacteristic
106C2×C42×C11C2311yescharacteristic
107C2×C42×C11C2311yescharacteristic
108C2×C42×C11C2311yescharacteristic
109C2×C22⋊Dic11C2314yes—
110C2×C22⋊Dic11C2314yes—
111C2×C22⋊Dic11C2314yes—
112C2×C22⋊Dic11C2314yes—
113#66989—28no—
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4⋊Dic11C2312yes—
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2312yes—
119C2×C4⋊Dic11C2312yes—
120C2×C4⋊Dic11C2312yes—
121C2×C4⋊Dic11C2312yes—
122#66977—28no—
123C2×Dic11⋊C4C2314yes—
124C2×Dic11⋊C4C2312yes—
125C2×Dic11⋊C4C2312yes—
126C2×Dic11⋊C4C2312yes—
127C2×Dic11⋊C4C2314yes—
128C2×Dic11⋊C4C2314yes—
129C2×C4×Dic11C2312yes—
130C2×C4×Dic11C2312yes—
131C2×C4×Dic11C2312yes—
132C2×C4×Dic11C2314yes—
133C2×C4×Dic11C2312yes—
134C2×C4×Dic11C2312yes—
135C2×C4×Dic11C2312yes—
136#66922—24no—
137C4×Dic22—24no—
138C4×Dic22—28no—
139C4×Dic22—24no—
140C4×Dic22—24no—
141C11×#95C2312yes—
142C11×#95C2312yes—
143C11×#95C2312yes—
144C11⋊#95C2314yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2312yes—
155C11⋊#95C2314yes—
156C11⋊#95C2312yes—
157C11⋊#95C2314yes—
158C11⋊#95C2312yes—
159#34945—111nomaximal, Sylow
160C24×C11C2412yes—
161C2×D4×C11—22no—
162C2×D4×C11—22no—
163C2×D4×C11#4114yes—
164C22×C4×C11—24no—
165C22×C4×C11—24no—
166C22×C4×C11—24no—
167C22×C4×C11—24no—
168C22×C4×C11—24no—
169C22×C4×C11—24no—
170C22×C4×C11—24no—
171C22×C4×C11—24no—
172C22×C4×C11—42no—
173C22×C4×C11C2412yes—
174C22×C4×C11C2411yescharacteristic
175C22×C4×C11C2412yes—
176C22×C4×C11C2412yes—
177C22×C4×C11C2411yescharacteristic
178C22×C4×C11C2411yescharacteristic
179C22×C4×C11C2411yescharacteristic
180C22×C4×C11C2411yescharacteristic
181C22×C4×C11C2411yescharacteristic
182C22×C4×C11C2411yescharacteristic
183C22×Dic11C2412yes—
184C22×Dic11C2412yes—
185C22×Dic11C2414yes—
186C22×Dic11C2412yes—
187C22×Dic11C2414yes—
188C22×Dic11C2412yes—
189C2×Dic22—22no—
190C2×Dic22—22no—
191C2×Dic22—24no—
192C2×Dic22—24no—
193C2×Dic22—24no—
194C2×Dic22#4114yes—
195C11×C4⋊C4—22no—
196C11×C4⋊C4—22no—
197C11×C4⋊C4—22no—
198C11×C22⋊C4—24no—
199C11×C22⋊C4—24no—
200C11×C22⋊C4—24no—
201C42×C11—22no—
202C42×C11—24no—
203C42×C11—24no—
204C42×C11—24no—
205C42×C11—22no—
206C42×C11—22no—
207C42×C11—41no—
208C42×C11#4114yes—
209C42×C11#4114yes—
210C42×C11#4114yes—
211C22⋊Dic11—28no—
212C22⋊Dic11—28no—
213C22⋊Dic11—28no—
214C22⋊Dic11—44no—
215C4⋊Dic11—22no—
216C4⋊Dic11—24no—
217C4⋊Dic11—22no—
218C4⋊Dic11—22no—
219C4⋊Dic11—24no—
220C4⋊Dic11—24no—
221C4⋊Dic11—24no—
222C4⋊Dic11—42no—
223Dic11⋊C4—24no—
224Dic11⋊C4—28no—
225Dic11⋊C4—28no—
226Dic11⋊C4—24no—
227Dic11⋊C4—24no—
228Dic11⋊C4—44no—
229C4×Dic11—24no—
230C4×Dic11—24no—
231C4×Dic11—28no—
232C4×Dic11—24no—
233C4×Dic11—24no—
234C4×Dic11—24no—
235C4×Dic11—42no—
236#2573—114no—
237#2571—111no—
238#2568—111no—
239#2547—111no—
240#2538—111no—
241#2514—112no—
242#2494—112no—
243#2447—112no—
244#2421—112no—
245#2401—114no—
246C4×C4⋊Q8—111no—
247C4×#124—112no—
248C4×C22⋊Q8—112no—
249#2295—112no—
250#2283—112no—
251C42×Q8—111no—
252C42×D4D1111yescharacteristic
253C23×C11—22no—
254C23×C11—22no—
255C23×C11—22no—
256C23×C11—22no—
257C23×C11—22no—
258C23×C11—22no—
259C23×C11C2×#4114yes—
260C23×C11C2511yescharacteristic
261D4×C11—28no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—21no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—21no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—48no—
281C2×C4×C11—48no—
282C2×C4×C11—48no—
283C2×C4×C11C2×#4112yes—
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×C4×C11C2×#4112yes—
291C2×C4×C11C2×#4112yes—
292C2×C4×C11C2×#4112yes—
293C2×C4×C11C2×#4112yes—
294C2×C4×C112−1+412yes—
295C2×Dic11—22no—
296C2×Dic11—22no—
297C2×Dic11—22no—
298C2×Dic11—24no—
299C2×Dic11—22no—
300C2×Dic11—22no—
301C2×Dic11—24no—
302C2×Dic11—22no—
303C2×Dic11—22no—
304C2×Dic11—24no—
305C2×Dic11—24no—
306C2×Dic11—24no—
307C2×Dic11—22no—
308C2×Dic11—22no—
309C2×Dic11—22no—
310C2×Dic11—22no—
311C2×Dic11—24no—
312C2×Dic11C2×#4114yes—
313Dic22—28no—
314Dic22—48no—
315C2×C4⋊Q8—111no—
316C2×#124—112no—
317C2×C22⋊Q8—112no—
318C2×C4×Q8—112no—
319C2×C4×Q8—111no—
320C2×C4×Q8—111no—
321C2×C4×Q8—111no—
322C2×C4×D4C2×D1111yescharacteristic
323C2×C4×D4C2×D1111yescharacteristic
324C2×C4×D4C2×D1111yescharacteristic
325C22×C42C2×D1112yes—
326#401—114no—
327#400—114no—
328#400—114no—
329#400—114no—
330#397—114no—
331#397—114no—
332#397—114no—
333#396—114no—
334#391—112no—
335#391—112no—
336#391—112no—
337#391—112no—
338#391—112no—
339#390—112no—
340#389—112no—
341#389—112no—
342#389—112no—
343#389—112no—
344#389—112no—
345#388—114no—
346#388—114no—
347#387—114no—
348#387—114no—
349#387—114no—
350#385—114no—
351#384—111no—
352#383—114no—
353#382—112no—
354#382—112no—
355#382—112no—
356#381—114no—
357#380—112no—
358#380—112no—
359#380—112no—
360C4×C4⋊C4—112no—
361C4×C4⋊C4—112no—
362C4×C4⋊C4—111no—
363C4×C4⋊C4—112no—
364C4×C4⋊C4—112no—
365C4×C4⋊C4—114no—
366C4×C4⋊C4—112no—
367C4×C4⋊C4—111no—
368C4×C4⋊C4—111no—
369C4×C4⋊C4C2×D1111yescharacteristic
370C4×C4⋊C4C2×D1111yescharacteristic
371C4×C4⋊C4C2×D1111yescharacteristic
372C4×C22⋊C4—114no—
373C4×C22⋊C4—114no—
374C4×C22⋊C4C2×D1112yes—
375C4×C22⋊C4C2×D1112yes—
376C4×C22⋊C4C2×D1112yes—
377#376—114no—
378C43—112no—
379C43C2×D1111yescharacteristic
380C22×C11—24no—
381C22×C11—24no—
382C22×C11—24no—
383C22×C11—42no—
384C22×C11—42no—
385C22×C11—42no—
386C22×C11—42no—
387C22×C11C22×#4111yescharacteristic
388C22×C11C22×#4111yescharacteristic
389C22×C11C22×#4111yescharacteristic
390C22×C11C22×#4111yescharacteristic
391C22×C11C22×#4111yescharacteristic
392C22×C11C2×2−1+411yescharacteristic
393C22×C11#58511yescharacteristic
394C4×C11—22no—
395C4×C11—22no—
396C4×C11—22no—
397C4×C11—42no—
398C4×C11—42no—
399C4×C11—42no—
400C4×C11—41no—
401C4×C11#52914yes—
402C4×C11#52914yes—
403C4×C11#55614yes—
404Dic11—24no—
405Dic11—44no—
406Dic11—42no—
407Dic11—42no—
408Dic11—44no—
409Dic11—42no—
410C22×Q8—111no—
411C22×Q8—112no—
412C22×D4C22×D1111yescharacteristic
413C23×C4C22×D1112yes—
414C23×C4C22×D1112yes—
415C23×C4C22×D1112yes—
416C4⋊Q8—224no—
417#124—228no—
418C22⋊Q8—228no—
419C4×Q8—224no—
420C4×Q8—228no—
421C4×Q8—224no—
422C4×Q8—224no—
423C4×D4—24no—
424C4×D4—24no—
425C4×D4—24no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—112no—
430C2×C4⋊C4—112no—
431C2×C4⋊C4—112no—
432C2×C4⋊C4—112no—
433C2×C4⋊C4—114no—
434C2×C4⋊C4—112no—
435C2×C4⋊C4—114no—
436C2×C4⋊C4—112no—
437C2×C4⋊C4—112no—
438C2×C4⋊C4—112no—
439C2×C4⋊C4—114no—
440C2×C4⋊C4C22×D1111yescharacteristic
441C2×C4⋊C4C22×D1111yescharacteristic
442C2×C4⋊C4C22×D1111yescharacteristic
443C2×C22⋊C4—114no—
444C2×C22⋊C4—114no—
445C2×C22⋊C4—114no—
446C2×C22⋊C4—114no—
447C2×C22⋊C4C22×D1112yes—
448C2×C22⋊C4C22×D1112yes—
449C2×C22⋊C4C22×D1112yes—
450C2×C42—28no—
451C2×C42—112no—
452C2×C42—112no—
453C2×C42—112no—
454C2×C42—112no—
455C2×C42—114no—
456C2×C42—112no—
457C2×C42—112no—
458C2×C42C22×D1111yescharacteristic
459C2×C42C22×D1111yescharacteristic
460C2×C42C22×D1112yes—
461C2×C42C22×D1112yes—
462C2×C42C22×D1111yescharacteristic
463C2×C42C22×D1112yes—
464C2×C42C22×D1111yescharacteristic
465C2×C42C22×D1111yescharacteristic
466C2×C42C22×D1111yescharacteristic
467C2×C42C22×D1111yescharacteristic
468#95—114no—
469#95—114no—
470#95—114no—
471#95—114no—
472#95—114no—
473#95—114no—
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×D1112yes—
485#95C22×D1112yes—
486C2×C11—44no—
487C2×C11C2×#52911yescharacteristic
488C2×C11C2×#52911yescharacteristic
489C2×C11#346111yescharacteristic
490C2×C11C2×#55611yescharacteristic
491C2×C11#347511yescharacteristic
492C2×C11#348011yescharacteristic
493C2×C11#348211yescharacteristic
494C24C23×D1112yes—
495C2×Q8—114no—
496C2×Q8—222no—
497C2×Q8—224no—
498C2×Q8—224no—
499C2×Q8—224no—
500C2×Q8—222no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4#433914yes—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—42no—
513C22×C4—112no—
514C22×C4—112no—
515C22×C4—112no—
516C22×C4—114no—
517C22×C4—112no—
518C22×C4—114no—
519C22×C4C23×D1112yes—
520C22×C4C23×D1111yescharacteristic
521C22×C4C23×D1112yes—
522C22×C4C23×D1112yes—
523C22×C4C23×D1111yescharacteristic
524C22×C4C23×D1111yescharacteristic
525C22×C4C23×D1111yescharacteristic
526C22×C4C23×D1111yescharacteristic
527C22×C4C23×D1111yescharacteristic
528C22×C4C23×D1111yescharacteristic
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—224no—
533C4⋊C4—228no—
534C4⋊C4—224no—
535C4⋊C4—228no—
536C4⋊C4—224no—
537C4⋊C4—222no—
538C4⋊C4—224no—
539C4⋊C4—224no—
540C4⋊C4—224no—
541C4⋊C4—222no—
542C4⋊C4—222no—
543C4⋊C4—224no—
544C4⋊C4—444no—
545C4⋊C4—442no—
546C22⋊C4—24no—
547C22⋊C4—24no—
548C22⋊C4—24no—
549C22⋊C4—228no—
550C22⋊C4—228no—
551C22⋊C4—228no—
552C22⋊C4—444no—
553C42—22no—
554C42—24no—
555C42—24no—
556C42—24no—
557C42—22no—
558C42—22no—
559C42—41no—
560C42—224no—
561C42—224no—
562C42—228no—
563C42—224no—
564C42—224no—
565C42—224no—
566C42—442no—
567C42#433914yes—
568C42#433914yes—
569C42#434114yes—
570C11#3494511yescharacteristic, complemented, Sylow
571C23—22no—
572C23—22no—
573C23—22no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23C2×#433914yes—
578C23C24×D1111yescharacteristic
579Q8—228no—
580Q8—448no—
581D4—28no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—22no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—48no—
601C2×C4—48no—
602C2×C4—48no—
603C2×C4—114no—
604C2×C4—222no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—222no—
608C2×C4—224no—
609C2×C4—222no—
610C2×C4—224no—
611C2×C4—224no—
612C2×C4—224no—
613C2×C4—222no—
614C2×C4—222no—
615C2×C4—224no—
616C2×C4—222no—
617C2×C4—222no—
618C2×C4—222no—
619C2×C4—222no—
620C2×C4—224no—
621C2×C4C2×#433912yes—
622C2×C4C2×#433912yes—
623C2×C4C2×#433912yes—
624C2×C4C2×#433912yes—
625C2×C4C2×#433912yes—
626C2×C4C2×#433912yes—
627C2×C4C2×#433912yes—
628C2×C4C2×#434112yes—
629C2×C4C2×#434112yes—
630C2×C4C2×#434112yes—
631C2×C4#41×D1112yes—
632C2×C4#6704312yes—
633C22—24no—
634C22—24no—
635C22—24no—
636C22—42no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22C22×#433911yescharacteristic
641C22C22×#433911yescharacteristic
642C22C22×#433911yescharacteristic
643C22C22×#434111yescharacteristic
644C22C2×#41×D1111yescharacteristic
645C22C2×#6704311yescharacteristic
646C22#1062345311yescharacteristic
647C4—22no—
648C4—22no—
649C4—22no—
650C4—42no—
651C4—42no—
652C4—42no—
653C4—41no—
654C4—224no—
655C4—444no—
656C4—442no—
657C4—444no—
658C4—442no—
659C4—442no—
660C4#1062301014yes—
661C4#1062307314yes—
662C4#1062308814yes—
663C2—44no—
664C2C2×#1062308811yescharacteristic
665C2C2×#1062301011yescharacteristic
666C2#1308204311yescharacteristic
667C2C2×#1062307311yescharacteristic
668C2#1308217411yescharacteristic
669C2#1308220911yescharacteristic
670C2#1308223111yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC42×D4×C11C2
prime radicalC22×D4×C11C23
hypercenterC42×D4D11
hypocenterC11#34945
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C42×D4

Complements

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

NH ≅ G/Ntype
1. #13073875C2semidirect
2. #13073855C2semidirect
3. #13073831C2semidirect
6. #13073218C2semidirect
7. #13073016C2semidirect
9. #13072119C2semidirect
10. #13071916C2semidirect
11. C4×#66922C2semidirect
13. C4×#66977C2semidirect
14. #13071090C2semidirect
15. #13071014C2semidirect
16. C42×Dic22C2semidirect
570. C11#34945semidirect

Maximal subgroups

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

subgroupindex
#130738752
#130738552
#130738312
#130736082
#130735382
#130732182
#130730162
#130723972
#130721192
#130719162
C4×#669222
C4×#669892
C4×#669772
#130710902
#130710142
C42×Dic222
C42×D4×C112
#3494511