Finite Group Databasebeta

← #14914097

Subgroups — #14914097

Order 2816.

3038 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66977C211yesmaximal, characteristic
2C2×#10623047C211yesmaximal, characteristic, complemented
3C22×#66979C211yesmaximal, characteristic
4#13071641C214yesmaximal, complemented
5#13071619C214yesmaximal, complemented
6#13071480C214yesmaximal, complemented
7#13071467C214yesmaximal
8#13071294C214yesmaximal, complemented
9#13071232C211yesmaximal, characteristic, complemented
10#13071200C211yesmaximal, characteristic, complemented
11#13071144C214yesmaximal, complemented
12#13070972C211yesmaximal, characteristic, complemented
13C11×#2280C211yesmaximal, characteristic
14C24×C4×C11C2211yescharacteristic
15C23×Dic22C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2212yes—
20C2×#66979—28no—
21C2×#66979C2212yes—
22C2×#66979C2211yescharacteristic
23C2×#66979C2212yes—
24C2×#66979C2212yes—
25C2×#66979C2211yescharacteristic
26C22×C4⋊Dic11C2212yes—
27C22×C4⋊Dic11C2211yescharacteristic
28C2×#66977C4116yescomplemented
29C2×#66977C2212yes—
30C2×#66977C2212yes—
31C2×#66977C2212yes—
32C2×#66977C2212yes—
33C22×Dic11⋊C4C2212yes—
34C22×C4×Dic11C2212yes—
35#10623047—28no—
36C2×#66940C2214yescomplemented
37C2×#66930C2214yes—
38C2×C4×Dic22C2214yescomplemented
39C11×#381C2212yes—
40C11×#380C2212yes—
41C11×#380C2212yes—
42C11×#379C2212yes—
43C4×C11×C22⋊C4C2212yes—
44C4×C11×C22⋊C4C2212yes—
45C4⋊C4×Dic11C2214yescomplemented
46#10622587C2214yescomplemented
47#10622586C2214yescomplemented
48#10622559C2218yes—
49#10622558C2218yes—
50#10622557C2218yes—
51#10622556C2214yes—
52#10622555C2214yes—
53C22⋊C4×Dic11C2218yes—
54C22⋊C4×Dic11C2214yes—
55C4×C4⋊Dic11C2214yescomplemented
56#10622542C2214yescomplemented
57#10622541C2214yescomplemented
58#10622268C2218yescomplemented
59#10622265C2218yescomplemented
60#10622262C2218yescomplemented
61#10622260C2218yescomplemented
62C25×C11C2311yescharacteristic
63C23×C4×C11—24no—
64C23×C4×C11—24no—
65C23×C4×C11C2×C418yes—
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×Dic11C2314yes—
73C23×Dic11C2312yes—
74C23×Dic11C2312yes—
75C22×Dic22—24no—
76C22×Dic22—24no—
77C22×Dic22C2×C418yescomplemented
78C22×Dic22C2312yes—
79C22×Dic22C2312yes—
80C11×#117—24no—
81C11×#117—24no—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C22⋊C4C2312yes—
85C2×C11×C22⋊C4C2312yes—
86C2×C11×C22⋊C4C2314yes—
87C2×C11×C22⋊C4C2314yes—
88C2×C42×C11C2312yes—
89C2×C42×C11C2312yes—
90C2×C22⋊Dic11—28no—
91C2×C22⋊Dic11C2×C4116yes—
92C2×C22⋊Dic11C2312yes—
93C2×C22⋊Dic11C2314yes—
94C2×C22⋊Dic11C2314yes—
95C2×C22⋊Dic11C2314yes—
96C2×C22⋊Dic11C2312yes—
97#66979—24no—
98#66979—28no—
99#66979—28no—
100#66979—28no—
101#66979D418yes—
102C2×C4⋊Dic11—28no—
103C2×C4⋊Dic11C2×C418yescomplemented
104C2×C4⋊Dic11C2314yes—
105C2×C4⋊Dic11C2312yes—
106C2×C4⋊Dic11C2312yes—
107C2×C4⋊Dic11C2312yes—
108C2×C4⋊Dic11C2312yes—
109#66977C2×C4116yes—
110#66977C2×C4116yes—
111#66977C2×C4116yescomplemented
112#66977C2×C4116yescomplemented
113C2×Dic11⋊C4C2×C4116yescomplemented
114C2×Dic11⋊C4C2318yes—
115C2×Dic11⋊C4C2318yes—
116C2×Dic11⋊C4C2314yes—
117C2×Dic11⋊C4C2314yes—
118C2×C4×Dic11—28no—
119C2×C4×Dic11C2318yes—
120C2×C4×Dic11C2314yes—
121C2×C4×Dic11C2312yes—
122C2×C4×Dic11C2318yes—
123C2×C4×Dic11C2312yes—
124#66940—216no—
125#66930—216no—
126C4×Dic22—216no—
127C11×#95C2314yes—
128C11×#95C2314yes—
129C11⋊#95C2318yes—
130C11⋊#95C2318yes—
131C11⋊#95C2318yes—
132C11⋊#95C2318yes—
133#34203—111nomaximal, Sylow
134C24×C11—22no—
135C24×C11—22no—
136C24×C11—24no—
137C24×C11—42no—
138C24×C11C22×C414yes—
139C24×C11C2411yescharacteristic
140C24×C11C2411yescharacteristic
141C24×C11C2411yescharacteristic
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—232no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11C22×C414yes—
154C22×C4×C11C22×C414yes—
155C22×C4×C11C22×C414yes—
156C22×C4×C11C22×C414yes—
157C22×C4×C11C22×C414yes—
158C22×C4×C11C22×C414yes—
159C22×C4×C11C2×D414yes—
160C22×C4×C11#4114yes—
161C22×C4×C11C2414yes—
162C22×C4×C11C2414yes—
163C22×C4×C11C2411yescharacteristic
164C22×C4×C11C2411yescharacteristic
165C22×C4×C11C2411yescharacteristic
166C22×C4×C11C2411yescharacteristic
167C22×Dic11—28no—
168C22×Dic11—24no—
169C22×Dic11—24no—
170C22×Dic11—28no—
171C22×Dic11—44no—
172C22×Dic11—44no—
173C22×Dic11C22×C418yes—
174C22×Dic11C22×C418yes—
175C22×Dic11C2414yes—
176C22×Dic11C2414yes—
177C22×Dic11C2414yes—
178C22×Dic11C2414yes—
179C2×Dic22—232no—
180C2×Dic22—24no—
181C2×Dic22—24no—
182C2×Dic22—24no—
183C2×Dic22—24no—
184C2×Dic22C22×C418yes—
185C2×Dic22C22×C418yes—
186C11×C4⋊C4—24no—
187C11×C4⋊C4—24no—
188C11×C22⋊C4—24no—
189C11×C22⋊C4—24no—
190C11×C22⋊C4—28no—
191C11×C22⋊C4—44no—
192C42×C11—24no—
193C42×C11—24no—
194C22⋊Dic11—28no—
195C22⋊Dic11—24no—
196C22⋊Dic11C22×C4116yes—
197C22⋊Dic11C22×C4116yes—
198C22⋊Dic11C2×D418yes—
199C4⋊Dic11—28no—
200C4⋊Dic11—24no—
201C4⋊Dic11C22×C418yes—
202C4⋊Dic11C22×C418yes—
203C4⋊Dic11C2×D418yes—
204Dic11⋊C4—216no—
205Dic11⋊C4—48no—
206Dic11⋊C4C22×C4116yes—
207Dic11⋊C4C22×C4116yes—
208C4×Dic11—216no—
209C4×Dic11—28no—
210C4×Dic11—24no—
211C4×Dic11—48no—
212C4×Dic11C2×D418yes—
213C22×C22⋊Q8—111no—
214C2×#519—111no—
215C22×#117—111no—
216#2362—114no—
217#2360—114no—
218#2344—114no—
219#2342—114no—
220#2323—114no—
221#2316—111no—
222#2310—111no—
223C4×C22⋊Q8—114no—
224#2280D1111yescharacteristic
225#2274—111no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—22no—
229C23×C11—22no—
230C23×C11—22no—
231C23×C11—28no—
232C23×C11—28no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—22no—
236C23×C11—22no—
237C23×C11—44no—
238C23×C11—48no—
239C23×C11—48no—
240C23×C11C23×C412yes—
241C23×C11C23×C412yes—
242C23×C11C23×C412yes—
243C23×C11C22×D412yes—
244C23×C11C2×#4112yes—
245C23×C112−1+414yes—
246C23×C11C2511yescharacteristic
247C2×C4×C11—28no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—28no—
253C2×C4×C11—28no—
254C2×C4×C11—28no—
255C2×C4×C11—28no—
256C2×C4×C11—24no—
257C2×C4×C11—24no—
258C2×C4×C11—24no—
259C2×C4×C11—24no—
260C2×C4×C11—24no—
261C2×C4×C11—24no—
262C2×C4×C11C4×D4116yes—
263C2×C4×C11C23×C412yes—
264C2×C4×C11C23×C412yes—
265C2×C4×C11C23×C412yes—
266C2×C4×C11C23×C412yes—
267C2×C4×C11C22×D412yes—
268C2×C4×C11C22×D412yes—
269C2×C4×C11C2×#4112yes—
270C2×C4×C11C2×#4112yes—
271C2×Dic11—216no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—24no—
275C2×Dic11—24no—
276C2×Dic11—28no—
277C2×Dic11—24no—
278C2×Dic11—24no—
279C2×Dic11—24no—
280C2×Dic11—48no—
281C2×Dic11—416no—
282C2×Dic11C23×C418yes—
283C2×Dic11C23×C418yes—
284C2×Dic11C22×D418yes—
285Dic22—216no—
286Dic22—216no—
287C23×Q8—111no—
288C24×C4C2×D1111yescharacteristic
289C2×C22⋊Q8—112no—
290C2×C22⋊Q8—112no—
291C2×C22⋊Q8—112no—
292C2×C22⋊Q8—112no—
293C2×C22⋊Q8—1116no—
294#519—228no—
295C2×C4×Q8—114no—
296C2×C4×Q8—114no—
297C2×#117—111no—
298C2×#117—111no—
299C2×#117—112no—
300C2×#117—112no—
301C2×#117—112no—
302C2×#117—114no—
303C2×#117—228no—
304C2×#117C2×D1111yescharacteristic
305C2×#117C2×D1111yescharacteristic
306C22×C4⋊C4—111no—
307C22×C4⋊C4—112no—
308C22×C4⋊C4—112no—
309C22×C22⋊C4—112no—
310C22×C22⋊C4—112no—
311C22×C42—112no—
312#391—114no—
313#391—114no—
314#389—114no—
315#389—114no—
316#389—118no—
317#388—118no—
318#388—118no—
319#387—118no—
320#387—118no—
321#385—118no—
322#381—114no—
323#381C2×D1112yes—
324#380—114no—
325#380C2×D1112yes—
326#380C2×D1112yes—
327#379C2×D1112yes—
328C4×C4⋊C4—114no—
329C4×C4⋊C4—114no—
330C4×C4⋊C4—118no—
331C4×C22⋊C4—114no—
332C4×C22⋊C4—118no—
333C4×C22⋊C4C2×D1112yes—
334C4×C22⋊C4C2×D1112yes—
335C22×C11—22no—
336C22×C11—22no—
337C22×C11—22no—
338C22×C11—22no—
339C22×C11—24no—
340C22×C11—24no—
341C22×C11—24no—
342C22×C11—24no—
343C22×C11—22no—
344C22×C11—22no—
345C22×C11—22no—
346C22×C11—416no—
347C22×C11—42no—
348C22×C11—42no—
349C22×C11C2×C4×D414yes—
350C22×C11#51914yescomplemented
351C22×C11C24×C411yescharacteristic
352C22×C11C23×D411yescharacteristic
353C22×C11C22×#4111yescharacteristic
354C22×C11C2×2−1+412yes—
355C22×C11#58512yes—
356C4×C11—22no—
357C4×C11—22no—
358C4×C11—44no—
359C4×C11—44no—
360C4×C11C2×C4×D414yes—
361C4×C11C2×C4×D414yes—
362Dic11—28no—
363Dic11—28no—
364Dic11—28no—
365Dic11—44no—
366C25C22×D1111yescharacteristic
367C22×Q8—118no—
368C22×Q8—112no—
369C22×Q8—112no—
370C22×Q8—224no—
371C22×Q8—224no—
372C23×C4—24no—
373C23×C4—24no—
374C23×C4—112no—
375C23×C4—112no—
376C23×C4—114no—
377C23×C4C4×D1118yes—
378C23×C4C22×D1111yescharacteristic
379C23×C4C22×D1111yescharacteristic
380C23×C4C22×D1111yescharacteristic
381C23×C4C22×D1111yescharacteristic
382C23×C4C22×D1111yescharacteristic
383C23×C4C22×D1111yescharacteristic
384C22⋊Q8—1116no—
385C22⋊Q8—1116no—
386C22⋊Q8—1116no—
387C22⋊Q8—1116no—
388C4×Q8—2216no—
389C4×Q8—2216no—
390#117—24no—
391#117—24no—
392#117—118no—
393#117—228no—
394#117—2216no—
395#117—228no—
396#117—228no—
397#117—224no—
398C2×C4⋊C4—1116no—
399C2×C4⋊C4—118no—
400C2×C4⋊C4—112no—
401C2×C4⋊C4—114no—
402C2×C4⋊C4—112no—
403C2×C4⋊C4—112no—
404C2×C4⋊C4—114no—
405C2×C4⋊C4—114no—
406C2×C4⋊C4—112no—
407C2×C4⋊C4—118no—
408C2×C4⋊C4—118no—
409C2×C4⋊C4—228no—
410C2×C4⋊C4C22×D1112yes—
411C2×C4⋊C4C22×D1112yes—
412C2×C22⋊C4—1116no—
413C2×C22⋊C4—112no—
414C2×C22⋊C4—114no—
415C2×C22⋊C4—114no—
416C2×C22⋊C4—112no—
417C2×C22⋊C4—114no—
418C2×C22⋊C4—228no—
419C2×C22⋊C4C22×D1112yes—
420C2×C22⋊C4C22×D1112yes—
421C2×C22⋊C4C22×D1114yes—
422C2×C22⋊C4C22×D1114yes—
423C2×C42—112no—
424C2×C42—114no—
425C2×C42—112no—
426C2×C42—118no—
427C2×C42—118no—
428C2×C42—228no—
429C2×C42C22×D1112yes—
430C2×C42C22×D1112yes—
431#95—118no—
432#95—118no—
433#95—118no—
434#95—118no—
435#95C22×D1114yes—
436#95C22×D1114yes—
437C2×C11—24no—
438C2×C11—24no—
439C2×C11—42no—
440C2×C11C22×C4×D411yescharacteristic
441C2×C11C2×#51911yescharacteristic
442C2×C11#342811yescharacteristic
443C2×C11#348912yes—
444C2×C11#349512yes—
445C24—22no—
446C24—22no—
447C24—24no—
448C24—42no—
449C24C2×C4×D1114yes—
450C24C23×D1111yescharacteristic
451C24C23×D1111yescharacteristic
452C24C23×D1111yescharacteristic
453C2×Q8—118no—
454C2×Q8—118no—
455C2×Q8—2232no—
456C2×Q8—224no—
457C2×Q8—224no—
458C2×Q8—224no—
459C2×Q8—224no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—232no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—118no—
472C22×C4—114no—
473C22×C4—114no—
474C22×C4—114no—
475C22×C4—118no—
476C22×C4—114no—
477C22×C4—228no—
478C22×C4—224no—
479C22×C4—224no—
480C22×C4—228no—
481C22×C4—444no—
482C22×C4—444no—
483C22×C4C2×C4×D1114yes—
484C22×C4C2×C4×D1114yes—
485C22×C4C2×C4×D1114yes—
486C22×C4C2×C4×D1114yes—
487C22×C4C2×C4×D1114yes—
488C22×C4C2×C4×D1114yes—
489C22×C4D4×D1114yes—
490C22×C4#434114yes—
491C22×C4C23×D1114yes—
492C22×C4C23×D1114yes—
493C22×C4C23×D1111yescharacteristic
494C22×C4C23×D1111yescharacteristic
495C22×C4C23×D1111yescharacteristic
496C22×C4C23×D1111yescharacteristic
497C4⋊C4—24no—
498C4⋊C4—24no—
499C4⋊C4—1116no—
500C4⋊C4—1116no—
501C4⋊C4—118no—
502C4⋊C4—118no—
503C4⋊C4—118no—
504C4⋊C4—228no—
505C4⋊C4—2216no—
506C4⋊C4—224no—
507C4⋊C4—448no—
508C22⋊C4—24no—
509C22⋊C4—24no—
510C22⋊C4—28no—
511C22⋊C4—44no—
512C22⋊C4—1116no—
513C22⋊C4—1116no—
514C22⋊C4—118no—
515C22⋊C4—228no—
516C22⋊C4—224no—
517C42—24no—
518C42—24no—
519C42—118no—
520C42—228no—
521C42—2216no—
522C42—224no—
523C42—448no—
524C11#3420311yescharacteristic, complemented, Sylow
525C23—21no—
526C23—21no—
527C23—22no—
528C23—22no—
529C23—22no—
530C23—28no—
531C23—28no—
532C23—21no—
533C23—21no—
534C23—22no—
535C23—22no—
536C23—44no—
537C23—48no—
538C23—48no—
539C23C22×C4×D1112yes—
540C23C22×C4×D1112yes—
541C23C22×C4×D1112yes—
542C23C2×D4×D1112yes—
543C23C2×#434112yes—
544C23#6704314yes—
545C23C24×D1111yescharacteristic
546Q8—2216no—
547Q8—2216no—
548C2×C4—28no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—28no—
554C2×C4—28no—
555C2×C4—28no—
556C2×C4—28no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—118no—
564C2×C4—118no—
565C2×C4—118no—
566C2×C4—2216no—
567C2×C4—224no—
568C2×C4—224no—
569C2×C4—224no—
570C2×C4—224no—
571C2×C4—228no—
572C2×C4—224no—
573C2×C4—224no—
574C2×C4—224no—
575C2×C4—448no—
576C2×C4—4416no—
577C2×C4(C22⋊D11)⋊C4116yes—
578C2×C4C22×C4×D1112yes—
579C2×C4C22×C4×D1112yes—
580C2×C4C22×C4×D1112yes—
581C2×C4C22×C4×D1112yes—
582C2×C4C2×D4×D1112yes—
583C2×C4C2×D4×D1112yes—
584C2×C4C2×#434112yes—
585C2×C4C2×#434112yes—
586C22—24no—
587C22—24no—
588C22—24no—
589C22—24no—
590C22—22no—
591C22—22no—
592C22—22no—
593C22—22no—
594C22—22no—
595C22—22no—
596C22—22no—
597C22—416no—
598C22—42no—
599C22—42no—
600C22C2×(C22⋊D11)⋊C414yes—
601C22#1062304714yescomplemented
602C22C23×C4×D1111yescharacteristic
603C22C22×D4×D1111yescharacteristic
604C22C22×#434111yescharacteristic
605C22C2×#6704312yes—
606C22#1062345312yes—
607C4—22no—
608C4—22no—
609C4—44no—
610C4—44no—
611C4—228no—
612C4—228no—
613C4—228no—
614C4—444no—
615C4C2×(C22⋊D11)⋊C414yes—
616C4C2×(C22⋊D11)⋊C414yes—
617C2—24no—
618C2—24no—
619C2—42no—
620C2C22×(C22⋊D11)⋊C411yescharacteristic
621C2C2×#1062304711yescharacteristic
622C2#1308181711yescharacteristic
623C2#1308228812yes—
624C2#1308237012yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2280C2
socle, cosocleC23×C11C25
prime radicalC25×C11C23
hypercenter#2280D11
hypocenterC11#34203
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. C2×#10623047C2semidirect
4. #13071641C2semidirect
5. #13071619C2semidirect
6. #13071480C2semidirect
8. #13071294C2semidirect
9. #13071232C2semidirect
10. #13071200C2semidirect
11. #13071144C2semidirect
12. #13070972C2semidirect
28. C2×#66977C4semidirect
36. C2×#66940C22semidirect
38. C2×C4×Dic22C22semidirect
45. C4⋊C4×Dic11C22semidirect
46. #10622587C22semidirect
47. #10622586C22semidirect
55. C4×C4⋊Dic11C22semidirect
56. #10622542C22semidirect
57. #10622541C22semidirect
58. #10622268C22semidirect
59. #10622265C22semidirect
60. #10622262C22semidirect
61. #10622260C22semidirect
77. C22×Dic22C2×C4semidirect
103. C2×C4⋊Dic11C2×C4semidirect
111. #66977C2×C4semidirect
112. #66977C2×C4semidirect
113. C2×Dic11⋊C4C2×C4semidirect
350. C22×C11#519semidirect
524. C11#34203semidirect
601. C22#10623047semidirect

Maximal subgroups

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

subgroupindex
C22×#669772
C2×#106230472
C22×#669792
#130716412
#130716192
#130714802
#130714672
#130712942
#130712322
#130712002
#130711442
#130709722
C11×#22802
#3420311