Finite Group Databasebeta

← #14923639

Subgroups — #14923639

Order 2816.

2926 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D11C211yesmaximal, characteristic
2C22×#66979C211yesmaximal, characteristic, complemented
3#13072934C212yesmaximal, complemented
4#13072925C212yesmaximal, complemented
5#13072914C214yesmaximal, complemented
6#13072905C212yesmaximal, complemented
7#13072897C212yesmaximal, complemented
8#13072892C212yesmaximal, complemented
9#13071944C212yesmaximal
10#13071876C214yesmaximal, complemented
11C4×#66939C214yesmaximal, complemented
12#13071100C212yesmaximal, complemented
13#13070995C212yesmaximal, complemented
14C11×#2280C211yesmaximal, characteristic, complemented
15C24×C4×C11C2211yescharacteristic
16C23×C22⋊D11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C2×C11×#117C2212yes—
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2212yes—
21C2×C4×C22⋊D11—28no—
22C2×C4×C22⋊D11C2212yes—
23C2×C4×C22⋊D11C2212yes—
24C2×C4×C22⋊D11C2212yes—
25C2×C4×C22⋊D11C2212yes—
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C2×#66979—28no—
28C2×#66979C2212yes—
29C2×#66979C2212yes—
30C2×#66979C2212yescomplemented
31C2×#66979C2212yescomplemented
32C22×C4⋊Dic11C2211yescharacteristic, complemented
33C22×C4⋊Dic11C2211yescharacteristic, complemented
34C22×Dic11⋊C4C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C22×C4×Dic11C2212yescomplemented
37C2×#66939C2214yes—
38C11×#381C2212yes—
39C11×#380C2212yescomplemented
40C11×#380C2212yescomplemented
41C11×#379C2212yes—
42C4×C11×C22⋊C4C2212yescomplemented
43C4×C11×C22⋊C4C2212yescomplemented
44#10622600C2214yescomplemented
45#10622600C2214yescomplemented
46#10622598C2214yescomplemented
47#10622598C2214yescomplemented
48#10622574C2218yes—
49#10622571C2214yes—
50#10622568C2214yes—
51#10622566C2218yescomplemented
52#10622563C2214yes—
53#10622563C2214yes—
54#10622563C2214yescomplemented
55#10622556C2214yes—
56#10622556C2214yescomplemented
57C4×(C2×D11)⋊C4C2218yescomplemented
58C4×C4⋊Dic11C2218yescomplemented
59#10622290C2214yescomplemented
60#10622287C2214yescomplemented
61#10622283C2218yescomplemented
62#10622274C2214yescomplemented
63#10622272C2214yescomplemented
64#10622266C2218yescomplemented
65C25×C11C2311yescharacteristic
66C24×D11C2311yescharacteristic
67C23×C4×C11—28no—
68C23×C4×C11D418yes—
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C22×C22⋊D11—24no—
76C22×C22⋊D11—28no—
77C22×C22⋊D11C2312yes—
78C22×C22⋊D11C2312yes—
79C23×Dic11C2312yes—
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2312yes—
84C22×C4×D11—24no—
85C22×C4×D11—28no—
86C22×C4×D11C2312yes—
87C22×C4×D11C2312yes—
88C11×#117—28no—
89C2×C11×C4⋊C4C2314yes—
90C2×C11×C22⋊C4C2314yes—
91C2×C11×C22⋊C4C2314yes—
92C2×C11×C22⋊C4C2314yes—
93C2×C42×C11C2314yes—
94C2×C22⋊Dic11—28no—
95C2×C22⋊Dic11—24no—
96C2×C22⋊Dic11C2314yes—
97C2×C22⋊Dic11C2314yes—
98C2×C22⋊Dic11C2312yes—
99C2×C22⋊Dic11C2312yes—
100C4×C22⋊D11—28no—
101C4×C22⋊D11—28no—
102C4×C22⋊D11—28no—
103C4×C22⋊D11—28no—
104C2×(C2×D11)⋊C4—24no—
105C2×(C2×D11)⋊C4C2318yes—
106C2×(C2×D11)⋊C4C2312yes—
107C2×(C2×D11)⋊C4C2312yes—
108C2×(C2×D11)⋊C4C2318yes—
109#66979—28no—
110#66979—28no—
111#66979—28no—
112#66979—28no—
113C2×C4⋊Dic11—24no—
114C2×C4⋊Dic11—24no—
115C2×C4⋊Dic11C2318yes—
116C2×C4⋊Dic11C2312yes—
117C2×C4⋊Dic11C2312yes—
118C2×C4⋊Dic11C2312yes—
119C2×C4⋊Dic11C2312yes—
120C2×C4⋊Dic11C2318yes—
121C2×Dic11⋊C4—24no—
122C2×Dic11⋊C4C2312yes—
123C2×Dic11⋊C4C2312yes—
124C2×C4×Dic11—24no—
125C2×C4×Dic11—28no—
126C2×C4×Dic11C2314yes—
127C2×C4×Dic11C2312yes—
128C2×C4×Dic11C2312yes—
129C2×C4×Dic11C2314yes—
130#66939—216no—
131C11×#95C2314yes—
132C11×#95C2314yes—
133C11⋊#95C2318yes—
134C11⋊#95C2318yes—
135C11⋊#95C2318yes—
136C11⋊#95C2318yes—
137#34809—111nomaximal, Sylow
138C24×C11—24no—
139C24×C11—24no—
140C24×C11—42no—
141C24×C11C2×D414yes—
142C24×C11C2411yescharacteristic
143C24×C11C2411yescharacteristic
144C24×C11C2411yescharacteristic
145C23×D11—22no—
146C23×D11—24no—
147C23×D11—24no—
148C23×D11—42no—
149C23×D11C2412yes—
150C22×C4×C11—24no—
151C22×C4×C11—232no—
152C22×C4×C11—24no—
153C22×C4×C11—24no—
154C22×C4×C11—24no—
155C22×C4×C11—24no—
156C22×C4×C11C2×D414yes—
157C22×C4×C11C2×D414yes—
158C22×C4×C11C2×D414yes—
159C22×C4×C11C2×D414yes—
160C22×C4×C11C2×D414yes—
161C22×C4×C11C2×D414yes—
162C22×C4×C11#4118yes—
163C22×C4×C11C2418yes—
164C22×C4×C11C2411yescharacteristic
165C22×C4×C11C2411yescharacteristic
166C22×C4×C11C2411yescharacteristic
167C22×C4×C11C2411yescharacteristic
168C2×C22⋊D11—232no—
169C2×C22⋊D11—24no—
170C2×C22⋊D11—24no—
171C2×C22⋊D11—24no—
172C2×C22⋊D11—24no—
173C2×C22⋊D11—24no—
174C2×C22⋊D11#4118yes—
175C22×Dic11—24no—
176C22×Dic11—22no—
177C22×Dic11—24no—
178C22×Dic11—24no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—28no—
182C22×Dic11—24no—
183C22×Dic11—44no—
184C22×Dic11—42no—
185C22×Dic11C2412yes—
186C22×Dic11C2414yes—
187C22×Dic11C2414yes—
188C22×Dic11C2412yes—
189C22×Dic11C2412yes—
190C2×C4×D11—24no—
191C2×C4×D11—24no—
192C2×C4×D11—28no—
193C2×C4×D11—28no—
194C2×C4×D11—416no—
195C11×C4⋊C4—28no—
196C11×C22⋊C4—28no—
197C11×C22⋊C4—28no—
198C11×C22⋊C4—44no—
199C42×C11—28no—
200C22⋊Dic11—28no—
201C22⋊Dic11—28no—
202C22⋊Dic11—24no—
203C22⋊Dic11—24no—
204(C2×D11)⋊C4—216no—
205(C2×D11)⋊C4—24no—
206(C2×D11)⋊C4—24no—
207(C2×D11)⋊C4—48no—
208C4⋊Dic11—216no—
209C4⋊Dic11—24no—
210C4⋊Dic11—24no—
211C4⋊Dic11—24no—
212C4⋊Dic11—24no—
213C4⋊Dic11—48no—
214Dic11⋊C4—24no—
215Dic11⋊C4—24no—
216C4×Dic11—28no—
217C4×Dic11—28no—
218C4×Dic11—24no—
219C4×Dic11—24no—
220C22×C4×D4—111no—
221C22×#117—111no—
222#2487—112no—
223#2486—112no—
224#2485—114no—
225#2484—112no—
226#2483—112no—
227#2482—112no—
228#2405—112no—
229#2395—114no—
230C4×#123—114no—
231#2296—112no—
232#2280—112no—
233#2280D1111yescharacteristic, complemented
234C23×C11—22no—
235C23×C11—22no—
236C23×C11—22no—
237C23×C11—22no—
238C23×C11—28no—
239C23×C11—28no—
240C23×C11—22no—
241C23×C11—22no—
242C23×C11—22no—
243C23×C11—44no—
244C23×C11—416no—
245C23×C11C22×D412yes—
246C23×C11C22×D412yes—
247C23×C11C22×D412yes—
248C23×C11C2×#4114yes—
249C23×C11C2×#4114yes—
250C23×C11C2511yescharacteristic
251C22×D11—28no—
252C22×D11—22no—
253C22×D11—24no—
254C22×D11—22no—
255C22×D11—24no—
256C22×D11—416no—
257C22×D11—44no—
258C22×D11—44no—
259C22×D11C2×#4114yes—
260C2×C4×C11—28no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—28no—
264C2×C4×C11—28no—
265C2×C4×C11—28no—
266C2×C4×C11—28no—
267C2×C4×C11—28no—
268C2×C4×C11—28no—
269C2×C4×C11—28no—
270C2×C4×C11#123116yescomplemented
271C2×C4×C11C22×D412yes—
272C2×C4×C11C22×D412yes—
273C2×C4×C11C22×D412yes—
274C2×C4×C11C22×D412yes—
275C2×C4×C11C2×#4114yes—
276C2×C4×C11C2×#4114yes—
277C22⋊D11—216no—
278C22⋊D11—216no—
279C2×Dic11—28no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—24no—
283C2×Dic11—24no—
284C2×Dic11—22no—
285C2×Dic11—22no—
286C2×Dic11—28no—
287C2×Dic11—24no—
288C2×Dic11—24no—
289C2×Dic11—28no—
290C2×Dic11—44no—
291C2×Dic11—48no—
292C2×Dic11—44no—
293C2×Dic11—48no—
294C2×Dic11C2×#4114yes—
295C4×D11—48no—
296C4×D11—48no—
297C23×D4—111no—
298C24×C4—111no—
299C24×C4C2×D1111yescharacteristic
300C2×#123—114no—
301C2×C4×D4—112no—
302C2×C4×D4—112no—
303C2×C4×D4—112no—
304C2×C4×D4—112no—
305C2×C4×D4—228no—
306C2×#117—112no—
307C2×#117—112no—
308C2×#117—112no—
309C2×#117—112no—
310C2×#117—228no—
311C2×#117C2×D1112yes—
312C22×C4⋊C4—111no—
313C22×C4⋊C4—111no—
314C22×C4⋊C4—111no—
315C22×C22⋊C4—112no—
316C22×C22⋊C4—111no—
317C22×C22⋊C4—111no—
318C22×C42—111no—
319C22×C42—112no—
320#400—114no—
321#399—114no—
322#398—114no—
323#397—118no—
324#397—114no—
325#394—118no—
326#389—114no—
327#389—114no—
328#388—118no—
329#387—118no—
330#386—114no—
331#385—114no—
332#385—114no—
333#385—114no—
334#381—114no—
335#381—114no—
336#381C2×D1112yes—
337#380—114no—
338#380—114no—
339#380C2×D1112yescomplemented
340#380C2×D1112yescomplemented
341#379—114no—
342#379C2×D1112yes—
343C4×C4⋊C4—118no—
344C4×C22⋊C4—118no—
345C4×C22⋊C4C2×D1112yescomplemented
346C4×C22⋊C4C2×D1112yescomplemented
347C22×C11—22no—
348C22×C11—22no—
349C22×C11—22no—
350C22×C11—22no—
351C22×C11—28no—
352C22×C11—28no—
353C22×C11—22no—
354C22×C11—22no—
355C22×C11—22no—
356C22×C11—416no—
357C22×C11—44no—
358C22×C11C2×#12314yes—
359C22×C11#52514yes—
360C22×C11C23×D411yescharacteristic
361C22×C11C22×#4112yes—
362C22×C11C22×#4112yes—
363C22×C11#58512yes—
364C2×D11—24no—
365C2×D11—28no—
366C2×D11—416no—
367C2×D11—42no—
368C2×D11—42no—
369C2×D11—44no—
370C4×C11—22no—
371C4×C11—22no—
372C4×C11—48no—
373C4×C11C2×#12314yes—
374C4×C11C2×#12314yes—
375Dic11—24no—
376Dic11—42no—
377Dic11—44no—
378Dic11—44no—
379Dic11—42no—
380C25—111no—
381C25C22×D1111yescharacteristic
382C22×D4—112no—
383C22×D4—112no—
384C22×D4—228no—
385C22×D4—224no—
386C23×C4—28no—
387C23×C4—112no—
388C23×C4—111no—
389C23×C4—111no—
390C23×C4—111no—
391C23×C4—112no—
392C23×C4—112no—
393C23×C4—112no—
394C23×C4—224no—
395C23×C4—228no—
396C23×C4D4418yes—
397C23×C4C22×D1111yescharacteristic
398C23×C4C22×D1111yescharacteristic
399C23×C4C22×D1111yescharacteristic
400C23×C4C22×D1111yescharacteristic
401C23×C4C22×D1111yescharacteristic
402C23×C4C22×D1111yescharacteristic
403#123—2216no—
404C4×D4—228no—
405C4×D4—228no—
406C4×D4—228no—
407C4×D4—228no—
408#117—28no—
409#117—228no—
410#117—228no—
411#117—228no—
412#117—228no—
413C2×C4⋊C4—112no—
414C2×C4⋊C4—112no—
415C2×C4⋊C4—112no—
416C2×C4⋊C4—112no—
417C2×C4⋊C4—112no—
418C2×C4⋊C4—112no—
419C2×C4⋊C4—118no—
420C2×C4⋊C4—118no—
421C2×C4⋊C4—224no—
422C2×C4⋊C4—224no—
423C2×C4⋊C4—224no—
424C2×C4⋊C4C22×D1114yes—
425C2×C22⋊C4—114no—
426C2×C22⋊C4—114no—
427C2×C22⋊C4—112no—
428C2×C22⋊C4—112no—
429C2×C22⋊C4—112no—
430C2×C22⋊C4—112no—
431C2×C22⋊C4—118no—
432C2×C22⋊C4—118no—
433C2×C22⋊C4—228no—
434C2×C22⋊C4—224no—
435C2×C22⋊C4—224no—
436C2×C22⋊C4C22×D1114yes—
437C2×C22⋊C4C22×D1114yes—
438C2×C22⋊C4C22×D1114yes—
439C2×C42—114no—
440C2×C42—112no—
441C2×C42—114no—
442C2×C42—112no—
443C2×C42—228no—
444C2×C42—224no—
445C2×C42C22×D1114yes—
446#95—118no—
447#95—118no—
448#95—118no—
449#95—118no—
450#95C22×D1114yes—
451#95C22×D1114yes—
452C2×C11—24no—
453C2×C11—24no—
454C2×C11—42no—
455C2×C11C22×#12311yescharacteristic
456C2×C11C2×#52511yescharacteristic
457C2×C11#344911yescharacteristic
458C2×C11#347514yes—
459D11—44no—
460C24—24no—
461C24—24no—
462C24—42no—
463C24—112no—
464C24—224no—
465C24—222no—
466C24—224no—
467C24—442no—
468C24C2×D4414yes—
469C24C23×D1111yescharacteristic
470C24C23×D1111yescharacteristic
471C24C23×D1111yescharacteristic
472C2×D4—118no—
473C2×D4—224no—
474C2×D4—224no—
475C2×D4—2232no—
476C2×D4—224no—
477C2×D4—224no—
478C2×D4—224no—
479C22×C4—24no—
480C22×C4—232no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—112no—
486C22×C4—112no—
487C22×C4—112no—
488C22×C4—114no—
489C22×C4—114no—
490C22×C4—224no—
491C22×C4—222no—
492C22×C4—222no—
493C22×C4—224no—
494C22×C4—224no—
495C22×C4—222no—
496C22×C4—224no—
497C22×C4—228no—
498C22×C4—224no—
499C22×C4—224no—
500C22×C4—228no—
501C22×C4—228no—
502C22×C4—444no—
503C22×C4—442no—
504C22×C4—4416no—
505C22×C4C2×D4414yes—
506C22×C4C2×D4414yes—
507C22×C4C2×D4414yes—
508C22×C4C2×D4414yes—
509C22×C4C2×D4414yes—
510C22×C4C2×D4414yes—
511C22×C4#434118yes—
512C22×C4C23×D1118yes—
513C22×C4C23×D1111yescharacteristic
514C22×C4C23×D1111yescharacteristic
515C22×C4C23×D1111yescharacteristic
516C22×C4C23×D1111yescharacteristic
517C4⋊C4—28no—
518C4⋊C4—2216no—
519C4⋊C4—224no—
520C4⋊C4—224no—
521C4⋊C4—224no—
522C4⋊C4—224no—
523C4⋊C4—224no—
524C4⋊C4—224no—
525C4⋊C4—448no—
526C22⋊C4—28no—
527C22⋊C4—28no—
528C22⋊C4—44no—
529C22⋊C4—2216no—
530C22⋊C4—228no—
531C22⋊C4—228no—
532C22⋊C4—224no—
533C22⋊C4—224no—
534C22⋊C4—224no—
535C22⋊C4—224no—
536C22⋊C4—448no—
537C42—28no—
538C42—228no—
539C42—228no—
540C42—224no—
541C42—224no—
542C11#3480911yescharacteristic, complemented, Sylow
543C23—22no—
544C23—22no—
545C23—22no—
546C23—22no—
547C23—28no—
548C23—28no—
549C23—22no—
550C23—22no—
551C23—22no—
552C23—44no—
553C23—416no—
554C23—114no—
555C23—228no—
556C23—222no—
557C23—224no—
558C23—222no—
559C23—224no—
560C23—4416no—
561C23—444no—
562C23—444no—
563C23C22×D4412yes—
564C23C22×D4412yes—
565C23C22×D4412yes—
566C23C2×#434114yes—
567C23#41×D1114yes—
568C23C24×D1111yescharacteristic
569D4—2216no—
570D4—2216no—
571C2×C4—28no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—28no—
575C2×C4—28no—
576C2×C4—28no—
577C2×C4—28no—
578C2×C4—28no—
579C2×C4—28no—
580C2×C4—28no—
581C2×C4—114no—
582C2×C4—228no—
583C2×C4—222no—
584C2×C4—222no—
585C2×C4—222no—
586C2×C4—224no—
587C2×C4—224no—
588C2×C4—222no—
589C2×C4—224no—
590C2×C4—228no—
591C2×C4—228no—
592C2×C4—224no—
593C2×C4—448no—
594C2×C4—444no—
595C2×C4—444no—
596C2×C4—448no—
597C2×C4—448no—
598C2×C4—448no—
599C2×C4#66939116yescomplemented
600C2×C4C22×D4412yes—
601C2×C4C22×D4412yes—
602C2×C4C22×D4412yes—
603C2×C4C22×D4412yes—
604C2×C4C2×#434114yes—
605C2×C4C2×#434114yes—
606C22—22no—
607C22—28no—
608C22—28no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—416no—
616C22—44no—
617C22—224no—
618C22—228no—
619C22—4416no—
620C22—444no—
621C22—442no—
622C22—442no—
623C22C2×#6693914yes—
624C22#1062305514yes—
625C22C23×D4411yescharacteristic
626C22C22×#434112yes—
627C22C2×#41×D1112yes—
628C22#1062345312yes—
629C4—22no—
630C4—22no—
631C4—48no—
632C4—224no—
633C4—444no—
634C4—442no—
635C4—444no—
636C4—442no—
637C4C2×#6693914yes—
638C4C2×#6693914yes—
639C2—24no—
640C2—24no—
641C2—42no—
642C2—444no—
643C2C22×#6693911yescharacteristic
644C2C2×#1062305511yescharacteristic
645C2#1308194911yescharacteristic
646C2#1308217614yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC11×#2280C2
prime radicalC23×C22⋊D11C22
hypercenter#2280D11
hypocenterC11#34809
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. C22×#66979C2semidirect
3. #13072934C2semidirect
4. #13072925C2semidirect
5. #13072914C2semidirect
6. #13072905C2semidirect
7. #13072897C2semidirect
8. #13072892C2semidirect
10. #13071876C2semidirect
11. C4×#66939C2semidirect
12. #13071100C2semidirect
13. #13070995C2semidirect
14. C11×#2280C2semidirect
30. C2×#66979C22semidirect
31. C2×#66979C22semidirect
32. C22×C4⋊Dic11C22semidirect
33. C22×C4⋊Dic11C22semidirect
36. C22×C4×Dic11C22semidirect
39. C11×#380C22semidirect
40. C11×#380C22semidirect
42. C4×C11×C22⋊C4C22semidirect
43. C4×C11×C22⋊C4C22semidirect
44. #10622600C22semidirect
45. #10622600C22semidirect
46. #10622598C22semidirect
47. #10622598C22semidirect
51. #10622566C22semidirect
54. #10622563C22semidirect
56. #10622556C22semidirect
57. C4×(C2×D11)⋊C4C22semidirect
58. C4×C4⋊Dic11C22semidirect
59. #10622290C22semidirect
60. #10622287C22semidirect
61. #10622283C22semidirect
62. #10622274C22semidirect
63. #10622272C22semidirect
64. #10622266C22semidirect
233. #2280D11semidirect
270. C2×C4×C11#123semidirect
339. #380C2×D11semidirect
340. #380C2×D11semidirect
345. C4×C22⋊C4C2×D11semidirect
346. C4×C22⋊C4C2×D11semidirect
542. C11#34809semidirect
599. C2×C4#66939semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D112
C22×#669792
#130729342
#130729252
#130729142
#130729052
#130728972
#130728922
#130719442
#130718762
C4×#669392
#130711002
#130709952
C11×#22802
#3480911