Finite Group Databasebeta

← #14769888

Subgroups — #14769888

Order 2816.

1196 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623010C211yesmaximal, characteristic
2C2×#10622301C211yesmaximal, characteristic, complemented
3C2×C8×D44C211yesmaximal, characteristic, complemented
4#13069552C211yesmaximal, characteristic, complemented
5#13069552C211yesmaximal, characteristic, complemented
6#13068910C212yesmaximal, complemented
7#13068905C212yesmaximal, complemented
8#13068686C212yesmaximal, complemented
9#13068596C211yesmaximal, characteristic, complemented
10#13068311C212yesmaximal, complemented
11C4×C11×C22⋊C8C211yesmaximal, characteristic, complemented
12C22×C42×C11C2211yescharacteristic
13C2×#66983C411yescharacteristic
14C2×#66982C412yes—
15C2×C4×C22⋊D11C2212yes—
16C2×#66977C411yescharacteristic
17C22×#4313C2212yes—
18C22×C8×D11C2212yes—
19#10623010—24no—
20#10623010—24no—
21C2×#66929C412yes—
22C2×#66928C411yescharacteristic
23C2×C4×D44C2211yescharacteristic
24C2×#66925C2212yes—
25C2×#66923C411yescharacteristic
26C2×C4×Dic22C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C2×C11×C22⋊C8C2211yescharacteristic
29C2×C4×C8×C11C2211yescharacteristic
30C2×C4×C8×C11C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2212yes—
32C2×(C2×D11)⋊C8C2212yes—
33C2×(C2×D11)⋊C8C2212yes—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622301—24no—
37C8×D44—24no—
38C11×#336C2211yescharacteristic
39C11×#336C2211yescharacteristic
40#10622188C2212yes—
41#10622188C2212yes—
42#10622188C2212yes—
43#10622188C2212yes—
44#10622162C2212yes—
45C23×C4×C11C2×C411yescharacteristic
46C23×C4×C11C2×C411yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C22×C22⋊D11C2×C412yes—
49C22×D44C2×C411yescharacteristic
50C22×C4×D11C2312yes—
51C22×Dic22C2×C411yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2311yescharacteristic
56C2×C42×C11—22no—
57C2×C42×C11—22no—
58C2×C42×C11C2×C411yescharacteristic
59C2×C42×C11C2×C411yescharacteristic
60C2×C42×C11C2311yescharacteristic
61C2×C42×C11C2311yescharacteristic
62C2×C22⋊Dic11C2×C412yes—
63#66983—24no—
64#66982—28no—
65C4×C22⋊D11—24no—
66C4×C22⋊D11—24no—
67C2×(C2×D11)⋊C4C2×C412yes—
68C2×(C2×D11)⋊C4C2×C412yes—
69C2×(C2×D11)⋊C4C2×C412yes—
70C2×(C2×D11)⋊C4C2×C412yes—
71C2×C4⋊Dic11C2×C411yescharacteristic
72C2×C4⋊Dic11C2×C411yescharacteristic
73#66977—24no—
74C2×Dic11⋊C4C2×C412yes—
75C2×Dic11⋊C4C2×C412yes—
76C2×Dic11⋊C4C2×C412yes—
77C2×Dic11⋊C4C2×C412yes—
78C2×C4×Dic11C2312yes—
79C22×C11⋊C8C2312yes—
80C22×C11⋊C8C2312yes—
81C2×#4313—24no—
82C2×#4313—24no—
83C2×#4313—42no—
84C2×C8×D11—24no—
85C2×C8×D11—24no—
86C2×C8×D11—42no—
87#66929—28no—
88#66928—24no—
89C4×D44D414yes—
90C4×D44D414yes—
91#66925—24no—
92#66925—24no—
93#66923—24no—
94C4×Dic22—22no—
95C4×Dic22—22no—
96C11×C22⋊C8—22no—
97C11×C22⋊C8—22no—
98C4×C8×C11—22no—
99C4×C8×C11—22no—
100C22⋊(C11⋊C8)—42no—
101(C2×D11)⋊C8—24no—
102(C2×D11)⋊C8—24no—
103C4⋊(C11⋊C8)—22no—
104C4⋊(C11⋊C8)—22no—
105#22474—111nomaximal, Sylow
106C24×C11C22×C411yescharacteristic
107C23×D11C22×C412yes—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—41no—
120C22×C4×C11C22×C411yescharacteristic
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C22×C411yescharacteristic
123C22×C4×C11C22×C411yescharacteristic
124C22×C4×C11C22×C411yescharacteristic
125C22×C4×C11C2411yescharacteristic
126C2×C22⋊D11—24no—
127C2×C22⋊D11—24no—
128C2×C22⋊D11—42no—
129C22×Dic11C22×C412yes—
130C22×Dic11C22×C412yes—
131C22×Dic11C22×C412yes—
132C2×D44—22no—
133C2×D44—22no—
134C2×D44C22⋊C414yes—
135C2×C4×D11—22no—
136C2×C4×D11—22no—
137C2×C4×D11—22no—
138C2×C4×D11—22no—
139C2×C4×D11C2×D414yes—
140C2×C4×D11C2×D414yes—
141C2×Dic22—22no—
142C2×Dic22—22no—
143C2×Dic22—22no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11#4112yes—
155C2×C8×C11#4112yes—
156C42×C11—22no—
157C42×C11—22no—
158C42×C11—21no—
159C42×C11—21no—
160C42×C11C2×D412yes—
161C42×C11C2×D412yes—
162C22⋊Dic11—24no—
163(C2×D11)⋊C4—24no—
164(C2×D11)⋊C4—24no—
165(C2×D11)⋊C4—24no—
166(C2×D11)⋊C4C22⋊C418yes—
167C4⋊Dic11—22no—
168C4⋊Dic11C22⋊C414yes—
169Dic11⋊C4—24no—
170Dic11⋊C4—24no—
171Dic11⋊C4—24no—
172Dic11⋊C4—24no—
173C4×Dic11—22no—
174C4×Dic11—22no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181#4313—48no—
182C8×D11—48no—
183C2×#529—111no—
184C2×#436—111no—
185C2×C8×D4—111no—
186#1984—111no—
187#1984—111no—
188#1870—112no—
189#1869—112no—
190#1818—112no—
191#1797—111no—
192C4×C22⋊C8D1111yescharacteristic, complemented
193#1729—112no—
194C23×C11—21no—
195C23×C11—21no—
196C23×C11—21no—
197C23×C11—21no—
198C23×C11—21no—
199C23×C11—21no—
200C23×C11#13112yes—
201C23×C11C23×C411yescharacteristic
202C22×D11—22no—
203C22×D11—22no—
204C22×D11—22no—
205C22×D11—22no—
206C22×D11—22no—
207C22×D11—22no—
208C22×D11C2×C22⋊C414yes—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—44no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—44no—
226C2×C4×C11C2×C22⋊C412yes—
227C2×C4×C11C2×C22⋊C412yes—
228C2×C4×C11#13112yes—
229C2×C4×C11#13112yes—
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C2×C4×C11H(5,𝔽2)11yescharacteristic
235C2×C4×C112−1+411yescharacteristic
236C22⋊D11—48no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11C2×C22⋊C414yes—
246D44—28no—
247C4×D11—24no—
248C4×D11—24no—
249C4×D11—24no—
250C4×D11—24no—
251Dic22—44no—
252C8×C11—22no—
253C8×C11—22no—
254C8×C11—41no—
255C8×C11—41no—
256C11⋊C8—42no—
257C11⋊C8—42no—
258C22×M16—112no—
259C23×C8—112no—
260#529—224no—
261#529—224no—
262C2×#126—112no—
263C2×#125—111no—
264C2×#124—111no—
265C2×#123—112no—
266C2×C22⋊Q8—111no—
267C2×#121—111no—
268C2×C4×Q8—111no—
269C2×C4×D4—112no—
270C2×C4×D4—111no—
271C2×#117—112no—
272C22×C42C2×D1111yescharacteristic
273#436—224no—
274C8×D4—224no—
275C2×C4⋊C8—111no—
276C2×C4⋊C8—111no—
277C2×C22⋊C8—112no—
278C2×C22⋊C8—112no—
279C2×C22⋊C8—112no—
280C2×C22⋊C8C2×D1111yescharacteristic
281C2×C22⋊C8C2×D1111yescharacteristic
282C2×C4×C8C2×D1111yescharacteristic
283C2×C4×C8C2×D1111yescharacteristic
284#336—112no—
285#336—112no—
286#336—112no—
287#336—112no—
288#336—112no—
289#336C2×D1111yescharacteristic
290#336C2×D1111yescharacteristic
291C22×C11—22no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—41no—
295C22×C11—41no—
296C22×C11—41no—
297C22×C11—41no—
298C22×C11C22×C22⋊C411yescharacteristic
299C22×C11C4×#4111yescharacteristic
300C22×C11#52011yescharacteristic
301C22×C11C2×#13111yescharacteristic
302C22×C11C2×#13111yescharacteristic
303C22×C11C2×#13111yescharacteristic
304C22×C11#56811yescharacteristic
305C2×D11—24no—
306C2×D11—24no—
307C2×D11—24no—
308C2×D11—42no—
309C2×D11—42no—
310C2×D11—42no—
311C2×D11—42no—
312C4×C11—22no—
313C4×C11—41no—
314C4×C11—41no—
315C4×C11—41no—
316C4×C11#40814yes—
317C4×C11#54611yescharacteristic
318C4×C11#54611yescharacteristic
319C4×C11#54711yescharacteristic
320C4×C11#54711yescharacteristic
321Dic11—24no—
322Dic11—42no—
323Dic11—42no—
324C22×Q8—111no—
325C22×D4—112no—
326C22×D4—111no—
327C23×C4—112no—
328C23×C4C4×D1111yescharacteristic
329C23×C4C4×D1111yescharacteristic
330C23×C4C22×D1111yescharacteristic
331C2×M16—224no—
332C2×M16—224no—
333C2×M16—442no—
334C22×C8—112no—
335C22×C8—112no—
336C22×C8—224no—
337C22×C8—224no—
338C22×C8—442no—
339C22×C8C22×D1111yescharacteristic
340C22×C8C22×D1111yescharacteristic
341C22×C8C22×D1111yescharacteristic
342C22×C8C22×D1111yescharacteristic
343#126—228no—
344#125—224no—
345#124—224no—
346#123—228no—
347C22⋊Q8—224no—
348#121—224no—
349C4×Q8—222no—
350C4×Q8—222no—
351C4×D4—114no—
352C4×D4—114no—
353C4×D4—224no—
354C4×D4—224no—
355#117—224no—
356#117—224no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—112no—
359C2×C4⋊C4—112no—
360C2×C4⋊C4—112no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—112no—
363C2×C22⋊C4—112no—
364C2×C22⋊C4—112no—
365C2×C22⋊C4—112no—
366C2×C22⋊C4—112no—
367C2×C22⋊C4—112no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—112no—
371C2×C42C4×D1111yescharacteristic
372C2×C42C4×D1111yescharacteristic
373C2×C42C22×D1111yescharacteristic
374C2×C42C22×D1111yescharacteristic
375C4⋊C8—222no—
376C4⋊C8—222no—
377C22⋊C8—22no—
378C22⋊C8—22no—
379C22⋊C8—224no—
380C22⋊C8—224no—
381C22⋊C8—442no—
382C4×C8—22no—
383C4×C8—22no—
384C2×C11—42no—
385C2×C11#233911yescharacteristic
386C2×C11C2×#40811yescharacteristic
387C2×C11#288011yescharacteristic
388C2×C11#296611yescharacteristic
389C2×C11#296911yescharacteristic
390C2×C11#299311yescharacteristic
391C2×C11#299411yescharacteristic
392D11—44no—
393C24—112no—
394C24C2×C4×D1111yescharacteristic
395C2×Q8—222no—
396C2×Q8—222no—
397C2×Q8—222no—
398C2×D4—114no—
399C2×D4—224no—
400C2×D4—224no—
401C2×D4—222no—
402C2×D4—222no—
403C2×D4—442no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—41no—
416C22×C4—112no—
417C22×C4—114no—
418C22×C4—114no—
419C22×C4—112no—
420C22×C4—112no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4C2×C4×D1111yescharacteristic
426C22×C4C2×C4×D1111yescharacteristic
427C22×C4C2×C4×D1111yescharacteristic
428C22×C4C2×C4×D1111yescharacteristic
429C22×C4C2×C4×D1111yescharacteristic
430C22×C4C23×D1111yescharacteristic
431M16—448no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—222no—
443C2×C8—222no—
444C2×C8—222no—
445C2×C8—222no—
446C2×C8—222no—
447C2×C8—222no—
448C2×C8—448no—
449C2×C8#433912yes—
450C2×C8#433912yes—
451C4⋊C4—114no—
452C4⋊C4—224no—
453C4⋊C4—224no—
454C4⋊C4—224no—
455C4⋊C4—222no—
456C4⋊C4—224no—
457C22⋊C4—118no—
458C22⋊C4—224no—
459C22⋊C4—224no—
460C22⋊C4—224no—
461C22⋊C4—224no—
462C42—22no—
463C42—22no—
464C42—21no—
465C42—21no—
466C42—222no—
467C42—222no—
468C42D4×D1112yes—
469C42D4×D1112yes—
470C11#2247411yescharacteristic, complemented, Sylow
471C23—21no—
472C23—21no—
473C23—21no—
474C23—21no—
475C23—21no—
476C23—21no—
477C23—114no—
478C23—222no—
479C23—222no—
480C23—222no—
481C23—222no—
482C23—222no—
483C23—222no—
484C23#6695412yes—
485C23C22×C4×D1111yescharacteristic
486Q8—444no—
487D4—228no—
488D4—448no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—44no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—44no—
506C2×C4—114no—
507C2×C4—222no—
508C2×C4—222no—
509C2×C4—224no—
510C2×C4—224no—
511C2×C4—224no—
512C2×C4—224no—
513C2×C4—222no—
514C2×C4—222no—
515C2×C4—222no—
516C2×C4—222no—
517C2×C4—222no—
518C2×C4—222no—
519C2×C4C22⋊C4×D1112yes—
520C2×C4C22⋊C4×D1112yes—
521C2×C4#6695412yes—
522C2×C4#6696012yes—
523C2×C4C2×#433911yescharacteristic
524C2×C4C2×#433911yescharacteristic
525C2×C4C2×D4×D1111yescharacteristic
526C2×C4C2×D4×D1111yescharacteristic
527C2×C4#6704211yescharacteristic
528C2×C4#6704311yescharacteristic
529C8—22no—
530C8—22no—
531C8—41no—
532C8—41no—
533C8—442no—
534C8—442no—
535C22—22no—
536C22—22no—
537C22—22no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—224no—
543C22—224no—
544C22—224no—
545C22—442no—
546C22—442no—
547C22—442no—
548C22—442no—
549C22C4×#433911yescharacteristic
550C22C2×C22⋊C4×D1111yescharacteristic
551C22#1062305411yescharacteristic
552C22C2×#6695411yescharacteristic
553C22C2×#6695411yescharacteristic
554C22C2×#6696011yescharacteristic
555C22#1062327611yescharacteristic
556C4—22no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—224no—
561C4—442no—
562C4—442no—
563C4#1062234014yes—
564C4#1062308111yescharacteristic
565C4#1062308111yescharacteristic
566C4#1062308211yescharacteristic
567C4#1062308211yescharacteristic
568C2—42no—
569C2—444no—
570C2#1307144711yescharacteristic
571C2C2×#1062234011yescharacteristic
572C2#1307706211yescharacteristic
573C2#1307759111yescharacteristic
574C2#1307762011yescharacteristic
575C2#1307776711yescharacteristic
576C2#1307777811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC4×C11×C22⋊C8C2
prime radicalC2×#66983C4
cosocleC22×C4×C11C24
hypercenterC4×C22⋊C8D11
hypocenterC11#22474
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#10622301C2semidirect
3. C2×C8×D44C2semidirect
4. #13069552C2semidirect
5. #13069552C2semidirect
6. #13068910C2semidirect
7. #13068905C2semidirect
8. #13068686C2semidirect
9. #13068596C2semidirect
10. #13068311C2semidirect
11. C4×C11×C22⋊C8C2semidirect
192. C4×C22⋊C8D11semidirect
470. C11#22474semidirect

Maximal subgroups

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

subgroupindex
C2×#106230102
C2×#106223012
C2×C8×D442
#130695522
#130689102
#130689052
#130686862
#130685962
#130683112
C4×C11×C22⋊C82
#2247411