Finite Group Databasebeta

← #14769887

Subgroups — #14769887

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×#10623088C211yesmaximal, characteristic
2C2×D4×C11⋊C8C211yesmaximal, characteristic, complemented
3#13069552C211yesmaximal, characteristic, complemented
4#13069551C211yesmaximal, characteristic, complemented
5#13068913C212yesmaximal, complemented
6#13068906C212yesmaximal, complemented
7#13068685C212yesmaximal, complemented
8#13068593C211yesmaximal, characteristic, complemented
9C4×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
10#13068314C212yesmaximal, complemented
11C2×C11×#436C211yesmaximal, characteristic, complemented
12C22×C11×M16C2212yes—
13C2×C4×D4×C11C2211yescharacteristic
14C2×#66991C411yescharacteristic
15C2×#66989C411yescharacteristic
16C2×C4×C22⋊D11C2212yes—
17C2×#66979C2212yes—
18C23×C11⋊C8C2212yes—
19#10623088—24no—
20#10623088—24no—
21C2×#66950C411yescharacteristic
22C2×#66943C411yescharacteristic
23C2×#66936C412yes—
24C2×#66932C412yes—
25C2×C42×D11C2211yescharacteristic
26C2×C4×Dic22C2211yescharacteristic
27C11×#436—24no—
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×C22⋊C8C2212yes—
30C2×C4×C8×C11C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2212yes—
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×(C2×D11)⋊C8C2212yes—
35D4×C11⋊C8—24no—
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622188C2211yescharacteristic
39#10622188C2212yes—
40#10622188C2212yes—
41#10622188C2212yes—
42#10622188C2211yescharacteristic
43#10622188C2212yes—
44#10622188C2212yes—
45C22×D4×C11C2×C411yescharacteristic
46C23×C4×C11C2312yes—
47C22×C22⋊D11C2×C412yes—
48C22×C4×D11C2×C411yescharacteristic
49C22×C4×D11C2×C411yescharacteristic
50C22×C4×D11C2311yescharacteristic
51C22×Dic22C2×C411yescharacteristic
52C2×C11×M16—24no—
53C2×C11×M16—24no—
54C2×C11×M16—42no—
55C22×C8×C11C2311yescharacteristic
56C22×C8×C11C2312yes—
57C22×C8×C11C2311yescharacteristic
58C4×D4×C11D414yes—
59C4×D4×C11D414yes—
60C2×C11×C4⋊C4C2×C411yescharacteristic
61C2×C11×C22⋊C4C2×C412yes—
62C2×C42×C11C2311yescharacteristic
63C2×C22⋊Dic11C2×C412yes—
64C2×C22⋊Dic11C2×C412yes—
65C2×C22⋊Dic11C2×C412yes—
66#66991—24no—
67#66989—24no—
68C4×C22⋊D11—24no—
69C4×C22⋊D11—24no—
70C2×(C2×D11)⋊C4C2×C412yes—
71#66979—24no—
72#66979—24no—
73C2×C4⋊Dic11C2×C411yescharacteristic
74C2×C4⋊Dic11C2×C412yes—
75C2×C4⋊Dic11C2×C412yes—
76C2×Dic11⋊C4C2×C412yes—
77C2×Dic11⋊C4C2×C412yes—
78C2×C4×Dic11C2×C411yescharacteristic
79C2×C4×Dic11C2×C411yescharacteristic
80C2×C4×Dic11C2312yes—
81C2×C4×Dic11C2311yescharacteristic
82C22×C11⋊C8—24no—
83C22×C11⋊C8—24no—
84C22×C11⋊C8—42no—
85C22×C11⋊C8C2311yescharacteristic
86C22×C11⋊C8C2312yes—
87C22×C11⋊C8C2311yescharacteristic
88#66950—24no—
89#66943—24no—
90#66936—28no—
91#66932—28no—
92C42×D11—22no—
93C42×D11—22no—
94C4×Dic22—22no—
95C4×Dic22—22no—
96C11×C4⋊C8—22no—
97C11×C22⋊C8—24no—
98C4×C8×C11—22no—
99C22⋊(C11⋊C8)—24no—
100(C2×D11)⋊C8—22no—
101(C2×D11)⋊C8—22no—
102(C2×D11)⋊C8—42no—
103C4⋊(C11⋊C8)—22no—
104C4×C11⋊C8—22no—
105#22474—111nomaximal, Sylow
106C24×C11C22×C412yes—
107C23×D11C22×C411yescharacteristic
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11C22⋊C414yes—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11C22×C411yescharacteristic
116C22×C4×C11C22×C412yes—
117C22×C4×C11C22×C411yescharacteristic
118C22×C4×C11C2×D414yes—
119C22×C4×C11C2×D414yes—
120C22×C4×C11C2411yescharacteristic
121C2×C22⋊D11—24no—
122C2×C22⋊D11—24no—
123C2×C22⋊D11—42no—
124C22×Dic11C22×C411yescharacteristic
125C22×Dic11C22×C411yescharacteristic
126C22×Dic11C22×C411yescharacteristic
127C22×Dic11C22×C412yes—
128C22×Dic11C22×C412yes—
129C2×C4×D11—22no—
130C2×C4×D11—22no—
131C2×C4×D11—22no—
132C2×C4×D11—22no—
133C2×C4×D11—22no—
134C2×C4×D11—21no—
135C2×C4×D11—21no—
136C2×C4×D11—21no—
137C2×C4×D11—21no—
138C2×C4×D11—21no—
139C2×C4×D11—21no—
140C2×C4×D11—41no—
141C2×Dic22—22no—
142C2×Dic22—22no—
143C2×Dic22—22no—
144C11×M16—48no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—22no—
148C2×C8×C11—21no—
149C2×C8×C11—22no—
150C2×C8×C11—21no—
151C2×C8×C11—22no—
152C2×C8×C11—21no—
153C2×C8×C11#4112yes—
154C11×C4⋊C4C22⋊C414yes—
155C11×C22⋊C4C22⋊C418yes—
156C42×C11C2×D412yes—
157C42×C11C2×D412yes—
158C22⋊Dic11—24no—
159C22⋊Dic11—24no—
160C22⋊Dic11—24no—
161(C2×D11)⋊C4—24no—
162C4⋊Dic11—22no—
163C4⋊Dic11—24no—
164C4⋊Dic11—24no—
165Dic11⋊C4—24no—
166Dic11⋊C4—24no—
167C4×Dic11—22no—
168C4×Dic11—22no—
169C4×Dic11—22no—
170C4×Dic11—22no—
171C4×Dic11—21no—
172C4×Dic11—21no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—48no—
182C2×C11⋊C8#4112yes—
183C2×#529—111no—
184C2×#436D1111yescharacteristic, complemented
185C2×C8×D4—111no—
186#1984—111no—
187#1984—111no—
188#1870—112no—
189#1869—112no—
190#1818—112no—
191#1797—111no—
192C4×C22⋊C8—111no—
193#1729—112no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11C2×C22⋊C414yes—
201C23×C11C23×C411yescharacteristic
202C22×D11—21no—
203C22×D11—21no—
204C22×D11—21no—
205C22×D11—21no—
206C22×D11—21no—
207C22×D11—21no—
208C22×D11#13112yes—
209D4×C11—28no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11C2×C22⋊C412yes—
219C2×C4×C11C2×C22⋊C414yes—
220C2×C4×C11C2×C22⋊C412yes—
221C2×C4×C11#13112yes—
222C2×C4×C11#13112yes—
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C11C2×#4111yescharacteristic
227C2×C4×C11H(5,𝔽2)11yescharacteristic
228C2×C4×C112−1+411yescharacteristic
229C22⋊D11—48no—
230C2×Dic11—21no—
231C2×Dic11—21no—
232C2×Dic11—21no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—21no—
236C2×Dic11—21no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—22no—
243C2×Dic11—21no—
244C2×Dic11—22no—
245C4×D11—44no—
246C4×D11—41no—
247C4×D11—41no—
248C4×D11—41no—
249C4×D11—41no—
250C4×D11—44no—
251Dic22—44no—
252C8×C11—22no—
253C8×C11—42no—
254C8×C11—41no—
255C11⋊C8—22no—
256C11⋊C8—42no—
257C11⋊C8—41no—
258C22×M16C2×D1112yes—
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×D4C2×D1111yescharacteristic
271C2×#117—112no—
272C22×C42—111no—
273#436—24no—
274C8×D4—224no—
275C2×C4⋊C8—111no—
276C2×C4⋊C8C2×D1111yescharacteristic
277C2×C22⋊C8—112no—
278C2×C22⋊C8—111no—
279C2×C22⋊C8—111no—
280C2×C22⋊C8—112no—
281C2×C22⋊C8C2×D1112yes—
282C2×C4×C8—111no—
283C2×C4×C8C2×D1111yescharacteristic
284#336—112no—
285#336—111no—
286#336—112no—
287#336—112no—
288#336—112no—
289#336—112no—
290#336—111no—
291C22×C11—24no—
292C22×C11—24no—
293C22×C11—24no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11C22×C22⋊C411yescharacteristic
299C22×C11C4×#4111yescharacteristic
300C22×C11#52011yescharacteristic
301C22×C11C2×#13111yescharacteristic
302C22×C11C2×#13111yescharacteristic
303C22×C11C2×#13111yescharacteristic
304C22×C11#56811yescharacteristic
305C2×D11—22no—
306C2×D11—22no—
307C2×D11—22no—
308C2×D11—41no—
309C2×D11—41no—
310C2×D11—41no—
311C2×D11—41no—
312C4×C11—24no—
313C4×C11—22no—
314C4×C11#40814yes—
315C4×C11#54611yescharacteristic
316C4×C11#54611yescharacteristic
317C4×C11#54711yescharacteristic
318C4×C11#54711yescharacteristic
319Dic11—41no—
320Dic11—42no—
321Dic11—41no—
322Dic11—41no—
323Dic11—42no—
324C22×Q8—111no—
325C22×D4—112no—
326C22×D4C4×D1111yescharacteristic
327C23×C4—111no—
328C23×C4—111no—
329C23×C4—111no—
330C23×C4C22×D1112yes—
331C2×M16—24no—
332C2×M16—24no—
333C2×M16—42no—
334C22×C8—111no—
335C22×C8—112no—
336C22×C8—111no—
337C22×C8—224no—
338C22×C8—224no—
339C22×C8—442no—
340C22×C8C22×D1112yes—
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—224no—
352C4×D4—224no—
353C4×D4D4414yes—
354C4×D4C22⋊D1114yes—
355#117—224no—
356#117—224no—
357C2×C4⋊C4—112no—
358C2×C4⋊C4—112no—
359C2×C4⋊C4—112no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—112no—
362C2×C4⋊C4C4×D1111yescharacteristic
363C2×C22⋊C4—112no—
364C2×C22⋊C4—112no—
365C2×C22⋊C4—112no—
366C2×C22⋊C4—112no—
367C2×C22⋊C4C4×D1112yes—
368C2×C42—111no—
369C2×C42—111no—
370C2×C42—111no—
371C2×C42—112no—
372C2×C42—222no—
373C2×C42—222no—
374C2×C42C22×D1111yescharacteristic
375C4⋊C8—22no—
376C4⋊C8—222no—
377C22⋊C8—24no—
378C22⋊C8—222no—
379C22⋊C8—224no—
380C22⋊C8—222no—
381C22⋊C8—442no—
382C4×C8—22no—
383C4×C8—222no—
384C2×C11—44no—
385C2×C11#233911yescharacteristic
386C2×C11C2×#40811yescharacteristic
387C2×C11#288011yescharacteristic
388C2×C11#296611yescharacteristic
389C2×C11#296911yescharacteristic
390C2×C11#299311yescharacteristic
391C2×C11#299411yescharacteristic
392D11—42no—
393C24—111no—
394C24C2×C4×D1112yes—
395C2×Q8—222no—
396C2×Q8—222no—
397C2×Q8—222no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—224no—
401C2×D4—224no—
402C2×D4—442no—
403C2×D4(C2×D11)⋊C414yes—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—111no—
409C22×C4—111no—
410C22×C4—111no—
411C22×C4—112no—
412C22×C4—112no—
413C22×C4—222no—
414C22×C4—222no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—221no—
419C22×C4—221no—
420C22×C4—221no—
421C22×C4—221no—
422C22×C4—221no—
423C22×C4—221no—
424C22×C4—441no—
425C22×C4C2×C4×D1111yescharacteristic
426C22×C4C2×C4×D1112yes—
427C22×C4C2×C4×D1111yescharacteristic
428C22×C4C2×D4414yes—
429C22×C4C2×C22⋊D1114yes—
430C22×C4C23×D1111yescharacteristic
431M16—48no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—22no—
440C2×C8—112no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8—222no—
445C2×C8—221no—
446C2×C8—222no—
447C2×C8—222no—
448C2×C8—221no—
449C2×C8—448no—
450C2×C8#434112yes—
451C4⋊C4—224no—
452C4⋊C4—224no—
453C4⋊C4—224no—
454C4⋊C4—222no—
455C4⋊C4—224no—
456C4⋊C4(C2×D11)⋊C414yes—
457C22⋊C4—224no—
458C22⋊C4—224no—
459C22⋊C4—224no—
460C22⋊C4—224no—
461C22⋊C4(C2×D11)⋊C418yes—
462C42—222no—
463C42—222no—
464C42—221no—
465C42—222no—
466C42—221no—
467C42—222no—
468C42C2×D4412yes—
469C42C2×C22⋊D1112yes—
470C11#2247411yescharacteristic, complemented, Sylow
471C23—22no—
472C23—22no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—112no—
478C23—221no—
479C23—221no—
480C23—221no—
481C23—221no—
482C23—221no—
483C23—221no—
484C23C2×(C2×D11)⋊C414yes—
485C23C22×C4×D1111yescharacteristic
486Q8—444no—
487D4—28no—
488D4—448no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—221no—
498C2×C4—221no—
499C2×C4—222no—
500C2×C4—222no—
501C2×C4—221no—
502C2×C4—222no—
503C2×C4—221no—
504C2×C4—222no—
505C2×C4—221no—
506C2×C4—221no—
507C2×C4—221no—
508C2×C4—222no—
509C2×C4—222no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—444no—
513C2×C4—444no—
514C2×C4—441no—
515C2×C4—441no—
516C2×C4—441no—
517C2×C4—441no—
518C2×C4#6696012yes—
519C2×C4#6696012yes—
520C2×C4C2×(C2×D11)⋊C412yes—
521C2×C4C2×(C2×D11)⋊C414yes—
522C2×C4C2×(C2×D11)⋊C412yes—
523C2×C4C22×D4411yescharacteristic
524C2×C4C2×#434111yescharacteristic
525C2×C4#6703711yescharacteristic
526C2×C4#41×D1111yescharacteristic
527C2×C4#6704311yescharacteristic
528C2×C4C22×C22⋊D1111yescharacteristic
529C8—22no—
530C8—42no—
531C8—41no—
532C8—222no—
533C8—442no—
534C8—441no—
535C22—24no—
536C22—24no—
537C22—24no—
538C22—42no—
539C22—42no—
540C22—42no—
541C22—42no—
542C22—222no—
543C22—222no—
544C22—222no—
545C22—441no—
546C22—441no—
547C22—441no—
548C22—441no—
549C22C4×#434111yescharacteristic
550C22#1062307711yescharacteristic
551C22C2×#6696011yescharacteristic
552C22C2×#6696011yescharacteristic
553C22D11×#13111yescharacteristic
554C22#1062328111yescharacteristic
555C22C22×(C2×D11)⋊C411yescharacteristic
556C4—22no—
557C4—24no—
558C4—441no—
559C4—442no—
560C4—441no—
561C4—442no—
562C4—441no—
563C4#1062274214yes—
564C4#1062308511yescharacteristic
565C4#1062308611yescharacteristic
566C4#1062333711yescharacteristic
567C4#1062335511yescharacteristic
568C2—44no—
569C2—442no—
570C2#1307144111yescharacteristic
571C2C2×#1062274211yescharacteristic
572C2#1307706311yescharacteristic
573C2#1307759411yescharacteristic
574C2#1307762311yescharacteristic
575C2#1307776011yescharacteristic
576C2#1307777711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC2×C11×#436C2
prime radicalC2×#66991C4
cosocleC22×C4×C11C24
hypercenterC2×#436D11
hypocenterC11#22474
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
2. C2×D4×C11⋊C8C2semidirect
3. #13069552C2semidirect
4. #13069551C2semidirect
5. #13068913C2semidirect
6. #13068906C2semidirect
7. #13068685C2semidirect
8. #13068593C2semidirect
9. C4×(C2×D11)⋊C8C2semidirect
10. #13068314C2semidirect
11. C2×C11×#436C2semidirect
184. C2×#436D11semidirect
470. C11#22474semidirect

Maximal subgroups

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

subgroupindex
C2×#106230882
C2×D4×C11⋊C82
#130695522
#130695512
#130689132
#130689062
#130686852
#130685932
C4×(C2×D11)⋊C82
#130683142
C2×C11×#4362
#2247411