Finite Group Databasebeta

← #14769889

Subgroups — #14769889

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×#10623111C211yesmaximal, characteristic
2C2×#10622451C211yesmaximal, characteristic, complemented
3C2×C8×D44C211yesmaximal, characteristic, complemented
4#13069553C211yesmaximal, characteristic, complemented
5#13068912C212yesmaximal, complemented
6#13068907C212yesmaximal, complemented
7#13068686C212yesmaximal, complemented
8#13068593C211yesmaximal, characteristic, complemented
9C4×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
10#13068311C212yesmaximal, complemented
11C11×#1984C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#67000C411yescharacteristic
14C2×#66999C411yescharacteristic
15C22×#4313C2212yes—
16C22×C8×D11C2212yes—
17#10623111—24no—
18#10623111—24no—
19C2×#66951C412yes—
20C2×#66948C411yescharacteristic
21C2×#66947C412yes—
22C2×#66943C411yescharacteristic
23C2×C4×D44C2212yes—
24C2×C4×D44C2211yescharacteristic
25C2×#66925C2212yes—
26C2×C42×D11C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C4×C8×C11C2211yescharacteristic
29C2×(C2×D11)⋊C8C2212yes—
30C2×(C2×D11)⋊C8C2212yes—
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×(C2×D11)⋊C8C2212yes—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622451—24no—
37C8×D44—24no—
38C11×#336C2212yes—
39C11×#336C2212yes—
40#10622188C2211yescharacteristic
41#10622188C2212yes—
42#10622188C2211yescharacteristic
43#10622162C2212yes—
44#10622162C2212yes—
45C22×Q8×C11C2×C411yescharacteristic
46C22×D44C2×C412yes—
47C22×D44C2×C411yescharacteristic
48C22×C4×D11C2×C411yescharacteristic
49C22×C4×D11C2×C411yescharacteristic
50C22×C4×D11C2311yescharacteristic
51C22×C4×D11C2312yes—
52C22×C8×C11C2311yescharacteristic
53C22×C8×C11C2312yes—
54C22×C8×C11C2311yescharacteristic
55C4×Q8×C11—22no—
56C4×Q8×C11—22no—
57C2×C11×C4⋊C4C2×C411yescharacteristic
58C2×C11×C4⋊C4C2×C412yes—
59C2×C42×C11C2312yes—
60C2×C42×C11C2311yescharacteristic
61#67000—24no—
62#66999—24no—
63C2×(C2×D11)⋊C4C2×C412yes—
64C2×(C2×D11)⋊C4C2×C412yes—
65C2×(C2×D11)⋊C4C2×C412yes—
66C2×(C2×D11)⋊C4C2×C412yes—
67C2×(C2×D11)⋊C4C2×C412yes—
68C2×C4⋊Dic11C2×C412yes—
69C2×C4⋊Dic11C2×C411yescharacteristic
70C2×Dic11⋊C4C2×C412yes—
71C2×Dic11⋊C4C2×C412yes—
72C2×C4×Dic11C2×C411yescharacteristic
73C2×C4×Dic11C2×C411yescharacteristic
74C2×C4×Dic11C2311yescharacteristic
75C22×C11⋊C8C2311yescharacteristic
76C22×C11⋊C8C2312yes—
77C22×C11⋊C8C2311yescharacteristic
78C2×#4313—24no—
79C2×#4313—24no—
80C2×#4313—42no—
81C2×C8×D11—24no—
82C2×C8×D11—24no—
83C2×C8×D11—42no—
84#66951—28no—
85#66948—24no—
86#66947—28no—
87#66943—24no—
88C4×D44—24no—
89C4×D44—24no—
90C4×D44D414yes—
91C4×D44D414yes—
92#66925—24no—
93#66925—24no—
94C42×D11—22no—
95C42×D11—22no—
96C11×C4⋊C8—22no—
97C4×C8×C11—22no—
98(C2×D11)⋊C8—24no—
99(C2×D11)⋊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
106C23×D11C22×C412yes—
107C23×D11C22×C411yescharacteristic
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C22×C4×C11C22×C412yes—
112C22×C4×C11C22×C412yes—
113C22×C4×C11C22×C411yescharacteristic
114C22×C4×C11C22×C411yescharacteristic
115C22×C4×C11C2411yescharacteristic
116C22×Dic11C22×C411yescharacteristic
117C22×Dic11C22×C411yescharacteristic
118C22×Dic11C22×C411yescharacteristic
119C22×Dic11C22×C412yes—
120C2×D44—24no—
121C2×D44—24no—
122C2×D44—22no—
123C2×D44—22no—
124C2×D44—42no—
125C2×D44C22⋊C414yes—
126C2×C4×D11—22no—
127C2×C4×D11—22no—
128C2×C4×D11—22no—
129C2×C4×D11—22no—
130C2×C4×D11—22no—
131C2×C4×D11—21no—
132C2×C4×D11—21no—
133C2×C4×D11—22no—
134C2×C4×D11—22no—
135C2×C4×D11—21no—
136C2×C4×D11—21no—
137C2×C4×D11—22no—
138C2×C4×D11—21no—
139C2×C4×D11—22no—
140C2×C4×D11—21no—
141C2×C4×D11—41no—
142C2×C4×D11C2×D414yes—
143C2×C4×D11C2×D414yes—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—22no—
147C2×C8×C11—21no—
148C2×C8×C11—22no—
149C2×C8×C11—21no—
150C2×C8×C11—22no—
151C2×C8×C11—21no—
152C2×C8×C11#4112yes—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—24no—
155C42×C11—22no—
156C42×C11—22no—
157C42×C11C2×D412yes—
158C42×C11C2×D412yes—
159(C2×D11)⋊C4—24no—
160(C2×D11)⋊C4—24no—
161(C2×D11)⋊C4—24no—
162(C2×D11)⋊C4—24no—
163(C2×D11)⋊C4C22⋊C418yes—
164C4⋊Dic11—24no—
165C4⋊Dic11C22⋊C414yes—
166Dic11⋊C4—24no—
167Dic11⋊C4—24no—
168C4×Dic11—22no—
169C4×Dic11—22no—
170C4×Dic11—21no—
171C4×Dic11—21no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—21no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8#4112yes—
181#4313—48no—
182C8×D11—48no—
183C2×#529—111no—
184C2×#436—111no—
185C2×C8×D4—111no—
186#1984—111no—
187#1984D1111yescharacteristic, complemented
188#1870—112no—
189#1869—112no—
190#1818—112no—
191#1797—111no—
192C4×C22⋊C8—111no—
193#1729—112no—
194C23×C11C23×C411yescharacteristic
195C22×D11—21no—
196C22×D11—22no—
197C22×D11—21no—
198C22×D11—22no—
199C22×D11—21no—
200C22×D11—21no—
201C22×D11—21no—
202C22×D11—22no—
203C22×D11—22no—
204C22×D11—22no—
205C22×D11—21no—
206C22×D11—22no—
207C22×D11C2×C22⋊C414yes—
208C22×D11#13112yes—
209Q8×C11—44no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11C2×C22⋊C412yes—
219C2×C4×C11C2×C22⋊C412yes—
220C2×C4×C11#13112yes—
221C2×C4×C11#13112yes—
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C2×#4111yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C11H(5,𝔽2)11yescharacteristic
227C2×C4×C112−1+411yescharacteristic
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—21no—
231C2×Dic11—21no—
232C2×Dic11—21no—
233C2×Dic11—21no—
234C2×Dic11—21no—
235C2×Dic11—21no—
236C2×Dic11—21no—
237C2×Dic11—21no—
238C2×Dic11—21no—
239C2×Dic11C2×C22⋊C414yes—
240D44—28no—
241D44—48no—
242C4×D11—24no—
243C4×D11—24no—
244C4×D11—24no—
245C4×D11—24no—
246C4×D11—44no—
247C4×D11—41no—
248C4×D11—41no—
249C4×D11—41no—
250C4×D11—41no—
251C4×D11—44no—
252C8×C11—22no—
253C8×C11—42no—
254C8×C11—41no—
255C11⋊C8—22no—
256C11⋊C8—42no—
257C11⋊C8—41no—
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×Q8C2×D1111yescharacteristic
269C2×C4×D4—111no—
270C2×C4×D4—112no—
271C2×#117—112no—
272C22×C42—111no—
273#436—224no—
274C8×D4—224no—
275C2×C4⋊C8—111no—
276C2×C4⋊C8C2×D1111yescharacteristic
277C2×C22⋊C8—112no—
278C2×C22⋊C8—112no—
279C2×C22⋊C8—111no—
280C2×C22⋊C8—111no—
281C2×C22⋊C8—112no—
282C2×C4×C8—111no—
283C2×C4×C8C2×D1111yescharacteristic
284#336—112no—
285#336—111no—
286#336—111no—
287#336—112no—
288#336—112no—
289#336C2×D1112yes—
290#336C2×D1112yes—
291C22×C11C22×C22⋊C411yescharacteristic
292C22×C11C4×#4111yescharacteristic
293C22×C11#52011yescharacteristic
294C22×C11C2×#13111yescharacteristic
295C22×C11C2×#13111yescharacteristic
296C22×C11C2×#13111yescharacteristic
297C22×C11#56811yescharacteristic
298C2×D11—24no—
299C2×D11—24no—
300C2×D11—24no—
301C2×D11—22no—
302C2×D11—22no—
303C2×D11—22no—
304C2×D11—41no—
305C2×D11—41no—
306C2×D11—42no—
307C2×D11—41no—
308C2×D11—42no—
309C2×D11—41no—
310C2×D11—42no—
311C2×D11—42no—
312C4×C11—22no—
313C4×C11—42no—
314C4×C11—42no—
315C4×C11#40814yes—
316C4×C11#54611yescharacteristic
317C4×C11#54611yescharacteristic
318C4×C11#54711yescharacteristic
319C4×C11#54711yescharacteristic
320Dic11—24no—
321Dic11—41no—
322Dic11—41no—
323Dic11—41no—
324C22×Q8C4×D1111yescharacteristic
325C22×D4—111no—
326C22×D4—112no—
327C23×C4—112no—
328C23×C4—111no—
329C23×C4—111no—
330C23×C4—111no—
331C2×M16—224no—
332C2×M16—224no—
333C2×M16—442no—
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—22no—
350C4×Q8—22no—
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⋊C4C4×D1111yescharacteristic
362C2×C4⋊C4C4×D1112yes—
363C2×C22⋊C4—112no—
364C2×C22⋊C4—112no—
365C2×C22⋊C4—112no—
366C2×C22⋊C4—112no—
367C2×C22⋊C4—112no—
368C2×C42—111no—
369C2×C42—111no—
370C2×C42—111no—
371C2×C42—222no—
372C2×C42—222no—
373C2×C42C22×D1112yes—
374C2×C42C22×D1111yescharacteristic
375C4⋊C8—22no—
376C4⋊C8—222no—
377C22⋊C8—222no—
378C22⋊C8—224no—
379C22⋊C8—224no—
380C22⋊C8—222no—
381C22⋊C8—442no—
382C4×C8—22no—
383C4×C8—222no—
384C2×C11#233911yescharacteristic
385C2×C11C2×#40811yescharacteristic
386C2×C11#288011yescharacteristic
387C2×C11#296611yescharacteristic
388C2×C11#296911yescharacteristic
389C2×C11#299311yescharacteristic
390C2×C11#299411yescharacteristic
391D11—44no—
392D11—42no—
393C24—112no—
394C24—111no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×D4—114no—
399C2×D4—224no—
400C2×D4—224no—
401C2×D4—222no—
402C2×D4—222no—
403C2×D4—442no—
404C22×C4—112no—
405C22×C4—114no—
406C22×C4—114no—
407C22×C4—111no—
408C22×C4—111no—
409C22×C4—111no—
410C22×C4—222no—
411C22×C4—222no—
412C22×C4—222no—
413C22×C4—222no—
414C22×C4—222no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—221no—
420C22×C4—221no—
421C22×C4—221no—
422C22×C4—221no—
423C22×C4—221no—
424C22×C4—221no—
425C22×C4—441no—
426C22×C4C2×C4×D1112yes—
427C22×C4C2×C4×D1112yes—
428C22×C4C2×C4×D1111yescharacteristic
429C22×C4C2×C4×D1111yescharacteristic
430C22×C4C23×D1111yescharacteristic
431M16—448no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—22no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—22no—
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—221no—
448C2×C8—222no—
449C2×C8—448no—
450C2×C8#434312yes—
451C4⋊C4—22no—
452C4⋊C4—24no—
453C4⋊C4—114no—
454C4⋊C4—224no—
455C4⋊C4—224no—
456C4⋊C4—224no—
457C22⋊C4—118no—
458C22⋊C4—224no—
459C22⋊C4—224no—
460C22⋊C4—224no—
461C22⋊C4—224no—
462C42—22no—
463C42—22no—
464C42—222no—
465C42—222no—
466C42—221no—
467C42—221no—
468C42D4×D1112yes—
469C42D4×D1112yes—
470C11#2247411yescharacteristic, complemented, Sylow
471C23—114no—
472C23—112no—
473C23—221no—
474C23—222no—
475C23—221no—
476C23—221no—
477C23—222no—
478C23—222no—
479C23—221no—
480C23—222no—
481C23—222no—
482C23—221no—
483C23—221no—
484C23—222no—
485C23C22×C4×D1111yescharacteristic
486Q8—44no—
487D4—228no—
488D4—448no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—114no—
498C2×C4—222no—
499C2×C4—222no—
500C2×C4—224no—
501C2×C4—224no—
502C2×C4—224no—
503C2×C4—224no—
504C2×C4—221no—
505C2×C4—221no—
506C2×C4—221no—
507C2×C4—221no—
508C2×C4—221no—
509C2×C4—221no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—221no—
513C2×C4—444no—
514C2×C4—441no—
515C2×C4—444no—
516C2×C4—441no—
517C2×C4—441no—
518C2×C4—441no—
519C2×C4C22⋊C4×D1112yes—
520C2×C4C22⋊C4×D1112yes—
521C2×C4#6695412yes—
522C2×C4#6696012yes—
523C2×C4C2×D4×D1111yescharacteristic
524C2×C4C2×D4×D1111yescharacteristic
525C2×C4C2×#434311yescharacteristic
526C2×C4#6704011yescharacteristic
527C2×C4#41×D1111yescharacteristic
528C2×C4#6704211yescharacteristic
529C8—22no—
530C8—41no—
531C8—42no—
532C8—222no—
533C8—441no—
534C8—442no—
535C22—222no—
536C22—224no—
537C22—222no—
538C22—224no—
539C22—224no—
540C22—222no—
541C22—441no—
542C22—442no—
543C22—442no—
544C22—441no—
545C22—441no—
546C22—442no—
547C22—441no—
548C22—442no—
549C22C2×C22⋊C4×D1111yescharacteristic
550C22C4×#434311yescharacteristic
551C22#1062310511yescharacteristic
552C22C2×#6695411yescharacteristic
553C22C2×#6696011yescharacteristic
554C22D11×#13111yescharacteristic
555C22#1062328111yescharacteristic
556C4—22no—
557C4—42no—
558C4—42no—
559C4—224no—
560C4—441no—
561C4—441no—
562C4—441no—
563C4#1062234014yes—
564C4#1062316111yescharacteristic
565C4#1062316211yescharacteristic
566C4#1062320711yescharacteristic
567C4#1062325711yescharacteristic
568C2—442no—
569C2—444no—
570C2#1307144511yescharacteristic
571C2C2×#1062234011yescharacteristic
572C2#1307706411yescharacteristic
573C2#1307759311yescharacteristic
574C2#1307762211yescharacteristic
575C2#1307776411yescharacteristic
576C2#1307777911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1984C2
prime radicalC2×#66948C4
cosocleC22×C4×C11C24
hypercenter#1984D11
hypocenterC11#22474
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1984

Complements

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

NH ≅ G/Ntype
2. C2×#10622451C2semidirect
3. C2×C8×D44C2semidirect
4. #13069553C2semidirect
5. #13068912C2semidirect
6. #13068907C2semidirect
7. #13068686C2semidirect
8. #13068593C2semidirect
9. C4×(C2×D11)⋊C8C2semidirect
10. #13068311C2semidirect
11. C11×#1984C2semidirect
187. #1984D11semidirect
470. C11#22474semidirect

Maximal subgroups

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

subgroupindex
C2×#106231112
C2×#106224512
C2×C8×D442
#130695532
#130689122
#130689072
#130686862
#130685932
C4×(C2×D11)⋊C82
#130683112
C11×#19842
#2247411