Finite Group Databasebeta

← #14770497

Subgroups — #14770497

Order 2816.

1136 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623111C211yesmaximal, characteristic
2C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
3#13069414C212yesmaximal, complemented
4#13069410C211yesmaximal, characteristic, complemented
5#13069409C212yesmaximal, complemented
6#13069409C211yesmaximal, characteristic, complemented
7#13068597C212yesmaximal, complemented
8#13068593C211yesmaximal, characteristic, complemented
9#13068385C212yesmaximal, complemented
10C4×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
11C2×C11×#446C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#67000C411yescharacteristic
14C2×#66999C411yescharacteristic
15#10623111—24no—
16#10623111—24no—
17C2×#66951C412yes—
18C2×#66948C411yescharacteristic
19C2×#66947C412yes—
20C2×#66943C411yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C2×C4×D44C2212yes—
23C2×#66925C2212yes—
24C2×C42×D11C2211yescharacteristic
25C11×#446—24no—
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×C4⋊C8C2212yes—
28C2×C11×#97C2212yes—
29C2×C4×C8×C11C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×(C2×D11)⋊C8C2212yes—
33C2×(C2×D11)⋊C8C2212yes—
34C2×(C2×D11)⋊C8C2212yes—
35C2×(C2×D11)⋊C8C2212yes—
36C2×(C2×D11)⋊C8C2212yes—
37Q8×C11⋊C8—24no—
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2212yes—
40C2×C4×C11⋊C8C2211yescharacteristic
41C2×C4×C11⋊C8C2212yes—
42#10622188C2212yes—
43#10622188C2211yescharacteristic
44#10622188C2211yescharacteristic
45C22×Q8×C11C2×C411yescharacteristic
46C22×D44C2×C411yescharacteristic
47C22×D44C2×C412yes—
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×C11D414yes—
56C4×Q8×C11D414yes—
57C2×C11×C4⋊C4C2×C411yescharacteristic
58C2×C11×C4⋊C4C2×C412yes—
59C2×C42×C11C2311yescharacteristic
60C2×C42×C11C2312yes—
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
78#66951—28no—
79#66948—24no—
80#66947—28no—
81#66943—24no—
82C4×D44—24no—
83C4×D44—22no—
84C4×D44—24no—
85C4×D44—22no—
86#66925—24no—
87#66925—24no—
88C42×D11—22no—
89C42×D11—22no—
90C11×C4⋊C8—22no—
91C11×C4⋊C8—24no—
92C11×#97—24no—
93C4×C8×C11—22no—
94(C2×D11)⋊C8—22no—
95(C2×D11)⋊C8—24no—
96(C2×D11)⋊C8—22no—
97(C2×D11)⋊C8—24no—
98(C2×D11)⋊C8—42no—
99(C2×D11)⋊C8—42no—
100(C2×D11)⋊C8—42no—
101C4⋊(C11⋊C8)—22no—
102C4⋊(C11⋊C8)—24no—
103C4×C11⋊C8—22no—
104C4×C11⋊C8—24no—
105#22531—111nomaximal, Sylow
106C23×D11C22×C412yes—
107C23×D11C22×C411yescharacteristic
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11C22⋊C414yes—
111C22×C4×C11C22×C411yescharacteristic
112C22×C4×C11C22×C412yes—
113C22×C4×C11C22×C412yes—
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—22no—
125C2×D44—42no—
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—22no—
137C2×C4×D11—21no—
138C2×C4×D11—22no—
139C2×C4×D11—21no—
140C2×C4×D11—22no—
141C2×C4×D11—21no—
142C2×C4×D11—22no—
143C2×C4×D11—41no—
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⋊C4C22⋊C414yes—
154C11×C4⋊C4C22⋊C418yes—
155C42×C11C2×D412yes—
156C42×C11C2×D414yes—
157C42×C11C2×D412yes—
158C42×C11C2×D414yes—
159(C2×D11)⋊C4—24no—
160(C2×D11)⋊C4—24no—
161(C2×D11)⋊C4—24no—
162(C2×D11)⋊C4—24no—
163(C2×D11)⋊C4—24no—
164C4⋊Dic11—24no—
165C4⋊Dic11—22no—
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—22no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8#4112yes—
181C2×#529—111no—
182C2×#446D1111yescharacteristic, complemented
183C2×C8×Q8—111no—
184#1955—112no—
185#1954—111no—
186#1954—112no—
187#1954—111no—
188#1798—112no—
189#1797—111no—
190#1750—112no—
191C4×C22⋊C8—111no—
192C23×C11C23×C411yescharacteristic
193C22×D11—21no—
194C22×D11—21no—
195C22×D11—21no—
196C22×D11—21no—
197C22×D11—21no—
198C22×D11—21no—
199C22×D11—22no—
200C22×D11—22no—
201C22×D11—22no—
202C22×D11—22no—
203C22×D11—22no—
204C22×D11—22no—
205C22×D11—22no—
206C22×D11#13112yes—
207Q8×C11—28no—
208C2×C4×C11—21no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—21no—
213C2×C4×C11—22no—
214C2×C4×C11C2×C22⋊C412yes—
215C2×C4×C11C2×C22⋊C414yes—
216C2×C4×C11C2×C22⋊C414yes—
217C2×C4×C11C2×C22⋊C412yes—
218C2×C4×C11#13112yes—
219C2×C4×C11#13112yes—
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C2×#4111yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C2×C4×C11H(5,𝔽2)11yescharacteristic
225C2×C4×C112−1+411yescharacteristic
226C2×Dic11—21no—
227C2×Dic11—21no—
228C2×Dic11—21no—
229C2×Dic11—22no—
230C2×Dic11—21no—
231C2×Dic11—22no—
232C2×Dic11—21no—
233C2×Dic11—22no—
234C2×Dic11—21no—
235C2×Dic11—21no—
236C2×Dic11—21no—
237C2×Dic11—21no—
238D44—48no—
239D44—44no—
240C4×D11—44no—
241C4×D11—41no—
242C4×D11—42no—
243C4×D11—41no—
244C4×D11—42no—
245C4×D11—41no—
246C4×D11—42no—
247C4×D11—41no—
248C4×D11—42no—
249C4×D11—44no—
250C8×C11—22no—
251C8×C11—41no—
252C8×C11—42no—
253C11⋊C8—22no—
254C11⋊C8—41no—
255C11⋊C8—42no—
256#529—224no—
257#529—224no—
258C2×#126—112no—
259C2×#125—111no—
260C2×#124—111no—
261C2×#123—112no—
262C2×C22⋊Q8—111no—
263C2×#121—111no—
264C2×C4×Q8C2×D1111yescharacteristic
265C2×C4×D4—111no—
266C2×C4×D4—112no—
267C2×#117—112no—
268C22×C42—111no—
269#446—24no—
270C8×Q8—224no—
271C2×C4⋊C8—111no—
272C2×C4⋊C8—112no—
273C2×C4⋊C8C2×D1111yescharacteristic
274C2×C4⋊C8C2×D1112yes—
275C2×C22⋊C8—111no—
276C2×C22⋊C8—112no—
277C2×C22⋊C8—112no—
278C2×C22⋊C8—111no—
279C2×C22⋊C8—112no—
280C2×C22⋊C8—112no—
281C2×C22⋊C8—112no—
282C2×#97C2×D1112yes—
283C2×C4×C8—111no—
284C2×C4×C8—112no—
285C2×C4×C8C2×D1111yescharacteristic
286#336—112no—
287#336—111no—
288#336—111no—
289C22×C11C22×C22⋊C411yescharacteristic
290C22×C11C4×#4111yescharacteristic
291C22×C11#52011yescharacteristic
292C22×C11C2×#13111yescharacteristic
293C22×C11C2×#13111yescharacteristic
294C22×C11C2×#13111yescharacteristic
295C22×C11#56811yescharacteristic
296C2×D11—22no—
297C2×D11—22no—
298C2×D11—22no—
299C2×D11—41no—
300C2×D11—41no—
301C2×D11—41no—
302C2×D11—41no—
303C2×D11—42no—
304C2×D11—42no—
305C2×D11—42no—
306C2×D11—42no—
307C2×D11—42no—
308C2×D11—42no—
309C2×D11—42no—
310C4×C11—24no—
311C4×C11—22no—
312C4×C11—24no—
313C4×C11#40814yes—
314C4×C11#54811yescharacteristic
315C4×C11#54811yescharacteristic
316C4×C11#55011yescharacteristic
317C4×C11#55011yescharacteristic
318Dic11—41no—
319Dic11—42no—
320Dic11—41no—
321Dic11—41no—
322C22×Q8C4×D1111yescharacteristic
323C22×D4—111no—
324C22×D4—112no—
325C23×C4—111no—
326C23×C4—112no—
327C23×C4—111no—
328C23×C4—111no—
329C22×C8—111no—
330C22×C8—112no—
331C22×C8—111no—
332C22×C8C22×D1111yescharacteristic
333C22×C8C22×D1112yes—
334C22×C8C22×D1111yescharacteristic
335#126—228no—
336#125—224no—
337#124—224no—
338#123—228no—
339C22⋊Q8—224no—
340#121—224no—
341C4×Q8D4414yes—
342C4×Q8C22⋊D1114yes—
343C4×D4—222no—
344C4×D4—224no—
345C4×D4—222no—
346C4×D4—224no—
347#117—224no—
348#117—224no—
349C2×C4⋊C4—112no—
350C2×C4⋊C4—112no—
351C2×C4⋊C4—111no—
352C2×C4⋊C4—112no—
353C2×C4⋊C4C4×D1111yescharacteristic
354C2×C4⋊C4C4×D1112yes—
355C2×C22⋊C4—112no—
356C2×C22⋊C4—112no—
357C2×C22⋊C4—112no—
358C2×C22⋊C4—112no—
359C2×C22⋊C4—112no—
360C2×C42—111no—
361C2×C42—111no—
362C2×C42—111no—
363C2×C42—222no—
364C2×C42—222no—
365C2×C42C22×D1112yes—
366C2×C42C22×D1111yescharacteristic
367C4⋊C8—22no—
368C4⋊C8—24no—
369C4⋊C8—222no—
370C4⋊C8—224no—
371C22⋊C8—222no—
372C22⋊C8—224no—
373C22⋊C8—224no—
374C22⋊C8—222no—
375C22⋊C8—442no—
376C22⋊C8—442no—
377C22⋊C8—442no—
378#97—24no—
379C4×C8—22no—
380C4×C8—222no—
381C4×C8—224no—
382C2×C11#234111yescharacteristic
383C2×C11C2×#40811yescharacteristic
384C2×C11#288011yescharacteristic
385C2×C11#296611yescharacteristic
386C2×C11#296911yescharacteristic
387C2×C11#299311yescharacteristic
388C2×C11#299411yescharacteristic
389D11—42no—
390D11—82no—
391C24—111no—
392C24—112no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8(C2×D11)⋊C414yes—
396C2×D4—224no—
397C2×D4—222no—
398C2×D4—222no—
399C2×D4—224no—
400C2×D4—222no—
401C2×D4—442no—
402C22×C4—111no—
403C22×C4—111no—
404C22×C4—111no—
405C22×C4—112no—
406C22×C4—222no—
407C22×C4—222no—
408C22×C4—222no—
409C22×C4—222no—
410C22×C4—222no—
411C22×C4—221no—
412C22×C4—222no—
413C22×C4—221no—
414C22×C4—222no—
415C22×C4—221no—
416C22×C4—222no—
417C22×C4—221no—
418C22×C4—222no—
419C22×C4—221no—
420C22×C4—222no—
421C22×C4—221no—
422C22×C4—222no—
423C22×C4—441no—
424C22×C4C2×C4×D1111yescharacteristic
425C22×C4C2×C4×D1112yes—
426C22×C4C2×C4×D1112yes—
427C22×C4C2×C4×D1111yescharacteristic
428C22×C4C23×D1111yescharacteristic
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—22no—
433C2×C8—21no—
434C2×C8—22no—
435C2×C8—21no—
436C2×C8—22no—
437C2×C8—112no—
438C2×C8—221no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—222no—
442C2×C8—222no—
443C2×C8—221no—
444C2×C8—222no—
445C2×C8—221no—
446C2×C8#434312yes—
447C4⋊C4—224no—
448C4⋊C4—224no—
449C4⋊C4—222no—
450C4⋊C4—224no—
451C4⋊C4(C2×D11)⋊C414yes—
452C4⋊C4(C2×D11)⋊C418yes—
453C22⋊C4—224no—
454C22⋊C4—224no—
455C22⋊C4—224no—
456C22⋊C4—224no—
457C22⋊C4—224no—
458C42—222no—
459C42—222no—
460C42—221no—
461C42—221no—
462C42C2×D4412yes—
463C42C2×D4414yes—
464C42C2×C22⋊D1112yes—
465C42C2×C22⋊D1114yes—
466C11#2253111yescharacteristic, complemented, Sylow
467C23—112no—
468C23—221no—
469C23—221no—
470C23—221no—
471C23—221no—
472C23—221no—
473C23—221no—
474C23—222no—
475C23—222no—
476C23—222no—
477C23—222no—
478C23—222no—
479C23—222no—
480C23—222no—
481C23C22×C4×D1111yescharacteristic
482Q8—28no—
483D4—448no—
484D4—444no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—21no—
488C2×C4—22no—
489C2×C4—21no—
490C2×C4—22no—
491C2×C4—221no—
492C2×C4—221no—
493C2×C4—221no—
494C2×C4—221no—
495C2×C4—221no—
496C2×C4—221no—
497C2×C4—221no—
498C2×C4—222no—
499C2×C4—221no—
500C2×C4—222no—
501C2×C4—221no—
502C2×C4—222no—
503C2×C4—444no—
504C2×C4—444no—
505C2×C4—441no—
506C2×C4—442no—
507C2×C4—441no—
508C2×C4—442no—
509C2×C4—441no—
510C2×C4—442no—
511C2×C4—441no—
512C2×C4—442no—
513C2×C4#6696012yes—
514C2×C4#6696012yes—
515C2×C4C2×(C2×D11)⋊C412yes—
516C2×C4C2×(C2×D11)⋊C414yes—
517C2×C4C2×(C2×D11)⋊C414yes—
518C2×C4C2×(C2×D11)⋊C412yes—
519C2×C4C22×D4411yescharacteristic
520C2×C4C2×#434311yescharacteristic
521C2×C4#6704011yescharacteristic
522C2×C4#41×D1111yescharacteristic
523C2×C4#6704211yescharacteristic
524C2×C4C22×C22⋊D1111yescharacteristic
525C8—22no—
526C8—41no—
527C8—42no—
528C8—222no—
529C8—441no—
530C8—442no—
531C22—222no—
532C22—222no—
533C22—222no—
534C22—441no—
535C22—441no—
536C22—441no—
537C22—441no—
538C22—442no—
539C22—442no—
540C22—442no—
541C22—442no—
542C22—442no—
543C22—442no—
544C22—442no—
545C22C4×#434311yescharacteristic
546C22#1062310511yescharacteristic
547C22C2×#6696011yescharacteristic
548C22C2×#6696011yescharacteristic
549C22D11×#13111yescharacteristic
550C22#1062328111yescharacteristic
551C22C22×(C2×D11)⋊C411yescharacteristic
552C4—24no—
553C4—22no—
554C4—24no—
555C4—441no—
556C4—441no—
557C4—441no—
558C4—442no—
559C4#1062274214yes—
560C4#1062310711yescharacteristic
561C4#1062310811yescharacteristic
562C4#1062334811yescharacteristic
563C4#1062336511yescharacteristic
564C2—442no—
565C2—882no—
566C2#1307145411yescharacteristic
567C2C2×#1062274211yescharacteristic
568C2#1307706311yescharacteristic
569C2#1307759011yescharacteristic
570C2#1307762211yescharacteristic
571C2#1307776811yescharacteristic
572C2#1307777911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC2×C11×#446C2
prime radicalC2×#66948C4
cosocleC22×C4×C11C24
hypercenterC2×#446D11
hypocenterC11#22531
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. C2×Q8×C11⋊C8C2semidirect
3. #13069414C2semidirect
4. #13069410C2semidirect
5. #13069409C2semidirect
6. #13069409C2semidirect
7. #13068597C2semidirect
8. #13068593C2semidirect
9. #13068385C2semidirect
10. C4×(C2×D11)⋊C8C2semidirect
11. C2×C11×#446C2semidirect
182. C2×#446D11semidirect
466. C11#22531semidirect

Maximal subgroups

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

subgroupindex
C2×#106231112
C2×Q8×C11⋊C82
#130694142
#130694102
#130694092
#130685972
#130685932
#130683852
C4×(C2×D11)⋊C82
C2×C11×#4462
#2253111