Finite Group Databasebeta

← #14753587

Subgroups — #14753587

Order 2816.

1374 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×#10623358C211yesmaximal, characteristic
2C2×#10622847C211yesmaximal, characteristic
3#13068708C212yesmaximal, complemented
4#13068708C212yesmaximal, complemented
5#13068704C212yesmaximal, complemented
6#13068700C212yesmaximal, complemented
7#13068337C211yesmaximal, characteristic, complemented
8#13068335C211yesmaximal, characteristic, complemented
9#13068332C211yesmaximal, characteristic, complemented
10C2×#10622167C211yesmaximal, characteristic, complemented
11C11×#2311C211yesmaximal, characteristic
12C22×C11×#41C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15#10623358—24no—
16#10623358C418yescomplemented
17C2×Q8×Dic11—21no—
18C2×D4×Dic11—22no—
19C2×D4×Dic11—21no—
20C2×#66979C2211yescharacteristic
21C2×#66979C2212yes—
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4⋊Dic11C2212yes—
24C22×#4318C2211yescharacteristic
25C23×C11⋊C8C2211yescharacteristic
26C11×#391—21no—
27C11×#390—21no—
28C11×#386—22no—
29C11×#380C2212yes—
30C11×#380C2212yes—
31#10622847—24no—
32C2×C22⋊(C11⋊C8)C2212yes—
33C2×C22⋊(C11⋊C8)C2212yes—
34#10622167C2212yes—
35#10622167C2212yes—
36#10622167C2211yescharacteristic
37#10622167C2211yescharacteristic
38#10622167C2211yescharacteristic
39#10622167C2211yescharacteristic
40#10622167C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41C2×C414yes—
49C2×C11×#41D414yes—
50C22×Q8×C11D411yescharacteristic
51C22×D4×C11D412yes—
52C22×D4×C11D411yescharacteristic
53C23×C4×C11—21no—
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C23×Dic11—21no—
57C23×Dic11—22no—
58C11×#117—22no—
59C11×#117—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C42×C11—21no—
70C2×C22⋊Dic11—21no—
71C2×C22⋊Dic11—22no—
72Q8×Dic11—28no—
73D4×Dic11—28no—
74D4×Dic11—216no—
75#66979—22no—
76#66979—24no—
77#66979C2×C414yes—
78#66979C2×C418yescomplemented
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11—24no—
83C2×C4⋊Dic11C2×C414yes—
84C2×C4⋊Dic11C2×C418yescomplemented
85C2×C4⋊Dic11C2312yes—
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4×Dic11—21no—
89C2×C4×Dic11—22no—
90C2×#4318—22no—
91C2×#4318—22no—
92C2×#4318—22no—
93C22×C11⋊C8—22no—
94C22×C11⋊C8—22no—
95C22×C11⋊C8—22no—
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2312yes—
99C11×#95—22no—
100C11×#95—22no—
101C22⋊(C11⋊C8)—24no—
102C22⋊(C11⋊C8)—24no—
103#20703—111nomaximal, Sylow
104C24×C11C2×D412yes—
105C24×C11C2×D411yescharacteristic
106C11×#41—28no—
107C11×#41—28no—
108C11×#41—28no—
109C11×#41—28no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11C22⋊C414yes—
113C2×D4×C11—24no—
114C2×D4×C11—24no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11C22⋊C418yes—
118C2×D4×C11C22⋊C414yes—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—22no—
126C22×C4×C11—42no—
127C22×C4×C11—81no—
128C22×C4×C11—81no—
129C22×C4×C11C22×C414yes—
130C22×C4×C11C22×C412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D414yes—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D412yes—
135C22×C4×C11#4112yes—
136C22×C4×C11#4112yes—
137C22×C4×C11#4112yes—
138C22×C4×C11#4112yes—
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—24no—
141C22×Dic11—28no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—22no—
145C22×Dic11—81no—
146C22×Dic11—81no—
147C22×Dic11—82no—
148C22×Dic11—82no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—42no—
156C11×C22⋊C4—42no—
157C11×C22⋊C4—82no—
158C11×C22⋊C4—82no—
159C42×C11—42no—
160C22⋊Dic11—24no—
161C22⋊Dic11—28no—
162C4⋊Dic11—24no—
163C4⋊Dic11—28no—
164C4⋊Dic11—21no—
165C4⋊Dic11—22no—
166C4⋊Dic11—21no—
167C4⋊Dic11C22×C414yes—
168C4⋊Dic11C22×C412yes—
169C4⋊Dic11C22×C412yes—
170C4×Dic11—24no—
171C4×Dic11—28no—
172#4318—44no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—21no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—44no—
183C2×#520—111no—
184C2×#408—111no—
185#2311D1111yescharacteristic
186#1825—112no—
187#1825—112no—
188#1824—112no—
189#1823—112no—
190#1736—111no—
191#1736—111no—
192#1735—111no—
193C2×#340—111no—
194C23×C11—21no—
195C23×C11—21no—
196C23×C11—21no—
197C23×C11—21no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—22no—
204C23×C11C2×C22⋊C414yes—
205C23×C11C2×C22⋊C412yes—
206C23×C11#12312yes—
207C23×C11#12312yes—
208C23×C11C22×D411yescharacteristic
209Q8×C11—28no—
210D4×C11—216no—
211D4×C11—28no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—42no—
221C2×C4×C11—41no—
222C2×C4×C11—42no—
223C2×C4×C11—41no—
224C2×C4×C11—42no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—84no—
228C2×C4×C11C2×C22⋊C414yes—
229C2×C4×C11C2×C22⋊C412yes—
230C2×C4×C11#11714yes—
231C2×C4×C11#11714yes—
232C2×C4×C11#12314yes—
233C2×C4×C11#12314yes—
234C2×C4×C11#12312yes—
235C2×C4×C11#12312yes—
236C2×C4×C11C23×C411yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—24no—
245C2×Dic11—42no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—42no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—84no—
252C2×Dic11—88no—
253C11⋊C8—41no—
254C11⋊C8—41no—
255C11⋊C8—42no—
256C22×#41C2×D1111yescharacteristic
257C22×M16—111no—
258C23×C8—111no—
259#520—118no—
260#520—224no—
261C2×C4×Q8—221no—
262C2×C4×D4—222no—
263C2×C4×D4—221no—
264C2×#117—112no—
265C2×#117—111no—
266C2×#117C2×D1111yescharacteristic
267C22×C4⋊C4—112no—
268C22×C4⋊C4—111no—
269C22×C4⋊C4C2×D1111yescharacteristic
270#408—224no—
271C2×C22⋊C8—112no—
272C2×C22⋊C8—112no—
273#391—21no—
274#390—21no—
275#386—22no—
276#380C2×D1112yes—
277#380C2×D1112yes—
278#340—111no—
279#340—112no—
280#340—112no—
281#340—112no—
282#340—111no—
283#340—112no—
284#340—112no—
285#340—111no—
286#340—111no—
287#340—112no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—22no—
291C22×C11—22no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—24no—
295C22×C11—24no—
296C22×C11—24no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11#38114yes—
302C22×C11C22×C22⋊C411yescharacteristic
303C22×C11C2×#12311yescharacteristic
304C22×C11C2×#12311yescharacteristic
305C22×C11#57611yescharacteristic
306C22×C11#57711yescharacteristic
307C22×C11#57711yescharacteristic
308C22×C11#57811yescharacteristic
309C4×C11—24no—
310C4×C11—82no—
311C4×C11—81no—
312C4×C11—81no—
313C4×C11#38114yes—
314C4×C11C2×#11711yescharacteristic
315C4×C11C2×#11711yescharacteristic
316C4×C11C2×#12311yescharacteristic
317C4×C11C2×#12311yescharacteristic
318Dic11—42no—
319Dic11—44no—
320Dic11—42no—
321C2×#41—22no—
322C2×#41—22no—
323C2×#41—22no—
324C2×#41—22no—
325C2×#41C4×D1114yes—
326C2×#41D4414yes—
327C22×Q8C22⋊D1111yescharacteristic
328C22×D4C22⋊D1112yes—
329C22×D4C22⋊D1111yescharacteristic
330C23×C4—21no—
331C23×C4—222no—
332C23×C4—221no—
333C23×C4C22×D1112yes—
334C23×C4C22×D1111yescharacteristic
335C2×M16—222no—
336C2×M16—222no—
337C2×M16—222no—
338C22×C8—111no—
339C22×C8—111no—
340C22×C8—112no—
341C22×C8—222no—
342C22×C8—222no—
343C22×C8—222no—
344C4×Q8—228no—
345C4×D4—2216no—
346C4×D4—228no—
347#117—22no—
348#117—22no—
349#117—114no—
350#117—118no—
351#117—224no—
352#117—222no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—114no—
357C2×C4⋊C4—118no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—112no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—224no—
362C2×C4⋊C4—222no—
363C2×C4⋊C4—222no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4C22×D1112yes—
366C2×C4⋊C4C22×D1111yescharacteristic
367C2×C4⋊C4C22×D1111yescharacteristic
368C2×C22⋊C4—21no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—222no—
372C2×C22⋊C4—221no—
373C2×C42—21no—
374C2×C42—222no—
375C2×C42—221no—
376C22⋊C8—224no—
377C22⋊C8—224no—
378#95—22no—
379#95—22no—
380C2×C11—24no—
381C2×C11—44no—
382C2×C11C2×#38111yescharacteristic
383C2×C11#289711yescharacteristic
384C2×C11#289811yescharacteristic
385C2×C11#309611yescharacteristic
386C2×C11#309711yescharacteristic
387C2×C11#309811yescharacteristic
388C2×C11#309911yescharacteristic
389C24C2×C22⋊D1112yes—
390C24C2×C22⋊D1111yescharacteristic
391#41—28no—
392#41—28no—
393#41—28no—
394#41—28no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8(C2×D11)⋊C414yes—
398C2×D4—24no—
399C2×D4—24no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4(C2×D11)⋊C418yes—
403C2×D4(C2×D11)⋊C414yes—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—42no—
412C22×C4—81no—
413C22×C4—81no—
414C22×C4—221no—
415C22×C4—222no—
416C22×C4—221no—
417C22×C4—228no—
418C22×C4—224no—
419C22×C4—881no—
420C22×C4—882no—
421C22×C4—881no—
422C22×C4—882no—
423C22×C4C2×C4×D1114yes—
424C22×C4C2×C4×D1112yes—
425C22×C4C2×D4414yes—
426C22×C4C2×D4412yes—
427C22×C4#434112yes—
428C22×C4#434112yes—
429C22×C4#434112yes—
430C22×C4#434112yes—
431C22×C4C2×C22⋊D1112yes—
432C22×C4C2×C22⋊D1111yescharacteristic
433C22×C4C23×D1111yescharacteristic
434M16—444no—
435C2×C8—221no—
436C2×C8—221no—
437C2×C8—222no—
438C2×C8—221no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—222no—
443C2×C8—222no—
444C2×C8—444no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—42no—
452C4⋊C4—114no—
453C4⋊C4—112no—
454C4⋊C4—112no—
455C4⋊C4—228no—
456C4⋊C4—224no—
457C4⋊C4—221no—
458C4⋊C4—222no—
459C4⋊C4—221no—
460C22⋊C4—42no—
461C22⋊C4—82no—
462C22⋊C4—82no—
463C22⋊C4—228no—
464C22⋊C4—224no—
465C42—42no—
466C42—228no—
467C42—224no—
468C11#2070311yescharacteristic, complemented, Sylow
469C23—21no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23C2×(C2×D11)⋊C414yes—
480C23C2×(C2×D11)⋊C412yes—
481C23#6698812yes—
482C23#6698812yes—
483C23C22×C22⋊D1111yescharacteristic
484Q8—28no—
485D4—216no—
486D4—28no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—84no—
503C2×C4—222no—
504C2×C4—224no—
505C2×C4—222no—
506C2×C4—442no—
507C2×C4—441no—
508C2×C4—441no—
509C2×C4—442no—
510C2×C4—441no—
511C2×C4—441no—
512C2×C4—884no—
513C2×C4—888no—
514C2×C4#6693014yes—
515C2×C4#6693014yes—
516C2×C4#6693914yes—
517C2×C4#6693914yes—
518C2×C4C2×(C2×D11)⋊C414yes—
519C2×C4C2×(C2×D11)⋊C412yes—
520C2×C4#6698812yes—
521C2×C4#6698812yes—
522C2×C4C22×C4×D1111yescharacteristic
523C2×C4C22×D4411yescharacteristic
524C2×C4C2×#434111yescharacteristic
525C2×C4C2×#434111yescharacteristic
526C2×C4C2×#434111yescharacteristic
527C2×C4C2×#434111yescharacteristic
528C8—441no—
529C8—441no—
530C8—442no—
531C22—22no—
532C22—22no—
533C22—22no—
534C22—22no—
535C22—22no—
536C22—22no—
537C22—24no—
538C22—24no—
539C22—24no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—42no—
544C22#1062255614yes—
545C22C22×(C2×D11)⋊C411yescharacteristic
546C22C2×#6698811yescharacteristic
547C22C2×#6698811yescharacteristic
548C22#1062336611yescharacteristic
549C22#1062336711yescharacteristic
550C22#1062336811yescharacteristic
551C22#1062336911yescharacteristic
552C4—24no—
553C4—82no—
554C4—81no—
555C4—81no—
556C4—444no—
557C4—442no—
558C4—442no—
559C4#1062255614yes—
560C4C2×#6693011yescharacteristic
561C4C2×#6693011yescharacteristic
562C4C2×#6693911yescharacteristic
563C4C2×#6693911yescharacteristic
564C2—24no—
565C2—44no—
566C2C2×#1062255611yescharacteristic
567C2#1307713911yescharacteristic
568C2#1307714611yescharacteristic
569C2#1307856811yescharacteristic
570C2#1307857911yescharacteristic
571C2#1307859011yescharacteristic
572C2#1307860111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2311C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenter#2311D11
hypocenterC11#20703
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41 ◁ #2311

Complements

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

NH ≅ G/Ntype
3. #13068708C2semidirect
4. #13068708C2semidirect
5. #13068704C2semidirect
6. #13068700C2semidirect
7. #13068337C2semidirect
8. #13068335C2semidirect
9. #13068332C2semidirect
10. C2×#10622167C2semidirect
16. #10623358C4semidirect
78. #66979C2×C4semidirect
84. C2×C4⋊Dic11C2×C4semidirect
468. C11#20703semidirect

Maximal subgroups

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

subgroupindex
C2×#106233582
C2×#106228472
#130687082
#130687042
#130687002
#130683372
#130683352
#130683322
C2×#106221672
C11×#23112
#2070311