Finite Group Databasebeta

← #14646524

Subgroups — #14646524

Order 2816.

742 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
1#121×Dic11C211yesmaximal, characteristic
2#13068594C211yesmaximal, characteristic, complemented
3C2×#10622175C211yesmaximal, characteristic
4Dic11⋊#95C211yesmaximal, characteristic, complemented
5#13066496C211yesmaximal, characteristic, complemented
6#13066495C211yesmaximal, characteristic, complemented
7C2×C11×#327C211yesmaximal, characteristic
8C2×C11×#121C2211yescharacteristic
9C2×D4×Dic11—21no—
10C2×D4×Dic11C411yescharacteristic, complemented
11C22×Dic11⋊C4—21no—
12C22×C4×Dic11C2211yescharacteristic
13C2×C11×C22⋊C8C2211yescharacteristic
14C2×C11×#95C2211yescharacteristic
15#10622834C411yescharacteristic, complemented
16#10622833—21no—
17#10622825C2211yescharacteristic
18C2×C11⋊#95—21no—
19C2×C11⋊#95C2211yescharacteristic
20C2×C22⋊(C11⋊C8)C2211yescharacteristic
21C2×Dic11⋊C8—21no—
22#10622598C411yescharacteristic, complemented
23C4⋊C4×Dic11C411yescharacteristic, complemented
24#10622564—21no—
25C22⋊C4×Dic11—21no—
26C11×#327—22no—
27#10622188—21no—
28#10622175—22no—
29C22×D4×C11—21no—
30C22×D4×C11C2×C411yescharacteristic
31C23×C4×C11—21no—
32C23×C4×C11C2311yescharacteristic
33C23×Dic11—21no—
34C23×Dic11—21no—
35C23×Dic11D411yescharacteristic
36C23×Dic11D411yescharacteristic
37C22×C8×C11—21no—
38C11×#121—21no—
39C11×#121—21no—
40C11×#121D412yes—
41C11×#121Q812yes—
42C2×C11×C4⋊C4C2×C411yescharacteristic
43C2×C11×C22⋊C4—21no—
44C2×C22⋊Dic11—21no—
45C2×C22⋊Dic11—21no—
46C2×C22⋊Dic11—21no—
47C2×C22⋊Dic11—21no—
48D4×Dic11—42no—
49D4×Dic11—42no—
50D4×Dic11—42no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11C2×C411yescharacteristic
53C2×C4⋊Dic11C2×C411yescharacteristic
54C2×Dic11⋊C4—24no—
55C2×Dic11⋊C4—42no—
56C2×Dic11⋊C4—42no—
57C2×C4×Dic11—21no—
58C2×C4×Dic11—42no—
59C2×C4×Dic11C2×C411yescharacteristic
60C2×C4×Dic11C2×C411yescharacteristic
61C2×C4×Dic11D411yescharacteristic
62C2×C4×Dic11D411yescharacteristic
63C22×C11⋊C8—21no—
64C11×C22⋊C8—21no—
65C11×C22⋊C8—21no—
66C11×#95—21no—
67C11×#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C11⋊#95—21no—
73C11⋊#95—42no—
74C22⋊(C11⋊C8)—21no—
75C22⋊(C11⋊C8)—21no—
76Dic11⋊C8—42no—
77#8577—111nomaximal, Sylow
78C24×C11—21no—
79C24×C11C2×D411yescharacteristic
80C2×D4×C11—22no—
81C2×D4×C11—22no—
82C2×D4×C11—21no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11C4⋊C412yescomplemented
90C22×C4×C11—21no—
91C22×C4×C11—22no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11C22×C411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×Q811yescharacteristic
104C22×C4×C11#4111yescharacteristic
105C22×C4×C11#4111yescharacteristic
106C22×Dic11—22no—
107C22×Dic11—22no—
108C22×Dic11—22no—
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—41no—
114C22×Dic11—41no—
115C22×Dic11—41no—
116C22×Dic11—41no—
117C22×Dic11—41no—
118C22×Dic11—42no—
119C22×Dic11—42no—
120C22×Dic11—42no—
121C22×Dic11—41no—
122C22×Dic11—41no—
123C22×Dic11—41no—
124C22×Dic11C22⋊C411yescharacteristic
125C22×Dic11C22⋊C411yescharacteristic
126C22×Dic11C22⋊C411yescharacteristic
127C22×Dic11C22⋊C411yescharacteristic
128C22×Dic11D812yes—
129C22×Dic11SD1612yes—
130C2×C8×C11—41no—
131C2×C8×C11—41no—
132C2×C8×C11—41no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4C4⋊C412yescomplemented
135C11×C22⋊C4—22no—
136C11×C22⋊C4—22no—
137C22⋊Dic11—42no—
138C22⋊Dic11—42no—
139C22⋊Dic11—42no—
140C22⋊Dic11—41no—
141C22⋊Dic11—41no—
142C4⋊Dic11—41no—
143C4⋊Dic11—41no—
144C4⋊Dic11—42no—
145Dic11⋊C4—48no—
146C4×Dic11—22no—
147C4×Dic11—22no—
148C4×Dic11—41no—
149C4×Dic11—41no—
150C4×Dic11—42no—
151C2×C11⋊C8—41no—
152C2×C11⋊C8—41no—
153C2×C11⋊C8—41no—
154C4×#121—111no—
155#1797—111no—
156C2×#327—111no—
157C2×#327D1111yescharacteristic
158C4⋊#95—111no—
159#1294—111no—
160#1294—111no—
161C23×C11—21no—
162C23×C11—21no—
163C23×C11—21no—
164C23×C11—21no—
165C23×C11—22no—
166C23×C11—41no—
167C23×C11—41no—
168C23×C11—41no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11—41no—
172C23×C11C2×C22⋊C411yescharacteristic
173C23×C11#12111yescharacteristic
174C23×C11C22⋊Q811yescharacteristic
175C23×C11C2×D811yescharacteristic
176C23×C11C2×SD1611yescharacteristic
177C23×C11AGL(1,ℤ/8)11yescharacteristic
178C23×C11#13711yescharacteristic
179D4×C11—42no—
180D4×C11—42no—
181D4×C11—42no—
182D4×C11—42no—
183D4×C11—42no—
184D4×C11—42no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—22no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—81no—
200C2×C4×C11—81no—
201C2×C4×C11—81no—
202C2×C4×C11—81no—
203C2×C4×C11C2×C4⋊C411yescharacteristic
204C2×C4×C11#11711yescharacteristic
205C2×C4×C11#12111yescharacteristic
206C2×C4×C11C22⋊Q811yescharacteristic
207C2×Dic11—24no—
208C2×Dic11—24no—
209C2×Dic11—21no—
210C2×Dic11—21no—
211C2×Dic11—21no—
212C2×Dic11—21no—
213C2×Dic11—21no—
214C2×Dic11—21no—
215C2×Dic11—21no—
216C2×Dic11—21no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—84no—
229C2×Dic11—81no—
230C2×Dic11—81no—
231C2×Dic11—81no—
232C2×Dic11—81no—
233C2×Dic11#9912yes—
234C2×Dic11#10212yes—
235C2×Dic11#10212yes—
236C2×Dic11#10412yes—
237C8×C11—81no—
238C11⋊C8—81no—
239C2×#121C2×D1111yescharacteristic
240C2×C4×D4—111no—
241C2×C4×D4—221no—
242C22×C4⋊C4—221no—
243C22×C42—111no—
244C2×C4⋊C8—221no—
245C2×C22⋊C8—111no—
246C2×C22⋊C8C2×D1111yescharacteristic
247#390—111no—
248#389—111no—
249#388—221no—
250#386—221no—
251#380—111no—
252C4×C4⋊C4—111no—
253C4×C22⋊C4—221no—
254C2×#95—111no—
255C2×#95—221no—
256C2×#95C2×D1111yescharacteristic
257#336—221no—
258#327—22no—
259#327—222no—
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—21no—
271C22×C11—21no—
272C22×C11—42no—
273C22×C11—42no—
274C22×C11—42no—
275C22×C11—81no—
276C22×C11—81no—
277C22×C11—81no—
278C22×C11—81no—
279C22×C11#38011yescharacteristic
280C22×C11C2×#9911yescharacteristic
281C22×C11#41011yescharacteristic
282C22×C11C2×#10211yescharacteristic
283C22×C11#41711yescharacteristic
284C22×C11C2×#10411yescharacteristic
285C22×C11#42111yescharacteristic
286C22×C11#45911yescharacteristic
287C22×C11#46111yescharacteristic
288C22×C11#47411yescharacteristic
289C22×C11#47611yescharacteristic
290C4×C11—21no—
291C4×C11—21no—
292C4×C11—21no—
293C4×C11—21no—
294C4×C11—42no—
295C4×C11—82no—
296Dic11—22no—
297Dic11—22no—
298Dic11—22no—
299Dic11—22no—
300Dic11—82no—
301Dic11—81no—
302Dic11—81no—
303C22×D4—21no—
304C22×D4C4×D1111yescharacteristic
305C23×C4—21no—
306C23×C4—111no—
307C23×C4—111no—
308C23×C4—221no—
309C23×C4—221no—
310C23×C4C22×D1111yescharacteristic
311C22×C8—21no—
312C22×C8—221no—
313#121—21no—
314#121—21no—
315#121Dic2212yes—
316#121C22⋊D1112yes—
317C4×D4—442no—
318C4×D4—442no—
319C4×D4—442no—
320C2×C4⋊C4—111no—
321C2×C4⋊C4—111no—
322C2×C4⋊C4—221no—
323C2×C4⋊C4—224no—
324C2×C4⋊C4—442no—
325C2×C4⋊C4—442no—
326C2×C4⋊C4C4×D1111yescharacteristic
327C2×C22⋊C4—21no—
328C2×C22⋊C4—221no—
329C2×C22⋊C4—221no—
330C2×C22⋊C4—221no—
331C2×C22⋊C4—221no—
332C2×C42—111no—
333C2×C42—111no—
334C2×C42—111no—
335C2×C42—111no—
336C2×C42—221no—
337C2×C42—442no—
338C4⋊C8—442no—
339C22⋊C8—21no—
340C22⋊C8—21no—
341C22⋊C8—221no—
342C22⋊C8—221no—
343#95—21no—
344#95—21no—
345#95—221no—
346#95—221no—
347#95—221no—
348#95—221no—
349#95—221no—
350#95—442no—
351C2×C11—21no—
352C2×C11—21no—
353C2×C11—21no—
354C2×C11—21no—
355C2×C11—82no—
356C2×C11#150211yescharacteristic
357C2×C11#150411yescharacteristic
358C2×C11#151211yescharacteristic
359C2×C11#151911yescharacteristic
360C2×C11#179911yescharacteristic
361C2×C11#180211yescharacteristic
362C2×C11#180611yescharacteristic
363C24—21no—
364C24D4×D1111yescharacteristic
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—21no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4Dic11⋊C412yescomplemented
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—111no—
386C22×C4—111no—
387C22×C4—111no—
388C22×C4—111no—
389C22×C4—112no—
390C22×C4—112no—
391C22×C4—222no—
392C22×C4—222no—
393C22×C4—221no—
394C22×C4—221no—
395C22×C4—222no—
396C22×C4—221no—
397C22×C4—221no—
398C22×C4—442no—
399C22×C4—441no—
400C22×C4—441no—
401C22×C4—442no—
402C22×C4—442no—
403C22×C4—441no—
404C22×C4—441no—
405C22×C4—441no—
406C22×C4—441no—
407C22×C4—441no—
408C22×C4—441no—
409C22×C4C2×Dic2211yescharacteristic
410C22×C4C2×C4×D1111yescharacteristic
411C22×C4D4×D1111yescharacteristic
412C22×C4#434111yescharacteristic
413C22×C4#434111yescharacteristic
414C22×C4C2×C22⋊D1111yescharacteristic
415C2×C8—41no—
416C2×C8—41no—
417C2×C8—41no—
418C2×C8—441no—
419C2×C8—441no—
420C2×C8—441no—
421C4⋊C4—21no—
422C4⋊C4—441no—
423C4⋊C4—441no—
424C4⋊C4—442no—
425C4⋊C4—448no—
426C4⋊C4Dic11⋊C412yescomplemented
427C22⋊C4—22no—
428C22⋊C4—22no—
429C22⋊C4—442no—
430C22⋊C4—442no—
431C22⋊C4—442no—
432C22⋊C4—441no—
433C22⋊C4—441no—
434C42—222no—
435C42—222no—
436C42—441no—
437C42—441no—
438C42—442no—
439C11#857711yescharacteristic, complemented, Sylow
440C23—21no—
441C23—21no—
442C23—21no—
443C23—21no—
444C23—22no—
445C23—41no—
446C23—41no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23#6693111yescharacteristic
452C23C22⋊C4×D1111yescharacteristic
453C23D8×D1111yescharacteristic
454C23#6696411yescharacteristic
455C23SD16×D1111yescharacteristic
456C23#6696811yescharacteristic
457C23#6699211yescharacteristic
458D4—42no—
459D4—42no—
460D4—42no—
461D4—42no—
462D4—42no—
463D4—42no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—22no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—81no—
479C2×C4—81no—
480C2×C4—81no—
481C2×C4—81no—
482C2×C4—112no—
483C2×C4—112no—
484C2×C4—112no—
485C2×C4—112no—
486C2×C4—224no—
487C2×C4—224no—
488C2×C4—221no—
489C2×C4—221no—
490C2×C4—221no—
491C2×C4—221no—
492C2×C4—221no—
493C2×C4—221no—
494C2×C4—221no—
495C2×C4—221no—
496C2×C4—442no—
497C2×C4—442no—
498C2×C4—442no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—441no—
502C2×C4—441no—
503C2×C4—441no—
504C2×C4—441no—
505C2×C4—441no—
506C2×C4—441no—
507C2×C4—884no—
508C2×C4—881no—
509C2×C4—881no—
510C2×C4—881no—
511C2×C4—881no—
512C2×C4#6693011yescharacteristic
513C2×C4#6693111yescharacteristic
514C2×C4C2×Dic11⋊C411yescharacteristic
515C2×C4#6699211yescharacteristic
516C8—81no—
517C8—881no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—81no—
534C22—81no—
535C22—81no—
536C22—81no—
537C22#1062235311yescharacteristic
538C22D11×#9911yescharacteristic
539C22#1062237211yescharacteristic
540C22#1062237411yescharacteristic
541C22D11×#10211yescharacteristic
542C22#1062238411yescharacteristic
543C22D11×#10411yescharacteristic
544C22#1062243411yescharacteristic
545C22#1062255511yescharacteristic
546C22#1062276311yescharacteristic
547C22#1062277511yescharacteristic
548C4—21no—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—42no—
553C4—82no—
554C4—222no—
555C4—222no—
556C4—222no—
557C4—222no—
558C4—882no—
559C4—881no—
560C4—881no—
561C2—21no—
562C2—21no—
563C2—21no—
564C2—21no—
565C2—82no—
566C2#1306710911yescharacteristic
567C2#1306711711yescharacteristic
568C2#1306715111yescharacteristic
569C2#1306718211yescharacteristic
570C2#1306860211yescharacteristic
571C2#1306861411yescharacteristic
572C2#1306863411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#327C2
socleC23×C11C2×C22⋊C4
prime radicalC2×C11×#121C22
cosocleC23×C4×C11C23
hypercenterC2×#327D11
hypocenterC11#8577
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. #13068594C2semidirect
4. Dic11⋊#95C2semidirect
5. #13066496C2semidirect
6. #13066495C2semidirect
10. C2×D4×Dic11C4semidirect
15. #10622834C4semidirect
22. #10622598C4semidirect
23. C4⋊C4×Dic11C4semidirect
89. C2×D4×C11C4⋊C4semidirect
134. C11×C4⋊C4C4⋊C4semidirect
374. C2×D4Dic11⋊C4semidirect
426. C4⋊C4Dic11⋊C4semidirect
439. C11#8577semidirect

Maximal subgroups

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

subgroupindex
#121×Dic112
#130685942
C2×#106221752
Dic11⋊#952
#130664962
#130664952
C2×C11×#3272
#857711