Finite Group Databasebeta

← #14643435

Subgroups — #14643435

Order 2816.

954 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622339C211yesmaximal, characteristic
2C2×D11×C22⋊C8C211yesmaximal, characteristic
3#13070997C211yesmaximal, characteristic
4#13066464C211yesmaximal, characteristic, complemented
5#13066463C211yesmaximal, characteristic, complemented
6#13066462C211yesmaximal, characteristic, complemented
7C11×#1282C211yesmaximal, characteristic, complemented
8C23×C4×D11C2211yescharacteristic
9C22×#4313—21no—
10C22×C8×D11C412yescomplemented
11C2×#66925—21no—
12C2×C11×C22⋊C8C2211yescharacteristic
13C2×C11×C22⋊C8C2211yescharacteristic
14C4×C11×C22⋊C4C2211yescharacteristic
15C4×C22⋊Dic11C2211yescharacteristic
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17C2×C22⋊(C11⋊C8)C2211yescharacteristic
18C2×(C2×D11)⋊C8—21no—
19C2×(C2×D11)⋊C8C412yescomplemented
20#10622568C412yes—
21#10622555C412yes—
22C4×(C2×D11)⋊C4—21no—
23#10622339—21no—
24#10622339—21no—
25#10622339C412yescomplemented
26#10622339C412yescomplemented
27D11×C22⋊C8—21no—
28D11×C22⋊C8—21no—
29D11×C22⋊C8—21no—
30D11×C22⋊C8—21no—
31#10622280—21no—
32#10622277—21no—
33C24×D11C2×C411yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C23×Dic11C2×C411yescharacteristic
36C22×C4×D11—44no—
37C22×C4×D11C2×C411yescharacteristic
38C22×C4×D11C2×C411yescharacteristic
39C22×C4×D11C2×C411yescharacteristic
40C22×C4×D11C2×C411yescharacteristic
41C22×C4×D11D411yescharacteristic
42C22×C4×D11D411yescharacteristic
43C22×C4×D11D411yescharacteristic
44C22×C4×D11D411yescharacteristic
45C22×C4×D11D411yescharacteristic
46C22×C4×D11D411yescharacteristic
47C22×C4×D11Q811yescharacteristic
48C22×C4×D11Q811yescharacteristic
49C22×C8×C11—21no—
50C22×C8×C11C2×C412yes—
51C2×C11×C22⋊C4C2×C412yes—
52C2×C42×C11—21no—
53C2×C22⋊Dic11C2×C412yes—
54C2×(C2×D11)⋊C4—22no—
55C2×(C2×D11)⋊C4—22no—
56C2×Dic11⋊C4—22no—
57C2×C4×Dic11—21no—
58C22×C11⋊C8—21no—
59C22×C11⋊C8C2×C412yes—
60C2×#4313—22no—
61C2×#4313—22no—
62C2×#4313—44no—
63C2×C8×D11—22no—
64C2×C8×D11—22no—
65C2×C8×D11—44no—
66#66925—44no—
67C11×C22⋊C8—21no—
68C11×C22⋊C8—21no—
69C11×C22⋊C8—21no—
70C11×C22⋊C8C2×C412yes—
71C11×#95—21no—
72C11⋊#95—21no—
73C11⋊#95—22no—
74C22⋊(C11⋊C8)—21no—
75C22⋊(C11⋊C8)—21no—
76C22⋊(C11⋊C8)—21no—
77C22⋊(C11⋊C8)C2×C412yes—
78(C2×D11)⋊C8—22no—
79(C2×D11)⋊C8—22no—
80(C2×D11)⋊C8—22no—
81(C2×D11)⋊C8—22no—
82#7927—111nomaximal, Sylow
83C24×C11C22×C411yescharacteristic
84C23×D11—22no—
85C23×D11—22no—
86C23×D11—42no—
87C23×D11—42no—
88C23×D11C4211yescharacteristic
89C23×D11C4211yescharacteristic
90C23×D11C22⋊C411yescharacteristic
91C23×D11C22⋊C411yescharacteristic
92C23×D11C4⋊C411yescharacteristic
93C23×D11C4⋊C411yescharacteristic
94C22×C4×C11—22no—
95C22×C4×C11—42no—
96C22×C4×C11C22×C411yescharacteristic
97C22×C4×C11C22×C411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×Q811yescharacteristic
102C22×Dic11—22no—
103C22×Dic11—42no—
104C22×Dic11C4211yescharacteristic
105C22×Dic11C4211yescharacteristic
106C22×Dic11C22⋊C411yescharacteristic
107C22×Dic11C22⋊C411yescharacteristic
108C22×Dic11C4⋊C411yescharacteristic
109C22×Dic11C4⋊C411yescharacteristic
110C2×C4×D11—24no—
111C2×C4×D11—24no—
112C2×C4×D11—24no—
113C2×C4×D11—42no—
114C2×C4×D11—42no—
115C2×C4×D11—42no—
116C2×C4×D11—42no—
117C2×C4×D11—42no—
118C2×C4×D11—42no—
119C2×C4×D11—42no—
120C2×C4×D11—42no—
121C2×C4×D11—42no—
122C2×C4×D11C22⋊C411yescharacteristic
123C2×C4×D11C22⋊C411yescharacteristic
124C2×C4×D11C22⋊C411yescharacteristic
125C2×C4×D11C22⋊C411yescharacteristic
126C2×C4×D11C22⋊C411yescharacteristic
127C2×C4×D11C22⋊C411yescharacteristic
128C2×C4×D11C22⋊C411yescharacteristic
129C2×C4×D11C22⋊C411yescharacteristic
130C2×C4×D11C4⋊C411yescharacteristic
131C2×C4×D11C4⋊C411yescharacteristic
132C2×C4×D11C4⋊C411yescharacteristic
133C2×C4×D11C4⋊C411yescharacteristic
134C2×C4×D11C4⋊C411yescharacteristic
135C2×C4×D11C4⋊C411yescharacteristic
136C2×C4×D11C4⋊C411yescharacteristic
137C2×C4×D11C4⋊C411yescharacteristic
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—42no—
141C2×C8×C11—42no—
142C11×C22⋊C4—22no—
143C11×C22⋊C4—22no—
144C42×C11—42no—
145C22⋊Dic11—22no—
146C22⋊Dic11—22no—
147(C2×D11)⋊C4—44no—
148(C2×D11)⋊C4—44no—
149Dic11⋊C4—44no—
150C4×Dic11—42no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—42no—
154C2×C11⋊C8—42no—
155#4313—44no—
156#4313—44no—
157C8×D11—44no—
158C8×D11—44no—
159C2×#407—111no—
160C22×C22⋊C8—111no—
161#2280—111no—
162#1282—111no—
163#1282—111no—
164#1282—111no—
165#1282D1111yescharacteristic, complemented
166C23×C11—41no—
167C23×C11—41no—
168C23×C11C2×C4211yescharacteristic
169C23×C11C2×C22⋊C411yescharacteristic
170C23×C11C2×C4⋊C411yescharacteristic
171C23×C11#13112yes—
172C23×C11#13112yes—
173C22×D11—21no—
174C22×D11—21no—
175C22×D11—22no—
176C22×D11—22no—
177C22×D11—21no—
178C22×D11—21no—
179C22×D11—22no—
180C22×D11—22no—
181C22×D11—22no—
182C22×D11—22no—
183C22×D11—22no—
184C22×D11—22no—
185C22×D11—22no—
186C22×D11—22no—
187C22×D11—41no—
188C22×D11—41no—
189C22×D11—41no—
190C22×D11—41no—
191C22×D11—41no—
192C22×D11—41no—
193C22×D11—48no—
194C22×D11—48no—
195C22×D11#9511yescharacteristic
196C22×D11#9511yescharacteristic
197C22×D11#9511yescharacteristic
198C22×D11#9511yescharacteristic
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11C2×C22⋊C411yescharacteristic
209C2×C4×C11C2×C22⋊C411yescharacteristic
210C2×C4×C11C2×C4⋊C411yescharacteristic
211C2×C4×C11C2×C4⋊C411yescharacteristic
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11#9511yescharacteristic
222C2×Dic11#9511yescharacteristic
223C2×Dic11#9511yescharacteristic
224C2×Dic11#9511yescharacteristic
225C4×D11—22no—
226C4×D11—22no—
227C4×D11—22no—
228C4×D11—22no—
229C4×D11—22no—
230C4×D11—22no—
231C4×D11—22no—
232C4×D11—22no—
233C4×D11—22no—
234C4×D11—41no—
235C4×D11—41no—
236C4×D11—41no—
237C4×D11—41no—
238C4×D11—41no—
239C4×D11—41no—
240C4×D11#9914yes—
241C8×C11—42no—
242C8×C11—42no—
243C11⋊C8—42no—
244C11⋊C8—42no—
245C24×C4—111no—
246C22×M16—221no—
247C23×C8—112no—
248C2×#117—221no—
249#407—112no—
250#407—112no—
251#407—221no—
252#407—221no—
253C2×C22⋊C8—111no—
254C2×C22⋊C8—111no—
255C2×C22⋊C8—112no—
256C2×C22⋊C8—221no—
257C2×C22⋊C8—221no—
258C2×C22⋊C8—221no—
259C2×C22⋊C8—221no—
260C2×C22⋊C8—221no—
261C2×C22⋊C8C2×D1111yescharacteristic
262C2×C22⋊C8C2×D1111yescharacteristic
263#381—221no—
264#380—112no—
265#380—221no—
266#379—112no—
267C4×C22⋊C4—111no—
268C4×C22⋊C4—221no—
269C4×C22⋊C4C2×D1111yescharacteristic
270C22×C11—21no—
271C22×C11—21no—
272C22×C11—21no—
273C22×C11—21no—
274C22×C11—21no—
275C22×C11—21no—
276C22×C11—42no—
277C22×C11—42no—
278C22×C11C2×#9511yescharacteristic
279C22×C11#40511yescharacteristic
280C22×C11#40511yescharacteristic
281C22×C11#40812yes—
282C22×C11#42412yes—
283C2×D11—24no—
284C2×D11—24no—
285C2×D11—21no—
286C2×D11—21no—
287C2×D11—21no—
288C2×D11—21no—
289C2×D11—21no—
290C2×D11—21no—
291C2×D11—21no—
292C2×D11—21no—
293C2×D11—21no—
294C2×D11—21no—
295C2×D11—44no—
296C2×D11—44no—
297C2×D11—44no—
298C2×D11—44no—
299C2×D11—42no—
300C2×D11—42no—
301C2×D11#34212yes—
302C2×D11#34412yes—
303C4×C11—21no—
304C4×C11—21no—
305C4×C11—21no—
306C4×C11—82no—
307C4×C11C2×#9912yes—
308Dic11—21no—
309Dic11—21no—
310Dic11—21no—
311Dic11—82no—
312Dic11#34212yes—
313C25—111no—
314C23×C4—111no—
315C23×C4—111no—
316C23×C4—111no—
317C23×C4—111no—
318C23×C4—111no—
319C23×C4—111no—
320C23×C4—111no—
321C23×C4—111no—
322C23×C4—111no—
323C23×C4—111no—
324C23×C4—111no—
325C23×C4—111no—
326C23×C4—111no—
327C23×C4—444no—
328C23×C4C22×D1111yescharacteristic
329C2×M16—222no—
330C2×M16—222no—
331C2×M16—444no—
332C22×C8—21no—
333C22×C8—112no—
334C22×C8—222no—
335C22×C8—222no—
336C22×C8—221no—
337C22×C8—444no—
338C22×C8C4×D1112yes—
339#117—444no—
340C2×C4⋊C4—222no—
341C2×C22⋊C4—112no—
342C2×C22⋊C4—222no—
343C2×C22⋊C4—222no—
344C2×C22⋊C4C4×D1112yes—
345C2×C42—21no—
346C2×C42—221no—
347C22⋊C8—21no—
348C22⋊C8—21no—
349C22⋊C8—21no—
350C22⋊C8—112no—
351C22⋊C8—222no—
352C22⋊C8—222no—
353C22⋊C8—222no—
354C22⋊C8—222no—
355C22⋊C8—221no—
356C22⋊C8—221no—
357C22⋊C8—221no—
358C22⋊C8C4×D1112yes—
359#95—21no—
360#95—222no—
361#95—221no—
362C2×C11—22no—
363C2×C11—21no—
364C2×C11—21no—
365C2×C11—22no—
366C2×C11#172911yescharacteristic
367C2×C11C2×#34211yescharacteristic
368C2×C11C2×#34411yescharacteristic
369D11—22no—
370D11—22no—
371D11—41no—
372D11—41no—
373C24—111no—
374C24—111no—
375C24—111no—
376C24—111no—
377C24—111no—
378C24—111no—
379C24—222no—
380C24—222no—
381C24—442no—
382C24—442no—
383C24C2×C4×D1111yescharacteristic
384C22×C4—22no—
385C22×C4—42no—
386C22×C4—111no—
387C22×C4—111no—
388C22×C4—111no—
389C22×C4—111no—
390C22×C4—111no—
391C22×C4—111no—
392C22×C4—111no—
393C22×C4—111no—
394C22×C4—111no—
395C22×C4—111no—
396C22×C4—111no—
397C22×C4—111no—
398C22×C4—111no—
399C22×C4—111no—
400C22×C4—111no—
401C22×C4—111no—
402C22×C4—111no—
403C22×C4—111no—
404C22×C4—111no—
405C22×C4—111no—
406C22×C4—111no—
407C22×C4—111no—
408C22×C4—224no—
409C22×C4—224no—
410C22×C4—224no—
411C22×C4—222no—
412C22×C4—442no—
413C22×C4—442no—
414C22×C4—442no—
415C22×C4—442no—
416C22×C4—442no—
417C22×C4—442no—
418C22×C4—442no—
419C22×C4—442no—
420C22×C4—442no—
421C22×C4—442no—
422C22×C4C2×C4×D1111yescharacteristic
423C22×C4C2×C4×D1111yescharacteristic
424C22×C4D4×D1111yescharacteristic
425C22×C4D4×D1111yescharacteristic
426C22×C4D4×D1111yescharacteristic
427C22×C4Q8×D1111yescharacteristic
428M16—444no—
429M16—444no—
430C2×C8—22no—
431C2×C8—22no—
432C2×C8—42no—
433C2×C8—42no—
434C2×C8—222no—
435C2×C8—222no—
436C2×C8—444no—
437C2×C8—444no—
438C2×C8—442no—
439C2×C8—442no—
440C4⋊C4—444no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—222no—
444C22⋊C4—222no—
445C22⋊C4—444no—
446C22⋊C4—444no—
447C42—42no—
448C42—442no—
449C11#792711yescharacteristic, complemented, Sylow
450C23—41no—
451C23—41no—
452C23—111no—
453C23—111no—
454C23—111no—
455C23—111no—
456C23—222no—
457C23—222no—
458C23—222no—
459C23—222no—
460C23—222no—
461C23—222no—
462C23—221no—
463C23—221no—
464C23—221no—
465C23—221no—
466C23—222no—
467C23—222no—
468C23—222no—
469C23—222no—
470C23—441no—
471C23—441no—
472C23—441no—
473C23—441no—
474C23—441no—
475C23—441no—
476C23—448no—
477C23—448no—
478C23C42×D1111yescharacteristic
479C23C22⋊C4×D1111yescharacteristic
480C23C4⋊C4×D1111yescharacteristic
481C23#6695412yes—
482C23#6696012yes—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—111no—
493C2×C4—114no—
494C2×C4—111no—
495C2×C4—111no—
496C2×C4—111no—
497C2×C4—222no—
498C2×C4—222no—
499C2×C4—222no—
500C2×C4—222no—
501C2×C4—222no—
502C2×C4—222no—
503C2×C4—222no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—222no—
507C2×C4—222no—
508C2×C4—222no—
509C2×C4—441no—
510C2×C4—441no—
511C2×C4—441no—
512C2×C4—441no—
513C2×C4—441no—
514C2×C4—441no—
515C2×C4—441no—
516C2×C4—441no—
517C2×C4—441no—
518C2×C4—442no—
519C2×C4—442no—
520C2×C4—442no—
521C2×C4C22⋊C4×D1111yescharacteristic
522C2×C4C22⋊C4×D1111yescharacteristic
523C2×C4C4⋊C4×D1111yescharacteristic
524C2×C4C4⋊C4×D1111yescharacteristic
525C8—42no—
526C8—42no—
527C8—442no—
528C8—442no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—42no—
536C22—42no—
537C22—112no—
538C22—112no—
539C22—224no—
540C22—224no—
541C22—221no—
542C22—221no—
543C22—221no—
544C22—221no—
545C22—221no—
546C22—221no—
547C22—221no—
548C22—221no—
549C22—221no—
550C22—221no—
551C22—444no—
552C22—444no—
553C22—444no—
554C22—444no—
555C22—442no—
556C22—442no—
557C22D11×#9511yescharacteristic
558C22#1062230211yescharacteristic
559C22#1062232111yescharacteristic
560C22#1062234012yes—
561C22#1062245212yes—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—82no—
566C4—112no—
567C4—221no—
568C4—221no—
569C4—221no—
570C4—882no—
571C4D11×#9912yes—
572C2—22no—
573C2—21no—
574C2—21no—
575C2—22no—
576C2—222no—
577C2—222no—
578C2—441no—
579C2—441no—
580C2#1306831111yescharacteristic
581C2D11×#34211yescharacteristic
582C2D11×#34411yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D11
commutatorC23×C11C2×C42
FrattiniC23×C4C22×D11
FittingC11×#1282C2
socleC22×C11C2×#95
prime radicalC24×D11C2×C4
cosocleC23×C4×C11C23
hypercenter#1282D11
hypocenterC11#7927
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1282

Complements

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

NH ≅ G/Ntype
4. #13066464C2semidirect
5. #13066463C2semidirect
6. #13066462C2semidirect
7. C11×#1282C2semidirect
10. C22×C8×D11C4semidirect
19. C2×(C2×D11)⋊C8C4semidirect
25. #10622339C4semidirect
26. #10622339C4semidirect
165. #1282D11semidirect
449. C11#7927semidirect

Maximal subgroups

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

subgroupindex
C2×#106223392
C2×D11×C22⋊C82
#130709972
#130664642
#130664632
#130664622
C11×#12822
#792711