Finite Group Databasebeta

← #14771123

Subgroups — #14771123

Order 2816.

894 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622615C211yesmaximal, characteristic
2#13077062C211yesmaximal, characteristic
3#13069326C212yesmaximal, complemented
4#13069264C212yesmaximal, complemented
5#13068890C212yesmaximal, complemented
6#13068715C211yesmaximal, characteristic, complemented
7#13068652C211yesmaximal, characteristic, complemented
8#13068559C211yesmaximal, characteristic
9#13068462C212yesmaximal, complemented
10#13068395C211yesmaximal, characteristic, complemented
11C11×#2924C211yesmaximal, characteristic, complemented
12C22×#4339C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C23×C11⋊C8C2211yescharacteristic
15C2×#66954C2212yes—
16C11×#433—22no—
17C11×#432—21no—
18C11×#431—21no—
19C11×#424C2212yescomplemented
20C11×#407C2211yescharacteristic
21C2×C11×C22⋊C8C2211yescharacteristic
22C11×#405C2212yescomplemented
23C4×C22⋊Dic11C2211yescharacteristic
24#10622820C2211yescharacteristic
25C2×#66889C2212yes—
26C2×#66889C2212yes—
27C2×#66886C2212yescomplemented
28#10622723C2212yes—
29C2×#66879C2212yescomplemented
30#10622615C411yescharacteristic, complemented
31#10622615C411yescharacteristic, complemented
32#10622615C411yescharacteristic, complemented
33#10622615C411yescharacteristic, complemented
34#10622615C2211yescharacteristic
35#10622615C2211yescharacteristic
36#10622615C2211yescharacteristic
37#10622615C2211yescharacteristic
38C2×#66874C411yescharacteristic, complemented
39C2×#66874C411yescharacteristic, complemented
40C2×#66873C411yescharacteristic, complemented
41C2×#66873C411yescharacteristic, complemented
42#10622340—22no—
43#10622339—21no—
44D11×C22⋊C8—21no—
45#10622196C2212yescomplemented
46#10622188C2212yescomplemented
47#10622170C2212yescomplemented
48#10622170C2212yescomplemented
49C23×C4×C11C2311yescharacteristic
50C22×C22⋊D11—21no—
51C2×#4339—21no—
52C2×#4339—21no—
53C2×#4339—24no—
54C2×#4339—42no—
55C2×#4339C2×C411yescharacteristic
56C2×#4339C2×C411yescharacteristic
57C2×#4339C2311yescharacteristic
58C2×#4339C2311yescharacteristic
59C22×D44C2×C411yescharacteristic
60C22×C4×D11—21no—
61C22×Dic22C2×C411yescharacteristic
62C2×C11×M16C2312yes—
63C22×C8×C11C2312yes—
64C11×#117—21no—
65C11×#117—21no—
66C11×#117C2×C411yescharacteristic
67C11×#117C2×C411yescharacteristic
68C11×#117C2311yescharacteristic
69C11×#117C2311yescharacteristic
70C2×C11×C4⋊C4C2×C411yescharacteristic
71C2×C11×C4⋊C4C2×C411yescharacteristic
72C2×C11×C22⋊C4—21no—
73C2×C42×C11—21no—
74C2×C22⋊Dic11—21no—
75C2×C4×Dic11C2312yes—
76C2×#4318C2312yes—
77C22×C11⋊C8—42no—
78C22×C11⋊C8C2×C411yescharacteristic
79C22×C11⋊C8C2×C411yescharacteristic
80C22×C11⋊C8C2×C411yescharacteristic
81C22×C11⋊C8C2×C411yescharacteristic
82C22×C11⋊C8C2311yescharacteristic
83C22×C11⋊C8C2311yescharacteristic
84#66954—24no—
85#66954—42no—
86C2×#4313—22no—
87C2×C8×D11—22no—
88C11×C4⋊C8—22no—
89C11×C4⋊C8—22no—
90C11×C22⋊C8—21no—
91C11×C22⋊C8—21no—
92C11×C22⋊C8D411yescharacteristic
93C11×C22⋊C8D411yescharacteristic
94C11×C22⋊C8D412yes—
95C11×#97—22no—
96C4×C8×C11—22no—
97C11⋊#95—21no—
98C22⋊(C11⋊C8)—21no—
99C22⋊(C11⋊C8)—21no—
100#66889—24no—
101#66889—42no—
102#66886—42no—
103(C2×D11)⋊C8—22no—
104(C2×D11)⋊C8—22no—
105#66879—42no—
106#66874C2×C411yescharacteristic
107#66874C2×C411yescharacteristic
108#66874C2×C411yescharacteristic
109#66874C2×C411yescharacteristic
110#66874C2×C411yescharacteristic
111#66874C2×C411yescharacteristic
112#66874C2×C411yescharacteristic
113#66874C2×C411yescharacteristic
114#66873C2×C411yescharacteristic
115#66873C2×C411yescharacteristic
116#66873C2×C411yescharacteristic
117#66873C2×C411yescharacteristic
118#66873C2×C411yescharacteristic
119#66873C2×C411yescharacteristic
120#66873C2×C411yescharacteristic
121#66873C2×C411yescharacteristic
122#22586—111nomaximal, Sylow
123C24×C11#4111yescharacteristic
124C23×D11—21no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11C22×C411yescharacteristic
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11#4111yescharacteristic
134C22×C4×C11C2411yescharacteristic
135C2×C22⋊D11—21no—
136C2×C22⋊D11—21no—
137C2×C22⋊D11—21no—
138C2×C22⋊D11—21no—
139C2×C22⋊D11—44no—
140C22×Dic11—21no—
141C22×Dic11—22no—
142#4339—22no—
143#4339—22no—
144#4339—22no—
145#4339—22no—
146#4339—22no—
147#4339—41no—
148#4339—41no—
149#4339—44no—
150#4339—44no—
151#4339#4114yes—
152C2×D44—22no—
153C2×D44—21no—
154C2×D44—41no—
155C2×D44C22×C411yescharacteristic
156C2×D44C22×C411yescharacteristic
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—44no—
162C2×Dic22—22no—
163C2×Dic22—21no—
164C2×Dic22—41no—
165C2×Dic22C22×C411yescharacteristic
166C2×Dic22C22×C411yescharacteristic
167C11×M16—22no—
168C11×M16—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11C2×D412yes—
173C2×C8×C11C2×D412yes—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4C22×C411yescharacteristic
177C11×C4⋊C4C22×C411yescharacteristic
178C11×C4⋊C4C22×C411yescharacteristic
179C11×C4⋊C4C22×C411yescharacteristic
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C11×C22⋊C4—21no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C22⋊Dic11—42no—
189C4×Dic11—22no—
190C4×Dic11—22no—
191#4318—22no—
192#4318—22no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8—41no—
197C2×C11⋊C8—41no—
198C2×C11⋊C8—41no—
199C2×C11⋊C8—41no—
200C2×C11⋊C8C22×C411yescharacteristic
201C2×C11⋊C8C22×C411yescharacteristic
202C2×C11⋊C8C22×C411yescharacteristic
203C2×C11⋊C8C22×C411yescharacteristic
204#4313—44no—
205C8×D11—44no—
206#2924D1111yescharacteristic, complemented
207C2×#416—111no—
208#2880—111no—
209#1938—112no—
210#1929—112no—
211#1866—112no—
212#1826—111no—
213#1810—111no—
214#1789—111no—
215#1765—112no—
216#1752—111no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—41no—
220C23×C11C4×D411yescharacteristic
221C23×C11C4×D411yescharacteristic
222C23×C11C2×#4111yescharacteristic
223C22×D11—21no—
224C22×D11—21no—
225C22×D11—42no—
226C22×D11—42no—
227C22×D11—81no—
228C2×C4×C11—22no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—42no—
240C2×C4×C11—81no—
241C2×C4×C11C4×D411yescharacteristic
242C2×C4×C11C4×D411yescharacteristic
243C2×C4×C11C23×C411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C2×#4112yes—
246C2×C4×C11H(5,𝔽2)12yes—
247C22⋊D11—24no—
248C22⋊D11—42no—
249C22⋊D11—42no—
250C22⋊D11—42no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257D44—21no—
258D44—21no—
259D44—21no—
260D44—42no—
261D44#11712yes—
262C4×D11—24no—
263C4×D11—42no—
264C4×D11—42no—
265C4×D11—42no—
266Dic22—21no—
267Dic22—21no—
268Dic22—21no—
269Dic22—42no—
270Dic22#11712yes—
271C8×C11—22no—
272C8×C11—22no—
273C8×C11—42no—
274C11⋊C8—21no—
275C11⋊C8—21no—
276C11⋊C8—21no—
277C11⋊C8—21no—
278C11⋊C8—42no—
279C22×#41—111no—
280C2×#131—112no—
281C23×C8—111no—
282C2×#117C2×D1111yescharacteristic
283#433—22no—
284#432—21no—
285#431—21no—
286C2×#108—112no—
287#424C2×D1112yescomplemented
288C2×#104—112no—
289C2×#104—112no—
290#416—111no—
291#416—111no—
292#416—111no—
293#416—111no—
294#416—111no—
295#416—111no—
296#416—111no—
297#416—111no—
298C2×#103—111no—
299C2×#103—111no—
300C2×#102—111no—
301C2×#102—111no—
302#408—112no—
303#408—222no—
304#407—111no—
305#407—221no—
306#407C2×D1111yescharacteristic
307C2×C22⋊C8—221no—
308C2×C22⋊C8C2×D1111yescharacteristic
309#405C2×D1112yescomplemented
310C2×#97—112no—
311C4×C22⋊C4—111no—
312#341—112no—
313#339—112no—
314#339—112no—
315#336—112no—
316C22×C11—21no—
317C22×C11—21no—
318C22×C11—21no—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11—21no—
323C22×C11—44no—
324C22×C11#44412yes—
325C22×C11C2×C4×D411yescharacteristic
326C22×C11#55112yes—
327C2×D11—22no—
328C2×D11—41no—
329C2×D11—41no—
330C2×D11—41no—
331C2×D11—41no—
332C2×D11—41no—
333C2×D11—84no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11C2×#11711yescharacteristic
341C4×C11#51811yescharacteristic
342C4×C11#54612yes—
343Dic11—22no—
344Dic11—41no—
345Dic11—82no—
346C2×#41—111no—
347C2×#41—111no—
348C2×#41—111no—
349C2×#41—111no—
350C2×#41—224no—
351C2×#41—221no—
352C2×#41—221no—
353C2×#41—442no—
354C22×Q8—111no—
355C22×D4—111no—
356C22×D4—221no—
357C23×C4—221no—
358C23×C4C22×D1111yescharacteristic
359#131—224no—
360#131—442no—
361C2×M16—112no—
362C2×M16—222no—
363C2×M16C22×D1112yes—
364C22×C8—111no—
365C22×C8—111no—
366C22×C8—111no—
367C22×C8—111no—
368C22×C8—111no—
369C22×C8—111no—
370C22×C8—222no—
371C22×C8—442no—
372C22×C8C22×D1112yes—
373#117—21no—
374#117—21no—
375#117C4×D1111yescharacteristic
376#117C4×D1111yescharacteristic
377#117C22×D1111yescharacteristic
378#117C22×D1111yescharacteristic
379C2×C4⋊C4C4×D1111yescharacteristic
380C2×C4⋊C4C4×D1111yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—221no—
383C2×C42—21no—
384C2×C42—112no—
385#108—442no—
386C4⋊C8—22no—
387C4⋊C8—22no—
388#104—224no—
389#104—442no—
390#103—111no—
391#103—111no—
392#103—111no—
393#103—111no—
394#103—111no—
395#103—111no—
396#103—111no—
397#103—111no—
398#102—111no—
399#102—111no—
400#102—111no—
401#102—111no—
402#102—111no—
403#102—111no—
404#102—111no—
405#102—111no—
406C22⋊C8—21no—
407C22⋊C8—21no—
408C22⋊C8—221no—
409C22⋊C8—221no—
410C22⋊C8—222no—
411C22⋊C8—222no—
412C22⋊C8C22⋊D1111yescharacteristic
413C22⋊C8C22⋊D1111yescharacteristic
414C22⋊C8C22⋊D1112yes—
415#97—22no—
416#97—442no—
417C4×C8—22no—
418#95—221no—
419C2×C11—22no—
420C2×C11—22no—
421C2×C11—41no—
422C2×C11#234211yescharacteristic
423C2×C11C2×#44411yescharacteristic
424C2×C11#295711yescharacteristic
425D11—42no—
426D11—81no—
427C24—221no—
428C24#433911yescharacteristic
429#41—114no—
430#41—222no—
431#41—222no—
432#41—222no—
433#41—222no—
434#41—222no—
435#41—444no—
436#41—441no—
437#41—441no—
438#41—444no—
439C2×Q8—111no—
440C2×Q8—111no—
441C2×Q8—222no—
442C2×Q8—221no—
443C2×Q8—441no—
444C2×D4—111no—
445C2×D4—111no—
446C2×D4—222no—
447C2×D4—221no—
448C2×D4—221no—
449C2×D4—221no—
450C2×D4—221no—
451C2×D4—221no—
452C2×D4—441no—
453C2×D4—444no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—222no—
464C22×C4—444no—
465C22×C4C2×C4×D1111yescharacteristic
466C22×C4C2×C4×D1111yescharacteristic
467C22×C4#433911yescharacteristic
468C22×C4C2×C22⋊D1111yescharacteristic
469C22×C4C2×C22⋊D1111yescharacteristic
470C22×C4C23×D1111yescharacteristic
471M16—22no—
472M16—22no—
473M16—222no—
474M16—222no—
475M16—444no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—111no—
480C2×C8—111no—
481C2×C8—111no—
482C2×C8—111no—
483C2×C8—222no—
484C2×C8—222no—
485C2×C8—222no—
486C2×C8—444no—
487C2×C8—441no—
488C2×C8—441no—
489C2×C8—441no—
490C2×C8—441no—
491C2×C8C2×C22⋊D1112yes—
492C2×C8C2×C22⋊D1112yes—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4C2×C4×D1111yescharacteristic
496C4⋊C4C2×C4×D1111yescharacteristic
497C4⋊C4C2×C4×D1111yescharacteristic
498C4⋊C4C2×C4×D1111yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—442no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—222no—
509C42—222no—
510C11#2258611yescharacteristic, complemented, Sylow
511C23—22no—
512C23—22no—
513C23—41no—
514C23—221no—
515C23—221no—
516C23—442no—
517C23—442no—
518C23—881no—
519C23C4×C22⋊D1111yescharacteristic
520C23C4×C22⋊D1111yescharacteristic
521C23C2×#433911yescharacteristic
522Q8—112no—
523Q8—221no—
524Q8—221no—
525Q8—221no—
526Q8—442no—
527D4—112no—
528D4—224no—
529D4—221no—
530D4—221no—
531D4—221no—
532D4—442no—
533D4—442no—
534D4—442no—
535D4—442no—
536C2×C4—22no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—42no—
548C2×C4—81no—
549C2×C4—221no—
550C2×C4—224no—
551C2×C4—221no—
552C2×C4—442no—
553C2×C4—442no—
554C2×C4—442no—
555C2×C4—442no—
556C2×C4—442no—
557C2×C4—442no—
558C2×C4—442no—
559C2×C4C4×C22⋊D1111yescharacteristic
560C2×C4C4×C22⋊D1111yescharacteristic
561C2×C4C22×C4×D1111yescharacteristic
562C2×C4#41×D1112yes—
563C2×C4#6704212yes—
564C2×C4C22×C22⋊D1111yescharacteristic
565C8—22no—
566C8—22no—
567C8—42no—
568C8—221no—
569C8—221no—
570C8—221no—
571C8—221no—
572C8—442no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—44no—
581C22—222no—
582C22—441no—
583C22—441no—
584C22—441no—
585C22—441no—
586C22—441no—
587C22—884no—
588C22#1062275812yes—
589C22#1062305812yes—
590C22C2×C4×C22⋊D1111yescharacteristic
591C4—21no—
592C4—21no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—222no—
598C4—441no—
599C4—882no—
600C4D11×#11711yescharacteristic
601C4#1062305211yescharacteristic
602C4#1062336012yes—
603C2—22no—
604C2—22no—
605C2—41no—
606C2—442no—
607C2—881no—
608C2#1307146611yescharacteristic
609C2C2×#1062275811yescharacteristic
610C2#1307753111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2924C2
socleC22×C11C2×C4×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenter#2924D11
hypocenterC11#22586
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2924

Complements

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

NH ≅ G/Ntype
3. #13069326C2semidirect
4. #13069264C2semidirect
5. #13068890C2semidirect
6. #13068715C2semidirect
7. #13068652C2semidirect
9. #13068462C2semidirect
10. #13068395C2semidirect
11. C11×#2924C2semidirect
19. C11×#424C22semidirect
22. C11×#405C22semidirect
27. C2×#66886C22semidirect
29. C2×#66879C22semidirect
30. #10622615C4semidirect
31. #10622615C4semidirect
32. #10622615C4semidirect
33. #10622615C4semidirect
38. C2×#66874C4semidirect
39. C2×#66874C4semidirect
40. C2×#66873C4semidirect
41. C2×#66873C4semidirect
45. #10622196C22semidirect
46. #10622188C22semidirect
47. #10622170C22semidirect
48. #10622170C22semidirect
206. #2924D11semidirect
287. #424C2×D11semidirect
309. #405C2×D11semidirect
510. C11#22586semidirect

Maximal subgroups

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

subgroupindex
C2×#106226152
#130770622
#130693262
#130692642
#130688902
#130687152
#130686522
#130685592
#130684622
#130683952
C11×#29242
#2258611