Finite Group Databasebeta

← #14765174

Subgroups — #14765174

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077838C211yesmaximal, characteristic
2#13077310C211yesmaximal, characteristic, complemented
3C2×#10622723C211yesmaximal, characteristic, complemented
4#13069504C212yesmaximal, complemented
5#13069320C212yesmaximal, complemented
6#13069265C212yesmaximal, complemented
7#13068942C212yesmaximal, complemented
8#13068916C211yesmaximal, characteristic, complemented
9#13068823C211yesmaximal, characteristic, complemented
10#13068561C211yesmaximal, characteristic, complemented
11C8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
12C22×#4339C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14#10623322C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16C2×#66957C2212yes—
17C2×#66954C2211yescharacteristic, complemented
18C2×C11×C22⋊C8C2211yescharacteristic
19C2×C4×C8×C11C2212yescomplemented
20C4×C11×C22⋊C4C2211yescharacteristic
21#10622820C2211yescharacteristic
22#10622726C2212yes—
23#10622724—21no—
24#10622724—21no—
25#10622723—21no—
26#10622723—21no—
27#10622723C2212yes—
28#10622723C2212yes—
29#10622723C2211yescharacteristic, complemented
30C8×C22⋊D11—21no—
31C8×C22⋊D11—21no—
32C2×(C2×D11)⋊C8—21no—
33C2×(C2×D11)⋊C8—21no—
34C2×#66883C2212yescomplemented
35#10622715C2211yescharacteristic, complemented
36#10622714C2211yescharacteristic, complemented
37C2×#66869C2212yes—
38C2×#66869C2212yes—
39C2×#66869C2212yescomplemented
40#10622352C411yescharacteristic, complemented
41#10622351C411yescharacteristic, complemented
42#10622347C412yescomplemented
43#10622346C412yescomplemented
44#10622345C411yescharacteristic, complemented
45#10622344C411yescharacteristic, complemented
46C11×#336C2212yescomplemented
47#10622190C2212yescomplemented
48#10622161C2212yescomplemented
49C23×C4×C11C2311yescharacteristic
50C22×C22⋊D11—21no—
51C2×#4339—21no—
52C2×#4339—21no—
53C2×#4339—42no—
54C2×#4339—42no—
55C2×#4339C2×C412yes—
56C2×#4339C2312yes—
57C2×#4339C2311yescharacteristic
58C22×D44C2×C411yescharacteristic
59C22×C4×D11—21no—
60C22×Dic22C2×C411yescharacteristic
61C22×C8×C11—42no—
62C22×C8×C11D411yescharacteristic
63C22×C8×C11D411yescharacteristic
64C22×C8×C11D411yescharacteristic
65C22×C8×C11D411yescharacteristic
66C22×C8×C11C2312yes—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C2×C11×C22⋊C4—21no—
70C2×C42×C11C2312yes—
71#67006—21no—
72#66983C2×C411yescharacteristic
73#66983C2×C411yescharacteristic
74#66982—21no—
75C4×C22⋊D11—21no—
76C4×C22⋊D11—21no—
77#66979C2311yescharacteristic
78#66977C2×C411yescharacteristic
79#66977C2×C411yescharacteristic
80C2×#4318—21no—
81C2×#4318—42no—
82C2×#4318C2311yescharacteristic
83C2×#4318C2312yes—
84C2×#4318C2311yescharacteristic
85C22×C11⋊C8—21no—
86C2×Dic44C2×C412yes—
87#66957—42no—
88#66957—42no—
89C2×D88C2×C412yes—
90C2×#4314C2×C412yes—
91C2×#4314C2×C412yes—
92#66954—42no—
93C2×#4313—21no—
94C2×C8×D11—21no—
95C11×C22⋊C8C2×C411yescharacteristic
96C11×C22⋊C8C2×C411yescharacteristic
97C11×C22⋊C8C2×C412yes—
98C4×C8×C11—42no—
99C11×#95—21no—
100C22⋊(C11⋊C8)—21no—
101C22⋊(C11⋊C8)—21no—
102#66885C2×C412yes—
103#66885C2×C412yes—
104(C2×D11)⋊C8—22no—
105(C2×D11)⋊C8—22no—
106(C2×D11)⋊C8—22no—
107(C2×D11)⋊C8—22no—
108(C2×D11)⋊C8—21no—
109(C2×D11)⋊C8—21no—
110#66883—42no—
111#66880C2×C412yes—
112#66880C2×C412yes—
113#66879—21no—
114Dic11⋊C8—21no—
115Dic11⋊C8—21no—
116C8×Dic11—21no—
117#66869—42no—
118#66869—42no—
119#66869—42no—
120#22060—111nomaximal, Sylow
121C24×C11#4111yescharacteristic
122C23×D11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11C22×C411yescharacteristic
127C22×C4×C11C22×C411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11#4111yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C2×C22⋊D11—21no—
133C2×C22⋊D11—21no—
134C2×C22⋊D11—22no—
135C2×C22⋊D11—21no—
136C2×C22⋊D11—22no—
137C2×C22⋊D11—44no—
138C22×Dic11—21no—
139#4339—22no—
140#4339—22no—
141#4339—22no—
142#4339—22no—
143#4339—22no—
144#4339—22no—
145#4339—42no—
146#4339—42no—
147#4339—44no—
148#4339—42no—
149#4339—42no—
150C2×D44—21no—
151C2×D44—42no—
152C2×D44C22×C412yes—
153C2×D44C22×C411yescharacteristic
154C2×C4×D11—22no—
155C2×C4×D11—22no—
156C2×C4×D11—21no—
157C2×C4×D11—42no—
158C2×C4×D11—42no—
159C2×Dic22—21no—
160C2×Dic22—42no—
161C2×Dic22C22×C412yes—
162C2×Dic22C22×C411yescharacteristic
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11—41no—
168C2×C8×C11—41no—
169C2×C8×C11—41no—
170C2×C8×C11—41no—
171C2×C8×C11C22×C412yes—
172C2×C8×C11C22×C412yes—
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
176C2×C8×C11C2×D411yescharacteristic
177C11×C22⋊C4—24no—
178C42×C11—22no—
179C42×C11—22no—
180C22⋊Dic11—21no—
181C22⋊Dic11—21no—
182C22⋊Dic11—21no—
183(C2×D11)⋊C4—21no—
184(C2×D11)⋊C4—21no—
185C4⋊Dic11C22×C411yescharacteristic
186C4⋊Dic11C22×C411yescharacteristic
187Dic11⋊C4—21no—
188Dic11⋊C4—21no—
189C4×Dic11—21no—
190#4318—22no—
191#4318—22no—
192#4318—22no—
193#4318—22no—
194#4318—42no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8—42no—
199Dic44—42no—
200D88—42no—
201#4314—42no—
202#4314—42no—
203#4313—42no—
204C8×D11—42no—
205#3002—111no—
206#2929—111no—
207C2×#408—111no—
208#1974—112no—
209#1937—112no—
210#1929—112no—
211#1876—112no—
212#1871—111no—
213#1855—111no—
214#1789—111no—
215C8×C22⋊C4D1111yescharacteristic, complemented
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—41no—
219C23×C11C4×D411yescharacteristic
220C23×C11C4×D411yescharacteristic
221C23×C11C2×#4111yescharacteristic
222C22×D11—21no—
223C22×D11—22no—
224C22×D11—42no—
225C22×D11—42no—
226C22×D11—42no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—24no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11C4×D411yescharacteristic
238C2×C4×C11C4×D411yescharacteristic
239C2×C4×C11C23×C411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11H(5,𝔽2)12yes—
242C2×C4×C11H(5,𝔽2)12yes—
243C22⋊D11—44no—
244C22⋊D11—42no—
245C22⋊D11—42no—
246C22⋊D11—42no—
247C22⋊D11—42no—
248C22⋊D11—42no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—22no—
253C2×Dic11—42no—
254D44—22no—
255D44—22no—
256D44—22no—
257D44—42no—
258C4×D11—44no—
259C4×D11—41no—
260C4×D11—42no—
261C4×D11—42no—
262C4×D11—41no—
263Dic22—22no—
264Dic22—22no—
265Dic22—22no—
266Dic22—42no—
267C8×C11—22no—
268C8×C11—22no—
269C8×C11—21no—
270C8×C11—21no—
271C8×C11—21no—
272C8×C11—21no—
273C11⋊C8—41no—
274C11⋊C8—42no—
275C11⋊C8—41no—
276C22×#41—111no—
277C2×#135—112no—
278C2×#131—111no—
279C22×M16—111no—
280C23×C8C2×D1111yescharacteristic
281#525—111no—
282#452—112no—
283#451—111no—
284#450—111no—
285#449—112no—
286#448—111no—
287#447—111no—
288#435—221no—
289#435—221no—
290C8×D4—221no—
291C8×D4—221no—
292C2×#108—112no—
293#424—111no—
294C2×#104—112no—
295C2×#104—112no—
296C2×#104—112no—
297#416—112no—
298#408—112no—
299#408—112no—
300#408—111no—
301#408—221no—
302#408—221no—
303#407—111no—
304C2×C22⋊C8—221no—
305C2×C22⋊C8—221no—
306C2×C22⋊C8C2×D1111yescharacteristic
307#405—111no—
308C2×C4×C8C2×D1112yescomplemented
309C4×C22⋊C4C2×D1111yescharacteristic
310#341—112no—
311#339—112no—
312#336C2×D1112yescomplemented
313C22×C11—21no—
314C22×C11—21no—
315C22×C11—21no—
316C22×C11—21no—
317C22×C11—21no—
318C22×C11—21no—
319C22×C11—21no—
320C22×C11—44no—
321C22×C11#44312yes—
322C22×C11C2×C4×D411yescharacteristic
323C22×C11#53812yes—
324C2×D11—42no—
325C2×D11—41no—
326C2×D11—42no—
327C2×D11—41no—
328C2×D11—42no—
329C2×D11—41no—
330C2×D11—84no—
331C4×C11—21no—
332C4×C11—21no—
333C4×C11—44no—
334C4×C11#51812yes—
335C4×C11#53411yescharacteristic
336C4×C11#53511yescharacteristic
337Dic11—42no—
338Dic11—41no—
339Dic11—41no—
340Dic11—41no—
341C2×#41—112no—
342C2×#41—111no—
343C2×#41—112no—
344C2×#41—221no—
345C2×#41—221no—
346C2×#41—442no—
347C2×#41—442no—
348C22×Q8—111no—
349C22×D4—111no—
350C22×D4—221no—
351C23×C4—221no—
352C23×C4C22×D1111yescharacteristic
353#135—442no—
354#135—442no—
355C2×Q16—112no—
356C2×SD16—112no—
357C2×SD16—112no—
358C2×D8—112no—
359#131—442no—
360C2×M16—112no—
361C2×M16—111no—
362C2×M16—111no—
363C2×M16—221no—
364C2×M16—221no—
365C2×M16—442no—
366C22×C8—42no—
367C22×C8—221no—
368C22×C8—221no—
369C22×C8D4411yescharacteristic
370C22×C8D4411yescharacteristic
371C22×C8D4411yescharacteristic
372C22×C8D4411yescharacteristic
373C22×C8C22×D1112yes—
374C22×C8C22×D1111yescharacteristic
375C22×C8C22×D1111yescharacteristic
376#123—221no—
377C22⋊Q8—111no—
378C22⋊Q8—111no—
379#121—111no—
380#121—111no—
381#120—221no—
382C4×D4—221no—
383C4×D4—221no—
384#117—111no—
385C2×C22⋊C4—21no—
386C2×C42C22×D1112yes—
387#108—442no—
388C4⋊C8—221no—
389C4⋊C8—221no—
390#104—442no—
391#104—442no—
392#104—442no—
393#103—112no—
394#103—112no—
395#102—112no—
396#102—112no—
397C22⋊C8—221no—
398C22⋊C8—221no—
399C22⋊C8—222no—
400C22⋊C8—222no—
401C22⋊C8—222no—
402C22⋊C8—222no—
403C22⋊C8—221no—
404C22⋊C8—221no—
405C22⋊C8C4×D1111yescharacteristic
406C22⋊C8C4×D1111yescharacteristic
407C22⋊C8C4×D1112yes—
408#97—221no—
409C4×C8—42no—
410C4×C8—221no—
411#95—21no—
412C2×C11—22no—
413C2×C11—22no—
414C2×C11—41no—
415C2×C11#232111yescharacteristic
416C2×C11C2×#44311yescharacteristic
417C2×C11#295511yescharacteristic
418D11—81no—
419D11—82no—
420C24—221no—
421C24#433911yescharacteristic
422#41—222no—
423#41—222no—
424#41—222no—
425#41—222no—
426#41—222no—
427#41—222no—
428#41—442no—
429#41—442no—
430#41—444no—
431#41—442no—
432#41—442no—
433C2×Q8—112no—
434C2×Q8—111no—
435C2×Q8—221no—
436C2×Q8—442no—
437C2×D4—112no—
438C2×D4—111no—
439C2×D4—221no—
440C2×D4—221no—
441C2×D4—222no—
442C2×D4—221no—
443C2×D4—222no—
444C2×D4—221no—
445C2×D4—442no—
446C2×D4—444no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—221no—
451C22×C4—222no—
452C22×C4—222no—
453C22×C4—221no—
454C22×C4—442no—
455C22×C4—442no—
456C22×C4C2×C4×D1111yescharacteristic
457C22×C4C2×C4×D1111yescharacteristic
458C22×C4C2×D4411yescharacteristic
459C22×C4C2×D4411yescharacteristic
460C22×C4#433911yescharacteristic
461C22×C4C23×D1111yescharacteristic
462Q16—442no—
463SD16—442no—
464SD16—442no—
465D8—442no—
466M16—222no—
467M16—222no—
468M16—222no—
469M16—222no—
470M16—442no—
471M16—442no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—221no—
481C2×C8—222no—
482C2×C8—221no—
483C2×C8—442no—
484C2×C8—442no—
485C2×C8C2×C4×D1112yes—
486C2×C8C2×C4×D1112yes—
487C2×C8C2×D4411yescharacteristic
488C2×C8C2×D4411yescharacteristic
489C2×C8C2×D4411yescharacteristic
490C2×C8C2×D4411yescharacteristic
491C4⋊C4—111no—
492C4⋊C4—111no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C22⋊C4—24no—
496C22⋊C4—221no—
497C22⋊C4—221no—
498C22⋊C4—221no—
499C22⋊C4—221no—
500C22⋊C4—221no—
501C42—22no—
502C42—22no—
503C42—221no—
504C11#2206011yescharacteristic, complemented, Sylow
505C23—22no—
506C23—22no—
507C23—41no—
508C23—221no—
509C23—222no—
510C23—442no—
511C23—442no—
512C23—442no—
513C23C4×D4411yescharacteristic
514C23C4×D4411yescharacteristic
515C23C2×#433911yescharacteristic
516Q8—222no—
517Q8—222no—
518Q8—222no—
519Q8—442no—
520D4—222no—
521D4—222no—
522D4—222no—
523D4—442no—
524D4—444no—
525D4—442no—
526D4—442no—
527D4—442no—
528D4—442no—
529D4—442no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—222no—
544C2×C4—444no—
545C2×C4—442no—
546C2×C4—441no—
547C2×C4—442no—
548C2×C4—442no—
549C2×C4—441no—
550C2×C4C4×D4411yescharacteristic
551C2×C4C4×D4411yescharacteristic
552C2×C4C22×C4×D1111yescharacteristic
553C2×C4C22×D4411yescharacteristic
554C2×C4#6703712yes—
555C2×C4#6704212yes—
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—22no—
561C8—22no—
562C8—441no—
563C8—442no—
564C8—441no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—21no—
572C22—44no—
573C22—441no—
574C22—442no—
575C22—441no—
576C22—442no—
577C22—442no—
578C22—441no—
579C22—884no—
580C22#1062231312yes—
581C22C2×C4×D4411yescharacteristic
582C22#1062309112yes—
583C4—21no—
584C4—21no—
585C4—44no—
586C4—441no—
587C4—441no—
588C4—442no—
589C4—441no—
590C4#1062302411yescharacteristic
591C4#1062305611yescharacteristic
592C4#1062307612yes—
593C2—22no—
594C2—22no—
595C2—41no—
596C2—882no—
597C2—881no—
598C2#1307127611yescharacteristic
599C2C2×#1062231311yescharacteristic
600C2#1307752011yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC8×C11×C22⋊C4C2
socleC22×C11C2×C4×D4
prime radical#13077838C2
cosocleC22×C4×C11C24
hypercenterC8×C22⋊C4D11
hypocenterC11#22060
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C8 ◁ C8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #13077310C2semidirect
3. C2×#10622723C2semidirect
4. #13069504C2semidirect
5. #13069320C2semidirect
6. #13069265C2semidirect
7. #13068942C2semidirect
8. #13068916C2semidirect
9. #13068823C2semidirect
10. #13068561C2semidirect
11. C8×C11×C22⋊C4C2semidirect
17. C2×#66954C22semidirect
19. C2×C4×C8×C11C22semidirect
29. #10622723C22semidirect
34. C2×#66883C22semidirect
35. #10622715C22semidirect
36. #10622714C22semidirect
39. C2×#66869C22semidirect
40. #10622352C4semidirect
41. #10622351C4semidirect
42. #10622347C4semidirect
43. #10622346C4semidirect
44. #10622345C4semidirect
45. #10622344C4semidirect
46. C11×#336C22semidirect
47. #10622190C22semidirect
48. #10622161C22semidirect
215. C8×C22⋊C4D11semidirect
308. C2×C4×C8C2×D11semidirect
312. #336C2×D11semidirect
504. C11#22060semidirect

Maximal subgroups

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

subgroupindex
#130778382
#130773102
C2×#106227232
#130695042
#130693202
#130692652
#130689422
#130689162
#130688232
#130685612
C8×C11×C22⋊C42
#2206011