Finite Group Databasebeta

← #14771125

Subgroups — #14771125

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
1#13077270C211yesmaximal, characteristic, complemented
2C2×#10622726C211yesmaximal, characteristic
3#13077062C211yesmaximal, characteristic
4#13069327C212yesmaximal, complemented
5#13069265C212yesmaximal, complemented
6#13068894C212yesmaximal, complemented
7#13068716C211yesmaximal, characteristic, complemented
8#13068654C211yesmaximal, characteristic, complemented
9#13068561C211yesmaximal, characteristic
10#13068460C212yesmaximal, complemented
11C11×#1752C211yesmaximal, characteristic, complemented
12C22×#4339C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C2×#66954C2212yes—
16C2×C11×C22⋊C8C2211yescharacteristic
17C2×C11×#97C2212yescomplemented
18C4×C11×C22⋊C4C2211yescharacteristic
19#10622820C2211yescharacteristic
20#10622820C2211yescharacteristic
21#10622726C411yescharacteristic, complemented
22#10622726C411yescharacteristic, complemented
23#10622726C411yescharacteristic, complemented
24#10622726C411yescharacteristic, complemented
25#10622726C2211yescharacteristic
26#10622726C2211yescharacteristic
27#10622726C2211yescharacteristic
28#10622726C2211yescharacteristic
29C2×#66885C411yescharacteristic, complemented
30C2×#66885C411yescharacteristic, complemented
31#10622723C2212yes—
32C2×#66883C2212yescomplemented
33C2×#66880C411yescharacteristic, complemented
34C2×#66880C411yescharacteristic, complemented
35#10622715C2212yescomplemented
36#10622714C2212yescomplemented
37C2×#66869C2212yes—
38C2×#66869C2212yes—
39#10622340—22no—
40#10622339—21no—
41D11×C22⋊C8—21no—
42#10622333—22no—
43#10622332—21no—
44#10622331—21no—
45C11×#336C2212yescomplemented
46#10622190C2212yescomplemented
47#10622161C2212yescomplemented
48#10622161C2212yescomplemented
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
62C22×C8×C11—42no—
63C22×C8×C11C2×C411yescharacteristic
64C22×C8×C11C2×C411yescharacteristic
65C22×C8×C11C2×C411yescharacteristic
66C22×C8×C11C2×C411yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2312yes—
70C2×C11×C22⋊C4—21no—
71C2×C42×C11C2312yes—
72C2×C22⋊Dic11—21no—
73#66979—21no—
74#66979—21no—
75#66979C2×C411yescharacteristic
76#66979C2×C411yescharacteristic
77#66979C2311yescharacteristic
78#66979C2311yescharacteristic
79C2×C4⋊Dic11C2×C411yescharacteristic
80C2×C4⋊Dic11C2×C411yescharacteristic
81C2×C4×Dic11—21no—
82C2×#4318C2312yes—
83C2×#4318C2312yes—
84#66954—24no—
85#66954—42no—
86C2×#4313—22no—
87C2×C8×D11—22no—
88C11×C22⋊C8D411yescharacteristic
89C11×C22⋊C8D411yescharacteristic
90C11×C22⋊C8D412yes—
91C11×#97—42no—
92C11×#95—21no—
93C22⋊(C11⋊C8)—21no—
94C22⋊(C11⋊C8)—21no—
95C22⋊(C11⋊C8)—21no—
96C22⋊(C11⋊C8)—21no—
97#66885C2×C411yescharacteristic
98#66885C2×C411yescharacteristic
99#66885C2×C411yescharacteristic
100#66885C2×C411yescharacteristic
101#66885C2×C411yescharacteristic
102#66885C2×C411yescharacteristic
103#66885C2×C411yescharacteristic
104#66885C2×C411yescharacteristic
105(C2×D11)⋊C8—22no—
106(C2×D11)⋊C8—22no—
107#66883—42no—
108#66880C2×C411yescharacteristic
109#66880C2×C411yescharacteristic
110#66880C2×C411yescharacteristic
111#66880C2×C411yescharacteristic
112#66880C2×C411yescharacteristic
113#66880C2×C411yescharacteristic
114#66880C2×C411yescharacteristic
115#66880C2×C411yescharacteristic
116#66879—22no—
117Dic11⋊C8—22no—
118Dic11⋊C8—22no—
119C8×Dic11—22no—
120#66869—24no—
121#66869—42no—
122#22586—111nomaximal, Sylow
123C24×C11#4111yescharacteristic
124C23×D11—21no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11C22×C411yescharacteristic
129C22×C4×C11C22×C411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11#4111yescharacteristic
133C22×C4×C11C2411yescharacteristic
134C2×C22⋊D11—21no—
135C2×C22⋊D11—21no—
136C2×C22⋊D11—21no—
137C2×C22⋊D11—21no—
138C2×C22⋊D11—44no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
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
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—41no—
172C2×C8×C11—41no—
173C2×C8×C11—41no—
174C2×C8×C11—41no—
175C2×C8×C11C22×C411yescharacteristic
176C2×C8×C11C22×C411yescharacteristic
177C2×C8×C11C22×C411yescharacteristic
178C2×C8×C11C22×C411yescharacteristic
179C2×C8×C11C2×D412yes—
180C2×C8×C11C2×D412yes—
181C11×C22⋊C4—42no—
182C42×C11—22no—
183C42×C11—22no—
184C22⋊Dic11—21no—
185C22⋊Dic11—21no—
186C22⋊Dic11—21no—
187C22⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11C22×C411yescharacteristic
191C4⋊Dic11C22×C411yescharacteristic
192C4⋊Dic11C22×C411yescharacteristic
193C4⋊Dic11C22×C411yescharacteristic
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198#4318—22no—
199#4318—22no—
200#4318—22no—
201#4318—22no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—22no—
204#4313—44no—
205C8×D11—44no—
206#2924—111no—
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#1752D1111yescharacteristic, complemented
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—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11C4×D411yescharacteristic
239C2×C4×C11C4×D411yescharacteristic
240C2×C4×C11C23×C411yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C2×#4112yes—
243C2×C4×C11H(5,𝔽2)12yes—
244C22⋊D11—24no—
245C22⋊D11—42no—
246C22⋊D11—42no—
247C22⋊D11—42no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—81no—
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—21no—
272C8×C11—21no—
273C8×C11—21no—
274C8×C11—21no—
275C8×C11—22no—
276C8×C11—22no—
277C11⋊C8—42no—
278C11⋊C8—42no—
279C22×#41—111no—
280C2×#131—112no—
281C23×C8C2×D1111yescharacteristic
282C2×#117—111no—
283#433—222no—
284#432—221no—
285#431—221no—
286C2×#108—112no—
287#424—112no—
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—111no—
306#407—221no—
307C2×C22⋊C8—221no—
308C2×C22⋊C8C2×D1111yescharacteristic
309#405—112no—
310C2×#97C2×D1112yescomplemented
311C4×C22⋊C4C2×D1111yescharacteristic
312#341—112no—
313#339—112no—
314#339—112no—
315#336C2×D1112yescomplemented
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—82no—
337C4×C11C2×#11711yescharacteristic
338C4×C11#51811yescharacteristic
339C4×C11#54612yes—
340Dic11—22no—
341Dic11—41no—
342Dic11—41no—
343Dic11—41no—
344Dic11—41no—
345Dic11—41no—
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—112no—
363C2×M16—222no—
364C22×C8—42no—
365C22×C8—222no—
366C22×C8C4×D1111yescharacteristic
367C22×C8C4×D1111yescharacteristic
368C22×C8C4×D1111yescharacteristic
369C22×C8C4×D1111yescharacteristic
370C22×C8C22×D1111yescharacteristic
371C22×C8C22×D1111yescharacteristic
372C22×C8C22×D1112yes—
373#117—111no—
374#117—111no—
375#117—111no—
376#117—111no—
377#117—221no—
378#117—221no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—221no—
383C2×C42—221no—
384C2×C42C22×D1112yes—
385#108—442no—
386C4⋊C8—222no—
387C4⋊C8—222no—
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—221no—
407C22⋊C8—221no—
408C22⋊C8—221no—
409C22⋊C8—221no—
410C22⋊C8—222no—
411C22⋊C8—222no—
412C22⋊C8D4411yescharacteristic
413C22⋊C8D4411yescharacteristic
414C22⋊C8D4412yes—
415#97—42no—
416#97—222no—
417C4×C8—222no—
418#95—21no—
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—22no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—444no—
465C22×C4C2×C4×D1111yescharacteristic
466C22×C4C2×C4×D1111yescharacteristic
467C22×C4C2×D4411yescharacteristic
468C22×C4C2×D4411yescharacteristic
469C22×C4#433911yescharacteristic
470C22×C4C23×D1111yescharacteristic
471M16—222no—
472M16—222no—
473M16—222no—
474M16—222no—
475M16—444no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—222no—
485C2×C8—222no—
486C2×C8—444no—
487C2×C8C2×C4×D1111yescharacteristic
488C2×C8C2×C4×D1111yescharacteristic
489C2×C8C2×C4×D1111yescharacteristic
490C2×C8C2×C4×D1111yescharacteristic
491C2×C8C2×D4412yes—
492C2×C8C2×D4412yes—
493C4⋊C4—111no—
494C4⋊C4—111no—
495C4⋊C4—111no—
496C4⋊C4—111no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C22⋊C4—42no—
500C22⋊C4—221no—
501C22⋊C4—221no—
502C22⋊C4—221no—
503C22⋊C4—221no—
504C42—22no—
505C42—22no—
506C42—221no—
507C42—221no—
508C42—221no—
509C42—221no—
510C11#2258611yescharacteristic, complemented, Sylow
511C23—22no—
512C23—22no—
513C23—41no—
514C23—221no—
515C23—221no—
516C23—442no—
517C23—442no—
518C23—881no—
519C23C4×D4411yescharacteristic
520C23C4×D4411yescharacteristic
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—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—221no—
547C2×C4—224no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—442no—
554C2×C4—442no—
555C2×C4—442no—
556C2×C4—442no—
557C2×C4—442no—
558C2×C4—881no—
559C2×C4C4×D4411yescharacteristic
560C2×C4C4×D4411yescharacteristic
561C2×C4C22×C4×D1111yescharacteristic
562C2×C4C22×D4411yescharacteristic
563C2×C4#6703712yes—
564C2×C4#41×D1112yes—
565C8—21no—
566C8—21no—
567C8—21no—
568C8—21no—
569C8—22no—
570C8—22no—
571C8—442no—
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#1062233012yes—
589C22C2×C4×D4411yescharacteristic
590C22#1062308712yes—
591C4—21no—
592C4—21no—
593C4—82no—
594C4—222no—
595C4—441no—
596C4—441no—
597C4—441no—
598C4—441no—
599C4—441no—
600C4#1062301711yescharacteristic
601C4D11×#11711yescharacteristic
602C4#1062308512yes—
603C2—22no—
604C2—22no—
605C2—41no—
606C2—442no—
607C2—881no—
608C2#1307146811yescharacteristic
609C2C2×#1062233011yescharacteristic
610C2#1307753411yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1752C2
socleC22×C11C2×C4×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenter#1752D11
hypocenterC11#22586
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #1752

Complements

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

NH ≅ G/Ntype
1. #13077270C2semidirect
4. #13069327C2semidirect
5. #13069265C2semidirect
6. #13068894C2semidirect
7. #13068716C2semidirect
8. #13068654C2semidirect
10. #13068460C2semidirect
11. C11×#1752C2semidirect
17. C2×C11×#97C22semidirect
21. #10622726C4semidirect
22. #10622726C4semidirect
23. #10622726C4semidirect
24. #10622726C4semidirect
29. C2×#66885C4semidirect
30. C2×#66885C4semidirect
32. C2×#66883C22semidirect
33. C2×#66880C4semidirect
34. C2×#66880C4semidirect
35. #10622715C22semidirect
36. #10622714C22semidirect
45. C11×#336C22semidirect
46. #10622190C22semidirect
47. #10622161C22semidirect
48. #10622161C22semidirect
216. #1752D11semidirect
310. C2×#97C2×D11semidirect
315. #336C2×D11semidirect
510. C11#22586semidirect

Maximal subgroups

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

subgroupindex
#130772702
C2×#106227262
#130770622
#130693272
#130692652
#130688942
#130687162
#130686542
#130685612
#130684602
C11×#17522
#2258611