Finite Group Databasebeta

← #14792672

Subgroups — #14792672

Order 2816.

1002 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078556C211yesmaximal, characteristic, complemented
2C2×#10622345C211yesmaximal, characteristic
3C2×#10622614C211yesmaximal, characteristic, complemented
4#13069975C212yesmaximal, complemented
5#13069872C212yesmaximal, complemented
6#13069526C212yesmaximal, complemented
7#13069278C212yesmaximal, complemented
8#13069077C211yesmaximal, characteristic, complemented
9#13068823C211yesmaximal, characteristic, complemented
10#13068536C211yesmaximal, characteristic, complemented
11C11×#2924C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×#66983C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16C22×D88C2212yes—
17C11×#433—22no—
18C11×#432—21no—
19C11×#431—21no—
20C11×#424C2212yescomplemented
21C11×#407C2211yescharacteristic
22C2×C11×C22⋊C8C2211yescharacteristic
23C11×#405C2212yescomplemented
24#10622820C2211yescharacteristic
25C2×#66887C2212yes—
26C2×#66887C2212yes—
27C2×#66887C2212yescomplemented
28C2×#66885C2212yes—
29C2×#66883C2212yescomplemented
30#10622616—21no—
31#10622616—21no—
32#10622614—21no—
33#10622614—21no—
34#10622614C2212yes—
35#10622614C2212yes—
36#10622614C2211yescharacteristic, complemented
37#10622614C2211yescharacteristic, complemented
38#10622608C2211yescharacteristic, complemented
39#10622608C2211yescharacteristic, complemented
40#10622581—21no—
41#10622580—21no—
42C2×#66873—21no—
43C2×#66873—21no—
44#10622345—21no—
45#10622345—21no—
46#10622345—22no—
47#10622192C2212yescomplemented
48#10622190C2212yescomplemented
49C24×D11—21no—
50C23×C4×C11C2311yescharacteristic
51C22×C22⋊D11—21no—
52C22×D44—21no—
53C22×D44—21no—
54C22×D44—24no—
55C22×D44—21no—
56C22×D44—21no—
57C22×D44—21no—
58C22×D44—42no—
59C22×D44C2311yescharacteristic
60C22×D44C2312yes—
61C2×C11×M16C2312yes—
62C22×C8×C11C2312yes—
63C11×#117—21no—
64C11×#117—21no—
65C11×#117D411yescharacteristic
66C11×#117D411yescharacteristic
67C11×#117C2311yescharacteristic
68C11×#117C2311yescharacteristic
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C42×C11—21no—
73#66983—21no—
74#66983—21no—
75#66983—21no—
76#66983—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×#4318—21no—
80C2×#4318—42no—
81C2×#4318C2311yescharacteristic
82C2×#4318C2312yes—
83C2×#4318C2311yescharacteristic
84C22×C11⋊C8—21no—
85C2×D88—24no—
86C2×D88—22no—
87C2×D88—22no—
88C2×D88—42no—
89C11×C4⋊C8—22no—
90C11×C4⋊C8—22no—
91C11×C22⋊C8—21no—
92C11×C22⋊C8—21no—
93C11×C22⋊C8D411yescharacteristic
94C11×C22⋊C8D411yescharacteristic
95C11×C22⋊C8D412yes—
96C11×#97—22no—
97C4×C8×C11—22no—
98C22⋊(C11⋊C8)—21no—
99C22⋊(C11⋊C8)—21no—
100#66887—24no—
101#66887—42no—
102#66887—42no—
103#66885—22no—
104#66885—22no—
105#66883—42no—
106#66873—22no—
107#66873—22no—
108#66873—22no—
109#66873—22no—
110#66873—21no—
111#66873—21no—
112#66873—21no—
113#66873—21no—
114#66872—21no—
115#66872—21no—
116#66871—21no—
117#66871—21no—
118#24520—111nomaximal, Sylow
119C24×C11#4111yescharacteristic
120C23×D11—22no—
121C23×D11—21no—
122C23×D11—44no—
123C23×D11—41no—
124C23×D11—41no—
125C23×D11—82no—
126C23×D11—82no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11#4111yescharacteristic
136C22×C4×C11C2411yescharacteristic
137C2×C22⋊D11—41no—
138C2×C22⋊D11—41no—
139C2×C22⋊D11—82no—
140C22×Dic11—21no—
141C2×D44—24no—
142C2×D44—24no—
143C2×D44—22no—
144C2×D44—22no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—22no—
148C2×D44—22no—
149C2×D44—22no—
150C2×D44—22no—
151C2×D44—22no—
152C2×D44—44no—
153C2×D44—44no—
154C2×D44—44no—
155C2×D44—42no—
156C2×D44—42no—
157C2×D44—41no—
158C2×D44—41no—
159C2×D44#4114yes—
160C11×M16—22no—
161C11×M16—22no—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11C2×D412yes—
166C2×C8×C11C2×D412yes—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4C2×D411yescharacteristic
170C11×C4⋊C4C2×D411yescharacteristic
171C11×C4⋊C4C2×D411yescharacteristic
172C11×C4⋊C4C2×D411yescharacteristic
173C11×C22⋊C4—21no—
174C11×C22⋊C4—21no—
175C11×C22⋊C4—21no—
176C11×C22⋊C4—21no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181(C2×D11)⋊C4—41no—
182(C2×D11)⋊C4—41no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185#4318—22no—
186#4318—22no—
187#4318—22no—
188#4318—22no—
189#4318—42no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—42no—
194D88—44no—
195D88—44no—
196#3094—111no—
197C2×#447—111no—
198#2924D1111yescharacteristic, complemented
199C2×#418—111no—
200#2063—112no—
201#2045—112no—
202#1978—112no—
203#1931—112no—
204#1900—111no—
205#1855—111no—
206#1783—111no—
207C23×C11—22no—
208C23×C11—22no—
209C23×C11—41no—
210C23×C11#12111yescharacteristic
211C23×C11#12111yescharacteristic
212C23×C11C2×#4111yescharacteristic
213C22×D11—24no—
214C22×D11—44no—
215C22×D11—44no—
216C22×D11—42no—
217C22×D11—42no—
218C22×D11—41no—
219C22×D11—42no—
220C22×D11—82no—
221C22×D11—82no—
222C22×D11—82no—
223C22×D11—816no—
224C22×D11—82no—
225C22×D11—82no—
226C22×D11—82no—
227C22×D11—81no—
228C22×D11—81no—
229C2×C4×C11—22no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—42no—
241C2×C4×C11—81no—
242C2×C4×C11#12111yescharacteristic
243C2×C4×C11#12111yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C2×#4112yes—
247C2×C4×C11H(5,𝔽2)12yes—
248C22⋊D11—82no—
249C22⋊D11—82no—
250C2×Dic11—41no—
251C2×Dic11—81no—
252D44—24no—
253D44—24no—
254D44—44no—
255D44—44no—
256D44—41no—
257D44—42no—
258D44—41no—
259D44—42no—
260D44—42no—
261C8×C11—22no—
262C8×C11—22no—
263C8×C11—42no—
264C11⋊C8—41no—
265C11⋊C8—42no—
266C11⋊C8—41no—
267C23×D4—111no—
268C22×D8—112no—
269C22×M16—111no—
270C2×#121—111no—
271C2×#117C2×D1111yescharacteristic
272#482—221no—
273#482—221no—
274#481—221no—
275#480—221no—
276#447—221no—
277#447—221no—
278#447—222no—
279#433—22no—
280#432—21no—
281#431—21no—
282C2×#108—112no—
283#428—111no—
284#428—111no—
285#424C2×D1112yescomplemented
286#418—112no—
287#418—111no—
288#418—111no—
289#418—112no—
290#418—221no—
291#418—221no—
292C2×#102—112no—
293C2×#102—221no—
294C2×#102—221no—
295C2×#100—112no—
296C2×#100—112no—
297C2×#100—112no—
298#407—111no—
299#407C2×D1111yescharacteristic
300C2×C22⋊C8C2×D1111yescharacteristic
301#405C2×D1112yescomplemented
302#343—112no—
303#341—112no—
304C22×C11—21no—
305C22×C11—21no—
306C22×C11—21no—
307C22×C11—21no—
308C22×C11—21no—
309C22×C11—21no—
310C22×C11—21no—
311C22×C11—44no—
312C22×C11#47212yes—
313C22×C11C2×#12111yescharacteristic
314C22×C11#55112yes—
315C2×D11—44no—
316C2×D11—84no—
317C2×D11—88no—
318C2×D11—88no—
319C2×D11—82no—
320C2×D11—82no—
321C2×D11—84no—
322C2×D11—81no—
323C2×D11—81no—
324C2×D11—81no—
325C2×D11—162no—
326C4×C11—21no—
327C4×C11—21no—
328C4×C11—41no—
329C4×C11—41no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11#52511yescharacteristic
333C4×C11#53511yescharacteristic
334C4×C11#54612yes—
335Dic11—81no—
336C25—221no—
337C22×D4—112no—
338C22×D4—111no—
339C22×D4—224no—
340C22×D4—221no—
341C22×D4—221no—
342C22×D4—221no—
343C22×D4—221no—
344C22×D4—221no—
345C22×D4—221no—
346C22×D4—442no—
347C23×C4C22×D1111yescharacteristic
348C2×D8—224no—
349C2×D8—222no—
350C2×D8—222no—
351C2×D8—442no—
352C2×M16—112no—
353C2×M16—111no—
354C2×M16—111no—
355C2×M16—221no—
356C2×M16—442no—
357C2×M16C22×D1112yes—
358C22×C8—221no—
359C22×C8C22×D1112yes—
360#121—221no—
361#121—221no—
362#121—221no—
363#121—221no—
364#117—21no—
365#117—21no—
366#117D4411yescharacteristic
367#117D4411yescharacteristic
368#117C22×D1111yescharacteristic
369#117C22×D1111yescharacteristic
370C2×C4⋊C4—111no—
371C2×C4⋊C4D4411yescharacteristic
372C2×C4⋊C4D4411yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—221no—
375C2×C42—21no—
376#108—442no—
377#107—221no—
378#107—221no—
379#106—221no—
380#106—221no—
381C4⋊C8—22no—
382C4⋊C8—22no—
383#102—222no—
384#102—222no—
385#102—222no—
386#102—222no—
387#102—222no—
388#102—222no—
389#102—221no—
390#102—221no—
391#102—221no—
392#102—221no—
393#100—224no—
394#100—442no—
395#100—442no—
396C22⋊C8—21no—
397C22⋊C8—21no—
398C22⋊C8—221no—
399C22⋊C8—221no—
400C22⋊C8C22⋊D1111yescharacteristic
401C22⋊C8C22⋊D1111yescharacteristic
402C22⋊C8C22⋊D1112yes—
403#97—22no—
404C4×C8—22no—
405C2×C11—22no—
406C2×C11—22no—
407C2×C11—41no—
408C2×C11#241111yescharacteristic
409C2×C11C2×#47211yescharacteristic
410C2×C11#306811yescharacteristic
411D11—84no—
412D11—161no—
413C24—222no—
414C24—221no—
415C24—444no—
416C24—441no—
417C24—441no—
418C24—882no—
419C24—882no—
420C24#433911yescharacteristic
421C2×D4—114no—
422C2×D4—224no—
423C2×D4—224no—
424C2×D4—222no—
425C2×D4—221no—
426C2×D4—222no—
427C2×D4—222no—
428C2×D4—222no—
429C2×D4—222no—
430C2×D4—222no—
431C2×D4—222no—
432C2×D4—221no—
433C2×D4—444no—
434C2×D4—444no—
435C2×D4—444no—
436C2×D4—442no—
437C2×D4—442no—
438C2×D4—441no—
439C2×D4—441no—
440C2×D4—441no—
441C2×D4—441no—
442C2×D4—882no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—221no—
448C22×C4C2×D4411yescharacteristic
449C22×C4C2×D4411yescharacteristic
450C22×C4#433911yescharacteristic
451C22×C4C2×C22⋊D1111yescharacteristic
452C22×C4C2×C22⋊D1111yescharacteristic
453C22×C4C23×D1111yescharacteristic
454D8—444no—
455D8—444no—
456M16—22no—
457M16—22no—
458M16—222no—
459M16—222no—
460M16—222no—
461M16—222no—
462M16—442no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—222no—
469C2×C8—442no—
470C2×C8C2×C22⋊D1112yes—
471C2×C8C2×C22⋊D1112yes—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4C2×D4411yescharacteristic
477C4⋊C4C2×D4411yescharacteristic
478C4⋊C4C2×D4411yescharacteristic
479C4⋊C4C2×D4411yescharacteristic
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—441no—
485C22⋊C4—441no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—21no—
490C11#2452011yescharacteristic, complemented, Sylow
491C23—22no—
492C23—22no—
493C23—41no—
494C23—224no—
495C23—444no—
496C23—444no—
497C23—442no—
498C23—442no—
499C23—441no—
500C23—442no—
501C23—882no—
502C23—882no—
503C23—882no—
504C23—882no—
505C23—882no—
506C23—881no—
507C23—881no—
508C23—8816no—
509C23—882no—
510C23#6698311yescharacteristic
511C23#6698311yescharacteristic
512C23C2×#433911yescharacteristic
513D4—224no—
514D4—224no—
515D4—444no—
516D4—444no—
517D4—441no—
518D4—442no—
519D4—441no—
520D4—442no—
521D4—442no—
522D4—882no—
523D4—882no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—42no—
536C2×C4—81no—
537C2×C4—441no—
538C2×C4—881no—
539C2×C4#6698311yescharacteristic
540C2×C4#6698311yescharacteristic
541C2×C4C22×D4411yescharacteristic
542C2×C4#41×D1112yes—
543C2×C4#6704212yes—
544C2×C4C22×C22⋊D1111yescharacteristic
545C8—22no—
546C8—22no—
547C8—42no—
548C8—441no—
549C8—442no—
550C8—441no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—44no—
559C22—444no—
560C22—884no—
561C22—884no—
562C22—888no—
563C22—888no—
564C22—882no—
565C22—882no—
566C22—881no—
567C22—881no—
568C22—881no—
569C22—1762no—
570C22#1062275512yes—
571C22#1062305812yes—
572C22C2×#6698311yescharacteristic
573C4—21no—
574C4—21no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—881no—
580C4#1062305511yescharacteristic
581C4#1062305611yescharacteristic
582C4#1062336012yes—
583C2—22no—
584C2—22no—
585C2—41no—
586C2—884no—
587C2—1761no—
588C2#1307199511yescharacteristic
589C2C2×#1062275511yescharacteristic
590C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2924C2
socleC22×C11C2×#121
prime radicalC2×#10622345C2
hypercenter#2924D11
hypocenterC11#24520
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2924

Complements

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

NH ≅ G/Ntype
1. #13078556C2semidirect
3. C2×#10622614C2semidirect
4. #13069975C2semidirect
5. #13069872C2semidirect
6. #13069526C2semidirect
7. #13069278C2semidirect
8. #13069077C2semidirect
9. #13068823C2semidirect
10. #13068536C2semidirect
11. C11×#2924C2semidirect
20. C11×#424C22semidirect
23. C11×#405C22semidirect
27. C2×#66887C22semidirect
29. C2×#66883C22semidirect
36. #10622614C22semidirect
37. #10622614C22semidirect
38. #10622608C22semidirect
39. #10622608C22semidirect
47. #10622192C22semidirect
48. #10622190C22semidirect
198. #2924D11semidirect
285. #424C2×D11semidirect
301. #405C2×D11semidirect
490. C11#24520semidirect

Maximal subgroups

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

subgroupindex
#130785562
C2×#106223452
C2×#106226142
#130699752
#130698722
#130695262
#130692782
#130690772
#130688232
#130685362
C11×#29242
#2452011