Finite Group Databasebeta

← #14792674

Subgroups — #14792674

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#13078552C211yesmaximal, characteristic, complemented
2#13077270C211yesmaximal, characteristic, complemented
3C2×#10622828C211yesmaximal, characteristic, complemented
4#13069974C212yesmaximal, complemented
5#13069869C212yesmaximal, complemented
6#13069527C212yesmaximal, complemented
7#13069275C212yesmaximal, complemented
8#13069080C211yesmaximal, characteristic, complemented
9#13068823C211yesmaximal, characteristic, complemented
10#13068537C211yesmaximal, characteristic, complemented
11C2×C11×#447C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C22×C11×D8C2212yes—
14C2×C11×#121C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C22×#4318C2211yescharacteristic
17C11×#447—21no—
18C11×#447—21no—
19C11×#447—22no—
20C2×C11×#102C2212yes—
21C2×C11×C22⋊C8C2211yescharacteristic
22C2×#66897C2212yes—
23C2×#66897C2212yes—
24C2×#66897C2212yescomplemented
25#10622828—21no—
26#10622828—21no—
27#10622828C2212yes—
28#10622828C2212yes—
29#10622828C2211yescharacteristic, complemented
30#10622828C2211yescharacteristic, complemented
31C2×#66896—21no—
32C2×#66896—21no—
33#10622820C2211yescharacteristic
34#10622820C2211yescharacteristic
35C2×#66883C2212yescomplemented
36#10622715C2212yescomplemented
37#10622714C2212yescomplemented
38#10622648—21no—
39#10622648—21no—
40#10622647—21no—
41#10622646—21no—
42#10622577C2211yescharacteristic, complemented
43#10622577C2211yescharacteristic, complemented
44#10622333—22no—
45#10622332—21no—
46#10622331—21no—
47#10622190C2212yescomplemented
48#10622168C2212yescomplemented
49C25×C11—21no—
50C22×D4×C11—24no—
51C22×D4×C11—21no—
52C22×D4×C11—21no—
53C22×D4×C11—21no—
54C22×D4×C11—21no—
55C22×D4×C11—21no—
56C22×D4×C11—21no—
57C22×D4×C11—42no—
58C22×D4×C11C2311yescharacteristic
59C22×D4×C11C2312yes—
60C23×C4×C11C2311yescharacteristic
61C2×C11×D8—24no—
62C2×C11×D8—22no—
63C2×C11×D8—22no—
64C2×C11×D8—42no—
65C22×C8×C11C2312yes—
66C11×#121—21no—
67C11×#121—21no—
68C11×#121—21no—
69C11×#121—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C22⋊Dic11—21no—
73#66979—21no—
74#66979—21no—
75#66979D411yescharacteristic
76#66979D411yescharacteristic
77#66979C2311yescharacteristic
78#66979C2311yescharacteristic
79C2×C4⋊Dic11D411yescharacteristic
80C2×C4⋊Dic11D411yescharacteristic
81C2×C4×Dic11—21no—
82C2×#4318—21no—
83C2×#4318—42no—
84C2×#4318C2311yescharacteristic
85C2×#4318C2312yes—
86C2×#4318C2311yescharacteristic
87C2×#4318C2312yes—
88C22×C11⋊C8—21no—
89C11×#102—22no—
90C11×#102—22no—
91C11×C22⋊C8D411yescharacteristic
92C11×C22⋊C8D411yescharacteristic
93C11×C22⋊C8D412yes—
94#66897—24no—
95#66897—42no—
96#66897—42no—
97#66896—22no—
98#66896—22no—
99#66896—22no—
100#66896—22no—
101#66896—21no—
102#66896—21no—
103#66896—21no—
104#66896—21no—
105C22⋊(C11⋊C8)—21no—
106C22⋊(C11⋊C8)—21no—
107C22⋊(C11⋊C8)—21no—
108C22⋊(C11⋊C8)—21no—
109#66883—42no—
110#66879—22no—
111Dic11⋊C8—22no—
112Dic11⋊C8—22no—
113C8×Dic11—22no—
114#66872—21no—
115#66872—21no—
116#66871—21no—
117#66871—21no—
118#24520—111nomaximal, Sylow
119C24×C11—22no—
120C24×C11—21no—
121C24×C11—44no—
122C24×C11—41no—
123C24×C11—41no—
124C24×C11—82no—
125C24×C11—82no—
126C24×C11#4111yescharacteristic
127C2×D4×C11—24no—
128C2×D4×C11—24no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—44no—
139C2×D4×C11—44no—
140C2×D4×C11—44no—
141C2×D4×C11—42no—
142C2×D4×C11—42no—
143C2×D4×C11—41no—
144C2×D4×C11—41no—
145C2×D4×C11—41no—
146C2×D4×C11—41no—
147C2×D4×C11—82no—
148C2×D4×C11#4114yes—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—21no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11#4111yescharacteristic
157C22×C4×C11C2411yescharacteristic
158C22×Dic11—21no—
159C22×Dic11—21no—
160C11×D8—44no—
161C11×D8—44no—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C2×C8×C11C2×D412yes—
165C2×C8×C11C2×D412yes—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C22⋊C4—41no—
169C11×C22⋊C4—41no—
170C22⋊Dic11—21no—
171C22⋊Dic11—21no—
172C22⋊Dic11—21no—
173C22⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11C2×D411yescharacteristic
177C4⋊Dic11C2×D411yescharacteristic
178C4⋊Dic11C2×D411yescharacteristic
179C4⋊Dic11C2×D411yescharacteristic
180C4×Dic11—21no—
181C4×Dic11—21no—
182C4×Dic11—21no—
183C4×Dic11—21no—
184#4318—22no—
185#4318—22no—
186#4318—22no—
187#4318—22no—
188#4318—22no—
189#4318—22no—
190#4318—42no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—42no—
196#3094—111no—
197C2×#447D1111yescharacteristic
198#2924—111no—
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—24no—
210C23×C11—41no—
211C23×C11—44no—
212C23×C11—44no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—41no—
216C23×C11—42no—
217C23×C11—82no—
218C23×C11—82no—
219C23×C11—82no—
220C23×C11—82no—
221C23×C11—82no—
222C23×C11—81no—
223C23×C11—81no—
224C23×C11—816no—
225C23×C11—82no—
226C23×C11#12111yescharacteristic
227C23×C11#12111yescharacteristic
228C23×C11C2×#4111yescharacteristic
229D4×C11—24no—
230D4×C11—24no—
231D4×C11—44no—
232D4×C11—44no—
233D4×C11—41no—
234D4×C11—42no—
235D4×C11—41no—
236D4×C11—42no—
237D4×C11—42no—
238D4×C11—82no—
239D4×C11—82no—
240C2×C4×C11—22no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—41no—
248C2×C4×C11—81no—
249C2×C4×C11#12111yescharacteristic
250C2×C4×C11#12111yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C2×#4112yes—
254C2×C4×C11H(5,𝔽2)12yes—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—42no—
260C2×Dic11—81no—
261C8×C11—22no—
262C8×C11—22no—
263C11⋊C8—41no—
264C11⋊C8—42no—
265C11⋊C8—41no—
266C11⋊C8—42no—
267C23×D4C2×D1111yescharacteristic
268C22×D8C2×D1112yes—
269C22×M16—111no—
270C2×#121C2×D1111yescharacteristic
271C2×#117—111no—
272#482—221no—
273#482—221no—
274#481—221no—
275#480—221no—
276#447—21no—
277#447—21no—
278#447—22no—
279#433—222no—
280#432—221no—
281#431—221no—
282C2×#108—112no—
283#428—111no—
284#428—111no—
285#424—112no—
286#418—112no—
287#418—111no—
288#418—111no—
289#418—112no—
290#418—221no—
291#418—221no—
292C2×#102—221no—
293C2×#102—221no—
294C2×#102C2×D1112yes—
295C2×#100—112no—
296C2×#100—112no—
297C2×#100—112no—
298#407—111no—
299#407—111no—
300C2×C22⋊C8C2×D1111yescharacteristic
301#405—112no—
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—44no—
313C22×C11—84no—
314C22×C11—84no—
315C22×C11—88no—
316C22×C11—88no—
317C22×C11—82no—
318C22×C11—82no—
319C22×C11—81no—
320C22×C11—81no—
321C22×C11—81no—
322C22×C11—162no—
323C22×C11#47212yes—
324C22×C11C2×#12111yescharacteristic
325C22×C11#55112yes—
326C4×C11—21no—
327C4×C11—21no—
328C4×C11—81no—
329C4×C11#52511yescharacteristic
330C4×C11#53511yescharacteristic
331C4×C11#54612yes—
332Dic11—41no—
333Dic11—41no—
334Dic11—41no—
335Dic11—41no—
336C25—21no—
337C22×D4—24no—
338C22×D4—21no—
339C22×D4—21no—
340C22×D4—21no—
341C22×D4—21no—
342C22×D4—21no—
343C22×D4—21no—
344C22×D4—42no—
345C22×D4C22×D1111yescharacteristic
346C22×D4C22×D1112yes—
347C23×C4C22×D1111yescharacteristic
348C2×D8—24no—
349C2×D8—22no—
350C2×D8—22no—
351C2×D8—42no—
352C2×M16—112no—
353C2×M16—111no—
354C2×M16—112no—
355C2×M16—111no—
356C2×M16—221no—
357C2×M16—442no—
358C22×C8—221no—
359C22×C8C22×D1112yes—
360#121—21no—
361#121—21no—
362#121—21no—
363#121—21no—
364#117—111no—
365#117—111no—
366#117—111no—
367#117—111no—
368#117—221no—
369#117—221no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4C22×D1111yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—221no—
375C2×C42—221no—
376#108—442no—
377#107—221no—
378#107—221no—
379#106—221no—
380#106—221no—
381C4⋊C8—222no—
382C4⋊C8—222no—
383#102—22no—
384#102—22no—
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—221no—
397C22⋊C8—221no—
398C22⋊C8—221no—
399C22⋊C8—221no—
400C22⋊C8C22⋊D1111yescharacteristic
401C22⋊C8C22⋊D1111yescharacteristic
402C22⋊C8C22⋊D1112yes—
403#97—222no—
404C4×C8—222no—
405C2×C11—22no—
406C2×C11—22no—
407C2×C11—41no—
408C2×C11—84no—
409C2×C11—161no—
410C2×C11#241111yescharacteristic
411C2×C11C2×#47211yescharacteristic
412C2×C11#306811yescharacteristic
413C24—22no—
414C24—21no—
415C24—44no—
416C24—41no—
417C24—41no—
418C24—82no—
419C24—82no—
420C24#434111yescharacteristic
421C2×D4—24no—
422C2×D4—24no—
423C2×D4—22no—
424C2×D4—21no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—21no—
432C2×D4—44no—
433C2×D4—44no—
434C2×D4—44no—
435C2×D4—42no—
436C2×D4—42no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—82no—
442C2×D4#434114yes—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4D4×D1111yescharacteristic
449C22×C4D4×D1111yescharacteristic
450C22×C4#434111yescharacteristic
451C22×C4C2×C22⋊D1111yescharacteristic
452C22×C4C2×C22⋊D1111yescharacteristic
453C22×C4C23×D1111yescharacteristic
454D8—44no—
455D8—44no—
456M16—222no—
457M16—222no—
458M16—222no—
459M16—222no—
460M16—222no—
461M16—222no—
462M16—442no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—222no—
468C2×C8—222no—
469C2×C8—442no—
470C2×C8C2×C22⋊D1112yes—
471C2×C8C2×C22⋊D1112yes—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—111no—
475C4⋊C4—111no—
476C4⋊C4—111no—
477C4⋊C4—111no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—221no—
483C22⋊C4—221no—
484C22⋊C4—221no—
485C22⋊C4—221no—
486C42—221no—
487C42—221no—
488C42—221no—
489C42—221no—
490C11#2452011yescharacteristic, complemented, Sylow
491C23—22no—
492C23—22no—
493C23—24no—
494C23—41no—
495C23—44no—
496C23—44no—
497C23—42no—
498C23—42no—
499C23—41no—
500C23—42no—
501C23—82no—
502C23—82no—
503C23—82no—
504C23—82no—
505C23—82no—
506C23—81no—
507C23—81no—
508C23—816no—
509C23—82no—
510C23#6699111yescharacteristic
511C23#6699111yescharacteristic
512C23C2×#434111yescharacteristic
513D4—24no—
514D4—24no—
515D4—44no—
516D4—44no—
517D4—42no—
518D4—42no—
519D4—41no—
520D4—42no—
521D4—41no—
522D4—82no—
523D4—82no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—81no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—442no—
538C2×C4—881no—
539C2×C4#6699111yescharacteristic
540C2×C4#6699111yescharacteristic
541C2×C4C2×D4×D1111yescharacteristic
542C2×C4C2×#434112yes—
543C2×C4#6703712yes—
544C2×C4C22×C22⋊D1111yescharacteristic
545C8—22no—
546C8—22no—
547C8—442no—
548C8—441no—
549C8—442no—
550C8—441no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—44no—
559C22—44no—
560C22—84no—
561C22—84no—
562C22—88no—
563C22—88no—
564C22—82no—
565C22—82no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22—162no—
570C22#1062277312yes—
571C22#1062311812yes—
572C22C2×#6699111yescharacteristic
573C4—21no—
574C4—21no—
575C4—81no—
576C4—441no—
577C4—441no—
578C4—441no—
579C4—441no—
580C4#1062311711yescharacteristic
581C4#1062312311yescharacteristic
582C4#1062333712yes—
583C2—22no—
584C2—22no—
585C2—41no—
586C2—84no—
587C2—161no—
588C2#1307199711yescharacteristic
589C2C2×#1062277311yescharacteristic
590C2#1307834011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#447C2
socleC22×C11C2×#121
hypercenterC2×#447D11
hypocenterC11#24520
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. #13078552C2semidirect
2. #13077270C2semidirect
3. C2×#10622828C2semidirect
4. #13069974C2semidirect
5. #13069869C2semidirect
6. #13069527C2semidirect
7. #13069275C2semidirect
8. #13069080C2semidirect
9. #13068823C2semidirect
10. #13068537C2semidirect
24. C2×#66897C22semidirect
29. #10622828C22semidirect
30. #10622828C22semidirect
35. C2×#66883C22semidirect
36. #10622715C22semidirect
37. #10622714C22semidirect
42. #10622577C22semidirect
43. #10622577C22semidirect
47. #10622190C22semidirect
48. #10622168C22semidirect
490. C11#24520semidirect

Maximal subgroups

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

subgroupindex
#130785522
#130772702
C2×#106228282
#130699742
#130698692
#130695272
#130692752
#130690802
#130688232
#130685372
C2×C11×#4472
#2452011