Finite Group Databasebeta

← #14792689

Subgroups — #14792689

Order 2816.

976 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078564C211yesmaximal, characteristic, complemented
2C2×#10622831C211yesmaximal, characteristic
3#13077274C211yesmaximal, characteristic, complemented
4#13069976C212yesmaximal, complemented
5#13069878C212yesmaximal, complemented
6#13069522C212yesmaximal, complemented
7#13069281C212yesmaximal, complemented
8#13069084C211yesmaximal, characteristic, complemented
9#13068821C211yesmaximal, characteristic, complemented
10#13068537C211yesmaximal, characteristic
11C2×C11×#418C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C22×#4324C2212yes—
16C2×#66977C2211yescharacteristic
17C11×#418—21no—
18C11×#418—21no—
19C11×#418C2212yes—
20C11×#418C2212yes—
21C2×C11×#102—21no—
22C2×C11×#102—21no—
23#10622831—21no—
24#10622831—21no—
25#10622831—22no—
26C2×#66897C2212yes—
27C2×#66897C2212yes—
28C2×#66896C2212yes—
29#10622820C2211yescharacteristic
30#10622820C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×#66888C2212yescomplemented
33C2×#66886C2212yescomplemented
34#10622617C2211yescharacteristic, complemented
35#10622617C2211yescharacteristic, complemented
36#10622613—22no—
37#10622612C2212yescomplemented
38#10622610C2212yescomplemented
39#10622609—21no—
40#10622609—21no—
41#10622608C2211yescharacteristic, complemented
42#10622608C2211yescharacteristic, complemented
43#10622584—21no—
44#10622583—21no—
45#10622539—21no—
46#10622538—21no—
47#10622196C2212yescomplemented
48#10622192C2212yescomplemented
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—42no—
57C22×D4×C11C2312yes—
58C23×C4×C11C2311yescharacteristic
59C22×Dic22C2311yescharacteristic
60C2×C11×M16—21no—
61C2×C11×M16—42no—
62C2×C11×M16C2312yes—
63C22×C8×C11—21no—
64C11×#117—21no—
65C11×#117—21no—
66C11×#117D411yescharacteristic
67C11×#117D411yescharacteristic
68C11×#117C2311yescharacteristic
69C11×#117C2311yescharacteristic
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C22⋊C4—21no—
73C2×C42×C11—21no—
74C2×C22⋊Dic11—21no—
75C2×#4324—24no—
76C2×#4324—22no—
77C2×#4324—22no—
78C2×#4324—42no—
79C2×C4⋊Dic11C2311yescharacteristic
80#66977—21no—
81#66977—21no—
82#66977—21no—
83#66977—21no—
84C2×Dic11⋊C4—21no—
85C2×#4318C2311yescharacteristic
86C2×#4318C2312yes—
87C2×#4318C2311yescharacteristic
88C22×C11⋊C8C2312yes—
89C11×#102—22no—
90C11×#102—22no—
91C11×#102—22no—
92C11×#102—22no—
93#66897—24no—
94#66897—42no—
95#66896—22no—
96#66896—22no—
97C22⋊(C11⋊C8)—21no—
98C22⋊(C11⋊C8)—21no—
99C22⋊(C11⋊C8)—21no—
100C22⋊(C11⋊C8)—21no—
101C22⋊(C11⋊C8)D411yescharacteristic
102C22⋊(C11⋊C8)D411yescharacteristic
103C22⋊(C11⋊C8)D412yes—
104#66888—42no—
105#66886—42no—
106#66874—21no—
107#66874—21no—
108#66874—21no—
109#66874—21no—
110#66872—21no—
111#66872—21no—
112#66871—21no—
113#66871—21no—
114C4⋊(C11⋊C8)—22no—
115C4⋊(C11⋊C8)—22no—
116#66867—22no—
117C4×C11⋊C8—22no—
118#24521—111nomaximal, Sylow
119C24×C11—22no—
120C24×C11—44no—
121C24×C11—41no—
122C24×C11—41no—
123C24×C11—82no—
124C24×C11—82no—
125C24×C11#4111yescharacteristic
126C2×D4×C11—24no—
127C2×D4×C11—24no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11—44no—
134C2×D4×C11—44no—
135C2×D4×C11—44no—
136C2×D4×C11—42no—
137C2×D4×C11—42no—
138C2×D4×C11—41no—
139C2×D4×C11—41no—
140C2×D4×C11#4114yes—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11#4111yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C22×Dic11—21no—
152C22×Dic11—21no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22—22no—
156C2×Dic22—22no—
157C11×M16—22no—
158C11×M16—22no—
159C11×M16—42no—
160C2×C8×C11—22no—
161C2×C8×C11—42no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4C2×D411yescharacteristic
165C11×C4⋊C4C2×D411yescharacteristic
166C11×C4⋊C4C2×D411yescharacteristic
167C11×C4⋊C4C2×D411yescharacteristic
168C11×C22⋊C4—21no—
169C11×C22⋊C4—21no—
170C11×C22⋊C4—21no—
171C11×C22⋊C4—21no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—21no—
176C22⋊Dic11—41no—
177C22⋊Dic11—41no—
178#4324—44no—
179#4324—44no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182Dic11⋊C4—41no—
183Dic11⋊C4—41no—
184#4318—22no—
185#4318—22no—
186#4318—22no—
187#4318—22no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8C2×D412yes—
194C2×C11⋊C8C2×D412yes—
195#3095—111no—
196C2×#450—111no—
197#2924—111no—
198C2×#418D1111yescharacteristic
199#2063—112no—
200#2046—112no—
201#1977—112no—
202#1931—112no—
203#1901—111no—
204#1855—111no—
205#1783—111no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—24no—
209C23×C11—41no—
210C23×C11—44no—
211C23×C11—44no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—82no—
215C23×C11—82no—
216C23×C11—82no—
217C23×C11—82no—
218C23×C11—82no—
219C23×C11—816no—
220C23×C11—82no—
221C23×C11#12111yescharacteristic
222C23×C11#12111yescharacteristic
223C23×C11C2×#4111yescharacteristic
224D4×C11—24no—
225D4×C11—24no—
226D4×C11—44no—
227D4×C11—44no—
228D4×C11—42no—
229D4×C11—42no—
230C2×C4×C11—22no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—42no—
242C2×C4×C11—81no—
243C2×C4×C11#12111yescharacteristic
244C2×C4×C11#12111yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C2×#4112yes—
248C2×C4×C11H(5,𝔽2)12yes—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—42no—
252C2×Dic11—81no—
253Dic22—41no—
254Dic22—41no—
255Dic22—42no—
256C8×C11—42no—
257C11⋊C8—22no—
258C11⋊C8—22no—
259C11⋊C8—41no—
260C11⋊C8—41no—
261C11⋊C8—42no—
262C23×D4C2×D1111yescharacteristic
263C22×SD16—112no—
264C22×M16C2×D1111yescharacteristic
265C2×C22⋊Q8—111no—
266C2×#117C2×D1111yescharacteristic
267#485—221no—
268#485—221no—
269#484—221no—
270#483—221no—
271#450—221no—
272#450—221no—
273#450—222no—
274#433—222no—
275#432—221no—
276#431—221no—
277C2×#108—112no—
278#428—111no—
279#428—111no—
280#424—112no—
281#419—111no—
282#419—111no—
283#418—21no—
284#418—21no—
285#418C2×D1112yes—
286#418C2×D1112yes—
287C2×#102—21no—
288C2×#102—21no—
289C2×#102—112no—
290C2×#101—112no—
291C2×#100—112no—
292C2×#100—112no—
293#407—111no—
294#407—111no—
295C2×C22⋊C8—111no—
296#405—112no—
297#343—112no—
298#341—112no—
299C22×C11—21no—
300C22×C11—21no—
301C22×C11—21no—
302C22×C11—21no—
303C22×C11—21no—
304C22×C11—21no—
305C22×C11—21no—
306C22×C11—44no—
307C22×C11—44no—
308C22×C11—84no—
309C22×C11—84no—
310C22×C11—88no—
311C22×C11—88no—
312C22×C11—82no—
313C22×C11—82no—
314C22×C11#47112yes—
315C22×C11C2×#12111yescharacteristic
316C22×C11#55112yes—
317C4×C11—21no—
318C4×C11—21no—
319C4×C11—41no—
320C4×C11—41no—
321C4×C11—41no—
322C4×C11—41no—
323C4×C11#52511yescharacteristic
324C4×C11#53511yescharacteristic
325C4×C11#54612yes—
326Dic11—81no—
327Dic11—81no—
328C25—21no—
329C22×Q8—111no—
330C22×D4—24no—
331C22×D4—21no—
332C22×D4—21no—
333C22×D4—21no—
334C22×D4—21no—
335C22×D4—21no—
336C22×D4—42no—
337C22×D4C22×D1112yes—
338C23×C4C22×D1111yescharacteristic
339C2×SD16—222no—
340C2×SD16—222no—
341C2×SD16—224no—
342C2×SD16—442no—
343C2×M16—21no—
344C2×M16—42no—
345C2×M16—111no—
346C2×M16—112no—
347C2×M16—111no—
348C2×M16C22×D1112yes—
349C22×C8—21no—
350C22×C8—112no—
351C22⋊Q8—221no—
352C22⋊Q8—221no—
353C22⋊Q8—221no—
354C22⋊Q8—221no—
355#117—21no—
356#117—21no—
357#117C22⋊D1111yescharacteristic
358#117C22⋊D1111yescharacteristic
359#117C22×D1111yescharacteristic
360#117C22×D1111yescharacteristic
361C2×C4⋊C4—111no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4C22⋊D1111yescharacteristic
364C2×C4⋊C4C22⋊D1111yescharacteristic
365C2×C22⋊C4—21no—
366C2×C22⋊C4—221no—
367C2×C42—21no—
368#108—442no—
369#107—221no—
370#107—221no—
371#106—221no—
372#106—221no—
373C4⋊C8—222no—
374C4⋊C8—222no—
375#103—221no—
376#103—221no—
377#103—221no—
378#103—221no—
379#102—22no—
380#102—22no—
381#102—22no—
382#102—22no—
383#102—222no—
384#102—222no—
385#101—442no—
386#100—224no—
387#100—442no—
388C22⋊C8—111no—
389C22⋊C8—111no—
390C22⋊C8—112no—
391C22⋊C8—221no—
392C22⋊C8—221no—
393C22⋊C8—221no—
394C22⋊C8—221no—
395#97—222no—
396C4×C8—222no—
397C2×C11—22no—
398C2×C11—22no—
399C2×C11—41no—
400C2×C11—84no—
401C2×C11#241111yescharacteristic
402C2×C11C2×#47111yescharacteristic
403C2×C11#306811yescharacteristic
404C24—22no—
405C24—44no—
406C24—41no—
407C24—41no—
408C24—82no—
409C24—82no—
410C24#434111yescharacteristic
411C2×Q8—222no—
412C2×Q8—221no—
413C2×Q8—222no—
414C2×Q8—221no—
415C2×D4—24no—
416C2×D4—24no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—44no—
423C2×D4—44no—
424C2×D4—44no—
425C2×D4—42no—
426C2×D4—42no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4#433914yes—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4D4×D1111yescharacteristic
437C22×C4D4×D1111yescharacteristic
438C22×C4#434111yescharacteristic
439C22×C4C2×C22⋊D1111yescharacteristic
440C22×C4C2×C22⋊D1111yescharacteristic
441C22×C4C23×D1111yescharacteristic
442SD16—444no—
443SD16—444no—
444M16—22no—
445M16—22no—
446M16—42no—
447M16—222no—
448M16—222no—
449M16—222no—
450M16—222no—
451C2×C8—22no—
452C2×C8—42no—
453C2×C8—112no—
454C2×C8—112no—
455C2×C8—222no—
456C2×C8—222no—
457C2×C8—222no—
458C2×C8—221no—
459C2×C8—221no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—441no—
465C4⋊C4—441no—
466C4⋊C4C2×C22⋊D1111yescharacteristic
467C4⋊C4C2×C22⋊D1111yescharacteristic
468C4⋊C4C2×C22⋊D1111yescharacteristic
469C4⋊C4C2×C22⋊D1111yescharacteristic
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—441no—
475C22⋊C4—441no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—21no—
480C11#2452111yescharacteristic, complemented, Sylow
481C23—22no—
482C23—22no—
483C23—24no—
484C23—41no—
485C23—44no—
486C23—44no—
487C23—42no—
488C23—42no—
489C23—82no—
490C23—82no—
491C23—82no—
492C23—82no—
493C23—82no—
494C23—816no—
495C23—82no—
496C23#6699211yescharacteristic
497C23#6699211yescharacteristic
498C23C2×#434111yescharacteristic
499Q8—442no—
500Q8—441no—
501Q8—441no—
502D4—24no—
503D4—24no—
504D4—44no—
505D4—44no—
506D4—42no—
507D4—42no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—42no—
520C2×C4—81no—
521C2×C4—442no—
522C2×C4—441no—
523C2×C4—441no—
524C2×C4—881no—
525C2×C4#6699211yescharacteristic
526C2×C4#6699211yescharacteristic
527C2×C4C2×#433912yes—
528C2×C4C2×D4×D1111yescharacteristic
529C2×C4#6703712yes—
530C2×C4C22×C22⋊D1111yescharacteristic
531C8—42no—
532C8—222no—
533C8—222no—
534C8—442no—
535C8—441no—
536C8—441no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—44no—
545C22—44no—
546C22—84no—
547C22—84no—
548C22—88no—
549C22—88no—
550C22—82no—
551C22—82no—
552C22#1062281312yes—
553C22#1062302612yes—
554C22C2×#6699211yescharacteristic
555C4—21no—
556C4—21no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—881no—
562C4—881no—
563C4#1062302112yes—
564C4#1062332211yescharacteristic
565C4#1062333611yescharacteristic
566C2—22no—
567C2—22no—
568C2—41no—
569C2—84no—
570C2#1307200111yescharacteristic
571C2C2×#1062281311yescharacteristic
572C2#1307834111yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#418C2
socleC22×C11C2×#121
prime radicalC23×D4×C11C22
hypercenterC2×#418D11
hypocenterC11#24521
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
1. #13078564C2semidirect
3. #13077274C2semidirect
4. #13069976C2semidirect
5. #13069878C2semidirect
6. #13069522C2semidirect
7. #13069281C2semidirect
8. #13069084C2semidirect
9. #13068821C2semidirect
32. C2×#66888C22semidirect
33. C2×#66886C22semidirect
34. #10622617C22semidirect
35. #10622617C22semidirect
37. #10622612C22semidirect
38. #10622610C22semidirect
41. #10622608C22semidirect
42. #10622608C22semidirect
47. #10622196C22semidirect
48. #10622192C22semidirect
480. C11#24521semidirect

Maximal subgroups

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

subgroupindex
#130785642
C2×#106228312
#130772742
#130699762
#130698782
#130695222
#130692812
#130690842
#130688212
#130685372
C2×C11×#4182
#2452111