Finite Group Databasebeta

← #14660716

Subgroups — #14660716

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077179C211yesmaximal, characteristic, complemented
2C22×#66887C211yesmaximal, characteristic
3C22×#66887C211yesmaximal, characteristic
4#13071196C211yesmaximal, characteristic
5C2×#10622171C211yesmaximal, characteristic, complemented
6#13068354C211yesmaximal, characteristic, complemented
7C2×C11×#344C211yesmaximal, characteristic, complemented
8C23×D44C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×#66979C2211yescharacteristic
13C22×#4318C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C2×#66887—22no—
16C2×#66887—22no—
17C2×#66887—22no—
18C2×#66887—22no—
19C2×#66887—22no—
20C2×#66887—22no—
21#10622732—22no—
22#10622731—22no—
23#10622715—22no—
24#10622601—22no—
25#10622568C414yes—
26#10622552—22no—
27C11×#344—22no—
28#10622192—22no—
29#10622171—22no—
30C24×D11C2×C412yes—
31C23×C4×C11C2311yescharacteristic
32C22×D44—21no—
33C22×D44—21no—
34C22×D44—21no—
35C22×D44—21no—
36C22×D44—21no—
37C22×D44—21no—
38C22×D44—21no—
39C22×D44—21no—
40C22×D44—21no—
41C22×D44—21no—
42C22×D44—21no—
43C22×D44—21no—
44C22×D44D412yes—
45C22×D44Q812yes—
46C2×C11×M16—21no—
47C2×C11×M16—21no—
48C2×C11×M16—21no—
49C2×C11×M16—21no—
50C2×C11×M16—21no—
51C2×C11×M16—21no—
52C2×C11×M16—21no—
53C2×C11×M16—21no—
54C2×C11×M16—21no—
55C2×C11×M16—21no—
56C2×C11×M16D412yes—
57C2×C11×M16D412yes—
58C22×C8×C11—21no—
59C22×C8×C11—21no—
60C11×#117—21no—
61C11×#117—21no—
62C11×#117—21no—
63C11×#117—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C22⋊C4C2×C412yes—
66C2×C42×C11—21no—
67C2×C22⋊Dic11C2×C412yes—
68C2×(C2×D11)⋊C4—28no—
69#66979—21no—
70#66979—21no—
71#66979—21no—
72#66979—21no—
73C2×C4⋊Dic11D412yes—
74C2×C4×Dic11D412yes—
75C2×#4318—21no—
76C2×#4318—21no—
77C2×#4318—21no—
78C2×#4318—21no—
79C2×#4318—21no—
80C2×#4318—21no—
81C2×#4318—21no—
82C2×#4318—21no—
83C2×#4318—21no—
84C2×#4318—21no—
85C2×#4318D412yes—
86C2×#4318D412yes—
87C22×C11⋊C8—21no—
88C22×C11⋊C8—21no—
89#66887—28no—
90#66887—28no—
91Dic11⋊C8—28no—
92#11047—111nomaximal, Sylow
93C24×C11C22×C411yescharacteristic
94C23×D11—22no—
95C23×D11—22no—
96C23×D11—22no—
97C23×D11—22no—
98C23×D11—22no—
99C23×D11—22no—
100C23×D11—84no—
101C23×D11C4⋊C414yes—
102C22×C4×C11—22no—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×Q811yescharacteristic
111C22×C4×C11#4111yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C22×C4×C11#4111yescharacteristic
114C22×C4×C11#4111yescharacteristic
115C22×C4×C11#4111yescharacteristic
116C22×C4×C11#4111yescharacteristic
117C22×Dic11C22⋊C414yes—
118C2×D44—22no—
119C2×D44—22no—
120C2×D44—22no—
121C2×D44—22no—
122C2×D44—22no—
123C2×D44—22no—
124C2×D44—22no—
125C2×D44—22no—
126C2×D44—22no—
127C2×D44—22no—
128C2×D44—22no—
129C2×D44—22no—
130C2×D44—41no—
131C2×D44—41no—
132C2×D44—41no—
133C2×D44—41no—
134C2×D44—41no—
135C2×D44—41no—
136C2×D44—41no—
137C2×D44—41no—
138C2×D44—41no—
139C2×D44—41no—
140C2×D44—41no—
141C2×D44—41no—
142C2×D44—41no—
143C2×D44—41no—
144C2×D44—41no—
145C2×D44—41no—
146C11×M16—22no—
147C11×M16—22no—
148C11×M16—22no—
149C11×M16—22no—
150C11×M16—41no—
151C11×M16—41no—
152C11×M16—41no—
153C11×M16—41no—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C2×C8×C11—41no—
157C2×C8×C11—41no—
158C2×C8×C11—41no—
159C2×C8×C11—41no—
160C11×C4⋊C4—41no—
161C11×C4⋊C4—41no—
162C11×C22⋊C4—22no—
163C11×C22⋊C4—22no—
164C42×C11—41no—
165C42×C11—41no—
166C22⋊Dic11—22no—
167C22⋊Dic11—22no—
168(C2×D11)⋊C4—88no—
169C4⋊Dic11—22no—
170C4⋊Dic11—22no—
171C4×Dic11—22no—
172C4×Dic11—22no—
173#4318—22no—
174#4318—22no—
175#4318—22no—
176#4318—22no—
177#4318—41no—
178#4318—41no—
179#4318—41no—
180#4318—41no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—41no—
184C2×C11⋊C8—41no—
185C2×C11⋊C8—41no—
186C2×C11⋊C8—41no—
187#2905—111no—
188C22×#100—111no—
189C22×#100—111no—
190#2309—111no—
191C2×#344—111no—
192C2×#344D1111yescharacteristic, complemented
193#1742—111no—
194C23×C11—42no—
195C23×C11C2×C22⋊C411yescharacteristic
196C23×C11C2×C4⋊C411yescharacteristic
197C23×C11#11711yescharacteristic
198C23×C11C4×D411yescharacteristic
199C23×C11C4×D411yescharacteristic
200C23×C11C4×D411yescharacteristic
201C23×C11C4×D411yescharacteristic
202C22×D11—24no—
203C22×D11—24no—
204C22×D11—24no—
205C22×D11—48no—
206C22×D11—42no—
207C22×D11—42no—
208C22×D11—42no—
209C22×D11—42no—
210C22×D11—84no—
211C22×D11—84no—
212C22×D11—84no—
213C22×D11—84no—
214C22×D11—84no—
215C22×D11—84no—
216C2×C4×C11—44no—
217C2×C4×C11—42no—
218C2×C4×C11#12011yescharacteristic
219C2×C4×C11#12011yescharacteristic
220C2×C4×C11#12011yescharacteristic
221C2×C4×C11#12111yescharacteristic
222C2×C4×C11#12111yescharacteristic
223C2×C4×C11#12111yescharacteristic
224C2×C4×C11#12111yescharacteristic
225C2×C4×C11#12111yescharacteristic
226C2×C4×C11#12111yescharacteristic
227C2×C4×C11#12111yescharacteristic
228C2×C4×C11#12111yescharacteristic
229C2×C4×C11C22⋊Q811yescharacteristic
230C2×C4×C11C22⋊Q811yescharacteristic
231C2×C4×C11C22⋊Q811yescharacteristic
232C2×C4×C11C22⋊Q811yescharacteristic
233C2×C4×C11C22⋊Q811yescharacteristic
234C2×C4×C11C22⋊Q811yescharacteristic
235C2×C4×C11#12311yescharacteristic
236C2×C4×C11#12311yescharacteristic
237C2×C4×C11#12311yescharacteristic
238C2×C4×C11#12311yescharacteristic
239C2×C4×C11#12311yescharacteristic
240C2×C4×C11#12411yescharacteristic
241C2×C4×C11#12411yescharacteristic
242C2×C4×C11#12411yescharacteristic
243C2×C4×C11#12611yescharacteristic
244C2×C4×C11#12611yescharacteristic
245C2×C4×C11#12711yescharacteristic
246C2×Dic11—24no—
247C2×Dic11—44no—
248D44—42no—
249D44—42no—
250D44—42no—
251D44—42no—
252D44—42no—
253D44—42no—
254D44—42no—
255D44—42no—
256C8×C11—42no—
257C8×C11—42no—
258C11⋊C8—42no—
259C11⋊C8—42no—
260C23×D4—111no—
261C22×M16—111no—
262C22×M16—111no—
263C22×M16C2×D1111yescharacteristic
264C22×M16C2×D1111yescharacteristic
265C2×#117—111no—
266C2×#117C2×D1111yescharacteristic
267#424—222no—
268#424—222no—
269#423—222no—
270C2×#100—222no—
271C2×#100—222no—
272C2×#100—222no—
273C2×#100—222no—
274C2×#100—222no—
275C2×#100—222no—
276#390—222no—
277#390—222no—
278#379—114no—
279#344—22no—
280#344—222no—
281#343—222no—
282C22×C11—22no—
283C22×C11—22no—
284C22×C11—22no—
285C22×C11—41no—
286C22×C11—41no—
287C22×C11—41no—
288C22×C11—41no—
289C22×C11#38011yescharacteristic
290C22×C11#38511yescharacteristic
291C22×C11#38511yescharacteristic
292C22×C11#38611yescharacteristic
293C22×C11#38811yescharacteristic
294C22×C11#38811yescharacteristic
295C22×C11#39011yescharacteristic
296C2×D11—48no—
297C2×D11—44no—
298C2×D11—84no—
299C2×D11—84no—
300C2×D11—84no—
301C2×D11—84no—
302C2×D11—84no—
303C2×D11—84no—
304C4×C11—82no—
305C4×C11#39211yescharacteristic
306C4×C11#39311yescharacteristic
307C4×C11#39411yescharacteristic
308C4×C11#39411yescharacteristic
309C4×C11#39611yescharacteristic
310C4×C11#39611yescharacteristic
311C4×C11#39711yescharacteristic
312C4×C11#39911yescharacteristic
313Dic11—44no—
314C25—112no—
315C22×D4—112no—
316C22×D4—112no—
317C22×D4—221no—
318C22×D4—221no—
319C22×D4—221no—
320C22×D4—221no—
321C22×D4—221no—
322C22×D4—221no—
323C22×D4—221no—
324C22×D4—221no—
325C22×D4—221no—
326C22×D4—221no—
327C22×D4—221no—
328C22×D4—221no—
329C23×C4C22×D1111yescharacteristic
330C2×M16—21no—
331C2×M16—21no—
332C2×M16—21no—
333C2×M16—21no—
334C2×M16—21no—
335C2×M16—21no—
336C2×M16—21no—
337C2×M16—21no—
338C2×M16—21no—
339C2×M16—21no—
340C2×M16—112no—
341C2×M16—112no—
342C2×M16—221no—
343C2×M16—221no—
344C2×M16—221no—
345C2×M16—221no—
346C2×M16—221no—
347C2×M16—221no—
348C2×M16—221no—
349C2×M16—221no—
350C2×M16—221no—
351C2×M16—221no—
352C2×M16D4412yes—
353C2×M16C22⋊D1112yes—
354C22×C8—21no—
355C22×C8—21no—
356C22×C8—221no—
357C22×C8—221no—
358#117—21no—
359#117—21no—
360#117—21no—
361#117—21no—
362#117—221no—
363#117—221no—
364#117—221no—
365#117—221no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—112no—
368C2×C22⋊C4—112no—
369C2×C22⋊C4—228no—
370C2×C22⋊C4C4×D1112yes—
371C2×C42—21no—
372C2×C42—112no—
373C4⋊C8—228no—
374#100—228no—
375#100—228no—
376C2×C11—21no—
377C2×C11—21no—
378C2×C11—21no—
379C2×C11—21no—
380C2×C11—21no—
381C2×C11—21no—
382C2×C11#143911yescharacteristic
383C2×C11#191412yes—
384D11—84no—
385C24—114no—
386C24—222no—
387C24—222no—
388C24—222no—
389C24—222no—
390C24—222no—
391C24—222no—
392C24—884no—
393C24C2×C4×D1111yescharacteristic
394C2×D4—222no—
395C2×D4—222no—
396C2×D4—222no—
397C2×D4—222no—
398C2×D4—222no—
399C2×D4—222no—
400C2×D4—222no—
401C2×D4—222no—
402C2×D4—222no—
403C2×D4—222no—
404C2×D4—222no—
405C2×D4—222no—
406C2×D4—441no—
407C2×D4—441no—
408C2×D4—441no—
409C2×D4—441no—
410C2×D4—441no—
411C2×D4—441no—
412C2×D4—441no—
413C2×D4—441no—
414C2×D4—441no—
415C2×D4—441no—
416C2×D4—441no—
417C2×D4—441no—
418C2×D4—441no—
419C2×D4—441no—
420C2×D4—441no—
421C2×D4—441no—
422C22×C4—22no—
423C22×C4—114no—
424C22×C4C2×D4411yescharacteristic
425C22×C4#433911yescharacteristic
426C22×C4#433911yescharacteristic
427C22×C4#433911yescharacteristic
428C22×C4#433911yescharacteristic
429C22×C4D4×D1111yescharacteristic
430C22×C4D4×D1111yescharacteristic
431C22×C4D4×D1111yescharacteristic
432C22×C4D4×D1111yescharacteristic
433C22×C4D4×D1111yescharacteristic
434C22×C4#434111yescharacteristic
435C22×C4Q8×D1111yescharacteristic
436C22×C4#434311yescharacteristic
437C22×C4C2×C22⋊D1111yescharacteristic
438M16—22no—
439M16—22no—
440M16—22no—
441M16—22no—
442M16—41no—
443M16—41no—
444M16—41no—
445M16—41no—
446M16—222no—
447M16—222no—
448M16—222no—
449M16—222no—
450M16—441no—
451M16—441no—
452M16—441no—
453M16—441no—
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—41no—
457C2×C8—41no—
458C2×C8—41no—
459C2×C8—41no—
460C2×C8—222no—
461C2×C8—222no—
462C2×C8—441no—
463C2×C8—441no—
464C2×C8—441no—
465C2×C8—441no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—222no—
469C4⋊C4—222no—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—222no—
473C22⋊C4—222no—
474C22⋊C4—888no—
475C42—41no—
476C42—41no—
477C42—222no—
478C42—222no—
479C11#1104711yescharacteristic, complemented, Sylow
480C23—42no—
481C23—224no—
482C23—224no—
483C23—224no—
484C23—448no—
485C23—442no—
486C23—442no—
487C23—442no—
488C23—442no—
489C23—884no—
490C23—884no—
491C23—884no—
492C23—884no—
493C23—884no—
494C23—884no—
495C23#6692511yescharacteristic
496C23C4×D4411yescharacteristic
497C23C22⋊C4×D1111yescharacteristic
498C23(C22⋊D11)⋊C411yescharacteristic
499C23C4⋊C4×D1111yescharacteristic
500C23#6694611yescharacteristic
501C23C4×C22⋊D1111yescharacteristic
502D4—442no—
503D4—442no—
504D4—442no—
505D4—442no—
506D4—442no—
507D4—442no—
508D4—442no—
509D4—442no—
510C2×C4—44no—
511C2×C4—42no—
512C2×C4—224no—
513C2×C4—444no—
514C2×C4#6692811yescharacteristic
515C2×C4#6692911yescharacteristic
516C2×C4#6693511yescharacteristic
517C2×C4#6693511yescharacteristic
518C2×C4#6693611yescharacteristic
519C2×C4#6693711yescharacteristic
520C2×C4#6693711yescharacteristic
521C2×C4#6693711yescharacteristic
522C2×C4#6693711yescharacteristic
523C2×C4#6693711yescharacteristic
524C2×C4#6693811yescharacteristic
525C2×C4#6693811yescharacteristic
526C2×C4#6694711yescharacteristic
527C2×C4#6694711yescharacteristic
528C2×C4#6694711yescharacteristic
529C2×C4#6694811yescharacteristic
530C2×C4#6694911yescharacteristic
531C2×C4#6694911yescharacteristic
532C2×C4#6694911yescharacteristic
533C2×C4#6694911yescharacteristic
534C2×C4#6695011yescharacteristic
535C2×C4#6695111yescharacteristic
536C2×C4#6698211yescharacteristic
537C2×C4#6698311yescharacteristic
538C2×C4#6699011yescharacteristic
539C2×C4#6699211yescharacteristic
540C2×C4#6699311yescharacteristic
541C2×C4#6699911yescharacteristic
542C8—42no—
543C8—42no—
544C8—442no—
545C8—442no—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—448no—
554C22—444no—
555C22—884no—
556C22—884no—
557C22—884no—
558C22—884no—
559C22—884no—
560C22—884no—
561C22#1062227811yescharacteristic
562C22#1062228011yescharacteristic
563C22#1062228111yescharacteristic
564C22#1062228211yescharacteristic
565C22#1062255311yescharacteristic
566C22#1062257011yescharacteristic
567C22#1062260211yescharacteristic
568C4—82no—
569C4—444no—
570C4#1062228511yescharacteristic
571C4#1062228611yescharacteristic
572C4#1062228811yescharacteristic
573C4#1062228911yescharacteristic
574C4#1062257211yescharacteristic
575C4#1062257311yescharacteristic
576C4#1062260511yescharacteristic
577C4#1062260711yescharacteristic
578C2—21no—
579C2—21no—
580C2—21no—
581C2—21no—
582C2—21no—
583C2—21no—
584C2—884no—
585C2#1306686011yescharacteristic
586C2#1306916212yes—
subgroupG/H
centerC22#10622278
commutatorC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#344C2
socleC22×C11#386
prime radicalC23×D44C22
cosocleC23×C4×C11C23
hypercenterC2×#344D11
hypocenterC11#11047
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
1. #13077179C2semidirect
5. C2×#10622171C2semidirect
6. #13068354C2semidirect
7. C2×C11×#344C2semidirect
192. C2×#344D11semidirect
479. C11#11047semidirect

Maximal subgroups

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

subgroupindex
#130771792
C22×#668872
#130711962
C2×#106221712
#130683542
C2×C11×#3442
#1104711