Finite Group Databasebeta

← #14781594

Subgroups — #14781594

Order 2816.

1326 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66995C211yesmaximal, characteristic
2#13077179C211yesmaximal, characteristic, complemented
3#13077136C211yesmaximal, characteristic
4C2×#10622838C211yesmaximal, characteristic, complemented
5C2×#10622745C211yesmaximal, characteristic
6#13069882C214yesmaximal, complemented
7#13069875C214yesmaximal, complemented
8#13068342C211yesmaximal, characteristic, complemented
9C22×C11×#101C211yesmaximal, characteristic, complemented
10C23×Q8×C11C2211yescharacteristic
11C22×#4339C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C22×#4326C2212yes—
15C2×#66995—24no—
16C2×#66995—24no—
17C2×#66995—22no—
18C2×#66995—22no—
19C22×#4325C2212yes—
20C2×#66979C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C2×C11×#101—24no—
24C2×C11×#101C2214yes—
25#10622838—22no—
26#10622838C2214yes—
27C2×#66899—22no—
28C2×#66888C2212yes—
29#10622746—22no—
30#10622745—24no—
31#10622744C2212yes—
32C2×#66887C2212yes—
33#10622733C2212yes—
34#10622732C2214yes—
35#10622731—22no—
36#10622726—22no—
37#10622715—22no—
38#10622196C2214yes—
39C22×Q8×C11—22no—
40C22×Q8×C11—21no—
41C22×Q8×C11—21no—
42C22×Q8×C11—21no—
43C22×Q8×C11—22no—
44C22×Q8×C11—21no—
45C22×Q8×C11—21no—
46C22×Q8×C11—22no—
47C22×Q8×C11D414yes—
48C22×Q8×C11C2312yes—
49C23×C4×C11—21no—
50C23×C4×C11C2311yescharacteristic
51C22×C22⋊D11—21no—
52C2×#4339—22no—
53C2×#4339—21no—
54C2×#4339—21no—
55C2×#4339—21no—
56C2×#4339—21no—
57C2×#4339—22no—
58C2×#4339—22no—
59C2×#4339D414yes—
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
62C22×Dic22C2311yescharacteristic
63C2×C11×M16—21no—
64C2×C11×M16—21no—
65C2×C11×M16—22no—
66C2×C11×M16—22no—
67C2×C11×M16—22no—
68C2×C11×M16—22no—
69C2×C11×M16C2312yes—
70C2×C11×M16C2312yes—
71C22×C8×C11—21no—
72C22×C8×C11—21no—
73C2×C22⋊Dic11—21no—
74C2×#4326—24no—
75C2×#4326—24no—
76C2×#4326—24no—
77#66995—216no—
78#66995—216no—
79C2×#4325—24no—
80C2×#4325—24no—
81C2×#4325—24no—
82#66979—21no—
83#66979—21no—
84#66979D412yes—
85#66979C2312yes—
86C2×C4⋊Dic11D412yes—
87C2×C4×Dic11—21no—
88C2×#4318—22no—
89C2×#4318—22no—
90C2×#4318—21no—
91C2×#4318—22no—
92C2×#4318—22no—
93C2×#4318D412yes—
94C2×#4318D412yes—
95C2×#4318C2312yes—
96C22×C11⋊C8—21no—
97C22×C11⋊C8C2312yes—
98C11×#101—28no—
99#66899—28no—
100#66888—24no—
101#66887—24no—
102#66885—24no—
103#66880—24no—
104Dic11⋊C8—28no—
105#23522—111nomaximal, Sylow
106C24×C11#4111yescharacteristic
107C23×D11—21no—
108C2×Q8×C11—24no—
109C2×Q8×C11—22no—
110C2×Q8×C11—24no—
111C2×Q8×C11—24no—
112C2×Q8×C11—24no—
113C2×Q8×C11—24no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—41no—
119C2×Q8×C11—41no—
120C2×Q8×C11—42no—
121C2×Q8×C11—42no—
122C2×Q8×C11—42no—
123C2×Q8×C11—42no—
124C2×Q8×C11—42no—
125C2×Q8×C11C2×D414yes—
126C22×C4×C11—24no—
127C22×C4×C11—22no—
128C22×C4×C11—41no—
129C22×C4×C11—41no—
130C22×C4×C11—42no—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11#4111yescharacteristic
138C22×C4×C11#4112yes—
139C22×C4×C11#4112yes—
140C22×C4×C11C2411yescharacteristic
141C2×C22⋊D11—24no—
142C2×C22⋊D11—41no—
143C2×C22⋊D11—41no—
144C2×C22⋊D11—42no—
145C22×Dic11—22no—
146C22×Dic11—21no—
147#4339—24no—
148#4339—24no—
149#4339—24no—
150#4339—24no—
151#4339—42no—
152#4339—42no—
153#4339—42no—
154#4339—42no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44C2×D412yes—
161C2×C4×D11—24no—
162C2×C4×D11—41no—
163C2×C4×D11—41no—
164C2×C4×D11—42no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22C2×D412yes—
171C11×M16—22no—
172C11×M16—22no—
173C11×M16—22no—
174C11×M16—22no—
175C11×M16—42no—
176C11×M16—42no—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C2×C8×C11—42no—
180C2×C8×C11—42no—
181C22⋊Dic11—22no—
182C22⋊Dic11—22no—
183#4326—216no—
184#4325—216no—
185C4⋊Dic11—22no—
186C4⋊Dic11C2×D414yes—
187C4×Dic11—22no—
188C4×Dic11—22no—
189#4318—24no—
190#4318—24no—
191#4318—22no—
192#4318—22no—
193#4318—42no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—42no—
198C2×C11⋊C8C2×D414yes—
199C22×#137—111no—
200#2905—111no—
201#2896—111no—
202C2×#419—111no—
203C2×#413—111no—
204C22×#101D1111yescharacteristic, complemented
205#2047—114no—
206#2046—114no—
207#1738—111no—
208C23×C11—42no—
209C23×C11#12111yescharacteristic
210C23×C11#12111yescharacteristic
211C23×C11#12312yes—
212C23×C11#12312yes—
213C23×C11C2×#4111yescharacteristic
214C22×D11—22no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—82no—
218Q8×C11—24no—
219Q8×C11—24no—
220Q8×C11—42no—
221Q8×C11—42no—
222Q8×C11—44no—
223Q8×C11—44no—
224C2×C4×C11—24no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—44no—
228C2×C4×C11—44no—
229C2×C4×C11#12012yes—
230C2×C4×C11#12012yes—
231C2×C4×C11#12112yes—
232C2×C4×C11#12112yes—
233C2×C4×C11#12111yescharacteristic
234C2×C4×C11#12111yescharacteristic
235C2×C4×C11#12112yes—
236C2×C4×C11#12112yes—
237C2×C4×C11#12312yes—
238C2×C4×C11#12312yes—
239C2×C4×C11#12412yes—
240C2×C4×C11#12412yes—
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C22⋊D11—44no—
248C22⋊D11—44no—
249C2×Dic11—24no—
250C2×Dic11—22no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—82no—
254D44—22no—
255D44—22no—
256D44—41no—
257D44—41no—
258C4×D11—44no—
259C4×D11—44no—
260Dic22—22no—
261Dic22—22no—
262Dic22—41no—
263Dic22—41no—
264C8×C11—42no—
265C8×C11—42no—
266C11⋊C8—24no—
267C11⋊C8—42no—
268C22×#41—111no—
269C23×Q8C2×D1111yescharacteristic
270C2×#137—222no—
271C2×#137—222no—
272C2×#137—224no—
273C2×#137—224no—
274C22×Q16—112no—
275C22×SD16—112no—
276C22×M16—111no—
277C22×M16—111no—
278C22×M16C2×D1111yescharacteristic
279C22×M16C2×D1111yescharacteristic
280C2×#117—111no—
281#424—114no—
282#424—222no—
283#423—222no—
284#419—114no—
285#419—112no—
286#419—222no—
287#418—112no—
288#417—222no—
289#416—222no—
290C2×#103—222no—
291#413—224no—
292C2×#101—24no—
293C2×#101—112no—
294C2×#101C2×D1114yes—
295C2×#100—112no—
296#341—114no—
297C22×C11—22no—
298C22×C11—22no—
299C22×C11—22no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11#39412yes—
303C22×C11#39412yes—
304C22×C11C2×#12111yescharacteristic
305C22×C11C2×#12311yescharacteristic
306C22×C11C2×#12311yescharacteristic
307C2×D11—42no—
308C2×D11—82no—
309C2×D11—82no—
310C2×D11—82no—
311C4×C11—44no—
312C4×C11#39412yes—
313C4×C11#39412yes—
314C4×C11C2×#12011yescharacteristic
315C4×C11C2×#12111yescharacteristic
316C4×C11C2×#12111yescharacteristic
317C4×C11C2×#12411yescharacteristic
318Dic11—42no—
319Dic11—44no—
320C2×#41—114no—
321C2×#41—222no—
322C2×#41—222no—
323C2×#41—221no—
324C2×#41—221no—
325C2×#41—221no—
326C2×#41—221no—
327C2×#41—222no—
328C22×Q8—22no—
329C22×Q8—21no—
330C22×Q8—22no—
331C22×Q8—21no—
332C22×Q8—21no—
333C22×Q8—21no—
334C22×Q8—21no—
335C22×Q8—22no—
336C22×Q8—111no—
337C22×Q8C22⋊D1114yes—
338C22×Q8C22×D1112yes—
339C22×D4—111no—
340C22×D4—221no—
341C23×C4—21no—
342C23×C4—221no—
343C23×C4C22×D1111yescharacteristic
344#137—2216no—
345#137—2216no—
346C2×Q16—224no—
347C2×Q16—224no—
348C2×Q16—224no—
349C2×SD16—224no—
350C2×SD16—224no—
351C2×SD16—224no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—22no—
355C2×M16—22no—
356C2×M16—22no—
357C2×M16—22no—
358C2×M16—112no—
359C2×M16—112no—
360C2×M16—112no—
361C2×M16—222no—
362C2×M16—222no—
363C2×M16—221no—
364C2×M16—222no—
365C2×M16—222no—
366C2×M16C22×D1112yes—
367C2×M16C22×D1112yes—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8—112no—
371C22×C8—221no—
372#117—112no—
373#117—112no—
374#117—221no—
375#117—221no—
376C2×C4⋊C4—112no—
377C2×C22⋊C4—221no—
378C2×C42—221no—
379C4⋊C8—228no—
380#103—224no—
381#103—228no—
382#102—224no—
383#101—28no—
384#101—224no—
385#100—224no—
386C2×C11—21no—
387C2×C11—21no—
388C2×C11—22no—
389C2×C11—22no—
390C2×C11C2×#39411yescharacteristic
391C2×C11#306912yes—
392D11—82no—
393C24—221no—
394C24#433911yescharacteristic
395#41—224no—
396#41—224no—
397#41—224no—
398#41—224no—
399#41—442no—
400#41—442no—
401#41—442no—
402#41—442no—
403C2×Q8—24no—
404C2×Q8—22no—
405C2×Q8—24no—
406C2×Q8—24no—
407C2×Q8—24no—
408C2×Q8—24no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—42no—
414C2×Q8—41no—
415C2×Q8—41no—
416C2×Q8—42no—
417C2×Q8—42no—
418C2×Q8—42no—
419C2×Q8—42no—
420C2×Q8—112no—
421C2×Q8—221no—
422C2×Q8—221no—
423C2×Q8—221no—
424C2×Q8—221no—
425C2×Q8—221no—
426C2×Q8C2×C22⋊D1114yes—
427C2×D4—112no—
428C2×D4—224no—
429C2×D4—221no—
430C2×D4—221no—
431C2×D4—221no—
432C2×D4—221no—
433C2×D4—221no—
434C2×D4—441no—
435C2×D4—441no—
436C2×D4—442no—
437C22×C4—24no—
438C22×C4—22no—
439C22×C4—42no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—221no—
443C22×C4—222no—
444C22×C4—224no—
445C22×C4—441no—
446C22×C4—441no—
447C22×C4—442no—
448C22×C4#433911yescharacteristic
449C22×C4#433912yes—
450C22×C4D4×D1112yes—
451C22×C4D4×D1111yescharacteristic
452C22×C4D4×D1111yescharacteristic
453C22×C4D4×D1111yescharacteristic
454C22×C4D4×D1111yescharacteristic
455C22×C4#434112yes—
456C22×C4C2×C22⋊D1112yes—
457C22×C4C23×D1111yescharacteristic
458Q16—2216no—
459SD16—2216no—
460M16—22no—
461M16—22no—
462M16—22no—
463M16—22no—
464M16—42no—
465M16—42no—
466M16—224no—
467M16—224no—
468M16—222no—
469M16—222no—
470M16—442no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—42no—
474C2×C8—42no—
475C2×C8—114no—
476C2×C8—222no—
477C2×C8—222no—
478C2×C8—222no—
479C2×C8—442no—
480C4⋊C4—114no—
481C4⋊C4—222no—
482C22⋊C4—222no—
483C22⋊C4—222no—
484C42—222no—
485C42—222no—
486C11#2352211yescharacteristic, complemented, Sylow
487C23—42no—
488C23—222no—
489C23—441no—
490C23—441no—
491C23—882no—
492C23#6693612yes—
493C23#6693711yescharacteristic
494C23#6693711yescharacteristic
495C23#6698212yes—
496C23C2×#433911yescharacteristic
497Q8—24no—
498Q8—24no—
499Q8—42no—
500Q8—42no—
501Q8—44no—
502Q8—44no—
503Q8—222no—
504Q8—222no—
505Q8—441no—
506Q8—441no—
507D4—222no—
508D4—222no—
509D4—444no—
510D4—444no—
511D4—441no—
512D4—441no—
513C2×C4—24no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—44no—
517C2×C4—44no—
518C2×C4—222no—
519C2×C4—224no—
520C2×C4—441no—
521C2×C4—441no—
522C2×C4—444no—
523C2×C4—444no—
524C2×C4—882no—
525C2×C4#6693612yes—
526C2×C4#6693712yes—
527C2×C4#6693712yes—
528C2×C4#6693711yescharacteristic
529C2×C4#6693711yescharacteristic
530C2×C4#6693812yes—
531C2×C4#6693812yes—
532C2×C4#6698212yes—
533C2×C4#6699012yes—
534C2×C4#6699012yes—
535C2×C4#6699212yes—
536C2×C4#6699212yes—
537C2×C4C2×#433911yescharacteristic
538C2×C4C2×D4×D1111yescharacteristic
539C2×C4C2×D4×D1111yescharacteristic
540C2×C4C2×D4×D1111yescharacteristic
541C2×C4C2×#434111yescharacteristic
542C2×C4C22×C22⋊D1111yescharacteristic
543C8—42no—
544C8—42no—
545C8—224no—
546C8—442no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—42no—
551C22—42no—
552C22—442no—
553C22—882no—
554C22—882no—
555C22—882no—
556C22#1062257212yes—
557C22#1062257212yes—
558C22C2×#6693611yescharacteristic
559C22C2×#6693711yescharacteristic
560C22C2×#6698211yescharacteristic
561C4—44no—
562C4—444no—
563C4—442no—
564C4#1062257212yes—
565C4#1062257212yes—
566C4C2×#6693711yescharacteristic
567C4C2×#6693811yescharacteristic
568C4C2×#6699011yescharacteristic
569C4C2×#6699211yescharacteristic
570C2—21no—
571C2—21no—
572C2—22no—
573C2—22no—
574C2—882no—
575C2C2×#1062257211yescharacteristic
576C2#1307835212yes—
subgroupG/H
centerC22C2×#66937
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#101C2
socleC22×C11C2×#121
prime radicalC22×#4339C22
hypercenterC22×#101D11
hypocenterC11#23522
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#101

Complements

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

NH ≅ G/Ntype
2. #13077179C2semidirect
4. C2×#10622838C2semidirect
6. #13069882C2semidirect
7. #13069875C2semidirect
8. #13068342C2semidirect
9. C22×C11×#101C2semidirect
204. C22×#101D11semidirect
486. C11#23522semidirect

Maximal subgroups

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

subgroupindex
C22×#669952
#130771792
#130771362
C2×#106228382
C2×#106227452
#130698822
#130698752
#130683422
C22×C11×#1012
#2352211