Finite Group Databasebeta

← #14781782

Subgroups — #14781782

Order 2816.

1458 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622731C211yesmaximal, characteristic, complemented
2C2×#10622845C211yesmaximal, characteristic
3C2×#10622838C211yesmaximal, characteristic, complemented
4#13071107C211yesmaximal, characteristic
5C2×#10622843C211yesmaximal, characteristic, complemented
6#13069936C214yesmaximal, complemented
7#13069929C214yesmaximal, complemented
8#13068336C211yesmaximal, characteristic, complemented
9C22×C11×#137C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C23×Q8×C11C2211yescharacteristic
12C2×C11×#137—24no—
13C2×C11×#137—24no—
14C2×C11×#137—24no—
15C22×C11×Q16C2212yes—
16C22×C11×SD16C2212yes—
17C22×C11×M16C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4×Dic11C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22#10622845—24no—
23#10622843—21no—
24#10622843—21no—
25#10622843C2212yes—
26#10622843C2214yes—
27#10622838—24no—
28C2×#66899C2214yes—
29C2×#66899C2212yes—
30#10622834C2212yes—
31#10622833—22no—
32C2×#66896C2212yes—
33C4×C22⋊Dic11—21no—
34C4×C22⋊Dic11—21no—
35C2×C11⋊#95—22no—
36#10622731—24no—
37C2×Dic11⋊C8C2214yes—
38#10622189C2214yes—
39C2×C11×#41—22no—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41D414yes—
45C22×Q8×C11—21no—
46C22×Q8×C11—22no—
47C22×Q8×C11—22no—
48C22×Q8×C11—22no—
49C22×Q8×C11—22no—
50C22×Q8×C11—22no—
51C22×Q8×C11D414yes—
52C22×Q8×C11C2312yes—
53C22×Q8×C11C2311yescharacteristic
54C22×D4×C11—21no—
55C22×D4×C11C2311yescharacteristic
56C23×C4×C11—21no—
57C23×C4×C11—21no—
58C23×C4×C11C2311yescharacteristic
59C23×Dic11—21no—
60C23×Dic11D412yes—
61C11×#137—232no—
62C2×C11×Q16—24no—
63C2×C11×Q16—24no—
64C2×C11×Q16—24no—
65C2×C11×SD16—24no—
66C2×C11×SD16—24no—
67C2×C11×SD16—24no—
68C2×C11×M16—22no—
69C2×C11×M16—22no—
70C2×C11×M16D414yes—
71C22×C8×C11C2312yes—
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—22no—
74C2×C22⋊Dic11—22no—
75#66979—22no—
76#66979—22no—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11C2312yes—
81C2×C4⋊Dic11C2312yes—
82C2×C4×Dic11—22no—
83C2×C4×Dic11—22no—
84C2×C4×Dic11—21no—
85C2×C4×Dic11D411yescharacteristic
86C2×C4×Dic11D411yescharacteristic
87C2×C4×Dic11C2312yes—
88C2×#4318—22no—
89C2×#4318—22no—
90C2×#4318—22no—
91C22×C11⋊C8C2312yes—
92#66899—28no—
93#66899—24no—
94#66896—24no—
95C11⋊#95—24no—
96C11⋊#95—24no—
97C11⋊#95—22no—
98C11⋊#95—22no—
99Dic11⋊C8—28no—
100#23547—111nomaximal, Sylow
101C24×C11—21no—
102C24×C11C2×D411yescharacteristic
103C11×#41—28no—
104C11×#41—28no—
105C11×#41—44no—
106C11×#41—44no—
107C2×Q8×C11—24no—
108C2×Q8×C11—22no—
109C2×Q8×C11—21no—
110C2×Q8×C11—28no—
111C2×Q8×C11—28no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—21no—
119C2×Q8×C11—21no—
120C2×Q8×C11—42no—
121C2×Q8×C11—42no—
122C2×Q8×C11—44no—
123C2×Q8×C11—44no—
124C2×Q8×C11C2×D414yes—
125C2×Q8×C11C2×D412yes—
126C2×D4×C11—24no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—42no—
133C2×D4×C11—42no—
134C2×D4×C11C2×D412yes—
135C22×C4×C11—24no—
136C22×C4×C11—21no—
137C22×C4×C11—22no—
138C22×C4×C11—24no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11—42no—
142C22×C4×C11—42no—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11#4112yes—
148C22×C4×C11#4112yes—
149C22×C4×C11#4112yes—
150C22×C4×C11C2411yescharacteristic
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—42no—
156C22×Dic11—44no—
157C22×Dic11—42no—
158C22×Dic11C2×D412yes—
159C22×Dic11C2×D412yes—
160C11×Q16—216no—
161C11×SD16—216no—
162C11×M16—28no—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11C2×D414yes—
166C22⋊Dic11—44no—
167C22⋊Dic11—44no—
168C22⋊Dic11—42no—
169C4⋊Dic11—22no—
170C4⋊Dic11—22no—
171C4⋊Dic11—22no—
172C4⋊Dic11—22no—
173C4⋊Dic11—42no—
174C4×Dic11—22no—
175C4×Dic11—22no—
176C4×Dic11—22no—
177C4×Dic11—22no—
178C4×Dic11—42no—
179#4318—44no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—22no—
183C22×#137D1111yescharacteristic
184C2×#423—111no—
185C2×#417—111no—
186C2×#419—111no—
187#2297—111no—
188C2×#391—111no—
189#2056—114no—
190#2055—114no—
191#1736—111no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11#12112yes—
200C23×C11#12112yes—
201C23×C11#12112yes—
202C23×C11C22×D411yescharacteristic
203Q8×C11—24no—
204Q8×C11—22no—
205Q8×C11—24no—
206Q8×C11—22no—
207Q8×C11—42no—
208Q8×C11—41no—
209Q8×C11—42no—
210Q8×C11—41no—
211Q8×C11—48no—
212D4×C11—22no—
213D4×C11—22no—
214D4×C11—48no—
215D4×C11—41no—
216D4×C11—41no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—48no—
224C2×C4×C11—48no—
225C2×C4×C11#12014yes—
226C2×C4×C11#12112yes—
227C2×C4×C11#12112yes—
228C2×C4×C11#12112yes—
229C2×C4×C11#12314yes—
230C2×C4×C11#12314yes—
231C2×C4×C11#12414yes—
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—48no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—44no—
249C2×Dic11—84no—
250C2×Dic11#13714yescomplemented
251C8×C11—24no—
252C11⋊C8—42no—
253C22×#41C2×D1111yescharacteristic
254C23×Q8C2×D1111yescharacteristic
255C2×#137—24no—
256C2×#137—24no—
257C2×#137—24no—
258C22×Q16C2×D1112yes—
259C22×SD16C2×D1112yes—
260C22×M16—111no—
261C22×M16C2×D1111yescharacteristic
262C2×#117—111no—
263C22×C4⋊C4—111no—
264C22×C42—111no—
265#423—224no—
266C2×C4⋊C8—114no—
267#419—224no—
268#417—224no—
269C2×#103—114no—
270C2×#103—112no—
271C2×#102—112no—
272#391—114no—
273#391—112no—
274#391—221no—
275#391—221no—
276#390—112no—
277#386—222no—
278C4×C22⋊C4—221no—
279C4×C22⋊C4—221no—
280C2×#95—222no—
281#340—114no—
282C22×C11—24no—
283C22×C11—22no—
284C22×C11—22no—
285C22×C11—24no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—82no—
290C22×C11—82no—
291C22×C11#39414yes—
292C22×C11C2×#12111yescharacteristic
293C22×C11C2×#12111yescharacteristic
294C22×C11C2×#12111yescharacteristic
295C22×C11C2×#13712yes—
296C22×C11#57512yes—
297C4×C11—42no—
298C4×C11—44no—
299C4×C11#39414yes—
300C4×C11C2×#12011yescharacteristic
301C4×C11C2×#12311yescharacteristic
302C4×C11C2×#12311yescharacteristic
303C4×C11C2×#12411yescharacteristic
304Dic11—24no—
305Dic11—42no—
306Dic11—82no—
307Dic11—82no—
308C2×#41—22no—
309C2×#41—22no—
310C2×#41—22no—
311C2×#41—22no—
312C2×#41—22no—
313C2×#41C22⋊D1114yes—
314C22×Q8—21no—
315C22×Q8—22no—
316C22×Q8—22no—
317C22×Q8—22no—
318C22×Q8—22no—
319C22×Q8—22no—
320C22×Q8C22⋊D1114yes—
321C22×Q8C22×D1112yes—
322C22×Q8C22×D1111yescharacteristic
323C22×D4—21no—
324C22×D4C22×D1111yescharacteristic
325C23×C4—21no—
326C23×C4—21no—
327C23×C4—112no—
328C23×C4—221no—
329C23×C4C22×D1111yescharacteristic
330#137—232no—
331C2×Q16—24no—
332C2×Q16—24no—
333C2×Q16—24no—
334C2×SD16—24no—
335C2×SD16—24no—
336C2×SD16—24no—
337C2×M16—22no—
338C2×M16—22no—
339C2×M16—222no—
340C2×M16—222no—
341C2×M16—222no—
342C2×M16C22⋊D1114yes—
343C22×C8—112no—
344C22×C8C22×D1112yes—
345#117—222no—
346#117—222no—
347C2×C4⋊C4—112no—
348C2×C4⋊C4—112no—
349C2×C4⋊C4—222no—
350C2×C4⋊C4—222no—
351C2×C4⋊C4—221no—
352C2×C22⋊C4—222no—
353C2×C22⋊C4—222no—
354C2×C22⋊C4—221no—
355C2×C42—111no—
356C2×C42—111no—
357C2×C42—112no—
358C2×C42—222no—
359C2×C42—222no—
360C2×C42—221no—
361C4⋊C8—228no—
362#103—224no—
363#103—228no—
364#102—224no—
365#95—224no—
366#95—224no—
367#95—222no—
368#95—222no—
369C2×C11—24no—
370C2×C11—82no—
371C2×C11C2×#39411yescharacteristic
372C2×C11#303712yes—
373C2×C11#303911yescharacteristic
374C2×C11#304011yescharacteristic
375C2×C11#305612yes—
376C24—21no—
377C24D4×D1111yescharacteristic
378#41—28no—
379#41—28no—
380#41—44no—
381#41—44no—
382C2×Q8—24no—
383C2×Q8—22no—
384C2×Q8—21no—
385C2×Q8—28no—
386C2×Q8—28no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8—44no—
396C2×Q8—44no—
397C2×Q8—42no—
398C2×Q8—42no—
399C2×Q8C2×C22⋊D1114yes—
400C2×Q8C2×C22⋊D1112yes—
401C2×D4—24no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—42no—
408C2×D4—42no—
409C2×D4C2×C22⋊D1112yes—
410C22×C4—24no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—24no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—112no—
419C22×C4—112no—
420C22×C4—224no—
421C22×C4—224no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—442no—
425C22×C4—444no—
426C22×C4—442no—
427C22×C4D4×D1111yescharacteristic
428C22×C4#434112yes—
429C22×C4#434112yes—
430C22×C4#434112yes—
431C22×C4C2×C22⋊D1112yes—
432C22×C4C2×C22⋊D1112yes—
433C22×C4C2×C22⋊D1112yes—
434C22×C4C23×D1111yescharacteristic
435Q16—216no—
436SD16—216no—
437M16—28no—
438M16—444no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—222no—
442C2×C8—222no—
443C2×C8—222no—
444C2×C8C2×C22⋊D1114yes—
445C4⋊C4—222no—
446C4⋊C4—222no—
447C4⋊C4—222no—
448C4⋊C4—222no—
449C4⋊C4—442no—
450C22⋊C4—444no—
451C22⋊C4—444no—
452C22⋊C4—442no—
453C42—222no—
454C42—222no—
455C42—222no—
456C42—222no—
457C42—442no—
458C11#2354711yescharacteristic, complemented, Sylow
459C23—22no—
460C23—22no—
461C23—22no—
462C23—42no—
463C23—42no—
464C23—41no—
465C23—41no—
466C23#6699112yes—
467C23#6699212yes—
468C23#6699212yes—
469C23C2×D4×D1111yescharacteristic
470Q8—24no—
471Q8—22no—
472Q8—24no—
473Q8—22no—
474Q8—42no—
475Q8—41no—
476Q8—42no—
477Q8—41no—
478Q8—48no—
479D4—22no—
480D4—22no—
481D4—48no—
482D4—41no—
483D4—41no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—48no—
491C2×C4—48no—
492C2×C4—114no—
493C2×C4—222no—
494C2×C4—222no—
495C2×C4—222no—
496C2×C4—222no—
497C2×C4—222no—
498C2×C4—448no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—444no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4—884no—
505C2×C4#6698814yes—
506C2×C4#6698814yes—
507C2×C4#6698914yes—
508C2×C4#6699112yes—
509C2×C4#6699212yes—
510C2×C4#6699212yes—
511C2×C4#6700614yes—
512C2×C4C2×#434111yescharacteristic
513C2×C4C2×#434111yescharacteristic
514C2×C4C2×#434111yescharacteristic
515C2×C4C22×C22⋊D1111yescharacteristic
516C2×C4C22×C22⋊D1111yescharacteristic
517C2×C4C22×C22⋊D1111yescharacteristic
518C8—24no—
519C8—442no—
520C22—24no—
521C22—22no—
522C22—22no—
523C22—24no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—82no—
528C22—82no—
529C22#1062283514yes—
530C22D11×#13712yes—
531C22#1062330812yes—
532C22C2×#6699111yescharacteristic
533C22C2×#6699211yescharacteristic
534C22C2×#6699211yescharacteristic
535C4—42no—
536C4—44no—
537C4—224no—
538C4—442no—
539C4—882no—
540C4—882no—
541C4#1062283514yes—
542C4C2×#6698811yescharacteristic
543C4C2×#6698811yescharacteristic
544C4C2×#6698911yescharacteristic
545C4C2×#6700611yescharacteristic
546C2—24no—
547C2—82no—
548C2C2×#1062283511yescharacteristic
549C2#1307808512yes—
550C2#1307810111yescharacteristic
551C2#1307811211yescharacteristic
552C2#1307824012yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#137C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
hypercenterC22×#137D11
hypocenterC11#23547
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
1. C2×#10622731C2semidirect
3. C2×#10622838C2semidirect
5. C2×#10622843C2semidirect
6. #13069936C2semidirect
7. #13069929C2semidirect
8. #13068336C2semidirect
250. C2×Dic11#137semidirect
458. C11#23547semidirect

Maximal subgroups

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

subgroupindex
C2×#106227312
C2×#106228452
C2×#106228382
#130711072
C2×#106228432
#130699362
#130699292
#130683362
C22×C11×#1372
#2354711