Finite Group Databasebeta

← #14763613

Subgroups — #14763613

Order 2816.

1044 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic
2#13077247C211yesmaximal, characteristic
3D11×#423C211yesmaximal, characteristic
4#13069606C211yesmaximal, characteristic, complemented
5#13069460C211yesmaximal, characteristic, complemented
6#13069459C211yesmaximal, characteristic, complemented
7#13069083C214yesmaximal
8#13068611C214yesmaximal, complemented
9C11×#1997C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#66999C412yes—
12C2×Q8×Dic11C412yes—
13C2×M16×D11C2212yes—
14#10623259—21no—
15#10623259—21no—
16#10623259—21no—
17#10623259—21no—
18#10623259—21no—
19#10623259—21no—
20#10623259—21no—
21#10623259—21no—
22C2×#66950C2212yes—
23C2×#66945C412yes—
24C2×#66943C412yes—
25C2×#66940C2212yes—
26C2×C42×D11C2211yescharacteristic
27C2×#66922C2211yescharacteristic
28C11×#423C2211yescharacteristic
29C4×C11×M16C2211yescharacteristic
30C2×#66888C2214yes—
31C2×#66888C2214yes—
32#10622739C2212yes—
33#10622731C2212yes—
34#10622731C2212yes—
35#10622537C2211yescharacteristic
36C4×#4318C2211yescharacteristic
37#10622450—21no—
38#10622450—21no—
39D11×C4⋊C8—21no—
40D11×C4⋊C8—21no—
41#10622318—21no—
42#10622318—21no—
43#10622298—21no—
44#10622298—21no—
45C11×#343C2214yes—
46#10622168C2214yes—
47C22×Q8×C11C2×C412yes—
48C22×C4×D11C2×C411yescharacteristic
49C22×C4×D11C2×C411yescharacteristic
50C22×C4×D11C2311yescharacteristic
51C22×Dic22C2312yes—
52C2×C11×M16C2312yes—
53C2×C11×M16C2312yes—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8—21no—
58C2×C11×C4⋊C4C2×C412yes—
59C2×C11×C4⋊C4C2312yes—
60C2×C42×C11C2311yescharacteristic
61#66999—22no—
62#66999—22no—
63#66999—22no—
64#66999—22no—
65Q8×Dic11—22no—
66Q8×Dic11—22no—
67Q8×Dic11—22no—
68Q8×Dic11—22no—
69C2×(C2×D11)⋊C4C2×C414yes—
70C2×C4⋊Dic11C2×C412yes—
71C2×C4⋊Dic11C2×C412yes—
72C2×C4⋊Dic11C2×C414yes—
73C2×Dic11⋊C4C2×C414yes—
74C2×C4×Dic11C2×C414yes—
75C2×C4×Dic11C2×C411yescharacteristic
76C2×C4×Dic11C2×C411yescharacteristic
77C2×C4×Dic11C2311yescharacteristic
78C2×#4318C2312yes—
79C2×#4318C2312yes—
80M16×D11—44no—
81C2×#4313—22no—
82C2×C8×D11—22no—
83#66950—22no—
84#66950—22no—
85#66950—22no—
86#66950—22no—
87#66945—22no—
88#66945—22no—
89#66945—22no—
90#66945—22no—
91#66943—22no—
92#66943—22no—
93#66943—22no—
94#66943—22no—
95#66940—22no—
96#66940—22no—
97#66940—22no—
98#66940—22no—
99C42×D11D411yescharacteristic
100C42×D11D411yescharacteristic
101C42×D11D411yescharacteristic
102C42×D11D411yescharacteristic
103C42×D11D411yescharacteristic
104C42×D11D411yescharacteristic
105C42×D11D411yescharacteristic
106C42×D11D411yescharacteristic
107#66922—21no—
108#66922—21no—
109#66922—21no—
110#66922—21no—
111C11×C4⋊C8—21no—
112C11×C4⋊C8—21no—
113C11×#97—21no—
114C4×C8×C11—21no—
115#66888—44no—
116#66888—44no—
117(C2×D11)⋊C8—22no—
118(C2×D11)⋊C8—22no—
119Dic11⋊C8—22no—
120Dic11⋊C8—22no—
121Dic11⋊C8—22no—
122Dic11⋊C8—22no—
123C4⋊(C11⋊C8)—21no—
124C4⋊(C11⋊C8)—21no—
125#66867—21no—
126C4×C11⋊C8—21no—
127#21879—111nomaximal, Sylow
128C23×D11C22×C411yescharacteristic
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11—44no—
132C22×C4×C11C22×C411yescharacteristic
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C22×C414yes—
135C22×C4×C11C2411yescharacteristic
136C22×Dic11C22×C414yes—
137C22×Dic11C22×C411yescharacteristic
138C22×Dic11C22×C411yescharacteristic
139C22×Dic11C22×C411yescharacteristic
140C2×C4×D11—24no—
141C2×C4×D11—22no—
142C2×C4×D11—22no—
143C2×C4×D11—42no—
144C2×C4×D11C22⋊C411yescharacteristic
145C2×C4×D11C22⋊C411yescharacteristic
146C2×C4×D11C22⋊C411yescharacteristic
147C2×C4×D11C22⋊C411yescharacteristic
148C2×C4×D11C22⋊C411yescharacteristic
149C2×C4×D11C22⋊C411yescharacteristic
150C2×C4×D11C22⋊C411yescharacteristic
151C2×C4×D11C22⋊C411yescharacteristic
152C2×C4×D11C2×D411yescharacteristic
153C2×C4×D11C2×D411yescharacteristic
154C2×C4×D11C2×D411yescharacteristic
155C2×C4×D11C2×D411yescharacteristic
156C2×Dic22—22no—
157C2×Dic22—22no—
158C2×Dic22—24no—
159C2×Dic22—24no—
160C11×M16—22no—
161C11×M16—24no—
162C11×M16—22no—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C42×C11C2×D411yescharacteristic
170C42×C11C2×D411yescharacteristic
171C42×C11C2×D411yescharacteristic
172C42×C11C2×D411yescharacteristic
173(C2×D11)⋊C4—24no—
174(C2×D11)⋊C4—24no—
175C4⋊Dic11—24no—
176C4⋊Dic11—24no—
177C4⋊Dic11—22no—
178C4⋊Dic11—22no—
179C4⋊Dic11—22no—
180C4⋊Dic11—22no—
181Dic11⋊C4—24no—
182Dic11⋊C4—24no—
183C4×Dic11—24no—
184C4×Dic11—24no—
185C4×Dic11C22⋊C411yescharacteristic
186C4×Dic11C22⋊C411yescharacteristic
187C4×Dic11C22⋊C411yescharacteristic
188C4×Dic11C22⋊C411yescharacteristic
189C4×Dic11C22⋊C411yescharacteristic
190C4×Dic11C22⋊C411yescharacteristic
191C4×Dic11C22⋊C411yescharacteristic
192C4×Dic11C22⋊C411yescharacteristic
193C4×Dic11C2×D411yescharacteristic
194C4×Dic11C2×D411yescharacteristic
195C4×Dic11C2×D411yescharacteristic
196C4×Dic11C2×D411yescharacteristic
197#4318—22no—
198#4318—24no—
199#4318—22no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—22no—
202#4313—44no—
203C8×D11—44no—
204C2×#533—111no—
205#2920—111no—
206C2×#423—111no—
207#1997—111no—
208#1997D1111yescharacteristic, complemented
209#1966—111no—
210#1966—111no—
211#1901—114no—
212#1801—114no—
213C23×C11C23×C411yescharacteristic
214C22×D11—22no—
215C22×D11—22no—
216C22×D11—41no—
217C22×D11C2×C22⋊C411yescharacteristic
218C22×D11C2×C22⋊C411yescharacteristic
219Q8×C11—44no—
220Q8×C11—44no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—44no—
225C2×C4×C11C2×C22⋊C411yescharacteristic
226C2×C4×C11C2×C22⋊C411yescharacteristic
227C2×C4×C11C2×C22⋊C411yescharacteristic
228C2×C4×C11C2×C22⋊C411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11H(5,𝔽2)12yes—
232C2×C4×C112−1+412yes—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—24no—
236C2×Dic11—28no—
237C2×Dic11—41no—
238C2×Dic11C2×C22⋊C411yescharacteristic
239C2×Dic11C2×C22⋊C411yescharacteristic
240C2×Dic11C2×C22⋊C411yescharacteristic
241C2×Dic11C2×C22⋊C411yescharacteristic
242C2×Dic11C2×C22⋊C411yescharacteristic
243C2×Dic11C2×C22⋊C411yescharacteristic
244C4×D11—22no—
245C4×D11—21no—
246C4×D11—21no—
247C4×D11—21no—
248C4×D11—21no—
249C4×D11—22no—
250C4×D11—22no—
251C4×D11—22no—
252C4×D11—22no—
253C4×D11—22no—
254C4×D11—22no—
255C4×D11—41no—
256C4×D11—41no—
257C4×D11#10114yescomplemented
258Dic22—42no—
259Dic22—42no—
260Dic22—44no—
261C8×C11—42no—
262C8×C11—42no—
263C11⋊C8—42no—
264C11⋊C8—42no—
265C22×M16—112no—
266#533—221no—
267#533—221no—
268#533—221no—
269#533—221no—
270#533—221no—
271#533—221no—
272#533—221no—
273#533—221no—
274C2×C4⋊Q8—111no—
275C2×C4⋊Q8C2×D1111yescharacteristic
276C2×#125—112no—
277C2×C22⋊Q8—112no—
278C2×C22⋊Q8—112no—
279C2×C4×Q8—112no—
280C2×C4×Q8—112no—
281C2×#117—112no—
282C22×C42—111no—
283#432—221no—
284#432—221no—
285#431—221no—
286#431—221no—
287#423—112no—
288#423—112no—
289#423—111no—
290#423—221no—
291#423—221no—
292#423C2×D1111yescharacteristic
293C2×C4⋊C8—221no—
294C2×C4⋊C8—221no—
295C2×#101—114no—
296C2×#101—114no—
297#407—112no—
298C4×M16—111no—
299C4×M16C2×D1111yescharacteristic
300#343—114no—
301#343C2×D1114yes—
302C22×C11—21no—
303C22×C11—21no—
304C22×C11C22×C22⋊C411yescharacteristic
305C22×C11#52012yes—
306C2×D11—21no—
307C2×D11—21no—
308C2×D11—21no—
309C2×D11—21no—
310C2×D11—21no—
311C2×D11—44no—
312C2×D11C2×#10112yes—
313C4×C11—21no—
314C4×C11—21no—
315C4×C11—44no—
316C4×C11C2×#10112yes—
317C4×C11#41312yes—
318C4×C11#53511yescharacteristic
319C4×C11#53611yescharacteristic
320C4×C11#53712yes—
321Dic11—21no—
322Dic11—21no—
323Dic11—21no—
324Dic11—21no—
325Dic11—21no—
326Dic11—44no—
327Dic11C2×#10112yes—
328C22×Q8—112no—
329C22×Q8C4×D1112yes—
330C23×C4—111no—
331C23×C4—111no—
332C23×C4—111no—
333C2×M16—112no—
334C2×M16—112no—
335C2×M16—222no—
336C2×M16—444no—
337C2×M16C22×D1112yes—
338C2×M16C22×D1112yes—
339C22×C8—222no—
340C4⋊Q8—21no—
341C4⋊Q8—21no—
342C4⋊Q8—21no—
343C4⋊Q8—21no—
344C4⋊Q8—221no—
345C4⋊Q8—221no—
346C4⋊Q8—221no—
347C4⋊Q8—221no—
348#125—222no—
349#125—222no—
350#125—222no—
351#125—222no—
352C22⋊Q8—222no—
353C22⋊Q8—222no—
354C22⋊Q8—222no—
355C22⋊Q8—222no—
356C22⋊Q8—222no—
357C22⋊Q8—222no—
358C22⋊Q8—222no—
359C22⋊Q8—222no—
360C4×Q8—222no—
361C4×Q8—222no—
362C4×Q8—222no—
363C4×Q8—222no—
364C4×Q8—222no—
365C4×Q8—222no—
366C4×Q8—222no—
367C4×Q8—222no—
368#117—222no—
369#117—222no—
370#117—222no—
371#117—222no—
372C2×C4⋊C4—112no—
373C2×C4⋊C4—114no—
374C2×C4⋊C4—114no—
375C2×C4⋊C4—112no—
376C2×C4⋊C4C4×D1112yes—
377C2×C4⋊C4C22×D1112yes—
378C2×C22⋊C4—114no—
379C2×C42—111no—
380C2×C42—111no—
381C2×C42—111no—
382C2×C42—111no—
383C2×C42—111no—
384C2×C42—111no—
385C2×C42—111no—
386C2×C42—111no—
387C2×C42—111no—
388C2×C42—111no—
389C2×C42—111no—
390C2×C42—114no—
391C2×C42C22×D1111yescharacteristic
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8—222no—
395C4⋊C8—222no—
396C4⋊C8—222no—
397C4⋊C8—222no—
398C4⋊C8—221no—
399C4⋊C8—221no—
400#101—444no—
401#101—444no—
402C22⋊C8—222no—
403C22⋊C8—222no—
404#97—21no—
405#97—221no—
406C4×C8—21no—
407C4×C8—221no—
408C2×C11—22no—
409C2×C11#231111yescharacteristic
410C2×C11C22×#10111yescharacteristic
411C2×C11C2×#41311yescharacteristic
412D11—22no—
413D11—41no—
414C24—111no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8—44no—
418C2×Q8—222no—
419C2×Q8—222no—
420C2×Q8—224no—
421C2×Q8—224no—
422C22×C4—111no—
423C22×C4—111no—
424C22×C4—111no—
425C22×C4—111no—
426C22×C4—111no—
427C22×C4—111no—
428C22×C4—111no—
429C22×C4—111no—
430C22×C4—111no—
431C22×C4—111no—
432C22×C4—111no—
433C22×C4—111no—
434C22×C4—111no—
435C22×C4—111no—
436C22×C4—111no—
437C22×C4—114no—
438C22×C4—224no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—442no—
442C22×C4C2×C4×D1111yescharacteristic
443C22×C4C2×C4×D1111yescharacteristic
444C22×C4C2×C4×D1114yes—
445C22×C4C23×D1111yescharacteristic
446M16—22no—
447M16—22no—
448M16—24no—
449M16—222no—
450M16—222no—
451M16—224no—
452M16—444no—
453C2×C8—22no—
454C2×C8—22no—
455C2×C8—222no—
456C2×C8—222no—
457C2×C8—444no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—224no—
463C4⋊C4—224no—
464C4⋊C4—224no—
465C4⋊C4—224no—
466C4⋊C4—222no—
467C4⋊C4—222no—
468C4⋊C4—222no—
469C4⋊C4—222no—
470C22⋊C4—224no—
471C22⋊C4—224no—
472C42—111no—
473C42—111no—
474C42—111no—
475C42—111no—
476C42—111no—
477C42—111no—
478C42—111no—
479C42—111no—
480C42—111no—
481C42—111no—
482C42—111no—
483C42—111no—
484C42—224no—
485C42—224no—
486C42D4×D1111yescharacteristic
487C42D4×D1111yescharacteristic
488C42D4×D1111yescharacteristic
489C42D4×D1111yescharacteristic
490C11#2187911yescharacteristic, complemented, Sylow
491C23—111no—
492C23—111no—
493C23—222no—
494C23—222no—
495C23—441no—
496C23C22×C4×D1111yescharacteristic
497Q8—44no—
498Q8—44no—
499Q8—442no—
500Q8—444no—
501Q8—442no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—24no—
505C2×C4—44no—
506C2×C4—111no—
507C2×C4—114no—
508C2×C4—111no—
509C2×C4—111no—
510C2×C4—111no—
511C2×C4—111no—
512C2×C4—111no—
513C2×C4—222no—
514C2×C4—222no—
515C2×C4—222no—
516C2×C4—222no—
517C2×C4—221no—
518C2×C4—221no—
519C2×C4—222no—
520C2×C4—222no—
521C2×C4—222no—
522C2×C4—222no—
523C2×C4—222no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—224no—
527C2×C4—228no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4C22⋊C4×D1111yescharacteristic
532C2×C4C22⋊C4×D1111yescharacteristic
533C2×C4C22⋊C4×D1111yescharacteristic
534C2×C4C22⋊C4×D1111yescharacteristic
535C2×C4C2×D4×D1111yescharacteristic
536C2×C4C2×D4×D1111yescharacteristic
537C2×C4#6704012yes—
538C2×C4#6704212yes—
539C8—42no—
540C8—42no—
541C8—442no—
542C8—442no—
543C22—21no—
544C22—21no—
545C22—112no—
546C22—221no—
547C22—221no—
548C22—221no—
549C22—221no—
550C22—221no—
551C22—444no—
552C22C2×C22⋊C4×D1111yescharacteristic
553C22#1062310512yes—
554C4—21no—
555C4—21no—
556C4—44no—
557C4—112no—
558C4—221no—
559C4—221no—
560C4—221no—
561C4—221no—
562C4—221no—
563C4—444no—
564C4#1062235812yes—
565C4D11×#10112yes—
566C4#1062316012yes—
567C4#1062320511yescharacteristic
568C4#1062325511yescharacteristic
569C2—22no—
570C2—222no—
571C2—441no—
572C2#1307120711yescharacteristic
573C2C2×D11×#10111yescharacteristic
574C2C2×#1062235811yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1997C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C22×C4
cosocleC22×C4×C11C24
hypercenter#1997D11
hypocenterC11#21879
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1997

Complements

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

NH ≅ G/Ntype
4. #13069606C2semidirect
5. #13069460C2semidirect
6. #13069459C2semidirect
8. #13068611C2semidirect
9. C11×#1997C2semidirect
208. #1997D11semidirect
257. C4×D11#101semidirect
490. C11#21879semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
#130772472
D11×#4232
#130696062
#130694602
#130694592
#130690832
#130686112
C11×#19972
#2187911