Finite Group Databasebeta

← #14719701

Subgroups — #14719701

Order 2816.

1098 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623047C211yesmaximal, characteristic
2#13077700C212yesmaximal, complemented
3#13066959C212yesmaximal, complemented
4#13066958C212yesmaximal, complemented
5#13066950C211yesmaximal, characteristic
6#13066947C212yesmaximal
7#13066938C212yesmaximal, complemented
8#13066927C212yesmaximal
9C11×#1464C211yesmaximal, characteristic
10C23×Dic22C411yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×#66979C411yescharacteristic
13#10623047—24no—
14#10623047—24no—
15C2×#66940C411yescharacteristic
16C2×#66940C411yescharacteristic
17C2×#66940C2211yescharacteristic
18C2×#66940C2211yescharacteristic
19C2×#66930C411yescharacteristic
20C2×#66930C411yescharacteristic
21C2×#66930C2211yescharacteristic
22C2×#66930C2211yescharacteristic
23C2×C4×Dic22C411yescharacteristic
24C2×C4×Dic22C411yescharacteristic
25C2×C4×Dic22C2211yescharacteristic
26C2×C4×Dic22C2211yescharacteristic
27C11×#432C2212yes—
28#10622539C2212yes—
29#10622441—24no—
30#10622332C2214yes—
31#10622331C2214yes—
32#10622314—24no—
33C11×#324C2212yes—
34C11×#323C2212yes—
35#10622166C2212yes—
36#10622163C2212yes—
37#10622107C2214yes—
38#10622107C2214yes—
39C23×C4×C11C2×C411yescharacteristic
40C23×Dic11C2×C411yescharacteristic
41C23×Dic11C2×C411yescharacteristic
42C22×Dic22—24no—
43C22×Dic22—22no—
44C22×Dic22—22no—
45C22×Dic22—24no—
46C22×Dic22C2×C411yescharacteristic
47C22×Dic22C2×C411yescharacteristic
48C22×Dic22C2×C411yescharacteristic
49C22×Dic22C2×C411yescharacteristic
50C11×#117—22no—
51C11×#117—22no—
52C2×C11×C4⋊C4C2×C411yescharacteristic
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C22⋊C4C2×C411yescharacteristic
55C2×C11×C22⋊C4C2311yescharacteristic
56C2×C42×C11C2×C411yescharacteristic
57C2×C42×C11C2311yescharacteristic
58C2×C22⋊Dic11C2×C411yescharacteristic
59C2×C22⋊Dic11C2×C411yescharacteristic
60#66979—22no—
61#66979—22no—
62C2×C4⋊Dic11C2×C411yescharacteristic
63C2×C4⋊Dic11C2×C411yescharacteristic
64C2×Dic11⋊C4C2×C411yescharacteristic
65C2×Dic11⋊C4C2×C411yescharacteristic
66C2×Dic11⋊C4C2×C411yescharacteristic
67C2×Dic11⋊C4C2×C411yescharacteristic
68C2×Dic11⋊C4C2×C411yescharacteristic
69C2×Dic11⋊C4C2×C411yescharacteristic
70C2×Dic11⋊C4C2311yescharacteristic
71C2×Dic11⋊C4C2311yescharacteristic
72C2×C4×Dic11C2×C411yescharacteristic
73C2×C4×Dic11C2×C411yescharacteristic
74C2×C4×Dic11C2×C411yescharacteristic
75C2×C4×Dic11C2×C411yescharacteristic
76C2×C4×Dic11C2×C411yescharacteristic
77C2×C4×Dic11C2×C411yescharacteristic
78C2×C4×Dic11C2×C411yescharacteristic
79C2×C4×Dic11C2×C411yescharacteristic
80C2×C4×Dic11C2311yescharacteristic
81C2×C4×Dic11C2311yescharacteristic
82#66940—24no—
83#66940—24no—
84#66940—24no—
85#66940—24no—
86#66930—24no—
87#66930—24no—
88#66930—24no—
89#66930—24no—
90C4×Dic22—22no—
91C4×Dic22—22no—
92C4×Dic22—22no—
93C4×Dic22—22no—
94C4×Dic22—22no—
95C4×Dic22—22no—
96C4×Dic22D414yes—
97C4×Dic22D414yes—
98C11×C4⋊C8—22no—
99C11×C22⋊C8C2314yes—
100C11×#97—22no—
101C22⋊(C11⋊C8)C2314yes—
102#66879—24no—
103Dic11⋊C8—24no—
104Dic11⋊C8—24no—
105C8×Dic11—24no—
106C4⋊(C11⋊C8)—22no—
107#66867—22no—
108#17371—111nomaximal, Sylow
109C24×C11C22×C411yescharacteristic
110C22×C4×C11—22no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11C22×C411yescharacteristic
115C22×C4×C11C22×C411yescharacteristic
116C22×C4×C11C22×C411yescharacteristic
117C22×C4×C11C22×C411yescharacteristic
118C22×C4×C11C22×C411yescharacteristic
119C22×C4×C11C2411yescharacteristic
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11M1614yes—
126C22×Dic11C22×C411yescharacteristic
127C22×Dic11C22×C411yescharacteristic
128C22×Dic11C22×C411yescharacteristic
129C22×Dic11C22×C411yescharacteristic
130C22×Dic11C22×C411yescharacteristic
131C22×Dic11C22×C411yescharacteristic
132C22×Dic11C22×C411yescharacteristic
133C22×Dic11C22×C411yescharacteristic
134C2×Dic22—216no—
135C2×Dic22—216no—
136C2×Dic22—22no—
137C2×Dic22—22no—
138C2×Dic22—22no—
139C2×Dic22—22no—
140C2×Dic22—22no—
141C2×Dic22—22no—
142C2×Dic22—22no—
143C2×Dic22—22no—
144C2×Dic22—21no—
145C2×Dic22—21no—
146C2×Dic22—22no—
147C2×Dic22C22⋊C412yes—
148C2×Dic22C22⋊C412yes—
149C2×Dic22M1614yes—
150C2×C8×C11—24no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C22⋊C4—22no—
154C11×C22⋊C4—22no—
155C42×C11—21no—
156C42×C11—21no—
157C42×C11C2×D412yes—
158C42×C11C2×D412yes—
159C22⋊Dic11—22no—
160C22⋊Dic11—22no—
161C4⋊Dic11—21no—
162C4⋊Dic11—21no—
163C4⋊Dic11C22⋊C412yes—
164C4⋊Dic11C22⋊C412yes—
165Dic11⋊C4—22no—
166Dic11⋊C4—22no—
167Dic11⋊C4—22no—
168Dic11⋊C4—22no—
169Dic11⋊C4—22no—
170Dic11⋊C4—22no—
171Dic11⋊C4C22⋊C414yes—
172Dic11⋊C4C22⋊C414yes—
173C4×Dic11—22no—
174C4×Dic11—22no—
175C4×Dic11—22no—
176C4×Dic11—22no—
177C4×Dic11—22no—
178C4×Dic11—22no—
179C4×Dic11—22no—
180C4×Dic11—22no—
181C4×Dic11C2×D414yes—
182C4×Dic11C2×D414yes—
183C2×C11⋊C8—24no—
184C2×#519—111no—
185#2983—112no—
186#1467—112no—
187#1467—112no—
188#1464—112no—
189#1464—111no—
190#1464D1111yescharacteristic
191#1461—112no—
192#1458—112no—
193C23×C11—21no—
194C23×C11—21no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11C2×M1612yes—
198C23×C11C23×C411yescharacteristic
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11C2×C22⋊C412yes—
212C2×C4×C11C2×C22⋊C411yescharacteristic
213C2×C4×C11C2×C22⋊C411yescharacteristic
214C2×C4×C11C2×M1612yes—
215C2×C4×C11C22×D412yes—
216C2×Dic11—28no—
217C2×Dic11—21no—
218C2×Dic11—21no—
219C2×Dic11—21no—
220C2×Dic11—21no—
221C2×Dic11—21no—
222C2×Dic11—21no—
223C2×Dic11—28no—
224C2×Dic11—21no—
225C2×Dic11—21no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230C2×Dic11C2×C22⋊C412yes—
231C2×Dic11C2×C22⋊C412yes—
232C2×Dic11C2×C22⋊C412yes—
233C2×Dic11C2×C22⋊C412yes—
234C2×Dic11C2×M1612yes—
235C2×Dic11C2×M1612yes—
236C2×Dic11C2×M1612yes—
237C2×Dic11C2×M1612yes—
238Dic22—28no—
239Dic22—24no—
240Dic22—24no—
241Dic22—24no—
242Dic22—24no—
243Dic22—28no—
244C8×C11—44no—
245C11⋊C8—44no—
246C23×Q8—111no—
247#519—224no—
248#519—224no—
249C2×C4×Q8—111no—
250C2×C4×Q8—111no—
251C2×C4×Q8—111no—
252C2×C4×Q8—111no—
253C2×C4×Q8—111no—
254C2×C4×Q8—111no—
255C2×C4×Q8—111no—
256C2×C4×Q8—111no—
257C2×#117—111no—
258C2×#117—111no—
259C2×#117—111no—
260C2×#117—111no—
261C2×#117—111no—
262C2×#117C2×D1111yescharacteristic
263#446—224no—
264#446—224no—
265#432—112no—
266#432—114no—
267#432C2×D1112yes—
268#431—114no—
269#324—112no—
270#324—114no—
271#324—114no—
272#324C2×D1112yes—
273#323—112no—
274#323C2×D1112yes—
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—22no—
278C22×C11—42no—
279C22×C11—42no—
280C22×C11—41no—
281C22×C11—41no—
282C22×C11C22×C22⋊C411yescharacteristic
283C22×C11C22×M1611yescharacteristic
284C22×C11C22×M1611yescharacteristic
285C4×C11—21no—
286C4×C11—21no—
287C4×C11—22no—
288C4×C11—22no—
289C4×C11—22no—
290C4×C11—41no—
291C4×C11—41no—
292Dic11—22no—
293Dic11—22no—
294Dic11—22no—
295Dic11—22no—
296Dic11—22no—
297Dic11—41no—
298Dic11—41no—
299Dic11#40714yes—
300C22×Q8—111no—
301C22×Q8—111no—
302C22×Q8—111no—
303C22×Q8—111no—
304C22×Q8—224no—
305C22×Q8—222no—
306C22×Q8—222no—
307C22×Q8—224no—
308C23×C4—111no—
309C23×C4—111no—
310C23×C4C4×D1111yescharacteristic
311C4×Q8—114no—
312C4×Q8—114no—
313C4×Q8—222no—
314C4×Q8—222no—
315C4×Q8—222no—
316C4×Q8—222no—
317C4×Q8—224no—
318C4×Q8—224no—
319C4×Q8—224no—
320C4×Q8—224no—
321C4×Q8—222no—
322C4×Q8—222no—
323#117—22no—
324#117—22no—
325#117—224no—
326#117—224no—
327#117—224no—
328#117—224no—
329#117—222no—
330#117—222no—
331C2×C4⋊C4—111no—
332C2×C4⋊C4—111no—
333C2×C4⋊C4—111no—
334C2×C4⋊C4—111no—
335C2×C4⋊C4—111no—
336C2×C4⋊C4—111no—
337C2×C4⋊C4—111no—
338C2×C4⋊C4—111no—
339C2×C4⋊C4—111no—
340C2×C4⋊C4—111no—
341C2×C4⋊C4C4×D1111yescharacteristic
342C2×C4⋊C4C22×D1111yescharacteristic
343C2×C22⋊C4—111no—
344C2×C22⋊C4—111no—
345C2×C22⋊C4C4×D1111yescharacteristic
346C2×C22⋊C4C22×D1111yescharacteristic
347C2×C42—111no—
348C2×C42—111no—
349C2×C42—111no—
350C2×C42—111no—
351C2×C42—111no—
352C2×C42—111no—
353C2×C42—111no—
354C2×C42—111no—
355C2×C42—111no—
356C2×C42—111no—
357C2×C42C4×D1111yescharacteristic
358C2×C42C22×D1111yescharacteristic
359C4⋊C8—22no—
360C4⋊C8—224no—
361C4⋊C8—224no—
362C4⋊C8—222no—
363C22⋊C8—114no—
364C22⋊C8C22×D1114yes—
365#97—22no—
366#97—224no—
367#97—222no—
368C4×C8—224no—
369C2×C11—21no—
370C2×C11—21no—
371C2×C11—42no—
372C2×C11C2×#40711yescharacteristic
373C2×C11#288411yescharacteristic
374C2×C11#288911yescharacteristic
375C24C2×C4×D1111yescharacteristic
376C2×Q8—112no—
377C2×Q8—112no—
378C2×Q8—114no—
379C2×Q8—222no—
380C2×Q8—222no—
381C2×Q8—222no—
382C2×Q8—222no—
383C2×Q8—222no—
384C2×Q8—222no—
385C2×Q8—222no—
386C2×Q8—222no—
387C2×Q8—2216no—
388C2×Q8—2216no—
389C2×Q8—221no—
390C2×Q8—221no—
391C2×Q8—222no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—111no—
397C22×C4—114no—
398C22×C4—111no—
399C22×C4—111no—
400C22×C4—111no—
401C22×C4—111no—
402C22×C4—111no—
403C22×C4—111no—
404C22×C4—111no—
405C22×C4—222no—
406C22×C4—222no—
407C22×C4—222no—
408C22×C4—222no—
409C22×C4—222no—
410C22×C4C2×C4×D1111yescharacteristic
411C22×C4C2×C4×D1111yescharacteristic
412C22×C4C2×C4×D1111yescharacteristic
413C22×C4C2×C4×D1111yescharacteristic
414C22×C4C2×C4×D1111yescharacteristic
415C22×C4C23×D1111yescharacteristic
416C2×C8—24no—
417C2×C8—224no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—114no—
421C4⋊C4—114no—
422C4⋊C4—112no—
423C4⋊C4—112no—
424C4⋊C4—222no—
425C4⋊C4—222no—
426C4⋊C4—222no—
427C4⋊C4—222no—
428C4⋊C4—221no—
429C4⋊C4—221no—
430C4⋊C4—222no—
431C4⋊C4—222no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—222no—
435C22⋊C4—222no—
436C42—21no—
437C42—21no—
438C42—114no—
439C42—114no—
440C42—222no—
441C42—222no—
442C42—222no—
443C42—222no—
444C42—222no—
445C42—222no—
446C42—222no—
447C42—222no—
448C42D4×D1112yes—
449C42D4×D1112yes—
450C11#1737111yescharacteristic, complemented, Sylow
451C23—21no—
452C23—21no—
453C23—41no—
454C23—41no—
455C23M16×D1112yes—
456C23C22×C4×D1111yescharacteristic
457Q8—224no—
458Q8—224no—
459Q8—228no—
460Q8—224no—
461Q8—224no—
462Q8—228no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—112no—
476C2×C4—112no—
477C2×C4—112no—
478C2×C4—112no—
479C2×C4—112no—
480C2×C4—112no—
481C2×C4—112no—
482C2×C4—112no—
483C2×C4—228no—
484C2×C4—228no—
485C2×C4—221no—
486C2×C4—221no—
487C2×C4—221no—
488C2×C4—221no—
489C2×C4—221no—
490C2×C4—221no—
491C2×C4—221no—
492C2×C4—221no—
493C2×C4—441no—
494C2×C4—441no—
495C2×C4—441no—
496C2×C4—441no—
497C2×C4C22⋊C4×D1111yescharacteristic
498C2×C4C22⋊C4×D1111yescharacteristic
499C2×C4C22⋊C4×D1112yes—
500C2×C4M16×D1112yes—
501C2×C4C2×D4×D1112yes—
502C8—44no—
503C8—444no—
504C22—21no—
505C22—21no—
506C22—22no—
507C22—42no—
508C22—42no—
509C22—41no—
510C22—41no—
511C22C2×C22⋊C4×D1111yescharacteristic
512C22C2×M16×D1111yescharacteristic
513C22C2×M16×D1111yescharacteristic
514C4—21no—
515C4—21no—
516C4—22no—
517C4—22no—
518C4—22no—
519C4—41no—
520C4—41no—
521C4—114no—
522C4—222no—
523C4—222no—
524C4—222no—
525C4—222no—
526C4—222no—
527C4—441no—
528C4—441no—
529C2—21no—
530C2—21no—
531C2—42no—
532C2D11×#40711yescharacteristic
533C2#1307707811yescharacteristic
534C2#1307709711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1464C2
socleC22×C11C22×C22⋊C4
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenter#1464D11
hypocenterC11#17371
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1464

Complements

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

NH ≅ G/Ntype
2. #13077700C2semidirect
3. #13066959C2semidirect
4. #13066958C2semidirect
7. #13066938C2semidirect
450. C11#17371semidirect

Maximal subgroups

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

subgroupindex
C2×#106230472
#130777002
#130669592
#130669582
#130669502
#130669472
#130669382
#130669272
C11×#14642
#1737111