Finite Group Databasebeta

← #14759012

Subgroups — #14759012

Order 2816.

1186 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623153C211yesmaximal, characteristic
2C2×M16×Dic11C211yesmaximal, characteristic
3#13071018C211yesmaximal, characteristic
4#13069575C212yesmaximal, complemented
5#13069416C212yesmaximal, complemented
6#13069050C211yesmaximal, characteristic
7#13069049C211yesmaximal, characteristic
8#13069047C211yesmaximal, characteristic
9#13068448C212yesmaximal, complemented
10#13068445C212yesmaximal, complemented
11C11×#1894C211yesmaximal, characteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×C22⋊Q8C2211yescharacteristic
14C2×Q8×Dic11C2211yescharacteristic
15C2×#66997C2211yescharacteristic
16C2×#66977C2211yescharacteristic
17C22×C4×Dic11C2211yescharacteristic
18C22×#4318C2211yescharacteristic
19#10623153—24no—
20#10623153C418yescomplemented
21C2×#66942—21no—
22C2×#66941C2211yescharacteristic
23C2×#66940—21no—
24C2×#66940C2211yescharacteristic
25C2×#66931—21no—
26C2×#66930—21no—
27C2×#66930—21no—
28C2×C11×#103C2212yes—
29C11×#380C2211yescharacteristic
30C2×#66899C2212yes—
31#10622825C2211yescharacteristic
32M16×Dic11—24no—
33C2×#66880C2212yes—
34C2×#66879C2212yes—
35C2×C8×Dic11C2212yes—
36#10622589C2212yes—
37C4⋊C4×Dic11C2212yes—
38C2×#66874C2212yes—
39#10622555—21no—
40#10622263—21no—
41#10622262—21no—
42C11×#340C2212yes—
43#10622189C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C22×Q8×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×Dic11D411yescharacteristic
49C23×Dic11D411yescharacteristic
50C22×Dic22—21no—
51C22×Dic22C2311yescharacteristic
52C2×C11×M16—22no—
53C2×C11×M16—24no—
54C22×C8×C11C2312yes—
55C11×C22⋊Q8—22no—
56C11×C22⋊Q8C2×C414yes—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C22⋊C4—21no—
61C2×C11×C22⋊C4—21no—
62C2×C22⋊Dic11—21no—
63C2×C22⋊Dic11—21no—
64Q8×Dic11—22no—
65Q8×Dic11C2×C414yes—
66#66997—22no—
67#66997C2×C414yes—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11C2312yes—
70C2×C4⋊Dic11C2311yescharacteristic
71#66977—22no—
72#66977C2×C414yes—
73C2×Dic11⋊C4—21no—
74C2×Dic11⋊C4—21no—
75C2×Dic11⋊C4—21no—
76C2×Dic11⋊C4—21no—
77C2×Dic11⋊C4—21no—
78C2×Dic11⋊C4—22no—
79C2×Dic11⋊C4—22no—
80C2×C4×Dic11—21no—
81C2×C4×Dic11—21no—
82C2×C4×Dic11—22no—
83C2×C4×Dic11C2×C414yes—
84C2×C4×Dic11D411yescharacteristic
85C2×C4×Dic11D411yescharacteristic
86C2×C4×Dic11D414yes—
87C2×C4×Dic11C2311yescharacteristic
88C2×C4×Dic11C2311yescharacteristic
89C2×#4318—22no—
90C2×#4318—24no—
91C22×C11⋊C8C2312yes—
92#66942—28no—
93#66941—22no—
94#66941C2×C414yes—
95#66940—28no—
96#66940—22no—
97#66940C2×C414yes—
98#66931—28no—
99#66930—28no—
100#66930—44no—
101C11×#103—24no—
102C11×#95—21no—
103#66899—24no—
104C11⋊#95—21no—
105C11⋊#95—22no—
106#66880—24no—
107#66879—24no—
108C8×Dic11—24no—
109#66874—24no—
110#21409—111nomaximal, Sylow
111C24×C11C2×D411yescharacteristic
112C2×Q8×C11—21no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11C22×C412yes—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11C22×C412yes—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2411yescharacteristic
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—24no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—22no—
131C22×Dic11C22⋊C414yes—
132C22×Dic11C22⋊C414yes—
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C22×Dic11C2×D411yescharacteristic
136C22×Dic11C2×D411yescharacteristic
137C2×Dic22—24no—
138C2×Dic22—21no—
139C2×Dic22—22no—
140C2×Dic22—22no—
141C2×Dic22—42no—
142C2×Dic22—42no—
143C2×Dic22C22×C412yes—
144C11×M16—28no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11#4114yes—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4C22×C412yes—
153C11×C22⋊C4—24no—
154C11×C22⋊C4—42no—
155C22⋊Dic11—24no—
156C22⋊Dic11—42no—
157C4⋊Dic11—24no—
158C4⋊Dic11—21no—
159C4⋊Dic11—22no—
160C4⋊Dic11—22no—
161C4⋊Dic11C22×C412yes—
162Dic11⋊C4—24no—
163Dic11⋊C4—24no—
164Dic11⋊C4—24no—
165Dic11⋊C4—24no—
166Dic11⋊C4—24no—
167Dic11⋊C4—44no—
168Dic11⋊C4—44no—
169C4×Dic11—24no—
170C4×Dic11—24no—
171C4×Dic11—44no—
172C4×Dic11C22⋊C414yes—
173C4×Dic11C22⋊C414yes—
174C4×Dic11C22×C412yes—
175C4×Dic11C22×C412yes—
176C4×Dic11C2×D412yes—
177C4×Dic11C2×D412yes—
178#4318—28no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8#4114yes—
182C2×#533—111no—
183C2×C4×M16—111no—
184#2285—111no—
185#1990—112no—
186#1956—112no—
187#1894—111no—
188#1894—111no—
189#1894—111no—
190#1894D1111yescharacteristic
191#1763—112no—
192#1763—112no—
193C23×C11—22no—
194C23×C11—21no—
195C23×C11—22no—
196C23×C11—21no—
197C23×C11C2×C22⋊C412yes—
198C23×C11C22×D411yescharacteristic
199Q8×C11—24no—
200Q8×C11—41no—
201Q8×C11—41no—
202C2×C4×C11—22no—
203C2×C4×C11—24no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—42no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11C2×C22⋊C412yes—
215C2×C4×C11C23×C411yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C2×#4112yes—
218C2×C4×C11C2×#4112yes—
219C2×Dic11—21no—
220C2×Dic11—22no—
221C2×Dic11—21no—
222C2×Dic11—28no—
223C2×Dic11—28no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—42no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11C2×C22⋊C412yes—
233C2×Dic11C2×C22⋊C412yes—
234C2×Dic11C2×C22⋊C412yes—
235C2×Dic11C2×C22⋊C412yes—
236C2×Dic11AGL(1,ℤ/8)12yes—
237C2×Dic11#13712yes—
238C2×Dic11#13714yes—
239Dic22—24no—
240Dic22—41no—
241Dic22—41no—
242Dic22—48no—
243C8×C11—24no—
244C11⋊C8—24no—
245C22×M16—111no—
246C22×M16C2×D1111yescharacteristic
247#533—118no—
248#533—224no—
249C2×C4⋊Q8—111no—
250C2×C4⋊Q8—111no—
251C2×#125—221no—
252C2×C22⋊Q8—111no—
253C2×C22⋊Q8—221no—
254C2×C22⋊Q8C2×D1111yescharacteristic
255C2×C4×Q8—111no—
256C2×C4×Q8—111no—
257C2×C4×Q8—221no—
258C2×#117—221no—
259C2×#117—221no—
260C22×C42—111no—
261C2×#103—112no—
262C2×#103—112no—
263C2×#103—112no—
264C2×#103C2×D1112yes—
265C4×M16—224no—
266C2×#97—112no—
267C2×C4×C8—112no—
268#384—112no—
269#382—221no—
270#380—111no—
271#380—221no—
272#380C2×D1111yescharacteristic
273C4×C4⋊C4—112no—
274C4×C4⋊C4—221no—
275#340—112no—
276#340—112no—
277#340—112no—
278#340C2×D1112yes—
279C22×C11—22no—
280C22×C11—22no—
281C22×C11—22no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11C22×C22⋊C411yescharacteristic
285C22×C11#53212yes—
286C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
287C22×C11C2×#13712yes—
288C22×C11C2×#13711yescharacteristic
289C4×C11—22no—
290C4×C11—42no—
291C4×C11—42no—
292C4×C11—82no—
293C4×C11C4×#4112yes—
294C4×C11#52511yescharacteristic
295C4×C11#52511yescharacteristic
296Dic11—22no—
297Dic11—22no—
298Dic11—42no—
299Dic11—42no—
300Dic11—82no—
301Dic11#41714yes—
302Dic11#41914yes—
303C22×Q8—111no—
304C22×Q8—221no—
305C22×Q8C22×D1111yescharacteristic
306C23×C4—111no—
307C23×C4—111no—
308C23×C4C22×D1111yescharacteristic
309C2×M16—22no—
310C2×M16—24no—
311C2×M16—224no—
312C2×M16—222no—
313C22×C8—112no—
314C22×C8C22×D1112yes—
315C4⋊Q8—114no—
316C4⋊Q8—114no—
317C4⋊Q8—222no—
318C4⋊Q8—222no—
319#125—228no—
320C22⋊Q8—22no—
321C22⋊Q8—114no—
322C22⋊Q8—228no—
323C22⋊Q8—222no—
324C22⋊Q8C4×D1114yes—
325C4×Q8—114no—
326C4×Q8—114no—
327C4×Q8—222no—
328C4×Q8—228no—
329C4×Q8—222no—
330#117—228no—
331#117—444no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—111no—
334C2×C4⋊C4—112no—
335C2×C4⋊C4—221no—
336C2×C4⋊C4—221no—
337C2×C4⋊C4—221no—
338C2×C4⋊C4—221no—
339C2×C4⋊C4—221no—
340C2×C4⋊C4—221no—
341C2×C4⋊C4—222no—
342C2×C4⋊C4—222no—
343C2×C4⋊C4C22×D1112yes—
344C2×C4⋊C4C22×D1111yescharacteristic
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—221no—
348C2×C22⋊C4—221no—
349C2×C42—114no—
350C2×C42—111no—
351C2×C42—111no—
352C2×C42—114no—
353C2×C42—111no—
354C2×C42—111no—
355C2×C42—221no—
356C2×C42—221no—
357C2×C42—222no—
358#103—24no—
359#103—224no—
360#103—224no—
361#103—224no—
362#97—224no—
363C4×C8—224no—
364#95—21no—
365#95—222no—
366#95—221no—
367C2×C11—42no—
368C2×C11#229711yescharacteristic
369C2×C11C2×#41911yescharacteristic
370C2×C11C2×#41711yescharacteristic
371C2×C11#318212yes—
372C2×C11#318512yes—
373C24D4×D1111yescharacteristic
374C2×Q8—21no—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8—112no—
378C2×Q8—224no—
379C2×Q8—221no—
380C2×Q8—222no—
381C2×Q8—222no—
382C2×Q8—442no—
383C2×Q8—442no—
384C2×Q8C2×C4×D1112yes—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—111no—
391C22×C4—111no—
392C22×C4—114no—
393C22×C4—114no—
394C22×C4—111no—
395C22×C4—111no—
396C22×C4—222no—
397C22×C4—224no—
398C22×C4—222no—
399C22×C4—221no—
400C22×C4—221no—
401C22×C4—222no—
402C22×C4C2×C4×D1112yes—
403C22×C4D4×D1111yescharacteristic
404C22×C4D4×D1112yes—
405C22×C4C23×D1111yescharacteristic
406M16—28no—
407M16—228no—
408C2×C8—22no—
409C2×C8—22no—
410C2×C8—114no—
411C2×C8—222no—
412C2×C8—222no—
413C2×C8#434114yes—
414C4⋊C4—24no—
415C4⋊C4—21no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—112no—
419C4⋊C4—224no—
420C4⋊C4—224no—
421C4⋊C4—224no—
422C4⋊C4—224no—
423C4⋊C4—224no—
424C4⋊C4—224no—
425C4⋊C4—221no—
426C4⋊C4—222no—
427C4⋊C4—222no—
428C4⋊C4—444no—
429C4⋊C4—444no—
430C4⋊C4C2×C4×D1112yes—
431C22⋊C4—24no—
432C22⋊C4—42no—
433C22⋊C4—224no—
434C22⋊C4—442no—
435C42—114no—
436C42—114no—
437C42—112no—
438C42—112no—
439C42—112no—
440C42—112no—
441C42—224no—
442C42—224no—
443C42—444no—
444C11#2140911yescharacteristic, complemented, Sylow
445C23—21no—
446C23—22no—
447C23—21no—
448C23—22no—
449C23C22⋊C4×D1112yes—
450C23C2×D4×D1111yescharacteristic
451Q8—24no—
452Q8—41no—
453Q8—41no—
454Q8—224no—
455Q8—448no—
456Q8—441no—
457Q8—441no—
458C2×C4—22no—
459C2×C4—24no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—112no—
471C2×C4—112no—
472C2×C4—112no—
473C2×C4—114no—
474C2×C4—112no—
475C2×C4—112no—
476C2×C4—112no—
477C2×C4—228no—
478C2×C4—228no—
479C2×C4—221no—
480C2×C4—222no—
481C2×C4—221no—
482C2×C4—222no—
483C2×C4—222no—
484C2×C4—441no—
485C2×C4—441no—
486C2×C4—442no—
487C2×C4—442no—
488C2×C4—442no—
489C2×C4—442no—
490C2×C4C22⋊C4×D1112yes—
491C2×C4C22×C4×D1111yescharacteristic
492C2×C4C2×D4×D1111yescharacteristic
493C2×C4C2×#434112yes—
494C2×C4#41×D1112yes—
495C8—24no—
496C8—224no—
497C22—22no—
498C22—22no—
499C22—22no—
500C22—42no—
501C22—42no—
502C22C2×C22⋊C4×D1111yescharacteristic
503C22#1062312712yes—
504C22D11×AGL(1,ℤ/8)11yescharacteristic
505C22D11×#13712yes—
506C22D11×#13711yescharacteristic
507C4—22no—
508C4—42no—
509C4—42no—
510C4—82no—
511C4—114no—
512C4—114no—
513C4—222no—
514C4—222no—
515C4—442no—
516C4—442no—
517C4—882no—
518C4C4×#434112yes—
519C4#1062311711yescharacteristic
520C4#1062318711yescharacteristic
521C2—42no—
522C2#1307110111yescharacteristic
523C2D11×#41911yescharacteristic
524C2D11×#41711yescharacteristic
525C2#1307932912yes—
526C2#1307935612yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1894C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1894D11
hypocenterC11#21409
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1894

Complements

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

NH ≅ G/Ntype
4. #13069575C2semidirect
5. #13069416C2semidirect
9. #13068448C2semidirect
10. #13068445C2semidirect
20. #10623153C4semidirect
444. C11#21409semidirect

Maximal subgroups

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

subgroupindex
C2×#106231532
C2×M16×Dic112
#130710182
#130695752
#130694162
#130690502
#130690492
#130690472
#130684482
#130684452
C11×#18942
#2140911