Finite Group Databasebeta

← #14732555

Subgroups — #14732555

Order 2816.

1138 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×D44C211yesmaximal, characteristic
2#13079757C211yesmaximal, characteristic, complemented
3#13078620C211yesmaximal, characteristic
4#13067878C214yesmaximal, complemented
5#13067779C214yesmaximal, complemented
6#13067289C211yesmaximal, characteristic, complemented
7#13067040C211yesmaximal, characteristic
8#13067011C211yesmaximal, characteristic, complemented
9C11×#3078C211yesmaximal, characteristic, complemented
10C22×Q8×D11—21no—
11C11×#533C2211yescharacteristic
12C2×C4×Q8×C11C2211yescharacteristic
13Q8×D44—22no—
14Q8×D44—22no—
15Q8×D44—22no—
16Q8×D44C2214yes—
17C2×#66950—21no—
18C2×#66950—22no—
19C2×C4×D44—21no—
20C2×C4×D44C2211yescharacteristic
21C2×#66922—21no—
22C2×#66922C2211yescharacteristic
23C11×#479—22no—
24C11×#477C2212yescomplemented
25C11×#475C2212yescomplemented
26C11×#428—21no—
27C11×#423C2211yescharacteristic
28C11×#419—21no—
29#10622697C2212yes—
30#10622696C2212yes—
31#10622694C2212yescomplemented
32#10622692C2212yescomplemented
33#10622659—21no—
34#10622656—21no—
35#10622656—22no—
36C4×#4325—22no—
37#10622633—22no—
38#10622538C2211yescharacteristic
39#10622538C2211yescharacteristic
40Q8⋊(C11⋊C8)C2214yescomplemented
41#10622121C2214yes—
42#10622120C2214yescomplemented
43C22×Q8×C11D411yescharacteristic
44C2×Q8×D11—24no—
45C2×Q8×D11—24no—
46C2×Q8×D11—44no—
47C2×Q8×D11—44no—
48C22×D44D411yescharacteristic
49C22×C4×D11—22no—
50C22×C4×D11—21no—
51C22×Dic22—22no—
52C22×Dic22—21no—
53C2×C11×M16—21no—
54C11×C4⋊Q8C2311yescharacteristic
55C11×C4⋊Q8C2311yescharacteristic
56C11×#125—21no—
57C11×C22⋊Q8—21no—
58C11×C22⋊Q8—21no—
59C4×Q8×C11—21no—
60C4×Q8×C11—21no—
61C4×Q8×C11—21no—
62C4×Q8×C11—21no—
63C4×Q8×C11D412yes—
64C4×Q8×C11C2312yes—
65C11×#117—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C42×C11—21no—
69C2×C42×C11C2311yescharacteristic
70C2×#4325—22no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—21no—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11D411yescharacteristic
76C2×C4⋊Dic11D412yes—
77#66950—24no—
78#66950—28no—
79#66950—24no—
80#66950—28no—
81C4×D44—24no—
82C4×D44—24no—
83C4×D44—21no—
84C4×D44—21no—
85C4×D44D412yes—
86C4×D44C2312yes—
87#66922—24no—
88#66922—21no—
89#66922—21no—
90#66922—24no—
91#66922D412yes—
92#66922C2312yes—
93C11×#107—22no—
94C11×#106—22no—
95C11×C4⋊C8—21no—
96C11×C4⋊C8C2312yes—
97C11×#103—22no—
98C11×#103—22no—
99#66899—24no—
100#66899—22no—
101C22⋊(C11⋊C8)—21no—
102C22⋊(C11⋊C8)—21no—
103#66873—22no—
104#66872—24no—
105#66872—22no—
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)C2312yes—
108C4×C11⋊C8—21no—
109C4×C11⋊C8C2312yes—
110#18777—111nomaximal, Sylow
111C23×D11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—22no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11SD1614yescomplemented
117C2×Q8×C11C2×D412yes—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×Dic11—21no—
124C22×Dic11—22no—
125Q8×D11—48no—
126Q8×D11—416no—
127Q8×D11—48no—
128C2×D44—24no—
129C2×D44—21no—
130C2×D44C2×D412yes—
131C2×C4×D11—28no—
132C2×C4×D11—22no—
133C2×C4×D11—22no—
134C2×C4×D11—48no—
135C2×C4×D11—42no—
136C2×C4×D11—42no—
137C2×Dic22—28no—
138C2×Dic22—22no—
139C2×Dic22—22no—
140C2×Dic22—48no—
141C2×Dic22—42no—
142C2×Dic22—42no—
143C11×M16—42no—
144C2×C8×C11—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—41no—
153C11×C4⋊C4—41no—
154C11×C4⋊C4C2×D412yes—
155C11×C22⋊C4—41no—
156C42×C11—22no—
157C42×C11—22no—
158C42×C11—41no—
159C42×C11C2×D411yescharacteristic
160C42×C11C2×D411yescharacteristic
161C42×C11C2×D411yescharacteristic
162C42×C11C2411yescharacteristic
163#4325—44no—
164(C2×D11)⋊C4—28no—
165(C2×D11)⋊C4—22no—
166(C2×D11)⋊C4—22no—
167C4⋊Dic11—28no—
168C4⋊Dic11—21no—
169C4⋊Dic11—22no—
170C4⋊Dic11—22no—
171C4⋊Dic11—22no—
172C4⋊Dic11C2×D412yes—
173C4⋊Dic11C2×D414yes—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—22no—
176C2×D4×Q8—111no—
177#3229—111no—
178#3101—111no—
179#3078D1111yescharacteristic, complemented
180#1651—114no—
181#1637—114no—
182#1546—111no—
183#1486—111no—
184#1479—111no—
185C23×C11#12011yescharacteristic
186C22×D11—24no—
187C22×D11—22no—
188C22×D11—42no—
189C22×D11—42no—
190Q8×C11—22no—
191Q8×C11—24no—
192Q8×C11—42no—
193Q8×C11—42no—
194Q8×C11C2×SD1614yes—
195C2×C4×C11—22no—
196C2×C4×C11—24no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—41no—
200C2×C4×C11—42no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11#12011yescharacteristic
204C2×C4×C11#12011yescharacteristic
205C2×C4×C11#12011yescharacteristic
206C2×C4×C11C2×SD1612yes—
207C2×C4×C11AGL(1,ℤ/8)12yes—
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C22×D411yescharacteristic
211C2×Dic11—22no—
212C2×Dic11—24no—
213C2×Dic11—42no—
214C2×Dic11—44no—
215D44—24no—
216D44—22no—
217D44#13714yes—
218C4×D11—416no—
219C4×D11—42no—
220C4×D11—42no—
221C4×D11—44no—
222Dic22—416no—
223Dic22—42no—
224Dic22—42no—
225Dic22—44no—
226C8×C11—42no—
227C11⋊C8—42no—
228C11⋊C8—42no—
229C23×Q8—221no—
230D4×Q8—114no—
231D4×Q8—222no—
232D4×Q8—222no—
233D4×Q8—222no—
234#533C2×D1111yescharacteristic
235C2×C4⋊Q8—111no—
236C2×C4⋊Q8—221no—
237C2×C22⋊Q8—222no—
238C2×C22⋊Q8—221no—
239C2×C4×Q8C2×D1111yescharacteristic
240C2×C4×D4—111no—
241C2×C4×D4—221no—
242#498—112no—
243#487—112no—
244#483—221no—
245#483—222no—
246#479—22no—
247#477C2×D1112yescomplemented
248#476—112no—
249#475—222no—
250#475C2×D1112yescomplemented
251#461—112no—
252#450—221no—
253C4×SD16—222no—
254#431—111no—
255#431—111no—
256#428—21no—
257#423C2×D1111yescharacteristic
258#419—21no—
259#332—114no—
260Q8⋊C8—114no—
261D4⋊C8—114no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11#45012yes—
265C22×C11C2×#12011yescharacteristic
266C2×D11—24no—
267C2×D11—48no—
268C2×D11—42no—
269C2×D11—42no—
270C4×C11—24no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—21no—
274C4×C11—42no—
275C4×C11—81no—
276C4×C11—81no—
277C4×C11#45012yes—
278C4×C11C22×SD1611yescharacteristic
279C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
280C4×C11C2×#13712yes—
281Dic11—42no—
282Dic11—44no—
283C22×Q8—222no—
284C22×Q8—224no—
285C22×Q8—224no—
286C22×Q8—221no—
287C22×Q8—444no—
288C22×Q8—444no—
289C22×Q8C22⋊D1111yescharacteristic
290C22×D4—111no—
291C23×C4—222no—
292C23×C4—221no—
293C2×SD16—222no—
294C2×M16—21no—
295C4⋊Q8—112no—
296C4⋊Q8—112no—
297C4⋊Q8—224no—
298C4⋊Q8—224no—
299C4⋊Q8—221no—
300C4⋊Q8—221no—
301C4⋊Q8C22×D1111yescharacteristic
302C4⋊Q8C22×D1111yescharacteristic
303#125—21no—
304C22⋊Q8—21no—
305C22⋊Q8—21no—
306C22⋊Q8—228no—
307C22⋊Q8—224no—
308C22⋊Q8—228no—
309C22⋊Q8—224no—
310C4×Q8—21no—
311C4×Q8—21no—
312C4×Q8—21no—
313C4×Q8—21no—
314C4×Q8C22⋊D1112yes—
315C4×Q8C22×D1112yes—
316C4×D4—112no—
317C4×D4—112no—
318C4×D4—224no—
319C4×D4—224no—
320C4×D4—221no—
321C4×D4—221no—
322#117—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—111no—
325C2×C4⋊C4—112no—
326C2×C4⋊C4—222no—
327C2×C4⋊C4—221no—
328C2×C4⋊C4C22⋊D1111yescharacteristic
329C2×C22⋊C4—222no—
330C2×C22⋊C4—221no—
331C2×C42—21no—
332C2×C42C22×D1111yescharacteristic
333#107—22no—
334#106—22no—
335#106—222no—
336#106—224no—
337C4⋊C8—21no—
338C4⋊C8—112no—
339C4⋊C8—221no—
340C4⋊C8C22×D1112yes—
341#103—22no—
342#103—22no—
343#103—222no—
344#103—224no—
345#102—222no—
346C22⋊C8—221no—
347C22⋊C8—221no—
348C4×C8—112no—
349C4×C8—221no—
350C2×C11—22no—
351C2×C11C2×#45011yescharacteristic
352C2×C11#300411yescharacteristic
353C2×C11#302011yescharacteristic
354D11—44no—
355C24—221no—
356C2×Q8—21no—
357C2×Q8—22no—
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8—228no—
361C2×Q8—222no—
362C2×Q8—222no—
363C2×Q8—448no—
364C2×Q8—448no—
365C2×Q8—4416no—
366C2×Q8—448no—
367C2×Q8—442no—
368C2×Q8—442no—
369C2×Q8#432514yescomplemented
370C2×Q8C2×C22⋊D1112yes—
371C2×D4—112no—
372C2×D4—224no—
373C2×D4—221no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—228no—
377C22×C4—222no—
378C22×C4—221no—
379C22×C4—222no—
380C22×C4—222no—
381C22×C4—448no—
382C22×C4—442no—
383C22×C4—442no—
384C22×C4D4×D1111yescharacteristic
385C22×C4D4×D1111yescharacteristic
386C22×C4C2×C22⋊D1111yescharacteristic
387SD16—444no—
388M16—42no—
389C2×C8—22no—
390C2×C8—222no—
391C2×C8—222no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—22no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—41no—
400C4⋊C4—41no—
401C4⋊C4—112no—
402C4⋊C4—114no—
403C4⋊C4—228no—
404C4⋊C4—221no—
405C4⋊C4—222no—
406C4⋊C4—222no—
407C4⋊C4—222no—
408C4⋊C4C2×C22⋊D1112yes—
409C22⋊C4—41no—
410C22⋊C4—228no—
411C22⋊C4—222no—
412C22⋊C4—222no—
413C42—22no—
414C42—22no—
415C42—41no—
416C42D4×D1111yescharacteristic
417C42D4×D1111yescharacteristic
418C42C2×C22⋊D1111yescharacteristic
419C42C23×D1111yescharacteristic
420C11#1877711yescharacteristic, complemented, Sylow
421C23—224no—
422C23—222no—
423C23—442no—
424C23—442no—
425C23#6699011yescharacteristic
426Q8—22no—
427Q8—24no—
428Q8—42no—
429Q8—42no—
430Q8—4416no—
431Q8—442no—
432Q8—442no—
433Q8—444no—
434Q8C2×#432514yes—
435D4—114no—
436D4—224no—
437D4—222no—
438C2×C4—22no—
439C2×C4—24no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—224no—
447C2×C4—222no—
448C2×C4—4416no—
449C2×C4—444no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—442no—
453C2×C4—444no—
454C2×C4#6699011yescharacteristic
455C2×C4#6699011yescharacteristic
456C2×C4#6699011yescharacteristic
457C2×C4C2×#432512yes—
458C2×C4#6700212yes—
459C2×C4C2×D4×D1111yescharacteristic
460C2×C4C2×D4×D1111yescharacteristic
461C2×C4C22×C22⋊D1111yescharacteristic
462C8—42no—
463C8—442no—
464C8—442no—
465C22—21no—
466C22—21no—
467C22—224no—
468C22—448no—
469C22—442no—
470C22—442no—
471C22#1062265912yes—
472C22C2×#6699011yescharacteristic
473C4—24no—
474C4—21no—
475C4—21no—
476C4—21no—
477C4—42no—
478C4—81no—
479C4—81no—
480C4—444no—
481C4—442no—
482C4#1062265912yes—
483C4D11×#13712yes—
484C4C22×#432511yescharacteristic
485C4C2×#6700211yescharacteristic
486C2—22no—
487C2—444no—
488C2C2×#1062265911yescharacteristic
489C2#1307784811yescharacteristic
490C2#1307797811yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3078C2
socleC22×C11C2×#120
prime radicalC22×D44D4
hypercenter#3078D11
hypocenterC11#18777
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3078

Complements

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

NH ≅ G/Ntype
2. #13079757C2semidirect
4. #13067878C2semidirect
5. #13067779C2semidirect
6. #13067289C2semidirect
8. #13067011C2semidirect
9. C11×#3078C2semidirect
24. C11×#477C22semidirect
25. C11×#475C22semidirect
31. #10622694C22semidirect
32. #10622692C22semidirect
40. Q8⋊(C11⋊C8)C22semidirect
42. #10622120C22semidirect
116. C2×Q8×C11SD16semidirect
179. #3078D11semidirect
247. #477C2×D11semidirect
250. #475C2×D11semidirect
369. C2×Q8#4325semidirect
420. C11#18777semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×D442
#130797572
#130786202
#130678782
#130677792
#130672892
#130670402
#130670112
C11×#30782
#1877711