Finite Group Databasebeta

← #14763247

Subgroups — #14763247

Order 2816.

914 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623220C211yesmaximal, characteristic
2#13077253C211yesmaximal, characteristic
3#13077252C211yesmaximal, characteristic
4#13069610C211yesmaximal, characteristic, complemented
5#13069607C212yesmaximal, complemented
6#13069605C211yesmaximal, characteristic, complemented
7#13069604C211yesmaximal, characteristic, complemented
8#13069603C212yesmaximal, complemented
9#13068698C212yesmaximal
10#13068695C212yesmaximal
11C11×#1998C211yesmaximal, characteristic, complemented
12C2×C11×#125C2211yescharacteristic
13#10623220—22no—
14#10623220—22no—
15#10623220—22no—
16#10623220—22no—
17C2×#66950C412yes—
18C2×#66949C412yes—
19C2×#66945C2211yescharacteristic
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×#66943C2211yescharacteristic
22C2×#66942C412yes—
23C2×#66941C412yes—
24C2×#66941C2211yescharacteristic
25C2×#66925C2211yescharacteristic
26C2×#66922C2211yescharacteristic
27C11×#423C2211yescharacteristic
28C4×C11×M16C2211yescharacteristic
29#10622739C2212yes—
30#10622739C2212yes—
31#10622731C2212yes—
32M16×Dic11C2212yes—
33#10622537C2211yescharacteristic
34C4×#4318C2211yescharacteristic
35#10622453—22no—
36#10622453—22no—
37#10622322—22no—
38#10622303—22no—
39C11×#343C2212yes—
40C11×#343C2212yes—
41#10622192C2212yes—
42#10622192C2212yes—
43#10622192C2212yes—
44#10622192C2212yes—
45#10622168C2212yes—
46#10622168C2212yes—
47C22×C4×D11C2×C412yes—
48C22×C4×D11C2311yescharacteristic
49C22×Dic22C2×C412yes—
50C22×Dic22C2×C412yes—
51C2×C11×M16C2312yes—
52C2×C11×M16C2312yes—
53C11×#125—21no—
54C11×#125—21no—
55C11×#125—21no—
56C11×#125—21no—
57C2×C11×C4⋊C4C2×C412yes—
58C2×C11×C4⋊C4C2×C412yes—
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C42×C11C2311yescharacteristic
62C2×(C2×D11)⋊C4C2×C412yes—
63C2×(C2×D11)⋊C4C2×C411yescharacteristic
64C2×(C2×D11)⋊C4C2×C411yescharacteristic
65C2×C4⋊Dic11C2×C412yes—
66C2×C4⋊Dic11C2×C412yes—
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2311yescharacteristic
69C2×Dic11⋊C4C2×C412yes—
70C2×Dic11⋊C4C2×C412yes—
71C2×Dic11⋊C4C2×C412yes—
72C2×Dic11⋊C4C2×C411yescharacteristic
73C2×Dic11⋊C4C2×C411yescharacteristic
74C2×C4×Dic11C2×C412yes—
75C2×C4×Dic11C2311yescharacteristic
76C2×#4318C2312yes—
77C2×#4318C2312yes—
78#66950—24no—
79#66950—24no—
80#66949—24no—
81#66949—24no—
82#66945—22no—
83#66945—22no—
84C4⋊C4×D11—22no—
85C4⋊C4×D11—22no—
86#66943—22no—
87#66943—22no—
88#66942—24no—
89#66942—24no—
90#66941—24no—
91#66941—24no—
92#66941—22no—
93#66941—22no—
94#66925D412yes—
95#66925D412yes—
96#66925D412yes—
97#66925D412yes—
98#66922—21no—
99#66922—21no—
100#66922—21no—
101#66922—21no—
102C11×C4⋊C8—21no—
103C11×C4⋊C8—21no—
104C11×#97—21no—
105C4×C8×C11—21no—
106(C2×D11)⋊C8—24no—
107(C2×D11)⋊C8—24no—
108#66879—22no—
109Dic11⋊C8—24no—
110C8×Dic11—22no—
111C4⋊(C11⋊C8)—21no—
112C4⋊(C11⋊C8)—21no—
113#66867—21no—
114C4×C11⋊C8—21no—
115#21832—111nomaximal, Sylow
116C23×D11C22×C411yescharacteristic
117C22×C4×C11C22×C412yes—
118C22×C4×C11C22×C412yes—
119C22×C4×C11C22×C411yescharacteristic
120C22×C4×C11C22×C411yescharacteristic
121C22×C4×C11C2411yescharacteristic
122C22×Dic11C22×C411yescharacteristic
123C22×Dic11C22×C412yes—
124C22×Dic11C22×C412yes—
125C22×Dic11C22×C411yescharacteristic
126C22×Dic11C22×C411yescharacteristic
127C2×C4×D11—24no—
128C2×C4×D11—22no—
129C2×C4×D11—22no—
130C2×C4×D11—82no—
131C2×C4×D11C2×D412yes—
132C2×C4×D11C2×D412yes—
133C2×Dic22—24no—
134C2×Dic22—22no—
135C2×Dic22—22no—
136C2×Dic22—82no—
137C2×Dic22—82no—
138C11×M16—22no—
139C11×M16—24no—
140C11×M16—22no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C42×C11C2×D411yescharacteristic
152C42×C11C2×D411yescharacteristic
153C42×C11C2×D411yescharacteristic
154C42×C11C2×D411yescharacteristic
155(C2×D11)⋊C4—24no—
156(C2×D11)⋊C4C22⋊C412yes—
157(C2×D11)⋊C4C22⋊C412yes—
158(C2×D11)⋊C4C22⋊C412yes—
159(C2×D11)⋊C4C22⋊C412yes—
160C4⋊Dic11—24no—
161C4⋊Dic11—22no—
162C4⋊Dic11—22no—
163C4⋊Dic11—21no—
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167Dic11⋊C4—24no—
168Dic11⋊C4—24no—
169Dic11⋊C4—24no—
170Dic11⋊C4C22⋊C412yes—
171Dic11⋊C4C22⋊C412yes—
172Dic11⋊C4C22⋊C412yes—
173Dic11⋊C4C22⋊C412yes—
174C4×Dic11—24no—
175C4×Dic11C2×D412yes—
176C4×Dic11C2×D412yes—
177#4318—24no—
178#4318—22no—
179#4318—22no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C2×#544—111no—
183#2921—111no—
184#2921—111no—
185#1998—112no—
186#1998—111no—
187#1998D1111yescharacteristic, complemented
188#1997—111no—
189#1997—111no—
190#1997—112no—
191#1822—112no—
192#1821—112no—
193C23×C11C23×C411yescharacteristic
194C22×D11—22no—
195C22×D11—41no—
196C22×D11—41no—
197C22×D11C2×C22⋊C412yes—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11C2×C22⋊C411yescharacteristic
205C2×C4×C11C2×C22⋊C411yescharacteristic
206C2×C4×C11C2×C22⋊C411yescharacteristic
207C2×C4×C11C2×C22⋊C411yescharacteristic
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C112−1+412yes—
211C2×C4×C112−1+412yes—
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11C2×C22⋊C412yes—
220C2×Dic11C2×C22⋊C412yes—
221C2×Dic11C2×C22⋊C412yes—
222C4×D11—22no—
223C4×D11—24no—
224C4×D11—22no—
225C4×D11—84no—
226Dic22—84no—
227Dic22—82no—
228Dic22—82no—
229C8×C11—42no—
230C8×C11—42no—
231C11⋊C8—42no—
232C11⋊C8—42no—
233#544—222no—
234#544—222no—
235#544—222no—
236#544—222no—
237C2×C4⋊Q8—111no—
238C2×C4⋊Q8—112no—
239C2×C4⋊Q8—111no—
240C2×#125—111no—
241C2×#125—112no—
242C2×#125C2×D1111yescharacteristic
243C2×C22⋊Q8—112no—
244C2×C22⋊Q8—112no—
245C2×#117—111no—
246C2×#117—111no—
247C22×C4⋊C4—111no—
248#433—222no—
249#433—222no—
250#433—222no—
251#433—222no—
252#423—112no—
253#423—111no—
254#423C2×D1111yescharacteristic
255#407—112no—
256#407—112no—
257C4×M16—112no—
258C4×M16—111no—
259C4×M16C2×D1111yescharacteristic
260#343—112no—
261#343—112no—
262#343—112no—
263#343—112no—
264#343—112no—
265#343—112no—
266#343C2×D1112yes—
267#343C2×D1112yes—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11C22×C22⋊C411yescharacteristic
271C22×C11#51912yes—
272C2×D11—22no—
273C2×D11—22no—
274C2×D11—22no—
275C2×D11—44no—
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—42no—
281C4×C11—42no—
282C4×C11#53611yescharacteristic
283C4×C11#53612yes—
284C4×C11#53611yescharacteristic
285Dic11—22no—
286Dic11—22no—
287Dic11—22no—
288Dic11—42no—
289Dic11—42no—
290C22×Q8—112no—
291C22×Q8—112no—
292C23×C4—111no—
293C23×C4—112no—
294C2×M16—112no—
295C2×M16—112no—
296C2×M16C22×D1112yes—
297C2×M16C22×D1112yes—
298C4⋊Q8—222no—
299C4⋊Q8—222no—
300C4⋊Q8—224no—
301C4⋊Q8—224no—
302C4⋊Q8—221no—
303C4⋊Q8—221no—
304C4⋊Q8—221no—
305C4⋊Q8—221no—
306#125—21no—
307#125—21no—
308#125—21no—
309#125—21no—
310#125—222no—
311#125—222no—
312#125—224no—
313#125—224no—
314C22⋊Q8—224no—
315C22⋊Q8—224no—
316C22⋊Q8—224no—
317C22⋊Q8—224no—
318#117—112no—
319#117—112no—
320#117—112no—
321#117—112no—
322#117—222no—
323#117—222no—
324C2×C4⋊C4—111no—
325C2×C4⋊C4—111no—
326C2×C4⋊C4—112no—
327C2×C4⋊C4—112no—
328C2×C4⋊C4—112no—
329C2×C4⋊C4—112no—
330C2×C4⋊C4—112no—
331C2×C4⋊C4—111no—
332C2×C4⋊C4—111no—
333C2×C4⋊C4—222no—
334C2×C4⋊C4—222no—
335C2×C4⋊C4C4×D1112yes—
336C2×C4⋊C4C4×D1112yes—
337C2×C4⋊C4C22×D1111yescharacteristic
338C2×C4⋊C4C22×D1111yescharacteristic
339C2×C22⋊C4—111no—
340C2×C22⋊C4—111no—
341C2×C22⋊C4—112no—
342C2×C42—111no—
343C2×C42—112no—
344C2×C42C22×D1111yescharacteristic
345C4⋊C8—21no—
346C4⋊C8—21no—
347C4⋊C8—224no—
348C4⋊C8—221no—
349C4⋊C8—221no—
350C22⋊C8—224no—
351C22⋊C8—224no—
352#97—21no—
353#97—222no—
354#97—221no—
355C4×C8—21no—
356C4×C8—222no—
357C4×C8—221no—
358C2×C11—22no—
359C2×C11#231011yescharacteristic
360C2×C11#288811yescharacteristic
361C2×C11#288911yescharacteristic
362D11—42no—
363C24—111no—
364C2×Q8—224no—
365C2×Q8—222no—
366C2×Q8—222no—
367C2×Q8—882no—
368C2×Q8—882no—
369C22×C4—111no—
370C22×C4—111no—
371C22×C4—111no—
372C22×C4—112no—
373C22×C4—112no—
374C22×C4—112no—
375C22×C4—112no—
376C22×C4—224no—
377C22×C4—222no—
378C22×C4—222no—
379C22×C4—882no—
380C22×C4C2×C4×D1112yes—
381C22×C4C2×C4×D1112yes—
382C22×C4C2×C4×D1111yescharacteristic
383C22×C4C2×C4×D1111yescharacteristic
384C22×C4C23×D1111yescharacteristic
385M16—22no—
386M16—22no—
387M16—24no—
388M16—224no—
389M16—222no—
390M16—222no—
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—222no—
394C2×C8—222no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—112no—
404C4⋊C4—112no—
405C4⋊C4—112no—
406C4⋊C4—112no—
407C4⋊C4—224no—
408C4⋊C4—224no—
409C4⋊C4—224no—
410C4⋊C4—224no—
411C4⋊C4—222no—
412C4⋊C4—222no—
413C4⋊C4—221no—
414C4⋊C4—221no—
415C4⋊C4—221no—
416C4⋊C4—221no—
417C22⋊C4—112no—
418C22⋊C4—112no—
419C22⋊C4—112no—
420C22⋊C4—112no—
421C22⋊C4—224no—
422C42—112no—
423C42—112no—
424C42—224no—
425C42D4×D1111yescharacteristic
426C42D4×D1111yescharacteristic
427C42D4×D1111yescharacteristic
428C42D4×D1111yescharacteristic
429C11#2183211yescharacteristic, complemented, Sylow
430C23—112no—
431C23—222no—
432C23—441no—
433C23—441no—
434C23C22×C4×D1111yescharacteristic
435Q8—882no—
436Q8—882no—
437Q8—884no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—112no—
445C2×C4—112no—
446C2×C4—112no—
447C2×C4—222no—
448C2×C4—222no—
449C2×C4—224no—
450C2×C4—222no—
451C2×C4—222no—
452C2×C4—222no—
453C2×C4—441no—
454C2×C4—441no—
455C2×C4—442no—
456C2×C4—442no—
457C2×C4—884no—
458C2×C4C22⋊C4×D1111yescharacteristic
459C2×C4C22⋊C4×D1111yescharacteristic
460C2×C4C22⋊C4×D1111yescharacteristic
461C2×C4C22⋊C4×D1111yescharacteristic
462C2×C4C2×D4×D1111yescharacteristic
463C2×C4C2×D4×D1111yescharacteristic
464C2×C4#6704012yes—
465C2×C4#6704312yes—
466C8—42no—
467C8—42no—
468C8—442no—
469C8—442no—
470C22—21no—
471C22—21no—
472C22—222no—
473C22—222no—
474C22—222no—
475C22—444no—
476C22C2×C22⋊C4×D1111yescharacteristic
477C22#1062310312yes—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—42no—
483C4—42no—
484C4—222no—
485C4—222no—
486C4—222no—
487C4—442no—
488C4—442no—
489C4#1062315912yes—
490C4#1062320611yescharacteristic
491C4#1062325511yescharacteristic
492C2—22no—
493C2—442no—
494C2#1307119911yescharacteristic
495C2#1307709311yescharacteristic
496C2#1307709711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1998C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C22×C4
cosocleC22×C4×C11C24
hypercenter#1998D11
hypocenterC11#21832
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1998

Complements

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

NH ≅ G/Ntype
4. #13069610C2semidirect
5. #13069607C2semidirect
6. #13069605C2semidirect
7. #13069604C2semidirect
8. #13069603C2semidirect
11. C11×#1998C2semidirect
187. #1998D11semidirect
429. C11#21832semidirect

Maximal subgroups

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

subgroupindex
C2×#106232202
#130772532
#130772522
#130696102
#130696072
#130696052
#130696042
#130696032
#130686982
#130686952
C11×#19982
#2183211