Finite Group Databasebeta

← #14759023

Subgroups — #14759023

Order 2816.

1466 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623256C211yesmaximal, characteristic
2C2×C4×#4313C211yesmaximal, characteristic, complemented
3#13071021C211yesmaximal, characteristic, complemented
4#13069578C211yesmaximal, characteristic, complemented
5#13069422C211yesmaximal, characteristic, complemented
6#13069421C211yesmaximal, characteristic, complemented
7#13069053C214yesmaximal, complemented
8#13068440C214yesmaximal, complemented
9C11×#1990C211yesmaximal, characteristic, complemented
10C22×#4343—21no—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#67000—21no—
13C22×#4313C2212yes—
14#10623256—24no—
15#10623256C418yescomplemented
16C2×#66948—21no—
17C2×#66948C2212yes—
18C2×#66946—21no—
19C2×#66946C2212yes—
20C2×#66945—21no—
21C2×#66927C2211yescharacteristic
22C2×C42×D11C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C11×#384C2211yescharacteristic
25C2×#66885C2214yes—
26C2×#66879C2212yes—
27#10622600—21no—
28#10622600C2212yes—
29#10622590—21no—
30C4⋊C4×Dic11—21no—
31C4⋊C4×Dic11C2212yes—
32C2×#66873C2214yes—
33#10622548C2211yescharacteristic
34C2×C4×C11⋊C8C2211yescharacteristic
35C4×#4313—24no—
36C11×#340C2214yes—
37#10622167C2214yes—
38C22×Q8×C11—21no—
39C2×#4343—28no—
40C2×#4343—44no—
41C2×#4343—44no—
42C22×D44—22no—
43C22×D44—21no—
44C22×D44—21no—
45C22×D44C2312yes—
46C22×C4×D11—22no—
47C22×C4×D11D411yescharacteristic
48C22×C4×D11D411yescharacteristic
49C22×C4×D11C2311yescharacteristic
50C22×C8×C11C2312yes—
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8C2×C414yes—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C4⋊C4C2312yes—
58C2×C42×C11C2311yescharacteristic
59#67000—28no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—22no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11C2312yes—
66C2×C4×Dic11—22no—
67C2×C4×Dic11D411yescharacteristic
68C2×C4×Dic11D411yescharacteristic
69C2×C4×Dic11C2311yescharacteristic
70C22×C11⋊C8C2312yes—
71C2×#4313—24no—
72C2×#4313—24no—
73C2×#4313—24no—
74#66948—28no—
75#66948—24no—
76#66948C2×C418yes—
77#66946—28no—
78#66946—24no—
79#66946C2×C418yes—
80#66945—44no—
81#66927—22no—
82#66927C2×C414yes—
83C42×D11C2×C414yes—
84C42×D11D414yes—
85C4×C8×C11—22no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88#66885—28no—
89#66879—24no—
90#66873—28no—
91C4×C11⋊C8—22no—
92#21410—111nomaximal, Sylow
93C23×D11—22no—
94C23×D11C2×D411yescharacteristic
95C2×Q8×C11—24no—
96C2×Q8×C11—42no—
97C2×Q8×C11—42no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2411yescharacteristic
103C22×Dic11—22no—
104C22×Dic11C2×D411yescharacteristic
105C22×Dic11C2×D411yescharacteristic
106C22×Dic11C2×D411yescharacteristic
107#4343—432no—
108C2×D44—28no—
109C2×D44—24no—
110C2×D44—24no—
111C2×D44—22no—
112C2×D44—24no—
113C2×D44—24no—
114C2×D44—44no—
115C2×D44—44no—
116C2×D44—42no—
117C2×D44—42no—
118C2×D44—42no—
119C2×D44—42no—
120C2×D44C22×C414yes—
121C2×C4×D11—28no—
122C2×C4×D11—22no—
123C2×C4×D11—22no—
124C2×C4×D11—22no—
125C2×C4×D11—22no—
126C2×C4×D11—22no—
127C2×C4×D11—22no—
128C2×C4×D11—44no—
129C2×C4×D11—44no—
130C2×C4×D11C22⋊C414yes—
131C2×C4×D11C22⋊C414yes—
132C2×C4×D11C22×C412yes—
133C2×C4×D11C2×D412yes—
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C2×C8×C11#4114yescomplemented
137C11×C4⋊C4—24no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—42no—
141C11×C4⋊C4—42no—
142C11×C4⋊C4C22×C414yes—
143C42×C11C22×C412yes—
144C42×C11C2×D412yes—
145(C2×D11)⋊C4—28no—
146(C2×D11)⋊C4—28no—
147(C2×D11)⋊C4—44no—
148C4⋊Dic11—24no—
149C4⋊Dic11—42no—
150C4⋊Dic11—42no—
151C4×Dic11—44no—
152C4×Dic11C22⋊C414yes—
153C4×Dic11C22⋊C414yes—
154C4×Dic11C22×C412yes—
155C4×Dic11C2×D412yes—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8#4114yescomplemented
159#4313—216no—
160C2×#532—111no—
161C2×C4×M16—111no—
162#2285—111no—
163#1990—111no—
164#1990D1111yescharacteristic, complemented
165#1957—111no—
166#1957—111no—
167#1895—114no—
168#1762—114no—
169C23×C11C22×D411yescharacteristic
170C22×D11—21no—
171C22×D11—21no—
172C22×D11—21no—
173C22×D11—21no—
174C22×D11—21no—
175C22×D11—21no—
176C22×D11—24no—
177C22×D11—42no—
178C22×D11—42no—
179C22×D11—42no—
180C22×D11—42no—
181C22×D11—42no—
182C22×D11—42no—
183C22×D11C2×C22⋊C412yes—
184Q8×C11—48no—
185C2×C4×C11—24no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11C2×C22⋊C412yes—
192C2×C4×C11C2×C22⋊C412yes—
193C2×C4×C11AGL(1,ℤ/8)12yes—
194C2×C4×C11AGL(1,ℤ/8)12yes—
195C2×C4×C11AGL(1,ℤ/8)12yes—
196C2×C4×C11#13712yes—
197C2×C4×C11C23×C411yescharacteristic
198C2×C4×C11C22×D411yescharacteristic
199C2×C4×C11C2×#4112yes—
200C2×C4×C11C2×#4112yes—
201C2×Dic11—21no—
202C2×Dic11—21no—
203C2×Dic11—21no—
204C2×Dic11—21no—
205C2×Dic11—21no—
206C2×Dic11—21no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11C2×C22⋊C412yes—
211C2×Dic11C2×C22⋊C412yes—
212C2×Dic11C2×C22⋊C412yes—
213D44—28no—
214D44—416no—
215D44—44no—
216D44—48no—
217D44—48no—
218C4×D11—24no—
219C4×D11—24no—
220C4×D11—28no—
221C4×D11—28no—
222C4×D11—416no—
223C8×C11—24no—
224C11⋊C8—24no—
225C22×#41—221no—
226C22×M16—112no—
227#532—118no—
228#532—224no—
229C2×C4⋊Q8C2×D1111yescharacteristic
230C2×#127—111no—
231C2×#124—221no—
232C2×#121—112no—
233C2×#121—221no—
234C2×C4×D4—112no—
235C2×C4×D4—221no—
236C2×#117—221no—
237C22×C42—111no—
238C2×#102—114no—
239C2×#102—114no—
240C4×M16—224no—
241C2×#97—112no—
242C2×C4×C8—111no—
243C2×C4×C8C2×D1111yescharacteristic
244#384—111no—
245#384C2×D1111yescharacteristic
246#382—221no—
247#380—112no—
248#380—221no—
249C4×C4⋊C4—112no—
250C4×C4⋊C4—221no—
251#340—114no—
252#340C2×D1114yes—
253C22×C11C22×C22⋊C411yescharacteristic
254C22×C11#53211yescharacteristic
255C22×C11#53211yescharacteristic
256C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
257C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
258C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
259C22×C11C2×#13711yescharacteristic
260C2×D11—22no—
261C2×D11—22no—
262C2×D11—22no—
263C2×D11—41no—
264C2×D11—41no—
265C2×D11—41no—
266C2×D11—41no—
267C2×D11—44no—
268C2×D11—44no—
269C2×D11—44no—
270C2×D11—82no—
271C2×D11—82no—
272C2×D11—82no—
273C2×D11—82no—
274C4×C11—44no—
275C4×C11—82no—
276C4×C11#41714yes—
277C4×C11#41814yes—
278C4×C11C4×#4112yes—
279C4×C11#52512yes—
280Dic11—22no—
281Dic11—22no—
282Dic11—22no—
283Dic11—82no—
284C2×#41—228no—
285C2×#41—444no—
286C2×#41—444no—
287C22×Q8—21no—
288C22×D4—112no—
289C22×D4—222no—
290C22×D4—221no—
291C22×D4—221no—
292C23×C4—111no—
293C23×C4—111no—
294C23×C4—111no—
295C23×C4—222no—
296C2×M16—224no—
297C2×M16—224no—
298C2×M16—224no—
299C22×C8—112no—
300C22×C8C22×D1112yes—
301C4⋊Q8—22no—
302C4⋊Q8C4×D1114yes—
303#127—114no—
304#127—222no—
305#124—228no—
306#121—118no—
307#121—224no—
308#121—228no—
309C4×D4—118no—
310C4×D4—224no—
311C4×D4—228no—
312#117—444no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—112no—
317C2×C4⋊C4—221no—
318C2×C4⋊C4—221no—
319C2×C4⋊C4C22×D1112yes—
320C2×C4⋊C4C22×D1112yes—
321C2×C22⋊C4—222no—
322C2×C22⋊C4—222no—
323C2×C22⋊C4—222no—
324C2×C42—111no—
325C2×C42—111no—
326C2×C42—111no—
327C2×C42—114no—
328C2×C42—114no—
329C2×C42—222no—
330C2×C42C22×D1111yescharacteristic
331#102—228no—
332#102—228no—
333#97—224no—
334C4×C8—22no—
335C4×C8—222no—
336#95—222no—
337#95—222no—
338C2×C11#229711yescharacteristic
339C2×C11C2×#41811yescharacteristic
340C2×C11C2×#41711yescharacteristic
341C2×C11#318211yescharacteristic
342C2×C11#318211yescharacteristic
343C2×C11#318411yescharacteristic
344C2×C11#318411yescharacteristic
345D11—42no—
346D11—84no—
347C24—111no—
348C24—222no—
349#41—4432no—
350C2×Q8—24no—
351C2×Q8—42no—
352C2×Q8—42no—
353C2×D4—114no—
354C2×D4—228no—
355C2×D4—224no—
356C2×D4—224no—
357C2×D4—222no—
358C2×D4—224no—
359C2×D4—224no—
360C2×D4—444no—
361C2×D4—444no—
362C2×D4—442no—
363C2×D4—442no—
364C2×D4—442no—
365C2×D4—442no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—111no—
369C22×C4—111no—
370C22×C4—111no—
371C22×C4—114no—
372C22×C4—114no—
373C22×C4—112no—
374C22×C4—112no—
375C22×C4—228no—
376C22×C4—222no—
377C22×C4—222no—
378C22×C4—222no—
379C22×C4—222no—
380C22×C4—222no—
381C22×C4—222no—
382C22×C4—222no—
383C22×C4—444no—
384C22×C4—444no—
385C22×C4D4×D1111yescharacteristic
386C22×C4D4×D1111yescharacteristic
387C22×C4C23×D1111yescharacteristic
388M16—2216no—
389C2×C8—22no—
390C2×C8—22no—
391C2×C8—114no—
392C2×C8—222no—
393C2×C8—222no—
394C2×C8#434314yescomplemented
395C4⋊C4—24no—
396C4⋊C4—22no—
397C4⋊C4—24no—
398C4⋊C4—42no—
399C4⋊C4—42no—
400C4⋊C4—224no—
401C4⋊C4—442no—
402C4⋊C4—442no—
403C4⋊C4C2×C4×D1114yes—
404C22⋊C4—228no—
405C22⋊C4—228no—
406C22⋊C4—444no—
407C42—114no—
408C42—114no—
409C42—112no—
410C42—112no—
411C42—444no—
412C42C2×C4×D1112yes—
413C42D4×D1112yes—
414C11#2141011yescharacteristic, complemented, Sylow
415C23—112no—
416C23—221no—
417C23—221no—
418C23—221no—
419C23—221no—
420C23—221no—
421C23—221no—
422C23—224no—
423C23—442no—
424C23—442no—
425C23—442no—
426C23—442no—
427C23—442no—
428C23—442no—
429C23C2×D4×D1111yescharacteristic
430Q8—48no—
431D4—228no—
432D4—4416no—
433D4—448no—
434D4—444no—
435D4—448no—
436C2×C4—24no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—112no—
443C2×C4—112no—
444C2×C4—112no—
445C2×C4—221no—
446C2×C4—221no—
447C2×C4—221no—
448C2×C4—221no—
449C2×C4—221no—
450C2×C4—221no—
451C2×C4—224no—
452C2×C4—228no—
453C2×C4—224no—
454C2×C4—228no—
455C2×C4—4416no—
456C2×C4—442no—
457C2×C4—442no—
458C2×C4—442no—
459C2×C4C22⋊C4×D1112yes—
460C2×C4C22⋊C4×D1112yes—
461C2×C4#6696412yes—
462C2×C4#6696712yes—
463C2×C4#6696712yes—
464C2×C4#6697112yes—
465C2×C4C22×C4×D1111yescharacteristic
466C2×C4C2×D4×D1111yescharacteristic
467C2×C4C2×#434312yes—
468C2×C4#41×D1112yes—
469C8—24no—
470C8—224no—
471C22—222no—
472C22—222no—
473C22—222no—
474C22—441no—
475C22—441no—
476C22—441no—
477C22—441no—
478C22—444no—
479C22—444no—
480C22—444no—
481C22—882no—
482C22—882no—
483C22—882no—
484C22—882no—
485C22C2×C22⋊C4×D1111yescharacteristic
486C22#1062319911yescharacteristic
487C22#1062325611yescharacteristic
488C22C2×#6696411yescharacteristic
489C22C2×#6696711yescharacteristic
490C22C2×#6696711yescharacteristic
491C22C2×#6697111yescharacteristic
492C4—44no—
493C4—82no—
494C4—222no—
495C4—222no—
496C4—222no—
497C4—882no—
498C4#1062238314yes—
499C4#1062241614yes—
500C4C4×#434312yes—
501C4#1062315812yes—
502C2—442no—
503C2—884no—
504C2#1307110511yescharacteristic
505C2C2×#1062238311yescharacteristic
506C2C2×#1062241611yescharacteristic
507C2#1307933611yescharacteristic
508C2#1307933711yescharacteristic
509C2#1307935311yescharacteristic
510C2#1307935511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1990C2
socleC23×C11C22×D4
prime radicalC2×#10623256C2
cosocleC22×C4×C11C24
hypercenter#1990D11
hypocenterC11#21410
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4313C2semidirect
3. #13071021C2semidirect
4. #13069578C2semidirect
5. #13069422C2semidirect
6. #13069421C2semidirect
7. #13069053C2semidirect
8. #13068440C2semidirect
9. C11×#1990C2semidirect
15. #10623256C4semidirect
136. C2×C8×C11#41semidirect
158. C2×C11⋊C8#41semidirect
164. #1990D11semidirect
394. C2×C8#4343semidirect
414. C11#21410semidirect

Maximal subgroups

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

subgroupindex
C2×#106232562
C2×C4×#43132
#130710212
#130695782
#130694222
#130694212
#130690532
#130684402
C11×#19902
#2141011