Finite Group Databasebeta

← #14759108

Subgroups — #14759108

Order 2816.

1122 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082008C211yesmaximal, characteristic
2#13077253C211yesmaximal, characteristic, complemented
3C4×#66925C211yesmaximal, characteristic, complemented
4#13069598C211yesmaximal, characteristic, complemented
5#13069447C211yesmaximal, characteristic, complemented
6#13069444C211yesmaximal, characteristic, complemented
7#13069063C212yesmaximal, complemented
8#13069058C212yesmaximal, complemented
9#13068425C212yesmaximal, complemented
10#13068420C212yesmaximal, complemented
11C11×#1994C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13#10623264C414yescomplemented
14#10623229C412yescomplemented
15#10623228C412yescomplemented
16#10623176—22no—
17#10623175—22no—
18#10623111—24no—
19#10623055C2212yes—
20#10623053C2212yes—
21#10623008C2211yescharacteristic
22C2×#66925C2211yescharacteristic
23C2×#66925C2211yescharacteristic
24C2×C42×D11C2211yescharacteristic
25C11×#423C2211yescharacteristic
26C43×C11C2211yescharacteristic
27C2×#66889C2212yes—
28C2×#66889C2212yes—
29#10622739C2212yes—
30M16×Dic11C2212yes—
31C4×(C2×D11)⋊C4—22no—
32#10622545C2211yescharacteristic
33#10622545C2211yescharacteristic
34C4×Dic11⋊C4—22no—
35C42×Dic11C2211yescharacteristic
36C2×#66869C2212yes—
37C2×#66869C2212yes—
38#10622537C2211yescharacteristic
39#10622453—24no—
40C11×#339C2212yes—
41C11×#339C2212yes—
42#10622170C2212yes—
43#10622170C2212yes—
44C2×#4339C2312yes—
45C22×C4×D11—21no—
46C22×C4×D11C2311yescharacteristic
47C2×C11×M16C2312yes—
48C11×C4⋊Q8C2×C412yescomplemented
49C11×#125C2×C412yescomplemented
50C11×C22⋊Q8—22no—
51C4×Q8×C11—22no—
52C11×#117C2312yes—
53C2×C42×C11—22no—
54C2×C42×C11C2311yescharacteristic
55C2×C42×C11C2311yescharacteristic
56C2×C42×C11C2311yescharacteristic
57#67000—24no—
58#66999—24no—
59#66983—22no—
60C2×(C2×D11)⋊C4—21no—
61C2×(C2×D11)⋊C4D412yes—
62C2×Dic11⋊C4—21no—
63C2×Dic11⋊C4D412yes—
64C2×C4×Dic11—21no—
65C2×C4×Dic11—22no—
66C2×C4×Dic11C2311yescharacteristic
67C2×C4×Dic11C2311yescharacteristic
68C2×C4×Dic11C2311yescharacteristic
69C2×#4318C2312yes—
70#66951—24no—
71#66951—24no—
72#66950C2×C414yes—
73#66948—24no—
74#66948C2×C414yes—
75#66947—24no—
76#66947—24no—
77#66946C2×C414yescomplemented
78#66943—24no—
79#66940C2×C414yescomplemented
80#66939—22no—
81#66935—22no—
82(C22⋊D11)⋊C4—24no—
83#66928C2×C412yescomplemented
84#66927C2×C411yescharacteristic, complemented
85C4×D44—24no—
86C4×D44—22no—
87#66925—22no—
88#66925—22no—
89#66925—22no—
90#66925C2×C412yes—
91#66925C2×C412yes—
92#66925D414yes—
93C42×D11—22no—
94C42×D11—22no—
95C42×D11—22no—
96#66922C2×C411yescharacteristic, complemented
97C11×C4⋊C8—22no—
98C11⋊#95—22no—
99C11⋊#95—22no—
100#66889—24no—
101#66889—24no—
102(C2×D11)⋊C8—24no—
103#66879—22no—
104C8×Dic11—22no—
105#66869—24no—
106#66869—24no—
107C4⋊(C11⋊C8)—22no—
108#21419—111nomaximal, Sylow
109C23×D11C2×D411yescharacteristic
110C2×Q8×C11—22no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2411yescharacteristic
115C2×C22⋊D11—22no—
116C22×Dic11—21no—
117C22×Dic11—21no—
118C22×Dic11C2×D411yescharacteristic
119C22×Dic11C2×D412yes—
120#4339—22no—
121#4339—22no—
122#4339—22no—
123#4339—22no—
124C2×D44—24no—
125C2×D44—22no—
126C2×D44C22×C412yes—
127C2×C4×D11—24no—
128C2×C4×D11—24no—
129C2×C4×D11—22no—
130C2×C4×D11—21no—
131C2×C4×D11—21no—
132C2×C4×D11—21no—
133C2×C4×D11—21no—
134C2×C4×D11—44no—
135C2×C4×D11C22×C412yes—
136C2×C4×D11C2×D412yes—
137C2×Dic22C22×C412yes—
138C11×M16—22no—
139C11×M16—22no—
140C2×C8×C11—22no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4C22×C414yes—
144C11×C22⋊C4—22no—
145C42×C11—22no—
146C42×C11—21no—
147C42×C11—21no—
148C42×C11—44no—
149C42×C11C22×C411yescharacteristic
150C42×C11C22×C411yescharacteristic
151C42×C11C2×D412yes—
152C42×C11#4112yes—
153C42×C11#4112yes—
154(C2×D11)⋊C4—24no—
155(C2×D11)⋊C4—24no—
156(C2×D11)⋊C4—24no—
157(C2×D11)⋊C4—24no—
158(C2×D11)⋊C4—24no—
159(C2×D11)⋊C4C22⋊C414yes—
160(C2×D11)⋊C4C22⋊C414yes—
161C4⋊Dic11—24no—
162C4⋊Dic11—22no—
163Dic11⋊C4—24no—
164Dic11⋊C4—24no—
165Dic11⋊C4C22⋊C414yes—
166Dic11⋊C4C22⋊C414yes—
167C4×Dic11—24no—
168C4×Dic11—24no—
169C4×Dic11—21no—
170C4×Dic11—21no—
171C4×Dic11—44no—
172C4×Dic11C22×C412yes—
173C4×Dic11C2×D412yes—
174C4×Dic11#4112yes—
175C4×Dic11#4112yes—
176#4318—22no—
177#4318—22no—
178C2×C11⋊C8—22no—
179#3455—111no—
180#2921—111no—
181C4×#117—111no—
182#1995—111no—
183#1994D1111yescharacteristic, complemented
184#1963—111no—
185#1962—111no—
186#1897—112no—
187#1896—112no—
188#1759—112no—
189C4×#104—112no—
190C23×C11C22×D411yescharacteristic
191C22×D11—21no—
192C22×D11—21no—
193C22×D11—22no—
194C22×D11—42no—
195C22×D11C2×C22⋊C412yes—
196Q8×C11—82no—
197C2×C4×C11—24no—
198C2×C4×C11—22no—
199C2×C4×C11—24no—
200C2×C4×C11—22no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11C2×C22⋊C412yes—
204C2×C4×C11C2×C22⋊C412yes—
205C2×C4×C11C23×C411yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C22⋊D11—42no—
212C22⋊D11—42no—
213C2×Dic11—21no—
214C2×Dic11—21no—
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11C2×C22⋊C414yes—
222C2×Dic11C2×C22⋊C412yes—
223D44—22no—
224D44—22no—
225D44—82no—
226D44—84no—
227C4×D11—22no—
228C4×D11—22no—
229C4×D11—22no—
230C4×D11—22no—
231C4×D11—48no—
232C4×D11—42no—
233C4×D11—42no—
234C4×D11—84no—
235Dic22—22no—
236Dic22—22no—
237C8×C11—42no—
238C11⋊C8—42no—
239#542—114no—
240#541—112no—
241#540—112no—
242#539—222no—
243#538—222no—
244#533C2×D1111yescharacteristic
245#532—111no—
246#529—224no—
247#525—112no—
248C4×#41—112no—
249C2×#117—111no—
250C2×#117—111no—
251C22×C42—111no—
252#433—224no—
253#423—111no—
254#423C2×D1111yescharacteristic
255C2×#104—112no—
256C2×#104—112no—
257C2×#104—112no—
258C2×#104—112no—
259#407—112no—
260C4×M16—112no—
261C4×C4⋊C4—222no—
262C4×C22⋊C4—222no—
263#376—111no—
264#376—111no—
265C43—111no—
266C43C2×D1111yescharacteristic
267#339—112no—
268#339—112no—
269#339C2×D1112yes—
270#339C2×D1112yes—
271C22×C11—22no—
272C22×C11C22×C22⋊C411yescharacteristic
273C22×C11#52511yescharacteristic
274C22×C11#52511yescharacteristic
275C2×D11—24no—
276C2×D11—22no—
277C2×D11—42no—
278C2×D11—42no—
279C2×D11—44no—
280C2×D11—42no—
281C4×C11—24no—
282C4×C11—22no—
283C4×C11—22no—
284C4×C11—42no—
285C4×C11—44no—
286C4×C11C4×#4111yescharacteristic
287C4×C11C4×#4111yescharacteristic
288C4×C11#53211yescharacteristic
289C4×C11#53211yescharacteristic
290Dic11—24no—
291Dic11—22no—
292Dic11—42no—
293Dic11—42no—
294Dic11—42no—
295C2×#41—112no—
296C23×C4—111no—
297C23×C4—221no—
298C2×M16—112no—
299C2×M16C22×D1112yes—
300C4⋊Q8—111no—
301C4⋊Q8C4×D1112yescomplemented
302#127—111no—
303#126—224no—
304#126—224no—
305#125—224no—
306#125C4×D1112yescomplemented
307#124—112no—
308#124—224no—
309#123—222no—
310#123—224no—
311#123—224no—
312C22⋊Q8—22no—
313C22⋊Q8—114no—
314C22⋊Q8—224no—
315#121—114no—
316#121—224no—
317#121—222no—
318#120—222no—
319C4×Q8—22no—
320C4×Q8—114no—
321C4×D4—114no—
322C4×D4—224no—
323C4×D4—224no—
324C4×D4—222no—
325#117—112no—
326#117—112no—
327#117—114no—
328#117—222no—
329#117—222no—
330#117—222no—
331#117C22×D1112yes—
332C2×C4⋊C4—112no—
333C2×C4⋊C4—221no—
334C2×C22⋊C4—112no—
335C2×C22⋊C4—221no—
336C2×C42—22no—
337C2×C42—111no—
338C2×C42—111no—
339C2×C42—111no—
340C2×C42—222no—
341C2×C42—222no—
342C2×C42—221no—
343C2×C42—222no—
344C2×C42—222no—
345C2×C42C22×D1111yescharacteristic
346C2×C42C22×D1111yescharacteristic
347C2×C42C22×D1111yescharacteristic
348C4⋊C8—22no—
349C4⋊C8—222no—
350#104—224no—
351#104—224no—
352#104—224no—
353#104—224no—
354C22⋊C8—224no—
355#97—222no—
356C4×C8—222no—
357#95—222no—
358#95—222no—
359C2×C11—21no—
360C2×C11—21no—
361C2×C11#229711yescharacteristic
362C2×C11#290112yes—
363D11—42no—
364D11—82no—
365C24—111no—
366#41—222no—
367#41—222no—
368#41—222no—
369#41—222no—
370C2×Q8—22no—
371C2×Q8—112no—
372C2×D4—112no—
373C2×D4—224no—
374C2×D4—222no—
375C2×D4—222no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—111no—
379C22×C4—112no—
380C22×C4—112no—
381C22×C4—112no—
382C22×C4—224no—
383C22×C4—224no—
384C22×C4—221no—
385C22×C4—221no—
386C22×C4—221no—
387C22×C4—221no—
388C22×C4—221no—
389C22×C4—221no—
390C22×C4—222no—
391C22×C4—444no—
392C22×C4D4×D1112yes—
393C22×C4C23×D1111yescharacteristic
394M16—22no—
395M16—22no—
396M16—222no—
397M16—222no—
398C2×C8—22no—
399C2×C8—222no—
400C4⋊C4—24no—
401C4⋊C4—22no—
402C4⋊C4—114no—
403C4⋊C4—114no—
404C4⋊C4—224no—
405C4⋊C4—224no—
406C4⋊C4—224no—
407C4⋊C4—222no—
408C4⋊C4C2×C4×D1114yes—
409C22⋊C4—22no—
410C22⋊C4—114no—
411C22⋊C4—114no—
412C22⋊C4—224no—
413C22⋊C4—224no—
414C22⋊C4—224no—
415C22⋊C4—224no—
416C22⋊C4—224no—
417C42—22no—
418C42—21no—
419C42—21no—
420C42—44no—
421C42—112no—
422C42—112no—
423C42—112no—
424C42—112no—
425C42—224no—
426C42—224no—
427C42—221no—
428C42—221no—
429C42—444no—
430C42C2×C4×D1111yescharacteristic
431C42C2×C4×D1111yescharacteristic
432C42D4×D1112yes—
433C42#434312yes—
434C42#434312yes—
435C11#2141911yescharacteristic, complemented, Sylow
436C23—112no—
437C23—221no—
438C23—221no—
439C23—222no—
440C23—442no—
441C23C2×D4×D1111yescharacteristic
442Q8—82no—
443Q8—222no—
444Q8—222no—
445D4—222no—
446D4—222no—
447D4—442no—
448D4—442no—
449D4—882no—
450D4—884no—
451C2×C4—24no—
452C2×C4—22no—
453C2×C4—24no—
454C2×C4—22no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—114no—
458C2×C4—112no—
459C2×C4—221no—
460C2×C4—221no—
461C2×C4—222no—
462C2×C4—222no—
463C2×C4—222no—
464C2×C4—222no—
465C2×C4—222no—
466C2×C4—222no—
467C2×C4—222no—
468C2×C4—448no—
469C2×C4—442no—
470C2×C4—442no—
471C2×C4—442no—
472C2×C4—442no—
473C2×C4—442no—
474C2×C4—884no—
475C2×C4C22⋊C4×D1112yes—
476C2×C4C22⋊C4×D1112yes—
477C2×C4C22×C4×D1111yescharacteristic
478C2×C4C2×D4×D1111yescharacteristic
479C2×C4C2×#434311yescharacteristic
480C2×C4C2×#434311yescharacteristic
481C2×C4#41×D1111yescharacteristic
482C2×C4#41×D1111yescharacteristic
483C8—42no—
484C8—442no—
485C22—22no—
486C22—222no—
487C22—224no—
488C22—442no—
489C22—442no—
490C22—442no—
491C22—444no—
492C22C2×C22⋊C4×D1111yescharacteristic
493C22#1062315811yescharacteristic
494C22#1062315811yescharacteristic
495C4—24no—
496C4—22no—
497C4—22no—
498C4—42no—
499C4—44no—
500C4—222no—
501C4—224no—
502C4—442no—
503C4—442no—
504C4—442no—
505C4C4×#434311yescharacteristic
506C4C4×#434311yescharacteristic
507C4#1062319911yescharacteristic
508C4#1062325611yescharacteristic
509C2—21no—
510C2—21no—
511C2—442no—
512C2—882no—
513C2#1307110511yescharacteristic
514C2#1307716012yes—
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1994C2
socleC22×C11C22×C22⋊C4
prime radical#13082008C2
cosocleC22×C4×C11C24
hypercenter#1994D11
hypocenterC11#21419
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1994

Complements

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

NH ≅ G/Ntype
2. #13077253C2semidirect
3. C4×#66925C2semidirect
4. #13069598C2semidirect
5. #13069447C2semidirect
6. #13069444C2semidirect
7. #13069063C2semidirect
8. #13069058C2semidirect
9. #13068425C2semidirect
10. #13068420C2semidirect
11. C11×#1994C2semidirect
13. #10623264C4semidirect
14. #10623229C4semidirect
15. #10623228C4semidirect
48. C11×C4⋊Q8C2×C4semidirect
49. C11×#125C2×C4semidirect
77. #66946C2×C4semidirect
79. #66940C2×C4semidirect
83. #66928C2×C4semidirect
84. #66927C2×C4semidirect
96. #66922C2×C4semidirect
183. #1994D11semidirect
301. C4⋊Q8C4×D11semidirect
306. #125C4×D11semidirect
435. C11#21419semidirect

Maximal subgroups

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

subgroupindex
#130820082
#130772532
C4×#669252
#130695982
#130694472
#130694442
#130690632
#130690582
#130684252
#130684202
C11×#19942
#2141911