Finite Group Databasebeta

← #14770827

Subgroups — #14770827

Order 2816.

1206 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66873C211yesmaximal, characteristic
2C22⋊C4×D44C211yesmaximal, characteristic
3#13069312C212yesmaximal, complemented
4#13069243C212yesmaximal, complemented
5#13068876C212yesmaximal, complemented
6#13068702C211yesmaximal, characteristic, complemented
7#13068639C211yesmaximal, characteristic, complemented
8#13068546C211yesmaximal, characteristic
9#13068444C212yesmaximal, complemented
10#13068394C211yesmaximal, characteristic, complemented
11C11×#2344C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C2×C11×#117—21no—
14C22×C11×C4⋊C4C2211yescharacteristic
15C23×C11⋊C8C2211yescharacteristic
16C2×C22⋊C4×D11—21no—
17C2×C4×D44C2212yes—
18C11×#389C2212yescomplemented
19C11×#387—22no—
20C11×#381—21no—
21C11×#380C2211yescharacteristic
22C4×C11×C4⋊C4C2212yescomplemented
23C4×C11×C22⋊C4C2211yescharacteristic
24#10622825C2211yescharacteristic
25C2×C22⋊(C11⋊C8)C2211yescharacteristic
26C2×#66873C418yescomplemented
27C2×#66873C2212yes—
28C2×#66873C2212yes—
29C2×#66873C2211yescharacteristic
30C2×#66873C2211yescharacteristic
31C2×#66873C2211yescharacteristic
32C2×#66873C2211yescharacteristic
33C2×#66872C2212yescomplemented
34#10622568—21no—
35#10622552C2212yes—
36C2×#66867C2212yescomplemented
37#10622278—22no—
38#10622167C2212yescomplemented
39#10622167C2212yescomplemented
40#10622167C2212yescomplemented
41#10622162C2212yescomplemented
42C24×D11—21no—
43C23×C4×C11—21no—
44C23×C4×C11C2311yescharacteristic
45C22×D44—24no—
46C22×D44—21no—
47C22×D44—22no—
48C22×D44—42no—
49C22×D44C2×C414yes—
50C22×D44C2311yescharacteristic
51C22×D44C2311yescharacteristic
52C22×C4×D11—22no—
53C11×#117—44no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4C2×C414yescomplemented
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C22⋊C4—21no—
62C2×C11×C22⋊C4D411yescharacteristic
63C2×C11×C22⋊C4D411yescharacteristic
64C2×C42×C11—22no—
65C2×C42×C11C2312yes—
66C2×C22⋊Dic11—21no—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—22no—
70C2×C4⋊Dic11C2312yes—
71C22×C11⋊C8—42no—
72C22×C11⋊C8C2×C414yescomplemented
73C22×C11⋊C8C2312yes—
74C22×C11⋊C8C2311yescharacteristic
75C22×C11⋊C8C2311yescharacteristic
76C22⋊C4×D11—44no—
77C4×D44—24no—
78C4×D44—42no—
79C11×#95—22no—
80C11×#95—21no—
81C11×#95—22no—
82C11×#95D412yes—
83C11⋊#95—21no—
84C22⋊(C11⋊C8)—22no—
85#66873—24no—
86#66873—42no—
87#66873C2×C414yes—
88#66873C2×C414yes—
89#66873C2×C414yescomplemented
90#66873C2×C414yescomplemented
91#66872—42no—
92#66867—42no—
93#22562—111nomaximal, Sylow
94C24×C11C2×D411yescharacteristic
95C23×D11—21no—
96C23×D11—21no—
97C23×D11—24no—
98C23×D11—44no—
99C23×D11—42no—
100C23×D11—42no—
101C23×D11—82no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—24no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11C22×C412yes—
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11#4112yes—
115C22×C4×C11C2411yescharacteristic
116C22×Dic11—22no—
117C2×D44—28no—
118C2×D44—24no—
119C2×D44—21no—
120C2×D44—21no—
121C2×D44—22no—
122C2×D44—22no—
123C2×D44—22no—
124C2×D44—44no—
125C2×D44—44no—
126C2×D44—48no—
127C2×D44C22×C412yes—
128C2×D44C22×C412yes—
129C2×D44#4114yes—
130C2×C4×D11—44no—
131C2×C4×D11—44no—
132C2×C4×D11—82no—
133C11×C4⋊C4—24no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—44no—
139C11×C4⋊C4C22×C412yes—
140C11×C4⋊C4C22×C412yes—
141C11×C22⋊C4—22no—
142C11×C22⋊C4—22no—
143C11×C22⋊C4—42no—
144C42×C11—22no—
145C42×C11—22no—
146C42×C11—44no—
147C22⋊Dic11—42no—
148(C2×D11)⋊C4—44no—
149(C2×D11)⋊C4—44no—
150(C2×D11)⋊C4—82no—
151C4⋊Dic11—22no—
152C4⋊Dic11—22no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—44no—
159C2×C11⋊C8C22×C412yes—
160C2×C11⋊C8C22×C412yes—
161C22×#102—111no—
162#2344D1111yescharacteristic, complemented
163D4×C22⋊C4—111no—
164#1936—112no—
165#1926—112no—
166#1864—112no—
167#1823—111no—
168#1807—111no—
169#1786—111no—
170#1762—112no—
171#1752—111no—
172C23×C11—22no—
173C23×C11—22no—
174C23×C11C4×D412yes—
175C23×C11AGL(1,ℤ/8)12yes—
176C23×C11AGL(1,ℤ/8)12yes—
177C23×C11C22×D411yescharacteristic
178C22×D11—22no—
179C22×D11—24no—
180C22×D11—22no—
181C22×D11—48no—
182C22×D11—41no—
183C22×D11—41no—
184C22×D11—42no—
185C22×D11—42no—
186C22×D11—41no—
187C22×D11—41no—
188C22×D11—42no—
189C22×D11—48no—
190C22×D11—84no—
191C22×D11—88no—
192C22×D11—88no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—24no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—48no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11C4×D412yes—
214C2×C4×C11C23×C411yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11C2×#4112yes—
217C2×C4×C11H(5,𝔽2)12yes—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221D44—22no—
222D44—22no—
223D44—22no—
224D44—24no—
225D44—48no—
226D44—42no—
227D44#11714yescomplemented
228C4×D11—88no—
229C11⋊C8—22no—
230C11⋊C8—22no—
231C11⋊C8—42no—
232C23×D4—111no—
233C23×C8—111no—
234C2×C4×D4—112no—
235C2×#117—21no—
236C22×C4⋊C4C2×D1111yescharacteristic
237C22×C22⋊C4—221no—
238C2×#106—112no—
239C2×#102—111no—
240C2×#102—111no—
241C2×#102—111no—
242C2×#102—111no—
243C2×#102—118no—
244C2×#102—112no—
245C2×#102—112no—
246C2×C22⋊C8—111no—
247C2×#97—112no—
248#390—112no—
249#389C2×D1112yescomplemented
250#387—22no—
251#386—222no—
252#381—21no—
253#380—111no—
254#380C2×D1111yescharacteristic
255#379—221no—
256C4×C4⋊C4C2×D1112yescomplemented
257C4×C22⋊C4C2×D1111yescharacteristic
258#340—112no—
259#340—112no—
260#340—112no—
261#336—112no—
262C22×C11—22no—
263C22×C11—22no—
264C22×C11—24no—
265C22×C11—24no—
266C22×C11#44214yes—
267C22×C11C2×C4×D411yescharacteristic
268C22×C11#54612yes—
269C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
270C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
271C22×C11#57712yes—
272C2×D11—24no—
273C2×D11—42no—
274C2×D11—42no—
275C2×D11—44no—
276C2×D11—44no—
277C2×D11—42no—
278C2×D11—42no—
279C2×D11—42no—
280C2×D11—816no—
281C2×D11—82no—
282C2×D11—82no—
283C4×C11—22no—
284C4×C11—42no—
285C4×C11—42no—
286C4×C11—42no—
287C4×C11—42no—
288C4×C11—82no—
289C4×C11C2×#11711yescharacteristic
290C4×C11#51811yescharacteristic
291C4×C11#55112yes—
292Dic11—82no—
293C25—221no—
294C22×D4—114no—
295C22×D4—111no—
296C22×D4—111no—
297C22×D4—224no—
298C22×D4—222no—
299C22×D4—221no—
300C22×D4—442no—
301C23×C4—21no—
302C23×C4—222no—
303C23×C4C22×D1111yescharacteristic
304C22×C8—111no—
305C22×C8—111no—
306C22×C8—114no—
307C22×C8—112no—
308C22×C8—442no—
309C4×D4—224no—
310C4×D4—442no—
311#117—44no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—112no—
316C2×C4⋊C4C4×D1114yescomplemented
317C2×C4⋊C4C22×D1112yes—
318C2×C4⋊C4C22×D1111yescharacteristic
319C2×C4⋊C4C22×D1111yescharacteristic
320C2×C22⋊C4—21no—
321C2×C22⋊C4—221no—
322C2×C22⋊C4—222no—
323C2×C22⋊C4—222no—
324C2×C22⋊C4—222no—
325C2×C22⋊C4—444no—
326C2×C22⋊C4C22⋊D1111yescharacteristic
327C2×C22⋊C4C22⋊D1111yescharacteristic
328C2×C42—22no—
329C2×C42C22×D1112yes—
330#106—442no—
331#102—114no—
332#102—114no—
333#102—114no—
334#102—114no—
335#102—224no—
336#102—442no—
337C22⋊C8—222no—
338#97—442no—
339#95—22no—
340#95—21no—
341#95—22no—
342#95—221no—
343#95C22⋊D1112yes—
344C2×C11—24no—
345C2×C11#234211yescharacteristic
346C2×C11C2×#44211yescharacteristic
347C2×C11#294911yescharacteristic
348C2×C11#330612yes—
349C2×C11#331012yes—
350D11—44no—
351D11—82no—
352C24—221no—
353C24—221no—
354C24—224no—
355C24—444no—
356C24—442no—
357C24—442no—
358C24—882no—
359C24C2×C22⋊D1111yescharacteristic
360C2×D4—112no—
361C2×D4—112no—
362C2×D4—114no—
363C2×D4—228no—
364C2×D4—224no—
365C2×D4—221no—
366C2×D4—221no—
367C2×D4—222no—
368C2×D4—222no—
369C2×D4—222no—
370C2×D4—444no—
371C2×D4—448no—
372C2×D4—444no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—24no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4—222no—
382C22×C4—444no—
383C22×C4—444no—
384C22×C4—882no—
385C22×C4C2×C4×D1112yes—
386C22×C4#433912yes—
387C22×C4C2×C22⋊D1112yes—
388C22×C4C2×C22⋊D1112yes—
389C22×C4C2×C22⋊D1111yescharacteristic
390C22×C4C23×D1111yescharacteristic
391C2×C8—112no—
392C2×C8—112no—
393C2×C8—222no—
394C2×C8—222no—
395C2×C8—222no—
396C2×C8—222no—
397C2×C8—222no—
398C2×C8—444no—
399C4⋊C4—24no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—44no—
405C4⋊C4—222no—
406C4⋊C4—222no—
407C4⋊C4C2×C4×D1112yes—
408C4⋊C4C2×C4×D1112yes—
409C22⋊C4—22no—
410C22⋊C4—22no—
411C22⋊C4—42no—
412C22⋊C4—444no—
413C22⋊C4—444no—
414C22⋊C4—442no—
415C22⋊C4—882no—
416C42—22no—
417C42—22no—
418C42—44no—
419C11#2256211yescharacteristic, complemented, Sylow
420C23—22no—
421C23—22no—
422C23—222no—
423C23—224no—
424C23—222no—
425C23—448no—
426C23—441no—
427C23—441no—
428C23—442no—
429C23—441no—
430C23—441no—
431C23—442no—
432C23—442no—
433C23—448no—
434C23—884no—
435C23—888no—
436C23—888no—
437C23C4×C22⋊D1112yes—
438C23#6698512yes—
439C23#6700212yes—
440C23C22×C22⋊D1111yescharacteristic
441D4—114no—
442D4—222no—
443D4—222no—
444D4—222no—
445D4—224no—
446D4—448no—
447D4—442no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—24no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—48no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—442no—
469C2×C4—442no—
470C2×C4—442no—
471C2×C4—888no—
472C2×C4C4×C22⋊D1112yes—
473C2×C4C22×C4×D1111yescharacteristic
474C2×C4C2×#433911yescharacteristic
475C2×C4#41×D1112yes—
476C2×C4#6704212yes—
477C8—222no—
478C8—222no—
479C8—442no—
480C22—24no—
481C22—22no—
482C22—22no—
483C22—24no—
484C22—224no—
485C22—444no—
486C22—442no—
487C22—442no—
488C22—444no—
489C22—442no—
490C22—442no—
491C22—442no—
492C22—8816no—
493C22—882no—
494C22—882no—
495C22#1062262714yes—
496C22C2×C4×C22⋊D1111yescharacteristic
497C22C2×#6698511yescharacteristic
498C22C2×#6700211yescharacteristic
499C22#1062336012yes—
500C22#1062336812yes—
501C4—22no—
502C4—42no—
503C4—42no—
504C4—42no—
505C4—42no—
506C4—82no—
507C4—882no—
508C4D11×#11711yescharacteristic
509C4#1062305211yescharacteristic
510C4#1062305812yes—
511C2—24no—
512C2—444no—
513C2—882no—
514C2#1307146611yescharacteristic
515C2C2×#1062262711yescharacteristic
516C2#1307747511yescharacteristic
517C2#1308057112yes—
518C2#1308063112yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2344C2
socleC23×C11C22×D4
prime radicalC23×D44C22
cosocleC22×C4×C11C24
hypercenter#2344D11
hypocenterC11#22562
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2344

Complements

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

NH ≅ G/Ntype
3. #13069312C2semidirect
4. #13069243C2semidirect
5. #13068876C2semidirect
6. #13068702C2semidirect
7. #13068639C2semidirect
9. #13068444C2semidirect
10. #13068394C2semidirect
11. C11×#2344C2semidirect
18. C11×#389C22semidirect
22. C4×C11×C4⋊C4C22semidirect
26. C2×#66873C4semidirect
33. C2×#66872C22semidirect
36. C2×#66867C22semidirect
38. #10622167C22semidirect
39. #10622167C22semidirect
40. #10622167C22semidirect
41. #10622162C22semidirect
57. C2×C11×C4⋊C4C2×C4semidirect
72. C22×C11⋊C8C2×C4semidirect
89. #66873C2×C4semidirect
90. #66873C2×C4semidirect
162. #2344D11semidirect
227. D44#117semidirect
249. #389C2×D11semidirect
256. C4×C4⋊C4C2×D11semidirect
316. C2×C4⋊C4C4×D11semidirect
419. C11#22562semidirect

Maximal subgroups

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

subgroupindex
C22×#668732
C22⋊C4×D442
#130693122
#130692432
#130688762
#130687022
#130686392
#130685462
#130684442
#130683942
C11×#23442
#2256211