Finite Group Databasebeta

← #14770822

Subgroups — #14770822

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×#66896C211yesmaximal, characteristic
2#13071483C211yesmaximal, characteristic, complemented
3#13069316C212yesmaximal, complemented
4#13069240C212yesmaximal, complemented
5#13068877C212yesmaximal, complemented
6#13068700C211yesmaximal, characteristic, complemented
7#13068639C211yesmaximal, characteristic, complemented
8#13068547C211yesmaximal, characteristic
9#13068441C212yesmaximal, complemented
10#13068394C211yesmaximal, characteristic, complemented
11D4×C11×C22⋊C4C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C2×C4×D4×C11C2212yes—
14C22×C11×C22⋊C4—21no—
15C22×C4⋊Dic11C2211yescharacteristic
16C23×C11⋊C8C2211yescharacteristic
17C2×#66930—21no—
18C11×#390C2212yes—
19C11×#386—22no—
20C11×#380C2211yescharacteristic
21C11×#379—21no—
22C4×C11×C22⋊C4C2211yescharacteristic
23C2×#66896C418yescomplemented
24C2×#66896C2212yes—
25C2×#66896C2212yes—
26C2×#66896C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30#10622825C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×#66872C2212yescomplemented
33#10622556—21no—
34C4×C4⋊Dic11C2212yescomplemented
35#10622541C2212yescomplemented
36C2×#66867C2212yescomplemented
37#10622266—22no—
38#10622167C2212yescomplemented
39#10622167C2212yescomplemented
40#10622167C2212yescomplemented
41#10622162C2212yescomplemented
42C25×C11—21no—
43C22×D4×C11—24no—
44C22×D4×C11—21no—
45C22×D4×C11—22no—
46C22×D4×C11—42no—
47C22×D4×C11C2×C414yes—
48C22×D4×C11C2311yescharacteristic
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11—22no—
51C23×C4×C11C2311yescharacteristic
52C23×Dic11—21no—
53C4×D4×C11—24no—
54C4×D4×C11—42no—
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C22⋊C4—21no—
57C2×C11×C22⋊C4—22no—
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—44no—
61C2×C11×C22⋊C4D411yescharacteristic
62C2×C11×C22⋊C4D411yescharacteristic
63C2×C42×C11C2312yes—
64C2×C22⋊Dic11—21no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—22no—
67C2×C4⋊Dic11C2×C414yescomplemented
68C2×C4⋊Dic11C2312yes—
69C2×C4⋊Dic11C2311yescharacteristic
70C2×C4⋊Dic11C2311yescharacteristic
71C2×Dic11⋊C4—22no—
72C2×C4×Dic11—22no—
73C22×C11⋊C8—42no—
74C22×C11⋊C8C2×C414yescomplemented
75C22×C11⋊C8C2312yes—
76C22×C11⋊C8C2311yescharacteristic
77C22×C11⋊C8C2311yescharacteristic
78#66930—44no—
79C11×#95—21no—
80C11×#95D412yes—
81#66896—24no—
82#66896—42no—
83#66896C2×C414yes—
84#66896C2×C414yes—
85#66896C2×C414yescomplemented
86#66896C2×C414yescomplemented
87C11⋊#95—21no—
88C11⋊#95—22no—
89C11⋊#95—22no—
90C22⋊(C11⋊C8)—22no—
91#66872—42no—
92#66867—42no—
93#22562—111nomaximal, Sylow
94C24×C11—21no—
95C24×C11—21no—
96C24×C11—24no—
97C24×C11—44no—
98C24×C11—42no—
99C24×C11—42no—
100C24×C11—82no—
101C24×C11C2×D411yescharacteristic
102C2×D4×C11—28no—
103C2×D4×C11—24no—
104C2×D4×C11—21no—
105C2×D4×C11—22no—
106C2×D4×C11—21no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—44no—
110C2×D4×C11—48no—
111C2×D4×C11—44no—
112C2×D4×C11C22×C412yes—
113C2×D4×C11C22×C412yes—
114C2×D4×C11#4114yes—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—44no—
119C22×C4×C11—44no—
120C22×C4×C11—82no—
121C22×C4×C11C22×C412yes—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11#4112yes—
126C22×C4×C11C2411yescharacteristic
127C22×Dic11—24no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—22no—
131C22×Dic11—42no—
132C22×Dic11—42no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C22⋊C4—22no—
136C11×C22⋊C4—22no—
137C11×C22⋊C4—44no—
138C11×C22⋊C4—44no—
139C11×C22⋊C4—42no—
140C11×C22⋊C4—82no—
141C42×C11—22no—
142C42×C11—22no—
143C22⋊Dic11—42no—
144C4⋊Dic11—24no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—22no—
148C4⋊Dic11—22no—
149C4⋊Dic11C22×C412yes—
150C4⋊Dic11C22×C412yes—
151Dic11⋊C4—44no—
152C4×Dic11—44no—
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#2344—111no—
163D4×C22⋊C4D1111yescharacteristic
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×C11—22no—
175C23×C11—24no—
176C23×C11—22no—
177C23×C11—48no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11—42no—
185C23×C11—48no—
186C23×C11—84no—
187C23×C11—88no—
188C23×C11—88no—
189C23×C11C4×D412yes—
190C23×C11AGL(1,ℤ/8)12yes—
191C23×C11AGL(1,ℤ/8)12yes—
192C23×C11C22×D411yescharacteristic
193D4×C11—22no—
194D4×C11—22no—
195D4×C11—22no—
196D4×C11—24no—
197D4×C11—48no—
198D4×C11—42no—
199D4×C11#11714yescomplemented
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—24no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—88no—
214C2×C4×C11C4×D412yes—
215C2×C4×C11C23×C411yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C11C2×#4112yes—
218C2×C4×C11H(5,𝔽2)12yes—
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—48no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228C2×Dic11—42no—
229C11⋊C8—22no—
230C11⋊C8—22no—
231C11⋊C8—42no—
232C23×D4C2×D1111yescharacteristic
233C23×C8—111no—
234C2×C4×D4C2×D1112yes—
235C2×#117—221no—
236C22×C4⋊C4—111no—
237C22×C22⋊C4—21no—
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#390C2×D1112yes—
249#389—112no—
250#387—222no—
251#386—22no—
252#381—221no—
253#380—111no—
254#380C2×D1111yescharacteristic
255#379—21no—
256C4×C4⋊C4—112no—
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—24no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—44no—
270C22×C11—44no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—42no—
274C22×C11—816no—
275C22×C11—82no—
276C22×C11—82no—
277C22×C11#44214yes—
278C22×C11C2×C4×D411yescharacteristic
279C22×C11#54612yes—
280C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
281C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
282C22×C11#57712yes—
283C4×C11—22no—
284C4×C11—42no—
285C4×C11—42no—
286C4×C11—82no—
287C4×C11C2×#11711yescharacteristic
288C4×C11#51811yescharacteristic
289C4×C11#55112yes—
290Dic11—42no—
291Dic11—42no—
292Dic11—82no—
293C25—21no—
294C22×D4—24no—
295C22×D4—22no—
296C22×D4—21no—
297C22×D4—42no—
298C22×D4C4×D1114yes—
299C22×D4C22×D1111yescharacteristic
300C22×D4C22×D1111yescharacteristic
301C23×C4—22no—
302C23×C4—221no—
303C23×C4C22×D1111yescharacteristic
304C22×C8—111no—
305C22×C8—111no—
306C22×C8—114no—
307C22×C8—112no—
308C22×C8—442no—
309C4×D4—24no—
310C4×D4—42no—
311#117—444no—
312C2×C4⋊C4—114no—
313C2×C4⋊C4—111no—
314C2×C4⋊C4—111no—
315C2×C4⋊C4—112no—
316C2×C4⋊C4—222no—
317C2×C4⋊C4—221no—
318C2×C4⋊C4—222no—
319C2×C4⋊C4C22×D1112yes—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—44no—
325C2×C22⋊C4—221no—
326C2×C22⋊C4C22⋊D1111yescharacteristic
327C2×C22⋊C4C22⋊D1111yescharacteristic
328C2×C42—222no—
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—21no—
340#95—222no—
341#95—221no—
342#95—222no—
343#95C22⋊D1112yes—
344C2×C11—24no—
345C2×C11—44no—
346C2×C11—82no—
347C2×C11#234211yescharacteristic
348C2×C11C2×#44211yescharacteristic
349C2×C11#294911yescharacteristic
350C2×C11#330612yes—
351C2×C11#331012yes—
352C24—21no—
353C24—21no—
354C24—24no—
355C24—44no—
356C24—42no—
357C24—42no—
358C24—82no—
359C24C2×C22⋊D1111yescharacteristic
360C2×D4—28no—
361C2×D4—24no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—44no—
368C2×D4—48no—
369C2×D4—44no—
370C2×D4C2×C4×D1112yes—
371C2×D4C2×C4×D1112yes—
372C2×D4#434114yes—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—44no—
377C22×C4—44no—
378C22×C4—82no—
379C22×C4—224no—
380C22×C4—221no—
381C22×C4—221no—
382C22×C4—222no—
383C22×C4—442no—
384C22×C4—442no—
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—22no—
400C4⋊C4—22no—
401C4⋊C4—112no—
402C4⋊C4—112no—
403C4⋊C4—224no—
404C4⋊C4—221no—
405C4⋊C4—221no—
406C4⋊C4—222no—
407C4⋊C4—222no—
408C4⋊C4—444no—
409C22⋊C4—22no—
410C22⋊C4—22no—
411C22⋊C4—44no—
412C22⋊C4—44no—
413C22⋊C4—42no—
414C22⋊C4—82no—
415C22⋊C4—442no—
416C42—22no—
417C42—22no—
418C42—444no—
419C11#2256211yescharacteristic, complemented, Sylow
420C23—22no—
421C23—22no—
422C23—22no—
423C23—24no—
424C23—22no—
425C23—48no—
426C23—41no—
427C23—41no—
428C23—42no—
429C23—41no—
430C23—42no—
431C23—41no—
432C23—42no—
433C23—48no—
434C23—84no—
435C23—88no—
436C23—88no—
437C23C4×C22⋊D1112yes—
438C23#6698512yes—
439C23#6700212yes—
440C23C22×C22⋊D1111yescharacteristic
441D4—22no—
442D4—22no—
443D4—22no—
444D4—24no—
445D4—48no—
446D4—42no—
447D4#6693014yescomplemented
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—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—88no—
462C2×C4—222no—
463C2×C4—222no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4—441no—
467C2×C4—441no—
468C2×C4—448no—
469C2×C4—442no—
470C2×C4—442no—
471C2×C4—442no—
472C2×C4C4×C22⋊D1112yes—
473C2×C4C22×C4×D1111yescharacteristic
474C2×C4C2×#433911yescharacteristic
475C2×C4C2×#434112yes—
476C2×C4#6703712yes—
477C8—222no—
478C8—222no—
479C8—442no—
480C22—24no—
481C22—24no—
482C22—22no—
483C22—22no—
484C22—24no—
485C22—44no—
486C22—44no—
487C22—42no—
488C22—42no—
489C22—42no—
490C22—42no—
491C22—42no—
492C22—816no—
493C22—82no—
494C22—82no—
495C22#1062262714yes—
496C22C2×C4×C22⋊D1111yescharacteristic
497C22C2×#6698511yescharacteristic
498C22#1062333712yes—
499C22C2×#6700211yescharacteristic
500C22#1062336712yes—
501C4—22no—
502C4—42no—
503C4—42no—
504C4—82no—
505C4—442no—
506C4—442no—
507C4—882no—
508C4C2×#6693011yescharacteristic
509C4#1062301711yescharacteristic
510C4#1062302612yes—
511C2—24no—
512C2—44no—
513C2—82no—
514C2#1307146111yescharacteristic
515C2C2×#1062262711yescharacteristic
516C2#1307747311yescharacteristic
517C2#1308057712yes—
518C2#1308063712yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingD4×C11×C22⋊C4C2
socleC23×C11C22×D4
prime radicalC23×D4×C11C22
cosocleC22×C4×C11C24
hypercenterD4×C22⋊C4D11
hypocenterC11#22562
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #13071483C2semidirect
3. #13069316C2semidirect
4. #13069240C2semidirect
5. #13068877C2semidirect
6. #13068700C2semidirect
7. #13068639C2semidirect
9. #13068441C2semidirect
10. #13068394C2semidirect
23. C2×#66896C4semidirect
32. C2×#66872C22semidirect
34. C4×C4⋊Dic11C22semidirect
35. #10622541C22semidirect
36. C2×#66867C22semidirect
38. #10622167C22semidirect
39. #10622167C22semidirect
40. #10622167C22semidirect
41. #10622162C22semidirect
67. C2×C4⋊Dic11C2×C4semidirect
74. C22×C11⋊C8C2×C4semidirect
85. #66896C2×C4semidirect
86. #66896C2×C4semidirect
199. D4×C11#117semidirect
419. C11#22562semidirect
447. D4#66930semidirect

Maximal subgroups

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

subgroupindex
C22×#668962
#130714832
#130693162
#130692402
#130688772
#130687002
#130686392
#130685472
#130684412
#130683942
D4×C11×C22⋊C42
#2256211