Finite Group Databasebeta

← #14762840

Subgroups — #14762840

Order 2816.

1486 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622820C211yesmaximal, characteristic, complemented
2#13070999C211yesmaximal, characteristic, complemented
3#13069055C212yesmaximal, complemented
4#13069050C212yesmaximal, complemented
5#13068939C212yesmaximal, complemented
6#13068929C212yesmaximal, complemented
7#13068711C212yesmaximal, complemented
8#13068556C212yesmaximal, complemented
9C2×C11×#525C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C11×#525—24no—
13C11×#525C418yescomplemented
14C2×C11×#123—21no—
15C2×C11×C22⋊Q8C2211yescharacteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C11×#121C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C2×C11×#120—21no—
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11—21no—
22C2×C11×#117C2211yescharacteristic
23C2×#66979C2212yes—
24C22×#4318C2212yes—
25#10622860—21no—
26C2×#66899C2214yescomplemented
27C2×#66896C2214yescomplemented
28#10622825C2212yes—
29#10622825C2212yes—
30#10622824—21no—
31C4×C22⋊Dic11—21no—
32C4×C22⋊Dic11—21no—
33#10622820—24no—
34C2×C22⋊(C11⋊C8)C2212yes—
35C2×C22⋊(C11⋊C8)C2212yes—
36#10622167C2214yescomplemented
37#10622167C2214yescomplemented
38C25×C11D411yescharacteristic
39C2×C11×#41—22no—
40C2×C11×#41—44no—
41C2×C11×#41C2×C414yes—
42C22×Q8×C11C2311yescharacteristic
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11—44no—
49C23×C4×C11C2×C414yes—
50C23×C4×C11D411yescharacteristic
51C23×C4×C11D411yescharacteristic
52C23×C4×C11D411yescharacteristic
53C23×C4×C11D414yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C11×#123—28no—
58C11×C22⋊Q8—22no—
59C11×C22⋊Q8—22no—
60C11×C22⋊Q8C2×C414yes—
61C11×C22⋊Q8C2×C414yes—
62C11×#121—22no—
63C11×#121—22no—
64C11×#121C2×C414yes—
65C11×#121C2×C414yes—
66C11×#120—28no—
67C4×D4×C11—28no—
68C4×D4×C11—28no—
69C11×#117—22no—
70C11×#117C2×C414yes—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C42×C11—21no—
81C2×C22⋊Dic11—22no—
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11—22no—
84#66979—44no—
85C2×C4⋊Dic11C2314yes—
86C2×C4×Dic11—22no—
87C2×#4318—24no—
88C2×#4318—44no—
89C22×C11⋊C8C2314yes—
90#66899—44no—
91#66896—44no—
92C11⋊#95—22no—
93C11⋊#95—22no—
94C22⋊(C11⋊C8)—24no—
95C22⋊(C11⋊C8)—24no—
96#21766—111nomaximal, Sylow
97C24×C11—21no—
98C24×C11—42no—
99C24×C11—42no—
100C24×C11—42no—
101C24×C11C22⋊C414yes—
102C24×C11C2×D411yescharacteristic
103C24×C11C2×D411yescharacteristic
104C24×C11C2×D411yescharacteristic
105C11×#41—48no—
106C11×#41—48no—
107C2×Q8×C11—21no—
108C2×Q8×C11—24no—
109C2×Q8×C11C22×C412yes—
110C2×D4×C11—24no—
111C2×D4×C11—24no—
112C2×D4×C11—24no—
113C2×D4×C11—21no—
114C2×D4×C11—24no—
115C2×D4×C11—44no—
116C2×D4×C11—44no—
117C2×D4×C11—44no—
118C2×D4×C11C22×C412yes—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—24no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—24no—
126C22×C4×C11—48no—
127C22×C4×C11—48no—
128C22×C4×C11—42no—
129C22×C4×C11—42no—
130C22×C4×C11—42no—
131C22×C4×C11—44no—
132C22×C4×C11C22⋊C414yes—
133C22×C4×C11C22⋊C414yes—
134C22×C4×C11C22⋊C414yes—
135C22×C4×C11C22×C412yes—
136C22×C4×C11C22×C412yes—
137C22×C4×C11C22×C412yes—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—24no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4C22×C412yes—
151C11×C4⋊C4C22×C412yes—
152C11×C22⋊C4—24no—
153C11×C22⋊C4—24no—
154C11×C22⋊C4—24no—
155C11×C22⋊C4—24no—
156C11×C22⋊C4—24no—
157C42×C11—24no—
158C22⋊Dic11—44no—
159C22⋊Dic11—44no—
160C22⋊Dic11—44no—
161C4⋊Dic11—24no—
162C4⋊Dic11—24no—
163C4×Dic11—44no—
164#4318—48no—
165C2×C11⋊C8—24no—
166C2×C11⋊C8—24no—
167C2×C11⋊C8—24no—
168C2×#525D1111yescharacteristic
169C2×#407—111no—
170#2280—111no—
171#1895—112no—
172#1894—112no—
173#1875—112no—
174#1873—112no—
175#1825—112no—
176#1788—112no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—22no—
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—22no—
186C23×C11—22no—
187C23×C11—44no—
188C23×C11—44no—
189C23×C11—44no—
190C23×C11—416no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11C2×C22⋊C412yes—
195C23×C11C2×C22⋊C412yes—
196C23×C11C2×C22⋊C412yes—
197C23×C11C22×D411yescharacteristic
198Q8×C11—24no—
199Q8×C11—42no—
200D4×C11—24no—
201D4×C11—48no—
202D4×C11—48no—
203D4×C11—48no—
204D4×C11—42no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—44no—
218C2×C4×C11—44no—
219C2×C4×C11—44no—
220C2×C4×C11—48no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11C2×C22⋊C412yes—
225C2×C4×C11C2×C22⋊C412yes—
226C2×C4×C11C2×C22⋊C412yes—
227C2×C4×C11C23×C411yescharacteristic
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11H(5,𝔽2)14yes—
230C2×Dic11—44no—
231C2×Dic11—44no—
232C2×Dic11—44no—
233C11⋊C8—44no—
234C22×#41C2×D1111yescharacteristic
235C24×C4C2×D1111yescharacteristic
236C22×M16—112no—
237#525—24no—
238#525Dic1118yescomplemented
239C2×#123—21no—
240C2×C22⋊Q8C2×D1111yescharacteristic
241C2×C22⋊Q8C2×D1111yescharacteristic
242C2×#121C2×D1111yescharacteristic
243C2×#121C2×D1111yescharacteristic
244C2×#120—21no—
245C2×C4×D4—21no—
246C2×C4×D4—21no—
247C2×#117—112no—
248C2×#117C2×D1111yescharacteristic
249C2×#103—114no—
250C2×#102—114no—
251#407—224no—
252C2×C22⋊C8—112no—
253C2×C22⋊C8—112no—
254#381—221no—
255#380—112no—
256#380—112no—
257#379—221no—
258C4×C22⋊C4—221no—
259C4×C22⋊C4—221no—
260#340—114no—
261#340—114no—
262C22×C11—22no—
263C22×C11—22no—
264C22×C11—22no—
265C22×C11—22no—
266C22×C11—22no—
267C22×C11—22no—
268C22×C11—22no—
269C22×C11—22no—
270C22×C11—22no—
271C22×C11—416no—
272C22×C11—44no—
273C22×C11—44no—
274C22×C11—44no—
275C22×C11—42no—
276C22×C11—42no—
277C22×C11—42no—
278C22×C11—84no—
279C22×C11C22×C22⋊C411yescharacteristic
280C22×C11#53412yes—
281C22×C11#57512yes—
282C22×C11#57512yes—
283C4×C11—22no—
284C4×C11—22no—
285C4×C11—22no—
286C4×C11—42no—
287C4×C11—42no—
288C4×C11—42no—
289C4×C11#51812yes—
290C4×C11#53412yes—
291Dic11—84no—
292C25C22⋊D1111yescharacteristic
293C2×#41—22no—
294C2×#41—44no—
295C2×#41C2×Dic1114yes—
296C22×Q8C22×D1111yescharacteristic
297C22×D4—21no—
298C22×D4—21no—
299C22×D4—21no—
300C22×D4C22×D1111yescharacteristic
301C23×C4—21no—
302C23×C4—44no—
303C23×C4C2×Dic1114yes—
304C23×C4C22⋊D1111yescharacteristic
305C23×C4C22⋊D1111yescharacteristic
306C23×C4C22⋊D1111yescharacteristic
307C23×C4C22⋊D1114yes—
308C23×C4C22×D1111yescharacteristic
309C23×C4C22×D1111yescharacteristic
310C23×C4C22×D1111yescharacteristic
311C2×M16—224no—
312C2×M16—444no—
313C22×C8—114no—
314#123—28no—
315C22⋊Q8—22no—
316C22⋊Q8—22no—
317C22⋊Q8C2×Dic1114yes—
318C22⋊Q8C2×Dic1114yes—
319#121—22no—
320#121—22no—
321#121C2×Dic1114yes—
322#121C2×Dic1114yes—
323#120—28no—
324C4×D4—28no—
325C4×D4—28no—
326#117—22no—
327#117—444no—
328#117C2×Dic1114yes—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—114no—
332C2×C4⋊C4C22×D1111yescharacteristic
333C2×C4⋊C4C22×D1111yescharacteristic
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—222no—
340C2×C22⋊C4—222no—
341C2×C22⋊C4—222no—
342C2×C42—21no—
343C2×C42—222no—
344#103—444no—
345#102—444no—
346C22⋊C8—224no—
347C22⋊C8—224no—
348#95—222no—
349#95—222no—
350C2×C11—42no—
351C2×C11—42no—
352C2×C11—42no—
353C2×C11—82no—
354C2×C11#230811yescharacteristic
355C2×C11#289611yescharacteristic
356C2×C11#289611yescharacteristic
357C2×C11#319714yes—
358C24—21no—
359C24—42no—
360C24—42no—
361C24—42no—
362C24C22⋊Dic1114yes—
363C24C2×C22⋊D1111yescharacteristic
364C24C2×C22⋊D1111yescharacteristic
365C24C2×C22⋊D1111yescharacteristic
366#41—48no—
367#41—48no—
368C2×Q8—21no—
369C2×Q8—24no—
370C2×Q8C22×Dic1112yes—
371C2×D4—24no—
372C2×D4—24no—
373C2×D4—24no—
374C2×D4—24no—
375C2×D4—21no—
376C2×D4—44no—
377C2×D4—44no—
378C2×D4—44no—
379C2×D4C22×Dic1112yes—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—24no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—24no—
387C22×C4—48no—
388C22×C4—48no—
389C22×C4—42no—
390C22×C4—42no—
391C22×C4—42no—
392C22×C4—44no—
393C22×C4—224no—
394C22×C4C22⋊Dic1114yes—
395C22×C4C22⋊Dic1114yes—
396C22×C4C22⋊Dic1114yes—
397C22×C4C22×Dic1112yes—
398C22×C4C22×Dic1112yes—
399C22×C4C22×Dic1112yes—
400C22×C4C2×C22⋊D1111yescharacteristic
401C22×C4C2×C22⋊D1111yescharacteristic
402C22×C4C2×C22⋊D1111yescharacteristic
403C22×C4C2×C22⋊D1112yes—
404C22×C4C2×C22⋊D1112yes—
405C22×C4C2×C22⋊D1112yes—
406C22×C4C23×D1111yescharacteristic
407M16—448no—
408C2×C8—224no—
409C2×C8—224no—
410C2×C8—224no—
411C4⋊C4—24no—
412C4⋊C4—24no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—224no—
416C4⋊C4—224no—
417C4⋊C4C22×Dic1112yes—
418C4⋊C4C22×Dic1112yes—
419C22⋊C4—24no—
420C22⋊C4—24no—
421C22⋊C4—24no—
422C22⋊C4—24no—
423C22⋊C4—24no—
424C22⋊C4—444no—
425C22⋊C4—444no—
426C22⋊C4—444no—
427C42—24no—
428C42—444no—
429C11#2176611yescharacteristic, complemented, Sylow
430C23—22no—
431C23—22no—
432C23—22no—
433C23—22no—
434C23—22no—
435C23—22no—
436C23—22no—
437C23—22no—
438C23—22no—
439C23—22no—
440C23—44no—
441C23—44no—
442C23—44no—
443C23—416no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23C2×C22⋊Dic1112yes—
448C23C2×C22⋊Dic1112yes—
449C23C2×C22⋊Dic1112yes—
450C23C22×C22⋊D1111yescharacteristic
451Q8—24no—
452Q8—42no—
453D4—24no—
454D4—48no—
455D4—48no—
456D4—48no—
457D4—42no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—44no—
471C2×C4—44no—
472C2×C4—44no—
473C2×C4—48no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—444no—
478C2×C4—444no—
479C2×C4—444no—
480C2×C4C2×C22⋊Dic1112yes—
481C2×C4C2×C22⋊Dic1112yes—
482C2×C4C2×C22⋊Dic1112yes—
483C2×C4#6703714yes—
484C2×C4C23×Dic1111yescharacteristic
485C2×C4C22×C22⋊D1111yescharacteristic
486C8—444no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—416no—
497C22—44no—
498C22—44no—
499C22—44no—
500C22—42no—
501C22—42no—
502C22—42no—
503C22—84no—
504C22#1062333512yes—
505C22#1062335312yes—
506C22#1062335312yes—
507C22C22×C22⋊Dic1111yescharacteristic
508C4—22no—
509C4—22no—
510C4—22no—
511C4—42no—
512C4—42no—
513C4—42no—
514C4—884no—
515C4#1062332912yes—
516C4#1062333512yes—
517C2—42no—
518C2—42no—
519C2—42no—
520C2—82no—
521C2#1307119411yescharacteristic
522C2#1307713511yescharacteristic
523C2#1307713511yescharacteristic
524C2#1307945314yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#525C2
socleC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC2×#525D11
hypocenterC11#21766
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#10622820C2semidirect
2. #13070999C2semidirect
3. #13069055C2semidirect
4. #13069050C2semidirect
5. #13068939C2semidirect
6. #13068929C2semidirect
7. #13068711C2semidirect
8. #13068556C2semidirect
13. C11×#525C4semidirect
26. C2×#66899C22semidirect
27. C2×#66896C22semidirect
36. #10622167C22semidirect
37. #10622167C22semidirect
238. #525Dic11semidirect
429. C11#21766semidirect

Maximal subgroups

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

subgroupindex
C2×#106228202
#130709992
#130690552
#130690502
#130689392
#130689292
#130687112
#130685562
C2×C11×#5252
#2176611