Finite Group Databasebeta

← #14680202

Subgroups — #14680202

Order 2816.

1926 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66979C211yesmaximal, characteristic
2C2×#10622586C212yesmaximal, complemented
3C2×#10622825C211yesmaximal, characteristic
4#13066880C212yesmaximal, complemented
5#13066872C212yesmaximal, complemented
6#13066859C214yesmaximal
7#13066845C212yesmaximal, complemented
8C2×C11×#380C211yesmaximal, characteristic
9C24×C4×C11C2211yescharacteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C22⋊C4C2212yes—
13C22×C22⋊Dic11C2212yes—
14C22×C22⋊Dic11C2212yes—
15C2×#66979—24no—
16C2×#66979—28no—
17C22×C4⋊Dic11C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2212yes—
20C22×Dic11⋊C4C2214yes—
21C22×C4×Dic11C2212yes—
22C11×#380—24no—
23C2×C11×#95C2212yes—
24#10622825C418yescomplemented
25C2×C11⋊#95C2214yes—
26C2×C11⋊#95C2214yes—
27C2×C11⋊#95C2214yes—
28C2×C11⋊#95C2212yes—
29#10622586—28no—
30C25×C11C2311yescharacteristic
31C23×C4×C11—24no—
32C23×C4×C11—24no—
33C23×C4×C11C2×C414yes—
34C23×C4×C11D414yes—
35C23×C4×C11Q814yes—
36C23×C4×C11C2312yes—
37C23×C4×C11C2312yes—
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C23×Dic11C2314yes—
41C23×Dic11C2312yes—
42C23×Dic11C2312yes—
43C2×C11×C4⋊C4—24no—
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4—24no—
47C2×C11×C22⋊C4—24no—
48C2×C11×C22⋊C4—44no—
49C2×C22⋊Dic11—24no—
50C2×C22⋊Dic11—24no—
51C2×C22⋊Dic11—24no—
52C2×C22⋊Dic11—42no—
53C2×C22⋊Dic11—42no—
54C2×C22⋊Dic11C2×C418yes—
55#66979—232no—
56C2×C4⋊Dic11—22no—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11—24no—
59C2×C4⋊Dic11—24no—
60C2×C4⋊Dic11—24no—
61C2×C4⋊Dic11—24no—
62C2×C4⋊Dic11C2×C418yes—
63C2×Dic11⋊C4—28no—
64C2×Dic11⋊C4—44no—
65C2×Dic11⋊C4—44no—
66C2×C4×Dic11—24no—
67C2×C4×Dic11—24no—
68C2×C4×Dic11D418yes—
69C11×#95—24no—
70C11⋊#95—28no—
71C11⋊#95—44no—
72C11⋊#95—44no—
73C11⋊#95C2×C418yes—
74#14264—111nomaximal, Sylow
75C24×C11—22no—
76C24×C11—22no—
77C24×C11—21no—
78C24×C11—21no—
79C24×C11—22no—
80C24×C11—21no—
81C24×C11—21no—
82C24×C11—22no—
83C24×C11C22×C412yes—
84C24×C11C2×D412yes—
85C24×C11C2×Q812yes—
86C24×C11C2411yescharacteristic
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—216no—
90C22×C4×C11—28no—
91C22×C4×C11—216no—
92C22×C4×C11—28no—
93C22×C4×C11—24no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—24no—
97C22×C4×C11—22no—
98C22×C4×C11—24no—
99C22×C4×C11—22no—
100C22×C4×C11—24no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11C4⋊C4116yescomplemented
104C22×C4×C11C22×C412yes—
105C22×C4×C11C22×C412yes—
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D414yes—
109C22×C4×C11C2×Q812yes—
110C22×C4×C11C2×Q812yes—
111C22×C4×C11#4114yes—
112C22×Dic11—24no—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—22no—
116C22×Dic11—22no—
117C22×Dic11—24no—
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11—24no—
121C22×Dic11—24no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—24no—
125C22×Dic11—24no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11C22×C418yes—
131C22×Dic11C2×D414yes—
132C22×Dic11C2×D414yes—
133C11×C4⋊C4—44no—
134C11×C4⋊C4—44no—
135C11×C22⋊C4—48no—
136C22⋊Dic11—216no—
137C22⋊Dic11—48no—
138C4⋊Dic11—28no—
139C4⋊Dic11—28no—
140C4⋊Dic11—216no—
141Dic11⋊C4—416no—
142C4×Dic11—216no—
143C22×#117—111no—
144C2×#389—112no—
145C2×#380—111no—
146C2×#380D1111yescharacteristic
147#1444—112no—
148#1442—112no—
149#1439—114no—
150C4⋊#95—112no—
151C23×C11—24no—
152C23×C11—22no—
153C23×C11—22no—
154C23×C11—24no—
155C23×C11—22no—
156C23×C11—24no—
157C23×C11—22no—
158C23×C11—22no—
159C23×C11—22no—
160C23×C11—22no—
161C23×C11—22no—
162C23×C11—24no—
163C23×C11—22no—
164C23×C11—22no—
165C23×C11—42no—
166C23×C11—42no—
167C23×C11—42no—
168C23×C11—42no—
169C23×C11—42no—
170C23×C11—42no—
171C23×C11—42no—
172C23×C11—42no—
173C23×C11C2×C4⋊C414yes—
174C23×C11C23×C411yescharacteristic
175C23×C11C22×D412yes—
176C23×C11C22×D411yescharacteristic
177C23×C11C22×Q811yescharacteristic
178C23×C11C2×#4112yes—
179C23×C11H(5,𝔽2)12yes—
180C23×C11H(5,𝔽2)11yescharacteristic
181C23×C11H(5,𝔽2)11yescharacteristic
182C23×C112−1+412yes—
183C23×C112−1+411yescharacteristic
184C23×C112−1+411yescharacteristic
185C2×C4×C11—24no—
186C2×C4×C11—22no—
187C2×C4×C11—24no—
188C2×C4×C11—22no—
189C2×C4×C11—232no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—44no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—44no—
198C2×C4×C11—44no—
199C2×C4×C11—44no—
200C2×C4×C11C2×C4⋊C414yes—
201C2×C4×C11C2×C4⋊C414yes—
202C2×C4×C11C4×D418yes—
203C2×C4×C11#12014yes—
204C2×C4×C11C22⋊Q818yes—
205C2×C4×C11#12314yes—
206C2×Dic11—28no—
207C2×Dic11—28no—
208C2×Dic11—28no—
209C2×Dic11—24no—
210C2×Dic11—24no—
211C2×Dic11—24no—
212C2×Dic11—24no—
213C2×Dic11—24no—
214C2×Dic11—24no—
215C2×Dic11—44no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—44no—
224C2×Dic11—42no—
225C2×Dic11—44no—
226C2×Dic11—44no—
227C24×C4C2×D1111yescharacteristic
228C2×#117—228no—
229C2×#117—224no—
230C22×C4⋊C4—112no—
231C22×C4⋊C4—111no—
232C22×C4⋊C4—111no—
233C22×C4⋊C4—114no—
234C22×C4⋊C4C2×D1111yescharacteristic
235C22×C4⋊C4C2×D1111yescharacteristic
236C22×C22⋊C4—112no—
237C22×C22⋊C4—112no—
238C22×C22⋊C4C2×D1112yes—
239C22×C42—112no—
240#389—228no—
241#380—24no—
242#380—118no—
243C2×#95—112no—
244C2×#95—114no—
245C2×#95—114no—
246C2×#95—114no—
247C2×#95C2×D1112yes—
248C22×C11—24no—
249C22×C11—24no—
250C22×C11—24no—
251C22×C11—44no—
252C22×C11—44no—
253C22×C11—42no—
254C22×C11—42no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11—44no—
258C22×C11—44no—
259C22×C11C22×C4⋊C411yescharacteristic
260C22×C11C2×C4×D412yes—
261C22×C11#51811yescharacteristic
262C22×C11#51911yescharacteristic
263C22×C11#52012yes—
264C22×C11C2×#12011yescharacteristic
265C22×C11C2×C22⋊Q812yes—
266C22×C11C2×#12311yescharacteristic
267C22×C11#53511yescharacteristic
268C22×C11#53512yes—
269C22×C11#53611yescharacteristic
270C22×C11#53612yes—
271C22×C11#53711yescharacteristic
272C22×C11#53711yescharacteristic
273C22×C11#53712yes—
274C22×C11#53712yes—
275C22×C11#54012yes—
276C22×C11#54112yes—
277C22×C11#54212yes—
278C22×C11#54212yes—
279C22×C11#54412yes—
280C22×C11#54411yescharacteristic
281C22×C11#54411yescharacteristic
282C4×C11—24no—
283C4×C11—82no—
284C4×C11—82no—
285C4×C11#38518yes—
286Dic11—48no—
287Dic11—44no—
288Dic11—44no—
289C25C22×D1111yescharacteristic
290C23×C4—24no—
291C23×C4—24no—
292C23×C4—112no—
293C23×C4—114no—
294C23×C4—112no—
295C23×C4Dic2214yes—
296C23×C4C4×D1114yes—
297C23×C4C22⋊D1114yes—
298C23×C4C22×D1112yes—
299C23×C4C22×D1112yes—
300C23×C4C22×D1111yescharacteristic
301C23×C4C22×D1111yescharacteristic
302#117—2232no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—118no—
308C2×C4⋊C4—224no—
309C2×C4⋊C4—224no—
310C2×C4⋊C4—224no—
311C2×C4⋊C4—224no—
312C2×C4⋊C4—222no—
313C2×C4⋊C4—222no—
314C2×C4⋊C4—228no—
315C2×C4⋊C4—444no—
316C2×C4⋊C4—444no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—44no—
319C2×C22⋊C4—118no—
320C2×C22⋊C4—224no—
321C2×C22⋊C4—224no—
322C2×C22⋊C4—224no—
323C2×C22⋊C4—442no—
324C2×C22⋊C4—442no—
325C2×C42—118no—
326C2×C42—224no—
327C2×C42—224no—
328#95—24no—
329#95—118no—
330#95—228no—
331#95—444no—
332#95—444no—
333C2×C11—44no—
334C2×C11C2×#38511yescharacteristic
335C2×C11#231611yescharacteristic
336C2×C11#231711yescharacteristic
337C2×C11#232312yes—
338C2×C11#232412yes—
339C2×C11#261511yescharacteristic
340C2×C11#261611yescharacteristic
341C2×C11#262411yescharacteristic
342C2×C11#262511yescharacteristic
343C2×C11#262812yes—
344C2×C11#262912yes—
345C24—22no—
346C24—22no—
347C24—22no—
348C24—22no—
349C24—21no—
350C24—21no—
351C24—21no—
352C24—21no—
353C24C2×Dic2212yes—
354C24C2×C4×D1112yes—
355C24C2×C22⋊D1112yes—
356C24C23×D1111yescharacteristic
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—216no—
360C22×C4—216no—
361C22×C4—28no—
362C22×C4—28no—
363C22×C4—24no—
364C22×C4—24no—
365C22×C4—24no—
366C22×C4—24no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—118no—
374C22×C4—114no—
375C22×C4—114no—
376C22×C4—224no—
377C22×C4—222no—
378C22×C4—222no—
379C22×C4—224no—
380C22×C4—222no—
381C22×C4—224no—
382C22×C4—222no—
383C22×C4—224no—
384C22×C4—222no—
385C22×C4—222no—
386C22×C4—222no—
387C22×C4—224no—
388C22×C4—224no—
389C22×C4—222no—
390C22×C4—222no—
391C22×C4—222no—
392C22×C4—222no—
393C22×C4—222no—
394C22×C4Dic11⋊C4116yescomplemented
395C22×C4C2×Dic2212yes—
396C22×C4C2×Dic2212yes—
397C22×C4C2×C4×D1112yes—
398C22×C4C2×C4×D1112yes—
399C22×C4D4×D1114yes—
400C22×C4#434114yes—
401C22×C4C2×C22⋊D1112yes—
402C22×C4C2×C22⋊D1112yes—
403C4⋊C4—44no—
404C4⋊C4—44no—
405C4⋊C4—228no—
406C4⋊C4—228no—
407C4⋊C4—2216no—
408C4⋊C4—4416no—
409C22⋊C4—48no—
410C22⋊C4—2216no—
411C22⋊C4—448no—
412C42—2216no—
413C11#1426411yescharacteristic, complemented, Sylow
414C23—24no—
415C23—24no—
416C23—24no—
417C23—24no—
418C23—22no—
419C23—22no—
420C23—22no—
421C23—22no—
422C23—22no—
423C23—22no—
424C23—22no—
425C23—22no—
426C23—22no—
427C23—22no—
428C23—42no—
429C23—42no—
430C23—42no—
431C23—42no—
432C23—42no—
433C23—42no—
434C23—42no—
435C23—42no—
436C23C2×Dic11⋊C414yes—
437C23C22×Dic2211yescharacteristic
438C23C22×C4×D1111yescharacteristic
439C23C2×D4×D1112yes—
440C23C2×#434112yes—
441C23#6703712yes—
442C23#6704012yes—
443C23#6704211yescharacteristic
444C23#6704211yescharacteristic
445C23#6704311yescharacteristic
446C23#6704311yescharacteristic
447C23C22×C22⋊D1111yescharacteristic
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—232no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—44no—
460C2×C4—44no—
461C2×C4—44no—
462C2×C4—44no—
463C2×C4—228no—
464C2×C4—228no—
465C2×C4—228no—
466C2×C4—224no—
467C2×C4—224no—
468C2×C4—224no—
469C2×C4—224no—
470C2×C4—224no—
471C2×C4—224no—
472C2×C4—442no—
473C2×C4—442no—
474C2×C4—442no—
475C2×C4—442no—
476C2×C4—444no—
477C2×C4—442no—
478C2×C4—442no—
479C2×C4—444no—
480C2×C4—442no—
481C2×C4—442no—
482C2×C4—444no—
483C2×C4—444no—
484C2×C4#6693118yes—
485C2×C4(C22⋊D11)⋊C418yes—
486C2×C4C2×Dic11⋊C414yes—
487C2×C4C2×Dic11⋊C414yes—
488C2×C4#6698814yes—
489C2×C4#6699014yes—
490C22—24no—
491C22—24no—
492C22—24no—
493C22—44no—
494C22—44no—
495C22—42no—
496C22—42no—
497C22—44no—
498C22—44no—
499C22—42no—
500C22—42no—
501C22C2×#6693112yes—
502C22C2×(C22⋊D11)⋊C412yes—
503C22#1062303112yes—
504C22#1062303512yes—
505C22#1062304711yescharacteristic
506C22#1062305011yescharacteristic
507C22#1062305011yescharacteristic
508C22#1062305211yescharacteristic
509C22#1062313412yes—
510C22#1062313812yes—
511C22#1062313912yes—
512C22#1062315012yes—
513C22#1062315612yes—
514C22#1062315912yes—
515C22#1062316012yes—
516C22#1062317412yes—
517C22C22×Dic11⋊C411yescharacteristic
518C22C2×#6698811yescharacteristic
519C22C2×#6699011yescharacteristic
520C22#1062333611yescharacteristic
521C22#1062334711yescharacteristic
522C22#1062336411yescharacteristic
523C22#1062336411yescharacteristic
524C4—24no—
525C4—82no—
526C4—82no—
527C4—444no—
528C4—444no—
529C4—448no—
530C4#1062255918yes—
531C2—44no—
532C2C2×#1062255911yescharacteristic
533C2#1307123211yescharacteristic
534C2#1307124011yescharacteristic
535C2#1307129412yes—
536C2#1307130512yes—
537C2#1307434111yescharacteristic
538C2#1307434611yescharacteristic
539C2#1307440611yescharacteristic
540C2#1307441411yescharacteristic
541C2#1307444112yes—
542C2#1307445012yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#380C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#380D11
hypocenterC11#14264
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×#10622586C2semidirect
4. #13066880C2semidirect
5. #13066872C2semidirect
7. #13066845C2semidirect
24. #10622825C4semidirect
103. C22×C4×C11C4⋊C4semidirect
394. C22×C4Dic11⋊C4semidirect
413. C11#14264semidirect

Maximal subgroups

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

subgroupindex
C22×#669792
C2×#106225862
C2×#106228252
#130668802
#130668722
#130668592
#130668452
C2×C11×#3802
#1426411