Finite Group Databasebeta

← #14680980

Subgroups — #14680980

Order 2816.

2150 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic11C211yesmaximal, characteristic
2C2×#10622264C211yesmaximal, characteristic, complemented
3C2×#10622263C211yesmaximal, characteristic, complemented
4#13066885C211yesmaximal, characteristic, complemented
5#13066883C211yesmaximal, characteristic, complemented
6#13066859C214yesmaximal, complemented
7#13066857C211yesmaximal, characteristic
8#13066838C214yesmaximal, complemented
9C11×#1438C211yesmaximal, characteristic
10C23×D4×C11C2211yescharacteristic
11C24×Dic11C2212yes—
12C22×C11×C22⋊C4C2214yes—
13C22×C22⋊Dic11C2212yes—
14C22×C22⋊Dic11C2214yes—
15C2×D4×Dic11—24no—
16C2×D4×Dic11—24no—
17C2×D4×Dic11C418yescomplemented
18C22×C4⋊Dic11C2211yescharacteristic
19C22×Dic11⋊C4C2212yes—
20C22×C4×Dic11C2211yescharacteristic
21C2×C11×#95C2211yescharacteristic
22C2×C11×#95C2211yescharacteristic
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2211yescharacteristic
26C2×C11⋊#95C2211yescharacteristic
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2214yes—
29C2×C11⋊#95C2214yes—
30#10622264—24no—
31#10622263—24no—
32C25×C11C2312yes—
33C22×D4×C11—28no—
34C22×D4×C11—22no—
35C22×D4×C11—22no—
36C22×D4×C11C2×C414yes—
37C23×C4×C11C2312yes—
38C23×C4×C11C2312yes—
39C23×C4×C11C2311yescharacteristic
40C23×Dic11—24no—
41C23×Dic11—24no—
42C23×Dic11—44no—
43C23×Dic11—44no—
44C23×Dic11C2×C418yes—
45C23×Dic11C2312yes—
46C23×Dic11C2312yes—
47C23×Dic11C2312yes—
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C2×C11×C22⋊C4—28no—
51C2×C11×C22⋊C4—44no—
52C2×C11×C22⋊C4—44no—
53C2×C22⋊Dic11—24no—
54C2×C22⋊Dic11—24no—
55C2×C22⋊Dic11—28no—
56C2×C22⋊Dic11—44no—
57C2×C22⋊Dic11—44no—
58C2×C22⋊Dic11C2×C418yes—
59D4×Dic11—232no—
60C2×C4⋊Dic11—22no—
61C2×C4⋊Dic11—22no—
62C2×C4⋊Dic11C2×C414yes—
63C2×Dic11⋊C4—24no—
64C2×Dic11⋊C4—44no—
65C2×C4×Dic11C2×C414yes—
66C2×C4×Dic11D414yes—
67C2×C4×Dic11D414yes—
68C11×#95—22no—
69C11×#95—22no—
70C11⋊#95—22no—
71C11⋊#95—22no—
72C11⋊#95—24no—
73C11⋊#95—24no—
74C11⋊#95—24no—
75C11⋊#95—44no—
76C11⋊#95—44no—
77#14345—111nomaximal, Sylow
78C24×C11—22no—
79C24×C11—22no—
80C24×C11—24no—
81C24×C11—24no—
82C24×C11—24no—
83C24×C11—24no—
84C24×C11—24no—
85C24×C11C22×C414yes—
86C24×C11#4118yes—
87C24×C11C2411yescharacteristic
88C2×D4×C11—216no—
89C2×D4×C11—216no—
90C2×D4×C11—216no—
91C2×D4×C11—28no—
92C22×C4×C11—24no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—24no—
96C22×C4×C11—24no—
97C22×C4×C11—22no—
98C22×C4×C11—24no—
99C22×C4×C11—24no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11C22×C412yes—
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D412yes—
106C22×Dic11—216no—
107C22×Dic11—22no—
108C22×Dic11—22no—
109C22×Dic11—22no—
110C22×Dic11—22no—
111C22×Dic11—24no—
112C22×Dic11—24no—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—22no—
116C22×Dic11—24no—
117C22×Dic11—24no—
118C22×Dic11—22no—
119C22×Dic11—24no—
120C22×Dic11—24no—
121C22×Dic11—22no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—416no—
126C22×Dic11—48no—
127C22×Dic11—416no—
128C22×Dic11—48no—
129C22×Dic11C22×C414yes—
130C22×Dic11C22×C412yes—
131C22×Dic11C22×C412yes—
132C22×Dic11C2×D412yes—
133C22×Dic11C2×D412yes—
134C22×Dic11C2×D412yes—
135C22×Dic11C2×D412yes—
136C11×C22⋊C4—416no—
137C22⋊Dic11—216no—
138C22⋊Dic11—416no—
139C4⋊Dic11—28no—
140Dic11⋊C4—48no—
141C4×Dic11C22⋊C4116yescomplemented
142C22×C4×D4—111no—
143C2×#383—111no—
144C2×#382—111no—
145#1445—111no—
146#1445—111no—
147#1439—114no—
148#1438—111no—
149#1438D1111yescharacteristic
150C22⋊#95—114no—
151C23×C11—24no—
152C23×C11—24no—
153C23×C11—28no—
154C23×C11—28no—
155C23×C11—28no—
156C23×C11—28no—
157C23×C11—28no—
158C23×C11—28no—
159C23×C11—28no—
160C23×C11—28no—
161C23×C11—42no—
162C23×C11—44no—
163C23×C11—42no—
164C23×C11—42no—
165C23×C11—42no—
166C23×C11—44no—
167C23×C11—44no—
168C23×C11—44no—
169C23×C11—44no—
170C23×C11—44no—
171C23×C11#11718yes—
172C23×C11C23×C411yescharacteristic
173C23×C11C22×D411yescharacteristic
174C23×C11C22×D411yescharacteristic
175C23×C11C2×#4114yes—
176C23×C11H(5,𝔽2)12yes—
177C23×C11H(5,𝔽2)12yes—
178C23×C11H(5,𝔽2)12yes—
179C23×C112−1+412yes—
180D4×C11—232no—
181C2×C4×C11—24no—
182C2×C4×C11—24no—
183C2×C4×C11—24no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—44no—
191C2×C4×C11—44no—
192C2×C4×C11—44no—
193C2×C4×C11—44no—
194C2×C4×C11C2×C22⋊C414yes—
195C2×Dic11—24no—
196C2×Dic11—24no—
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—24no—
200C2×Dic11—22no—
201C2×Dic11—22no—
202C2×Dic11—24no—
203C2×Dic11—24no—
204C2×Dic11—28no—
205C2×Dic11—432no—
206C2×Dic11—42no—
207C2×Dic11—44no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—44no—
216C2×Dic11—44no—
217C2×Dic11—44no—
218C2×Dic11—44no—
219C2×Dic11C2×C22⋊C414yes—
220C2×Dic11C2×C22⋊C414yes—
221C23×D4C2×D1111yescharacteristic
222C24×C4—112no—
223C2×C4×D4—118no—
224C2×C4×D4—224no—
225C2×C4×D4—224no—
226C22×C4⋊C4—111no—
227C22×C4⋊C4—112no—
228C22×C22⋊C4—112no—
229C22×C22⋊C4—114no—
230C22×C22⋊C4C2×D1114yes—
231C22×C42—111no—
232#383—224no—
233#382—224no—
234C2×#95—112no—
235C2×#95—112no—
236C2×#95—111no—
237C2×#95—111no—
238C2×#95—112no—
239C2×#95—114no—
240C2×#95—114no—
241C2×#95C2×D1111yescharacteristic
242C2×#95C2×D1111yescharacteristic
243C22×C11—216no—
244C22×C11—28no—
245C22×C11—44no—
246C22×C11—44no—
247C22×C11—48no—
248C22×C11—48no—
249C22×C11—48no—
250C22×C11—48no—
251C22×C11—48no—
252C22×C11C22×C22⋊C411yescharacteristic
253C22×C11C2×#11712yes—
254C22×C11#51812yes—
255C22×C11#52012yes—
256C22×C11#52512yes—
257C22×C11#52512yes—
258C22×C11#53511yescharacteristic
259C22×C11#53511yescharacteristic
260C22×C11#53512yes—
261C22×C11#53511yescharacteristic
262C22×C11#53611yescharacteristic
263C22×C11#53712yes—
264C22×C11#53814yes—
265C22×C11#53814yes—
266C22×C11#53914yes—
267C22×C11#53914yes—
268C4×C11—24no—
269C4×C11—82no—
270C4×C11—82no—
271Dic11—24no—
272Dic11—24no—
273Dic11—44no—
274Dic11—82no—
275Dic11—82no—
276C25C22×D1112yes—
277C22×D4—28no—
278C22×D4—22no—
279C22×D4—22no—
280C22×D4C4×D1114yes—
281C23×C4—111no—
282C23×C4—111no—
283C23×C4—112no—
284C23×C4—118no—
285C23×C4—112no—
286C23×C4—112no—
287C23×C4—224no—
288C23×C4—224no—
289C23×C4—444no—
290C23×C4—444no—
291C23×C4C22×D1112yes—
292C23×C4C22×D1112yes—
293C23×C4C22×D1111yescharacteristic
294C4×D4—2232no—
295C2×C4⋊C4—114no—
296C2×C4⋊C4—222no—
297C2×C4⋊C4—222no—
298C2×C4⋊C4—224no—
299C2×C4⋊C4—444no—
300C2×C22⋊C4—28no—
301C2×C22⋊C4—44no—
302C2×C22⋊C4—44no—
303C2×C22⋊C4—118no—
304C2×C22⋊C4—224no—
305C2×C22⋊C4—224no—
306C2×C22⋊C4—228no—
307C2×C22⋊C4—444no—
308C2×C22⋊C4—444no—
309C2×C42—114no—
310C2×C42—114no—
311C2×C42—114no—
312#95—22no—
313#95—22no—
314#95—224no—
315#95—224no—
316#95—224no—
317#95—222no—
318#95—222no—
319#95—444no—
320#95—444no—
321C2×C11—48no—
322C2×C11#228011yescharacteristic
323C2×C11#230911yescharacteristic
324C2×C11#231111yescharacteristic
325C2×C11#231814yes—
326C2×C11#263112yes—
327C2×C11#263312yes—
328C2×C11#263612yes—
329C2×C11#263612yes—
330C24—22no—
331C24—22no—
332C24—24no—
333C24—24no—
334C24—24no—
335C24—24no—
336C24—24no—
337C24C2×C4×D1114yes—
338C24#434118yes—
339C24C23×D1111yescharacteristic
340C2×D4—216no—
341C2×D4—216no—
342C2×D4—216no—
343C2×D4—28no—
344C22×C4—24no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—24no—
348C22×C4—24no—
349C22×C4—24no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—24no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—112no—
356C22×C4—112no—
357C22×C4—112no—
358C22×C4—112no—
359C22×C4—112no—
360C22×C4—112no—
361C22×C4—114no—
362C22×C4—2216no—
363C22×C4—222no—
364C22×C4—222no—
365C22×C4—222no—
366C22×C4—222no—
367C22×C4—222no—
368C22×C4—222no—
369C22×C4—224no—
370C22×C4—224no—
371C22×C4—222no—
372C22×C4—222no—
373C22×C4—224no—
374C22×C4—224no—
375C22×C4—222no—
376C22×C4—222no—
377C22×C4—224no—
378C22×C4—224no—
379C22×C4—222no—
380C22×C4—222no—
381C22×C4—4416no—
382C22×C4—448no—
383C22×C4—4416no—
384C22×C4—448no—
385C22×C4C2×C4×D1112yes—
386C22×C4D4×D1112yes—
387C22×C4D4×D1112yes—
388C4⋊C4—228no—
389C4⋊C4—448no—
390C22⋊C4—416no—
391C22⋊C4—2216no—
392C22⋊C4—4416no—
393C42—1116no—
394C11#1434511yescharacteristic, complemented, Sylow
395C23—24no—
396C23—24no—
397C23—28no—
398C23—28no—
399C23—28no—
400C23—28no—
401C23—28no—
402C23—28no—
403C23—28no—
404C23—28no—
405C23—42no—
406C23—42no—
407C23—44no—
408C23—44no—
409C23—44no—
410C23—44no—
411C23—44no—
412C23—44no—
413C23—42no—
414C23—42no—
415C23#6693018yes—
416C23C22×C4×D1111yescharacteristic
417C23C2×D4×D1111yescharacteristic
418C23C2×D4×D1111yescharacteristic
419C23C2×#434114yes—
420C23#6703712yes—
421C23#6703712yes—
422C23#6704212yes—
423C23#6704312yes—
424D4—232no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—44no—
433C2×C4—44no—
434C2×C4—44no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—44no—
438C2×C4—114no—
439C2×C4—114no—
440C2×C4—222no—
441C2×C4—222no—
442C2×C4—224no—
443C2×C4—224no—
444C2×C4—224no—
445C2×C4—224no—
446C2×C4—222no—
447C2×C4—222no—
448C2×C4—224no—
449C2×C4—228no—
450C2×C4—4432no—
451C2×C4—442no—
452C2×C4—444no—
453C2×C4—442no—
454C2×C4—442no—
455C2×C4—442no—
456C2×C4—442no—
457C2×C4—444no—
458C2×C4—442no—
459C2×C4—442no—
460C2×C4—444no—
461C2×C4—444no—
462C2×C4—444no—
463C2×C4—442no—
464C2×C4C22⋊C4×D1114yes—
465C22—216no—
466C22—28no—
467C22—48no—
468C22—48no—
469C22—48no—
470C22—48no—
471C22—44no—
472C22—44no—
473C22—48no—
474C22C2×#6693012yes—
475C22C2×C22⋊C4×D1111yescharacteristic
476C22#1062307612yes—
477C22#1062307712yes—
478C22#1062311712yes—
479C22#1062311712yes—
480C22#1062312414yes—
481C22#1062313314yes—
482C22#1062313812yes—
483C22#1062313912yes—
484C22#1062314814yes—
485C22#1062319614yes—
486C22#1062320511yescharacteristic
487C22#1062320611yescharacteristic
488C22#1062324611yescharacteristic
489C22#1062324611yescharacteristic
490C4—24no—
491C4—82no—
492C4—82no—
493C4—224no—
494C4—224no—
495C4—444no—
496C4—882no—
497C4—882no—
498C2—48no—
499C2#1307099411yescharacteristic
500C2#1307119511yescharacteristic
501C2#1307120611yescharacteristic
502C2#1307124214yes—
503C2#1307446712yes—
504C2#1307448312yes—
505C2#1307451012yes—
506C2#1307451212yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1438C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenter#1438D11
hypocenterC11#14345
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C2×#10622264C2semidirect
3. C2×#10622263C2semidirect
4. #13066885C2semidirect
5. #13066883C2semidirect
6. #13066859C2semidirect
8. #13066838C2semidirect
17. C2×D4×Dic11C4semidirect
141. C4×Dic11C22⋊C4semidirect
394. C11#14345semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic112
C2×#106222642
C2×#106222632
#130668852
#130668832
#130668592
#130668572
#130668382
C11×#14382
#1434511