Finite Group Databasebeta

← #14680365

Subgroups — #14680365

Order 2816.

2086 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66950C211yesmaximal, characteristic
2C2×#10622280C211yesmaximal, characteristic
3C2×D11×#95C211yesmaximal, characteristic
4#13066886C211yesmaximal, characteristic, complemented
5#13066886C211yesmaximal, characteristic, complemented
6#13066884C211yesmaximal, characteristic, complemented
7#13066868C214yesmaximal, complemented
8(C2×D11)⋊#95C214yesmaximal
9C11×#1445C211yesmaximal, characteristic, complemented
10C23×C4×D11C2212yes—
11C23×C4×D11C2211yescharacteristic
12C23×Dic22C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×(C2×D11)⋊C4C2212yes—
15C22×(C2×D11)⋊C4C2212yes—
16C22×C4⋊Dic11C2212yes—
17C22×Dic11⋊C4C2212yes—
18C2×#66950—24no—
19C2×#66950—24no—
20C2×#66950C418yescomplemented
21C2×C11×#95C2211yescharacteristic
22C2×C11×#95C2211yescharacteristic
23C2×C11×#95C2214yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2211yescharacteristic
26C2×C11⋊#95C2211yescharacteristic
27C2×C11⋊#95C2214yes—
28C2×C11⋊#95C2214yes—
29C2×C11⋊#95C2214yes—
30#10622280—24no—
31D11×#95—24no—
32C24×D11C2311yescharacteristic
33C23×C4×C11C2312yes—
34C23×C4×C11C2312yes—
35C23×C4×C11C2312yes—
36C23×C4×C11C2311yescharacteristic
37C23×Dic11C2312yes—
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C23×Dic11C2311yescharacteristic
41C22×C4×D11—24no—
42C22×C4×D11—24no—
43C22×C4×D11—44no—
44C22×C4×D11—44no—
45C22×C4×D11—44no—
46C22×C4×D11C2×C414yes—
47C22×C4×D11D414yes—
48C22×C4×D11D414yes—
49C22×C4×D11Q818yescomplemented
50C22×Dic22—22no—
51C22×Dic22—22no—
52C22×Dic22—44no—
53C22×Dic22C2×C414yescomplemented
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4C2×C414yescomplemented
57C2×(C2×D11)⋊C4—24no—
58C2×(C2×D11)⋊C4—24no—
59C2×(C2×D11)⋊C4—24no—
60C2×(C2×D11)⋊C4—28no—
61C2×(C2×D11)⋊C4C2×C418yes—
62C2×C4⋊Dic11—24no—
63C2×C4⋊Dic11—24no—
64C2×C4⋊Dic11C2×C418yescomplemented
65C2×Dic11⋊C4—24no—
66C2×Dic11⋊C4—44no—
67#66950—232no—
68C11×#95—22no—
69C11×#95—22no—
70C11×#95—44no—
71C11⋊#95—22no—
72C11⋊#95—22no—
73C11⋊#95—24no—
74C11⋊#95—44no—
75C11⋊#95—44no—
76C11⋊#95—44no—
77#14281—111nomaximal, Sylow
78C24×C11C2411yescharacteristic
79C23×D11—24no—
80C23×D11—22no—
81C23×D11—22no—
82C23×D11C22×C412yes—
83C23×D11C2×D412yes—
84C23×D11C2×D412yes—
85C23×D11C2×Q814yes—
86C23×D11#4114yes—
87C22×C4×C11—24no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—24no—
93C22×C4×C11—24no—
94C22×C4×C11—24no—
95C22×C4×C11—24no—
96C22×C4×C11—22no—
97C22×C4×C11—24no—
98C22×C4×C11—24no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11C22×C414yes—
102C22×C4×C11C22×C412yes—
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×Q814yes—
106C22×Dic11—22no—
107C22×Dic11—22no—
108C22×Dic11—22no—
109C22×Dic11—22no—
110C22×Dic11—22no—
111C22×Dic11—24no—
112C22×Dic11—24no—
113C22×Dic11—24no—
114C22×Dic11—24no—
115C22×Dic11—24no—
116C22×Dic11—24no—
117C22×Dic11—22no—
118C22×Dic11—24no—
119C22×Dic11—22no—
120C22×Dic11C22×C414yes—
121C22×Dic11C22×C412yes—
122C22×Dic11C2×D412yes—
123C22×Dic11C2×D412yes—
124C22×Dic11C2×Q814yes—
125C2×C4×D11—216no—
126C2×C4×D11—48no—
127C2×C4×D11—48no—
128C2×C4×D11—48no—
129C2×C4×D11—416no—
130C2×C4×D11—48no—
131C2×C4×D11—48no—
132C2×C4×D11—416no—
133C2×C4×D11C22⋊C4116yes—
134C2×Dic22—28no—
135C2×Dic22—48no—
136C2×Dic22—48no—
137C2×Dic22—48no—
138C11×C4⋊C4—28no—
139(C2×D11)⋊C4—216no—
140(C2×D11)⋊C4—48no—
141C4⋊Dic11—216no—
142Dic11⋊C4—48no—
143C22×C22⋊Q8—111no—
144C2×#380—111no—
145C22×#95—111no—
146#1446—111no—
147#1446—111no—
148#1445—111no—
149#1445D1111yescharacteristic, complemented
150#1441—114no—
151C22⋊#95—114no—
152C23×C11C23×C411yescharacteristic
153C23×C11C22×D411yescharacteristic
154C23×C11C22×D411yescharacteristic
155C23×C11C22×Q812yes—
156C23×C11C2×#4112yes—
157C23×C11H(5,𝔽2)12yes—
158C23×C11H(5,𝔽2)14yes—
159C23×C112−1+412yes—
160C22×D11—24no—
161C22×D11—24no—
162C22×D11—24no—
163C22×D11—24no—
164C22×D11—22no—
165C22×D11—22no—
166C22×D11—24no—
167C22×D11—28no—
168C22×D11—28no—
169C22×D11—28no—
170C22×D11—28no—
171C22×D11C2×C22⋊C414yes—
172C22×D11C4×Q818yes—
173C22×D11C22⋊Q818yes—
174C22×D11#12414yes—
175C22×D11C4⋊Q814yes—
176C2×C4×C11—24no—
177C2×C4×C11—24no—
178C2×C4×C11—24no—
179C2×C4×C11—24no—
180C2×C4×C11—28no—
181C2×C4×C11—24no—
182C2×C4×C11—28no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—44no—
188C2×C4×C11—44no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—44no—
193C2×C4×C11—44no—
194C2×C4×C11C2×C22⋊C414yes—
195C2×Dic11—24no—
196C2×Dic11—24no—
197C2×Dic11—24no—
198C2×Dic11—24no—
199C2×Dic11—24no—
200C2×Dic11—24no—
201C2×Dic11—24no—
202C2×Dic11—28no—
203C2×Dic11—44no—
204C2×Dic11—44no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—44no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—44no—
212C2×Dic11—44no—
213C2×Dic11C2×C22⋊C414yes—
214C4×D11—416no—
215C4×D11—432no—
216Dic22—416no—
217C23×Q8—111no—
218C24×C4—111no—
219C24×C4—112no—
220C2×C22⋊Q8—118no—
221C2×C22⋊Q8—224no—
222C2×C22⋊Q8—224no—
223C22×C4⋊C4—112no—
224C22×C4⋊C4—112no—
225C22×C4⋊C4C2×D1111yescharacteristic
226C22×C22⋊C4—112no—
227C22×C22⋊C4—112no—
228#380—224no—
229C2×#95—112no—
230C2×#95—111no—
231C2×#95—111no—
232C2×#95—114no—
233C2×#95—114no—
234C2×#95—114no—
235C2×#95—224no—
236C2×#95C2×D1111yescharacteristic
237C2×#95C2×D1111yescharacteristic
238C2×#95C2×D1114yes—
239C22×C11C22×C22⋊C411yescharacteristic
240C22×C11C2×C4×Q812yes—
241C22×C11#51812yes—
242C22×C11#52012yes—
243C22×C11C2×C22⋊Q812yes—
244C22×C11C2×#12411yescharacteristic
245C22×C11C2×C4⋊Q811yescharacteristic
246C22×C11#53412yes—
247C22×C11#53412yes—
248C22×C11#53511yescharacteristic
249C22×C11#53611yescharacteristic
250C22×C11#53712yes—
251C22×C11#53814yes—
252C22×C11#53914yes—
253C22×C11#54314yes—
254C22×C11#54414yes—
255C2×D11—24no—
256C2×D11—24no—
257C2×D11—216no—
258C2×D11—28no—
259C2×D11—28no—
260C2×D11—28no—
261C2×D11—28no—
262C2×D11#39118yes—
263C4×C11—24no—
264C4×C11—44no—
265C4×C11—44no—
266C4×C11—82no—
267Dic11—24no—
268Dic11—44no—
269Dic11—44no—
270Dic11—82no—
271C25—111no—
272C22×Q8—114no—
273C22×Q8—222no—
274C22×Q8—222no—
275C22×Q8—444no—
276C23×C4—111no—
277C23×C4—114no—
278C23×C4—114no—
279C23×C4—114no—
280C23×C4—112no—
281C23×C4—112no—
282C23×C4—118no—
283C23×C4—112no—
284C23×C4—224no—
285C23×C4—224no—
286C23×C4—444no—
287C23×C4—444no—
288C23×C4—444no—
289C23×C4C22×D1112yes—
290C23×C4C22×D1112yes—
291C23×C4C22×D1112yes—
292C23×C4C22×D1111yescharacteristic
293C22⋊Q8—2232no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—118no—
297C2×C4⋊C4—224no—
298C2×C4⋊C4—224no—
299C2×C4⋊C4—224no—
300C2×C4⋊C4—444no—
301C2×C4⋊C4C4×D1114yescomplemented
302C2×C22⋊C4—118no—
303C2×C22⋊C4—224no—
304C2×C22⋊C4—224no—
305C2×C22⋊C4—224no—
306C2×C22⋊C4—228no—
307#95—22no—
308#95—22no—
309#95—44no—
310#95—224no—
311#95—222no—
312#95—222no—
313#95—444no—
314#95—444no—
315#95—444no—
316C2×C11C2×#39111yescharacteristic
317C2×C11#230811yescharacteristic
318C2×C11#231111yescharacteristic
319C2×C11#232914yes—
320C2×C11#262612yes—
321C2×C11#262712yes—
322C2×C11#263912yes—
323C2×C11#265912yes—
324D11—28no—
325C24—112no—
326C24—112no—
327C24—112no—
328C24—114no—
329C24—114no—
330C24—222no—
331C24—224no—
332C24—222no—
333C24C23×D1111yescharacteristic
334C2×Q8—228no—
335C2×Q8—448no—
336C2×Q8—448no—
337C2×Q8—448no—
338C22×C4—24no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—24no—
343C22×C4—24no—
344C22×C4—22no—
345C22×C4—24no—
346C22×C4—24no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—24no—
350C22×C4—24no—
351C22×C4—22no—
352C22×C4—112no—
353C22×C4—112no—
354C22×C4—112no—
355C22×C4—1116no—
356C22×C4—114no—
357C22×C4—114no—
358C22×C4—2216no—
359C22×C4—224no—
360C22×C4—222no—
361C22×C4—222no—
362C22×C4—222no—
363C22×C4—224no—
364C22×C4—222no—
365C22×C4—224no—
366C22×C4—224no—
367C22×C4—224no—
368C22×C4—222no—
369C22×C4—222no—
370C22×C4—224no—
371C22×C4—224no—
372C22×C4—222no—
373C22×C4—448no—
374C22×C4—448no—
375C22×C4—448no—
376C22×C4—4416no—
377C22×C4—448no—
378C22×C4—448no—
379C22×C4—4416no—
380C22×C4C2×C4×D1114yes—
381C22×C4C2×C4×D1112yes—
382C22×C4D4×D1112yes—
383C22×C4D4×D1112yes—
384C22×C4Q8×D1114yes—
385C4⋊C4—28no—
386C4⋊C4—2216no—
387C4⋊C4—448no—
388C22⋊C4—2216no—
389C22⋊C4—448no—
390C11#1428111yescharacteristic, complemented, Sylow
391C23—114no—
392C23—114no—
393C23—118no—
394C23—118no—
395C23—114no—
396C23—228no—
397C23—222no—
398C23—224no—
399C23—224no—
400C23—224no—
401C23—228no—
402C23—224no—
403C23—224no—
404C23—228no—
405C23—222no—
406C23—228no—
407C23C22×C4×D1111yescharacteristic
408C23C2×D4×D1111yescharacteristic
409C23C2×D4×D1111yescharacteristic
410C23#6703712yes—
411C23C2×Q8×D1112yes—
412C23#41×D1112yes—
413C23#6704214yes—
414C23#6704312yes—
415Q8—4416no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—28no—
421C2×C4—24no—
422C2×C4—28no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—44no—
426C2×C4—42no—
427C2×C4—44no—
428C2×C4—42no—
429C2×C4—44no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—44no—
433C2×C4—42no—
434C2×C4—114no—
435C2×C4—224no—
436C2×C4—224no—
437C2×C4—224no—
438C2×C4—224no—
439C2×C4—224no—
440C2×C4—224no—
441C2×C4—224no—
442C2×C4—228no—
443C2×C4—4416no—
444C2×C4—4432no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4—444no—
448C2×C4—444no—
449C2×C4—444no—
450C2×C4—444no—
451C2×C4—442no—
452C2×C4—442no—
453C2×C4—444no—
454C2×C4—442no—
455C2×C4C22⋊C4×D1114yes—
456C22—118no—
457C22—228no—
458C22—224no—
459C22—224no—
460C22—228no—
461C22—2216no—
462C22—228no—
463C22—228no—
464C22C2×C22⋊C4×D1111yescharacteristic
465C22#1062305212yes—
466C22#1062307712yes—
467C22C4×Q8×D1112yes—
468C22#1062313912yes—
469C22D11×C22⋊Q812yes—
470C22#1062316514yes—
471C22#1062318412yes—
472C22#1062318412yes—
473C22#1062318814yes—
474C22D11×#12411yescharacteristic
475C22#1062320611yescharacteristic
476C22#1062322014yes—
477C22#1062323814yes—
478C22#1062324611yescharacteristic
479C22D11×C4⋊Q811yescharacteristic
480C4—24no—
481C4—44no—
482C4—44no—
483C4—82no—
484C4—224no—
485C4—444no—
486C4—444no—
487C4—882no—
488C2—228no—
489C2D11×#39111yescharacteristic
490C2#1307119311yescharacteristic
491C2#1307120611yescharacteristic
492C2#1307134514yes—
493C2#1307442212yes—
494C2#1307443012yes—
495C2#1307454312yes—
496C2#1307473112yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1445C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1445D11
hypocenterC11#14281
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
4. #13066886C2semidirect
5. #13066886C2semidirect
6. #13066884C2semidirect
7. #13066868C2semidirect
9. C11×#1445C2semidirect
20. C2×#66950C4semidirect
49. C22×C4×D11Q8semidirect
53. C22×Dic22C2×C4semidirect
56. C2×C11×C4⋊C4C2×C4semidirect
64. C2×C4⋊Dic11C2×C4semidirect
149. #1445D11semidirect
301. C2×C4⋊C4C4×D11semidirect
390. C11#14281semidirect

Maximal subgroups

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

subgroupindex
C22×#669502
C2×#106222802
C2×D11×#952
#130668862
#130668842
#130668682
(C2×D11)⋊#952
C11×#14452
#1428111