Finite Group Databasebeta

← #14680970

Subgroups — #14680970

Order 2816.

1782 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66945C211yesmaximal, characteristic
2C2×#10622280C211yesmaximal, characteristic
3C2×#10622280C211yesmaximal, characteristic
4#13066885C211yesmaximal, characteristic, complemented
5#13066884C211yesmaximal, characteristic, complemented
6#13066883C211yesmaximal, characteristic, complemented
7#13066864C214yesmaximal
8Dic11⋊#95C214yesmaximal, complemented
9C11×#1445C211yesmaximal, characteristic, complemented
10C23×C4×D11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×(C2×D11)⋊C4C2212yes—
13C22×(C2×D11)⋊C4C2212yes—
14C22×(C2×D11)⋊C4C2212yes—
15C22×C4⋊Dic11C2211yescharacteristic
16C22×Dic11⋊C4C2212yes—
17C22×Dic11⋊C4C2212yes—
18C22×C4×Dic11C2212yes—
19C2×#66945—24no—
20C2×#66945—24no—
21C2×#66945C418yescomplemented
22C2×C11×#95C2211yescharacteristic
23C2×C11×#95C2211yescharacteristic
24C2×C11×#95C2214yes—
25C2×C11⋊#95C2211yescharacteristic
26C2×C11⋊#95C2211yescharacteristic
27C2×C11⋊#95C2214yes—
28C2×C11⋊#95C2214yes—
29C2×C11⋊#95C2214yes—
30#10622280—24no—
31#10622280—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—28no—
42C22×C4×D11C2×C414yes—
43C22×C4×D11D414yes—
44C22×C4×D11D414yes—
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4C2×C414yes—
48C2×(C2×D11)⋊C4—24no—
49C2×(C2×D11)⋊C4—24no—
50C2×(C2×D11)⋊C4—24no—
51C2×(C2×D11)⋊C4—24no—
52C2×(C2×D11)⋊C4—44no—
53C2×(C2×D11)⋊C4—44no—
54C2×(C2×D11)⋊C4C2×C418yes—
55C2×C4⋊Dic11—22no—
56C2×C4⋊Dic11—22no—
57C2×C4⋊Dic11C2×C414yes—
58C2×Dic11⋊C4—24no—
59C2×Dic11⋊C4—24no—
60C2×Dic11⋊C4—28no—
61C2×Dic11⋊C4—28no—
62C2×C4×Dic11—24no—
63C2×C4×Dic11—24no—
64C2×C4×Dic11C2×C418yes—
65#66945—232no—
66C11×#95—22no—
67C11×#95—22no—
68C11×#95—44no—
69C11⋊#95—22no—
70C11⋊#95—22no—
71C11⋊#95—44no—
72C11⋊#95—44no—
73C11⋊#95—44no—
74#14343—111nomaximal, Sylow
75C24×C11C2411yescharacteristic
76C23×D11—24no—
77C23×D11—22no—
78C23×D11—22no—
79C23×D11—22no—
80C23×D11—22no—
81C23×D11C22×C412yes—
82C23×D11C2×D412yes—
83C23×D11C2×D412yes—
84C22×C4×C11—24no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—24no—
88C22×C4×C11—24no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—24no—
92C22×C4×C11—24no—
93C22×C4×C11—22no—
94C22×C4×C11—24no—
95C22×C4×C11—22no—
96C22×C4×C11—24no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11C22×C414yes—
100C22×C4×C11C22×C412yes—
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D412yes—
103C22×Dic11—22no—
104C22×Dic11—22no—
105C22×Dic11—22no—
106C22×Dic11—22no—
107C22×Dic11—24no—
108C22×Dic11—24no—
109C22×Dic11—24no—
110C22×Dic11—22no—
111C22×Dic11—22no—
112C22×Dic11—24no—
113C22×Dic11—24no—
114C22×Dic11—24no—
115C22×Dic11—22no—
116C22×Dic11—22no—
117C22×Dic11C22×C414yes—
118C22×Dic11C22×C412yes—
119C22×Dic11C2×D412yes—
120C22×Dic11C2×D412yes—
121C22×Dic11#4118yes—
122C2×C4×D11—216no—
123C2×C4×D11—216no—
124C2×C4×D11—216no—
125C2×C4×D11C22⋊C4116yes—
126C11×C4⋊C4—28no—
127(C2×D11)⋊C4—216no—
128(C2×D11)⋊C4—48no—
129(C2×D11)⋊C4—48no—
130C4⋊Dic11—28no—
131Dic11⋊C4—48no—
132Dic11⋊C4—48no—
133C4×Dic11—216no—
134C22×#117—111no—
135C2×#380—111no—
136C2×#380—111no—
137#1445—111no—
138#1445—111no—
139#1445—111no—
140#1445D1111yescharacteristic, complemented
141#1440—114no—
142C4⋊#95—114no—
143C23×C11C23×C411yescharacteristic
144C23×C11C22×D411yescharacteristic
145C23×C11C22×D411yescharacteristic
146C23×C11C2×#4114yes—
147C23×C11H(5,𝔽2)12yes—
148C23×C11H(5,𝔽2)12yes—
149C23×C112−1+412yes—
150C23×C112−1+412yes—
151C22×D11—24no—
152C22×D11—24no—
153C22×D11—24no—
154C22×D11—24no—
155C22×D11—24no—
156C22×D11—22no—
157C22×D11—22no—
158C22×D11—22no—
159C22×D11—22no—
160C22×D11—24no—
161C22×D11—24no—
162C22×D11—44no—
163C22×D11—44no—
164C22×D11—44no—
165C22×D11—44no—
166C22×D11C2×C22⋊C414yes—
167C2×C4×C11—24no—
168C2×C4×C11—24no—
169C2×C4×C11—24no—
170C2×C4×C11—24no—
171C2×C4×C11—28no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—44no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—44no—
182C2×C4×C11—44no—
183C2×C4×C11—44no—
184C2×C4×C11—44no—
185C2×C4×C11C2×C22⋊C414yes—
186C2×Dic11—24no—
187C2×Dic11—28no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—44no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11—44no—
198C2×Dic11—44no—
199C2×Dic11—44no—
200C2×Dic11—44no—
201C2×Dic11C2×C22⋊C414yes—
202C2×Dic11#11718yes—
203C2×Dic11#12318yes—
204C2×Dic11#12318yes—
205C4×D11—232no—
206C24×C4—111no—
207C2×#117—118no—
208C2×#117—224no—
209C2×#117—224no—
210C22×C4⋊C4—111no—
211C22×C4⋊C4—112no—
212C22×C4⋊C4—112no—
213C22×C4⋊C4C2×D1111yescharacteristic
214C22×C22⋊C4—112no—
215C22×C22⋊C4—112no—
216C22×C22⋊C4—112no—
217C22×C42—112no—
218#380—224no—
219#380—224no—
220C2×#95—111no—
221C2×#95—111no—
222C2×#95—114no—
223C2×#95—114no—
224C2×#95—114no—
225C2×#95C2×D1111yescharacteristic
226C2×#95C2×D1111yescharacteristic
227C2×#95C2×D1114yes—
228C22×C11C22×C22⋊C411yescharacteristic
229C22×C11C2×#11712yes—
230C22×C11#52012yes—
231C22×C11#52012yes—
232C22×C11C2×#12312yes—
233C22×C11C2×#12312yes—
234C22×C11#53511yescharacteristic
235C22×C11#53511yescharacteristic
236C22×C11#53611yescharacteristic
237C22×C11#53611yescharacteristic
238C22×C11#53712yes—
239C22×C11#53712yes—
240C22×C11#54014yes—
241C22×C11#54114yes—
242C22×C11#54214yes—
243C22×C11#54214yes—
244C2×D11—24no—
245C2×D11—24no—
246C2×D11—24no—
247C2×D11—48no—
248C2×D11—44no—
249C2×D11—44no—
250C2×D11—44no—
251C2×D11—44no—
252C4×C11—24no—
253C4×C11—44no—
254C4×C11—82no—
255C4×C11—82no—
256Dic11—44no—
257Dic11—82no—
258Dic11—82no—
259Dic11#38118yes—
260C25—111no—
261C23×C4—111no—
262C23×C4—114no—
263C23×C4—114no—
264C23×C4—114no—
265C23×C4—112no—
266C23×C4—112no—
267C23×C4—112no—
268C23×C4—228no—
269C23×C4C22×D1112yes—
270C23×C4C22×D1112yes—
271C23×C4C22×D1112yes—
272C23×C4C22×D1111yescharacteristic
273#117—2232no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—114no—
277C2×C4⋊C4—222no—
278C2×C4⋊C4—222no—
279C2×C4⋊C4—224no—
280C2×C4⋊C4—224no—
281C2×C4⋊C4—228no—
282C2×C4⋊C4—228no—
283C2×C4⋊C4C4×D1114yes—
284C2×C22⋊C4—118no—
285C2×C22⋊C4—224no—
286C2×C22⋊C4—224no—
287C2×C22⋊C4—224no—
288C2×C22⋊C4—224no—
289C2×C22⋊C4—444no—
290C2×C22⋊C4—444no—
291C2×C42—118no—
292C2×C42—224no—
293C2×C42—224no—
294#95—22no—
295#95—22no—
296#95—44no—
297#95—222no—
298#95—222no—
299#95—444no—
300#95—444no—
301#95—444no—
302C2×C11C2×#38111yescharacteristic
303C2×C11#231111yescharacteristic
304C2×C11#231111yescharacteristic
305C2×C11#231414yes—
306C2×C11#262412yes—
307C2×C11#262412yes—
308C2×C11#262512yes—
309C2×C11#262512yes—
310D11—44no—
311C24—112no—
312C24—112no—
313C24—112no—
314C24—222no—
315C24—222no—
316C24—224no—
317C24—222no—
318C24—222no—
319C24C23×D1111yescharacteristic
320C22×C4—24no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—24no—
324C22×C4—24no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—24no—
329C22×C4—22no—
330C22×C4—24no—
331C22×C4—24no—
332C22×C4—22no—
333C22×C4—24no—
334C22×C4—22no—
335C22×C4—112no—
336C22×C4—112no—
337C22×C4—112no—
338C22×C4—118no—
339C22×C4—1116no—
340C22×C4—114no—
341C22×C4—2216no—
342C22×C4—2216no—
343C22×C4—2216no—
344C22×C4—222no—
345C22×C4—222no—
346C22×C4—224no—
347C22×C4—224no—
348C22×C4—222no—
349C22×C4—222no—
350C22×C4—222no—
351C22×C4—224no—
352C22×C4—222no—
353C22×C4—224no—
354C22×C4—224no—
355C22×C4—222no—
356C22×C4—224no—
357C22×C4—222no—
358C22×C4C2×C4×D1114yes—
359C22×C4C2×C4×D1112yes—
360C22×C4D4×D1112yes—
361C22×C4D4×D1112yes—
362C4⋊C4—28no—
363C4⋊C4—228no—
364C4⋊C4—448no—
365C4⋊C4—448no—
366C22⋊C4—2216no—
367C22⋊C4—448no—
368C22⋊C4—448no—
369C42—2216no—
370C11#1434311yescharacteristic, complemented, Sylow
371C23—114no—
372C23—222no—
373C23—222no—
374C23—224no—
375C23—224no—
376C23—224no—
377C23—224no—
378C23—224no—
379C23—224no—
380C23—224no—
381C23—222no—
382C23—222no—
383C23—444no—
384C23—444no—
385C23—444no—
386C23—444no—
387C23C22×C4×D1111yescharacteristic
388C23C2×D4×D1111yescharacteristic
389C23C2×D4×D1111yescharacteristic
390C23#6703712yes—
391C23#6704012yes—
392C23#41×D1114yes—
393C23#6704212yes—
394C23#6704312yes—
395C2×C4—24no—
396C2×C4—24no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—28no—
400C2×C4—42no—
401C2×C4—44no—
402C2×C4—42no—
403C2×C4—44no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—44no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—44no—
411C2×C4—44no—
412C2×C4—42no—
413C2×C4—114no—
414C2×C4—118no—
415C2×C4—118no—
416C2×C4—118no—
417C2×C4—2232no—
418C2×C4—224no—
419C2×C4—228no—
420C2×C4—442no—
421C2×C4—444no—
422C2×C4—442no—
423C2×C4—444no—
424C2×C4—442no—
425C2×C4—442no—
426C2×C4—442no—
427C2×C4—444no—
428C2×C4—442no—
429C2×C4—442no—
430C2×C4—444no—
431C2×C4—444no—
432C2×C4—442no—
433C2×C4C22⋊C4×D1114yes—
434C22—224no—
435C22—224no—
436C22—224no—
437C22—448no—
438C22—444no—
439C22—444no—
440C22—444no—
441C22—444no—
442C22C2×C22⋊C4×D1111yescharacteristic
443C22D11×#11712yes—
444C22#1062307712yes—
445C22#1062310512yes—
446C22#1062313912yes—
447C22#1062316012yes—
448C22#1062317114yes—
449C22D11×#12312yes—
450C22D11×#12312yes—
451C22#1062319414yes—
452C22#1062320511yescharacteristic
453C22#1062320611yescharacteristic
454C22#1062322714yes—
455C22#1062324114yes—
456C22#1062324611yescharacteristic
457C22#1062325511yescharacteristic
458C4—24no—
459C4—44no—
460C4—82no—
461C4—82no—
462C4—118no—
463C4—444no—
464C4—882no—
465C4—882no—
466C2—444no—
467C2D11×#38111yescharacteristic
468C2#1307120611yescharacteristic
469C2#1307120711yescharacteristic
470C2#1307122214yes—
471C2#1307440912yes—
472C2#1307441112yes—
473C2#1307441712yes—
474C2#1307441912yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1445C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1445D11
hypocenterC11#14343
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
4. #13066885C2semidirect
5. #13066884C2semidirect
6. #13066883C2semidirect
8. Dic11⋊#95C2semidirect
9. C11×#1445C2semidirect
21. C2×#66945C4semidirect
140. #1445D11semidirect
370. C11#14343semidirect

Maximal subgroups

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

subgroupindex
C22×#669452
C2×#106222802
#130668852
#130668842
#130668832
#130668642
Dic11⋊#952
C11×#14452
#1434311