Finite Group Databasebeta

← #14676008

Subgroups — #14676008

Order 2816.

2430 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66946C211yesmaximal, characteristic
2C2×#10622263C211yesmaximal, characteristic, complemented
3C2×#10622280C214yesmaximal, complemented
4C2×#10622262C211yesmaximal, characteristic, complemented
5#13066884C211yesmaximal, characteristic, complemented
6#13066856C211yesmaximal, characteristic
7#13066856C211yesmaximal, characteristic
8#13066852C214yesmaximal, complemented
9C11×#1445C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C23×C4×D11C2212yes—
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×(C2×D11)⋊C4C2214yes—
14C22×(C2×D11)⋊C4C2214yes—
15C22×(C2×D11)⋊C4C2212yes—
16C22×Dic11⋊C4C2212yes—
17C22×Dic11⋊C4C2212yes—
18C22×C4×Dic11C2212yes—
19C22×C4×Dic11C2211yescharacteristic
20C2×#66946—24no—
21C2×#66946—24no—
22C2×#66946C418yescomplemented
23C2×C11×#95C2214yes—
24C2×C11×#95C2211yescharacteristic
25C2×C11×#95C2211yescharacteristic
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2214yes—
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2211yescharacteristic
30#10622280—216no—
31#10622263—24no—
32#10622262—24no—
33C24×D11C2312yes—
34C23×C4×C11C2312yes—
35C23×C4×C11C2312yes—
36C23×C4×C11C2312yes—
37C23×C4×C11C2311yescharacteristic
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C23×Dic11C2311yescharacteristic
41C23×Dic11C2311yescharacteristic
42C22×D44—28no—
43C22×D44—22no—
44C22×D44—22no—
45C22×D44C2×C414yes—
46C22×C4×D11—24no—
47C22×C4×D11—24no—
48C22×C4×D11—28no—
49C22×C4×D11—28no—
50C22×C4×D11C2×C418yes—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4C2×C414yes—
54C2×(C2×D11)⋊C4—24no—
55C2×(C2×D11)⋊C4—24no—
56C2×(C2×D11)⋊C4—28no—
57C2×(C2×D11)⋊C4—28no—
58C2×(C2×D11)⋊C4—28no—
59C2×(C2×D11)⋊C4—28no—
60C2×(C2×D11)⋊C4—44no—
61C2×(C2×D11)⋊C4—44no—
62C2×(C2×D11)⋊C4C2×C418yes—
63C2×Dic11⋊C4—24no—
64C2×Dic11⋊C4—24no—
65C2×Dic11⋊C4—24no—
66C2×Dic11⋊C4—28no—
67C2×Dic11⋊C4D418yescomplemented
68C2×C4×Dic11—24no—
69C2×C4×Dic11—44no—
70C2×C4×Dic11C2×C414yes—
71C2×C4×Dic11D414yes—
72C2×C4×Dic11D414yes—
73#66946—232no—
74C11×#95—22no—
75C11×#95—22no—
76C11×#95—28no—
77C11⋊#95—22no—
78C11⋊#95—22no—
79C11⋊#95—24no—
80C11⋊#95—28no—
81#13905—111nomaximal, Sylow
82C24×C11C2411yescharacteristic
83C23×D11—24no—
84C23×D11—22no—
85C23×D11—22no—
86C23×D11—24no—
87C23×D11—24no—
88C23×D11—24no—
89C23×D11—24no—
90C23×D11C22×C414yes—
91C23×D11#4118yes—
92C22×C4×C11—24no—
93C22×C4×C11—24no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—24no—
99C22×C4×C11—24no—
100C22×C4×C11—24no—
101C22×C4×C11—22no—
102C22×C4×C11—24no—
103C22×C4×C11—24no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11C22×C414yes—
107C22×C4×C11C22×C412yes—
108C22×C4×C11C2×D414yes—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D412yes—
111C22×Dic11—22no—
112C22×Dic11—22no—
113C22×Dic11—24no—
114C22×Dic11—22no—
115C22×Dic11—24no—
116C22×Dic11—24no—
117C22×Dic11—22no—
118C22×Dic11—24no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11C22×C412yes—
123C22×Dic11C22×C412yes—
124C22×Dic11C2×D414yes—
125C22×Dic11C2×D412yes—
126C22×Dic11C2×D412yes—
127C22×Dic11C2×D412yes—
128C22×Dic11C2×D412yes—
129C22×Dic11C2×D414yes—
130C22×Dic11#4114yes—
131C2×D44—216no—
132C2×D44—216no—
133C2×D44—216no—
134C2×D44—28no—
135C2×C4×D11—216no—
136C2×C4×D11—232no—
137C2×C4×D11—416no—
138C2×C4×D11—48no—
139C2×C4×D11—48no—
140C11×C4⋊C4—28no—
141(C2×D11)⋊C4—216no—
142(C2×D11)⋊C4—416no—
143(C2×D11)⋊C4—416no—
144Dic11⋊C4—216no—
145Dic11⋊C4—48no—
146C4×Dic11—48no—
147C4×Dic11C22⋊C4116yescomplemented
148C22×C4×D4—111no—
149C2×#382—111no—
150C2×#380—114no—
151C2×C4×C4⋊C4—111no—
152#1445—111no—
153#1445D1111yescharacteristic, complemented
154#1438—111no—
155#1438—111no—
156#1437—114no—
157C23×C11C23×C411yescharacteristic
158C23×C11C22×D411yescharacteristic
159C23×C11C22×D411yescharacteristic
160C23×C11C22×D412yes—
161C23×C11C2×#4114yes—
162C23×C11C2×#4112yes—
163C23×C11H(5,𝔽2)12yes—
164C23×C112−1+412yes—
165C22×D11—24no—
166C22×D11—24no—
167C22×D11—28no—
168C22×D11—28no—
169C22×D11—28no—
170C22×D11—28no—
171C22×D11—28no—
172C22×D11—28no—
173C22×D11—28no—
174C22×D11—28no—
175C22×D11—44no—
176C22×D11—42no—
177C22×D11—42no—
178C22×D11—42no—
179C22×D11—42no—
180C22×D11—44no—
181C22×D11—44no—
182C22×D11—44no—
183C22×D11—44no—
184C22×D11—44no—
185C22×D11#11718yes—
186C2×C4×C11—24no—
187C2×C4×C11—24no—
188C2×C4×C11—24no—
189C2×C4×C11—24no—
190C2×C4×C11—28no—
191C2×C4×C11—24no—
192C2×C4×C11—28no—
193C2×C4×C11—44no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—44no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—44no—
203C2×C4×C11—44no—
204C2×C4×C11C2×C22⋊C414yes—
205C2×Dic11—24no—
206C2×Dic11—22no—
207C2×Dic11—22no—
208C2×Dic11—24no—
209C2×Dic11—24no—
210C2×Dic11—28no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—44no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—44no—
218C2×Dic11—44no—
219C2×Dic11C2×C22⋊C414yes—
220C2×Dic11C2×C22⋊C414yes—
221C2×Dic11C4×D418yes—
222C2×Dic11#12118yes—
223C2×Dic11#12414yes—
224C2×Dic11#12714yes—
225D44—232no—
226C4×D11—432no—
227C23×D4—111no—
228C24×C4—112no—
229C2×C4×D4—118no—
230C2×C4×D4—224no—
231C2×C4×D4—224no—
232C22×C4⋊C4—112no—
233C22×C4⋊C4—112no—
234C22×C4⋊C4C2×D1111yescharacteristic
235C22×C22⋊C4—112no—
236C22×C22⋊C4—114no—
237C22×C22⋊C4—114no—
238C22×C42—111no—
239C22×C42—112no—
240#382—224no—
241#380—2216no—
242C4×C4⋊C4—224no—
243C2×#95—112no—
244C2×#95—114no—
245C2×#95—111no—
246C2×#95—111no—
247C2×#95C2×D1114yes—
248C2×#95C2×D1111yescharacteristic
249C2×#95C2×D1111yescharacteristic
250C22×C11C22×C22⋊C411yescharacteristic
251C22×C11C2×#11712yes—
252C22×C11C2×C4×D412yes—
253C22×C11#52012yes—
254C22×C11C2×#12112yes—
255C22×C11#52512yes—
256C22×C11#52512yes—
257C22×C11C2×#12411yescharacteristic
258C22×C11C2×#12711yescharacteristic
259C22×C11#53511yescharacteristic
260C22×C11#53611yescharacteristic
261C22×C11#53712yes—
262C22×C11#54614yes—
263C22×C11#54814yes—
264C22×C11#55214yes—
265C22×C11#55314yes—
266C2×D11—216no—
267C2×D11—28no—
268C2×D11—48no—
269C2×D11—44no—
270C2×D11—48no—
271C2×D11—48no—
272C2×D11—48no—
273C2×D11—48no—
274C2×D11—44no—
275C4×C11—24no—
276C4×C11—44no—
277C4×C11—44no—
278C4×C11—82no—
279Dic11—24no—
280Dic11—44no—
281Dic11—82no—
282Dic11#39018yes—
283C25—112no—
284C22×D4—114no—
285C22×D4—228no—
286C22×D4—222no—
287C22×D4—222no—
288C23×C4—111no—
289C23×C4—111no—
290C23×C4—112no—
291C23×C4—118no—
292C23×C4—112no—
293C23×C4—224no—
294C23×C4—224no—
295C23×C4—228no—
296C23×C4—228no—
297C23×C4C22×D1112yes—
298C23×C4C22×D1112yes—
299C23×C4C22×D1112yes—
300C23×C4C22×D1111yescharacteristic
301C4×D4—2232no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—118no—
305C2×C4⋊C4—224no—
306C2×C4⋊C4—224no—
307C2×C4⋊C4—228no—
308C2×C4⋊C4—224no—
309C2×C4⋊C4C4×D1114yes—
310C2×C22⋊C4—118no—
311C2×C22⋊C4—224no—
312C2×C22⋊C4—224no—
313C2×C22⋊C4—228no—
314C2×C22⋊C4—228no—
315C2×C22⋊C4—228no—
316C2×C22⋊C4—228no—
317C2×C22⋊C4—444no—
318C2×C22⋊C4—444no—
319C2×C42—114no—
320C2×C42—114no—
321C2×C42—114no—
322C2×C42—224no—
323C2×C42—444no—
324#95—22no—
325#95—28no—
326#95—22no—
327#95—228no—
328#95—224no—
329#95—222no—
330#95—222no—
331C2×C11#228011yescharacteristic
332C2×C11C2×#39011yescharacteristic
333C2×C11#231111yescharacteristic
334C2×C11#235214yes—
335C2×C11#253512yes—
336C2×C11#253612yes—
337C2×C11#254012yes—
338C2×C11#256212yes—
339D11—48no—
340C24—114no—
341C24—118no—
342C24—224no—
343C24—222no—
344C24—222no—
345C24—224no—
346C24—224no—
347C24—224no—
348C24—224no—
349C24C23×D1111yescharacteristic
350C2×D4—2216no—
351C2×D4—2216no—
352C2×D4—2216no—
353C2×D4—228no—
354C22×C4—24no—
355C22×C4—24no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—24no—
360C22×C4—22no—
361C22×C4—24no—
362C22×C4—24no—
363C22×C4—22no—
364C22×C4—24no—
365C22×C4—22no—
366C22×C4—24no—
367C22×C4—22no—
368C22×C4—112no—
369C22×C4—112no—
370C22×C4—112no—
371C22×C4—114no—
372C22×C4—114no—
373C22×C4—112no—
374C22×C4—112no—
375C22×C4—112no—
376C22×C4—114no—
377C22×C4—2216no—
378C22×C4—2232no—
379C22×C4—222no—
380C22×C4—222no—
381C22×C4—222no—
382C22×C4—224no—
383C22×C4—222no—
384C22×C4—224no—
385C22×C4—222no—
386C22×C4—224no—
387C22×C4—222no—
388C22×C4—224no—
389C22×C4—222no—
390C22×C4—448no—
391C22×C4—4416no—
392C22×C4—448no—
393C22×C4C2×C4×D1114yes—
394C22×C4C2×C4×D1112yes—
395C22×C4D4×D1114yes—
396C22×C4D4×D1112yes—
397C22×C4D4×D1112yes—
398C4⋊C4—28no—
399C4⋊C4—2216no—
400C4⋊C4—448no—
401C22⋊C4—2216no—
402C22⋊C4—4416no—
403C22⋊C4—4416no—
404C42—1116no—
405C42—448no—
406C11#1390511yescharacteristic, complemented, Sylow
407C23—118no—
408C23—228no—
409C23—224no—
410C23—224no—
411C23—228no—
412C23—228no—
413C23—228no—
414C23—228no—
415C23—228no—
416C23—228no—
417C23—228no—
418C23—444no—
419C23—442no—
420C23—442no—
421C23—444no—
422C23—444no—
423C23—444no—
424C23—444no—
425C23—442no—
426C23—442no—
427C23—444no—
428C23C22×C4×D1111yescharacteristic
429C23C2×D4×D1111yescharacteristic
430C23C2×D4×D1112yes—
431C23C2×D4×D1111yescharacteristic
432C23#6704012yes—
433C23#41×D1112yes—
434C23#41×D1114yes—
435C23#6704212yes—
436D4—2232no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—28no—
442C2×C4—24no—
443C2×C4—28no—
444C2×C4—44no—
445C2×C4—42no—
446C2×C4—44no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—44no—
453C2×C4—44no—
454C2×C4—42no—
455C2×C4—114no—
456C2×C4—114no—
457C2×C4—118no—
458C2×C4—118no—
459C2×C4—114no—
460C2×C4—114no—
461C2×C4—222no—
462C2×C4—224no—
463C2×C4—224no—
464C2×C4—222no—
465C2×C4—224no—
466C2×C4—228no—
467C2×C4—4432no—
468C2×C4—444no—
469C2×C4—442no—
470C2×C4—442no—
471C2×C4—442no—
472C2×C4—442no—
473C2×C4—444no—
474C2×C4—444no—
475C2×C4—442no—
476C2×C4C22⋊C4×D1114yes—
477C22—228no—
478C22—2216no—
479C22—444no—
480C22—448no—
481C22—448no—
482C22—448no—
483C22—448no—
484C22—448no—
485C22—444no—
486C22C2×C22⋊C4×D1111yescharacteristic
487C22D11×#11712yes—
488C22C4×D4×D1112yes—
489C22#1062310512yes—
490C22D11×#12112yes—
491C22#1062316012yes—
492C22#1062316414yes—
493C22#1062318514yes—
494C22#1062318712yes—
495C22#1062318712yes—
496C22D11×#12411yescharacteristic
497C22#1062320511yescharacteristic
498C22#1062322414yes—
499C22#1062324014yes—
500C22D11×#12711yescharacteristic
501C22#1062325511yescharacteristic
502C4—24no—
503C4—44no—
504C4—44no—
505C4—82no—
506C4—118no—
507C4—224no—
508C4—444no—
509C4—882no—
510C2—448no—
511C2#1307099611yescharacteristic
512C2D11×#39011yescharacteristic
513C2#1307120711yescharacteristic
514C2#1307154014yes—
515C2#1307351412yes—
516C2#1307352212yes—
517C2#1307355112yes—
518C2#1307377812yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1445C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1445D11
hypocenterC11#13905
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
2. C2×#10622263C2semidirect
3. C2×#10622280C2semidirect
4. C2×#10622262C2semidirect
5. #13066884C2semidirect
8. #13066852C2semidirect
9. C11×#1445C2semidirect
22. C2×#66946C4semidirect
67. C2×Dic11⋊C4D4semidirect
147. C4×Dic11C22⋊C4semidirect
153. #1445D11semidirect
406. C11#13905semidirect

Maximal subgroups

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

subgroupindex
C22×#669462
C2×#106222632
C2×#106222802
C2×#106222622
#130668842
#130668562
#130668522
C11×#14452
#1390511