Finite Group Databasebeta

← #14781551

Subgroups — #14781551

Order 2816.

1486 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081949C211yesmaximal, characteristic
2C2×#10622619C212yesmaximal, complemented
3#13071209C212yesmaximal, complemented
4#13069867C218yesmaximal, complemented
5#13068349C211yesmaximal, characteristic, complemented
6C11×#2317C211yesmaximal, characteristic, complemented
7C22×#4339C2212yes—
8C2×C11×#117C2211yescharacteristic
9C2×C11×#117C2211yescharacteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C2×#66979C2212yes—
12#10623057—22no—
13#10623056—22no—
14#10623055—24no—
15#10623041—21no—
16#10623041—21no—
17#10623024C2214yes—
18#10623008—22no—
19C11×#389—22no—
20C11×#385C2214yes—
21C11×#384—21no—
22C11×#382—21no—
23#10622826C2218yes—
24#10622619—28no—
25#10622601—22no—
26#10622600—24no—
27#10622587—22no—
28C2×#66870C2218yes—
29#10622164C2214yes—
30C23×C4×C11C2312yes—
31C23×C4×C11C2311yescharacteristic
32C22×C22⋊D11C2314yes—
33C2×#4339—22no—
34C2×#4339—22no—
35C2×#4339—22no—
36C2×#4339—22no—
37C2×#4339—24no—
38C2×#4339—24no—
39C2×#4339—24no—
40C2×#4339—24no—
41C22×D44D412yes—
42C22×C4×D11D414yes—
43C22×Dic22D412yes—
44C11×#117—22no—
45C11×#117—22no—
46C11×#117—22no—
47C11×#117D414yescomplemented
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—24no—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C22⋊C4C2312yes—
57C2×C11×C22⋊C4C2312yes—
58C2×C42×C11—21no—
59C2×C42×C11D412yes—
60C2×C22⋊Dic11C2314yes—
61#66983—24no—
62#66983—24no—
63C2×(C2×D11)⋊C4—28no—
64#66979—24no—
65#66979—24no—
66C2×C4⋊Dic11—22no—
67C2×C4×Dic11—22no—
68#66950—24no—
69#66950—24no—
70#66948—24no—
71#66948—24no—
72#66939—28no—
73#66935—28no—
74#66928—24no—
75#66927—22no—
76C4×D44—24no—
77C4×D44—24no—
78#66922—22no—
79C11×#95—24no—
80C11⋊#95—28no—
81#66870—216no—
82#23516—111nomaximal, Sylow
83C24×C11C2411yescharacteristic
84C23×D11C2×D414yes—
85C22×C4×C11—22no—
86C22×C4×C11—24no—
87C22×C4×C11—22no—
88C22×C4×C11—82no—
89C22×C4×C11C2×D412yes—
90C22×C4×C11C2×D412yes—
91C22×C4×C11C2×D412yes—
92C22×C4×C11C2×D412yes—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D412yes—
96C22×C4×C11#4112yes—
97C22×C4×C11#4114yes—
98C2×C22⋊D11—24no—
99C2×C22⋊D11—24no—
100C2×C22⋊D11—24no—
101C2×C22⋊D11—24no—
102C2×C22⋊D11—24no—
103C2×C22⋊D11—24no—
104C22×Dic11—24no—
105C22×Dic11C2×D414yes—
106#4339—44no—
107#4339—44no—
108#4339—44no—
109#4339—44no—
110#4339—44no—
111#4339—44no—
112#4339—44no—
113#4339—44no—
114C2×D44—24no—
115C2×D44—24no—
116C2×D44—22no—
117C2×D44—22no—
118C2×D44—24no—
119C2×D44—24no—
120C2×C4×D11—24no—
121C2×C4×D11—24no—
122C2×C4×D11—28no—
123C2×C4×D11—28no—
124C2×Dic22—22no—
125C2×Dic22—22no—
126C2×Dic22—24no—
127C2×Dic22—24no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—41no—
132C11×C4⋊C4—41no—
133C11×C4⋊C4—42no—
134C11×C4⋊C4—84no—
135C11×C22⋊C4—24no—
136C11×C22⋊C4—22no—
137C11×C22⋊C4C2×D414yes—
138C42×C11—22no—
139C42×C11—22no—
140C42×C11—24no—
141C22⋊Dic11—24no—
142C22⋊Dic11—24no—
143(C2×D11)⋊C4—28no—
144(C2×D11)⋊C4—28no—
145(C2×D11)⋊C4—88no—
146C4⋊Dic11—24no—
147C4⋊Dic11—24no—
148C4⋊Dic11—44no—
149C4×Dic11—44no—
150#3449—111no—
151C2×#410—112no—
152#2317D1111yescharacteristic, complemented
153#2311—112no—
154#2044—118no—
155#1740—111no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11C22×D411yescharacteristic
159C23×C11C22×D412yes—
160C23×C11C22×D411yescharacteristic
161C23×C11C2×#4111yescharacteristic
162C23×C11C2×#4112yes—
163C22×D11—24no—
164C22×D11—24no—
165C22×D11—24no—
166C22×D11—44no—
167C22×D11—44no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—24no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—48no—
176C2×C4×C11—44no—
177C2×C4×C11—42no—
178C2×C4×C11#12011yescharacteristic
179C2×C4×C11#12011yescharacteristic
180C2×C4×C11#12012yes—
181C2×C4×C11#12114yes—
182C2×C4×C11#12114yes—
183C2×C4×C11#12112yes—
184C2×C4×C11#12112yes—
185C2×C4×C11#12314yes—
186C2×C4×C11#12314yes—
187C2×C4×C11#12412yes—
188C2×C4×C11#12412yes—
189C22⋊D11—44no—
190C22⋊D11—44no—
191C22⋊D11—44no—
192C22⋊D11—44no—
193C2×Dic11—24no—
194C2×Dic11—24no—
195C2×Dic11—24no—
196C2×Dic11—44no—
197C2×Dic11—44no—
198C2×Dic11—44no—
199D44—44no—
200D44—44no—
201D44—84no—
202D44—84no—
203C4×D11—48no—
204C4×D11—48no—
205Dic22—44no—
206Dic22—44no—
207C22×#41—112no—
208#537—221no—
209#537—221no—
210#536—222no—
211#535—222no—
212#534—114no—
213#532—222no—
214#525—224no—
215C2×#117—112no—
216C2×#117C2×D1111yescharacteristic
217C2×#117C2×D1111yescharacteristic
218C22×C4⋊C4C2×D1111yescharacteristic
219#410—228no—
220C2×#99—118no—
221#391—222no—
222#390—222no—
223#389—22no—
224#386—118no—
225#385C2×D1114yes—
226#384—21no—
227#382—21no—
228#380—224no—
229#342—114no—
230C22×C11—21no—
231C22×C11—22no—
232C22×C11—21no—
233C22×C11—22no—
234C22×C11—41no—
235C22×C11—41no—
236C22×C11—42no—
237C22×C11C2×#12011yescharacteristic
238C22×C11C2×#12112yes—
239C22×C11C2×#12111yescharacteristic
240C22×C11C2×#12312yes—
241C22×C11C2×#12411yescharacteristic
242C2×D11—48no—
243C2×D11—44no—
244C2×D11—44no—
245C2×D11—44no—
246C2×D11—84no—
247C4×C11—44no—
248C4×C11—42no—
249C4×C11—42no—
250C4×C11—82no—
251C4×C11#39412yes—
252C4×C11#39414yes—
253C4×C11#39412yes—
254Dic11—44no—
255Dic11—84no—
256C2×#41—224no—
257C2×#41—224no—
258C2×#41—222no—
259C2×#41—222no—
260C2×#41—224no—
261C2×#41—224no—
262C2×#41—222no—
263C2×#41—222no—
264C22×Q8—112no—
265C22×D4—114no—
266C22×D4—112no—
267C23×C4—114no—
268C23×C4C22×D1112yes—
269C23×C4C22×D1111yescharacteristic
270C4⋊Q8—222no—
271#127—222no—
272#124—224no—
273#123—228no—
274C22⋊Q8—224no—
275C22⋊Q8—224no—
276#121—224no—
277#121—224no—
278#121—224no—
279#121—224no—
280#120—228no—
281C4×D4—224no—
282C4×D4—224no—
283#117—22no—
284#117—22no—
285#117—22no—
286#117—224no—
287#117—224no—
288#117D4414yescomplemented
289C2×C4⋊C4—21no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—222no—
296C2×C4⋊C4C22⋊D1111yescharacteristic
297C2×C4⋊C4C22⋊D1111yescharacteristic
298C2×C22⋊C4—114no—
299C2×C22⋊C4—228no—
300C2×C22⋊C4C22×D1112yes—
301C2×C22⋊C4C22×D1112yes—
302C2×C42—21no—
303C2×C42—222no—
304C2×C42C22⋊D1112yes—
305#99—2216no—
306#95—24no—
307#95—228no—
308C2×C11—22no—
309C2×C11—21no—
310C2×C11—22no—
311C2×C11—21no—
312C2×C11C2×#39411yescharacteristic
313C2×C11#302711yescharacteristic
314C2×C11#302811yescharacteristic
315D11—84no—
316C24—114no—
317C24C23×D1111yescharacteristic
318#41—444no—
319#41—444no—
320#41—444no—
321#41—444no—
322#41—444no—
323#41—444no—
324#41—444no—
325#41—444no—
326C2×Q8—224no—
327C2×Q8—224no—
328C2×Q8—222no—
329C2×Q8—222no—
330C2×D4—224no—
331C2×D4—224no—
332C2×D4—224no—
333C2×D4—224no—
334C2×D4—224no—
335C2×D4—224no—
336C2×D4—224no—
337C2×D4—224no—
338C2×D4—224no—
339C2×D4—224no—
340C2×D4—222no—
341C2×D4—222no—
342C22×C4—22no—
343C22×C4—24no—
344C22×C4—22no—
345C22×C4—82no—
346C22×C4—114no—
347C22×C4—228no—
348C22×C4—228no—
349C22×C4—224no—
350C22×C4—224no—
351C22×C4—224no—
352C22×C4C2×D4412yes—
353C22×C4#433912yes—
354C22×C4D4×D1112yes—
355C22×C4D4×D1112yes—
356C22×C4#434314yes—
357C22×C4C2×C22⋊D1112yes—
358C22×C4C2×C22⋊D1112yes—
359C22×C4C2×C22⋊D1111yescharacteristic
360C22×C4C2×C22⋊D1111yescharacteristic
361C4⋊C4—24no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—42no—
367C4⋊C4—84no—
368C4⋊C4—224no—
369C4⋊C4—224no—
370C4⋊C4—444no—
371C22⋊C4—22no—
372C22⋊C4—24no—
373C22⋊C4—228no—
374C22⋊C4—228no—
375C22⋊C4—224no—
376C22⋊C4—224no—
377C22⋊C4—888no—
378C22⋊C4C2×D4414yes—
379C42—24no—
380C42—22no—
381C42—22no—
382C42—444no—
383C11#2351611yescharacteristic, complemented, Sylow
384C23—41no—
385C23—41no—
386C23—224no—
387C23—224no—
388C23—224no—
389C23—444no—
390C23—444no—
391C23C22×D4411yescharacteristic
392C23C2×#433911yescharacteristic
393C23C2×D4×D1112yes—
394C23C2×#434312yes—
395C23C22×C22⋊D1111yescharacteristic
396Q8—444no—
397Q8—444no—
398D4—444no—
399D4—444no—
400D4—444no—
401D4—444no—
402D4—444no—
403D4—444no—
404D4—884no—
405D4—884no—
406C2×C4—24no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—48no—
414C2×C4—44no—
415C2×C4—42no—
416C2×C4—224no—
417C2×C4—224no—
418C2×C4—224no—
419C2×C4—448no—
420C2×C4—448no—
421C2×C4—444no—
422C2×C4—444no—
423C2×C4—444no—
424C2×C4#6694714yes—
425C2×C4#6694714yes—
426C2×C4#6694814yes—
427C2×C4#6694814yes—
428C2×C4#6698312yes—
429C2×C4#6698312yes—
430C2×C4#6699011yescharacteristic
431C2×C4#6699011yescharacteristic
432C2×C4#6699012yes—
433C2×C4#6700012yes—
434C2×C4#6700012yes—
435C22—21no—
436C22—22no—
437C22—21no—
438C22—22no—
439C22—41no—
440C22—41no—
441C22—42no—
442C22—448no—
443C22—444no—
444C22—444no—
445C22—444no—
446C22—884no—
447C22C2×#6694712yes—
448C22C2×#6694812yes—
449C22C2×#6698311yescharacteristic
450C22C2×#6699011yescharacteristic
451C22C2×#6700011yescharacteristic
452C4—44no—
453C4—42no—
454C4—42no—
455C4—82no—
456C4—444no—
457C4—884no—
458C4#1062260412yes—
459C4#1062260414yes—
460C4#1062260412yes—
461C2—21no—
462C2—22no—
463C2—22no—
464C2—21no—
465C2—884no—
466C2C2×#1062260411yescharacteristic
467C2#1307801711yescharacteristic
468C2#1307802111yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC11×#2317C2
socleC22×C11C2×#120
prime radical#13081949C2
hypercenter#2317D11
hypocenterC11#23516
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2317

Complements

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

NH ≅ G/Ntype
2. C2×#10622619C2semidirect
3. #13071209C2semidirect
4. #13069867C2semidirect
5. #13068349C2semidirect
6. C11×#2317C2semidirect
47. C11×#117D4semidirect
152. #2317D11semidirect
288. #117D44semidirect
383. C11#23516semidirect

Maximal subgroups

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

subgroupindex
#130819492
C2×#106226192
#130712092
#130698672
#130683492
C11×#23172
#2351611