Finite Group Databasebeta

← #14720080

Subgroups — #14720080

Order 2816.

996 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
1C2×#10623110C211yesmaximal, characteristic
2#13077653C212yesmaximal
3#13066978C214yesmaximal, complemented
4#13066973C212yesmaximal, complemented
5#13066944C212yesmaximal, complemented
6#13066940C211yesmaximal, characteristic, complemented
7D11×#324C212yesmaximal, complemented
8C11×#1467C211yesmaximal, characteristic, complemented
9C2×C4×Q8×C11C2211yescharacteristic
10C2×#66999C412yes—
11#10623110—24no—
12#10623110—22no—
13#10623110—22no—
14C2×#66949C412yes—
15C2×#66949C2212yes—
16C2×C4⋊C4×D11C2212yes—
17C2×C4×D44C411yescharacteristic
18C2×C4×D44C411yescharacteristic
19C2×C4×D44C2211yescharacteristic
20C2×#66923C411yescharacteristic
21C2×#66923C2211yescharacteristic
22C2×#66922C411yescharacteristic
23C11×#432C2212yes—
24#10622538C2212yes—
25#10622451—22no—
26#10622447—22no—
27#10622339C2214yes—
28D11×C22⋊C8C2214yes—
29#10622319—24no—
30C11×#324C2212yes—
31C11×#324C2212yes—
32#10622166C2211yescharacteristic
33#10622166C2211yescharacteristic
34#10622166C2212yes—
35#10622107C2214yes—
36#10622107C2214yes—
37C22×Q8×C11C2×C411yescharacteristic
38C22×D44C2×C411yescharacteristic
39C22×C4×D11C2×C412yes—
40C22×C4×D11C2×C412yes—
41C22×C4×D11C2312yes—
42C22×Dic22C2×C412yes—
43C4×Q8×C11—22no—
44C4×Q8×C11—22no—
45C2×C11×C4⋊C4C2×C411yescharacteristic
46C2×C11×C4⋊C4C2311yescharacteristic
47C2×C11×C4⋊C4C2311yescharacteristic
48C2×C42×C11C2×C411yescharacteristic
49C2×C42×C11C2×C411yescharacteristic
50C2×C42×C11C2311yescharacteristic
51#66999—24no—
52#66999—24no—
53C2×(C2×D11)⋊C4C2×C412yes—
54C2×(C2×D11)⋊C4C2×C412yes—
55C2×(C2×D11)⋊C4C2×C412yes—
56C2×C4⋊Dic11C2×C411yescharacteristic
57C2×C4⋊Dic11C2×C412yes—
58C2×C4⋊Dic11C2×C411yescharacteristic
59C2×C4⋊Dic11C2×C411yescharacteristic
60C2×Dic11⋊C4C2×C412yes—
61C2×Dic11⋊C4C2×C412yes—
62C2×Dic11⋊C4C2×C412yes—
63C2×Dic11⋊C4C2312yes—
64C2×#4313—24no—
65C2×C8×D11—24no—
66#66949—24no—
67#66949—24no—
68#66949—24no—
69#66949—24no—
70C4⋊C4×D11—24no—
71C4⋊C4×D11—24no—
72C4×D44—22no—
73C4×D44—21no—
74C4×D44—21no—
75C4×D44—22no—
76C4×D44—21no—
77C4×D44—21no—
78C4×D44D414yes—
79C4×D44D412yes—
80C4×D44D412yes—
81#66923—22no—
82#66923—22no—
83#66923—22no—
84#66923—22no—
85#66922—22no—
86#66922—22no—
87C11×C4⋊C8—22no—
88C11×C22⋊C8C2314yes—
89C11×#97—22no—
90C22⋊(C11⋊C8)C2312yes—
91C22⋊(C11⋊C8)C2312yes—
92(C2×D11)⋊C8—24no—
93(C2×D11)⋊C8—24no—
94C4⋊(C11⋊C8)—22no—
95C4×C11⋊C8—22no—
96#17426—111nomaximal, Sylow
97C23×D11C22×C412yes—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×Q8×C11—41no—
101C22×C4×C11C22×C411yescharacteristic
102C22×C4×C11C22×C411yescharacteristic
103C22×C4×C11C22×C411yescharacteristic
104C22×C4×C11C22×C411yescharacteristic
105C22×C4×C11C22×C411yescharacteristic
106C22×C4×C11C22×C411yescharacteristic
107C22×C4×C11C2411yescharacteristic
108C22×Dic11C22×C412yes—
109C22×Dic11C22×C412yes—
110C22×Dic11C22×C412yes—
111C2×D44—24no—
112C2×D44C22⋊C412yes—
113C2×D44C22⋊C411yescharacteristic
114C2×D44C22⋊C411yescharacteristic
115C2×C4×D11—22no—
116C2×C4×D11—22no—
117C2×C4×D11—22no—
118C2×C4×D11—22no—
119C2×C4×D11—24no—
120C2×C4×D11—42no—
121C2×C4×D11—82no—
122C2×C4×D11—82no—
123C2×C4×D11C2×D414yes—
124C2×C4×D11C2×D414yes—
125C2×Dic22—24no—
126C2×Dic22—82no—
127C2×C8×C11—24no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C42×C11—21no—
132C42×C11—21no—
133C42×C11—21no—
134C42×C11—21no—
135C42×C11C2×D412yes—
136C42×C11C2×D412yes—
137(C2×D11)⋊C4—22no—
138(C2×D11)⋊C4—22no—
139(C2×D11)⋊C4—22no—
140(C2×D11)⋊C4—22no—
141(C2×D11)⋊C4C22⋊C414yes—
142(C2×D11)⋊C4C22⋊C414yes—
143C4⋊Dic11—24no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11C22⋊C412yes—
149C4⋊Dic11C22⋊C412yes—
150Dic11⋊C4—24no—
151Dic11⋊C4—24no—
152Dic11⋊C4—24no—
153Dic11⋊C4—24no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—22no—
156#4313—84no—
157C8×D11—84no—
158C2×#554—111no—
159#2974—112no—
160#1472—114no—
161#1470—112no—
162#1467D1111yescharacteristic, complemented
163#1463—112no—
164#1461—111no—
165C2×#324—112no—
166C23×C11C23×C411yescharacteristic
167C22×D11—22no—
168C22×D11—22no—
169C22×D11—24no—
170C22×D11—42no—
171C22×D11C2×C22⋊C412yes—
172C22×D11C2×C22⋊C412yes—
173Q8×C11—44no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—22no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11C2×C22⋊C412yes—
188C2×C4×C11C2×C22⋊C411yescharacteristic
189C2×C4×C11C2×C22⋊C411yescharacteristic
190C2×C4×C11#13112yes—
191C2×C4×C11C22×D412yes—
192C2×Dic11—22no—
193C2×Dic11—22no—
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11C2×C22⋊C414yes—
199D44—24no—
200D44—22no—
201D44#10114yes—
202C4×D11—44no—
203C4×D11—44no—
204C4×D11—44no—
205C4×D11—44no—
206C4×D11—82no—
207C4×D11—82no—
208Dic22—84no—
209C8×C11—44no—
210C11⋊C8—42no—
211C11⋊C8—42no—
212#554—222no—
213#554—224no—
214#554—222no—
215C2×C4⋊Q8—111no—
216C2×#125—111no—
217C2×#125—111no—
218C2×C22⋊Q8—112no—
219C2×C22⋊Q8—112no—
220C2×C22⋊Q8—112no—
221C2×C4×Q8C2×D1111yescharacteristic
222C2×C4×D4—111no—
223C2×C4×D4—111no—
224C2×C4×D4—111no—
225C22×C4⋊C4—112no—
226#436—222no—
227#435—224no—
228C8×D4—222no—
229#432C2×D1112yes—
230#431—112no—
231#407—114no—
232C2×C22⋊C8—114no—
233#324—111no—
234#324—111no—
235#324—112no—
236#324—114no—
237#324—114no—
238#324C2×D1112yes—
239#324C2×D1112yes—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11C22×C22⋊C411yescharacteristic
243C22×C11C2×#13111yescharacteristic
244C22×C11#56811yescharacteristic
245C2×D11—22no—
246C2×D11—22no—
247C2×D11—22no—
248C2×D11—22no—
249C2×D11—22no—
250C2×D11—44no—
251C2×D11—44no—
252C2×D11C2×#10114yes—
253C4×C11—22no—
254C4×C11—22no—
255C4×C11—22no—
256C4×C11—21no—
257C4×C11—41no—
258C4×C11—41no—
259C4×C11—41no—
260C4×C11C2×#10112yes—
261Dic11—24no—
262Dic11—42no—
263Dic11—42no—
264C22×Q8—112no—
265C22×Q8C4×D1111yescharacteristic
266C22×D4—111no—
267C23×C4—112no—
268C23×C4—112no—
269C23×C4—112no—
270C2×M16—224no—
271C22×C8—224no—
272C4⋊Q8—222no—
273C4⋊Q8—222no—
274#125—222no—
275#125—222no—
276#125—222no—
277#125—222no—
278C22⋊Q8—224no—
279C22⋊Q8—224no—
280C22⋊Q8—224no—
281C22⋊Q8—224no—
282C22⋊Q8—224no—
283C22⋊Q8—224no—
284C4×Q8—22no—
285C4×Q8—22no—
286C4×D4—112no—
287C4×D4—114no—
288C4×D4—112no—
289C4×D4—221no—
290C4×D4—222no—
291C4×D4—221no—
292C4×D4—221no—
293C4×D4—222no—
294C4×D4—221no—
295C2×C4⋊C4—111no—
296C2×C4⋊C4—112no—
297C2×C4⋊C4—112no—
298C2×C4⋊C4—111no—
299C2×C4⋊C4—111no—
300C2×C4⋊C4—112no—
301C2×C4⋊C4—112no—
302C2×C4⋊C4—112no—
303C2×C4⋊C4—224no—
304C2×C4⋊C4—224no—
305C2×C4⋊C4C4×D1111yescharacteristic
306C2×C4⋊C4C22×D1111yescharacteristic
307C2×C4⋊C4C22×D1111yescharacteristic
308C2×C22⋊C4—112no—
309C2×C22⋊C4—112no—
310C2×C22⋊C4—112no—
311C2×C42C4×D1111yescharacteristic
312C2×C42C4×D1111yescharacteristic
313C2×C42C22×D1111yescharacteristic
314C4⋊C8—22no—
315C4⋊C8—222no—
316C22⋊C8—112no—
317C22⋊C8—112no—
318C22⋊C8—224no—
319C22⋊C8—224no—
320C22⋊C8C22×D1114yes—
321#97—22no—
322C4×C8—222no—
323C2×C11—21no—
324C2×C11—21no—
325C2×C11#288011yescharacteristic
326C2×C11#288311yescharacteristic
327C2×C11C22×#10111yescharacteristic
328D11—24no—
329D11—42no—
330C24—112no—
331C2×Q8—22no—
332C2×Q8—22no—
333C2×Q8—41no—
334C2×Q8—224no—
335C2×Q8—882no—
336C2×D4—111no—
337C2×D4—112no—
338C2×D4—111no—
339C2×D4—224no—
340C22×C4—112no—
341C22×C4—114no—
342C22×C4—114no—
343C22×C4—112no—
344C22×C4—112no—
345C22×C4—222no—
346C22×C4—222no—
347C22×C4—222no—
348C22×C4—222no—
349C22×C4—224no—
350C22×C4—442no—
351C22×C4—882no—
352C22×C4—882no—
353C22×C4C2×C4×D1111yescharacteristic
354C22×C4C2×C4×D1111yescharacteristic
355C22×C4C2×C4×D1111yescharacteristic
356C22×C4C2×C4×D1111yescharacteristic
357C22×C4C2×C4×D1111yescharacteristic
358C22×C4C2×C4×D1111yescharacteristic
359C22×C4C23×D1111yescharacteristic
360M16—884no—
361C2×C8—24no—
362C2×C8—222no—
363C2×C8—222no—
364C2×C8—884no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—112no—
369C4⋊C4—112no—
370C4⋊C4—224no—
371C4⋊C4—224no—
372C4⋊C4—224no—
373C4⋊C4—221no—
374C4⋊C4—221no—
375C4⋊C4—221no—
376C4⋊C4—221no—
377C4⋊C4—224no—
378C4⋊C4—224no—
379C22⋊C4—114no—
380C22⋊C4—114no—
381C22⋊C4—222no—
382C22⋊C4—222no—
383C22⋊C4—222no—
384C22⋊C4—222no—
385C42—21no—
386C42—21no—
387C42—21no—
388C42—21no—
389C42D4×D1112yes—
390C42D4×D1112yes—
391C11#1742611yescharacteristic, complemented, Sylow
392C23—112no—
393C23—112no—
394C23—224no—
395C23—222no—
396C23—222no—
397C23—442no—
398C23C22×C4×D1111yescharacteristic
399Q8—44no—
400Q8—884no—
401D4—114no—
402D4—224no—
403D4—222no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—114no—
418C2×C4—222no—
419C2×C4—222no—
420C2×C4—222no—
421C2×C4—222no—
422C2×C4—444no—
423C2×C4—444no—
424C2×C4—444no—
425C2×C4—444no—
426C2×C4—442no—
427C2×C4—442no—
428C2×C4—882no—
429C2×C4—882no—
430C2×C4C22⋊C4×D1111yescharacteristic
431C2×C4C22⋊C4×D1112yes—
432C2×C4C22⋊C4×D1111yescharacteristic
433C2×C4#6696012yes—
434C2×C4C2×D4×D1112yes—
435C8—44no—
436C8—442no—
437C8—442no—
438C22—21no—
439C22—21no—
440C22—114no—
441C22—222no—
442C22—222no—
443C22—222no—
444C22—222no—
445C22—222no—
446C22—444no—
447C22—444no—
448C22C2×C22⋊C4×D1111yescharacteristic
449C22C2×#6696011yescharacteristic
450C22#1062327611yescharacteristic
451C4—22no—
452C4—22no—
453C4—22no—
454C4—21no—
455C4—41no—
456C4—41no—
457C4—41no—
458C4—224no—
459C4—442no—
460C4—442no—
461C4D11×#10112yes—
462C2—21no—
463C2—21no—
464C2—224no—
465C2—442no—
466C2#1307706611yescharacteristic
467C2#1307707511yescharacteristic
468C2C2×D11×#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1467C2
socleC22×C11C22×C22⋊C4
prime radicalC22×D44C2×C4
cosocleC22×C4×C11C24
hypercenter#1467D11
hypocenterC11#17426
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
3. #13066978C2semidirect
4. #13066973C2semidirect
5. #13066944C2semidirect
6. #13066940C2semidirect
7. D11×#324C2semidirect
8. C11×#1467C2semidirect
162. #1467D11semidirect
391. C11#17426semidirect

Maximal subgroups

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

subgroupindex
C2×#106231102
#130776532
#130669782
#130669732
#130669442
#130669402
D11×#3242
C11×#14672
#1742611