Finite Group Databasebeta

← #14719693

Subgroups — #14719693

Order 2816.

1346 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623076C211yesmaximal, characteristic
2#13077656C212yesmaximal, complemented
3#13066951C214yesmaximal, complemented
4#13066941C214yesmaximal, complemented
5#13066937C211yesmaximal, characteristic, complemented
6#13066928C212yesmaximal, complemented
7C11×#1460C211yesmaximal, characteristic, complemented
8C22×D4×D11C411yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10C2×D4×Dic11C411yescharacteristic
11C2×C4×C22⋊D11C412yes—
12C22×(C2×D11)⋊C4C412yes—
13#10623076—24no—
14#10623076—24no—
15C2×#66946C411yescharacteristic
16C2×#66945C411yescharacteristic
17C2×(C22⋊D11)⋊C4C2212yes—
18C2×C22⋊C4×D11C2212yes—
19C2×C4×D44C2211yescharacteristic
20C2×#66925C2211yescharacteristic
21C11×#431C2212yescomplemented
22#10622538C2212yescomplemented
23#10622451—24no—
24#10622339C2218yescomplemented
25#10622301—24no—
26C11×#323C2214yescomplemented
27#10622163C2214yescomplemented
28#10622107C2214yescomplemented
29#10622106C2214yes—
30C24×D11C2×C412yes—
31C22×D4×C11C2×C411yescharacteristic
32C23×C4×C11C2×C412yes—
33C22×C22⋊D11C2×C412yes—
34C23×Dic11C2×C412yes—
35C2×D4×D11—24no—
36C2×D4×D11—24no—
37C2×D4×D11—24no—
38C22×D44C2×C411yescharacteristic
39C22×C4×D11C2×C411yescharacteristic
40C22×C4×D11C2×C412yes—
41C22×C4×D11C2312yes—
42C4×D4×C11—22no—
43C4×D4×C11—22no—
44C2×C11×C4⋊C4C2×C411yescharacteristic
45C2×C11×C22⋊C4C2312yes—
46C2×C42×C11C2311yescharacteristic
47C2×C22⋊Dic11C2×C412yes—
48D4×Dic11—24no—
49C4×C22⋊D11—24no—
50C4×C22⋊D11—24no—
51C2×(C2×D11)⋊C4—24no—
52C2×(C2×D11)⋊C4—24no—
53C2×(C2×D11)⋊C4C2×C411yescharacteristic
54C2×(C2×D11)⋊C4C2×C412yes—
55C2×(C2×D11)⋊C4C2×C412yes—
56C2×(C2×D11)⋊C4C2×C412yes—
57C2×(C2×D11)⋊C4C2311yescharacteristic
58C2×C4⋊Dic11C2×C411yescharacteristic
59C2×Dic11⋊C4C2×C411yescharacteristic
60C2×Dic11⋊C4C2311yescharacteristic
61C2×C4×Dic11C2×C411yescharacteristic
62C2×C4×Dic11C2×C412yes—
63C2×#4313—28no—
64#66946—24no—
65#66945—24no—
66(C22⋊D11)⋊C4—28no—
67C22⋊C4×D11—28no—
68C4×D44D414yes—
69C4×D44D414yes—
70#66925—22no—
71#66925—22no—
72C11×C4⋊C8—22no—
73C11×C22⋊C8C2314yes—
74C4×C8×C11—22no—
75C22⋊(C11⋊C8)C2314yes—
76(C2×D11)⋊C8—28no—
77C4⋊(C11⋊C8)—22no—
78C4×C11⋊C8—22no—
79#17369—111nomaximal, Sylow
80C24×C11C22×C412yes—
81C23×D11—24no—
82C23×D11—24no—
83C23×D11—24no—
84C23×D11—82no—
85C23×D11—82no—
86C23×D11C22×C412yes—
87C23×D11C22×C411yescharacteristic
88C2×D4×C11—22no—
89C2×D4×C11—22no—
90C2×D4×C11M1614yescomplemented
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—82no—
94C22×C4×C11C22×C412yes—
95C22×C4×C11C22×C411yescharacteristic
96C22×C4×C11C22×C411yescharacteristic
97C22×C4×C11C2411yescharacteristic
98C2×C22⋊D11—24no—
99C2×C22⋊D11—24no—
100C2×C22⋊D11—24no—
101C22×Dic11—24no—
102C22×Dic11—82no—
103C22×Dic11C22×C411yescharacteristic
104C22×Dic11C22×C411yescharacteristic
105C22×Dic11C22×C411yescharacteristic
106C22×Dic11C22×C412yes—
107D4×D11—232no—
108C2×D44—22no—
109C2×D44—22no—
110C2×D44C22⋊C414yes—
111C2×C4×D11—24no—
112C2×C4×D11—22no—
113C2×C4×D11—22no—
114C2×C4×D11—82no—
115C2×C4×D11—82no—
116C2×C4×D11M1614yescomplemented
117C2×C4×D11C2×D418yes—
118C2×C8×C11—24no—
119C11×C4⋊C4—22no—
120C11×C22⋊C4—24no—
121C42×C11C2×D412yes—
122C42×C11C2×D412yes—
123C22⋊Dic11—24no—
124(C2×D11)⋊C4—24no—
125(C2×D11)⋊C4—24no—
126(C2×D11)⋊C4—21no—
127(C2×D11)⋊C4—21no—
128(C2×D11)⋊C4—22no—
129(C2×D11)⋊C4C22⋊C414yes—
130(C2×D11)⋊C4C22⋊C414yes—
131C4⋊Dic11C22⋊C414yes—
132Dic11⋊C4—21no—
133Dic11⋊C4—21no—
134Dic11⋊C4—22no—
135C4×Dic11—24no—
136C4×Dic11—22no—
137C2×C11⋊C8—24no—
138#4313—88no—
139C2×#518—111no—
140#2975—112no—
141#1465—114no—
142#1462—114no—
143#1460—111no—
144#1460D1111yescharacteristic, complemented
145#1458—112no—
146C23×C11—22no—
147C23×C11—22no—
148C23×C11—42no—
149C23×C11—42no—
150C23×C11C2×M1614yes—
151C23×C11C23×C411yescharacteristic
152C22×D11—21no—
153C22×D11—21no—
154C22×D11—22no—
155C22×D11—22no—
156C22×D11—216no—
157C22×D11—42no—
158C22×D11—42no—
159C22×D11—41no—
160C22×D11—41no—
161C22×D11—84no—
162C22×D11—84no—
163C22×D11—88no—
164C22×D11—88no—
165C22×D11C2×C22⋊C414yes—
166C22×D11C2×M1612yes—
167D4×C11—28no—
168C2×C4×C11—22no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—42no—
172C2×C4×C11—82no—
173C2×C4×C11—82no—
174C2×C4×C11C2×C22⋊C411yescharacteristic
175C2×C4×C11C2×C22⋊C411yescharacteristic
176C2×C4×C11C2×C22⋊C412yes—
177C2×C4×C11C2×M1612yes—
178C2×C4×C11C2×M1612yes—
179C2×C4×C11C22×D412yes—
180C22⋊D11—216no—
181C2×Dic11—21no—
182C2×Dic11—21no—
183C2×Dic11—21no—
184C2×Dic11—21no—
185C2×Dic11—42no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—84no—
189C2×Dic11C2×C22⋊C414yes—
190C2×Dic11C2×M1612yes—
191D44—28no—
192C4×D11—28no—
193C4×D11—48no—
194C4×D11—84no—
195C8×C11—44no—
196C11⋊C8—44no—
197C23×D4—111no—
198#518—224no—
199#518—224no—
200C2×C4×D4—111no—
201C2×C4×D4—112no—
202C2×C4×D4—111no—
203C2×C4×D4—112no—
204C2×C4×D4—111no—
205C2×C4×D4C2×D1111yescharacteristic
206C2×#117—111no—
207C2×#117—111no—
208C22×C22⋊C4—112no—
209C22×C22⋊C4—112no—
210#436—224no—
211#436—224no—
212#431—112no—
213#431C2×D1112yescomplemented
214#407—118no—
215#324—114no—
216#323—114no—
217#323—114no—
218#323C2×D1114yescomplemented
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—24no—
222C22×C11—44no—
223C22×C11—44no—
224C22×C11—42no—
225C22×C11—42no—
226C22×C11C22×C22⋊C411yescharacteristic
227C22×C11C22×M1611yescharacteristic
228C22×C11C22×M1611yescharacteristic
229C2×D11—22no—
230C2×D11—24no—
231C2×D11—24no—
232C2×D11—24no—
233C2×D11—44no—
234C2×D11—44no—
235C2×D11—42no—
236C2×D11—41no—
237C2×D11—41no—
238C2×D11—42no—
239C2×D11—816no—
240C4×C11—22no—
241C4×C11—21no—
242C4×C11—21no—
243C4×C11—42no—
244C4×C11#40714yes—
245Dic11—22no—
246Dic11—24no—
247Dic11—41no—
248Dic11—41no—
249C25—112no—
250C22×D4—112no—
251C22×D4—111no—
252C22×D4—224no—
253C22×D4—224no—
254C22×D4—224no—
255C22×D4C4×D1111yescharacteristic
256C23×C4—111no—
257C23×C4—112no—
258C23×C4—112no—
259C23×C4—112no—
260C23×C4C4×D1112yes—
261C2×M16—228no—
262C4×D4—22no—
263C4×D4—22no—
264C4×D4—114no—
265C4×D4—114no—
266C4×D4—228no—
267C4×D4—224no—
268C4×D4—224no—
269C4×D4—224no—
270C4×D4—224no—
271#117—224no—
272#117—222no—
273#117—222no—
274C2×C4⋊C4—111no—
275C2×C4⋊C4—111no—
276C2×C4⋊C4—111no—
277C2×C4⋊C4C4×D1111yescharacteristic
278C2×C22⋊C4—112no—
279C2×C22⋊C4—112no—
280C2×C22⋊C4—112no—
281C2×C22⋊C4—111no—
282C2×C22⋊C4—112no—
283C2×C22⋊C4—111no—
284C2×C22⋊C4—228no—
285C2×C22⋊C4—224no—
286C2×C22⋊C4—224no—
287C2×C22⋊C4C22×D1112yes—
288C2×C42—112no—
289C2×C42—111no—
290C2×C42C22×D1111yescharacteristic
291C4⋊C8—22no—
292C4⋊C8—222no—
293C22⋊C8—114no—
294C22⋊C8—228no—
295C22⋊C8C22×D1114yes—
296C4×C8—22no—
297C4×C8—222no—
298C2×C11—21no—
299C2×C11—21no—
300C2×C11—44no—
301C2×C11C2×#40711yescharacteristic
302C2×C11#288311yescharacteristic
303C2×C11#288811yescharacteristic
304D11—44no—
305D11—42no—
306C24—111no—
307C24—112no—
308C24—224no—
309C24—224no—
310C24—224no—
311C24—882no—
312C24—882no—
313C24C2×C4×D1112yes—
314C2×D4—22no—
315C2×D4—22no—
316C2×D4—114no—
317C2×D4—224no—
318C2×D4—2232no—
319C2×D4—224no—
320C2×D4—224no—
321C2×D4—222no—
322C2×D4—222no—
323C2×D4#431314yescomplemented
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—82no—
327C22×C4—111no—
328C22×C4—112no—
329C22×C4—114no—
330C22×C4—118no—
331C22×C4—111no—
332C22×C4—111no—
333C22×C4—224no—
334C22×C4—224no—
335C22×C4—222no—
336C22×C4—222no—
337C22×C4—882no—
338C22×C4—882no—
339C22×C4—882no—
340C22×C4C2×C4×D1112yes—
341C22×C4C2×C4×D1111yescharacteristic
342C22×C4C2×C4×D1111yescharacteristic
343C22×C4C23×D1111yescharacteristic
344M16—888no—
345C2×C8—24no—
346C2×C8—224no—
347C4⋊C4—22no—
348C4⋊C4—114no—
349C4⋊C4—221no—
350C4⋊C4—221no—
351C4⋊C4—222no—
352C22⋊C4—24no—
353C22⋊C4—114no—
354C22⋊C4—114no—
355C22⋊C4—224no—
356C22⋊C4—224no—
357C22⋊C4—224no—
358C22⋊C4—221no—
359C22⋊C4—221no—
360C22⋊C4—222no—
361C42—224no—
362C42—222no—
363C42D4×D1112yes—
364C42D4×D1112yes—
365C11#1736911yescharacteristic, complemented, Sylow
366C23—22no—
367C23—22no—
368C23—42no—
369C23—42no—
370C23—114no—
371C23—112no—
372C23—2216no—
373C23—221no—
374C23—222no—
375C23—221no—
376C23—222no—
377C23—442no—
378C23—442no—
379C23—441no—
380C23—441no—
381C23—884no—
382C23—884no—
383C23—888no—
384C23—888no—
385C23C2×#431314yes—
386C23C22×C4×D1111yescharacteristic
387D4—28no—
388D4—2216no—
389D4—228no—
390C2×C4—22no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—82no—
395C2×C4—82no—
396C2×C4—114no—
397C2×C4—112no—
398C2×C4—221no—
399C2×C4—221no—
400C2×C4—228no—
401C2×C4—221no—
402C2×C4—221no—
403C2×C4—448no—
404C2×C4—442no—
405C2×C4—441no—
406C2×C4—441no—
407C2×C4—884no—
408C2×C4—884no—
409C2×C4C22⋊C4×D1111yescharacteristic
410C2×C4C22⋊C4×D1111yescharacteristic
411C2×C4C22⋊C4×D1112yes—
412C2×C4C2×#431312yes—
413C2×C4M16×D1112yes—
414C2×C4C2×D4×D1112yes—
415C8—44no—
416C8—444no—
417C22—21no—
418C22—21no—
419C22—24no—
420C22—44no—
421C22—44no—
422C22—42no—
423C22—42no—
424C22—222no—
425C22—224no—
426C22—224no—
427C22—224no—
428C22—442no—
429C22—442no—
430C22—444no—
431C22—444no—
432C22—441no—
433C22—441no—
434C22—8816no—
435C22C2×C22⋊C4×D1111yescharacteristic
436C22C22×#431311yescharacteristic
437C22C2×M16×D1111yescharacteristic
438C4—22no—
439C4—21no—
440C4—21no—
441C4—42no—
442C4—222no—
443C4—224no—
444C4—441no—
445C4—441no—
446C4#1062233914yes—
447C2—21no—
448C2—21no—
449C2—44no—
450C2—444no—
451C2—442no—
452C2C2×#1062233911yescharacteristic
453C2#1307707511yescharacteristic
454C2#1307709211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1460C2
socleC22×C11C22×C22⋊C4
prime radicalC22×D4×D11C4
cosocleC22×C4×C11C24
hypercenter#1460D11
hypocenterC11#17369
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1460

Complements

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

NH ≅ G/Ntype
2. #13077656C2semidirect
3. #13066951C2semidirect
4. #13066941C2semidirect
5. #13066937C2semidirect
6. #13066928C2semidirect
7. C11×#1460C2semidirect
21. C11×#431C22semidirect
22. #10622538C22semidirect
24. #10622339C22semidirect
26. C11×#323C22semidirect
27. #10622163C22semidirect
28. #10622107C22semidirect
90. C2×D4×C11M16semidirect
116. C2×C4×D11M16semidirect
144. #1460D11semidirect
213. #431C2×D11semidirect
218. #323C2×D11semidirect
323. C2×D4#4313semidirect
365. C11#17369semidirect

Maximal subgroups

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

subgroupindex
C2×#106230762
#130776562
#130669512
#130669412
#130669372
#130669282
C11×#14602
#1736911