Finite Group Databasebeta

← #14719869

Subgroups — #14719869

Order 2816.

1034 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66951C211yesmaximal, characteristic
2#13077245C212yesmaximal, complemented
3#13066984C218yesmaximal, complemented
4#13066946C211yesmaximal, characteristic, complemented
5#13066942C212yesmaximal
6C11×#1463C211yesmaximal, characteristic, complemented
7C22×C11×C4⋊C4C2211yescharacteristic
8C22×(C2×D11)⋊C4C411yescharacteristic
9C22×(C2×D11)⋊C4C411yescharacteristic
10C22×(C2×D11)⋊C4C2211yescharacteristic
11C22×C4⋊Dic11C411yescharacteristic
12C22×Dic11⋊C4C411yescharacteristic
13C22×C4×Dic11C2211yescharacteristic
14C2×#66951—22no—
15C2×#66951—22no—
16C2×#66951—22no—
17C2×#66951—22no—
18C2×#66951C414yes—
19C2×#66951C2214yes—
20C11×#407C2212yes—
21#10622820C2212yes—
22#10622731—22no—
23M16×Dic11—22no—
24#10622332—22no—
25#10622332C2214yescomplemented
26#10622331—22no—
27#10622331C2214yescomplemented
28C11×#324C2214yescomplemented
29#10622166C2214yescomplemented
30#10622106C2218yes—
31C24×D11C2×C411yescharacteristic
32C23×C4×C11C2×C411yescharacteristic
33C23×C4×C11C2×C411yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C23×Dic11C2×C411yescharacteristic
36C23×Dic11C2×C411yescharacteristic
37C23×Dic11C2×C411yescharacteristic
38C2×C11×M16—22no—
39C2×C11×C4⋊C4—22no—
40C2×C11×C4⋊C4—22no—
41C2×C11×C4⋊C4C2×C412yes—
42C2×C11×C4⋊C4C2312yes—
43C2×(C2×D11)⋊C4—22no—
44C2×(C2×D11)⋊C4—22no—
45C2×(C2×D11)⋊C4—22no—
46C2×(C2×D11)⋊C4—22no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—21no—
49C2×(C2×D11)⋊C4—21no—
50C2×(C2×D11)⋊C4—21no—
51C2×(C2×D11)⋊C4C2×C412yes—
52C2×(C2×D11)⋊C4C2×C414yes—
53C2×(C2×D11)⋊C4C2×C414yes—
54C2×(C2×D11)⋊C4C2312yes—
55C2×C4⋊Dic11—22no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11C2×C414yes—
59C2×Dic11⋊C4—22no—
60C2×Dic11⋊C4—21no—
61C2×Dic11⋊C4—21no—
62C2×Dic11⋊C4C2×C414yes—
63C2×C4×Dic11C2×C412yes—
64C2×C4×Dic11D412yes—
65C2×C4×Dic11D412yes—
66C2×C4×Dic11D412yes—
67C2×C4×Dic11D412yes—
68C2×C4×Dic11C2312yes—
69C2×#4318—22no—
70#66951—24no—
71#66951—24no—
72#66951—24no—
73#66951—24no—
74#66951—24no—
75#66951—24no—
76#66951—24no—
77#66951—24no—
78C11×C22⋊C8—22no—
79C11×C22⋊C8C2314yes—
80C22⋊(C11⋊C8)—22no—
81C22⋊(C11⋊C8)C2314yes—
82#66879—24no—
83Dic11⋊C8—24no—
84Dic11⋊C8—24no—
85C8×Dic11—24no—
86#17398—111nomaximal, Sylow
87C24×C11C22×C411yescharacteristic
88C23×D11—21no—
89C23×D11—21no—
90C23×D11—42no—
91C23×D11—42no—
92C23×D11—42no—
93C23×D11C22×C412yes—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—42no—
99C22×C4×C11—42no—
100C22×C4×C11—42no—
101C22×C4×C11C22×C412yes—
102C22×C4×C11C22×C412yes—
103C22×C4×C11C22×C411yescharacteristic
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2411yescharacteristic
107C22×Dic11—21no—
108C22×Dic11—21no—
109C22×Dic11—42no—
110C22×Dic11—42no—
111C22×Dic11—42no—
112C22×Dic11C22⋊C412yes—
113C22×Dic11C22⋊C412yes—
114C22×Dic11C22⋊C411yescharacteristic
115C22×Dic11C22⋊C411yescharacteristic
116C22×Dic11C22⋊C411yescharacteristic
117C22×Dic11C22⋊C411yescharacteristic
118C22×Dic11C22×C412yes—
119C22×Dic11C22×C412yes—
120C22×Dic11C22×C412yes—
121C11×M16—44no—
122C2×C8×C11—24no—
123C11×C4⋊C4—24no—
124C11×C4⋊C4—24no—
125(C2×D11)⋊C4—24no—
126(C2×D11)⋊C4—24no—
127(C2×D11)⋊C4—24no—
128(C2×D11)⋊C4—24no—
129(C2×D11)⋊C4—24no—
130(C2×D11)⋊C4—24no—
131C4⋊Dic11—24no—
132C4⋊Dic11—24no—
133Dic11⋊C4—24no—
134Dic11⋊C4—24no—
135C4×Dic11C22⋊C412yes—
136C4×Dic11C22⋊C412yes—
137C4×Dic11C22⋊C412yes—
138C4×Dic11C22⋊C412yes—
139C4×Dic11C2×D412yes—
140C4×Dic11C2×D412yes—
141C4×Dic11C2×D412yes—
142C4×Dic11C2×D412yes—
143#4318—44no—
144C2×C11⋊C8—24no—
145C22×#126—111no—
146#2920—112no—
147#1473—118no—
148#1463—111no—
149#1463D1111yescharacteristic, complemented
150#1462—112no—
151C23×C11—22no—
152C23×C11—22no—
153C23×C11—22no—
154C23×C11C2×C22⋊C411yescharacteristic
155C23×C11C2×C22⋊C411yescharacteristic
156C23×C11C23×C411yescharacteristic
157C22×D11—22no—
158C22×D11—24no—
159C22×D11—42no—
160C22×D11—42no—
161C22×D11—42no—
162C22×D11—42no—
163C22×D11—42no—
164C22×D11—42no—
165C22×D11—42no—
166C22×D11—42no—
167C22×D11—88no—
168C2×C4×C11—24no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—24no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—41no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11C2×C22⋊C412yes—
181C2×C4×C11C22×D412yes—
182C2×Dic11—24no—
183C2×Dic11—24no—
184C2×Dic11—22no—
185C2×Dic11—42no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194C2×Dic11C2×C22⋊C412yes—
195C2×Dic11C2×C22⋊C412yes—
196C2×Dic11C2×C22⋊C412yes—
197C2×Dic11C2×C22⋊C412yes—
198C8×C11—44no—
199C11⋊C8—44no—
200C2×#126—114no—
201C2×#126—114no—
202C2×#126—222no—
203C2×#126—222no—
204C2×#126—222no—
205C2×#126—222no—
206C22×C4⋊C4—111no—
207C22×C4⋊C4—111no—
208C22×C4⋊C4C2×D1111yescharacteristic
209C22×C22⋊C4—111no—
210C22×C22⋊C4—111no—
211C22×C22⋊C4—111no—
212C22×C42—111no—
213#432—114no—
214#432—222no—
215#431—114no—
216#431—222no—
217#423—222no—
218#407—112no—
219#407C2×D1112yes—
220C4×M16—222no—
221#324—114no—
222#324C2×D1114yescomplemented
223#323—118no—
224C22×C11—28no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11#41012yes—
232C22×C11#41312yes—
233C22×C11C22×C22⋊C411yescharacteristic
234C22×C11#56812yes—
235C2×D11—42no—
236C2×D11—42no—
237C2×D11—42no—
238C2×D11—84no—
239C2×D11—84no—
240C2×D11—84no—
241C4×C11—22no—
242C4×C11—22no—
243C4×C11—42no—
244C4×C11—42no—
245Dic11—22no—
246Dic11—22no—
247Dic11—22no—
248Dic11—22no—
249Dic11—42no—
250C25—111no—
251C23×C4—111no—
252C23×C4—111no—
253C23×C4—111no—
254C23×C4C4×D1111yescharacteristic
255C23×C4C4×D1111yescharacteristic
256C23×C4C22×D1111yescharacteristic
257C2×M16—22no—
258C2×M16—222no—
259#126—224no—
260#126—224no—
261#126—224no—
262#126—224no—
263#126—224no—
264#126—224no—
265#126—224no—
266#126—224no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—114no—
270C2×C4⋊C4—114no—
271C2×C4⋊C4—222no—
272C2×C4⋊C4—221no—
273C2×C4⋊C4—221no—
274C2×C4⋊C4—222no—
275C2×C4⋊C4—221no—
276C2×C4⋊C4—221no—
277C2×C4⋊C4C4×D1112yes—
278C2×C4⋊C4C22×D1112yes—
279C2×C22⋊C4—114no—
280C2×C22⋊C4—114no—
281C2×C22⋊C4—112no—
282C2×C22⋊C4—112no—
283C2×C22⋊C4—222no—
284C2×C22⋊C4—221no—
285C2×C22⋊C4—221no—
286C2×C22⋊C4—221no—
287C2×C22⋊C4—221no—
288C2×C22⋊C4—222no—
289C2×C22⋊C4—222no—
290C2×C22⋊C4—222no—
291C2×C42—112no—
292C2×C42—112no—
293C2×C42—112no—
294C2×C42—112no—
295C2×C42—112no—
296C2×C42—112no—
297C4⋊C8—224no—
298C4⋊C8—224no—
299C22⋊C8—22no—
300C22⋊C8—114no—
301C22⋊C8—222no—
302C22⋊C8C22×D1114yes—
303#97—224no—
304C4×C8—224no—
305C2×C11—22no—
306C2×C11—22no—
307C2×C11—22no—
308C2×C11#287911yescharacteristic
309C2×C11C2×#41011yescharacteristic
310C2×C11C2×#41311yescharacteristic
311D11—82no—
312C24—112no—
313C24—221no—
314C24—221no—
315C24—442no—
316C24—442no—
317C24—442no—
318C24C2×C4×D1111yescharacteristic
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—112no—
327C22×C4—112no—
328C22×C4—111no—
329C22×C4—112no—
330C22×C4—111no—
331C22×C4—111no—
332C22×C4—111no—
333C22×C4—112no—
334C22×C4—112no—
335C22×C4—221no—
336C22×C4—221no—
337C22×C4—442no—
338C22×C4—442no—
339C22×C4—442no—
340C22×C4C2×C4×D1112yes—
341C22×C4C2×C4×D1112yes—
342C22×C4C2×C4×D1111yescharacteristic
343C22×C4D4×D1112yes—
344C22×C4D4×D1112yes—
345C22×C4C23×D1111yescharacteristic
346M16—44no—
347M16—444no—
348C2×C8—24no—
349C2×C8—224no—
350C4⋊C4—24no—
351C4⋊C4—24no—
352C4⋊C4—224no—
353C4⋊C4—224no—
354C4⋊C4—224no—
355C4⋊C4—224no—
356C22⋊C4—224no—
357C22⋊C4—224no—
358C22⋊C4—224no—
359C22⋊C4—224no—
360C22⋊C4—224no—
361C22⋊C4—224no—
362C42—112no—
363C42—112no—
364C42—112no—
365C42—112no—
366C42—112no—
367C42—112no—
368C42—112no—
369C42—112no—
370C11#1739811yescharacteristic, complemented, Sylow
371C23—22no—
372C23—22no—
373C23—22no—
374C23—222no—
375C23—224no—
376C23—442no—
377C23—442no—
378C23—442no—
379C23—442no—
380C23—442no—
381C23—442no—
382C23—442no—
383C23—442no—
384C23—888no—
385C23C22⋊C4×D1111yescharacteristic
386C23C22⋊C4×D1111yescharacteristic
387C23C22×C4×D1111yescharacteristic
388C2×C4—24no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—24no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—112no—
401C2×C4—112no—
402C2×C4—112no—
403C2×C4—112no—
404C2×C4—224no—
405C2×C4—224no—
406C2×C4—222no—
407C2×C4—442no—
408C2×C4—441no—
409C2×C4—441no—
410C2×C4—441no—
411C2×C4—441no—
412C2×C4—442no—
413C2×C4—442no—
414C2×C4—442no—
415C2×C4—442no—
416C2×C4C22⋊C4×D1112yes—
417C2×C4C2×D4×D1112yes—
418C8—44no—
419C8—444no—
420C22—28no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—442no—
428C22—442no—
429C22—442no—
430C22—884no—
431C22—884no—
432C22—884no—
433C22#1062235312yes—
434C22#1062236412yes—
435C22C2×C22⋊C4×D1111yescharacteristic
436C22#1062327612yes—
437C4—22no—
438C4—22no—
439C4—42no—
440C4—42no—
441C4—222no—
442C4—222no—
443C4—222no—
444C4—222no—
445C4—442no—
446C2—22no—
447C2—22no—
448C2—22no—
449C2—882no—
450C2#1307705911yescharacteristic
451C2C2×#1062235311yescharacteristic
452C2C2×#1062236411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1463C2
socleC22×C11C22×C22⋊C4
prime radicalC24×D11C2×C4
cosocleC22×C4×C11C24
hypercenter#1463D11
hypocenterC11#17398
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
2. #13077245C2semidirect
3. #13066984C2semidirect
4. #13066946C2semidirect
6. C11×#1463C2semidirect
25. #10622332C22semidirect
27. #10622331C22semidirect
28. C11×#324C22semidirect
29. #10622166C22semidirect
149. #1463D11semidirect
222. #324C2×D11semidirect
370. C11#17398semidirect

Maximal subgroups

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

subgroupindex
C22×#669512
#130772452
#130669842
#130669462
#130669422
C11×#14632
#1739811