Finite Group Databasebeta

← #14719690

Subgroups — #14719690

Order 2816.

1346 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623052C211yesmaximal, characteristic
2#13077656C212yesmaximal, complemented
3#13066953C214yesmaximal, complemented
4#13066941C214yesmaximal, complemented
5#13066936C212yesmaximal, complemented
6#13066930C211yesmaximal, characteristic, complemented
7C11×#1458C211yesmaximal, characteristic, complemented
8C23×D44C411yescharacteristic
9C2×C11×#117C2211yescharacteristic
10C2×#66979C411yescharacteristic
11#10623052—24no—
12#10623052—24no—
13C2×#66946C412yes—
14C2×#66946C2212yes—
15C2×C22⋊C4×D11C412yes—
16C2×C22⋊C4×D11C2212yes—
17C2×C4×D44C411yescharacteristic
18C2×C4×D44C411yescharacteristic
19C2×C4×D44C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C11×#431C2212yescomplemented
22#10622538C2212yescomplemented
23#10622451—24no—
24#10622339C2218yescomplemented
25#10622301—24no—
26C11×#324C2212yescomplemented
27C11×#323C2212yes—
28#10622166C2212yescomplemented
29#10622163C2212yes—
30#10622106C2218yescomplemented
31C24×D11C2×C412yes—
32C23×C4×C11C2×C411yescharacteristic
33C22×D44—24no—
34C22×D44—22no—
35C22×D44—22no—
36C22×D44—24no—
37C22×D44C2×C412yes—
38C22×D44C2×C411yescharacteristic
39C22×D44C2×C411yescharacteristic
40C22×C4×D11C2×C412yes—
41C22×C4×D11C2×C412yes—
42C22×C4×D11C2×C412yes—
43C22×C4×D11C2312yes—
44C11×#117—22no—
45C11×#117—22no—
46C2×C11×C4⋊C4C2×C411yescharacteristic
47C2×C11×C4⋊C4C2311yescharacteristic
48C2×C11×C22⋊C4C2×C411yescharacteristic
49C2×C11×C22⋊C4C2311yescharacteristic
50C2×C42×C11C2×C411yescharacteristic
51C2×C42×C11C2311yescharacteristic
52C2×C22⋊Dic11C2×C412yes—
53C2×(C2×D11)⋊C4C2×C412yes—
54C2×(C2×D11)⋊C4C2×C412yes—
55C2×(C2×D11)⋊C4C2×C412yes—
56C2×(C2×D11)⋊C4C2312yes—
57#66979—22no—
58#66979—22no—
59C2×C4⋊Dic11C2×C411yescharacteristic
60C2×C4⋊Dic11C2×C411yescharacteristic
61C2×C4×Dic11C2×C412yes—
62C2×#4313—28no—
63#66946—28no—
64#66946—28no—
65C22⋊C4×D11—28no—
66C22⋊C4×D11—28no—
67C4×D44—22no—
68C4×D44—22no—
69C4×D44—22no—
70C4×D44—22no—
71C4×D44—22no—
72C4×D44—22no—
73C4×D44D414yes—
74C4×D44D414yes—
75C11×C4⋊C8—22no—
76C11×C22⋊C8C2314yes—
77C4×C8×C11—22no—
78C22⋊(C11⋊C8)C2314yes—
79(C2×D11)⋊C8—28no—
80C4⋊(C11⋊C8)—22no—
81C4×C11⋊C8—22no—
82#17369—111nomaximal, Sylow
83C24×C11C22×C411yescharacteristic
84C23×D11—24no—
85C23×D11—24no—
86C23×D11—24no—
87C23×D11—82no—
88C23×D11—82no—
89C23×D11C22×C412yes—
90C23×D11C22×C412yes—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—22no—
94C22×C4×C11M1614yescomplemented
95C22×C4×C11C22×C411yescharacteristic
96C22×C4×C11C22×C411yescharacteristic
97C22×C4×C11C22×C411yescharacteristic
98C22×C4×C11C22×C411yescharacteristic
99C22×C4×C11C22×C411yescharacteristic
100C22×C4×C11C2411yescharacteristic
101C22×Dic11C22×C412yes—
102C22×Dic11C22×C412yes—
103C2×D44—216no—
104C2×D44—216no—
105C2×D44—24no—
106C2×D44—24no—
107C2×D44—21no—
108C2×D44—21no—
109C2×D44—24no—
110C2×D44—22no—
111C2×D44—22no—
112C2×D44—22no—
113C2×D44C22⋊C412yes—
114C2×D44C22⋊C412yes—
115C2×D44M1614yescomplemented
116C2×C4×D11—24no—
117C2×C4×D11—24no—
118C2×C4×D11—24no—
119C2×C4×D11—82no—
120C2×C4×D11—82no—
121C2×C4×D11—82no—
122C2×C4×D11—82no—
123C2×C4×D11C2×D418yes—
124C2×C8×C11—24no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C22⋊C4—22no—
128C11×C22⋊C4—22no—
129C42×C11—21no—
130C42×C11—21no—
131C42×C11C2×D412yes—
132C42×C11C2×D412yes—
133C22⋊Dic11—24no—
134(C2×D11)⋊C4—24no—
135(C2×D11)⋊C4—24no—
136(C2×D11)⋊C4—24no—
137(C2×D11)⋊C4C22⋊C418yes—
138C4⋊Dic11—21no—
139C4⋊Dic11—21no—
140C4⋊Dic11C22⋊C412yes—
141C4⋊Dic11C22⋊C412yes—
142C4×Dic11—24no—
143C2×C11⋊C8—24no—
144#4313—88no—
145C2×#518—111no—
146#2975—112no—
147#1465—114no—
148#1462—114no—
149#1460—112no—
150#1458—111no—
151#1458D1111yescharacteristic, complemented
152C23×C11—21no—
153C23×C11—21no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11C2×M1612yes—
157C23×C11C23×C411yescharacteristic
158C22×D11—22no—
159C22×D11—22no—
160C22×D11—22no—
161C22×D11—22no—
162C22×D11—216no—
163C22×D11—42no—
164C22×D11—42no—
165C22×D11—42no—
166C22×D11—42no—
167C22×D11—84no—
168C22×D11—84no—
169C22×D11—88no—
170C22×D11—88no—
171C22×D11C2×C22⋊C414yes—
172C22×D11C2×M1614yes—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—24no—
176C2×C4×C11—24no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11C2×C22⋊C412yes—
184C2×C4×C11C2×C22⋊C411yescharacteristic
185C2×C4×C11C2×C22⋊C411yescharacteristic
186C2×C4×C11C2×M1612yes—
187C2×C4×C11C2×M1612yes—
188C2×C4×C11C2×M1612yes—
189C2×C4×C11C22×D412yes—
190C2×Dic11—22no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11C2×C22⋊C414yes—
194D44—216no—
195D44—24no—
196D44—24no—
197D44—24no—
198D44—24no—
199C4×D11—48no—
200C4×D11—84no—
201C4×D11—84no—
202C4×D11—84no—
203C8×C11—44no—
204C11⋊C8—44no—
205C23×D4—111no—
206#518—224no—
207#518—224no—
208C2×C4×D4—112no—
209C2×C4×D4—112no—
210C2×C4×D4—111no—
211C2×C4×D4—111no—
212C2×C4×D4—111no—
213C2×C4×D4—111no—
214C2×#117—111no—
215C2×#117C2×D1111yescharacteristic
216C22×C22⋊C4—112no—
217C22×C22⋊C4—112no—
218#436—224no—
219#436—224no—
220#431—112no—
221#431C2×D1112yescomplemented
222#407—118no—
223#324—112no—
224#324C2×D1112yescomplemented
225#323—112no—
226#323—118no—
227#323C2×D1112yes—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—22no—
231C22×C11—42no—
232C22×C11—42no—
233C22×C11—41no—
234C22×C11—41no—
235C22×C11C22×C22⋊C411yescharacteristic
236C22×C11C22×M1611yescharacteristic
237C22×C11C22×M1611yescharacteristic
238C2×D11—24no—
239C2×D11—24no—
240C2×D11—24no—
241C2×D11—24no—
242C2×D11—44no—
243C2×D11—44no—
244C2×D11—44no—
245C2×D11—42no—
246C2×D11—42no—
247C2×D11—44no—
248C2×D11—816no—
249C4×C11—22no—
250C4×C11—22no—
251C4×C11—22no—
252C4×C11—41no—
253C4×C11—41no—
254C4×C11#40712yes—
255C4×C11#40712yes—
256Dic11—24no—
257Dic11—42no—
258C25—112no—
259C22×D4—111no—
260C22×D4—111no—
261C22×D4—112no—
262C22×D4—222no—
263C22×D4—222no—
264C22×D4—224no—
265C22×D4—224no—
266C23×C4—112no—
267C23×C4—112no—
268C23×C4—112no—
269C23×C4—112no—
270C23×C4C4×D1111yescharacteristic
271C2×M16—228no—
272C4×D4—114no—
273C4×D4—114no—
274C4×D4—222no—
275C4×D4—222no—
276C4×D4—222no—
277C4×D4—222no—
278C4×D4—228no—
279C4×D4—228no—
280C4×D4—222no—
281C4×D4—222no—
282#117—22no—
283#117—22no—
284#117—222no—
285#117—222no—
286C2×C4⋊C4—111no—
287C2×C4⋊C4—111no—
288C2×C4⋊C4C4×D1111yescharacteristic
289C2×C4⋊C4C22×D1111yescharacteristic
290C2×C22⋊C4—112no—
291C2×C22⋊C4—112no—
292C2×C22⋊C4—112no—
293C2×C22⋊C4—112no—
294C2×C22⋊C4—112no—
295C2×C22⋊C4—228no—
296C2×C22⋊C4—228no—
297C2×C22⋊C4C4×D1111yescharacteristic
298C2×C22⋊C4C22×D1111yescharacteristic
299C2×C42—112no—
300C2×C42C4×D1111yescharacteristic
301C2×C42C22×D1111yescharacteristic
302C4⋊C8—22no—
303C4⋊C8—222no—
304C22⋊C8—114no—
305C22⋊C8—228no—
306C22⋊C8C22×D1114yes—
307C4×C8—22no—
308C4×C8—222no—
309C2×C11—21no—
310C2×C11—21no—
311C2×C11—42no—
312C2×C11C2×#40711yescharacteristic
313C2×C11#288311yescharacteristic
314C2×C11#288811yescharacteristic
315D11—44no—
316D11—44no—
317C24—112no—
318C24—112no—
319C24—224no—
320C24—224no—
321C24—224no—
322C24—882no—
323C24—882no—
324C24C2×C4×D1111yescharacteristic
325C2×D4—112no—
326C2×D4—112no—
327C2×D4—114no—
328C2×D4—224no—
329C2×D4—224no—
330C2×D4—2216no—
331C2×D4—2216no—
332C2×D4—221no—
333C2×D4—221no—
334C2×D4—224no—
335C2×D4—222no—
336C2×D4—222no—
337C2×D4—222no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—112no—
342C22×C4—118no—
343C22×C4—112no—
344C22×C4—224no—
345C22×C4—224no—
346C22×C4—224no—
347C22×C4—882no—
348C22×C4—882no—
349C22×C4—882no—
350C22×C4—882no—
351C22×C4#431314yescomplemented
352C22×C4C2×C4×D1111yescharacteristic
353C22×C4C2×C4×D1111yescharacteristic
354C22×C4C2×C4×D1111yescharacteristic
355C22×C4C2×C4×D1111yescharacteristic
356C22×C4C2×C4×D1111yescharacteristic
357C22×C4C23×D1111yescharacteristic
358M16—888no—
359C2×C8—24no—
360C2×C8—224no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—112no—
364C4⋊C4—112no—
365C4⋊C4—221no—
366C4⋊C4—221no—
367C22⋊C4—22no—
368C22⋊C4—22no—
369C22⋊C4—118no—
370C22⋊C4—224no—
371C22⋊C4—224no—
372C22⋊C4—224no—
373C22⋊C4—224no—
374C42—21no—
375C42—21no—
376C42—224no—
377C42D4×D1112yes—
378C42D4×D1112yes—
379C11#1736911yescharacteristic, complemented, Sylow
380C23—21no—
381C23—21no—
382C23—41no—
383C23—41no—
384C23—114no—
385C23—114no—
386C23—2216no—
387C23—222no—
388C23—222no—
389C23—222no—
390C23—222no—
391C23—442no—
392C23—442no—
393C23—442no—
394C23—442no—
395C23—884no—
396C23—884no—
397C23—888no—
398C23—888no—
399C23C2×#431312yes—
400C23C22×C4×D1111yescharacteristic
401D4—2216no—
402D4—224no—
403D4—224no—
404D4—224no—
405D4—224no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—114no—
417C2×C4—222no—
418C2×C4—448no—
419C2×C4—442no—
420C2×C4—442no—
421C2×C4—884no—
422C2×C4—884no—
423C2×C4—884no—
424C2×C4C22⋊C4×D1112yes—
425C2×C4C22⋊C4×D1111yescharacteristic
426C2×C4C22⋊C4×D1111yescharacteristic
427C2×C4C2×#431312yes—
428C2×C4C2×#431312yes—
429C2×C4M16×D1112yes—
430C2×C4C2×D4×D1112yes—
431C8—44no—
432C8—444no—
433C22—21no—
434C22—21no—
435C22—22no—
436C22—42no—
437C22—42no—
438C22—41no—
439C22—41no—
440C22—224no—
441C22—224no—
442C22—224no—
443C22—224no—
444C22—444no—
445C22—444no—
446C22—444no—
447C22—444no—
448C22—442no—
449C22—442no—
450C22—8816no—
451C22C2×C22⋊C4×D1111yescharacteristic
452C22C22×#431311yescharacteristic
453C22C2×M16×D1111yescharacteristic
454C4—22no—
455C4—22no—
456C4—22no—
457C4—41no—
458C4—41no—
459C4—224no—
460C4—442no—
461C4#1062233912yes—
462C4#1062233912yes—
463C2—21no—
464C2—21no—
465C2—42no—
466C2—444no—
467C2—444no—
468C2C2×#1062233911yescharacteristic
469C2#1307707511yescharacteristic
470C2#1307709311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1458C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D44C4
cosocleC22×C4×C11C24
hypercenter#1458D11
hypocenterC11#17369
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
2. #13077656C2semidirect
3. #13066953C2semidirect
4. #13066941C2semidirect
5. #13066936C2semidirect
6. #13066930C2semidirect
7. C11×#1458C2semidirect
21. C11×#431C22semidirect
22. #10622538C22semidirect
24. #10622339C22semidirect
26. C11×#324C22semidirect
28. #10622166C22semidirect
30. #10622106C22semidirect
94. C22×C4×C11M16semidirect
115. C2×D44M16semidirect
151. #1458D11semidirect
221. #431C2×D11semidirect
224. #324C2×D11semidirect
351. C22×C4#4313semidirect
379. C11#17369semidirect

Maximal subgroups

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

subgroupindex
C2×#106230522
#130776562
#130669532
#130669412
#130669362
#130669302
C11×#14582
#1736911