Finite Group Databasebeta

← #14762930

Subgroups — #14762930

Order 2816.

1318 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082261C211yesmaximal, characteristic
2#13077074C212yesmaximal, complemented
3#13069157C214yesmaximal, complemented
4#13069028C214yesmaximal, complemented
5#13068724C211yesmaximal, characteristic, complemented
6#13068532C212yesmaximal, complemented
7C11×#1828C211yesmaximal, characteristic, complemented
8C2×#67037C2211yescharacteristic
9C22×#4341C2211yescharacteristic
10C11×#518C2211yescharacteristic
11#10623086—24no—
12#10623085—24no—
13#10623057C412yescomplemented
14#10623055C412yescomplemented
15#10623024C412yescomplemented
16#10623024C2212yes—
17C2×#66939C412yescomplemented
18C2×#66939C2212yes—
19#10623017C2214yes—
20C2×C11×#99C2212yes—
21C2×#66898C2212yes—
22C2×#66870C2214yes—
23C2×#66870C2214yescomplemented
24#10622556C2214yescomplemented
25D11×#99—24no—
26#10622353—24no—
27C11×#342C2214yescomplemented
28#10622165C2214yescomplemented
29C22×D4×C11C2311yescharacteristic
30C22×C22⋊D11C2×C412yes—
31C22×C22⋊D11C2×C411yescharacteristic, complemented
32C22×C22⋊D11C2311yescharacteristic
33C22×C22⋊D11C2312yes—
34C23×Dic11C2×C411yescharacteristic, complemented
35C23×Dic11C2311yescharacteristic
36#67037—44no—
37C2×#4341—24no—
38C2×#4341—44no—
39C2×#4341D414yes—
40C2×D4×D11D414yes—
41C2×#4339C2×C412yes—
42C22×C4×D11C2×C411yescharacteristic, complemented
43C22×Dic22C2×C411yescharacteristic, complemented
44C4×D4×C11—24no—
45C11×#117C2×C412yescomplemented
46C2×C11×C22⋊C4C2×C412yescomplemented
47C2×C11×C22⋊C4C2314yes—
48C2×C11×C22⋊C4C2312yes—
49C2×C22⋊Dic11C2314yes—
50#66983—24no—
51#66983—24no—
52C4×C22⋊D11—44no—
53C2×(C2×D11)⋊C4—22no—
54C2×(C2×D11)⋊C4—22no—
55C2×C4⋊Dic11—22no—
56C2×C4⋊Dic11—22no—
57#66950—24no—
58#66950—22no—
59#66948—22no—
60#66939—24no—
61#66939—24no—
62#66939—22no—
63#66939—22no—
64#66939C2×C414yescomplemented
65#66939C2×C414yescomplemented
66#66939C2×C414yescomplemented
67#66935—22no—
68#66935—22no—
69#66935C2×C414yescomplemented
70(C22⋊D11)⋊C4—44no—
71C22⋊C4×D11—24no—
72#66930—24no—
73#66928—22no—
74C4×D44—24no—
75#66922—22no—
76C11×#99—24no—
77#66898—24no—
78C11⋊#95—44no—
79#66870—28no—
80#66870—44no—
81#21777—111nomaximal, Sylow
82C24×C11C22×C411yescharacteristic
83C24×C11C2411yescharacteristic
84C23×D11C22⋊C412yes—
85C23×D11C22×C411yescharacteristic
86C23×D11C2×D412yes—
87C2×D4×C11—24no—
88C2×D4×C11C2×D414yes—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—24no—
92C22×C4×C11C22×C411yescharacteristic
93C2×C22⋊D11—22no—
94C2×C22⋊D11—22no—
95C2×C22⋊D11—24no—
96C2×C22⋊D11—24no—
97C2×C22⋊D11—24no—
98C2×C22⋊D11—42no—
99C2×C22⋊D11—44no—
100C2×C22⋊D11C22⋊C414yes—
101C2×C22⋊D11C22×C414yes—
102C2×C22⋊D11C2×D414yes—
103C22×Dic11—22no—
104C22×Dic11—22no—
105C22×Dic11—24no—
106C22×Dic11—24no—
107C22×Dic11—42no—
108C22×Dic11C22⋊C412yes—
109C22×Dic11C22×C411yescharacteristic
110C22×Dic11C22×C411yescharacteristic
111C22×Dic11C22×C411yescharacteristic
112C22×Dic11C2×D412yes—
113#4341—48no—
114#4341—416no—
115D4×D11—48no—
116#4339—44no—
117C2×D44—24no—
118C2×D44C22⋊C412yes—
119C2×C4×D11—22no—
120C2×C4×D11—42no—
121C2×C4×D11—44no—
122C2×C4×D11C22⋊C414yes—
123C2×Dic22—22no—
124C2×Dic22—42no—
125C2×Dic22C22⋊C412yes—
126C11×C4⋊C4—22no—
127C11×C22⋊C4—22no—
128C11×C22⋊C4—22no—
129C11×C22⋊C4—24no—
130C11×C22⋊C4—24no—
131C11×C22⋊C4C22×C414yes—
132C42×C11—22no—
133C22⋊Dic11—24no—
134C22⋊Dic11—24no—
135(C2×D11)⋊C4—24no—
136(C2×D11)⋊C4—24no—
137(C2×D11)⋊C4—24no—
138(C2×D11)⋊C4—24no—
139(C2×D11)⋊C4—44no—
140C4⋊Dic11—24no—
141C4⋊Dic11—24no—
142C4⋊Dic11—24no—
143Dic11⋊C4—44no—
144C4×Dic11—44no—
145#3485—111no—
146#2883—112no—
147#1913—114no—
148#1890—114no—
149#1828—111no—
150#1828D1111yescharacteristic, complemented
151#1782—112no—
152C23×C11—22no—
153C23×C11—81no—
154C23×C11—81no—
155C23×C11C2×C22⋊C412yes—
156C23×C11C23×C411yescharacteristic
157C23×C11C22×D412yes—
158C23×C11H(5,𝔽2)14yes—
159C22×D11—24no—
160C22×D11—21no—
161C22×D11—22no—
162C22×D11—42no—
163C22×D11—81no—
164C22×D11—82no—
165C22×D11—82no—
166C22×D11C2×C22⋊C414yes—
167D4×C11—28no—
168C2×C4×C11—22no—
169C2×C4×C11—24no—
170C2×C4×C11—44no—
171C2×C4×C11—82no—
172C2×C4×C11—82no—
173C2×C4×C11—84no—
174C2×C4×C11C2×C22⋊C412yes—
175C22⋊D11—24no—
176C22⋊D11—24no—
177C22⋊D11—28no—
178C22⋊D11—44no—
179C22⋊D11—44no—
180C22⋊D11—44no—
181C2×Dic11—24no—
182C2×Dic11—21no—
183C2×Dic11—21no—
184C2×Dic11—21no—
185C2×Dic11—22no—
186C2×Dic11—22no—
187C2×Dic11—22no—
188C2×Dic11—42no—
189C2×Dic11—44no—
190C2×Dic11—44no—
191C2×Dic11—44no—
192C2×Dic11—84no—
193C2×Dic11C2×C22⋊C414yes—
194D44—42no—
195D44—84no—
196C4×D11—44no—
197C4×D11—44no—
198C4×D11—164no—
199Dic22—42no—
200Dic22—44no—
201C2×H(5,𝔽2)—111no—
202C22×#41—111no—
203#547—224no—
204#546—224no—
205#536—112no—
206#534—112no—
207#534—112no—
208#525—112no—
209C2×#123—112no—
210C2×#123—112no—
211#518—114no—
212#518C2×D1111yescharacteristic
213#410—224no—
214C2×#99—112no—
215C2×#99—114no—
216C2×#99—114no—
217C2×#99—224no—
218C2×#99C2×D1112yes—
219#381—114no—
220#342—114no—
221#342C2×D1114yescomplemented
222C22×C11—22no—
223C22×C11—42no—
224C22×C11—44no—
225C22×C11—41no—
226C22×C11—42no—
227C22×C11—82no—
228C22×C11C22×C22⋊C411yescharacteristic
229C22×C11#51812yes—
230C22×C11#53414yes—
231C2×D11—24no—
232C2×D11—44no—
233C2×D11—42no—
234C2×D11—41no—
235C2×D11—84no—
236C2×D11—82no—
237C2×D11—162no—
238C4×C11—22no—
239C4×C11—44no—
240C4×C11—84no—
241Dic11—24no—
242Dic11—41no—
243Dic11—41no—
244Dic11—41no—
245Dic11—84no—
246H(5,𝔽2)—444no—
247C2×#41—114no—
248C2×#41—112no—
249C2×#41—224no—
250C2×#41—444no—
251C22×Q8—111no—
252C22×D4—112no—
253C22×D4—112no—
254C22×D4—114no—
255C22×D4—111no—
256C22×D4—111no—
257C22×D4C22×D1111yescharacteristic
258C23×C4—111no—
259C23×C4—111no—
260C23×C4—111no—
261C4⋊Q8—222no—
262#124—222no—
263#123—114no—
264#123—114no—
265#123—114no—
266#123—222no—
267#123—222no—
268#123—224no—
269#123—224no—
270C22⋊Q8—224no—
271C22⋊Q8—222no—
272#121—222no—
273#121—224no—
274#121—224no—
275#120—114no—
276#120—222no—
277#120—222no—
278C4×D4—24no—
279C4×D4—224no—
280C4×D4—444no—
281C4×D4—444no—
282#117—224no—
283#117C4×D1112yescomplemented
284C2×C4⋊C4—222no—
285C2×C4⋊C4—222no—
286C2×C22⋊C4—114no—
287C2×C22⋊C4—224no—
288C2×C22⋊C4—222no—
289C2×C22⋊C4—222no—
290C2×C22⋊C4C4×D1112yescomplemented
291C2×C22⋊C4C22×D1114yes—
292C2×C22⋊C4C22×D1112yes—
293#99—24no—
294#99—228no—
295#99—224no—
296#99—444no—
297#95—444no—
298C2×C11—24no—
299C2×C11—21no—
300C2×C11—22no—
301C2×C11—42no—
302C2×C11#230811yescharacteristic
303D11—44no—
304D11—81no—
305C24—112no—
306C24—112no—
307C24—111no—
308C24C2×C4×D1111yescharacteristic
309C24C23×D1111yescharacteristic
310#41—444no—
311#41—448no—
312#41—4416no—
313C2×Q8—112no—
314C2×Q8—222no—
315C2×Q8—442no—
316C2×D4—24no—
317C2×D4—114no—
318C2×D4—114no—
319C2×D4—114no—
320C2×D4—112no—
321C2×D4—224no—
322C2×D4—224no—
323C2×D4—224no—
324C2×D4—222no—
325C2×D4—222no—
326C2×D4—224no—
327C2×D4—442no—
328C2×D4—448no—
329C2×D4—444no—
330C2×D4D4×D1114yes—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—24no—
334C22×C4—112no—
335C22×C4—112no—
336C22×C4—114no—
337C22×C4—111no—
338C22×C4—111no—
339C22×C4—111no—
340C22×C4—222no—
341C22×C4—222no—
342C22×C4—224no—
343C22×C4—222no—
344C22×C4—224no—
345C22×C4—442no—
346C22×C4—444no—
347C22×C4—442no—
348C22×C4C2×C4×D1111yescharacteristic
349C4⋊C4—22no—
350C4⋊C4—224no—
351C4⋊C4—224no—
352C4⋊C4—224no—
353C4⋊C4—444no—
354C22⋊C4—22no—
355C22⋊C4—22no—
356C22⋊C4—24no—
357C22⋊C4—24no—
358C22⋊C4—224no—
359C22⋊C4—224no—
360C22⋊C4—224no—
361C22⋊C4—224no—
362C22⋊C4—224no—
363C22⋊C4—224no—
364C22⋊C4—444no—
365C22⋊C4C2×C4×D1114yes—
366C42—22no—
367C42—444no—
368C11#2177711yescharacteristic, complemented, Sylow
369C23—22no—
370C23—81no—
371C23—81no—
372C23—114no—
373C23—224no—
374C23—221no—
375C23—222no—
376C23—442no—
377C23—882no—
378C23—881no—
379C23—882no—
380C23C22⋊C4×D1112yes—
381C23C22×C4×D1111yescharacteristic
382C23C2×D4×D1112yes—
383C23#6704214yes—
384Q8—442no—
385Q8—444no—
386D4—28no—
387D4—224no—
388D4—224no—
389D4—228no—
390D4—442no—
391D4—444no—
392D4—444no—
393D4—444no—
394D4—884no—
395C2×C4—22no—
396C2×C4—24no—
397C2×C4—44no—
398C2×C4—82no—
399C2×C4—82no—
400C2×C4—84no—
401C2×C4—114no—
402C2×C4—224no—
403C2×C4—221no—
404C2×C4—221no—
405C2×C4—221no—
406C2×C4—222no—
407C2×C4—222no—
408C2×C4—222no—
409C2×C4—444no—
410C2×C4—444no—
411C2×C4—442no—
412C2×C4—444no—
413C2×C4—444no—
414C2×C4—444no—
415C2×C4—884no—
416C2×C4—1764no—
417C2×C4C22⋊C4×D1112yes—
418C22—22no—
419C22—44no—
420C22—42no—
421C22—41no—
422C22—42no—
423C22—82no—
424C22—224no—
425C22—444no—
426C22—442no—
427C22—441no—
428C22—884no—
429C22—882no—
430C22—1762no—
431C22C2×C22⋊C4×D1111yescharacteristic
432C22#1062305212yes—
433C22#1062318414yes—
434C4—22no—
435C4—44no—
436C4—84no—
437C4—224no—
438C4—441no—
439C4—441no—
440C4—441no—
441C4—884no—
442C2—21no—
443C2—24no—
444C2—22no—
445C2—42no—
446C2—444no—
447C2—881no—
448C2#1307119311yescharacteristic
subgroupG/H
centerC2#13071193
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC11×#1828C2
socleC2×C11#2308
prime radical#13082261C2
cosocleC24×C11C24
hypercenter#1828D11
hypocenterC11#21777
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C24 ◁ #1828

Complements

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

NH ≅ G/Ntype
2. #13077074C2semidirect
3. #13069157C2semidirect
4. #13069028C2semidirect
5. #13068724C2semidirect
6. #13068532C2semidirect
7. C11×#1828C2semidirect
13. #10623057C4semidirect
14. #10623055C4semidirect
15. #10623024C4semidirect
17. C2×#66939C4semidirect
23. C2×#66870C22semidirect
24. #10622556C22semidirect
27. C11×#342C22semidirect
28. #10622165C22semidirect
31. C22×C22⋊D11C2×C4semidirect
34. C23×Dic11C2×C4semidirect
42. C22×C4×D11C2×C4semidirect
43. C22×Dic22C2×C4semidirect
45. C11×#117C2×C4semidirect
46. C2×C11×C22⋊C4C2×C4semidirect
64. #66939C2×C4semidirect
65. #66939C2×C4semidirect
66. #66939C2×C4semidirect
69. #66935C2×C4semidirect
150. #1828D11semidirect
221. #342C2×D11semidirect
283. #117C4×D11semidirect
290. C2×C22⋊C4C4×D11semidirect
368. C11#21777semidirect

Maximal subgroups

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

subgroupindex
#130822612
#130770742
#130691572
#130690282
#130687242
#130685322
C11×#18282
#2177711