Finite Group Databasebeta

← #14759128

Subgroups — #14759128

Order 2816.

1318 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623025C211yesmaximal, characteristic
2#13070969C211yesmaximal, characteristic, complemented
3#13069600C212yesmaximal, complemented
4#13069451C212yesmaximal, complemented
5#13069067C214yesmaximal, complemented
6C4×#66870C214yesmaximal, complemented
7C11×#2312C211yesmaximal, characteristic, complemented
8C22×C11×C22⋊C4C2211yescharacteristic
9C2×#67006C2212yes—
10C22×C22⋊Dic11C2212yes—
11C2×#66983C2211yescharacteristic
12C2×C4×C22⋊D11C2212yes—
13C2×#66977C2211yescharacteristic
14#10623025—24no—
15#10623025—24no—
16C2×#66938C412yescomplemented
17C2×#66937C412yescomplemented
18C2×#66936C412yescomplemented
19C2×#66932C412yescomplemented
20C11×#388—24no—
21C11×#380C2212yes—
22C11×#379C2212yes—
23C4×C11×C22⋊C4C2212yes—
24C4×C22⋊Dic11C2212yes—
25C4×C22⋊Dic11C2212yes—
26C2×#66870C2218yes—
27C22⋊C4×Dic11—24no—
28#10622165C2218yes—
29C25×C11C2311yescharacteristic
30C23×C4×C11C2311yescharacteristic
31C23×C4×C11C2311yescharacteristic
32C22×C22⋊D11C2×C412yes—
33C22×C22⋊D11C2×C412yes—
34C22×C22⋊D11C2312yes—
35C23×Dic11—22no—
36C22×D44C2×C411yescharacteristic, complemented
37C22×C4×D11C2×C412yescomplemented
38C22×Dic22C2×C411yescharacteristic, complemented
39C2×C11×C4⋊C4—22no—
40C2×C11×C22⋊C4—22no—
41C2×C11×C22⋊C4—22no—
42C2×C11×C22⋊C4C2×C412yes—
43C2×C11×C22⋊C4C2×C412yes—
44C2×C11×C22⋊C4D414yes—
45C2×C11×C22⋊C4D414yes—
46C2×C11×C22⋊C4C2314yes—
47C2×C42×C11—22no—
48#67006—24no—
49#67006—24no—
50C2×C22⋊Dic11—22no—
51C2×C22⋊Dic11—28no—
52C2×C22⋊Dic11C2×C412yes—
53C2×C22⋊Dic11C2×C412yes—
54C2×C22⋊Dic11C2312yes—
55C2×C22⋊Dic11C2314yes—
56#66983—22no—
57#66983—22no—
58C4×C22⋊D11—24no—
59C4×C22⋊D11—24no—
60C2×(C2×D11)⋊C4C2×C412yescomplemented
61C2×(C2×D11)⋊C4C2×C412yescomplemented
62C2×C4⋊Dic11C2×C411yescharacteristic, complemented
63C2×C4⋊Dic11C2×C411yescharacteristic, complemented
64#66977—22no—
65#66977—22no—
66C2×Dic11⋊C4C2×C412yescomplemented
67C2×Dic11⋊C4C2×C412yescomplemented
68C2×C4×Dic11—22no—
69C2×C4×Dic11—22no—
70C2×C4×Dic11C2×C412yescomplemented
71#66938—28no—
72#66937—28no—
73#66936—28no—
74#66932—28no—
75C11×#95—22no—
76C11×#95—22no—
77C11⋊#95—22no—
78C11⋊#95—22no—
79#66870—216no—
80#21422—111nomaximal, Sylow
81C24×C11—24no—
82C24×C11—81no—
83C24×C11—81no—
84C24×C11C22×C412yes—
85C24×C11C2×D412yes—
86C24×C11C2×D412yes—
87C24×C11C2411yescharacteristic
88C23×D11C22×C412yes—
89C22×C4×C11—24no—
90C22×C4×C11—81no—
91C22×C4×C11—81no—
92C22×C4×C11C22×C412yes—
93C22×C4×C11C22×C411yescharacteristic
94C22×C4×C11C22×C411yescharacteristic
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D412yes—
99C2×C22⋊D11—24no—
100C2×C22⋊D11—24no—
101C2×C22⋊D11—22no—
102C2×C22⋊D11—22no—
103C2×C22⋊D11—28no—
104C2×C22⋊D11—82no—
105C2×C22⋊D11—82no—
106C22×Dic11—28no—
107C22×Dic11—24no—
108C22×Dic11—82no—
109C22×Dic11—82no—
110C22×Dic11C22×C412yes—
111C22×Dic11C22×C412yes—
112C22×Dic11C22×C412yes—
113C2×D44—22no—
114C2×D44—81no—
115C2×C4×D11—24no—
116C2×C4×D11—82no—
117C2×Dic22—22no—
118C2×Dic22—81no—
119C11×C4⋊C4—82no—
120C11×C22⋊C4—28no—
121C11×C22⋊C4—82no—
122C11×C22⋊C4—82no—
123C11×C22⋊C4C22⋊C418yes—
124C11×C22⋊C4C22⋊C418yes—
125C42×C11—82no—
126C22⋊Dic11—28no—
127C22⋊Dic11—24no—
128C22⋊Dic11—24no—
129C22⋊Dic11—22no—
130C22⋊Dic11—22no—
131C22⋊Dic11—24no—
132C22⋊Dic11#4118yes—
133(C2×D11)⋊C4—24no—
134(C2×D11)⋊C4—24no—
135C4⋊Dic11—22no—
136C4⋊Dic11—22no—
137Dic11⋊C4—24no—
138Dic11⋊C4—24no—
139C4×Dic11—24no—
140C4×Dic11—82no—
141C4×Dic11—82no—
142C2×#538—111no—
143#2312D1111yescharacteristic, complemented
144#2273—111no—
145#1996—112no—
146#1964—112no—
147#1898—114no—
148C4×#99—114no—
149C23×C11—22no—
150C23×C11—22no—
151C23×C11—24no—
152C23×C11—24no—
153C23×C11—42no—
154C23×C11—42no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11—42no—
158C23×C11—42no—
159C23×C11—42no—
160C23×C11—42no—
161C23×C11—88no—
162C23×C11C2×C22⋊C414yes—
163C23×C11C23×C411yescharacteristic
164C23×C11C22×D411yescharacteristic
165C23×C11C22×D411yescharacteristic
166C23×C11C2×#4114yes—
167C22×D11—22no—
168C22×D11—24no—
169C22×D11—42no—
170C22×D11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—41no—
176C2×C4×C11—42no—
177C2×C4×C11—41no—
178C2×C4×C11—44no—
179C2×C4×C11—44no—
180C2×C4×C11—44no—
181C2×C4×C11C2×C22⋊C414yes—
182C2×C4×C11C2×C22⋊C412yes—
183C2×C4×C11C2×C22⋊C412yes—
184C22⋊D11—44no—
185C22⋊D11—44no—
186C22⋊D11—84no—
187C22⋊D11—84no—
188C2×Dic11—22no—
189C2×Dic11—22no—
190C2×Dic11—22no—
191C2×Dic11—24no—
192C2×Dic11—28no—
193C2×Dic11—44no—
194C2×Dic11—44no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11—88no—
198D44—82no—
199C4×D11—84no—
200Dic22—82no—
201#538—224no—
202#538—224no—
203C2×#126—112no—
204C2×#124—112no—
205C2×#123—112no—
206C2×C22⋊Q8—111no—
207C2×#121—111no—
208C2×#121—112no—
209C2×#120—112no—
210C2×C4×D4—112no—
211C22×C22⋊C4—112no—
212C22×C22⋊C4C2×D1111yescharacteristic
213C2×#99—118no—
214#388—24no—
215#380C2×D1112yes—
216#379C2×D1112yes—
217C4×C22⋊C4—112no—
218C4×C22⋊C4—112no—
219C4×C22⋊C4—224no—
220C4×C22⋊C4C2×D1112yes—
221#342—118no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—24no—
229C22×C11—24no—
230C22×C11—24no—
231C22×C11—44no—
232C22×C11—44no—
233C22×C11—44no—
234C22×C11—84no—
235C22×C11—84no—
236C22×C11C22×C22⋊C411yescharacteristic
237C22×C11C4×#4112yes—
238C22×C11#52512yes—
239C22×C11#53212yes—
240C2×D11—42no—
241C2×D11—42no—
242C2×D11—42no—
243C2×D11—84no—
244C4×C11—22no—
245C4×C11—24no—
246C4×C11—22no—
247C4×C11—84no—
248Dic11—48no—
249Dic11—42no—
250Dic11—42no—
251Dic11—42no—
252C25C22×D1111yescharacteristic
253C22×Q8—111no—
254C22×D4—112no—
255C22×D4—112no—
256C22×D4—112no—
257C22×D4—111no—
258C23×C4—112no—
259C23×C4—222no—
260C23×C4C22×D1111yescharacteristic
261C23×C4C22×D1111yescharacteristic
262#126—228no—
263#124—228no—
264#123—228no—
265C22⋊Q8—222no—
266C22⋊Q8—222no—
267#121—222no—
268#121—222no—
269#121—228no—
270#120—224no—
271#120—224no—
272C4×D4—224no—
273C4×D4—224no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—112no—
276C2×C4⋊C4—112no—
277C2×C4⋊C4—111no—
278C2×C4⋊C4—111no—
279C2×C22⋊C4—22no—
280C2×C22⋊C4—22no—
281C2×C22⋊C4—114no—
282C2×C22⋊C4—112no—
283C2×C22⋊C4—112no—
284C2×C22⋊C4—112no—
285C2×C22⋊C4—112no—
286C2×C22⋊C4—112no—
287C2×C22⋊C4—228no—
288C2×C22⋊C4—222no—
289C2×C22⋊C4C4×D1112yes—
290C2×C22⋊C4C4×D1112yes—
291C2×C22⋊C4D4414yes—
292C2×C22⋊C4C22⋊D1114yes—
293C2×C22⋊C4C22×D1114yes—
294C2×C42—22no—
295C2×C42—112no—
296C2×C42—222no—
297C2×C42—222no—
298#99—2216no—
299#95—22no—
300#95—22no—
301#95—222no—
302#95—222no—
303C2×C11—22no—
304C2×C11—22no—
305C2×C11—22no—
306C2×C11—44no—
307C2×C11#229711yescharacteristic
308C2×C11#288311yescharacteristic
309C2×C11#288311yescharacteristic
310D11—82no—
311C24—24no—
312C24—81no—
313C24—81no—
314C24—112no—
315C24C2×C4×D1112yes—
316C24C2×D4412yes—
317C24C2×C22⋊D1112yes—
318C24C23×D1111yescharacteristic
319C2×Q8—222no—
320C2×Q8—881no—
321C2×D4—222no—
322C2×D4—228no—
323C2×D4—222no—
324C2×D4—224no—
325C2×D4—224no—
326C2×D4—222no—
327C2×D4—881no—
328C2×D4—882no—
329C2×D4—882no—
330C22×C4—24no—
331C22×C4—81no—
332C22×C4—81no—
333C22×C4—112no—
334C22×C4—112no—
335C22×C4—112no—
336C22×C4—224no—
337C22×C4—228no—
338C22×C4—224no—
339C22×C4—882no—
340C22×C4—882no—
341C22×C4—882no—
342C22×C4C2×C4×D1112yes—
343C22×C4C2×C4×D1111yescharacteristic
344C22×C4C2×C4×D1111yescharacteristic
345C22×C4C2×D4412yes—
346C22×C4C2×D4412yes—
347C22×C4C2×C22⋊D1112yes—
348C22×C4C2×C22⋊D1112yes—
349C4⋊C4—82no—
350C4⋊C4—224no—
351C4⋊C4—224no—
352C4⋊C4—222no—
353C4⋊C4—222no—
354C22⋊C4—28no—
355C22⋊C4—82no—
356C22⋊C4—82no—
357C22⋊C4—118no—
358C22⋊C4—228no—
359C22⋊C4—224no—
360C22⋊C4—224no—
361C22⋊C4—222no—
362C22⋊C4—224no—
363C22⋊C4—222no—
364C22⋊C4—224no—
365C22⋊C4—224no—
366C22⋊C4(C2×D11)⋊C418yes—
367C22⋊C4(C2×D11)⋊C418yes—
368C42—82no—
369C42—224no—
370C42—882no—
371C42—882no—
372C11#2142211yescharacteristic, complemented, Sylow
373C23—22no—
374C23—22no—
375C23—24no—
376C23—24no—
377C23—41no—
378C23—41no—
379C23—42no—
380C23—42no—
381C23—42no—
382C23—42no—
383C23—42no—
384C23—42no—
385C23—88no—
386C23—222no—
387C23—224no—
388C23—442no—
389C23—442no—
390C23C2×(C2×D11)⋊C414yes—
391C23C22×C4×D1111yescharacteristic
392C23C22×D4411yescharacteristic
393C23#41×D1114yes—
394C23C22×C22⋊D1111yescharacteristic
395Q8—882no—
396D4—444no—
397D4—444no—
398D4—882no—
399D4—884no—
400D4—884no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—44no—
409C2×C4—44no—
410C2×C4—44no—
411C2×C4—224no—
412C2×C4—228no—
413C2×C4—222no—
414C2×C4—222no—
415C2×C4—222no—
416C2×C4—444no—
417C2×C4—444no—
418C2×C4—442no—
419C2×C4—442no—
420C2×C4—884no—
421C2×C4—888no—
422C2×C4C2×(C2×D11)⋊C414yes—
423C2×C4C2×(C2×D11)⋊C412yes—
424C2×C4C2×(C2×D11)⋊C412yes—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—24no—
432C22—24no—
433C22—24no—
434C22—44no—
435C22—44no—
436C22—44no—
437C22—84no—
438C22—84no—
439C22—442no—
440C22—442no—
441C22—442no—
442C22—884no—
443C22#1062305312yes—
444C22#1062305512yes—
445C22C22×(C2×D11)⋊C411yescharacteristic
446C22#1062336312yes—
447C4—24no—
448C4—22no—
449C4—22no—
450C4—84no—
451C4—448no—
452C4—442no—
453C4—442no—
454C4—442no—
455C2—22no—
456C2—22no—
457C2—22no—
458C2—44no—
459C2—882no—
460C2#1307110411yescharacteristic
461C2#1307707611yescharacteristic
462C2#1307707611yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC11×#2312C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623025C2
cosocleC24×C11C24
hypercenter#2312D11
hypocenterC11#21422
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C22⋊C4 ◁ #2312

Complements

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

NH ≅ G/Ntype
2. #13070969C2semidirect
3. #13069600C2semidirect
4. #13069451C2semidirect
5. #13069067C2semidirect
6. C4×#66870C2semidirect
7. C11×#2312C2semidirect
16. C2×#66938C4semidirect
17. C2×#66937C4semidirect
18. C2×#66936C4semidirect
19. C2×#66932C4semidirect
36. C22×D44C2×C4semidirect
37. C22×C4×D11C2×C4semidirect
38. C22×Dic22C2×C4semidirect
60. C2×(C2×D11)⋊C4C2×C4semidirect
61. C2×(C2×D11)⋊C4C2×C4semidirect
62. C2×C4⋊Dic11C2×C4semidirect
63. C2×C4⋊Dic11C2×C4semidirect
66. C2×Dic11⋊C4C2×C4semidirect
67. C2×Dic11⋊C4C2×C4semidirect
70. C2×C4×Dic11C2×C4semidirect
143. #2312D11semidirect
372. C11#21422semidirect

Maximal subgroups

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

subgroupindex
C2×#106230252
#130709692
#130696002
#130694512
#130690672
C4×#668702
C11×#23122
#2142211