Finite Group Databasebeta

← #14727675

Subgroups — #14727675

Order 2816.

1282 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079364C212yesmaximal, complemented
2#13074358C211yesmaximal, characteristic, complemented
3#13067619C214yesmaximal, complemented
4#13067551C214yesmaximal, complemented
5#13067184C212yesmaximal, complemented
6C2×#10622166C211yesmaximal, characteristic, complemented
7C2×C11×#537C211yesmaximal, characteristic, complemented
8C22×C11×#41—21no—
9C11×#537—24no—
10C11×#537—22no—
11C11×#537C2214yes—
12C2×C11×C22⋊Q8—22no—
13C2×C11×#121—22no—
14C2×C11×#121—21no—
15C2×C11×#121C2212yes—
16C22×C11×C4⋊C4C2211yescharacteristic
17C2×#66983C2211yescharacteristic
18C2×#66982—21no—
19#10622830—22no—
20#10622826—21no—
21#10622825C2211yescharacteristic
22C2×C22⋊(C11⋊C8)C2212yes—
23#10622651—24no—
24#10622649C2214yescomplemented
25#10622646C2214yescomplemented
26#10622607—22no—
27#10622604C2212yescomplemented
28#10622596C2212yescomplemented
29#10622580—22no—
30#10622175C2218yescomplemented
31#10622166C2214yescomplemented
32C2×C11×#41—24no—
33C2×C11×#41—24no—
34C2×C11×#41—44no—
35C2×C11×#41—44no—
36C22×Q8×C11—21no—
37C22×D4×C11—21no—
38C22×D4×C11—22no—
39C22×D4×C11—21no—
40C22×D4×C11D412yes—
41C23×C4×C11—22no—
42C23×C4×C11D411yescharacteristic
43C23×C4×C11D411yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C22×C22⋊D11—21no—
46C22×D44C2311yescharacteristic
47C11×C22⋊Q8—28no—
48C11×C22⋊Q8—28no—
49C11×#121—24no—
50C11×#121—28no—
51C11×#121—28no—
52C11×#121—24no—
53C11×#121—22no—
54C11×#121—22no—
55C11×#121D414yes—
56C11×#121C2314yes—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4D412yes—
61C2×C11×C4⋊C4D412yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—22no—
65C2×C22⋊Dic11—21no—
66C2×#4323—24no—
67#66983—22no—
68#66983—22no—
69#66982—44no—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—22no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11C2311yescharacteristic
75C2×Dic11⋊C4—22no—
76C22×C11⋊C8—22no—
77#66896—24no—
78C11⋊#95—22no—
79C11⋊#95C2312yes—
80C22⋊(C11⋊C8)—22no—
81C22⋊(C11⋊C8)C2314yes—
82#66873—24no—
83#66871—24no—
84#18292—111nomaximal, Sylow
85C24×C11—22no—
86C24×C11C2×D411yescharacteristic
87C23×D11—21no—
88C11×#41—48no—
89C11×#41—416no—
90C11×#41—48no—
91C2×Q8×C11—24no—
92C2×Q8×C11—44no—
93C2×D4×C11—24no—
94C2×D4×C11—24no—
95C2×D4×C11—24no—
96C2×D4×C11—24no—
97C2×D4×C11—22no—
98C2×D4×C11—44no—
99C2×D4×C11—44no—
100C2×D4×C11—44no—
101C2×D4×C11—82no—
102C2×D4×C11—82no—
103C2×D4×C11C2×D414yes—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—28no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—48no—
112C22×C4×C11—81no—
113C22×C4×C11—81no—
114C22×C4×C11D814yescomplemented
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2411yescharacteristic
121C2×C22⋊D11—41no—
122C2×C22⋊D11—41no—
123C2×C22⋊D11—42no—
124C2×C22⋊D11—42no—
125C22×Dic11—21no—
126C22×Dic11—22no—
127C2×D44—22no—
128C2×D44—81no—
129C11×C4⋊C4—24no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—24no—
133C11×C4⋊C4C2×D414yes—
134C11×C22⋊C4—28no—
135C11×C22⋊C4—24no—
136C11×C22⋊C4—24no—
137C22⋊Dic11—42no—
138#4323—84no—
139(C2×D11)⋊C4—42no—
140(C2×D11)⋊C4—44no—
141(C2×D11)⋊C4—82no—
142C4⋊Dic11—22no—
143C4⋊Dic11—81no—
144Dic11⋊C4—44no—
145C2×C11⋊C8—24no—
146C2×C11⋊C8—82no—
147C2×#537D1111yescharacteristic, complemented
148#3186—112no—
149#2618—111no—
150#1610—114no—
151#1598—114no—
152#1519—112no—
153C2×#324—111no—
154C23×C11—24no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11—44no—
158C23×C11—44no—
159C23×C11—44no—
160C23×C11#12011yescharacteristic
161C23×C11#12011yescharacteristic
162C23×C11C2×D812yes—
163C23×C11AGL(1,ℤ/8)12yes—
164C23×C11C22×D411yescharacteristic
165C22×D11—42no—
166C22×D11—42no—
167C22×D11—41no—
168C22×D11—41no—
169C22×D11—41no—
170Q8×C11—48no—
171D4×C11—44no—
172D4×C11—48no—
173D4×C11—44no—
174D4×C11—44no—
175D4×C11—48no—
176D4×C11—82no—
177D4×C11—84no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—24no—
181C2×C4×C11—24no—
182C2×C4×C11—22no—
183C2×C4×C11—24no—
184C2×C4×C11—42no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—42no—
188C2×C4×C11—416no—
189C2×C4×C11—42no—
190C2×C4×C11—44no—
191C2×C4×C11—42no—
192C2×C4×C11—81no—
193C2×C4×C11#12012yes—
194C2×C4×C11C2×D814yes—
195C2×C4×C11C22×D412yes—
196C22⋊D11—82no—
197C22⋊D11—82no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—42no—
203C2×Dic11—41no—
204D44—44no—
205C11⋊C8—44no—
206C22×#41—21no—
207#537—24no—
208#537—22no—
209#537C2×D1114yes—
210C2×#123—221no—
211C2×C22⋊Q8—22no—
212C2×#121—22no—
213C2×#121—21no—
214C2×#121—111no—
215C2×#121C2×D1112yes—
216C22×C4⋊C4C2×D1111yescharacteristic
217#480—114no—
218#480—222no—
219#466—224no—
220#447—114no—
221#447—222no—
222C2×C22⋊C8—112no—
223#398—112no—
224#396—222no—
225#394—112no—
226#386—221no—
227#380—111no—
228#327—118no—
229#324—114no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—42no—
237C22×C11—42no—
238C22×C11—44no—
239C22×C11—44no—
240C22×C11—44no—
241C22×C11—88no—
242C22×C11#44712yes—
243C22×C11#44712yes—
244C22×C11C2×#12011yescharacteristic
245C22×C11C22×D811yescharacteristic
246C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
247C2×D11—82no—
248C2×D11—82no—
249C2×D11—81no—
250C2×D11—81no—
251C2×D11—81no—
252C4×C11—24no—
253C4×C11—22no—
254C4×C11—22no—
255C4×C11—44no—
256C4×C11—42no—
257Dic11—82no—
258Dic11—81no—
259C2×#41—24no—
260C2×#41—24no—
261C2×#41—44no—
262C2×#41—44no—
263C22×Q8—21no—
264C22×D4—21no—
265C22×D4—22no—
266C22×D4—21no—
267C22×D4—111no—
268C22×D4—221no—
269C22×D4C22⋊D1112yes—
270C23×C4—22no—
271C23×C4C22⋊D1111yescharacteristic
272C23×C4C22⋊D1111yescharacteristic
273C23×C4C22×D1111yescharacteristic
274C2×D8—224no—
275C22×C8—222no—
276#123—444no—
277C22⋊Q8—28no—
278C22⋊Q8—28no—
279#121—24no—
280#121—28no—
281#121—28no—
282#121—24no—
283#121—22no—
284#121—22no—
285#121—222no—
286#121—222no—
287#121C22⋊D1114yes—
288#121C22×D1114yes—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—111no—
293C2×C4⋊C4—222no—
294C2×C4⋊C4—221no—
295C2×C4⋊C4C22⋊D1112yes—
296C2×C4⋊C4C22⋊D1112yes—
297C2×C4⋊C4C22×D1112yes—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—221no—
301C2×C22⋊C4—221no—
302C2×C22⋊C4—222no—
303C2×C22⋊C4—222no—
304#107—224no—
305#102—224no—
306#102—224no—
307C22⋊C8—114no—
308C22⋊C8—222no—
309#95—112no—
310#95—222no—
311C2×C11—21no—
312C2×C11—21no—
313C2×C11—22no—
314C2×C11—22no—
315C2×C11—84no—
316C2×C11C2×#44711yescharacteristic
317C2×C11#302011yescharacteristic
318C2×C11#302611yescharacteristic
319D11—161no—
320C24—22no—
321C24—221no—
322C24C2×C22⋊D1111yescharacteristic
323#41—48no—
324#41—416no—
325#41—48no—
326C2×Q8—24no—
327C2×Q8—44no—
328C2×D4—24no—
329C2×D4—24no—
330C2×D4—24no—
331C2×D4—24no—
332C2×D4—22no—
333C2×D4—44no—
334C2×D4—44no—
335C2×D4—44no—
336C2×D4—82no—
337C2×D4—82no—
338C2×D4—222no—
339C2×D4—442no—
340C2×D4—442no—
341C2×D4—441no—
342C2×D4—441no—
343C2×D4—881no—
344C2×D4C2×C22⋊D1114yes—
345C22×C4—22no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—28no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—21no—
352C22×C4—48no—
353C22×C4—81no—
354C22×C4—81no—
355C22×C4—222no—
356C22×C4—221no—
357C22×C4#432314yescomplemented
358C22×C4C2×C22⋊D1112yes—
359C22×C4C2×C22⋊D1112yes—
360C22×C4C2×C22⋊D1111yescharacteristic
361C22×C4C2×C22⋊D1112yes—
362C22×C4C2×C22⋊D1112yes—
363C22×C4C23×D1111yescharacteristic
364D8—884no—
365C2×C8—224no—
366C2×C8—882no—
367C4⋊C4—24no—
368C4⋊C4—24no—
369C4⋊C4—22no—
370C4⋊C4—24no—
371C4⋊C4—222no—
372C4⋊C4—444no—
373C4⋊C4—881no—
374C4⋊C4C2×C22⋊D1114yes—
375C22⋊C4—28no—
376C22⋊C4—24no—
377C22⋊C4—24no—
378C22⋊C4—442no—
379C22⋊C4—444no—
380C22⋊C4—442no—
381C22⋊C4—882no—
382C11#1829211yescharacteristic, complemented, Sylow
383C23—24no—
384C23—41no—
385C23—41no—
386C23—44no—
387C23—44no—
388C23—44no—
389C23—442no—
390C23—442no—
391C23—441no—
392C23—441no—
393C23—441no—
394C23C2×#432312yes—
395C23#6698512yes—
396C23#6700611yescharacteristic
397C23#6700611yescharacteristic
398C23C22×C22⋊D1111yescharacteristic
399Q8—48no—
400D4—44no—
401D4—48no—
402D4—44no—
403D4—44no—
404D4—48no—
405D4—82no—
406D4—84no—
407D4—444no—
408D4—882no—
409D4—882no—
410C2×C4—22no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—24no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—41no—
420C2×C4—416no—
421C2×C4—42no—
422C2×C4—44no—
423C2×C4—42no—
424C2×C4—81no—
425C2×C4—442no—
426C2×C4—442no—
427C2×C4—442no—
428C2×C4—441no—
429C2×C4—441no—
430C2×C4—441no—
431C2×C4C2×#432314yes—
432C2×C4#6700612yes—
433C2×C4C22×C22⋊D1112yes—
434C8—444no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—42no—
442C22—42no—
443C22—44no—
444C22—44no—
445C22—44no—
446C22—88no—
447C22—882no—
448C22—882no—
449C22—881no—
450C22—881no—
451C22—881no—
452C22#1062283012yes—
453C22#1062283012yes—
454C22C22×#432311yescharacteristic
455C22C2×#6698511yescharacteristic
456C22C2×#6700611yescharacteristic
457C4—24no—
458C4—22no—
459C4—22no—
460C4—44no—
461C4—42no—
462C4—882no—
463C4—881no—
464C2—21no—
465C2—22no—
466C2—21no—
467C2—22no—
468C2—84no—
469C2—1761no—
470C2C2×#1062283011yescharacteristic
471C2#1307798011yescharacteristic
472C2#1307801311yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#537C2
socleC22×C11C2×#120
hypercenterC2×#537D11
hypocenterC11#18292
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. #13079364C2semidirect
2. #13074358C2semidirect
3. #13067619C2semidirect
4. #13067551C2semidirect
5. #13067184C2semidirect
6. C2×#10622166C2semidirect
7. C2×C11×#537C2semidirect
24. #10622649C22semidirect
25. #10622646C22semidirect
27. #10622604C22semidirect
28. #10622596C22semidirect
30. #10622175C22semidirect
31. #10622166C22semidirect
114. C22×C4×C11D8semidirect
147. C2×#537D11semidirect
357. C22×C4#4323semidirect
382. C11#18292semidirect

Maximal subgroups

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

subgroupindex
#130793642
#130743582
#130676192
#130675512
#130671842
C2×#106221662
C2×C11×#5372
#1829211