Finite Group Databasebeta

← #14736636

Subgroups — #14736636

Order 2816.

682 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079073C211yesmaximal, characteristic
2#13078647C211yesmaximal, characteristic
3Q8×#4318C211yesmaximal, characteristic, complemented
4#13068108C212yesmaximal, complemented
5#13068090C212yesmaximal, complemented
6#13067984C212yesmaximal, complemented
7#13067966C212yesmaximal, complemented
8#13067366C211yesmaximal, characteristic, complemented
9#13067291C211yesmaximal, characteristic
10#13067288C211yesmaximal, characteristic, complemented
11C2×C11×#475C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×#66995—21no—
15C2×#66995—21no—
16#10623008C2211yescharacteristic
17C11×#475—21no—
18C11×#475—21no—
19C11×#475C2212yes—
20C11×#475C2212yes—
21C2×C11×#106—21no—
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×#103—21no—
24#10622840—21no—
25#10622705C2212yes—
26#10622699—22no—
27#10622698C2212yes—
28#10622640C2211yescharacteristic
29#10622640C2211yescharacteristic
30C4×#4325—21no—
31C4×#4325—21no—
32#10622637—22no—
33#10622637C2212yes—
34Q8×C11⋊C8C2212yes—
35#10622633C2211yescharacteristic
36#10622633C2211yescharacteristic
37#10622581—21no—
38#10622538C2211yescharacteristic
39#10622537—21no—
40#10622537C2211yescharacteristic
41C4×#4318—21no—
42C4×#4318C2211yescharacteristic
43#10622185C2212yes—
44#10622185C2212yes—
45#10622124C2212yes—
46#10622123C2212yes—
47#10622118C2212yes—
48#10622117C2212yes—
49C22×Q8×C11—21no—
50C22×Q8×C11D411yescharacteristic
51C2×#4339—21no—
52C22×C8×C11—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8C2312yes—
57C4×Q8×C11—21no—
58C4×Q8×C11—21no—
59C4×Q8×C11D411yescharacteristic
60C4×Q8×C11D411yescharacteristic
61C4×Q8×C11C2311yescharacteristic
62C4×Q8×C11C2311yescharacteristic
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C42×C11—21no—
68C2×C42×C11C2311yescharacteristic
69C2×#4326—22no—
70C2×#4326—22no—
71#66995—44no—
72#66995—44no—
73C2×#4325—21no—
74C2×#4325—21no—
75C2×#4325—22no—
76C2×#4325—22no—
77#66983—21no—
78#66983—21no—
79C2×#4318—21no—
80C2×#4318D411yescharacteristic
81C2×#4318D411yescharacteristic
82#66928—21no—
83#66927C2311yescharacteristic
84C4×D44—21no—
85C4×D44—21no—
86#66922C2311yescharacteristic
87C11×#106—22no—
88C11×#106—22no—
89C11×C4⋊C8—21no—
90C11×C4⋊C8C2312yes—
91C11×#103—22no—
92C11×#103—22no—
93#66899—21no—
94#66899—21no—
95C22⋊(C11⋊C8)—21no—
96#66873—21no—
97#66873—21no—
98#66872—21no—
99#66872—21no—
100C4⋊(C11⋊C8)—21no—
101C4⋊(C11⋊C8)—22no—
102C4⋊(C11⋊C8)—22no—
103C4⋊(C11⋊C8)C2312yes—
104C4⋊(C11⋊C8)C2311yescharacteristic
105C4⋊(C11⋊C8)C2311yescharacteristic
106#66867—22no—
107#66867D412yes—
108C4×C11⋊C8—21no—
109C4×C11⋊C8—22no—
110C4×C11⋊C8C2312yes—
111#19171—111nomaximal, Sylow
112C2×Q8×C11—21no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11—41no—
116C2×Q8×C11—41no—
117C2×Q8×C11—42no—
118C2×Q8×C11—42no—
119C2×Q8×C11C2×D411yescharacteristic
120C2×Q8×C11C2×D411yescharacteristic
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—41no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11#4111yescharacteristic
127C2×C22⋊D11—41no—
128#4339—42no—
129#4339—42no—
130C2×D44—21no—
131C2×D44—21no—
132C2×D44—21no—
133C2×C4×D11—41no—
134C2×Dic22—21no—
135C2×C8×C11—22no—
136C2×C8×C11—42no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—41no—
145C11×C4⋊C4—41no—
146C11×C4⋊C4C2×D411yescharacteristic
147C11×C4⋊C4C2×D411yescharacteristic
148C42×C11—21no—
149C42×C11—21no—
150C42×C11—21no—
151C42×C11—21no—
152C42×C11C2×D411yescharacteristic
153C42×C11C2×D411yescharacteristic
154C42×C11#4111yescharacteristic
155C42×C11C2411yescharacteristic
156#4326—44no—
157#4326—44no—
158#4325—42no—
159#4325—44no—
160#4325—44no—
161#4325—42no—
162(C2×D11)⋊C4—41no—
163(C2×D11)⋊C4—41no—
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166#4318—22no—
167#4318—42no—
168#4318SD1614yescomplemented
169C2×C11⋊C8—22no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8C2×D412yes—
173C2×C11⋊C8C2×D412yes—
174#3152—111no—
175#3103—111no—
176C2×#475D1111yescharacteristic, complemented
177Q8×M16—111no—
178#1690—112no—
179#1686—112no—
180#1670—112no—
181#1666—112no—
182#1565—111no—
183#1547—111no—
184#1546—111no—
185C23×C11#12111yescharacteristic
186C22×D11—41no—
187Q8×C11—21no—
188Q8×C11—21no—
189Q8×C11—21no—
190Q8×C11—42no—
191Q8×C11—42no—
192Q8×C11—42no—
193Q8×C11—82no—
194Q8×C11#13712yescomplemented
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—41no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—81no—
205C2×C4×C11—82no—
206C2×C4×C11#12111yescharacteristic
207C2×C4×C11#12111yescharacteristic
208C2×C4×C11#12111yescharacteristic
209C2×C4×C11C2×SD1612yes—
210C2×C4×C11AGL(1,ℤ/8)12yes—
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C2×#4111yescharacteristic
214C22⋊D11—82no—
215C2×Dic11—41no—
216D44—41no—
217D44—41no—
218D44—41no—
219D44—41no—
220D44—81no—
221C4×D11—82no—
222Dic22—41no—
223Dic22—41no—
224C8×C11—42no—
225C11⋊C8—22no—
226C11⋊C8—42no—
227C11⋊C8—41no—
228C11⋊C8—41no—
229C11⋊C8C2×SD1614yes—
230C2×#137—221no—
231C2×#137—221no—
232#532—111no—
233C2×C4⋊Q8C2×D1111yescharacteristic
234C2×C4×Q8C2×D1111yescharacteristic
235#497—222no—
236#494—112no—
237#492—112no—
238#481—221no—
239#475—21no—
240#475—21no—
241#475—111no—
242#475—111no—
243#475C2×D1112yes—
244#475C2×D1112yes—
245#460—111no—
246#460—111no—
247#448—221no—
248#446—112no—
249#446—222no—
250C8×Q8—112no—
251C4×SD16—221no—
252C4×SD16—221no—
253#431—111no—
254C2×#106—21no—
255#423—111no—
256#423—221no—
257C2×C4⋊C8C2×D1111yescharacteristic
258C2×#103—21no—
259C4×M16—111no—
260C4×M16—221no—
261#335—112no—
262#334—112no—
263#332—112no—
264#332—112no—
265#332—112no—
266#331—112no—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11#46012yes—
270C22×C11C2×#12111yescharacteristic
271C2×D11—81no—
272C2×D11—81no—
273C2×D11—81no—
274C4×C11—21no—
275C4×C11—22no—
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—41no—
279C4×C11—41no—
280C4×C11—41no—
281C4×C11—82no—
282C4×C11#46012yes—
283C4×C11C22×SD1611yescharacteristic
284C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
285C4×C11C2×#13711yescharacteristic
286C4×C11#57511yescharacteristic
287Dic11—81no—
288C2×#41—221no—
289C22×Q8—21no—
290C22×Q8C22⋊D1111yescharacteristic
291#137—444no—
292#137—444no—
293C2×Q16—222no—
294C2×Q16—222no—
295C2×SD16—222no—
296C2×SD16—222no—
297C2×SD16—221no—
298C2×SD16—221no—
299C2×M16—111no—
300C2×M16—111no—
301C2×M16—221no—
302C22×C8—21no—
303C4⋊Q8—21no—
304C4⋊Q8—21no—
305C4⋊Q8—21no—
306C4⋊Q8—111no—
307C4⋊Q8C22×D1112yes—
308#127—111no—
309#124—221no—
310#121—221no—
311#121—221no—
312C4×Q8—21no—
313C4×Q8—21no—
314C4×Q8C22⋊D1111yescharacteristic
315C4×Q8C22⋊D1111yescharacteristic
316C4×Q8C22×D1111yescharacteristic
317C4×Q8C22×D1111yescharacteristic
318C4×D4—221no—
319C4×D4—221no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4C22⋊D1111yescharacteristic
324C2×C42—21no—
325C2×C42C22×D1111yescharacteristic
326#106—22no—
327#106—22no—
328#106—221no—
329#106—221no—
330C4⋊C8—21no—
331C4⋊C8—112no—
332C4⋊C8—111no—
333C4⋊C8—111no—
334C4⋊C8—222no—
335C4⋊C8—222no—
336C4⋊C8—221no—
337C4⋊C8C22×D1112yes—
338#103—22no—
339#103—22no—
340#103—221no—
341#103—221no—
342#102—221no—
343#102—221no—
344C22⋊C8—221no—
345#97—112no—
346#97—222no—
347C4×C8—112no—
348C4×C8—222no—
349C4×C8—221no—
350C2×C11—22no—
351C2×C11C2×#46011yescharacteristic
352C2×C11#305611yescharacteristic
353C2×C11#306911yescharacteristic
354D11—161no—
355#41—442no—
356#41—442no—
357C2×Q8—21no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8—41no—
361C2×Q8—41no—
362C2×Q8—42no—
363C2×Q8—42no—
364C2×Q8—221no—
365C2×Q8C2×C22⋊D1111yescharacteristic
366C2×Q8C2×C22⋊D1111yescharacteristic
367C2×D4—221no—
368C2×D4—221no—
369C2×D4—221no—
370C2×D4—441no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—41no—
374C22×C4—441no—
375C22×C4D4×D1111yescharacteristic
376C22×C4#434111yescharacteristic
377C22×C4C2×C22⋊D1111yescharacteristic
378Q16—444no—
379Q16—444no—
380SD16—444no—
381SD16—444no—
382SD16—442no—
383SD16—442no—
384M16—114no—
385M16—222no—
386M16—442no—
387C2×C8—22no—
388C2×C8—42no—
389C2×C8—112no—
390C2×C8—112no—
391C2×C8—222no—
392C2×C8—221no—
393C2×C8—221no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—41no—
402C4⋊C4—41no—
403C4⋊C4—221no—
404C4⋊C4—221no—
405C4⋊C4C2×C22⋊D1111yescharacteristic
406C4⋊C4C2×C22⋊D1111yescharacteristic
407C22⋊C4—441no—
408C22⋊C4—441no—
409C42—21no—
410C42—21no—
411C42—21no—
412C42—21no—
413C42D4×D1111yescharacteristic
414C42#434111yescharacteristic
415C42C2×C22⋊D1111yescharacteristic
416C42C23×D1111yescharacteristic
417C11#1917111yescharacteristic, complemented, Sylow
418C23—441no—
419C23#6699211yescharacteristic
420Q8—21no—
421Q8—21no—
422Q8—21no—
423Q8—42no—
424Q8—42no—
425Q8—42no—
426Q8—82no—
427Q8—441no—
428Q8—441no—
429Q8#6699512yescomplemented
430D4—441no—
431D4—441no—
432D4—441no—
433D4—441no—
434D4—881no—
435D4—882no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—81no—
446C2×C4—82no—
447C2×C4—441no—
448C2×C4—882no—
449C2×C4SD16×D1112yes—
450C2×C4#6696712yes—
451C2×C4#6699211yescharacteristic
452C2×C4#6699211yescharacteristic
453C2×C4#6699211yescharacteristic
454C2×C4C2×D4×D1111yescharacteristic
455C2×C4C2×#434111yescharacteristic
456C2×C4C22×C22⋊D1111yescharacteristic
457C8—42no—
458C8—114no—
459C8—222no—
460C8—442no—
461C8—441no—
462C8—441no—
463C22—21no—
464C22—21no—
465C22—881no—
466C22—881no—
467C22—881no—
468C22#1062277612yes—
469C22C2×#6699211yescharacteristic
470C4—21no—
471C4—21no—
472C4—21no—
473C4—22no—
474C4—41no—
475C4—41no—
476C4—41no—
477C4—82no—
478C4—881no—
479C4#1062277612yes—
480C4C2×SD16×D1111yescharacteristic
481C4C2×#6696711yescharacteristic
482C4C2×#6699511yescharacteristic
483C4#1062335311yescharacteristic
484C2—22no—
485C2—1761no—
486C2C2×#1062277611yescharacteristic
487C2#1307824211yescharacteristic
488C2#1307835011yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#475C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenterC2×#475D11
hypocenterC11#19171
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
3. Q8×#4318C2semidirect
4. #13068108C2semidirect
5. #13068090C2semidirect
6. #13067984C2semidirect
7. #13067966C2semidirect
8. #13067366C2semidirect
10. #13067288C2semidirect
11. C2×C11×#475C2semidirect
168. #4318SD16semidirect
176. C2×#475D11semidirect
194. Q8×C11#137semidirect
417. C11#19171semidirect
429. Q8#66995semidirect

Maximal subgroups

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

subgroupindex
#130790732
#130786472
Q8×#43182
#130681082
#130680902
#130679842
#130679662
#130673662
#130672912
#130672882
C2×C11×#4752
#1917111