Finite Group Databasebeta

← #14737608

Subgroups — #14737608

Order 2816.

656 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079176C211yesmaximal, characteristic
2#13078088C211yesmaximal, characteristic
3C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
4#13068044C212yesmaximal, complemented
5#13068034C212yesmaximal, complemented
6#13068000C212yesmaximal, complemented
7#13067966C212yesmaximal, complemented
8#13067371C211yesmaximal, characteristic, complemented
9#13067306C211yesmaximal, characteristic, complemented
10#13067294C211yesmaximal, characteristic
11C11×#3078C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×#66995—21no—
15#10623008C2211yescharacteristic
16C11×#479—22no—
17C11×#477C2212yes—
18C11×#475C2212yes—
19C11×#428—21no—
20C11×#423C2211yescharacteristic
21C11×#419—21no—
22#10622701C2211yescharacteristic
23#10622698C2211yescharacteristic
24#10622694C2211yescharacteristic
25#10622692C2211yescharacteristic
26#10622661—21no—
27#10622661—21no—
28#10622644C2212yes—
29#10622641—22no—
30#10622640C2212yes—
31C4×#4325—21no—
32C4×#4325—21no—
33Q8×C11⋊C8—21no—
34Q8×C11⋊C8—21no—
35Q8×C11⋊C8C2212yes—
36Q8×C11⋊C8C2212yes—
37#10622579—21no—
38#10622537C2211yescharacteristic
39C2×C4⋊(C11⋊C8)—21no—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8—21no—
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622185C2212yes—
44#10622184C2212yes—
45#10622123C2212yes—
46#10622120C2212yes—
47#10622118C2212yes—
48#10622118C2212yes—
49C22×Q8×C11D411yescharacteristic
50C2×#4339—21no—
51C2×C11×M16—21no—
52C11×C4⋊Q8C2311yescharacteristic
53C11×C4⋊Q8C2311yescharacteristic
54C11×#125—21no—
55C11×C22⋊Q8—21no—
56C11×C22⋊Q8—21no—
57C4×Q8×C11—21no—
58C4×Q8×C11—21no—
59C4×Q8×C11—21no—
60C4×Q8×C11—21no—
61C4×Q8×C11D412yes—
62C4×Q8×C11C2312yes—
63C11×#117—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4D411yescharacteristic
66C2×C42×C11—21no—
67C2×C42×C11C2311yescharacteristic
68C2×#4326—22no—
69#66995—44no—
70C2×#4325—22no—
71C2×#4325—21no—
72C2×#4325—21no—
73#66983—21no—
74#66983—21no—
75C2×#4318—21no—
76C22×C11⋊C8—21no—
77C22×C11⋊C8D411yescharacteristic
78C22×C11⋊C8D411yescharacteristic
79#66928—21no—
80#66927C2311yescharacteristic
81C4×D44—21no—
82C4×D44—21no—
83#66922C2311yescharacteristic
84C11×#107—22no—
85C11×#106—22no—
86C11×C4⋊C8—21no—
87C11×C4⋊C8C2312yes—
88C11×#103—22no—
89C11×#103—22no—
90#66899—21no—
91#66899—21no—
92#66874—22no—
93#66873—22no—
94#66873—21no—
95#66873—21no—
96#66872—21no—
97#66872—21no—
98C4⋊(C11⋊C8)—21no—
99C4⋊(C11⋊C8)—21no—
100C4⋊(C11⋊C8)—22no—
101C4⋊(C11⋊C8)—22no—
102C4⋊(C11⋊C8)C2312yes—
103C4⋊(C11⋊C8)C2312yes—
104C4×C11⋊C8—22no—
105C4×C11⋊C8—22no—
106C4×C11⋊C8D411yescharacteristic
107C4×C11⋊C8D411yescharacteristic
108C4×C11⋊C8C2311yescharacteristic
109C4×C11⋊C8C2311yescharacteristic
110#19260—111nomaximal, Sylow
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11SD1614yescomplemented
116C2×Q8×C11C2×D412yes—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11#4111yescharacteristic
122C2×C22⋊D11—41no—
123#4339—42no—
124#4339—42no—
125C2×D44—21no—
126C2×D44—21no—
127C2×D44—21no—
128C2×C4×D11—41no—
129C2×Dic22—21no—
130C11×M16—42no—
131C2×C8×C11—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—41no—
140C11×C4⋊C4—41no—
141C11×C4⋊C4C2×D412yes—
142C11×C22⋊C4—41no—
143C42×C11—22no—
144C42×C11—22no—
145C42×C11—41no—
146C42×C11C2×D411yescharacteristic
147C42×C11C2×D411yescharacteristic
148C42×C11#4111yescharacteristic
149C42×C11C2411yescharacteristic
150#4326—44no—
151#4325—42no—
152#4325—42no—
153#4325—44no—
154(C2×D11)⋊C4—41no—
155(C2×D11)⋊C4—41no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158#4318—42no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—41no—
163C2×C11⋊C8—42no—
164C2×C11⋊C8C2×D411yescharacteristic
165C2×C11⋊C8C2×D411yescharacteristic
166C2×C11⋊C8C2×D411yescharacteristic
167C2×C11⋊C8C2×D411yescharacteristic
168#3167—111no—
169#3078D1111yescharacteristic, complemented
170#3037—111no—
171C2×C8×Q8—111no—
172#1680—112no—
173#1678—112no—
174#1672—112no—
175#1666—112no—
176#1566—111no—
177#1550—111no—
178#1547—111no—
179C23×C11#12111yescharacteristic
180C22×D11—41no—
181Q8×C11—22no—
182Q8×C11—24no—
183Q8×C11—41no—
184Q8×C11—41no—
185Q8×C11—81no—
186Q8×C11C2×SD1614yes—
187C2×C4×C11—22no—
188C2×C4×C11—24no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—22no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11#12111yescharacteristic
197C2×C4×C11#12111yescharacteristic
198C2×C4×C11#12111yescharacteristic
199C2×C4×C11C2×SD1612yes—
200C2×C4×C11#13512yes—
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C22⋊D11—82no—
205C2×Dic11—41no—
206D44—41no—
207D44—41no—
208D44—41no—
209D44—41no—
210D44—81no—
211C4×D11—82no—
212Dic22—41no—
213Dic22—41no—
214C8×C11—42no—
215C11⋊C8—21no—
216C11⋊C8—21no—
217C11⋊C8—21no—
218C11⋊C8—42no—
219C11⋊C8—42no—
220C11⋊C8#13712yescomplemented
221C2×#137—221no—
222#533C2×D1111yescharacteristic
223#532—111no—
224C2×C4×Q8C2×D1111yescharacteristic
225#498—111no—
226#492—111no—
227#487—111no—
228#486—111no—
229#479—22no—
230#477C2×D1112yes—
231#475C2×D1112yes—
232#465—221no—
233#465—221no—
234#464—222no—
235#462—112no—
236#460—112no—
237C8×Q8—112no—
238C8×Q8—112no—
239C8×Q8—221no—
240C8×Q8—221no—
241C4×SD16—221no—
242C4×SD16—221no—
243#428—21no—
244#423—111no—
245#423C2×D1111yescharacteristic
246C2×C4⋊C8—111no—
247C2×C4⋊C8—221no—
248#419—21no—
249#417—221no—
250C2×C4×C8—111no—
251C2×C4×C8—221no—
252#334—112no—
253#334—112no—
254#333—112no—
255#332—112no—
256#332—112no—
257#331—112no—
258C22×C11—21no—
259C22×C11—21no—
260C22×C11#46512yes—
261C22×C11C2×#12111yescharacteristic
262C2×D11—81no—
263C2×D11—81no—
264C2×D11—81no—
265C4×C11—21no—
266C4×C11—24no—
267C4×C11—21no—
268C4×C11—21no—
269C4×C11—42no—
270C4×C11—81no—
271C4×C11—81no—
272C4×C11#46512yes—
273C4×C11C22×SD1611yescharacteristic
274C4×C11C2×#13511yescharacteristic
275C4×C11C2×#13711yescharacteristic
276C4×C11#57511yescharacteristic
277Dic11—81no—
278C2×#41—221no—
279C22×Q8C22⋊D1111yescharacteristic
280#137—444no—
281C2×Q16—222no—
282C2×SD16—221no—
283C2×SD16—221no—
284C2×SD16—222no—
285C2×M16—21no—
286C2×M16—221no—
287C22×C8—111no—
288C22×C8—111no—
289C22×C8—221no—
290C4⋊Q8—111no—
291C4⋊Q8C22×D1111yescharacteristic
292C4⋊Q8C22×D1111yescharacteristic
293#127—111no—
294#125—21no—
295#124—221no—
296C22⋊Q8—21no—
297C22⋊Q8—21no—
298#121—221no—
299#121—221no—
300C4×Q8—21no—
301C4×Q8—21no—
302C4×Q8—21no—
303C4×Q8—21no—
304C4×Q8C22⋊D1112yes—
305C4×Q8C22×D1112yes—
306C4×D4—221no—
307C4×D4—221no—
308#117—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4C22⋊D1111yescharacteristic
311C2×C42—21no—
312C2×C42C22×D1111yescharacteristic
313#107—22no—
314#106—22no—
315#106—221no—
316#106—221no—
317C4⋊C8—21no—
318C4⋊C8—112no—
319C4⋊C8—112no—
320C4⋊C8—222no—
321C4⋊C8—222no—
322C4⋊C8—221no—
323C4⋊C8—221no—
324C4⋊C8C22×D1112yes—
325#103—22no—
326#103—22no—
327#103—221no—
328#103—221no—
329#103—222no—
330#102—221no—
331#102—221no—
332#102—222no—
333C4×C8—111no—
334C4×C8—111no—
335C4×C8—111no—
336C4×C8—111no—
337C4×C8—222no—
338C4×C8—222no—
339C2×C11—22no—
340C2×C11#303711yescharacteristic
341C2×C11C2×#46511yescharacteristic
342C2×C11#306711yescharacteristic
343D11—161no—
344#41—442no—
345#41—442no—
346C2×Q8—21no—
347C2×Q8—22no—
348C2×Q8—21no—
349C2×Q8—21no—
350C2×Q8—221no—
351C2×Q8#432514yescomplemented
352C2×Q8C2×C22⋊D1112yes—
353C2×D4—221no—
354C2×D4—221no—
355C2×D4—221no—
356C2×D4—441no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—441no—
360C22×C4D4×D1111yescharacteristic
361C22×C4#434111yescharacteristic
362C22×C4C2×C22⋊D1111yescharacteristic
363Q16—444no—
364SD16—442no—
365SD16—442no—
366SD16—444no—
367M16—42no—
368M16—442no—
369C2×C8—22no—
370C2×C8—111no—
371C2×C8—111no—
372C2×C8—111no—
373C2×C8—111no—
374C2×C8—222no—
375C2×C8—222no—
376C2×C8—222no—
377C2×C8—441no—
378C2×C8—442no—
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4—221no—
389C4⋊C4—221no—
390C4⋊C4C2×C22⋊D1112yes—
391C22⋊C4—41no—
392C22⋊C4—441no—
393C22⋊C4—441no—
394C42—22no—
395C42—22no—
396C42—41no—
397C42D4×D1111yescharacteristic
398C42#434111yescharacteristic
399C42C2×C22⋊D1111yescharacteristic
400C42C23×D1111yescharacteristic
401C11#1926011yescharacteristic, complemented, Sylow
402C23—441no—
403C23#6699211yescharacteristic
404Q8—22no—
405Q8—24no—
406Q8—41no—
407Q8—41no—
408Q8—81no—
409Q8—441no—
410Q8—441no—
411Q8C2×#432514yes—
412D4—441no—
413D4—441no—
414D4—441no—
415D4—441no—
416D4—881no—
417D4—882no—
418C2×C4—22no—
419C2×C4—24no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—22no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—441no—
428C2×C4—882no—
429C2×C4#6699211yescharacteristic
430C2×C4#6699211yescharacteristic
431C2×C4#6699211yescharacteristic
432C2×C4C2×#432512yes—
433C2×C4#6700312yes—
434C2×C4C2×D4×D1111yescharacteristic
435C2×C4C2×#434111yescharacteristic
436C2×C4C22×C22⋊D1111yescharacteristic
437C8—42no—
438C8—112no—
439C8—221no—
440C8—221no—
441C8—221no—
442C8—442no—
443C8—442no—
444C22—21no—
445C22—21no—
446C22—881no—
447C22—881no—
448C22—881no—
449C22#1062266112yes—
450C22C2×#6699211yescharacteristic
451C4—21no—
452C4—21no—
453C4—21no—
454C4—24no—
455C4—42no—
456C4—81no—
457C4—81no—
458C4—881no—
459C4#1062266112yes—
460C4D11×#13711yescharacteristic
461C4#1062330811yescharacteristic
462C4C22×#432511yescharacteristic
463C4C2×#6700311yescharacteristic
464C2—22no—
465C2—1761no—
466C2#1307808511yescharacteristic
467C2C2×#1062266111yescharacteristic
468C2#1307833311yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3078C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#3078D11
hypocenterC11#19260
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3078

Complements

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

NH ≅ G/Ntype
3. C2×Q8×C11⋊C8C2semidirect
4. #13068044C2semidirect
5. #13068034C2semidirect
6. #13068000C2semidirect
7. #13067966C2semidirect
8. #13067371C2semidirect
9. #13067306C2semidirect
11. C11×#3078C2semidirect
115. C2×Q8×C11SD16semidirect
169. #3078D11semidirect
220. C11⋊C8#137semidirect
351. C2×Q8#4325semidirect
401. C11#19260semidirect

Maximal subgroups

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

subgroupindex
#130791762
#130780882
C2×Q8×C11⋊C82
#130680442
#130680342
#130680002
#130679662
#130673712
#130673062
#130672942
C11×#30782
#1926011