Finite Group Databasebeta

← #14908034

Subgroups — #14908034

Order 2816.

718 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622807C212yesmaximal, complemented
2C4×#66957C211yesmaximal, characteristic, complemented
3#13070675C212yesmaximal, complemented
4#13070668C212yesmaximal, complemented
5#13070663C211yesmaximal, characteristic, complemented
6#13070658C211yesmaximal, characteristic, complemented
7#13070653C211yesmaximal, characteristic, complemented
8#13070648C211yesmaximal, characteristic, complemented
9C2×C4⋊(C11⋊C16)C211yesmaximal, characteristic, complemented
10#13070323C212yesmaximal, complemented
11C11×#3147C211yesmaximal, characteristic, complemented
12C2×C11×#135—21no—
13C2×C11×#135C2212yes—
14C11×#532—21no—
15C2×#66957C2211yescharacteristic
16C4×#4339—21no—
17C11×#495—21no—
18C11×#495C2212yes—
19C11×#494C2211yescharacteristic
20C11×#493C2211yescharacteristic
21C11×#492—21no—
22C2×C4×C8×C11C2211yescharacteristic
23#10622807—28no—
24C2×#66893C2212yes—
25C2×#66892C2212yes—
26C2×#66891C2212yes—
27C2×#66890C2212yes—
28#10622726—21no—
29#10622719C2211yescharacteristic
30C22×C11⋊C16C2212yes—
31C4×Dic44C2211yescharacteristic
32C4×Dic44C2211yescharacteristic
33C4×D88C2211yescharacteristic
34C4×D88C2211yescharacteristic
35C4×#4314—21no—
36C4×#4314—21no—
37#10622202C2212yes—
38#10622202C2212yes—
39#10622200C2212yes—
40#10622200C2212yes—
41C4⋊(C11⋊C16)C2211yescharacteristic
42C4⋊(C11⋊C16)C2211yescharacteristic
43C4⋊(C11⋊C16)C2212yes—
44C2×C11×#41—22no—
45C2×#4339—21no—
46C11×#135—24no—
47C11×#135—24no—
48C11×#135—44no—
49C2×C11×Q16—21no—
50C2×C11×Q16C2312yes—
51C2×C11×SD16—22no—
52C2×C11×SD16—22no—
53C2×C11×D8—21no—
54C2×C11×D8C2312yes—
55C22×C8×C11D411yescharacteristic
56C22×C8×C11C2311yescharacteristic
57C11×C4⋊Q8—21no—
58C11×#127—21no—
59C11×#124—22no—
60C11×#121—41no—
61C11×#121—41no—
62C4×D4×C11—41no—
63C4×D4×C11—41no—
64C2×C42×C11D411yescharacteristic
65C4×C22⋊D11—41no—
66C4×C22⋊D11—41no—
67#66979—21no—
68C2×Dic44C2311yescharacteristic
69#66957—22no—
70#66957D414yescomplemented
71C2×D88C2311yescharacteristic
72C2×#4314—21no—
73C4×D44—21no—
74C4×D44—21no—
75#66925—41no—
76C42×D11—41no—
77C4×Dic22—21no—
78C4×Dic22—21no—
79C4×C8×C11D411yescharacteristic
80C4×C8×C11D411yescharacteristic
81C4×C8×C11C2311yescharacteristic
82C4×C8×C11C2311yescharacteristic
83#66893—24no—
84#66892—24no—
85#66891—24no—
86#66890—24no—
87#66885—21no—
88#66885—21no—
89#66882C2311yescharacteristic
90#66882C2311yescharacteristic
91#66881—21no—
92#66880—21no—
93#66880—21no—
94C2×C11⋊C16—24no—
95C2×C11⋊C16C2312yes—
96C2×C11⋊C16C2312yes—
97#33579—111nomaximal, Sylow
98C11×#41—44no—
99C11×#41—44no—
100C2×Q8×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11—42no—
103C2×D4×C11—41no—
104C2×D4×C11—41no—
105C22×C4×C11—42no—
106C22×C4×C11D811yescharacteristic
107C22×C4×C11D811yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C2×C22⋊D11—41no—
110#4339—24no—
111#4339—42no—
112C2×D44—21no—
113C2×C4×D11—41no—
114C2×C4×D11—41no—
115C2×C4×D11—41no—
116C2×Dic22—21no—
117C11×Q16—22no—
118C11×Q16—22no—
119C11×Q16—42no—
120C11×SD16—44no—
121C11×SD16—44no—
122C11×D8—22no—
123C11×D8—22no—
124C11×D8—42no—
125C2×C8×C11—22no—
126C2×C8×C11C2×D412yes—
127C2×C8×C11C2×D411yescharacteristic
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2×D411yescharacteristic
130C2×C8×C11#4112yes—
131C2×C8×C11C2411yescharacteristic
132C11×C4⋊C4—41no—
133C11×C4⋊C4—41no—
134C11×C22⋊C4—42no—
135C11×C22⋊C4—42no—
136C42×C11D811yescharacteristic
137C42×C11D811yescharacteristic
138C42×C11C2×D411yescharacteristic
139C42×C11C2×D411yescharacteristic
140C22⋊Dic11—41no—
141(C2×D11)⋊C4—41no—
142(C2×D11)⋊C4—41no—
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145Dic11⋊C4—41no—
146Dic11⋊C4—41no—
147C4×Dic11—41no—
148C4×Dic11—41no—
149C4×Dic11—41no—
150Dic44—21no—
151Dic44C2×D412yes—
152D88—21no—
153D88C2×D412yes—
154#4314—24no—
155C11⋊C16—22no—
156C11⋊C16—22no—
157C2×#508—112no—
158#3147D1111yescharacteristic, complemented
159C4×#135—111no—
160#2211—112no—
161#2210—112no—
162#2209—111no—
163#2208—111no—
164#2207—111no—
165#2206—111no—
166C2×C4⋊C16—111no—
167#2138—112no—
168C23×C11—42no—
169C23×C11C2×D811yescharacteristic
170C22×D11—41no—
171Q8×C11—42no—
172Q8×C11—42no—
173D4×C11—42no—
174D4×C11—42no—
175D4×C11—82no—
176D4×C11—84no—
177D4×C11—82no—
178C2×C4×C11—22no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—84no—
182C2×C4×C11#12112yes—
183C2×C4×C11C2×D811yescharacteristic
184C2×C4×C11C2×D811yescharacteristic
185C2×C4×C11C2×D811yescharacteristic
186C2×C4×C11C2×D811yescharacteristic
187C2×C4×C11C2×D811yescharacteristic
188C2×C4×C11AGL(1,ℤ/8)12yes—
189C2×C4×C11C22×D411yescharacteristic
190C22⋊D11—44no—
191C2×Dic11—41no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194D44—22no—
195D44—41no—
196C4×D11—44no—
197C4×D11—82no—
198C4×D11—82no—
199Dic22—22no—
200Dic22—41no—
201C8×C11—21no—
202C8×C11—21no—
203C8×C11#12112yes—
204C8×C11C22×D411yescharacteristic
205C8×C11C2×#4111yescharacteristic
206C2×#135—21no—
207C2×#135—111no—
208C2×#135C2×D1112yes—
209#532—21no—
210C4×#41—221no—
211#508—228no—
212C2×Q32—112no—
213C2×SD32—112no—
214C2×SD32—112no—
215C2×D16—112no—
216C22×C16—112no—
217#495—21no—
218#495C2×D1112yes—
219#494C2×D1111yescharacteristic
220#493C2×D1111yescharacteristic
221#492—21no—
222C4×Q16—111no—
223C4×Q16—111no—
224C4×SD16—221no—
225C4×SD16—221no—
226C4×D8—111no—
227C4×D8—111no—
228#427—111no—
229#416—221no—
230C2×C4×C8C2×D1111yescharacteristic
231C4⋊C16—111no—
232C4⋊C16—111no—
233C4⋊C16—112no—
234#358—112no—
235#358—112no—
236#357—112no—
237#357—112no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—82no—
241C22×C11—82no—
242C22×C11—82no—
243C22×C11#45912yes—
244C22×C11C22×D811yescharacteristic
245C2×D11—42no—
246C2×D11—81no—
247C2×D11—81no—
248C4×C11—21no—
249C4×C11—21no—
250C4×C11—21no—
251C4×C11—82no—
252C4×C11#45912yes—
253C4×C11#50812yescomplemented
254C4×C11C2×#12111yescharacteristic
255C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
256Dic11—42no—
257Dic11—81no—
258Dic11—81no—
259C2×#41—22no—
260C2×#41—221no—
261#135—24no—
262#135—24no—
263#135—44no—
264#135—114no—
265#135—222no—
266C2×Q16—21no—
267C2×Q16—111no—
268C2×Q16C22×D1112yes—
269C2×SD16—22no—
270C2×SD16—22no—
271C2×SD16—221no—
272C2×D8—21no—
273C2×D8—111no—
274C2×D8C22×D1112yes—
275C22×C8C22⋊D1111yescharacteristic
276C22×C8C22×D1111yescharacteristic
277C4⋊Q8—21no—
278#127—21no—
279#124—22no—
280#121—41no—
281#121—41no—
282C4×Q8—221no—
283C4×Q8—221no—
284C4×D4—41no—
285C4×D4—41no—
286C4×D4—221no—
287C4×D4—221no—
288C4×D4—441no—
289C4×D4—441no—
290#117—221no—
291#117—441no—
292C2×C42—441no—
293C2×C42C22⋊D1111yescharacteristic
294Q32—224no—
295SD32—224no—
296SD32—224no—
297D16—224no—
298C2×C16—112no—
299C2×C16—112no—
300C2×C16—224no—
301#107—111no—
302#107—111no—
303#106—221no—
304#103—221no—
305#103—221no—
306#102—221no—
307#102—221no—
308C4×C8C22⋊D1111yescharacteristic
309C4×C8C22⋊D1111yescharacteristic
310C4×C8C22×D1111yescharacteristic
311C4×C8C22×D1111yescharacteristic
312C2×C11—22no—
313C2×C11—162no—
314C2×C11C2×#45911yescharacteristic
315C2×C11C2×#50811yescharacteristic
316C2×C11#341411yescharacteristic
317D11—82no—
318#41—44no—
319#41—44no—
320#41—224no—
321#41—442no—
322C2×Q8—22no—
323C2×Q8—221no—
324C2×D4—22no—
325C2×D4—42no—
326C2×D4—41no—
327C2×D4—41no—
328C2×D4—221no—
329C2×D4—441no—
330C22×C4—42no—
331C22×C4—441no—
332C22×C4—441no—
333C22×C4—441no—
334C22×C4#432311yescharacteristic
335C22×C4#432311yescharacteristic
336C22×C4C2×C22⋊D1111yescharacteristic
337Q16—22no—
338Q16—22no—
339Q16—42no—
340Q16—112no—
341Q16—221no—
342SD16—44no—
343SD16—44no—
344SD16—224no—
345D8—22no—
346D8—22no—
347D8—42no—
348D8—112no—
349D8—221no—
350C2×C8—22no—
351C2×C8D4×D1112yes—
352C2×C8#434112yes—
353C2×C8C2×C22⋊D1111yescharacteristic
354C2×C8C2×C22⋊D1111yescharacteristic
355C2×C8C2×C22⋊D1111yescharacteristic
356C2×C8C23×D1111yescharacteristic
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4—221no—
360C4⋊C4—221no—
361C4⋊C4—441no—
362C4⋊C4—441no—
363C22⋊C4—42no—
364C22⋊C4—42no—
365C22⋊C4—441no—
366C22⋊C4—441no—
367C22⋊C4—441no—
368C42—441no—
369C42—441no—
370C42—441no—
371C42#432311yescharacteristic
372C42#432311yescharacteristic
373C42C2×C22⋊D1111yescharacteristic
374C42C2×C22⋊D1111yescharacteristic
375C16—222no—
376C16—222no—
377C11#3357911yescharacteristic, complemented, Sylow
378C23—42no—
379C23—441no—
380C23C2×#432311yescharacteristic
381Q8—42no—
382Q8—42no—
383Q8—222no—
384Q8—441no—
385D4—42no—
386D4—42no—
387D4—82no—
388D4—84no—
389D4—82no—
390D4—222no—
391D4—444no—
392D4—441no—
393C2×C4—22no—
394C2×C4—41no—
395C2×C4—42no—
396C2×C4—84no—
397C2×C4—441no—
398C2×C4—444no—
399C2×C4—441no—
400C2×C4—441no—
401C2×C4—882no—
402C2×C4—882no—
403C2×C4C2×#432311yescharacteristic
404C2×C4C2×#432311yescharacteristic
405C2×C4C2×#432311yescharacteristic
406C2×C4C2×#432311yescharacteristic
407C2×C4C2×#432311yescharacteristic
408C2×C4#6698512yes—
409C2×C4#6699112yes—
410C2×C4C22×C22⋊D1111yescharacteristic
411C8—21no—
412C8—21no—
413C8#6699112yes—
414C8C2×D4×D1111yescharacteristic
415C8C2×#434111yescharacteristic
416C22—21no—
417C22—21no—
418C22—82no—
419C22—82no—
420C22—82no—
421C22—442no—
422C22—881no—
423C22—881no—
424C22#1062268512yes—
425C22C22×#432311yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—82no—
430C4—442no—
431C4—881no—
432C4—881no—
433C4#1062268512yes—
434C4#1062280712yescomplemented
435C4C2×#6698511yescharacteristic
436C4C2×#6699111yescharacteristic
437C2—22no—
438C2—162no—
439C2—882no—
440C2C2×#1062268511yescharacteristic
441C2C2×#1062280711yescharacteristic
442C2#1308175011yescharacteristic
subgroupG/H
centerC2×C4C2×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3147C2
socleC22×C11C22×D8
hypercenter#3147D11
hypocenterC11#33579
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3147

Complements

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

NH ≅ G/Ntype
1. C2×#10622807C2semidirect
2. C4×#66957C2semidirect
3. #13070675C2semidirect
4. #13070668C2semidirect
5. #13070663C2semidirect
6. #13070658C2semidirect
7. #13070653C2semidirect
8. #13070648C2semidirect
9. C2×C4⋊(C11⋊C16)C2semidirect
10. #13070323C2semidirect
11. C11×#3147C2semidirect
70. #66957D4semidirect
158. #3147D11semidirect
253. C4×C11#508semidirect
377. C11#33579semidirect
434. C4#10622807semidirect

Maximal subgroups

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

subgroupindex
C2×#106228072
C4×#669572
#130706752
#130706682
#130706632
#130706582
#130706532
#130706482
C2×C4⋊(C11⋊C16)2
#130703232
C11×#31472
#3357911