Finite Group Databasebeta

← #14909712

Subgroups — #14909712

Order 2816.

608 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622309C211yesmaximal, characteristic, complemented
2#13070875C212yesmaximal, complemented
3#13070850C212yesmaximal, complemented
4#13070678C212yesmaximal, complemented
5#13070671C212yesmaximal, complemented
6#13070549C211yesmaximal, characteristic, complemented
7#13070544C211yesmaximal, characteristic, complemented
8#13070532C211yesmaximal, characteristic, complemented
9#13070527C211yesmaximal, characteristic
10#13070415C211yesmaximal, characteristic, complemented
11C11×#3168C211yesmaximal, characteristic, complemented
12C11×#529—21no—
13C22×Dic44C2211yescharacteristic
14C22×D88C2211yescharacteristic
15C22×#4314—21no—
16C2×#66928—21no—
17C11×#499C2211yescharacteristic, complemented
18C11×#495C2211yescharacteristic, complemented
19C11×#488—21no—
20C11×#467C2211yescharacteristic
21C11×#466C2211yescharacteristic
22C11×#465—21no—
23C4×C11×Q16C2211yescharacteristic, complemented
24C4×C11×SD16—21no—
25C4×C11×D8C2211yescharacteristic, complemented
26C2×C4×C8×C11C2211yescharacteristic
27C2×#66893C2212yescomplemented
28C2×#66892C2212yes—
29C2×#66891C2212yescomplemented
30C2×#66890C2212yes—
31#10622309—21no—
32#10622309—21no—
33#10622309C2212yes—
34#10622309C2212yes—
35C22⋊(C11⋊C16)C2211yescharacteristic
36C22⋊(C11⋊C16)C2211yescharacteristic
37#10622130C2212yescomplemented
38#10622130C2212yescomplemented
39#10622129C2212yes—
40#10622129C2212yes—
41C4⋊(C11⋊C16)C2212yescomplemented
42C4×C11⋊C16C2212yescomplemented
43C22×D44—21no—
44C22×Dic22—21no—
45C2×C11×Q16C2311yescharacteristic
46C2×C11×SD16—21no—
47C2×C11×D8C2311yescharacteristic
48C22×C8×C11D411yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C11×#126—41no—
51C11×#125—21no—
52C11×#124—21no—
53C11×#123—41no—
54C11×C22⋊Q8—21no—
55C11×#121—21no—
56C4×Q8×C11—21no—
57C4×D4×C11—21no—
58C4×D4×C11—41no—
59C11×#117—41no—
60C2×C42×C11D411yescharacteristic
61C2×(C2×D11)⋊C4—41no—
62C2×(C2×D11)⋊C4—41no—
63C2×Dic44—21no—
64C2×Dic44—42no—
65C2×Dic44C2312yes—
66C2×D88—21no—
67C2×D88—42no—
68C2×D88C2312yes—
69C2×#4314—22no—
70C2×#4314—22no—
71C2×#4314—44no—
72#66928—22no—
73#66928—22no—
74#66928—41no—
75#66928—41no—
76C11×#107C2311yescharacteristic
77C11×#107C2311yescharacteristic
78C11×#106—21no—
79C11×#103—21no—
80C11×#103—21no—
81C11×#102—21no—
82C11×#102—21no—
83C4×C8×C11D411yescharacteristic
84C4×C8×C11D411yescharacteristic
85C4×C8×C11C2311yescharacteristic
86C4×C8×C11C2311yescharacteristic
87#66893—42no—
88#66892—42no—
89#66891—42no—
90#66890—42no—
91C2×C11⋊C16C2312yes—
92C2×C11⋊C16C2312yes—
93#33777—111nomaximal, Sylow
94C23×D11—41no—
95C2×Q8×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11D811yescharacteristic
100C22×C4×C11D811yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×Dic11—41no—
103C2×D44—22no—
104C2×D44—42no—
105C2×D44—42no—
106C2×D44—41no—
107C2×Dic22—22no—
108C2×Dic22—42no—
109C2×Dic22—42no—
110C2×Dic22—41no—
111C11×Q16—22no—
112C11×SD16—42no—
113C11×D8—22no—
114C2×C8×C11—22no—
115C2×C8×C11—22no—
116C2×C8×C11C2×D411yescharacteristic
117C2×C8×C11C2×D411yescharacteristic
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11C2411yescharacteristic
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C11×C4⋊C4—41no—
125C11×C4⋊C4—41no—
126C11×C22⋊C4—41no—
127C11×C22⋊C4—41no—
128C11×C22⋊C4—41no—
129C11×C22⋊C4—41no—
130C11×C22⋊C4—41no—
131C42×C11—41no—
132C42×C11D811yescharacteristic
133C42×C11D811yescharacteristic
134C42×C11C2×D411yescharacteristic
135C42×C11C2×D411yescharacteristic
136(C2×D11)⋊C4—42no—
137(C2×D11)⋊C4—42no—
138(C2×D11)⋊C4—42no—
139(C2×D11)⋊C4—42no—
140Dic44—22no—
141Dic44—22no—
142Dic44—42no—
143D88—22no—
144D88—22no—
145D88—42no—
146#4314—44no—
147#4314—44no—
148C11⋊C16—22no—
149C11⋊C16—22no—
150#3168D1111yescharacteristic, complemented
151C2×#495—111no—
152#2249—112no—
153#2242—112no—
154#2211—112no—
155#2210—112no—
156#2188—111no—
157#2187—111no—
158#2185—111no—
159#2184—111no—
160#2162—111no—
161C23×C11—41no—
162C23×C11C2×D811yescharacteristic
163C22×D11—42no—
164C22×D11—82no—
165C22×D11—82no—
166C22×D11—82no—
167Q8×C11—41no—
168Q8×C11—41no—
169D4×C11—41no—
170D4×C11—41no—
171D4×C11—82no—
172C2×C4×C11—22no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—82no—
180C2×C4×C11C2×D811yescharacteristic
181C2×C4×C11C2×D811yescharacteristic
182C2×C4×C11C2×D811yescharacteristic
183C2×C4×C11C2×D811yescharacteristic
184C2×C4×C11C2×D811yescharacteristic
185C2×C4×C11C22×D411yescharacteristic
186C2×Dic11—42no—
187C2×Dic11—82no—
188D44—42no—
189D44—42no—
190D44—82no—
191Dic22—42no—
192Dic22—42no—
193Dic22—82no—
194C8×C11—21no—
195C8×C11—21no—
196C8×C11AGL(1,ℤ/8)12yes—
197C8×C11H(5,𝔽2)12yes—
198C22×Q16—111no—
199C22×SD16—221no—
200C22×D8—111no—
201#529—21no—
202C2×#124—221no—
203C2×Q32—112no—
204C2×SD32—112no—
205C2×SD32—112no—
206C2×D16—112no—
207#499C2×D1111yescharacteristic, complemented
208#495—112no—
209#495—112no—
210#495—221no—
211#495—221no—
212#495C2×D1111yescharacteristic, complemented
213#488—21no—
214#467C2×D1111yescharacteristic
215#466C2×D1111yescharacteristic
216#465—21no—
217C4×Q16C2×D1111yescharacteristic, complemented
218C4×SD16—21no—
219C4×D8C2×D1111yescharacteristic, complemented
220C2×C4×C8C2×D1111yescharacteristic
221C4⋊C16—112no—
222#358—112no—
223#358—112no—
224#357—112no—
225#357—112no—
226C22⋊C16—111no—
227C22⋊C16—111no—
228C4×C16—112no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—81no—
232C22×C11—81no—
233C22×C11—81no—
234C22×C11#50812yes—
235C22×C11C22×D811yescharacteristic
236C2×D11—82no—
237C2×D11—82no—
238C2×D11—82no—
239C2×D11—164no—
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—21no—
243C4×C11—21no—
244C4×C11—21no—
245C4×C11—81no—
246C4×C11—81no—
247C4×C11—81no—
248C4×C11#53511yescharacteristic
249C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
250Dic11—82no—
251C22×Q8—221no—
252C22×D4—221no—
253C2×Q16—112no—
254C2×Q16—221no—
255C2×Q16—442no—
256C2×Q16C22×D1111yescharacteristic
257C2×SD16—21no—
258C2×SD16—222no—
259C2×SD16—222no—
260C2×SD16—444no—
261C2×D8—112no—
262C2×D8—221no—
263C2×D8—442no—
264C2×D8C22×D1111yescharacteristic
265C22×C8C22⋊D1111yescharacteristic
266C22×C8C22×D1111yescharacteristic
267#126—41no—
268#125—21no—
269#124—21no—
270#124—222no—
271#124—222no—
272#124—441no—
273#124—441no—
274#123—41no—
275C22⋊Q8—21no—
276#121—21no—
277C4×Q8—21no—
278C4×D4—21no—
279C4×D4—41no—
280#117—41no—
281C2×C22⋊C4—441no—
282C2×C22⋊C4—441no—
283C2×C42C22⋊D1111yescharacteristic
284Q32—442no—
285SD32—442no—
286SD32—442no—
287D16—442no—
288C2×C16—112no—
289C2×C16—112no—
290#107C22×D1111yescharacteristic
291#107C22×D1111yescharacteristic
292#106—21no—
293#103—21no—
294#103—21no—
295#102—21no—
296#102—21no—
297C4×C8C22⋊D1111yescharacteristic
298C4×C8C22⋊D1111yescharacteristic
299C4×C8C22×D1111yescharacteristic
300C4×C8C22×D1111yescharacteristic
301C2×C11—22no—
302C2×C11—161no—
303C2×C11#320511yescharacteristic
304C2×C11C2×#50811yescharacteristic
305C2×C11#341411yescharacteristic
306D11—162no—
307C24—441no—
308C2×Q8—21no—
309C2×Q8—222no—
310C2×Q8—442no—
311C2×Q8—442no—
312C2×Q8—441no—
313C2×D4—21no—
314C2×D4—41no—
315C2×D4—222no—
316C2×D4—442no—
317C2×D4—442no—
318C2×D4—441no—
319C22×C4—41no—
320C22×C4—441no—
321C22×C4#432311yescharacteristic
322C22×C4#432311yescharacteristic
323C22×C4C2×C22⋊D1111yescharacteristic
324Q16—22no—
325Q16—222no—
326Q16—222no—
327Q16—442no—
328SD16—42no—
329SD16—444no—
330SD16—444no—
331D8—22no—
332D8—222no—
333D8—222no—
334D8—442no—
335C2×C8—22no—
336C2×C8—22no—
337C2×C8C2×C22⋊D1111yescharacteristic
338C2×C8C2×C22⋊D1111yescharacteristic
339C2×C8C2×C22⋊D1111yescharacteristic
340C2×C8C23×D1111yescharacteristic
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—442no—
353C22⋊C4—442no—
354C22⋊C4—442no—
355C22⋊C4—442no—
356C42—41no—
357C42#432311yescharacteristic
358C42#432311yescharacteristic
359C42C2×C22⋊D1111yescharacteristic
360C42C2×C22⋊D1111yescharacteristic
361C16—222no—
362C16—222no—
363C11#3377711yescharacteristic, complemented, Sylow
364C23—41no—
365C23—442no—
366C23—882no—
367C23—882no—
368C23—882no—
369C23C2×#432311yescharacteristic
370Q8—41no—
371Q8—41no—
372Q8—442no—
373Q8—442no—
374Q8—882no—
375D4—41no—
376D4—41no—
377D4—82no—
378D4—442no—
379D4—442no—
380D4—882no—
381C2×C4—22no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—82no—
389C2×C4—442no—
390C2×C4—882no—
391C2×C4C2×#432311yescharacteristic
392C2×C4C2×#432311yescharacteristic
393C2×C4C2×#432311yescharacteristic
394C2×C4C2×#432311yescharacteristic
395C2×C4C2×#432311yescharacteristic
396C2×C4C22×C22⋊D1111yescharacteristic
397C8—21no—
398C8—21no—
399C8#6700212yes—
400C8#6704212yes—
401C22—21no—
402C22—21no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—882no—
407C22—882no—
408C22—882no—
409C22—1764no—
410C22#1062280712yes—
411C22C22×#432311yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—81no—
418C4—81no—
419C4—81no—
420C4—882no—
421C4C2×#6700211yescharacteristic
422C4#1062336111yescharacteristic
423C2—22no—
424C2—161no—
425C2—1762no—
426C2#1307953111yescharacteristic
427C2C2×#1062280711yescharacteristic
428C2#1308175011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3168C2
socleC22×C11C22×D8
prime radical#13070527C2
hypercenter#3168D11
hypocenterC11#33777
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3168

Complements

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

NH ≅ G/Ntype
1. C2×#10622309C2semidirect
2. #13070875C2semidirect
3. #13070850C2semidirect
4. #13070678C2semidirect
5. #13070671C2semidirect
6. #13070549C2semidirect
7. #13070544C2semidirect
8. #13070532C2semidirect
10. #13070415C2semidirect
11. C11×#3168C2semidirect
17. C11×#499C22semidirect
18. C11×#495C22semidirect
23. C4×C11×Q16C22semidirect
25. C4×C11×D8C22semidirect
27. C2×#66893C22semidirect
29. C2×#66891C22semidirect
37. #10622130C22semidirect
38. #10622130C22semidirect
41. C4⋊(C11⋊C16)C22semidirect
42. C4×C11⋊C16C22semidirect
150. #3168D11semidirect
207. #499C2×D11semidirect
212. #495C2×D11semidirect
217. C4×Q16C2×D11semidirect
219. C4×D8C2×D11semidirect
363. C11#33777semidirect

Maximal subgroups

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

subgroupindex
C2×#106223092
#130708752
#130708502
#130706782
#130706712
#130705492
#130705442
#130705322
#130705272
#130704152
C11×#31682
#3377711