Finite Group Databasebeta

← #14909734

Subgroups — #14909734

Order 2816.

642 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622309C211yesmaximal, characteristic, complemented
2#13070880C212yesmaximal, complemented
3#13070855C212yesmaximal, complemented
4#13070671C214yesmaximal, complemented
5#13070532C212yesmaximal, complemented
6#13070527C212yesmaximal, complemented
7#13070419C211yesmaximal, characteristic, complemented
8C11×#3169C211yesmaximal, characteristic, complemented
9C11×#532—21no—
10C22×Dic44C2211yescharacteristic
11C22×D88C2211yescharacteristic
12C22×#4314—21no—
13C2×#66928—21no—
14C11×#500C2211yescharacteristic, complemented
15C11×#493C2211yescharacteristic, complemented
16C11×#486—21no—
17C11×#466—21no—
18C11×#466C2212yes—
19C4×C11×D8—21no—
20C4×C11×D8C2212yescomplemented
21C2×C4×C8×C11C2211yescharacteristic
22C2×#66891C2214yescomplemented
23C2×#66890C2214yes—
24#10622309—21no—
25#10622309—21no—
26#10622309C2212yes—
27#10622309C2212yes—
28C22⋊(C11⋊C16)C2212yes—
29#10622130C2214yescomplemented
30#10622129C2214yes—
31C4⋊(C11⋊C16)C2212yescomplemented
32#10622099C2212yescomplemented
33C2×C11×#41—41no—
34C22×D44—21no—
35C22×Dic22—21no—
36C2×C11×D8—21no—
37C2×C11×D8C2312yes—
38C22×C8×C11D411yescharacteristic
39C22×C8×C11C2311yescharacteristic
40C11×C4⋊Q8—21no—
41C11×#127—21no—
42C11×#124—41no—
43C11×#121—22no—
44C11×#121—41no—
45C4×D4×C11—22no—
46C4×D4×C11—41no—
47C2×C42×C11D411yescharacteristic
48C2×(C2×D11)⋊C4—41no—
49C2×(C2×D11)⋊C4—41no—
50C2×Dic44—21no—
51C2×Dic44—42no—
52C2×Dic44C2312yes—
53C2×D88—21no—
54C2×D88—42no—
55C2×D88C2312yes—
56C2×#4314—22no—
57C2×#4314—22no—
58C2×#4314—44no—
59#66928—22no—
60#66928—22no—
61#66928—41no—
62#66928—41no—
63C11×#107—21no—
64C11×#107C2312yes—
65C11×#102—22no—
66C11×#102—22no—
67C4×C8×C11D411yescharacteristic
68C4×C8×C11D411yescharacteristic
69C4×C8×C11C2311yescharacteristic
70C4×C8×C11C2311yescharacteristic
71#66891—44no—
72#66890—44no—
73C2×C11⋊C16C2314yes—
74#33779—111nomaximal, Sylow
75C23×D11—41no—
76C11×#41—84no—
77C2×Q8×C11—41no—
78C2×D4×C11—22no—
79C2×D4×C11—42no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C22×C4×C11—42no—
83C22×C4×C11D811yescharacteristic
84C22×C4×C11D811yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×Dic11—41no—
87C2×D44—22no—
88C2×D44—42no—
89C2×D44—42no—
90C2×D44—41no—
91C2×Dic22—22no—
92C2×Dic22—42no—
93C2×Dic22—42no—
94C2×Dic22—41no—
95C11×D8—24no—
96C11×D8—42no—
97C2×C8×C11—22no—
98C2×C8×C11—22no—
99C2×C8×C11C2×D411yescharacteristic
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11C2411yescharacteristic
103C11×C4⋊C4—22no—
104C11×C4⋊C4—41no—
105C11×C22⋊C4—42no—
106C11×C22⋊C4—42no—
107C42×C11D811yescharacteristic
108C42×C11D811yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111(C2×D11)⋊C4—42no—
112(C2×D11)⋊C4—42no—
113(C2×D11)⋊C4—42no—
114(C2×D11)⋊C4—42no—
115Dic44—24no—
116Dic44—42no—
117D88—24no—
118D88—42no—
119#4314—44no—
120#4314—44no—
121C11⋊C16—24no—
122#3169D1111yescharacteristic, complemented
123C2×#495—111no—
124#2250—112no—
125#2243—112no—
126#2210—114no—
127#2185—112no—
128#2184—112no—
129#2163—111no—
130C23×C11—42no—
131C23×C11C2×D811yescharacteristic
132C22×D11—42no—
133C22×D11—82no—
134C22×D11—82no—
135C22×D11—82no—
136Q8×C11—82no—
137D4×C11—42no—
138D4×C11—42no—
139D4×C11—82no—
140D4×C11—82no—
141D4×C11—84no—
142C2×C4×C11—22no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—41no—
146C2×C4×C11—42no—
147C2×C4×C11—84no—
148C2×C4×C11C2×D811yescharacteristic
149C2×C4×C11C2×D811yescharacteristic
150C2×C4×C11C2×D811yescharacteristic
151C2×C4×C11C2×D811yescharacteristic
152C2×C4×C11C2×D811yescharacteristic
153C2×C4×C11C22×D411yescharacteristic
154C2×Dic11—42no—
155C2×Dic11—82no—
156D44—42no—
157D44—42no—
158D44—82no—
159Dic22—42no—
160Dic22—42no—
161Dic22—82no—
162C8×C11—21no—
163C8×C11—21no—
164C8×C11AGL(1,ℤ/8)12yes—
165C8×C11H(5,𝔽2)12yes—
166C22×Q16—111no—
167C22×SD16—221no—
168C22×D8—111no—
169#532—21no—
170C2×#124—221no—
171C2×SD32—114no—
172C2×D16—114no—
173#500C2×D1111yescharacteristic, complemented
174#495—112no—
175#495—112no—
176#495—221no—
177#495—221no—
178#493C2×D1111yescharacteristic, complemented
179#486—21no—
180#466—21no—
181#466C2×D1112yes—
182C4×D8—21no—
183C4×D8C2×D1112yescomplemented
184C2×C4×C8C2×D1111yescharacteristic
185C4⋊C16—112no—
186#358—114no—
187#357—114no—
188C22⋊C16—112no—
189#346—112no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—82no—
193C22×C11—82no—
194C22×C11—82no—
195C22×C11#50912yes—
196C22×C11C22×D811yescharacteristic
197C2×D11—82no—
198C2×D11—82no—
199C2×D11—82no—
200C2×D11—164no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—82no—
207C4×C11#53511yescharacteristic
208C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
209Dic11—82no—
210C2×#41—41no—
211C22×Q8—221no—
212C22×D4—221no—
213C2×Q16—112no—
214C2×Q16—221no—
215C2×Q16—442no—
216C2×SD16—222no—
217C2×SD16—222no—
218C2×SD16—444no—
219C2×D8—21no—
220C2×D8—112no—
221C2×D8—221no—
222C2×D8—442no—
223C2×D8C22×D1112yes—
224C22×C8C22⋊D1111yescharacteristic
225C22×C8C22×D1111yescharacteristic
226C4⋊Q8—21no—
227#127—21no—
228#124—41no—
229#124—222no—
230#124—222no—
231#124—441no—
232#124—441no—
233#121—22no—
234#121—41no—
235C4×D4—22no—
236C4×D4—41no—
237C2×C22⋊C4—441no—
238C2×C22⋊C4—441no—
239C2×C42C22⋊D1111yescharacteristic
240SD32—444no—
241D16—444no—
242C2×C16—114no—
243#107—21no—
244#107C22×D1112yes—
245#102—22no—
246#102—22no—
247C4×C8C22⋊D1111yescharacteristic
248C4×C8C22⋊D1111yescharacteristic
249C4×C8C22×D1111yescharacteristic
250C4×C8C22×D1111yescharacteristic
251C2×C11—22no—
252C2×C11—162no—
253C2×C11#320511yescharacteristic
254C2×C11C2×#50911yescharacteristic
255C2×C11#341411yescharacteristic
256D11—162no—
257C24—441no—
258#41—84no—
259C2×Q8—41no—
260C2×Q8—222no—
261C2×Q8—442no—
262C2×Q8—442no—
263C2×Q8—441no—
264C2×D4—22no—
265C2×D4—42no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—222no—
269C2×D4—442no—
270C2×D4—442no—
271C2×D4—441no—
272C22×C4—42no—
273C22×C4—441no—
274C22×C4#432311yescharacteristic
275C22×C4#432311yescharacteristic
276C22×C4C2×C22⋊D1111yescharacteristic
277Q16—224no—
278Q16—442no—
279SD16—444no—
280SD16—444no—
281D8—24no—
282D8—42no—
283D8—224no—
284D8—442no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8C2×C22⋊D1111yescharacteristic
288C2×C8C2×C22⋊D1111yescharacteristic
289C2×C8C2×C22⋊D1111yescharacteristic
290C2×C8C23×D1111yescharacteristic
291C4⋊C4—22no—
292C4⋊C4—41no—
293C22⋊C4—42no—
294C22⋊C4—42no—
295C22⋊C4—442no—
296C22⋊C4—442no—
297C22⋊C4—442no—
298C22⋊C4—442no—
299C42#432311yescharacteristic
300C42#432311yescharacteristic
301C42C2×C22⋊D1111yescharacteristic
302C42C2×C22⋊D1111yescharacteristic
303C16—224no—
304C11#3377911yescharacteristic, complemented, Sylow
305C23—42no—
306C23—442no—
307C23—882no—
308C23—882no—
309C23—882no—
310C23C2×#432311yescharacteristic
311Q8—82no—
312Q8—442no—
313Q8—442no—
314Q8—882no—
315D4—42no—
316D4—42no—
317D4—82no—
318D4—82no—
319D4—84no—
320D4—442no—
321D4—442no—
322D4—882no—
323C2×C4—22no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—84no—
329C2×C4—442no—
330C2×C4—882no—
331C2×C4C2×#432311yescharacteristic
332C2×C4C2×#432311yescharacteristic
333C2×C4C2×#432311yescharacteristic
334C2×C4C2×#432311yescharacteristic
335C2×C4C2×#432311yescharacteristic
336C2×C4C22×C22⋊D1111yescharacteristic
337C8—21no—
338C8—21no—
339C8#6700212yes—
340C8#6704212yes—
341C22—21no—
342C22—21no—
343C22—82no—
344C22—82no—
345C22—82no—
346C22—882no—
347C22—882no—
348C22—882no—
349C22—1764no—
350C22#1062276012yes—
351C22C22×#432311yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—82no—
358C4—882no—
359C4C2×#6700211yescharacteristic
360C4#1062336111yescharacteristic
361C2—22no—
362C2—162no—
363C2—1762no—
364C2#1307953111yescharacteristic
365C2C2×#1062276011yescharacteristic
366C2#1308175011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3169C2
socleC22×C11C22×D8
hypercenter#3169D11
hypocenterC11#33779
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3169

Complements

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

NH ≅ G/Ntype
1. C2×#10622309C2semidirect
2. #13070880C2semidirect
3. #13070855C2semidirect
4. #13070671C2semidirect
5. #13070532C2semidirect
6. #13070527C2semidirect
7. #13070419C2semidirect
8. C11×#3169C2semidirect
14. C11×#500C22semidirect
15. C11×#493C22semidirect
20. C4×C11×D8C22semidirect
22. C2×#66891C22semidirect
29. #10622130C22semidirect
31. C4⋊(C11⋊C16)C22semidirect
32. #10622099C22semidirect
122. #3169D11semidirect
173. #500C2×D11semidirect
178. #493C2×D11semidirect
183. C4×D8C2×D11semidirect
304. C11#33779semidirect

Maximal subgroups

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

subgroupindex
C2×#106223092
#130708802
#130708552
#130706712
#130705322
#130705272
#130704192
C11×#31692
#3377911