Finite Group Databasebeta

← #14909817

Subgroups — #14909817

Order 2816.

594 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079102C211yesmaximal, characteristic
2#13070885C211yesmaximal, characteristic, complemented
3#13070873C211yesmaximal, characteristic, complemented
4#13070859C211yesmaximal, characteristic, complemented
5#13070850C211yesmaximal, characteristic, complemented
6#13070678C212yesmaximal, complemented
7#13070656C212yesmaximal, complemented
8#13070554C212yesmaximal, complemented
9#13070544C212yesmaximal, complemented
10#13070423C211yesmaximal, characteristic, complemented
11C11×#3177C211yesmaximal, characteristic, complemented
12C11×#541—21no—
13C2×#66961—21no—
14C2×#66957C2211yescharacteristic
15C22×D88C2211yescharacteristic
16#10623056—21no—
17C11×#499C2211yescharacteristic, complemented
18C11×#494C2211yescharacteristic, complemented
19C11×#491—21no—
20C11×#470—21no—
21C11×#467C2212yes—
22C11×#441—21no—
23C4×C11×Q16C2212yescomplemented
24C11×#405C2211yescharacteristic
25C2×#66893C2212yescomplemented
26C2×#66892C2212yes—
27C2×#66892C2212yes—
28C2×#66892C2212yescomplemented
29#10622325—21no—
30#10622325—21no—
31#10622309C2211yescharacteristic
32#10622309C2211yescharacteristic
33#10622308C2211yescharacteristic
34#10622308C2211yescharacteristic
35C22⋊(C11⋊C16)C2212yes—
36#10622130C2212yescomplemented
37#10622129C2212yes—
38#10622129C2212yes—
39#10622129C2212yescomplemented
40C4⋊(C11⋊C16)C2212yescomplemented
41#10622099C2211yescharacteristic, complemented
42C4×C11⋊C16C2211yescharacteristic, complemented
43C2×#4339—21no—
44C22×D44—21no—
45C2×C11×Q16—21no—
46C2×C11×Q16C2312yes—
47C2×C11×M16D411yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C11×C4⋊Q8—21no—
50C11×#126—42no—
51C11×#125—21no—
52C11×#125—42no—
53C11×C22⋊Q8—22no—
54C4×Q8×C11—22no—
55C11×#117D411yescharacteristic
56#66961—44no—
57C2×Dic44C2311yescharacteristic
58#66957—42no—
59C2×D88—21no—
60C2×D88—21no—
61C2×D88—21no—
62C2×D88—42no—
63C2×D88C2311yescharacteristic
64C2×D88C2311yescharacteristic
65C2×D88C2311yescharacteristic
66C2×#4314—21no—
67C2×#4314—21no—
68C2×#4314—21no—
69#66948—42no—
70#66935—42no—
71#66928—21no—
72#66928—21no—
73#66927—21no—
74#66927—21no—
75C11×#107C2312yes—
76C11×#106—21no—
77C11×#103—22no—
78C11×#103—22no—
79C11×#97D411yescharacteristic
80C11×#97D411yescharacteristic
81C4×C8×C11C2311yescharacteristic
82C4×C8×C11C2311yescharacteristic
83#66893—42no—
84#66892—42no—
85#66892—42no—
86#66892—42no—
87C2×C11⋊C16C2312yes—
88C2×C11⋊C16C2312yes—
89#33788—111nomaximal, Sylow
90C23×D11—41no—
91C2×Q8×C11—22no—
92C22×C4×C11C2×D411yescharacteristic
93C2×C22⋊D11—41no—
94#4339—42no—
95#4339—42no—
96C2×D44—21no—
97C2×D44—21no—
98C2×D44—21no—
99C2×D44—42no—
100C2×D44—42no—
101C2×D44—41no—
102C2×D44—42no—
103C2×D44—42no—
104C2×C4×D11—41no—
105C2×Dic22—21no—
106C11×Q16—22no—
107C11×Q16—22no—
108C11×Q16—42no—
109C11×M16—22no—
110C2×C8×C11—22no—
111C2×C8×C11C2×D411yescharacteristic
112C2×C8×C11C2×D411yescharacteristic
113C2×C8×C11C2×D411yescharacteristic
114C2×C8×C11C2411yescharacteristic
115C11×C4⋊C4—22no—
116C11×C4⋊C4—42no—
117C11×C4⋊C4—42no—
118C11×C4⋊C4—42no—
119C11×C4⋊C4—42no—
120C11×C4⋊C4D812yes—
121C11×C22⋊C4—42no—
122C11×C22⋊C4D812yes—
123C42×C11—42no—
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126(C2×D11)⋊C4—42no—
127(C2×D11)⋊C4—42no—
128Dic44—22no—
129D88—22no—
130D88—22no—
131D88—22no—
132D88—42no—
133D88—42no—
134D88—42no—
135#4314—42no—
136#4314—42no—
137#4314—42no—
138C11⋊C16—22no—
139C11⋊C16—22no—
140#3177D1111yescharacteristic, complemented
141#3155—111no—
142#2251—111no—
143#2248—111no—
144#2244—111no—
145#2242—111no—
146#2211—112no—
147#2207—112no—
148#2189—112no—
149#2187—112no—
150#2164—111no—
151C23×C11C2×D811yescharacteristic
152C22×D11—41no—
153C22×D11—41no—
154C22×D11—41no—
155C22×D11—82no—
156C22×D11—162no—
157Q8×C11—42no—
158Q8×C11—42no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11C2×D812yes—
164C2×C4×C11C2×D812yes—
165C2×C4×C11C2×D811yescharacteristic
166C2×C4×C11C22×D411yescharacteristic
167C22⋊D11—82no—
168C2×Dic11—41no—
169D44—41no—
170D44—41no—
171D44—41no—
172D44—41no—
173D44—41no—
174D44—41no—
175D44—82no—
176D44—162no—
177D44—162no—
178C4×D11—82no—
179Dic22—41no—
180Dic22—41no—
181C8×C11—21no—
182C8×C11—21no—
183C8×C11AGL(1,ℤ/8)12yes—
184C8×C11H(5,𝔽2)12yes—
185C2×AGL(1,ℤ/8)—221no—
186C2×#135—111no—
187C22×D8—111no—
188#541—21no—
189#535—221no—
190C2×Q32—112no—
191C2×SD32—112no—
192C2×SD32—112no—
193C2×SD32—112no—
194#499C2×D1111yescharacteristic, complemented
195#496—221no—
196#496—221no—
197#495—111no—
198#495—111no—
199#494C2×D1111yescharacteristic, complemented
200#493—111no—
201#493—111no—
202#491—21no—
203#470—21no—
204#467C2×D1112yes—
205#441—21no—
206C4×Q16C2×D1112yescomplemented
207#405C2×D1111yescharacteristic
208C4⋊C16—112no—
209#358—112no—
210#357—112no—
211#357—112no—
212#357—112no—
213C22⋊C16—112no—
214#346—111no—
215C4×C16—111no—
216C22×C11—22no—
217C22×C11—21no—
218C22×C11C22×D811yescharacteristic
219C2×D11—82no—
220C2×D11—82no—
221C2×D11—82no—
222C2×D11—81no—
223C2×D11—81no—
224C2×D11—81no—
225C2×D11—164no—
226C4×C11—22no—
227C4×C11—22no—
228C4×C11—21no—
229C4×C11—82no—
230C4×C11—82no—
231C4×C11#53511yescharacteristic
232C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
233Dic11—81no—
234C2×#41—221no—
235C22×D4—221no—
236AGL(1,ℤ/8)—444no—
237#135—442no—
238C2×Q16—21no—
239C2×Q16—111no—
240C2×Q16C22×D1112yes—
241C2×SD16—221no—
242C2×SD16—221no—
243C2×SD16—221no—
244C2×D8—111no—
245C2×D8—111no—
246C2×D8—111no—
247C2×D8—221no—
248C2×D8—221no—
249C2×D8—221no—
250C2×D8—442no—
251C2×M16C22⋊D1111yescharacteristic
252C22×C8C22×D1111yescharacteristic
253C4⋊Q8—21no—
254#127—221no—
255#127—221no—
256#126—42no—
257#125—21no—
258#125—42no—
259#124—221no—
260#124—221no—
261C22⋊Q8—22no—
262#121—442no—
263#120—442no—
264C4×Q8—22no—
265#117C22⋊D1111yescharacteristic
266Q32—442no—
267SD32—442no—
268SD32—442no—
269SD32—442no—
270C2×C16—112no—
271C2×C16—112no—
272#107C22×D1112yes—
273#106—21no—
274#103—22no—
275#103—22no—
276#97C22⋊D1111yescharacteristic
277#97C22⋊D1111yescharacteristic
278C4×C8C22×D1111yescharacteristic
279C4×C8C22×D1111yescharacteristic
280C2×C11—41no—
281C2×C11#320511yescharacteristic
282C2×C11#341612yes—
283D11—161no—
284D11—161no—
285D11—161no—
286C24—441no—
287#41—442no—
288#41—442no—
289C2×Q8—22no—
290C2×Q8—221no—
291C2×D4—221no—
292C2×D4—221no—
293C2×D4—221no—
294C2×D4—442no—
295C2×D4—442no—
296C2×D4—441no—
297C2×D4—441no—
298C2×D4—442no—
299C2×D4—442no—
300C22×C4—441no—
301C22×C4C2×C22⋊D1111yescharacteristic
302Q16—22no—
303Q16—22no—
304Q16—42no—
305Q16—222no—
306SD16—442no—
307SD16—442no—
308SD16—442no—
309D8—222no—
310D8—222no—
311D8—222no—
312D8—442no—
313D8—442no—
314D8—442no—
315M16—22no—
316C2×C8—22no—
317C2×C8C2×C22⋊D1111yescharacteristic
318C2×C8C2×C22⋊D1111yescharacteristic
319C2×C8C2×C22⋊D1111yescharacteristic
320C2×C8C23×D1111yescharacteristic
321C4⋊C4—22no—
322C4⋊C4—42no—
323C4⋊C4—42no—
324C4⋊C4—42no—
325C4⋊C4—42no—
326C4⋊C4#432312yes—
327C22⋊C4—42no—
328C22⋊C4—442no—
329C22⋊C4—442no—
330C22⋊C4#432312yes—
331C42—42no—
332C42C2×C22⋊D1111yescharacteristic
333C42C2×C22⋊D1111yescharacteristic
334C16—222no—
335C16—222no—
336C11#3378811yescharacteristic, complemented, Sylow
337C23—441no—
338C23—441no—
339C23—441no—
340C23—882no—
341C23—1762no—
342C23C2×#432311yescharacteristic
343Q8—42no—
344Q8—42no—
345Q8—441no—
346Q8—441no—
347D4—441no—
348D4—441no—
349D4—441no—
350D4—441no—
351D4—441no—
352D4—441no—
353D4—882no—
354D4—882no—
355D4—1762no—
356D4—1762no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—441no—
362C2×C4—882no—
363C2×C4C2×#432312yes—
364C2×C4C2×#432312yes—
365C2×C4C2×#432311yescharacteristic
366C2×C4C22×C22⋊D1111yescharacteristic
367C8—21no—
368C8—21no—
369C8#6700212yes—
370C8#6704212yes—
371C22—22no—
372C22—21no—
373C22—882no—
374C22—882no—
375C22—882no—
376C22—881no—
377C22—881no—
378C22—881no—
379C22—1764no—
380C22C22×#432311yescharacteristic
381C4—22no—
382C4—22no—
383C4—21no—
384C4—82no—
385C4—82no—
386C4—881no—
387C4C2×#6700211yescharacteristic
388C4#1062336111yescharacteristic
389C2—41no—
390C2—1761no—
391C2—1761no—
392C2—1761no—
393C2#1307953111yescharacteristic
394C2#1308176012yes—
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3177C2
socleC22×C11C22×D8
prime radical#13079102C2
hypercenter#3177D11
hypocenterC11#33788
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3177

Complements

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

NH ≅ G/Ntype
2. #13070885C2semidirect
3. #13070873C2semidirect
4. #13070859C2semidirect
5. #13070850C2semidirect
6. #13070678C2semidirect
7. #13070656C2semidirect
8. #13070554C2semidirect
9. #13070544C2semidirect
10. #13070423C2semidirect
11. C11×#3177C2semidirect
17. C11×#499C22semidirect
18. C11×#494C22semidirect
23. C4×C11×Q16C22semidirect
25. C2×#66893C22semidirect
28. C2×#66892C22semidirect
36. #10622130C22semidirect
39. #10622129C22semidirect
40. C4⋊(C11⋊C16)C22semidirect
41. #10622099C22semidirect
42. C4×C11⋊C16C22semidirect
140. #3177D11semidirect
194. #499C2×D11semidirect
199. #494C2×D11semidirect
206. C4×Q16C2×D11semidirect
336. C11#33788semidirect

Maximal subgroups

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

subgroupindex
#130791022
#130708852
#130708732
#130708592
#130708502
#130706782
#130706562
#130705542
#130705442
#130704232
C11×#31772
#3378811