Finite Group Databasebeta

← #14909823

Subgroups — #14909823

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#13079275C211yesmaximal, characteristic, complemented
2#13070888C211yesmaximal, characteristic, complemented
3#13070871C211yesmaximal, characteristic, complemented
4#13070857C211yesmaximal, characteristic, complemented
5#13070847C211yesmaximal, characteristic, complemented
6#13070675C212yesmaximal, complemented
7#13070653C212yesmaximal, complemented
8#13070556C212yesmaximal, complemented
9#13070545C212yesmaximal, complemented
10#13070423C211yesmaximal, characteristic, complemented
11C11×#3155C211yesmaximal, characteristic
12C2×C11×AGL(1,ℤ/8)—21no—
13C2×C11×#135C2211yescharacteristic
14C22×C11×D8C2211yescharacteristic
15C11×#535—21no—
16#10623049—21no—
17C11×#496—21no—
18C11×#496—21no—
19C11×#495C2211yescharacteristic
20C11×#495C2211yescharacteristic
21C11×#493C2211yescharacteristic
22C11×#493C2211yescharacteristic
23C11×#405C2211yescharacteristic
24C2×#66893C2212yescomplemented
25C2×#66891C2212yes—
26C2×#66891C2212yes—
27C2×#66891C2212yescomplemented
28#10622750—21no—
29#10622729C2212yes—
30#10622329—21no—
31#10622316—21no—
32#10622312C2211yescharacteristic, complemented
33C4×Dic44C2212yescomplemented
34#10622296C2211yescharacteristic, complemented
35#10622202C2212yescomplemented
36#10622200C2212yes—
37#10622200C2212yes—
38#10622200C2212yescomplemented
39C22⋊(C11⋊C16)C2212yes—
40C4⋊(C11⋊C16)C2212yescomplemented
41#10622099C2211yescharacteristic, complemented
42C4×C11⋊C16C2211yescharacteristic, complemented
43C2×C11×#41—21no—
44C22×D4×C11—21no—
45C11×AGL(1,ℤ/8)—44no—
46C11×#135—42no—
47C2×C11×Q16C2311yescharacteristic
48C2×C11×SD16—21no—
49C2×C11×SD16—21no—
50C2×C11×SD16—21no—
51C2×C11×D8—21no—
52C2×C11×D8—21no—
53C2×C11×D8—21no—
54C2×C11×D8—42no—
55C2×C11×D8C2311yescharacteristic
56C2×C11×D8C2311yescharacteristic
57C2×C11×D8C2311yescharacteristic
58C2×C11×M16D411yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C11×#127—21no—
61C11×#127—21no—
62C11×#124—21no—
63C11×#124—21no—
64C11×#121—42no—
65C11×#120—42no—
66C11×#117D411yescharacteristic
67#66977—22no—
68C2×Dic44—21no—
69C2×Dic44C2312yes—
70#66942—42no—
71#66932—42no—
72#66923—21no—
73#66922—21no—
74C4×Dic22—22no—
75C11×#97D411yescharacteristic
76C11×#97D411yescharacteristic
77C4×C8×C11C2311yescharacteristic
78C4×C8×C11C2311yescharacteristic
79#66893—42no—
80#66891—42no—
81#66891—42no—
82#66891—42no—
83#66882C2312yes—
84#66881—21no—
85#66880—22no—
86#66880—22no—
87C2×C11⋊C16C2312yes—
88C2×C11⋊C16C2312yes—
89#33788—111nomaximal, Sylow
90C24×C11—41no—
91C11×#41—42no—
92C11×#41—42no—
93C2×Q8×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—42no—
98C2×D4×C11—42no—
99C2×D4×C11—41no—
100C2×D4×C11—41no—
101C2×D4×C11—42no—
102C2×D4×C11—42no—
103C22×C4×C11—41no—
104C22×C4×C11C2×D411yescharacteristic
105C2×Dic22—22no—
106C11×Q16—22no—
107C11×SD16—42no—
108C11×SD16—42no—
109C11×SD16—42no—
110C11×D8—22no—
111C11×D8—22no—
112C11×D8—22no—
113C11×D8—42no—
114C11×D8—42no—
115C11×D8—42no—
116C11×M16—22no—
117C2×C8×C11—22no—
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11C2×D411yescharacteristic
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11C2411yescharacteristic
122C11×C4⋊C4D812yes—
123C11×C22⋊C4—42no—
124C11×C22⋊C4—42no—
125C11×C22⋊C4D812yes—
126C42×C11C2×D411yescharacteristic
127C42×C11C2×D411yescharacteristic
128C22⋊Dic11—42no—
129C4⋊Dic11—22no—
130C4⋊Dic11—42no—
131Dic11⋊C4—42no—
132Dic11⋊C4—42no—
133Dic11⋊C4—42no—
134C4×Dic11—42no—
135Dic44—22no—
136Dic44—22no—
137Dic44—42no—
138C11⋊C16—22no—
139C11⋊C16—22no—
140#3177—111no—
141#3155D1111yescharacteristic
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×C11—41no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11—82no—
155C23×C11—162no—
156C23×C11C2×D811yescharacteristic
157Q8×C11—41no—
158Q8×C11—41no—
159D4×C11—41no—
160D4×C11—41no—
161D4×C11—41no—
162D4×C11—41no—
163D4×C11—41no—
164D4×C11—41no—
165D4×C11—82no—
166D4×C11—82no—
167D4×C11—162no—
168D4×C11—162no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—41no—
172C2×C4×C11—82no—
173C2×C4×C11C2×D812yes—
174C2×C4×C11C2×D811yescharacteristic
175C2×C4×C11C2×D812yes—
176C2×C4×C11C22×D411yescharacteristic
177C2×Dic11—42no—
178C2×Dic11—42no—
179Dic22—42no—
180Dic22—42no—
181C8×C11—21no—
182C8×C11—21no—
183C8×C11AGL(1,ℤ/8)12yes—
184C8×C11H(5,𝔽2)12yes—
185C2×AGL(1,ℤ/8)—21no—
186C2×#135C2×D1111yescharacteristic
187C22×D8C2×D1111yescharacteristic
188#541—221no—
189#535—21no—
190C2×Q32—112no—
191C2×SD32—112no—
192C2×SD32—112no—
193C2×SD32—112no—
194#499—111no—
195#496—21no—
196#496—21no—
197#495C2×D1111yescharacteristic
198#495C2×D1111yescharacteristic
199#494—111no—
200#493C2×D1111yescharacteristic
201#493C2×D1111yescharacteristic
202#491—221no—
203#470—221no—
204#467—112no—
205#441—221no—
206C4×Q16—112no—
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×C11—82no—
219C22×C11—82no—
220C22×C11—82no—
221C22×C11—81no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11—164no—
225C22×C11C22×D811yescharacteristic
226C4×C11—22no—
227C4×C11—22no—
228C4×C11—21no—
229C4×C11—81no—
230C4×C11#53511yescharacteristic
231C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
232Dic11—82no—
233Dic11—82no—
234C2×#41—21no—
235C22×D4—21no—
236AGL(1,ℤ/8)—44no—
237#135—42no—
238C2×Q16—112no—
239C2×Q16—221no—
240C2×Q16C22×D1111yescharacteristic
241C2×SD16—21no—
242C2×SD16—21no—
243C2×SD16—21no—
244C2×D8—21no—
245C2×D8—21no—
246C2×D8—21no—
247C2×D8—42no—
248C2×D8C22×D1111yescharacteristic
249C2×D8C22×D1111yescharacteristic
250C2×D8C22×D1111yescharacteristic
251C2×M16C22⋊D1111yescharacteristic
252C22×C8C22×D1111yescharacteristic
253C4⋊Q8—221no—
254#127—21no—
255#127—21no—
256#126—442no—
257#125—221no—
258#125—442no—
259#124—21no—
260#124—21no—
261C22⋊Q8—222no—
262#121—42no—
263#120—42no—
264C4×Q8—222no—
265#117C22⋊D1111yescharacteristic
266Q32—442no—
267SD32—442no—
268SD32—442no—
269SD32—442no—
270C2×C16—112no—
271C2×C16—112no—
272#107—112no—
273#106—221no—
274#103—222no—
275#103—222no—
276#97C22⋊D1111yescharacteristic
277#97C22⋊D1111yescharacteristic
278C4×C8C22×D1111yescharacteristic
279C4×C8C22×D1111yescharacteristic
280C2×C11—41no—
281C2×C11—161no—
282C2×C11—161no—
283C2×C11—161no—
284C2×C11#320511yescharacteristic
285C2×C11#341612yes—
286C24—41no—
287#41—42no—
288#41—42no—
289C2×Q8—21no—
290C2×Q8—222no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—42no—
295C2×D4—42no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—42no—
299C2×D4—42no—
300C22×C4—41no—
301C22×C4C2×C22⋊D1111yescharacteristic
302Q16—22no—
303Q16—222no—
304Q16—222no—
305Q16—442no—
306SD16—42no—
307SD16—42no—
308SD16—42no—
309D8—22no—
310D8—22no—
311D8—22no—
312D8—42no—
313D8—42no—
314D8—42no—
315M16—22no—
316C2×C8—22no—
317C2×C8C2×C22⋊D1111yescharacteristic
318C2×C8C2×C22⋊D1111yescharacteristic
319C2×C8C2×C22⋊D1111yescharacteristic
320C2×C8C23×D1111yescharacteristic
321C4⋊C4—222no—
322C4⋊C4—442no—
323C4⋊C4—442no—
324C4⋊C4—442no—
325C4⋊C4—442no—
326C4⋊C4#432312yes—
327C22⋊C4—42no—
328C22⋊C4—42no—
329C22⋊C4—442no—
330C22⋊C4#432312yes—
331C42—442no—
332C42C2×C22⋊D1111yescharacteristic
333C42C2×C22⋊D1111yescharacteristic
334C16—222no—
335C16—222no—
336C11#3378811yescharacteristic, complemented, Sylow
337C23—41no—
338C23—41no—
339C23—41no—
340C23—82no—
341C23—162no—
342C23C2×#432311yescharacteristic
343Q8—41no—
344Q8—41no—
345Q8—442no—
346Q8—442no—
347D4—41no—
348D4—41no—
349D4—41no—
350D4—41no—
351D4—41no—
352D4—41no—
353D4—82no—
354D4—82no—
355D4—162no—
356D4—162no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—41no—
360C2×C4—82no—
361C2×C4—442no—
362C2×C4—442no—
363C2×C4C2×#432312yes—
364C2×C4C2×#432312yes—
365C2×C4C2×#432311yescharacteristic
366C2×C4C22×C22⋊D1111yescharacteristic
367C8—21no—
368C8—21no—
369C8#6698512yes—
370C8#6703712yes—
371C22—22no—
372C22—21no—
373C22—82no—
374C22—82no—
375C22—82no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—164no—
380C22C22×#432311yescharacteristic
381C4—22no—
382C4—22no—
383C4—21no—
384C4—81no—
385C4—882no—
386C4—882no—
387C4C2×#6698511yescharacteristic
388C4#1062333611yescharacteristic
389C2—41no—
390C2—161no—
391C2—161no—
392C2—161no—
393C2#1307953411yescharacteristic
394C2#1308176312yes—
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
Fitting, prime radicalC11×#3155C2
socleC22×C11C22×D8
hypercenter#3155D11
hypocenterC11#33788
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3155

Complements

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

NH ≅ G/Ntype
1. #13079275C2semidirect
2. #13070888C2semidirect
3. #13070871C2semidirect
4. #13070857C2semidirect
5. #13070847C2semidirect
6. #13070675C2semidirect
7. #13070653C2semidirect
8. #13070556C2semidirect
9. #13070545C2semidirect
10. #13070423C2semidirect
24. C2×#66893C22semidirect
27. C2×#66891C22semidirect
32. #10622312C22semidirect
33. C4×Dic44C22semidirect
34. #10622296C22semidirect
35. #10622202C22semidirect
38. #10622200C22semidirect
40. C4⋊(C11⋊C16)C22semidirect
41. #10622099C22semidirect
42. C4×C11⋊C16C22semidirect
336. C11#33788semidirect

Maximal subgroups

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

subgroupindex
#130792752
#130708882
#130708712
#130708572
#130708472
#130706752
#130706532
#130705562
#130705452
#130704232
C11×#31552
#3378811