Finite Group Databasebeta

← #14909351

Subgroups — #14909351

Order 2816.

510 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079186C211yesmaximal, characteristic
2#13070899C211yesmaximal, characteristic, complemented
3#13070885C211yesmaximal, characteristic, complemented
4#13070861C211yesmaximal, characteristic, complemented
5#13070855C211yesmaximal, characteristic, complemented
6#13070731C212yesmaximal
7#13070722C212yesmaximal, complemented
8C4×#66893C212yesmaximal, complemented
9C4×#66892C212yesmaximal, complemented
10C4×#66876C211yesmaximal, characteristic, complemented
11C11×#3170C211yesmaximal, characteristic, complemented
12C11×#533—21no—
13#10623010—21no—
14C11×#500C2211yescharacteristic
15C11×#494C2211yescharacteristic
16C11×#487—21no—
17C11×#467—21no—
18C11×#467C2212yes—
19C4×C11×Q16—21no—
20C4×C11×Q16C2212yes—
21C2×C4×C8×C11C2211yescharacteristic
22C2×#66893C2212yes—
23C2×#66892C2212yes—
24#10622729C2211yescharacteristic
25#10622728C2211yescharacteristic
26#10622727—21no—
27C2×#66876C2212yes—
28C4×Dic44C2211yescharacteristic
29#10622310—21no—
30#10622309C2211yescharacteristic
31C4×D88C2211yescharacteristic
32C4×#4314—21no—
33#10622296C2211yescharacteristic
34#10622202C2212yes—
35#10622202C2212yes—
36#10622130C2212yes—
37#10622129C2212yes—
38#10622128C2212yes—
39#10622127C2212yes—
40#10622099C2211yescharacteristic
41#10622099C2211yescharacteristic
42C4×C11⋊C16C2212yes—
43C2×C11×Q16—21no—
44C2×C11×Q16C2312yes—
45C22×C8×C11D411yescharacteristic
46C22×C8×C11C2311yescharacteristic
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8—21no—
49C11×#125—41no—
50C11×C22⋊Q8—22no—
51C11×C22⋊Q8—41no—
52C4×Q8×C11—22no—
53C4×Q8×C11—41no—
54C11×#117—41no—
55C2×C42×C11D411yescharacteristic
56#66983—21no—
57#66982—41no—
58C4×C22⋊D11—41no—
59#66977—21no—
60C2×Dic44C2311yescharacteristic
61C2×D88C2311yescharacteristic
62C2×#4314—21no—
63#66929—41no—
64#66928—21no—
65C4×D44—21no—
66#66925—41no—
67#66923—21no—
68C4×Dic22—21no—
69C11×#107—21no—
70C11×#107C2312yes—
71C11×#103—22no—
72C11×#103—22no—
73C4×C8×C11D411yescharacteristic
74C4×C8×C11D411yescharacteristic
75C4×C8×C11C2311yescharacteristic
76C4×C8×C11C2311yescharacteristic
77#66893—24no—
78#66892—24no—
79#66885—21no—
80#66885—21no—
81#66882C2311yescharacteristic
82#66882C2311yescharacteristic
83#66881—21no—
84#66880—21no—
85#66880—21no—
86#66876—24no—
87C2×C11⋊C16C2312yes—
88C2×C11⋊C16C2312yes—
89#33738—111nomaximal, Sylow
90C2×Q8×C11—22no—
91C2×Q8×C11—41no—
92C22×C4×C11D811yescharacteristic
93C22×C4×C11D811yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C2×C22⋊D11—41no—
96C2×D44—21no—
97C2×C4×D11—41no—
98C2×Dic22—21no—
99C11×Q16—22no—
100C11×Q16—22no—
101C11×Q16—42no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11C2×D411yescharacteristic
105C2×C8×C11C2×D411yescharacteristic
106C2×C8×C11C2×D411yescharacteristic
107C2×C8×C11C2411yescharacteristic
108C11×C4⋊C4—22no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—42no—
112C11×C4⋊C4—42no—
113C11×C4⋊C4—41no—
114C11×C22⋊C4—42no—
115C42×C11—42no—
116C42×C11D811yescharacteristic
117C42×C11D811yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C22⋊Dic11—41no—
121(C2×D11)⋊C4—41no—
122(C2×D11)⋊C4—41no—
123(C2×D11)⋊C4—41no—
124(C2×D11)⋊C4—41no—
125C4⋊Dic11—21no—
126C4⋊Dic11—21no—
127Dic11⋊C4—41no—
128Dic11⋊C4—41no—
129Dic11⋊C4—41no—
130Dic11⋊C4—41no—
131C4×Dic11—41no—
132Dic44—22no—
133D88—22no—
134#4314—42no—
135C11⋊C16—22no—
136C11⋊C16#4114yes—
137#3170D1111yescharacteristic, complemented
138#3168—111no—
139#2255—111no—
140#2251—111no—
141#2245—111no—
142#2243—111no—
143#2220—112no—
144#2219—112no—
145C4×Q32—112no—
146C4×SD32—112no—
147C4×M32—111no—
148C23×C11C2×D811yescharacteristic
149C22×D11—41no—
150Q8×C11—42no—
151Q8×C11—42no—
152Q8×C11—82no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—22no—
156C2×C4×C11—41no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11C2×D811yescharacteristic
160C2×C4×C11C2×D811yescharacteristic
161C2×C4×C11C2×D811yescharacteristic
162C2×C4×C11C2×D811yescharacteristic
163C2×C4×C11C2×D811yescharacteristic
164C2×C4×C11C22×D411yescharacteristic
165C22⋊D11—82no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169D44—41no—
170D44—41no—
171C4×D11—82no—
172Dic22—41no—
173Dic22—41no—
174C8×C11—21no—
175C8×C11—21no—
176C8×C11#13512yes—
177C8×C11C2×#4112yes—
178#533—21no—
179#529—221no—
180C2×Q32—112no—
181C2×SD32—112no—
182C2×M32—112no—
183#500C2×D1111yescharacteristic
184#499—111no—
185#495—111no—
186#494C2×D1111yescharacteristic
187#488—221no—
188#487—21no—
189#467—21no—
190#467—111no—
191#467C2×D1112yes—
192#466—111no—
193#465—221no—
194C4×Q16—21no—
195C4×Q16—111no—
196C4×Q16C2×D1112yes—
197C4×SD16—221no—
198C4×D8—111no—
199C2×C4×C8C2×D1111yescharacteristic
200#367—112no—
201#366—112no—
202#358—112no—
203#358—112no—
204#358—112no—
205#357—112no—
206#346—111no—
207#346—111no—
208C4×C16—112no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11C22×D811yescharacteristic
213C2×D11—81no—
214C2×D11—81no—
215C2×D11—81no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—82no—
221C4×C11—82no—
222C4×C11#51012yes—
223C4×C11#53211yescharacteristic
224C4×C11C2×#13511yescharacteristic
225Dic11—81no—
226Dic11—81no—
227Dic11—81no—
228C2×Q16—21no—
229C2×Q16—111no—
230C2×Q16C22×D1112yes—
231C2×SD16—221no—
232C2×D8—111no—
233C22×C8C22⋊D1111yescharacteristic
234C22×C8C22×D1111yescharacteristic
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237#126—441no—
238#125—41no—
239#125—221no—
240#124—221no—
241#123—441no—
242C22⋊Q8—22no—
243C22⋊Q8—41no—
244C22⋊Q8—221no—
245#121—221no—
246C4×Q8—22no—
247C4×Q8—41no—
248C4×Q8—221no—
249C4×D4—221no—
250C4×D4—441no—
251#117—41no—
252#117—441no—
253C2×C42C22⋊D1111yescharacteristic
254Q32—224no—
255SD32—224no—
256M32—224no—
257C2×C16—112no—
258C2×C16—112no—
259#107—21no—
260#107—111no—
261#107—111no—
262#107C22×D1112yes—
263#106—221no—
264#103—22no—
265#103—22no—
266#103—221no—
267#103—221no—
268#102—221no—
269#102—221no—
270C4×C8C22⋊D1111yescharacteristic
271C4×C8C22⋊D1111yescharacteristic
272C4×C8C22×D1111yescharacteristic
273C4×C8C22×D1111yescharacteristic
274C2×C11—41no—
275C2×C11#316911yescharacteristic
276C2×C11C2×#51011yescharacteristic
277C2×C11#341411yescharacteristic
278D11—161no—
279C2×Q8—22no—
280C2×Q8—41no—
281C2×Q8—221no—
282C2×D4—221no—
283C2×D4—441no—
284C22×C4—441no—
285C22×C4#432311yescharacteristic
286C22×C4#432311yescharacteristic
287C22×C4C2×C22⋊D1111yescharacteristic
288Q16—22no—
289Q16—22no—
290Q16—42no—
291Q16—222no—
292SD16—442no—
293D8—222no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8C2×C22⋊D1111yescharacteristic
297C2×C8C2×C22⋊D1111yescharacteristic
298C2×C8C2×C22⋊D1111yescharacteristic
299C2×C8C23×D1111yescharacteristic
300C4⋊C4—22no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—41no—
306C4⋊C4—221no—
307C4⋊C4—221no—
308C4⋊C4—441no—
309C4⋊C4—441no—
310C4⋊C4—441no—
311C4⋊C4—441no—
312C22⋊C4—42no—
313C22⋊C4—441no—
314C22⋊C4—441no—
315C22⋊C4—441no—
316C22⋊C4—441no—
317C22⋊C4—441no—
318C42—42no—
319C42—441no—
320C42#432311yescharacteristic
321C42#432311yescharacteristic
322C42C2×C22⋊D1111yescharacteristic
323C42C2×C22⋊D1111yescharacteristic
324C16—114no—
325C16—222no—
326C11#3373811yescharacteristic, complemented, Sylow
327C23—441no—
328C23C2×#432311yescharacteristic
329Q8—42no—
330Q8—42no—
331Q8—82no—
332Q8—441no—
333Q8—441no—
334D4—441no—
335D4—441no—
336D4—882no—
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—441no—
346C2×C4—882no—
347C2×C4C2×#432311yescharacteristic
348C2×C4C2×#432311yescharacteristic
349C2×C4C2×#432311yescharacteristic
350C2×C4C2×#432311yescharacteristic
351C2×C4C2×#432311yescharacteristic
352C2×C4C22×C22⋊D1111yescharacteristic
353C8—21no—
354C8—21no—
355C8#6700312yes—
356C8#41×D1112yes—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—881no—
361C22—881no—
362C22—881no—
363C22C22×#432311yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—82no—
369C4—82no—
370C4—881no—
371C4—881no—
372C4—881no—
373C4#1062279212yes—
374C4C2×#6700311yescharacteristic
375C4#1062336311yescharacteristic
376C2—41no—
377C2—1761no—
378C2#1307919111yescharacteristic
379C2C2×#1062279211yescharacteristic
380C2#1308175011yescharacteristic
subgroupG/H
centerC2×C4C2×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3170C2
socleC22×C11C22×D8
prime radical#10622728C22
hypercenter#3170D11
hypocenterC11#33738
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3170

Complements

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

NH ≅ G/Ntype
2. #13070899C2semidirect
3. #13070885C2semidirect
4. #13070861C2semidirect
5. #13070855C2semidirect
7. #13070722C2semidirect
8. C4×#66893C2semidirect
9. C4×#66892C2semidirect
10. C4×#66876C2semidirect
11. C11×#3170C2semidirect
137. #3170D11semidirect
326. C11#33738semidirect

Maximal subgroups

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

subgroupindex
#130791862
#130708992
#130708852
#130708612
#130708552
#130707312
#130707222
C4×#668932
C4×#668922
C4×#668762
C11×#31702
#3373811