Finite Group Databasebeta

← #14909340

Subgroups — #14909340

Order 2816.

554 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079186C211yesmaximal, characteristic, complemented
2#13070899C211yesmaximal, characteristic, complemented
3#13070880C211yesmaximal, characteristic, complemented
4#13070857C211yesmaximal, characteristic, complemented
5#13070855C211yesmaximal, characteristic, complemented
6#13070727C212yesmaximal, complemented
7#13070717C212yesmaximal, complemented
8C4×#66891C212yesmaximal, complemented
9C4×#66890C212yesmaximal, complemented
10C4×#66876C211yesmaximal, characteristic, complemented
11C11×#3169C211yesmaximal, characteristic, complemented
12C11×#532—21no—
13#10623010—21no—
14C11×#500C2211yescharacteristic
15C11×#493C2211yescharacteristic
16C11×#486—21no—
17C11×#466—21no—
18C11×#466C2212yes—
19C4×C11×D8—21no—
20C4×C11×D8C2212yes—
21C2×C4×C8×C11C2211yescharacteristic
22C2×#66891C2212yes—
23C2×#66890C2212yes—
24#10622729C2211yescharacteristic
25#10622728C2211yescharacteristic
26#10622727—21no—
27C2×#66876C2212yes—
28C4×Dic44C2211yescharacteristic
29#10622310—21no—
30#10622309C2211yescharacteristic
31C4×D88C2211yescharacteristic
32C4×#4314—21no—
33#10622296C2211yescharacteristic
34#10622200C2212yes—
35#10622200C2212yes—
36#10622130C2212yes—
37#10622129C2212yes—
38#10622128C2212yes—
39#10622127C2212yes—
40#10622099C2211yescharacteristic
41#10622099C2211yescharacteristic
42C4×C11⋊C16C2212yes—
43C2×C11×#41—41no—
44C2×C11×D8—21no—
45C2×C11×D8C2312yes—
46C22×C8×C11D411yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C11×C4⋊Q8—21no—
49C11×#127—21no—
50C11×#124—41no—
51C11×#121—22no—
52C11×#121—41no—
53C4×D4×C11—22no—
54C4×D4×C11—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×#102—22no—
72C11×#102—22no—
73C4×C8×C11D411yescharacteristic
74C4×C8×C11D411yescharacteristic
75C4×C8×C11C2311yescharacteristic
76C4×C8×C11C2311yescharacteristic
77#66891—24no—
78#66890—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#33737—111nomaximal, Sylow
90C11×#41—84no—
91C2×Q8×C11—41no—
92C2×D4×C11—22no—
93C2×D4×C11—42no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C22×C4×C11—42no—
97C22×C4×C11D811yescharacteristic
98C22×C4×C11D811yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C2×C22⋊D11—41no—
101C2×D44—21no—
102C2×C4×D11—41no—
103C2×Dic22—21no—
104C11×D8—22no—
105C11×D8—22no—
106C11×D8—42no—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C2×C8×C11C2×D411yescharacteristic
110C2×C8×C11C2×D411yescharacteristic
111C2×C8×C11C2×D411yescharacteristic
112C2×C8×C11C2411yescharacteristic
113C11×C4⋊C4—22no—
114C11×C4⋊C4—41no—
115C11×C22⋊C4—42no—
116C11×C22⋊C4—42no—
117C42×C11D811yescharacteristic
118C42×C11D811yescharacteristic
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C22⋊Dic11—41no—
122(C2×D11)⋊C4—41no—
123(C2×D11)⋊C4—41no—
124(C2×D11)⋊C4—41no—
125(C2×D11)⋊C4—41no—
126C4⋊Dic11—21no—
127C4⋊Dic11—21no—
128Dic11⋊C4—41no—
129Dic11⋊C4—41no—
130Dic11⋊C4—41no—
131Dic11⋊C4—41no—
132C4×Dic11—41no—
133Dic44—22no—
134D88—22no—
135#4314—42no—
136C11⋊C16—22no—
137C11⋊C16#4114yescomplemented
138#3169D1111yescharacteristic, complemented
139#3168—111no—
140#2255—111no—
141#2250—111no—
142#2244—111no—
143#2243—111no—
144#2220—112no—
145#2218—112no—
146C4×SD32—112no—
147C4×D16—112no—
148C4×M32—111no—
149C23×C11—42no—
150C23×C11C2×D811yescharacteristic
151C22×D11—41no—
152Q8×C11—82no—
153D4×C11—42no—
154D4×C11—42no—
155D4×C11—82no—
156D4×C11—82no—
157D4×C11—84no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—22no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11—84no—
164C2×C4×C11C2×D811yescharacteristic
165C2×C4×C11C2×D811yescharacteristic
166C2×C4×C11C2×D811yescharacteristic
167C2×C4×C11C2×D811yescharacteristic
168C2×C4×C11C2×D811yescharacteristic
169C2×C4×C11C22×D411yescharacteristic
170C22⋊D11—82no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174D44—41no—
175D44—41no—
176C4×D11—82no—
177Dic22—41no—
178Dic22—41no—
179C8×C11—21no—
180C8×C11—21no—
181C8×C11#13512yes—
182C8×C11C2×#4112yes—
183#532—21no—
184#529—221no—
185C2×SD32—112no—
186C2×D16—112no—
187C2×M32—112no—
188#500C2×D1111yescharacteristic
189#499—111no—
190#495—111no—
191#493C2×D1111yescharacteristic
192#488—221no—
193#486—21no—
194#467—111no—
195#466—21no—
196#466—111no—
197#466C2×D1112yes—
198#465—221no—
199C4×Q16—111no—
200C4×SD16—221no—
201C4×D8—21no—
202C4×D8—111no—
203C4×D8C2×D1112yes—
204C2×C4×C8C2×D1111yescharacteristic
205#367—112no—
206#366—112no—
207#358—112no—
208#357—112no—
209#357—112no—
210#357—112no—
211#346—111no—
212#346—111no—
213C4×C16—112no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—82no—
218C22×C11—82no—
219C22×C11—82no—
220C22×C11C22×D811yescharacteristic
221C2×D11—81no—
222C2×D11—81no—
223C2×D11—81no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—82no—
229C4×C11#50912yes—
230C4×C11#53211yescharacteristic
231C4×C11C2×#13511yescharacteristic
232Dic11—81no—
233Dic11—81no—
234Dic11—81no—
235C2×#41—41no—
236C2×Q16—111no—
237C2×SD16—221no—
238C2×D8—21no—
239C2×D8—111no—
240C2×D8C22×D1112yes—
241C22×C8C22⋊D1111yescharacteristic
242C22×C8C22×D1111yescharacteristic
243C4⋊Q8—21no—
244#127—21no—
245#126—441no—
246#125—221no—
247#124—41no—
248#124—221no—
249#123—441no—
250C22⋊Q8—221no—
251#121—22no—
252#121—41no—
253#121—221no—
254C4×Q8—221no—
255C4×D4—22no—
256C4×D4—41no—
257C4×D4—221no—
258C4×D4—441no—
259#117—441no—
260C2×C42C22⋊D1111yescharacteristic
261SD32—224no—
262D16—224no—
263M32—224no—
264C2×C16—112no—
265C2×C16—112no—
266#107—21no—
267#107—111no—
268#107—111no—
269#107C22×D1112yes—
270#106—221no—
271#103—221no—
272#103—221no—
273#102—22no—
274#102—22no—
275#102—221no—
276#102—221no—
277C4×C8C22⋊D1111yescharacteristic
278C4×C8C22⋊D1111yescharacteristic
279C4×C8C22×D1111yescharacteristic
280C4×C8C22×D1111yescharacteristic
281C2×C11—41no—
282C2×C11—162no—
283C2×C11#316911yescharacteristic
284C2×C11C2×#50911yescharacteristic
285C2×C11#341411yescharacteristic
286D11—161no—
287#41—84no—
288C2×Q8—41no—
289C2×Q8—221no—
290C2×D4—22no—
291C2×D4—42no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—221no—
295C2×D4—441no—
296C22×C4—42no—
297C22×C4—441no—
298C22×C4#432311yescharacteristic
299C22×C4#432311yescharacteristic
300C22×C4C2×C22⋊D1111yescharacteristic
301Q16—222no—
302SD16—442no—
303D8—22no—
304D8—22no—
305D8—42no—
306D8—222no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8C2×C22⋊D1111yescharacteristic
310C2×C8C2×C22⋊D1111yescharacteristic
311C2×C8C2×C22⋊D1111yescharacteristic
312C2×C8C23×D1111yescharacteristic
313C4⋊C4—22no—
314C4⋊C4—41no—
315C4⋊C4—221no—
316C4⋊C4—221no—
317C4⋊C4—441no—
318C4⋊C4—441no—
319C4⋊C4—441no—
320C4⋊C4—441no—
321C22⋊C4—42no—
322C22⋊C4—42no—
323C22⋊C4—441no—
324C22⋊C4—441no—
325C22⋊C4—441no—
326C22⋊C4—441no—
327C22⋊C4—441no—
328C42—441no—
329C42#432311yescharacteristic
330C42#432311yescharacteristic
331C42C2×C22⋊D1111yescharacteristic
332C42C2×C22⋊D1111yescharacteristic
333C16—114no—
334C16—222no—
335C11#3373711yescharacteristic, complemented, Sylow
336C23—42no—
337C23—441no—
338C23C2×#432311yescharacteristic
339Q8—82no—
340Q8—441no—
341Q8—441no—
342D4—42no—
343D4—42no—
344D4—82no—
345D4—82no—
346D4—84no—
347D4—441no—
348D4—441no—
349D4—882no—
350C2×C4—22no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—84no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—882no—
360C2×C4C2×#432311yescharacteristic
361C2×C4C2×#432311yescharacteristic
362C2×C4C2×#432311yescharacteristic
363C2×C4C2×#432311yescharacteristic
364C2×C4C2×#432311yescharacteristic
365C2×C4C22×C22⋊D1111yescharacteristic
366C8—21no—
367C8—21no—
368C8#6700312yes—
369C8#41×D1112yes—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—82no—
374C22—82no—
375C22—82no—
376C22—881no—
377C22—881no—
378C22—881no—
379C22C22×#432311yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—82no—
385C4—881no—
386C4—881no—
387C4—881no—
388C4#1062276012yes—
389C4C2×#6700311yescharacteristic
390C4#1062336311yescharacteristic
391C2—41no—
392C2—162no—
393C2—1761no—
394C2#1307919111yescharacteristic
395C2C2×#1062276011yescharacteristic
396C2#1308175011yescharacteristic
subgroupG/H
centerC2×C4C2×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3169C2
socleC22×C11C22×D8
hypercenter#3169D11
hypocenterC11#33737
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3169

Complements

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

NH ≅ G/Ntype
1. #13079186C2semidirect
2. #13070899C2semidirect
3. #13070880C2semidirect
4. #13070857C2semidirect
5. #13070855C2semidirect
6. #13070727C2semidirect
7. #13070717C2semidirect
8. C4×#66891C2semidirect
9. C4×#66890C2semidirect
10. C4×#66876C2semidirect
11. C11×#3169C2semidirect
137. C11⋊C16#41semidirect
138. #3169D11semidirect
335. C11#33737semidirect

Maximal subgroups

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

subgroupindex
#130791862
#130708992
#130708802
#130708572
#130708552
#130707272
#130707172
C4×#668912
C4×#668902
C4×#668762
C11×#31692
#3373711