Finite Group Databasebeta

← #14909347

Subgroups — #14909347

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#13079195C211yesmaximal, characteristic, complemented
2#13070903C211yesmaximal, characteristic, complemented
3#13070883C211yesmaximal, characteristic, complemented
4#13070859C211yesmaximal, characteristic, complemented
5#13070852C211yesmaximal, characteristic, complemented
6#13070731C212yesmaximal, complemented
7#13070717C212yesmaximal, complemented
8C4×#66892C212yesmaximal, complemented
9C4×#66890C212yesmaximal, complemented
10C4×#66876C211yesmaximal, characteristic, complemented
11C11×#3168C211yesmaximal, characteristic, complemented
12C11×#529—21no—
13#10623008—21no—
14C11×#499C2211yescharacteristic
15C11×#495C2211yescharacteristic
16C11×#488—21no—
17C11×#467C2211yescharacteristic
18C11×#466C2211yescharacteristic
19C11×#465—21no—
20C4×C11×Q16C2211yescharacteristic
21C4×C11×SD16—21no—
22C4×C11×D8C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C2×#66892C2212yes—
25C2×#66890C2212yes—
26#10622728—21no—
27#10622728C2212yes—
28C2×#66876C2212yes—
29#10622308C2211yescharacteristic
30#10622307—21no—
31C4×D88—21no—
32C4×D88C2212yes—
33#10622295C2211yescharacteristic
34#10622202C2212yes—
35#10622200C2212yes—
36#10622129C2212yes—
37#10622129C2212yes—
38#10622128C2212yes—
39#10622127C2212yes—
40#10622099C2211yescharacteristic
41#10622099C2211yescharacteristic
42C4×C11⋊C16C2212yes—
43C2×#4339—41no—
44C2×C11×Q16C2311yescharacteristic
45C2×C11×SD16—21no—
46C2×C11×D8C2311yescharacteristic
47C22×C8×C11D411yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C11×#126—41no—
50C11×#125—21no—
51C11×#124—21no—
52C11×#123—41no—
53C11×C22⋊Q8—21no—
54C11×#121—21no—
55C4×Q8×C11—21no—
56C4×D4×C11—21no—
57C4×D4×C11—41no—
58C11×#117—41no—
59C2×C42×C11D411yescharacteristic
60#66983—22no—
61#66983—41no—
62C2×D88—21no—
63C2×D88C2312yes—
64#66928—41no—
65#66927—21no—
66C4×D44—22no—
67C4×D44—41no—
68#66922—21no—
69C11×#107C2311yescharacteristic
70C11×#107C2311yescharacteristic
71C11×#106—21no—
72C11×#103—21no—
73C11×#103—21no—
74C11×#102—21no—
75C11×#102—21no—
76C4×C8×C11D411yescharacteristic
77C4×C8×C11D411yescharacteristic
78C4×C8×C11C2311yescharacteristic
79C4×C8×C11C2311yescharacteristic
80#66892—24no—
81#66890—24no—
82#66885—22no—
83#66885—22no—
84#66882—21no—
85#66882C2312yes—
86#66876—24no—
87C2×C11⋊C16C2312yes—
88C2×C11⋊C16C2312yes—
89#33737—111nomaximal, Sylow
90C2×Q8×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11D811yescharacteristic
95C22×C4×C11D811yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C2×C22⋊D11—42no—
98#4339—84no—
99C2×D44—22no—
100C2×D44—41no—
101C2×D44—41no—
102C2×C4×D11—42no—
103C2×Dic22—41no—
104C11×Q16—22no—
105C11×SD16—42no—
106C11×D8—22no—
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—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—41no—
123C11×C22⋊C4—41no—
124C42×C11—41no—
125C42×C11D811yescharacteristic
126C42×C11D811yescharacteristic
127C42×C11C2×D411yescharacteristic
128C42×C11C2×D411yescharacteristic
129(C2×D11)⋊C4—42no—
130(C2×D11)⋊C4—42no—
131C4⋊Dic11—22no—
132C4⋊Dic11—41no—
133D88—22no—
134D88—22no—
135D88—42no—
136C11⋊C16—22no—
137C11⋊C16#4114yescomplemented
138#3169—111no—
139#3168D1111yescharacteristic, complemented
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—41no—
150C23×C11C2×D811yescharacteristic
151C22×D11—42no—
152Q8×C11—41no—
153Q8×C11—41no—
154D4×C11—41no—
155D4×C11—41no—
156D4×C11—82no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—22no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—82no—
165C2×C4×C11C2×D811yescharacteristic
166C2×C4×C11C2×D811yescharacteristic
167C2×C4×C11C2×D811yescharacteristic
168C2×C4×C11C2×D811yescharacteristic
169C2×C4×C11C2×D811yescharacteristic
170C2×C4×C11C22×D411yescharacteristic
171C22⋊D11—84no—
172C2×Dic11—42no—
173D44—42no—
174D44—42no—
175D44—82no—
176D44—82no—
177C4×D11—84no—
178Dic22—82no—
179C8×C11—21no—
180C8×C11—21no—
181C8×C11#13512yes—
182C8×C11C2×#4112yes—
183#532—221no—
184#529—21no—
185C2×SD32—112no—
186C2×D16—112no—
187C2×M32—112no—
188#500—111no—
189#499C2×D1111yescharacteristic
190#495C2×D1111yescharacteristic
191#493—111no—
192#488—21no—
193#486—221no—
194#467C2×D1111yescharacteristic
195#466—112no—
196#466—221no—
197#466C2×D1111yescharacteristic
198#465—21no—
199C4×Q16C2×D1111yescharacteristic
200C4×SD16—21no—
201C4×D8—112no—
202C4×D8—221no—
203C4×D8C2×D1111yescharacteristic
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—81no—
218C22×C11—81no—
219C22×C11—81no—
220C22×C11C22×D811yescharacteristic
221C2×D11—82no—
222C2×D11—82no—
223C2×D11—82no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—81no—
229C4×C11—81no—
230C4×C11—81no—
231C4×C11#50912yes—
232C4×C11#53211yescharacteristic
233C4×C11C2×#13511yescharacteristic
234Dic11—82no—
235C2×#41—441no—
236C2×Q16C22×D1111yescharacteristic
237C2×SD16—21no—
238C2×D8—112no—
239C2×D8—221no—
240C2×D8C22×D1111yescharacteristic
241C22×C8C22⋊D1111yescharacteristic
242C22×C8C22×D1111yescharacteristic
243C4⋊Q8—221no—
244#127—221no—
245#126—41no—
246#125—21no—
247#124—21no—
248#124—441no—
249#123—41no—
250C22⋊Q8—21no—
251#121—21no—
252#121—222no—
253#121—441no—
254C4×Q8—21no—
255C4×D4—21no—
256C4×D4—41no—
257C4×D4—222no—
258C4×D4—441no—
259#117—41no—
260C2×C42C22⋊D1111yescharacteristic
261SD32—224no—
262D16—224no—
263M32—224no—
264C2×C16—112no—
265C2×C16—112no—
266#107—112no—
267#107—221no—
268#107C22×D1111yescharacteristic
269#107C22×D1111yescharacteristic
270#106—21no—
271#103—21no—
272#103—21no—
273#102—21no—
274#102—21no—
275#102—222no—
276#102—222no—
277C4×C8C22⋊D1111yescharacteristic
278C4×C8C22⋊D1111yescharacteristic
279C4×C8C22×D1111yescharacteristic
280C4×C8C22×D1111yescharacteristic
281C2×C11—41no—
282C2×C11—161no—
283C2×C11#316911yescharacteristic
284C2×C11C2×#50911yescharacteristic
285C2×C11#341411yescharacteristic
286D11—162no—
287#41—884no—
288C2×Q8—21no—
289C2×Q8—441no—
290C2×D4—21no—
291C2×D4—41no—
292C2×D4—222no—
293C2×D4—442no—
294C2×D4—441no—
295C2×D4—441no—
296C22×C4—41no—
297C22×C4—442no—
298C22×C4#432311yescharacteristic
299C22×C4#432311yescharacteristic
300C22×C4C2×C22⋊D1111yescharacteristic
301Q16—22no—
302SD16—42no—
303D8—22no—
304D8—222no—
305D8—222no—
306D8—442no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8C2×C22⋊D1111yescharacteristic
310C2×C8C2×C22⋊D1111yescharacteristic
311C2×C8C2×C22⋊D1111yescharacteristic
312C2×C8C23×D1111yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—222no—
320C4⋊C4—441no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C22⋊C4—442no—
327C22⋊C4—442no—
328C42—41no—
329C42#432311yescharacteristic
330C42#432311yescharacteristic
331C42C2×C22⋊D1111yescharacteristic
332C42C2×C22⋊D1111yescharacteristic
333C16—114no—
334C16—222no—
335C11#3373711yescharacteristic, complemented, Sylow
336C23—41no—
337C23—442no—
338C23C2×#432311yescharacteristic
339Q8—41no—
340Q8—41no—
341Q8—882no—
342D4—41no—
343D4—41no—
344D4—82no—
345D4—442no—
346D4—442no—
347D4—882no—
348D4—882no—
349D4—884no—
350C2×C4—22no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—82no—
358C2×C4—442no—
359C2×C4—884no—
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—81no—
374C22—81no—
375C22—81no—
376C22—882no—
377C22—882no—
378C22—882no—
379C22C22×#432311yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—81no—
385C4—81no—
386C4—81no—
387C4—882no—
388C4#1062280612yes—
389C4C2×#6700311yescharacteristic
390C4#1062336311yescharacteristic
391C2—41no—
392C2—161no—
393C2—1762no—
394C2#1307919111yescharacteristic
395C2C2×#1062280611yescharacteristic
396C2#1308175011yescharacteristic
subgroupG/H
centerC2×C4C2×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3168C2
socleC22×C11C22×D8
hypercenter#3168D11
hypocenterC11#33737
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3168

Complements

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

NH ≅ G/Ntype
1. #13079195C2semidirect
2. #13070903C2semidirect
3. #13070883C2semidirect
4. #13070859C2semidirect
5. #13070852C2semidirect
6. #13070731C2semidirect
7. #13070717C2semidirect
8. C4×#66892C2semidirect
9. C4×#66890C2semidirect
10. C4×#66876C2semidirect
11. C11×#3168C2semidirect
137. C11⋊C16#41semidirect
139. #3168D11semidirect
335. C11#33737semidirect

Maximal subgroups

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

subgroupindex
#130791952
#130709032
#130708832
#130708592
#130708522
#130707312
#130707172
C4×#668922
C4×#668902
C4×#668762
C11×#31682
#3373711