Finite Group Databasebeta

← #14739011

Subgroups — #14739011

Order 2816.

728 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079734C211yesmaximal, characteristic, complemented
2C2×#10622632C211yesmaximal, characteristic, complemented
3#13077640C211yesmaximal, characteristic, complemented
4#13068051C214yesmaximal, complemented
5#13068003C214yesmaximal, complemented
6#13067392C211yesmaximal, characteristic, complemented
7#13067289C211yesmaximal, characteristic, complemented
8#13067265C211yesmaximal, characteristic, complemented
9C11×#3036C211yesmaximal, characteristic
10C2×C11×AGL(1,ℤ/8)—21no—
11C11×#532C2211yescharacteristic
12C2×C4×D4×C11C2211yescharacteristic
13C22×#4324—21no—
14C2×#66922C2211yescharacteristic
15C11×#463—22no—
16C11×#461C2212yes—
17C11×#459C2212yes—
18C11×#423C2211yescharacteristic
19C11×#417—21no—
20C2×C22⋊(C11⋊C8)—22no—
21#10622691C2212yescomplemented
22#10622683C2212yescomplemented
23#10622646—22no—
24#10622632—22no—
25#10622632C2214yes—
26D4×C11⋊C8—22no—
27D4×C11⋊C8C2214yes—
28#10622620—22no—
29C2×#66874—21no—
30#10622538C2211yescharacteristic
31#10622538C2211yescharacteristic
32C2×C4⋊(C11⋊C8)C2211yescharacteristic
33#10622185C2212yescomplemented
34#10622182C2212yescomplemented
35#10622120C2214yescomplemented
36#10622117C2214yescomplemented
37C2×C11×#41—21no—
38C22×D4×C11D411yescharacteristic
39C23×C4×C11—21no—
40C22×Dic22—21no—
41C11×AGL(1,ℤ/8)—44no—
42C2×C11×SD16—22no—
43C2×C11×D8—22no—
44C2×C11×M16—21no—
45C11×C4⋊Q8C2311yescharacteristic
46C11×#127C2311yescharacteristic
47C11×#124—21no—
48C11×#121—21no—
49C11×#121—21no—
50C4×D4×C11—21no—
51C4×D4×C11—21no—
52C4×D4×C11—21no—
53C4×D4×C11—21no—
54C4×D4×C11D412yes—
55C4×D4×C11C2312yes—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C22⋊C4—21no—
58C2×C42×C11C2311yescharacteristic
59C2×#4324—24no—
60C2×#4324—44no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—21no—
63C22×C11⋊C8—21no—
64C22×C11⋊C8—24no—
65#66922—21no—
66#66922—21no—
67#66922—21no—
68#66922C2312yes—
69C11×C4⋊C8—21no—
70C11×C4⋊C8C2312yes—
71C11×#103—22no—
72C11×#102—22no—
73#66896—24no—
74C22⋊(C11⋊C8)—21no—
75C22⋊(C11⋊C8)—24no—
76C22⋊(C11⋊C8)D412yes—
77#66874—24no—
78#66871—24no—
79C4⋊(C11⋊C8)—21no—
80C4⋊(C11⋊C8)D412yes—
81C4⋊(C11⋊C8)C2312yes—
82C4⋊(C11⋊C8)C2312yes—
83C4×C11⋊C8—21no—
84C4×C11⋊C8C2312yes—
85#19392—111nomaximal, Sylow
86C24×C11—21no—
87C11×#41—42no—
88C11×#41—42no—
89C2×Q8×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—22no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—41no—
96C2×D4×C11D814yes—
97C2×D4×C11C2×D412yes—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—41no—
102C22×C4×C11—82no—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11#4111yescharacteristic
106C22×Dic11—41no—
107C2×Dic22—22no—
108C2×Dic22—41no—
109C2×Dic22—42no—
110C2×Dic22—42no—
111C11×SD16—44no—
112C11×D8—44no—
113C11×M16—42no—
114C2×C8×C11—22no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4C2×D412yes—
119C11×C22⋊C4—22no—
120C11×C22⋊C4—22no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—41no—
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125C42×C11#4111yescharacteristic
126C42×C11C2411yescharacteristic
127#4324—48no—
128C4⋊Dic11—22no—
129C4⋊Dic11—22no—
130C4⋊Dic11—41no—
131C4⋊Dic11—41no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—42no—
135C2×C11⋊C8—84no—
136C2×C11⋊C8C2×D414yes—
137#3226—111no—
138#3036D1111yescharacteristic
139C2×#461—111no—
140#2972—111no—
141#1681—114no—
142#1673—114no—
143#1571—111no—
144#1546—111no—
145#1540—111no—
146C23×C11—22no—
147C23×C11—24no—
148C23×C11—41no—
149C23×C11—81no—
150C23×C11—81no—
151C23×C11#12111yescharacteristic
152Q8×C11—41no—
153Q8×C11—41no—
154D4×C11—22no—
155D4×C11—24no—
156D4×C11—41no—
157D4×C11—41no—
158D4×C11—42no—
159D4×C11—81no—
160D4×C11—82no—
161D4×C11C2×D814yes—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—41no—
165C2×C4×C11—44no—
166C2×C4×C11—41no—
167C2×C4×C11—82no—
168C2×C4×C11—81no—
169C2×C4×C11—82no—
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11C2×D812yes—
174C2×C4×C11#13512yes—
175C2×C4×C11C22×D411yescharacteristic
176C2×C4×C11C22×D411yescharacteristic
177C2×C4×C11C2×#4111yescharacteristic
178C2×Dic11—42no—
179C2×Dic11—82no—
180Dic22—42no—
181Dic22—42no—
182Dic22—82no—
183C8×C11—42no—
184C11⋊C8—24no—
185C11⋊C8—42no—
186C11⋊C8—42no—
187C2×AGL(1,ℤ/8)—21no—
188C22×SD16—221no—
189#532C2×D1111yescharacteristic
190C2×C4⋊Q8—111no—
191C2×C4×D4C2×D1111yescharacteristic
192#500—112no—
193#486—112no—
194#480—222no—
195#474—222no—
196#463—22no—
197#461—114no—
198#461—222no—
199#461C2×D1112yes—
200#459C2×D1112yes—
201C8×D4—114no—
202C8×D4—222no—
203#431—111no—
204#431—111no—
205#423C2×D1111yescharacteristic
206C2×C4⋊C8—111no—
207#417—21no—
208C2×#103—221no—
209C2×C22⋊C8—222no—
210#335—114no—
211#332—112no—
212#332—114no—
213#331—112no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—24no—
217C22×C11—42no—
218C22×C11—42no—
219C22×C11—84no—
220C22×C11—81no—
221C22×C11—81no—
222C22×C11—81no—
223C22×C11#46612yes—
224C22×C11C2×#12111yescharacteristic
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—42no—
229C4×C11—81no—
230C4×C11#46612yes—
231C4×C11C22×D811yescharacteristic
232C4×C11C2×#13511yescharacteristic
233C4×C11#57712yes—
234Dic11—82no—
235C2×#41—21no—
236C22×Q8—221no—
237C22×D4C22⋊D1111yescharacteristic
238C23×C4—21no—
239AGL(1,ℤ/8)—44no—
240C2×SD16—22no—
241C2×SD16—224no—
242C2×SD16—444no—
243C2×D8—22no—
244C2×M16—21no—
245C22×C8—224no—
246C22×C8—221no—
247C4⋊Q8—112no—
248C4⋊Q8—221no—
249C4⋊Q8—221no—
250C4⋊Q8—221no—
251C4⋊Q8C22×D1111yescharacteristic
252#127C22×D1111yescharacteristic
253#124—21no—
254#121—21no—
255#121—21no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4—21no—
259C4×D4—21no—
260C4×D4C22⋊D1112yes—
261C4×D4C22×D1112yes—
262C2×C4⋊C4—221no—
263C2×C4⋊C4—221no—
264C2×C4⋊C4C22⋊D1111yescharacteristic
265C2×C22⋊C4—21no—
266C2×C42C22×D1111yescharacteristic
267#107—224no—
268C4⋊C8—21no—
269C4⋊C8—112no—
270C4⋊C8—112no—
271C4⋊C8—112no—
272C4⋊C8—221no—
273C4⋊C8C22×D1112yes—
274#103—22no—
275#103—224no—
276#102—22no—
277#102—224no—
278C22⋊C8—112no—
279C22⋊C8—224no—
280C22⋊C8—221no—
281C4×C8—112no—
282C4×C8—221no—
283C2×C11—22no—
284C2×C11—44no—
285C2×C11—161no—
286C2×C11#304211yescharacteristic
287C2×C11C2×#46611yescharacteristic
288C2×C11#306911yescharacteristic
289C24—21no—
290#41—42no—
291#41—42no—
292C2×Q8—21no—
293C2×Q8—222no—
294C2×Q8—441no—
295C2×Q8—442no—
296C2×Q8—442no—
297C2×D4—21no—
298C2×D4—22no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—41no—
303C2×D4#432314yes—
304C2×D4C2×C22⋊D1112yes—
305C22×C4—21no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—41no—
309C22×C4—82no—
310C22×C4—441no—
311C22×C4D4×D1111yescharacteristic
312C22×C4#434111yescharacteristic
313C22×C4C2×C22⋊D1111yescharacteristic
314SD16—44no—
315SD16—448no—
316D8—44no—
317M16—42no—
318C2×C8—22no—
319C2×C8—114no—
320C2×C8—222no—
321C2×C8—222no—
322C2×C8—442no—
323C2×C8—884no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—222no—
328C4⋊C4—222no—
329C4⋊C4—441no—
330C4⋊C4—441no—
331C4⋊C4C2×C22⋊D1112yes—
332C22⋊C4—22no—
333C22⋊C4—22no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C42D4×D1111yescharacteristic
337C42#434111yescharacteristic
338C42C2×C22⋊D1111yescharacteristic
339C42C23×D1111yescharacteristic
340C11#1939211yescharacteristic, complemented, Sylow
341C23—22no—
342C23—24no—
343C23—41no—
344C23—81no—
345C23—81no—
346C23#6699211yescharacteristic
347Q8—41no—
348Q8—41no—
349Q8—442no—
350Q8—442no—
351Q8—882no—
352D4—22no—
353D4—24no—
354D4—42no—
355D4—41no—
356D4—41no—
357D4—81no—
358D4—82no—
359D4C2×#432314yes—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—44no—
364C2×C4—41no—
365C2×C4—82no—
366C2×C4—81no—
367C2×C4—82no—
368C2×C4—442no—
369C2×C4—882no—
370C2×C4C2×#432312yes—
371C2×C4#6699211yescharacteristic
372C2×C4#6699211yescharacteristic
373C2×C4#6699211yescharacteristic
374C2×C4#6700312yes—
375C2×C4C2×D4×D1111yescharacteristic
376C2×C4C2×#434111yescharacteristic
377C2×C4C22×C22⋊D1111yescharacteristic
378C8—42no—
379C8—224no—
380C8—442no—
381C8—442no—
382C22—21no—
383C22—21no—
384C22—24no—
385C22—42no—
386C22—42no—
387C22—84no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22#1062265112yes—
392C22C2×#6699211yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—42no—
397C4—81no—
398C4—882no—
399C4#1062265112yes—
400C4#1062330612yes—
401C4C22×#432311yescharacteristic
402C4C2×#6700311yescharacteristic
403C2—22no—
404C2—44no—
405C2—161no—
406C2#1307813011yescharacteristic
407C2C2×#1062265111yescharacteristic
408C2#1307835511yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3036C2
socleC22×C11C2×#121
hypercenter#3036D11
hypocenterC11#19392
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3036

Complements

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

NH ≅ G/Ntype
1. #13079734C2semidirect
2. C2×#10622632C2semidirect
3. #13077640C2semidirect
4. #13068051C2semidirect
5. #13068003C2semidirect
6. #13067392C2semidirect
7. #13067289C2semidirect
8. #13067265C2semidirect
21. #10622691C22semidirect
22. #10622683C22semidirect
33. #10622185C22semidirect
34. #10622182C22semidirect
35. #10622120C22semidirect
36. #10622117C22semidirect
340. C11#19392semidirect

Maximal subgroups

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

subgroupindex
#130797342
C2×#106226322
#130776402
#130680512
#130680032
#130673922
#130672892
#130672652
C11×#30362
#1939211