Finite Group Databasebeta

← #14739064

Subgroups — #14739064

Order 2816.

740 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079534C211yesmaximal, characteristic
2#13078088C211yesmaximal, characteristic, complemented
3#13077697C211yesmaximal, characteristic, complemented
4#13068058C214yesmaximal, complemented
5#13067974C214yesmaximal, complemented
6#13067390C211yesmaximal, characteristic, complemented
7#13067284C211yesmaximal, characteristic, complemented
8#13067266C211yesmaximal, characteristic, complemented
9C2×C11×#460C211yesmaximal, characteristic, complemented
10C22×C11×SD16—21no—
11C2×C11×#127C2211yescharacteristic
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#66995—21no—
14#10623008C2211yescharacteristic
15C11×#460—22no—
16C11×#460C2214yes—
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×#102—21no—
19#10622830—22no—
20#10622686C2212yes—
21#10622685—22no—
22#10622683C2212yes—
23#10622644C2212yescomplemented
24#10622641—22no—
25#10622640C2212yescomplemented
26Q8×C11⋊C8—22no—
27Q8×C11⋊C8C2214yescomplemented
28#10622579—21no—
29#10622538—22no—
30#10622538C2211yescharacteristic
31#10622538C2211yescharacteristic
32#10622537C2211yescharacteristic
33#10622182C2214yes—
34#10622123C2212yescomplemented
35#10622120C2212yescomplemented
36#10622117C2214yescomplemented
37C22×Q8×C11D411yescharacteristic
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C22×D4×C11—21no—
41C2×#4339—21no—
42C2×C11×SD16—24no—
43C2×C11×SD16—44no—
44C22×C8×C11—21no—
45C11×#127—21no—
46C11×#127—21no—
47C11×#127—21no—
48C11×#127C2312yes—
49C4×Q8×C11—21no—
50C4×Q8×C11—21no—
51C4×Q8×C11D412yes—
52C4×Q8×C11C2312yes—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C42×C11—21no—
56C2×C42×C11C2311yescharacteristic
57C2×#4326—22no—
58#66995—44no—
59C2×#4325—22no—
60C2×#4323—24no—
61#66983—21no—
62#66983—21no—
63C2×#4318—21no—
64#66928—21no—
65#66927C2311yescharacteristic
66C4×D44—21no—
67C4×D44—21no—
68#66922C2311yescharacteristic
69C11×C4⋊C8—21no—
70C11×C4⋊C8C2312yes—
71C11×#102—24no—
72#66896—24no—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)D412yes—
75#66874—22no—
76#66873—22no—
77C4⋊(C11⋊C8)—21no—
78C4⋊(C11⋊C8)—24no—
79C4⋊(C11⋊C8)D412yes—
80C4⋊(C11⋊C8)C2312yes—
81C4⋊(C11⋊C8)C2312yes—
82C4×C11⋊C8—21no—
83C4×C11⋊C8—24no—
84C4×C11⋊C8C2312yes—
85#19398—111nomaximal, Sylow
86C24×C11—41no—
87C2×Q8×C11—21no—
88C2×Q8×C11—22no—
89C2×Q8×C11D814yescomplemented
90C2×Q8×C11C2×D412yes—
91C2×D4×C11—22no—
92C2×D4×C11—22no—
93C2×D4×C11—22no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C2×D4×C11—42no—
98C2×D4×C11—42no—
99C2×D4×C11—82no—
100C2×D4×C11—82no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11#4111yescharacteristic
106C2×C22⋊D11—41no—
107#4339—42no—
108#4339—42no—
109C2×D44—21no—
110C2×D44—21no—
111C2×D44—21no—
112C2×C4×D11—41no—
113C2×Dic22—21no—
114C11×SD16—48no—
115C2×C8×C11—22no—
116C2×C8×C11—42no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4C2×D412yes—
121C42×C11—22no—
122C42×C11—22no—
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125C42×C11#4111yescharacteristic
126C42×C11C2411yescharacteristic
127#4326—44no—
128#4325—44no—
129#4323—84no—
130(C2×D11)⋊C4—41no—
131(C2×D11)⋊C4—41no—
132C4⋊Dic11—21no—
133C4⋊Dic11—21no—
134#4318—42no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8C2×D414yes—
138#3205—111no—
139#3037—111no—
140C2×#460D1111yescharacteristic, complemented
141#2982—111no—
142#1682—114no—
143#1668—114no—
144#1571—111no—
145#1545—111no—
146#1540—111no—
147C23×C11—42no—
148C23×C11—82no—
149C23×C11—82no—
150C23×C11—82no—
151C23×C11#12111yescharacteristic
152C22×D11—41no—
153Q8×C11—22no—
154Q8×C11—24no—
155Q8×C11C2×D814yes—
156D4×C11—42no—
157D4×C11—42no—
158D4×C11—44no—
159D4×C11—82no—
160D4×C11—82no—
161D4×C11—82no—
162D4×C11—82no—
163C2×C4×C11—22no—
164C2×C4×C11—24no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—41no—
168C2×C4×C11—81no—
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11C2×D812yes—
173C2×C4×C11#13512yes—
174C2×C4×C11C22×D411yescharacteristic
175C2×C4×C11C22×D411yescharacteristic
176C2×C4×C11C2×#4111yescharacteristic
177C22⋊D11—82no—
178C2×Dic11—41no—
179D44—41no—
180D44—41no—
181D44—42no—
182D44—81no—
183C4×D11—82no—
184Dic22—41no—
185Dic22—41no—
186C8×C11—42no—
187C11⋊C8—24no—
188C11⋊C8—42no—
189C11⋊C8—42no—
190C2×#137—221no—
191C22×SD16—21no—
192#532—111no—
193C2×#127C2×D1111yescharacteristic
194C2×C4×Q8C2×D1111yescharacteristic
195#493—112no—
196#486—112no—
197#464—222no—
198#462—112no—
199#460—22no—
200#460—112no—
201#460C2×D1114yes—
202#459—222no—
203#447—222no—
204C8×Q8—114no—
205C8×Q8—222no—
206#431—111no—
207#431—111no—
208#431—222no—
209#423—111no—
210C2×C4⋊C8C2×D1111yescharacteristic
211#417—221no—
212C2×#102—21no—
213#335—114no—
214#332—112no—
215#331—114no—
216#331—112no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—82no—
220C22×C11—82no—
221C22×C11—82no—
222C22×C11—164no—
223C22×C11#46612yes—
224C22×C11C2×#12111yescharacteristic
225C2×D11—81no—
226C2×D11—81no—
227C2×D11—81no—
228C4×C11—21no—
229C4×C11—24no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—42no—
233C4×C11#46612yes—
234C4×C11C22×D811yescharacteristic
235C4×C11C2×#13511yescharacteristic
236C4×C11#57712yes—
237Dic11—81no—
238C2×#41—221no—
239C22×Q8C22⋊D1111yescharacteristic
240C22×D4—21no—
241C22×D4—21no—
242C22×D4—21no—
243#137—444no—
244C2×Q16—222no—
245C2×SD16—24no—
246C2×SD16—44no—
247C2×SD16—222no—
248C2×D8—224no—
249C2×M16—221no—
250C22×C8—21no—
251C4⋊Q8—111no—
252#127—21no—
253#127—21no—
254#127—21no—
255#127—111no—
256#127C22×D1112yes—
257#124—221no—
258#121—221no—
259#121—221no—
260C4×Q8—21no—
261C4×Q8—21no—
262C4×Q8C22⋊D1112yes—
263C4×Q8C22×D1112yes—
264C4×D4—221no—
265C4×D4—221no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4C22⋊D1111yescharacteristic
268C2×C42—21no—
269C2×C42C22×D1111yescharacteristic
270C4⋊C8—21no—
271C4⋊C8—112no—
272C4⋊C8—112no—
273C4⋊C8—112no—
274C4⋊C8—224no—
275C4⋊C8—221no—
276C4⋊C8C22×D1112yes—
277#103—222no—
278#102—24no—
279#102—224no—
280#102—222no—
281C22⋊C8—112no—
282C22⋊C8—221no—
283C4×C8—112no—
284C4×C8—224no—
285C4×C8—221no—
286C2×C11—22no—
287C2×C11—162no—
288C2×C11#304311yescharacteristic
289C2×C11C2×#46611yescharacteristic
290C2×C11#306811yescharacteristic
291D11—161no—
292C24—41no—
293#41—442no—
294#41—442no—
295C2×Q8—21no—
296C2×Q8—22no—
297C2×Q8—221no—
298C2×Q8#432314yescomplemented
299C2×Q8C2×C22⋊D1112yes—
300C2×D4—22no—
301C2×D4—22no—
302C2×D4—22no—
303C2×D4—42no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—42no—
308C2×D4—82no—
309C2×D4—82no—
310C2×D4—221no—
311C2×D4—221no—
312C2×D4—221no—
313C2×D4—441no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—441no—
317C22×C4D4×D1111yescharacteristic
318C22×C4#434111yescharacteristic
319C22×C4C2×C22⋊D1111yescharacteristic
320Q16—444no—
321SD16—48no—
322SD16—444no—
323D8—884no—
324M16—442no—
325C2×C8—22no—
326C2×C8—42no—
327C2×C8—114no—
328C2×C8—222no—
329C2×C8—222no—
330C4⋊C4—22no—
331C4⋊C4—21no—
332C4⋊C4—22no—
333C4⋊C4—221no—
334C4⋊C4—221no—
335C4⋊C4C2×C22⋊D1112yes—
336C22⋊C4—441no—
337C22⋊C4—441no—
338C42—22no—
339C42—22no—
340C42D4×D1111yescharacteristic
341C42#434111yescharacteristic
342C42C2×C22⋊D1111yescharacteristic
343C42C23×D1111yescharacteristic
344C11#1939811yescharacteristic, complemented, Sylow
345C23—42no—
346C23—82no—
347C23—82no—
348C23—82no—
349C23—441no—
350C23#6699211yescharacteristic
351Q8—22no—
352Q8—24no—
353Q8—441no—
354Q8—441no—
355Q8C2×#432314yes—
356D4—44no—
357D4—42no—
358D4—42no—
359D4—82no—
360D4—82no—
361D4—82no—
362D4—82no—
363D4—442no—
364D4—441no—
365D4—441no—
366D4—881no—
367D4—882no—
368C2×C4—22no—
369C2×C4—24no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—41no—
373C2×C4—81no—
374C2×C4—441no—
375C2×C4—882no—
376C2×C4C2×#432312yes—
377C2×C4#6699211yescharacteristic
378C2×C4#6699211yescharacteristic
379C2×C4#6699211yescharacteristic
380C2×C4#6700312yes—
381C2×C4C2×D4×D1111yescharacteristic
382C2×C4C2×#434111yescharacteristic
383C2×C4C22×C22⋊D1111yescharacteristic
384C8—42no—
385C8—224no—
386C8—442no—
387C8—442no—
388C22—21no—
389C22—21no—
390C22—82no—
391C22—82no—
392C22—82no—
393C22—164no—
394C22—881no—
395C22—881no—
396C22—881no—
397C22#1062265112yes—
398C22C2×#6699211yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—24no—
403C4—42no—
404C4—881no—
405C4#1062265112yes—
406C4#1062329312yes—
407C4C22×#432311yescharacteristic
408C4C2×#6700311yescharacteristic
409C2—22no—
410C2—162no—
411C2—1761no—
412C2#1307813411yescharacteristic
413C2C2×#1062265111yescharacteristic
414C2#1307834111yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#460C2
socleC22×C11C2×#121
prime radical#13079534C2
hypercenterC2×#460D11
hypocenterC11#19398
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
2. #13078088C2semidirect
3. #13077697C2semidirect
4. #13068058C2semidirect
5. #13067974C2semidirect
6. #13067390C2semidirect
7. #13067284C2semidirect
8. #13067266C2semidirect
9. C2×C11×#460C2semidirect
23. #10622644C22semidirect
25. #10622640C22semidirect
27. Q8×C11⋊C8C22semidirect
34. #10622123C22semidirect
35. #10622120C22semidirect
36. #10622117C22semidirect
89. C2×Q8×C11D8semidirect
140. C2×#460D11semidirect
298. C2×Q8#4323semidirect
344. C11#19398semidirect

Maximal subgroups

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

subgroupindex
#130795342
#130780882
#130776972
#130680582
#130679742
#130673902
#130672842
#130672662
C2×C11×#4602
#1939811