Finite Group Databasebeta

← #14738939

Subgroups — #14738939

Order 2816.

708 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079541C211yesmaximal, characteristic, complemented
2#13078080C211yesmaximal, characteristic
3#13077640C211yesmaximal, characteristic, complemented
4#13068037C214yesmaximal, complemented
5#13067959C214yesmaximal, complemented
6#13067386C211yesmaximal, characteristic, complemented
7#13067301C211yesmaximal, characteristic, complemented
8#13067266C211yesmaximal, characteristic, complemented
9C2×C11×#474C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C2×#66985—21no—
13#10623008C2211yescharacteristic
14C11×#474—22no—
15C11×#474C2214yes—
16C2×C11×#107—21no—
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×#102—21no—
19#10622840—22no—
20C2×C22⋊(C11⋊C8)—22no—
21#10622698C2212yescomplemented
22#10622696—22no—
23#10622694C2212yescomplemented
24#10622632C2212yes—
25#10622629—22no—
26#10622628C2212yes—
27D4×C11⋊C8—22no—
28D4×C11⋊C8C2214yes—
29#10622579—21no—
30#10622538C2211yescharacteristic
31#10622538C2211yescharacteristic
32#10622537C2211yescharacteristic
33#10622185C2214yescomplemented
34#10622123C2212yescomplemented
35#10622120C2212yescomplemented
36#10622118C2214yescomplemented
37C22×Q8×C11—21no—
38C22×D4×C11D411yescharacteristic
39C23×C4×C11—21no—
40C2×#4339—21no—
41C22×C8×C11—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8C2312yes—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C4×D4×C11D412yes—
49C4×D4×C11C2312yes—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4D411yescharacteristic
53C2×C11×C22⋊C4—21no—
54C2×C42×C11C2311yescharacteristic
55C2×#4325—24no—
56C2×#4324—22no—
57#66985—44no—
58C2×#4323—22no—
59#66983—21no—
60#66983—21no—
61C2×#4318—21no—
62C22×C11⋊C8—24no—
63#66928—21no—
64#66927C2311yescharacteristic
65C4×D44—21no—
66C4×D44—21no—
67#66922C2311yescharacteristic
68C11×#107—24no—
69C11×C4⋊C8—21no—
70C11×C4⋊C8C2312yes—
71C11×#102—24no—
72#66899—24no—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)—24no—
75C22⋊(C11⋊C8)D412yes—
76#66874—22no—
77#66873—22no—
78C4⋊(C11⋊C8)—21no—
79C4⋊(C11⋊C8)D412yes—
80C4⋊(C11⋊C8)C2312yes—
81C4⋊(C11⋊C8)C2312yes—
82C4×C11⋊C8—21no—
83C4×C11⋊C8C2312yes—
84#19385—111nomaximal, Sylow
85C24×C11—21no—
86C2×Q8×C11—22no—
87C2×Q8×C11—41no—
88C2×Q8×C11—82no—
89C2×D4×C11—21no—
90C2×D4×C11—22no—
91C2×D4×C11SD1614yescomplemented
92C2×D4×C11C2×D412yes—
93C22×C4×C11—21no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—41no—
97C22×C4×C11—82no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11#4111yescharacteristic
101C2×C22⋊D11—41no—
102#4339—42no—
103#4339—42no—
104C2×D44—21no—
105C2×D44—21no—
106C2×D44—21no—
107C2×C4×D11—41no—
108C2×Dic22—21no—
109C2×C8×C11—22no—
110C2×C8×C11—42no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4C2×D412yes—
117C11×C22⋊C4—22no—
118C11×C22⋊C4—22no—
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11#4111yescharacteristic
122C42×C11C2411yescharacteristic
123#4325—84no—
124#4324—44no—
125#4323—44no—
126(C2×D11)⋊C4—41no—
127(C2×D11)⋊C4—41no—
128C4⋊Dic11—21no—
129C4⋊Dic11—21no—
130#4318—42no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—84no—
134C2×C11⋊C8C2×D414yes—
135#3206—111no—
136C2×#474D1111yescharacteristic, complemented
137#3036—111no—
138#2972—111no—
139#1679—114no—
140#1665—114no—
141#1570—111no—
142#1549—111no—
143#1540—111no—
144C23×C11—22no—
145C23×C11—24no—
146C23×C11—81no—
147C23×C11—81no—
148C23×C11#12111yescharacteristic
149C22×D11—41no—
150Q8×C11—44no—
151Q8×C11—82no—
152D4×C11—22no—
153D4×C11—24no—
154D4×C11C2×SD1614yes—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—41no—
158C2×C4×C11—44no—
159C2×C4×C11—42no—
160C2×C4×C11—82no—
161C2×C4×C11—81no—
162C2×C4×C11—82no—
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11C2×SD1612yes—
167C2×C4×C11#13512yes—
168C2×C4×C11C22×D411yescharacteristic
169C2×C4×C11C22×D411yescharacteristic
170C2×C4×C11C2×#4111yescharacteristic
171C22⋊D11—82no—
172C2×Dic11—41no—
173D44—41no—
174D44—41no—
175D44—42no—
176D44—81no—
177C4×D11—82no—
178Dic22—41no—
179Dic22—41no—
180C8×C11—42no—
181C11⋊C8—24no—
182C11⋊C8—42no—
183C11⋊C8—42no—
184C2×AGL(1,ℤ/8)—221no—
185#532—111no—
186C2×C4⋊Q8C2×D1111yescharacteristic
187C2×C4×D4C2×D1111yescharacteristic
188#492—112no—
189#487—112no—
190#474—22no—
191#474C2×D1114yes—
192#463—222no—
193#461—112no—
194#461—222no—
195#459—112no—
196#448—222no—
197C8×D4—114no—
198C8×D4—222no—
199#431—111no—
200#431—111no—
201C2×#107—21no—
202#423—111no—
203C2×C4⋊C8C2×D1111yescharacteristic
204#417—221no—
205C2×#102—21no—
206C2×C22⋊C8—222no—
207#334—114no—
208#332—114no—
209#332—112no—
210#331—112no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—24no—
214C22×C11—42no—
215C22×C11—42no—
216C22×C11—84no—
217C22×C11#46512yes—
218C22×C11C2×#12111yescharacteristic
219C2×D11—81no—
220C2×D11—81no—
221C2×D11—81no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—42no—
226C4×C11—82no—
227C4×C11#46512yes—
228C4×C11C22×SD1611yescharacteristic
229C4×C11C2×#13511yescharacteristic
230C4×C11#57612yes—
231Dic11—81no—
232C2×#41—221no—
233C22×Q8—21no—
234C22×D4C22⋊D1111yescharacteristic
235C23×C4—21no—
236AGL(1,ℤ/8)—444no—
237C2×SD16—224no—
238C2×SD16—222no—
239C2×D8—222no—
240C2×M16—221no—
241C22×C8—21no—
242C22×C8—224no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—111no—
247C4⋊Q8C22×D1112yes—
248#127—111no—
249#124—221no—
250#121—221no—
251#121—221no—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4—221no—
255C4×D4—221no—
256C4×D4C22⋊D1112yes—
257C4×D4C22×D1112yes—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4C22⋊D1111yescharacteristic
261C2×C22⋊C4—21no—
262C2×C42C22×D1111yescharacteristic
263#107—24no—
264C4⋊C8—21no—
265C4⋊C8—112no—
266C4⋊C8—112no—
267C4⋊C8—112no—
268C4⋊C8—221no—
269C4⋊C8C22×D1112yes—
270#103—224no—
271#103—222no—
272#102—24no—
273#102—222no—
274C22⋊C8—112no—
275C22⋊C8—224no—
276C22⋊C8—221no—
277C4×C8—112no—
278C4×C8—221no—
279C2×C11—22no—
280C2×C11—44no—
281C2×C11#304111yescharacteristic
282C2×C11C2×#46511yescharacteristic
283C2×C11#306911yescharacteristic
284D11—161no—
285C24—21no—
286#41—442no—
287#41—442no—
288C2×Q8—22no—
289C2×Q8—41no—
290C2×Q8—82no—
291C2×Q8—221no—
292C2×D4—21no—
293C2×D4—22no—
294C2×D4—221no—
295C2×D4—221no—
296C2×D4—221no—
297C2×D4—441no—
298C2×D4#432514yescomplemented
299C2×D4C2×C22⋊D1112yes—
300C22×C4—21no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—41no—
304C22×C4—82no—
305C22×C4—441no—
306C22×C4D4×D1111yescharacteristic
307C22×C4#434111yescharacteristic
308C22×C4C2×C22⋊D1111yescharacteristic
309SD16—444no—
310SD16—884no—
311D8—444no—
312M16—442no—
313C2×C8—22no—
314C2×C8—42no—
315C2×C8—114no—
316C2×C8—222no—
317C2×C8—222no—
318C2×C8—884no—
319C4⋊C4—21no—
320C4⋊C4—22no—
321C4⋊C4—22no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—221no—
325C4⋊C4—221no—
326C4⋊C4C2×C22⋊D1112yes—
327C22⋊C4—22no—
328C22⋊C4—22no—
329C22⋊C4—441no—
330C22⋊C4—441no—
331C42D4×D1111yescharacteristic
332C42#434111yescharacteristic
333C42C2×C22⋊D1111yescharacteristic
334C42C23×D1111yescharacteristic
335C11#1938511yescharacteristic, complemented, Sylow
336C23—22no—
337C23—24no—
338C23—81no—
339C23—81no—
340C23—441no—
341C23#6699211yescharacteristic
342Q8—44no—
343Q8—82no—
344Q8—441no—
345Q8—441no—
346D4—22no—
347D4—24no—
348D4—442no—
349D4—441no—
350D4—441no—
351D4—881no—
352D4—882no—
353D4C2×#432514yes—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—44no—
358C2×C4—42no—
359C2×C4—82no—
360C2×C4—81no—
361C2×C4—82no—
362C2×C4—441no—
363C2×C4—882no—
364C2×C4#6699211yescharacteristic
365C2×C4#6699211yescharacteristic
366C2×C4#6699211yescharacteristic
367C2×C4C2×#432512yes—
368C2×C4#6700312yes—
369C2×C4C2×D4×D1111yescharacteristic
370C2×C4C2×#434111yescharacteristic
371C2×C4C22×C22⋊D1111yescharacteristic
372C8—42no—
373C8—224no—
374C8—442no—
375C8—442no—
376C22—21no—
377C22—21no—
378C22—24no—
379C22—42no—
380C22—42no—
381C22—84no—
382C22—881no—
383C22—881no—
384C22—881no—
385C22#1062266112yes—
386C22C2×#6699211yescharacteristic
387C4—21no—
388C4—21no—
389C4—21no—
390C4—42no—
391C4—82no—
392C4—881no—
393C4#1062266112yes—
394C4#1062328812yes—
395C4C22×#432511yescharacteristic
396C4C2×#6700311yescharacteristic
397C2—22no—
398C2—44no—
399C2—1761no—
400C2#1307811611yescharacteristic
401C2C2×#1062266111yescharacteristic
402C2#1307835011yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#474C2
socleC22×C11C2×#121
prime radical#13078080C2
hypercenterC2×#474D11
hypocenterC11#19385
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. #13079541C2semidirect
3. #13077640C2semidirect
4. #13068037C2semidirect
5. #13067959C2semidirect
6. #13067386C2semidirect
7. #13067301C2semidirect
8. #13067266C2semidirect
9. C2×C11×#474C2semidirect
21. #10622698C22semidirect
23. #10622694C22semidirect
33. #10622185C22semidirect
34. #10622123C22semidirect
35. #10622120C22semidirect
36. #10622118C22semidirect
91. C2×D4×C11SD16semidirect
136. C2×#474D11semidirect
298. C2×D4#4325semidirect
335. C11#19385semidirect

Maximal subgroups

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

subgroupindex
#130795412
#130780802
#130776402
#130680372
#130679592
#130673862
#130673012
#130672662
C2×C11×#4742
#1938511