Finite Group Databasebeta

← #14738929

Subgroups — #14738929

Order 2816.

738 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078409C211yesmaximal, characteristic, complemented
2C2×#10622685C211yesmaximal, characteristic
3#13077639C211yesmaximal, characteristic, complemented
4#13068022C214yesmaximal, complemented
5#13067954C214yesmaximal, complemented
6#13067387C211yesmaximal, characteristic, complemented
7#13067284C211yesmaximal, characteristic, complemented
8#13067273C211yesmaximal, characteristic, complemented
9C11×#3208C211yesmaximal, characteristic, complemented
10C11×#533C2211yescharacteristic
11C2×C11×#127C2211yescharacteristic
12C22×#4323—21no—
13C2×C4×D44C2211yescharacteristic
14C11×#492C2212yescomplemented
15C11×#486C2212yescomplemented
16C11×#460—22no—
17C11×#450—22no—
18C11×#431C2211yescharacteristic
19C2×#66896—21no—
20#10622700C2212yescomplemented
21#10622697C2212yescomplemented
22#10622685—22no—
23#10622685C2214yes—
24#10622679—22no—
25#10622614—21no—
26#10622608—21no—
27#10622538C2211yescharacteristic
28#10622537C2211yescharacteristic
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30#10622447—22no—
31D11×C22⋊C8—22no—
32C8×D44C2214yescomplemented
33#10622185C2212yescomplemented
34#10622184C2212yescomplemented
35#10622182C2214yescomplemented
36#10622095C2214yescomplemented
37C22×D4×C11—21no—
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C22×D44D411yescharacteristic
41C22×C4×D11—21no—
42C2×C11×SD16—24no—
43C11×C4⋊Q8C2311yescharacteristic
44C11×C4⋊Q8C2311yescharacteristic
45C11×#127—21no—
46C11×#127—21no—
47C11×#127—21no—
48C11×#127C2312yes—
49C11×#125—21no—
50C11×C22⋊Q8—21no—
51C11×C22⋊Q8—21no—
52C4×Q8×C11—21no—
53C4×Q8×C11—21no—
54C11×#117—21no—
55C2×C42×C11C2311yescharacteristic
56C2×#4323—24no—
57C2×#4323—44no—
58C2×(C2×D11)⋊C4—21no—
59C2×C4⋊Dic11D411yescharacteristic
60C2×#4318—21no—
61C22×C11⋊C8—21no—
62C2×C8×D11—24no—
63C4×D44—21no—
64C4×D44—21no—
65C4×D44D412yes—
66C4×D44C2312yes—
67C11×C4⋊C8D412yes—
68C11×#102—24no—
69C11×C22⋊C8D412yes—
70C4×C8×C11C2312yes—
71#66896—24no—
72C22⋊(C11⋊C8)—21no—
73(C2×D11)⋊C8—24no—
74#66873—22no—
75#66873—22no—
76#66872—22no—
77#66871—22no—
78C4⋊(C11⋊C8)—21no—
79C4⋊(C11⋊C8)—21no—
80C4⋊(C11⋊C8)C2312yes—
81C4⋊(C11⋊C8)C2312yes—
82C4⋊(C11⋊C8)C2312yes—
83C4×C11⋊C8—21no—
84#19384—111nomaximal, Sylow
85C24×C11—41no—
86C23×D11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11—21no—
89C2×D4×C11—22no—
90C2×D4×C11—22no—
91C2×D4×C11—22no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C2×D4×C11—42no—
96C2×D4×C11—42no—
97C2×D4×C11—82no—
98C2×D4×C11—82no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11#4111yescharacteristic
102C22×Dic11—21no—
103C2×D44—21no—
104C2×D44—22no—
105C2×D44SD1614yescomplemented
106C2×D44C2×D412yes—
107C2×C4×D11—22no—
108C2×C4×D11—22no—
109C2×C4×D11—82no—
110C11×SD16—84no—
111C2×C8×C11C2×D414yes—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C22⋊C4—41no—
119C42×C11—41no—
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C42×C11#4111yescharacteristic
123C42×C11C2411yescharacteristic
124#4323—48no—
125(C2×D11)⋊C4—22no—
126(C2×D11)⋊C4—22no—
127C4⋊Dic11—21no—
128C4⋊Dic11C2×D412yes—
129#4318—42no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—42no—
134C8×D11—84no—
135#3208D1111yescharacteristic, complemented
136#3077—111no—
137C2×#459—111no—
138#2972—111no—
139#1677—114no—
140#1665—114no—
141#1570—111no—
142#1545—111no—
143#1542—111no—
144C23×C11—42no—
145C23×C11—82no—
146C23×C11—82no—
147C23×C11—82no—
148C23×C11#12111yescharacteristic
149C22×D11—22no—
150C22×D11—24no—
151C22×D11—81no—
152C22×D11—81no—
153Q8×C11—42no—
154Q8×C11—81no—
155D4×C11—42no—
156D4×C11—42no—
157D4×C11—44no—
158D4×C11—82no—
159D4×C11—82no—
160D4×C11—82no—
161D4×C11—82no—
162C2×C4×C11—22no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11C2×SD1612yes—
170C2×C4×C11#13512yes—
171C2×C4×C11C22×D411yescharacteristic
172C2×C4×C11C22×D411yescharacteristic
173C2×C4×C11C2×#4111yescharacteristic
174C2×Dic11—22no—
175C2×Dic11—81no—
176D44—22no—
177D44—24no—
178D44C2×SD1614yes—
179C4×D11—44no—
180C4×D11—82no—
181C8×C11—24no—
182C11⋊C8—42no—
183C11⋊C8—42no—
184C11⋊C8—42no—
185C22×D8—221no—
186#533C2×D1111yescharacteristic
187C2×#127C2×D1111yescharacteristic
188C2×C4×D4—111no—
189#492C2×D1112yescomplemented
190#486C2×D1112yescomplemented
191#478—222no—
192#476—112no—
193#474—112no—
194#460—22no—
195#459—114no—
196#459—222no—
197#450—22no—
198C8×D4—114no—
199C8×D4—222no—
200#431—111no—
201#431C2×D1111yescharacteristic
202#428—221no—
203#423—111no—
204C2×C4⋊C8—111no—
205#418—221no—
206C2×#102—221no—
207C2×C22⋊C8—222no—
208#334—114no—
209#333—112no—
210#332—112no—
211#331—114no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—82no—
215C22×C11—82no—
216C22×C11—82no—
217C22×C11—164no—
218C22×C11#46512yes—
219C22×C11C2×#12111yescharacteristic
220C2×D11—24no—
221C2×D11—42no—
222C2×D11—42no—
223C2×D11—84no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—81no—
228C4×C11—81no—
229C4×C11#46512yes—
230C4×C11C22×SD1611yescharacteristic
231C4×C11C2×#13511yescharacteristic
232C4×C11#57612yes—
233Dic11—42no—
234C22×D4—21no—
235C22×D4—21no—
236C22×D4—21no—
237C22×D4—111no—
238C23×C4—221no—
239C2×SD16—24no—
240C2×D8—224no—
241C2×D8—444no—
242C2×M16—221no—
243C22×C8—221no—
244C22×C8—224no—
245C4⋊Q8C22×D1111yescharacteristic
246C4⋊Q8C22×D1111yescharacteristic
247#127—21no—
248#127—21no—
249#127—21no—
250#127C22×D1112yes—
251#125—21no—
252C22⋊Q8—21no—
253C22⋊Q8—21no—
254C4×Q8—21no—
255C4×Q8—21no—
256C4×D4—112no—
257C4×D4—112no—
258C4×D4—221no—
259C4×D4—221no—
260#117—21no—
261C2×C4⋊C4—111no—
262C2×C22⋊C4—221no—
263C2×C42C22×D1111yescharacteristic
264#107—222no—
265#106—222no—
266C4⋊C8—112no—
267C4⋊C8—112no—
268C4⋊C8—112no—
269C4⋊C8—221no—
270C4⋊C8—221no—
271C4⋊C8C22⋊D1112yes—
272#102—24no—
273#102—222no—
274#102—222no—
275#102—224no—
276C22⋊C8—221no—
277C22⋊C8—224no—
278C22⋊C8C22⋊D1112yes—
279C4×C8—221no—
280C4×C8C22×D1112yes—
281C2×C11—22no—
282C2×C11—162no—
283C2×C11#304111yescharacteristic
284C2×C11C2×#46511yescharacteristic
285C2×C11#306811yescharacteristic
286D11—44no—
287C24—41no—
288C24—221no—
289C2×Q8—21no—
290C2×Q8—21no—
291C2×D4—22no—
292C2×D4—22no—
293C2×D4—22no—
294C2×D4—42no—
295C2×D4—42no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—82no—
300C2×D4—82no—
301C2×D4—114no—
302C2×D4—112no—
303C2×D4—222no—
304C2×D4—221no—
305C22×C4—221no—
306C22×C4—222no—
307C22×C4—222no—
308C22×C4—882no—
309C22×C4D4×D1111yescharacteristic
310C22×C4#434111yescharacteristic
311C22×C4C2×C22⋊D1111yescharacteristic
312SD16—84no—
313D8—448no—
314M16—442no—
315C2×C8—222no—
316C2×C8—222no—
317C2×C8—222no—
318C2×C8—442no—
319C2×C8—884no—
320C2×C8C2×C22⋊D1114yes—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—112no—
328C4⋊C4—221no—
329C22⋊C4—41no—
330C22⋊C4—222no—
331C22⋊C4—222no—
332C42—41no—
333C42D4×D1111yescharacteristic
334C42#434111yescharacteristic
335C42C2×C22⋊D1111yescharacteristic
336C42C23×D1111yescharacteristic
337C11#1938411yescharacteristic, complemented, Sylow
338C23—42no—
339C23—82no—
340C23—82no—
341C23—82no—
342C23—222no—
343C23—224no—
344C23—881no—
345C23—881no—
346C23#6699111yescharacteristic
347Q8—42no—
348Q8—81no—
349D4—42no—
350D4—42no—
351D4—44no—
352D4—82no—
353D4—82no—
354D4—82no—
355D4—82no—
356D4—114no—
357D4—222no—
358D4—224no—
359C2×C4—22no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—222no—
364C2×C4—444no—
365C2×C4—882no—
366C2×C4—881no—
367C2×C4SD16×D1112yes—
368C2×C4#6696912yes—
369C2×C4#6699111yescharacteristic
370C2×C4#6699111yescharacteristic
371C2×C4#6699111yescharacteristic
372C2×C4C2×D4×D1111yescharacteristic
373C2×C4C2×#434111yescharacteristic
374C2×C4C22×C22⋊D1111yescharacteristic
375C8—24no—
376C8—442no—
377C8—442no—
378C8—442no—
379C22—21no—
380C22—21no—
381C22—82no—
382C22—82no—
383C22—82no—
384C22—164no—
385C22—224no—
386C22—442no—
387C22—442no—
388C22—884no—
389C22#1062278412yes—
390C22C2×#6699111yescharacteristic
391C4—21no—
392C4—21no—
393C4—21no—
394C4—81no—
395C4—81no—
396C4—442no—
397C4#1062278412yes—
398C4C2×SD16×D1111yescharacteristic
399C4C2×#6696911yescharacteristic
400C4#1062336612yes—
401C2—22no—
402C2—162no—
403C2—444no—
404C2#1307811511yescharacteristic
405C2C2×#1062278411yescharacteristic
406C2#1307834011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3208C2
socleC22×C11C2×#121
prime radicalC2×#10622685C2
hypercenter#3208D11
hypocenterC11#19384
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3208

Complements

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

NH ≅ G/Ntype
1. #13078409C2semidirect
3. #13077639C2semidirect
4. #13068022C2semidirect
5. #13067954C2semidirect
6. #13067387C2semidirect
7. #13067284C2semidirect
8. #13067273C2semidirect
9. C11×#3208C2semidirect
14. C11×#492C22semidirect
15. C11×#486C22semidirect
20. #10622700C22semidirect
21. #10622697C22semidirect
32. C8×D44C22semidirect
33. #10622185C22semidirect
34. #10622184C22semidirect
35. #10622182C22semidirect
36. #10622095C22semidirect
105. C2×D44SD16semidirect
135. #3208D11semidirect
189. #492C2×D11semidirect
190. #486C2×D11semidirect
337. C11#19384semidirect

Maximal subgroups

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

subgroupindex
#130784092
C2×#106226852
#130776392
#130680222
#130679542
#130673872
#130672842
#130672732
C11×#32082
#1938411