Finite Group Databasebeta

← #14738945

Subgroups — #14738945

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#13079538C211yesmaximal, characteristic, complemented
2C2×#10622459C211yesmaximal, characteristic, complemented
3#13078076C211yesmaximal, characteristic
4#13077639C211yesmaximal, characteristic, complemented
5#13068042C214yesmaximal, complemented
6#13067956C214yesmaximal, complemented
7#13067386C211yesmaximal, characteristic, complemented
8#13067300C211yesmaximal, characteristic, complemented
9C11×#1540C211yesmaximal, characteristic, complemented
10C11×#532C2211yescharacteristic
11C2×#67002—21no—
12C2×C4×D44C2211yescharacteristic
13C2×#66922C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16#10622845—21no—
17C2×#66885—21no—
18C2×#66882—21no—
19#10622706C2212yescomplemented
20#10622696C2212yes—
21#10622689C2212yescomplemented
22#10622685C2212yes—
23#10622670—22no—
24#10622653—22no—
25#10622632—22no—
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622459—22no—
29#10622459C2214yes—
30#10622447C2214yes—
31D11×C22⋊C8—22no—
32C8×D44—22no—
33C11×#332C2212yescomplemented
34C11×#331C2212yescomplemented
35#10622120C2214yescomplemented
36#10622118C2214yescomplemented
37C2×C11×#41—21no—
38C22×D44D411yescharacteristic
39C22×C4×D11—21no—
40C22×Dic22—21no—
41C22×C8×C11—21no—
42C11×C4⋊Q8C2311yescharacteristic
43C11×#127C2311yescharacteristic
44C11×#124—21no—
45C11×#121—21no—
46C11×#121—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C2×C42×C11C2311yescharacteristic
50#67002—44no—
51C2×#4325—22no—
52C2×#4324—24no—
53C2×#4323—22no—
54C2×(C2×D11)⋊C4—21no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11D411yescharacteristic
58C2×#4318—21no—
59C2×C8×D11—24no—
60C4×D44—21no—
61C4×D44—21no—
62C4×D44D412yes—
63C4×D44C2312yes—
64#66922—21no—
65#66922—21no—
66#66922—21no—
67#66922C2312yes—
68C11×C4⋊C8—21no—
69C11×C4⋊C8C2312yes—
70C11×C4⋊C8C2312yes—
71C11×C22⋊C8—21no—
72C4×C8×C11—21no—
73#66899—22no—
74#66896—22no—
75C22⋊(C11⋊C8)D412yes—
76#66885—24no—
77(C2×D11)⋊C8—24no—
78#66882—24no—
79#66874—24no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)D412yes—
82C4⋊(C11⋊C8)C2312yes—
83C4×C11⋊C8C2312yes—
84#19385—111nomaximal, Sylow
85C23×D11—21no—
86C11×#41—42no—
87C11×#41—42no—
88C2×Q8×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11#4111yescharacteristic
97C22×Dic11—21no—
98C22×Dic11—41no—
99C2×D44—21no—
100C2×D44—22no—
101C2×D44SD1614yescomplemented
102C2×D44C2×D412yes—
103C2×C4×D11—22no—
104C2×C4×D11—22no—
105C2×C4×D11—82no—
106C2×Dic22—22no—
107C2×Dic22—41no—
108C2×Dic22—82no—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C2×C8×C11—42no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—41no—
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11#4111yescharacteristic
119C42×C11C2411yescharacteristic
120#4325—44no—
121#4324—84no—
122#4323—44no—
123(C2×D11)⋊C4—22no—
124(C2×D11)⋊C4—22no—
125C4⋊Dic11—21no—
126C4⋊Dic11—22no—
127C4⋊Dic11—22no—
128C4⋊Dic11—41no—
129C4⋊Dic11—41no—
130C4⋊Dic11C2×D412yes—
131#4318—42no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8C2×D414yes—
134C8×D11—84no—
135#3206—111no—
136C2×#474—111no—
137#3036—111no—
138#2972—111no—
139#1679—114no—
140#1665—114no—
141#1570—111no—
142#1549—111no—
143#1540D1111yescharacteristic, complemented
144C23×C11—41no—
145C23×C11#12111yescharacteristic
146C22×D11—22no—
147C22×D11—24no—
148C22×D11—81no—
149C22×D11—81no—
150Q8×C11—41no—
151Q8×C11—41no—
152D4×C11—41no—
153D4×C11—41no—
154D4×C11—42no—
155D4×C11—81no—
156D4×C11—82no—
157C2×C4×C11—22no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—82no—
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11C2×SD1612yes—
165C2×C4×C11#13512yes—
166C2×C4×C11C22×D411yescharacteristic
167C2×C4×C11C22×D411yescharacteristic
168C2×C4×C11C2×#4111yescharacteristic
169C2×Dic11—22no—
170C2×Dic11—42no—
171C2×Dic11—81no—
172C2×Dic11—82no—
173D44—22no—
174D44—24no—
175D44C2×SD1614yes—
176C4×D11—44no—
177C4×D11—82no—
178Dic22—44no—
179Dic22—82no—
180C8×C11—42no—
181C8×C11—42no—
182C11⋊C8—24no—
183C11⋊C8—42no—
184C2×AGL(1,ℤ/8)—221no—
185#532C2×D1111yescharacteristic
186C2×C4⋊Q8—111no—
187C2×C4×D4—111no—
188#492—112no—
189#487—112no—
190#474—114no—
191#474—222no—
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#431C2×D1111yescharacteristic
201C2×#107—221no—
202#423—111no—
203C2×C4⋊C8C2×D1111yescharacteristic
204#417—221no—
205C2×#102—221no—
206C2×C22⋊C8—222no—
207#334—114no—
208#332—114no—
209#332C2×D1112yescomplemented
210#331C2×D1112yescomplemented
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—81no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11#46512yes—
217C22×C11C2×#12111yescharacteristic
218C2×D11—24no—
219C2×D11—42no—
220C2×D11—42no—
221C2×D11—84no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—81no—
226C4×C11#46512yes—
227C4×C11C22×SD1611yescharacteristic
228C4×C11C2×#13511yescharacteristic
229C4×C11#57612yes—
230Dic11—42no—
231Dic11—82no—
232C2×#41—21no—
233C22×Q8—221no—
234C22×D4—111no—
235C23×C4—221no—
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—112no—
244C4⋊Q8—221no—
245C4⋊Q8—221no—
246C4⋊Q8—221no—
247C4⋊Q8C22×D1111yescharacteristic
248#127C22×D1111yescharacteristic
249#124—21no—
250#121—21no—
251#121—21no—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4—112no—
255C4×D4—112no—
256C4×D4—221no—
257C4×D4—221no—
258C2×C4⋊C4—111no—
259C2×C4⋊C4—221no—
260C2×C4⋊C4—221no—
261C2×C22⋊C4—221no—
262C2×C42C22×D1111yescharacteristic
263#107—224no—
264C4⋊C8—21no—
265C4⋊C8—112no—
266C4⋊C8—112no—
267C4⋊C8—221no—
268C4⋊C8C22×D1112yes—
269C4⋊C8C22×D1112yes—
270#103—224no—
271#103—222no—
272#102—222no—
273#102—224no—
274C22⋊C8—21no—
275C22⋊C8—112no—
276C22⋊C8—224no—
277C4×C8—21no—
278C4×C8—112no—
279C2×C11—22no—
280C2×C11—161no—
281C2×C11#304111yescharacteristic
282C2×C11C2×#46511yescharacteristic
283C2×C11#306911yescharacteristic
284D11—44no—
285C24—221no—
286#41—42no—
287#41—42no—
288C2×Q8—21no—
289C2×Q8—222no—
290C2×Q8—441no—
291C2×Q8—882no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—41no—
296C2×D4—114no—
297C2×D4—112no—
298C2×D4—221no—
299C2×D4—222no—
300C22×C4—41no—
301C22×C4—221no—
302C22×C4—222no—
303C22×C4—222no—
304C22×C4—441no—
305C22×C4—882no—
306C22×C4#433911yescharacteristic
307C22×C4D4×D1111yescharacteristic
308C22×C4D4×D1111yescharacteristic
309SD16—444no—
310SD16—884no—
311D8—444no—
312M16—442no—
313C2×C8—22no—
314C2×C8—22no—
315C2×C8—42no—
316C2×C8—114no—
317C2×C8—222no—
318C2×C8—884no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—112no—
322C4⋊C4—221no—
323C4⋊C4—222no—
324C4⋊C4—222no—
325C4⋊C4—441no—
326C4⋊C4—441no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—222no—
330C22⋊C4—222no—
331C42#433911yescharacteristic
332C42D4×D1111yescharacteristic
333C42D4×D1111yescharacteristic
334C42C23×D1111yescharacteristic
335C11#1938511yescharacteristic, complemented, Sylow
336C23—41no—
337C23—222no—
338C23—224no—
339C23—881no—
340C23—881no—
341C23#6693711yescharacteristic
342Q8—41no—
343Q8—41no—
344Q8—444no—
345Q8—882no—
346D4—41no—
347D4—41no—
348D4—42no—
349D4—81no—
350D4—82no—
351D4—114no—
352D4—222no—
353D4—224no—
354C2×C4—22no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—82no—
358C2×C4—222no—
359C2×C4—444no—
360C2×C4—442no—
361C2×C4—882no—
362C2×C4—881no—
363C2×C4—882no—
364C2×C4#6693711yescharacteristic
365C2×C4#6693711yescharacteristic
366C2×C4#6693711yescharacteristic
367C2×C4#6696512yes—
368C2×C4SD16×D1112yes—
369C2×C4C2×#433911yescharacteristic
370C2×C4C2×D4×D1111yescharacteristic
371C2×C4C2×D4×D1111yescharacteristic
372C8—42no—
373C8—42no—
374C8—224no—
375C8—442no—
376C22—21no—
377C22—21no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22—224no—
382C22—442no—
383C22—442no—
384C22—884no—
385C22#1062239112yes—
386C22C2×#6693711yescharacteristic
387C4—21no—
388C4—21no—
389C4—21no—
390C4—81no—
391C4—442no—
392C4—882no—
393C4#1062239112yes—
394C4C2×#6696511yescharacteristic
395C4C2×SD16×D1111yescharacteristic
396C4#1062330012yes—
397C2—22no—
398C2—161no—
399C2—444no—
400C2#1307812211yescharacteristic
401C2C2×#1062239111yescharacteristic
402C2#1307835611yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1540C2
socleC22×C11C2×#121
prime radical#13078076C2
hypercenter#1540D11
hypocenterC11#19385
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1540

Complements

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

NH ≅ G/Ntype
1. #13079538C2semidirect
2. C2×#10622459C2semidirect
4. #13077639C2semidirect
5. #13068042C2semidirect
6. #13067956C2semidirect
7. #13067386C2semidirect
8. #13067300C2semidirect
9. C11×#1540C2semidirect
19. #10622706C22semidirect
21. #10622689C22semidirect
33. C11×#332C22semidirect
34. C11×#331C22semidirect
35. #10622120C22semidirect
36. #10622118C22semidirect
101. C2×D44SD16semidirect
143. #1540D11semidirect
209. #332C2×D11semidirect
210. #331C2×D11semidirect
335. C11#19385semidirect

Maximal subgroups

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

subgroupindex
#130795382
C2×#106224592
#130780762
#130776392
#130680422
#130679562
#130673862
#130673002
C11×#15402
#1938511