Finite Group Databasebeta

← #14655676

Subgroups — #14655676

Order 2816.

642 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 642 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079534C211yesmaximal, characteristic
2#13079075C211yesmaximal, characteristic, complemented
3C2×#10622683C211yesmaximal, characteristic, complemented
4#13067289C211yesmaximal, characteristic, complemented
5#13067066C211yesmaximal, characteristic, complemented
6#13066454C211yesmaximal, characteristic, complemented
7C11×#1965C211yesmaximal, characteristic, complemented
8C2×C11×#127C2211yescharacteristic
9C2×#66962—22no—
10#10623008C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C2×C11×#100—22no—
14C4×C11×M16C2211yescharacteristic
15#10622830—22no—
16C2×#66896—22no—
17#10622686—21no—
18#10622685—22no—
19#10622683—22no—
20#10622683—21no—
21#10622683—22no—
22#10622538C2211yescharacteristic
23C2×C4×C11⋊C8C2211yescharacteristic
24#10622328—22no—
25#10622312—21no—
26#10622306—21no—
27#10622121—22no—
28#10622120—22no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11D412yes—
32C2×#4339—21no—
33C22×Dic22—21no—
34C2×C11×M16—21no—
35C2×C11×M16D412yes—
36C11×#127—21no—
37C11×#127—21no—
38C11×#127—21no—
39C11×#127—21no—
40C2×C42×C11C2311yescharacteristic
41C2×#4323—24no—
42#66983—21no—
43#66983—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—21no—
46C22×C11⋊C8—21no—
47#66962—44no—
48#66962—44no—
49C2×Dic44—24no—
50C2×#4314—24no—
51#66928—21no—
52#66927D411yescharacteristic
53C4×D44—21no—
54C4×D44—21no—
55#66922—21no—
56#66922—21no—
57#66922—21no—
58#66922D412yes—
59#66922D411yescharacteristic
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C11×#100—44no—
63C11×#97—21no—
64C4×C8×C11—21no—
65#66896—28no—
66#66896—24no—
67C22⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)D412yes—
69C4×C11⋊C8—21no—
70C4×C11⋊C8—21no—
71C4×C11⋊C8D412yes—
72#10168—111nomaximal, Sylow
73C24×C11—22no—
74C2×D4×C11—22no—
75C2×D4×C11—22no—
76C2×D4×C11—44no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11—42no—
82C2×D4×C11—42no—
83C2×D4×C11—82no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C2×C22⋊D11—41no—
88C22×Dic11—41no—
89#4339—42no—
90#4339—42no—
91C2×D44—21no—
92C2×D44—21no—
93C2×D44—21no—
94C2×C4×D11—41no—
95C2×Dic22—22no—
96C2×Dic22—21no—
97C2×Dic22—41no—
98C2×Dic22—42no—
99C2×Dic22—42no—
100C11×M16—22no—
101C11×M16—42no—
102C11×M16D814yescomplemented
103C2×C8×C11—22no—
104C2×C8×C11—41no—
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109#4323—84no—
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—41no—
112C4⋊Dic11—22no—
113C4⋊Dic11—21no—
114C4⋊Dic11—22no—
115C4⋊Dic11—21no—
116C4⋊Dic11—41no—
117C4⋊Dic11—41no—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—42no—
121Dic44—48no—
122#4314—48no—
123#3205—111no—
124#3152—111no—
125C2×#486—111no—
126#1965D1111yescharacteristic, complemented
127#1546—111no—
128#1492—111no—
129#1278—111no—
130C23×C11—42no—
131C23×C11—44no—
132C23×C11—82no—
133C23×C11—82no—
134C23×C11#12111yescharacteristic
135C22×D11—41no—
136D4×C11—44no—
137D4×C11—44no—
138D4×C11—82no—
139D4×C11—82no—
140D4×C11—82no—
141D4×C11—81no—
142D4×C11—81no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12711yescharacteristic
151C2×C4×C11C2×D812yes—
152C2×C4×C11AGL(1,ℤ/8)12yes—
153C22⋊D11—82no—
154C2×Dic11—42no—
155C2×Dic11—41no—
156C2×Dic11—82no—
157D44—42no—
158D44—42no—
159D44—42no—
160C4×D11—81no—
161C4×D11—81no—
162Dic22—44no—
163Dic22—42no—
164Dic22—81no—
165Dic22—81no—
166C8×C11—24no—
167C8×C11—81no—
168C11⋊C8—42no—
169C11⋊C8—42no—
170C2×#137—222no—
171#532—111no—
172C2×C4⋊Q8—111no—
173C2×#127C2×D1111yescharacteristic
174#497—222no—
175#494—221no—
176#493—221no—
177#492—221no—
178#486—222no—
179#486—222no—
180#486—221no—
181#459—222no—
182#447—222no—
183#431—111no—
184#423C2×D1111yescharacteristic
185C2×#102—222no—
186C2×#100—22no—
187C4×M16C2×D1111yescharacteristic
188C2×C4×C8—111no—
189#332—222no—
190D4⋊C8—222no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—82no—
194C22×C11—82no—
195C22×C11—82no—
196C22×C11—164no—
197C22×C11#39211yescharacteristic
198C22×C11#45912yes—
199C2×D11—81no—
200C2×D11—81no—
201C2×D11—81no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11#44712yes—
205C4×C11#45512yes—
206C4×C11#47112yes—
207C4×C11#49311yescharacteristic
208C4×C11#49611yescharacteristic
209Dic11—82no—
210Dic11—81no—
211C2×#41—221no—
212C22×Q8—221no—
213C22×D4—21no—
214C22×D4—21no—
215C22×D4D4412yes—
216#137—444no—
217#137—444no—
218C2×Q16—224no—
219C2×SD16—224no—
220C2×D8—224no—
221C2×M16—21no—
222C2×M16C22⋊D1112yes—
223C22×C8—221no—
224C4⋊Q8—112no—
225C4⋊Q8—111no—
226C4⋊Q8—221no—
227C4⋊Q8—221no—
228C4⋊Q8—221no—
229#127—21no—
230#127—21no—
231#127—21no—
232#127—21no—
233#127—111no—
234#124—221no—
235#121—221no—
236#121—221no—
237C4×D4—221no—
238C4×D4—221no—
239C2×C4⋊C4—221no—
240C2×C4⋊C4—221no—
241C2×C42C22×D1111yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—112no—
245#102—228no—
246#102—224no—
247#100—44no—
248C22⋊C8—221no—
249#97—21no—
250C4×C8—21no—
251C4×C8—112no—
252C4×C8—221no—
253C4×C8—221no—
254C2×C11—22no—
255C2×C11—162no—
256C2×C11#200411yescharacteristic
257C2×C11#201111yescharacteristic
258C2×C11#201911yescharacteristic
259D11—161no—
260C24—22no—
261#41—442no—
262#41—442no—
263C2×Q8—221no—
264C2×Q8—222no—
265C2×Q8—441no—
266C2×Q8—442no—
267C2×Q8—442no—
268C2×D4—22no—
269C2×D4—22no—
270C2×D4—44no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—42no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—42no—
277C2×D4—82no—
278C2×D4—221no—
279C2×D4—221no—
280C2×D4—221no—
281C2×D4—441no—
282C22×C4—441no—
283C22×C4—441no—
284C22×C4C2×D4411yescharacteristic
285C22×C4#433911yescharacteristic
286C22×C4C2×C22⋊D1111yescharacteristic
287Q16—448no—
288SD16—448no—
289D8—884no—
290M16—22no—
291M16—42no—
292M16#432314yescomplemented
293C2×C8—22no—
294C2×C8—41no—
295C2×C8—222no—
296C2×C8—222no—
297C2×C8—442no—
298C4⋊C4—222no—
299C4⋊C4—221no—
300C4⋊C4—222no—
301C4⋊C4—221no—
302C4⋊C4—441no—
303C4⋊C4—441no—
304C22⋊C4—441no—
305C22⋊C4—441no—
306C42D4×D1111yescharacteristic
307C42D4×D1111yescharacteristic
308C42D4×D1111yescharacteristic
309C42D4×D1111yescharacteristic
310C11#1016811yescharacteristic, complemented, Sylow
311C23—42no—
312C23—44no—
313C23—82no—
314C23—82no—
315C23—441no—
316C23#6698311yescharacteristic
317Q8—444no—
318Q8—442no—
319Q8—881no—
320Q8—881no—
321D4—44no—
322D4—44no—
323D4—82no—
324D4—82no—
325D4—82no—
326D4—81no—
327D4—81no—
328D4—442no—
329D4—442no—
330D4—442no—
331D4—882no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—441no—
335C2×C4—442no—
336C2×C4—882no—
337C2×C4—881no—
338C2×C4—881no—
339C2×C4#6693511yescharacteristic
340C2×C4#6693511yescharacteristic
341C2×C4#6693711yescharacteristic
342C2×C4#6693711yescharacteristic
343C2×C4C2×#432312yes—
344C2×C4#6699011yescharacteristic
345C2×C4#6699311yescharacteristic
346C2×C4#6700212yes—
347C8—24no—
348C8—81no—
349C8—442no—
350C8—442no—
351C22—21no—
352C22—21no—
353C22—82no—
354C22—82no—
355C22—82no—
356C22—164no—
357C22—881no—
358C22—881no—
359C22—881no—
360C22#1062257311yescharacteristic
361C22#1062262812yes—
362C4—21no—
363C4—21no—
364C4—881no—
365C4—882no—
366C4#1062235912yes—
367C4#1062236112yes—
368C4#1062264912yes—
369C4#1062267111yescharacteristic
370C4#1062268611yescharacteristic
371C2—22no—
372C2—162no—
373C2—1761no—
374C2#1306964711yescharacteristic
375C2#1306968611yescharacteristic
376C2#1306973211yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1965C2
socleC22×C11#392
prime radical#13079534C2
hypercenter#1965D11
hypocenterC11#10168
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1965

Complements

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

NH ≅ G/Ntype
2. #13079075C2semidirect
3. C2×#10622683C2semidirect
4. #13067289C2semidirect
5. #13067066C2semidirect
6. #13066454C2semidirect
7. C11×#1965C2semidirect
102. C11×M16D8semidirect
126. #1965D11semidirect
292. M16#4323semidirect
310. C11#10168semidirect

Maximal subgroups

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

subgroupindex
#130795342
#130790752
C2×#106226832
#130672892
#130670662
#130664542
C11×#19652
#1016811