Finite Group Databasebeta

← #14650458

Subgroups — #14650458

Order 2816.

558 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079531C211yesmaximal, characteristic
2#13069440C211yesmaximal, characteristic, complemented
3#13067285C211yesmaximal, characteristic, complemented
4#13067176C211yesmaximal, characteristic, complemented
5#13066476C211yesmaximal, characteristic, complemented
6#13066447C211yesmaximal, characteristic, complemented
7C11×#2932C211yesmaximal, characteristic, complemented
8C2×C11×#131—21no—
9C11×#532C2211yescharacteristic
10C2×#66927C2211yescharacteristic
11C11×#435—22no—
12C11×#435—22no—
13C11×#423C2211yescharacteristic
14C11×#408—21no—
15C2×C11×#97C2211yescharacteristic
16C2×#66885—21no—
17C2×#66885—21no—
18#10622701C412yescomplemented
19#10622686C412yescomplemented
20#10622649—22no—
21#10622628—22no—
22#10622549C2211yescharacteristic
23#10622538C2211yescharacteristic
24#10622538C2211yescharacteristic
25#10622175—22no—
26#10622123—22no—
27C2×C11×#41—21no—
28C22×D44—21no—
29C22×D44—21no—
30C22×D44—21no—
31C11×#131—42no—
32C11×#131—42no—
33C2×C11×M16—22no—
34C2×C11×M16—21no—
35C22×C8×C11—22no—
36C22×C8×C11D411yescharacteristic
37C22×C8×C11D411yescharacteristic
38C11×C4⋊Q8C2×C411yescharacteristic
39C11×#127C2×C411yescharacteristic
40C11×#124—21no—
41C11×#121—21no—
42C11×#121D412yes—
43C4×D4×C11—21no—
44C4×D4×C11D412yes—
45C2×C42×C11C2311yescharacteristic
46C2×#4323—24no—
47C2×C4⋊Dic11—21no—
48#66927—21no—
49#66927—21no—
50#66927—21no—
51#66927C2×C412yes—
52C11×C4⋊C8—21no—
53C11×C4⋊C8D412yes—
54C11×C22⋊C8—24no—
55C11×#97—21no—
56C11×#97—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C22⋊(C11⋊C8)—21no—
60C22⋊(C11⋊C8)—21no—
61#66885—42no—
62#66885—42no—
63#66873—24no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4×C11⋊C8—21no—
67C4×C11⋊C8C2×C412yes—
68#9293—111nomaximal, Sylow
69C23×D11—41no—
70C11×#41—41no—
71C11×#41—41no—
72C11×#41—41no—
73C11×#41—41no—
74C2×Q8×C11—21no—
75C2×D4×C11—22no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11C22⋊C412yes—
79C22×C4×C11—22no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C22×Dic11—41no—
84C2×D44—22no—
85C2×D44—22no—
86C2×D44—22no—
87C2×D44—41no—
88C2×D44—41no—
89C2×D44—41no—
90C2×D44—41no—
91C2×D44—41no—
92C2×D44—41no—
93C2×D44—41no—
94C2×D44—82no—
95C2×D44—82no—
96C11×M16—44no—
97C11×M16—41no—
98C11×M16—41no—
99C2×C8×C11—21no—
100C2×C8×C11—21no—
101C2×C8×C11—22no—
102C2×C8×C11—21no—
103C2×C8×C11—21no—
104C2×C8×C11—21no—
105C2×C8×C11—44no—
106C2×C8×C11D812yescomplemented
107C11×C4⋊C4—21no—
108C11×C4⋊C4C22⋊C412yes—
109C11×C22⋊C4—22no—
110C11×C22⋊C4—22no—
111C42×C11C22×C411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11#4111yescharacteristic
115#4323—84no—
116C4⋊Dic11—41no—
117C4⋊Dic11—41no—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—41no—
120#3205—111no—
121#2932D1111yescharacteristic, complemented
122#1961—111no—
123#1545—111no—
124#1517—111no—
125#1286—111no—
126#1275—111no—
127C23×C11—22no—
128C23×C11#12111yescharacteristic
129C22×D11—42no—
130C22×D11—82no—
131C22×D11—82no—
132C22×D11—81no—
133C22×D11—81no—
134Q8×C11—41no—
135Q8×C11—41no—
136D4×C11—42no—
137D4×C11—42no—
138D4×C11—42no—
139D4×C11—41no—
140D4×C11—41no—
141D4×C11—81no—
142C2×C4×C11—22no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11C2×C22⋊C411yescharacteristic
148C2×C4×C11C4×D411yescharacteristic
149C2×C4×C11C4×D411yescharacteristic
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12311yescharacteristic
153C2×C4×C11C2×D811yescharacteristic
154C2×C4×C11#13511yescharacteristic
155C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
157C2×Dic11—81no—
158C2×Dic11—81no—
159C2×Dic11—81no—
160D44—44no—
161D44—42no—
162D44—42no—
163D44—82no—
164D44—82no—
165D44—82no—
166D44—81no—
167D44—81no—
168C8×C11—22no—
169C8×C11—42no—
170C8×C11—41no—
171C11⋊C8—42no—
172C11⋊C8—81no—
173C2×#131—21no—
174#532C2×D1111yescharacteristic
175C2×#127—111no—
176#493—112no—
177#486—112no—
178#459—222no—
179#447—222no—
180#435—22no—
181#435—22no—
182#431—111no—
183#431—111no—
184#423C2×D1111yescharacteristic
185C2×#102—221no—
186C2×#102—221no—
187#408—21no—
188C2×#97C2×D1111yescharacteristic
189#382—111no—
190#331—222no—
191#327—222no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—42no—
195C22×C11—42no—
196C22×C11—42no—
197C22×C11#38611yescharacteristic
198C22×C11#45911yescharacteristic
199C22×C11#46311yescharacteristic
200C2×D11—82no—
201C2×D11—82no—
202C2×D11—82no—
203C2×D11—162no—
204C2×D11—162no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—42no—
210C4×C11C4×D811yescharacteristic
211C4×C11#44211yescharacteristic
212C4×C11#44711yescharacteristic
213C4×C11#44911yescharacteristic
214Dic11—161no—
215C2×#41—21no—
216C22×D4—221no—
217C22×D4—221no—
218C22×D4—221no—
219C2×D8—224no—
220#131—42no—
221#131—42no—
222C2×M16—22no—
223C2×M16—21no—
224C22×C8—22no—
225C22×C8C22⋊D1111yescharacteristic
226C22×C8C22⋊D1111yescharacteristic
227C4⋊Q8C4×D1111yescharacteristic
228#127—112no—
229#127—221no—
230#127—221no—
231#127—221no—
232#127C4×D1111yescharacteristic
233#124—21no—
234#121—21no—
235#121D4412yes—
236C4×D4—21no—
237C4×D4C22⋊D1112yes—
238C2×C4⋊C4—221no—
239C2×C42C22×D1111yescharacteristic
240C4⋊C8—21no—
241C4⋊C8—221no—
242C4⋊C8—221no—
243C4⋊C8C22⋊D1112yes—
244#102—224no—
245#102—442no—
246#102—442no—
247C22⋊C8—24no—
248C22⋊C8—221no—
249C22⋊C8—221no—
250#97—21no—
251#97—21no—
252C4×C8—112no—
253C4×C8—221no—
254#95—221no—
255#95—221no—
256C2×C11—21no—
257C2×C11—21no—
258C2×C11—82no—
259C2×C11#187911yescharacteristic
260C2×C11#190311yescharacteristic
261C2×C11#191011yescharacteristic
262D11—162no—
263C24—441no—
264#41—41no—
265#41—41no—
266#41—41no—
267#41—41no—
268C2×Q8—21no—
269C2×D4—22no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—222no—
273C2×D4—222no—
274C2×D4—222no—
275C2×D4—441no—
276C2×D4—441no—
277C2×D4—441no—
278C2×D4—441no—
279C2×D4—441no—
280C2×D4—441no—
281C2×D4—441no—
282C2×D4—882no—
283C2×D4—882no—
284C2×D4(C2×D11)⋊C412yes—
285C22×C4—22no—
286C22×C4—441no—
287C22×C4C2×D4411yescharacteristic
288C22×C4#433911yescharacteristic
289C22×C4C2×C22⋊D1111yescharacteristic
290D8—884no—
291M16—44no—
292M16—41no—
293M16—41no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—22no—
300C2×C8—44no—
301C2×C8—222no—
302C2×C8—441no—
303C2×C8#432312yescomplemented
304C4⋊C4—21no—
305C4⋊C4—441no—
306C4⋊C4—441no—
307C4⋊C4(C2×D11)⋊C412yes—
308C22⋊C4—22no—
309C22⋊C4—22no—
310C42C2×C4×D1111yescharacteristic
311C42#433911yescharacteristic
312C42C2×C22⋊D1111yescharacteristic
313C42C2×C22⋊D1111yescharacteristic
314C11#929311yescharacteristic, complemented, Sylow
315C23—22no—
316C23—442no—
317C23—882no—
318C23—882no—
319C23—881no—
320C23—881no—
321C23#6698311yescharacteristic
322Q8—41no—
323Q8—41no—
324D4—42no—
325D4—42no—
326D4—42no—
327D4—41no—
328D4—41no—
329D4—81no—
330D4—444no—
331D4—442no—
332D4—442no—
333D4—882no—
334D4—882no—
335D4—882no—
336D4—881no—
337D4—881no—
338C2×C4—22no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—881no—
344C2×C4—881no—
345C2×C4—881no—
346C2×C4C2×(C2×D11)⋊C411yescharacteristic
347C2×C4C4×C22⋊D1111yescharacteristic
348C2×C4C4×C22⋊D1111yescharacteristic
349C2×C4#6698211yescharacteristic
350C2×C4#6698311yescharacteristic
351C2×C4C2×#432311yescharacteristic
352C2×C4#6698511yescharacteristic
353C2×C4#6700211yescharacteristic
354C2×C4#6700311yescharacteristic
355C2×C4#6700611yescharacteristic
356C8—22no—
357C8—42no—
358C8—41no—
359C8—442no—
360C8—881no—
361C22—21no—
362C22—21no—
363C22—42no—
364C22—42no—
365C22—42no—
366C22—882no—
367C22—882no—
368C22—882no—
369C22—1762no—
370C22—1762no—
371C22#1062262811yescharacteristic
372C22#1062262911yescharacteristic
373C22#1062282611yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—42no—
379C4—1761no—
380C4C4×#432311yescharacteristic
381C4#1062262711yescharacteristic
382C4#1062283011yescharacteristic
383C4#1062285111yescharacteristic
384C2—21no—
385C2—21no—
386C2—82no—
387C2—1762no—
388C2#1306896411yescharacteristic
389C2#1306909611yescharacteristic
390C2#1306914311yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2932C2
socleC22×C11#386
prime radical#13079531C2
cosocleC2×C42×C11C23
hypercenter#2932D11
hypocenterC11#9293
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2932

Complements

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

NH ≅ G/Ntype
2. #13069440C2semidirect
3. #13067285C2semidirect
4. #13067176C2semidirect
5. #13066476C2semidirect
6. #13066447C2semidirect
7. C11×#2932C2semidirect
18. #10622701C4semidirect
19. #10622686C4semidirect
106. C2×C8×C11D8semidirect
121. #2932D11semidirect
303. C2×C8#4323semidirect
314. C11#9293semidirect

Maximal subgroups

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

subgroupindex
#130795312
#130694402
#130672852
#130671762
#130664762
#130664472
C11×#29322
#929311