Finite Group Databasebeta

← #14909716

Subgroups — #14909716

Order 2816.

608 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079186C211yesmaximal, characteristic, complemented
2#13070875C212yesmaximal, complemented
3#13070847C212yesmaximal, complemented
4#13070675C212yesmaximal, complemented
5#13070668C212yesmaximal, complemented
6#13070550C211yesmaximal, characteristic, complemented
7#13070545C211yesmaximal, characteristic, complemented
8#13070533C211yesmaximal, characteristic, complemented
9#13070528C211yesmaximal, characteristic
10#13070415C211yesmaximal, characteristic, complemented
11C2×C11×#495C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C22×C11×SD16—21no—
14C22×C11×D8C2211yescharacteristic
15C2×C11×#124—21no—
16#10623010—21no—
17C11×#495—21no—
18C11×#495—21no—
19C11×#495C2212yes—
20C11×#495C2212yes—
21C2×C4×C8×C11C2211yescharacteristic
22C2×#66893C2212yescomplemented
23C2×#66892C2212yescomplemented
24C2×#66891C2212yes—
25C2×#66890C2212yes—
26#10622729C2211yescharacteristic
27#10622728C2211yescharacteristic
28#10622727—21no—
29C4×Dic44C2211yescharacteristic, complemented
30#10622310—21no—
31#10622309C2211yescharacteristic, complemented
32C4×D88C2211yescharacteristic, complemented
33C4×#4314—21no—
34#10622296C2211yescharacteristic, complemented
35#10622202C2212yescomplemented
36#10622202C2212yescomplemented
37#10622200C2212yes—
38#10622200C2212yes—
39C22⋊(C11⋊C16)C2211yescharacteristic
40C22⋊(C11⋊C16)C2211yescharacteristic
41C4⋊(C11⋊C16)C2212yescomplemented
42C4×C11⋊C16C2212yescomplemented
43C22×Q8×C11—21no—
44C22×D4×C11—21no—
45C2×C11×Q16—21no—
46C2×C11×Q16—42no—
47C2×C11×Q16C2312yes—
48C2×C11×SD16—22no—
49C2×C11×SD16—22no—
50C2×C11×SD16—44no—
51C2×C11×D8—21no—
52C2×C11×D8—42no—
53C2×C11×D8C2312yes—
54C22×C8×C11D411yescharacteristic
55C22×C8×C11C2311yescharacteristic
56C11×#124—22no—
57C11×#124—22no—
58C11×#124—41no—
59C11×#124—41no—
60C2×C11×C22⋊C4—41no—
61C2×C11×C22⋊C4—41no—
62C2×C42×C11D411yescharacteristic
63#66983—21no—
64#66982—41no—
65C4×C22⋊D11—41no—
66#66977—21no—
67C2×Dic44C2311yescharacteristic
68C2×D88C2311yescharacteristic
69C2×#4314—21no—
70#66929—41no—
71#66928—21no—
72C4×D44—21no—
73#66925—41no—
74#66923—21no—
75C4×Dic22—21no—
76C4×C8×C11D411yescharacteristic
77C4×C8×C11D411yescharacteristic
78C4×C8×C11C2311yescharacteristic
79C4×C8×C11C2311yescharacteristic
80#66893—42no—
81#66892—42no—
82#66891—42no—
83#66890—42no—
84#66885—21no—
85#66885—21no—
86#66882C2311yescharacteristic
87#66882C2311yescharacteristic
88#66881—21no—
89#66880—21no—
90#66880—21no—
91C2×C11⋊C16C2312yes—
92C2×C11⋊C16C2312yes—
93#33777—111nomaximal, Sylow
94C24×C11—41no—
95C2×Q8×C11—22no—
96C2×Q8×C11—42no—
97C2×Q8×C11—42no—
98C2×Q8×C11—41no—
99C2×D4×C11—22no—
100C2×D4×C11—42no—
101C2×D4×C11—42no—
102C2×D4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11D811yescharacteristic
105C22×C4×C11D811yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C2×C22⋊D11—41no—
108C2×D44—21no—
109C2×C4×D11—41no—
110C2×Dic22—21no—
111C11×Q16—22no—
112C11×Q16—22no—
113C11×Q16—42no—
114C11×SD16—44no—
115C11×SD16—44no—
116C11×D8—22no—
117C11×D8—22no—
118C11×D8—42no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2×D411yescharacteristic
124C2×C8×C11C2411yescharacteristic
125C11×C22⋊C4—42no—
126C11×C22⋊C4—42no—
127C11×C22⋊C4—42no—
128C11×C22⋊C4—42no—
129C42×C11D811yescharacteristic
130C42×C11D811yescharacteristic
131C42×C11C2×D411yescharacteristic
132C42×C11C2×D411yescharacteristic
133C22⋊Dic11—41no—
134(C2×D11)⋊C4—41no—
135(C2×D11)⋊C4—41no—
136(C2×D11)⋊C4—41no—
137(C2×D11)⋊C4—41no—
138C4⋊Dic11—21no—
139C4⋊Dic11—21no—
140Dic11⋊C4—41no—
141Dic11⋊C4—41no—
142Dic11⋊C4—41no—
143Dic11⋊C4—41no—
144C4×Dic11—41no—
145Dic44—22no—
146D88—22no—
147#4314—42no—
148C11⋊C16—22no—
149C11⋊C16—22no—
150#3168—111no—
151C2×#495D1111yescharacteristic, complemented
152#2249—112no—
153#2242—112no—
154#2211—112no—
155#2210—112no—
156#2188—111no—
157#2187—111no—
158#2185—111no—
159#2184—111no—
160#2162—111no—
161C23×C11—42no—
162C23×C11—82no—
163C23×C11—82no—
164C23×C11—82no—
165C23×C11C2×D811yescharacteristic
166C22×D11—41no—
167Q8×C11—42no—
168Q8×C11—42no—
169Q8×C11—82no—
170D4×C11—42no—
171D4×C11—42no—
172D4×C11—82no—
173C2×C4×C11—22no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—41no—
177C2×C4×C11—42no—
178C2×C4×C11—82no—
179C2×C4×C11C2×D811yescharacteristic
180C2×C4×C11C2×D811yescharacteristic
181C2×C4×C11C2×D811yescharacteristic
182C2×C4×C11C2×D811yescharacteristic
183C2×C4×C11C2×D811yescharacteristic
184C2×C4×C11C22×D411yescharacteristic
185C22⋊D11—82no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189D44—41no—
190D44—41no—
191C4×D11—82no—
192Dic22—41no—
193Dic22—41no—
194C8×C11—21no—
195C8×C11—21no—
196C8×C11AGL(1,ℤ/8)12yes—
197C8×C11H(5,𝔽2)12yes—
198C22×Q16C2×D1111yescharacteristic
199C22×SD16—21no—
200C22×D8C2×D1111yescharacteristic
201#529—221no—
202C2×#124—21no—
203C2×Q32—112no—
204C2×SD32—112no—
205C2×SD32—112no—
206C2×D16—112no—
207#499—111no—
208#495—21no—
209#495—21no—
210#495—111no—
211#495C2×D1112yes—
212#495C2×D1112yes—
213#488—221no—
214#467—111no—
215#466—111no—
216#465—221no—
217C4×Q16—111no—
218C4×SD16—221no—
219C4×D8—111no—
220C2×C4×C8C2×D1111yescharacteristic
221C4⋊C16—112no—
222#358—112no—
223#358—112no—
224#357—112no—
225#357—112no—
226C22⋊C16—111no—
227C22⋊C16—111no—
228C4×C16—112no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—82no—
232C22×C11—82no—
233C22×C11—82no—
234C22×C11—164no—
235C22×C11#50812yes—
236C22×C11C22×D811yescharacteristic
237C2×D11—81no—
238C2×D11—81no—
239C2×D11—81no—
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—21no—
243C4×C11—21no—
244C4×C11—21no—
245C4×C11—82no—
246C4×C11#53511yescharacteristic
247C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
248Dic11—81no—
249Dic11—81no—
250Dic11—81no—
251C22×Q8—21no—
252C22×D4—21no—
253C2×Q16—21no—
254C2×Q16—42no—
255C2×Q16—111no—
256C2×Q16C22×D1112yes—
257C2×SD16—22no—
258C2×SD16—22no—
259C2×SD16—44no—
260C2×SD16—221no—
261C2×D8—21no—
262C2×D8—42no—
263C2×D8—111no—
264C2×D8C22×D1112yes—
265C22×C8C22⋊D1111yescharacteristic
266C22×C8C22×D1111yescharacteristic
267#126—441no—
268#125—221no—
269#124—22no—
270#124—22no—
271#124—41no—
272#124—41no—
273#124—221no—
274#123—441no—
275C22⋊Q8—221no—
276#121—221no—
277C4×Q8—221no—
278C4×D4—221no—
279C4×D4—441no—
280#117—441no—
281C2×C22⋊C4—41no—
282C2×C22⋊C4—41no—
283C2×C42C22⋊D1111yescharacteristic
284Q32—442no—
285SD32—442no—
286SD32—442no—
287D16—442no—
288C2×C16—112no—
289C2×C16—112no—
290#107—111no—
291#107—111no—
292#106—221no—
293#103—221no—
294#103—221no—
295#102—221no—
296#102—221no—
297C4×C8C22⋊D1111yescharacteristic
298C4×C8C22⋊D1111yescharacteristic
299C4×C8C22×D1111yescharacteristic
300C4×C8C22×D1111yescharacteristic
301C2×C11—22no—
302C2×C11—162no—
303C2×C11#320511yescharacteristic
304C2×C11C2×#50811yescharacteristic
305C2×C11#341411yescharacteristic
306D11—161no—
307C24—41no—
308C2×Q8—22no—
309C2×Q8—42no—
310C2×Q8—42no—
311C2×Q8—41no—
312C2×Q8—221no—
313C2×D4—22no—
314C2×D4—42no—
315C2×D4—42no—
316C2×D4—41no—
317C2×D4—221no—
318C2×D4—441no—
319C22×C4—41no—
320C22×C4—441no—
321C22×C4#432311yescharacteristic
322C22×C4#432311yescharacteristic
323C22×C4C2×C22⋊D1111yescharacteristic
324Q16—22no—
325Q16—22no—
326Q16—42no—
327Q16—222no—
328SD16—44no—
329SD16—44no—
330SD16—442no—
331D8—22no—
332D8—22no—
333D8—42no—
334D8—222no—
335C2×C8—22no—
336C2×C8—22no—
337C2×C8C2×C22⋊D1111yescharacteristic
338C2×C8C2×C22⋊D1111yescharacteristic
339C2×C8C2×C22⋊D1111yescharacteristic
340C2×C8C23×D1111yescharacteristic
341C4⋊C4—221no—
342C4⋊C4—221no—
343C4⋊C4—441no—
344C4⋊C4—441no—
345C4⋊C4—441no—
346C4⋊C4—441no—
347C22⋊C4—42no—
348C22⋊C4—42no—
349C22⋊C4—42no—
350C22⋊C4—42no—
351C22⋊C4—441no—
352C22⋊C4—441no—
353C22⋊C4—441no—
354C22⋊C4—441no—
355C22⋊C4—441no—
356C42—441no—
357C42#432311yescharacteristic
358C42#432311yescharacteristic
359C42C2×C22⋊D1111yescharacteristic
360C42C2×C22⋊D1111yescharacteristic
361C16—222no—
362C16—222no—
363C11#3377711yescharacteristic, complemented, Sylow
364C23—42no—
365C23—82no—
366C23—82no—
367C23—82no—
368C23—441no—
369C23C2×#432311yescharacteristic
370Q8—42no—
371Q8—42no—
372Q8—82no—
373Q8—441no—
374Q8—441no—
375D4—42no—
376D4—42no—
377D4—82no—
378D4—441no—
379D4—441no—
380D4—882no—
381C2×C4—22no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—82no—
387C2×C4—441no—
388C2×C4—441no—
389C2×C4—441no—
390C2×C4—882no—
391C2×C4C2×#432311yescharacteristic
392C2×C4C2×#432311yescharacteristic
393C2×C4C2×#432311yescharacteristic
394C2×C4C2×#432311yescharacteristic
395C2×C4C2×#432311yescharacteristic
396C2×C4C22×C22⋊D1111yescharacteristic
397C8—21no—
398C8—21no—
399C8#6698512yes—
400C8#6703712yes—
401C22—21no—
402C22—21no—
403C22—82no—
404C22—82no—
405C22—82no—
406C22—164no—
407C22—881no—
408C22—881no—
409C22—881no—
410C22#1062280712yes—
411C22C22×#432311yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—82no—
418C4—881no—
419C4—881no—
420C4—881no—
421C4C2×#6698511yescharacteristic
422C4#1062333611yescharacteristic
423C2—22no—
424C2—162no—
425C2—1761no—
426C2#1307953411yescharacteristic
427C2C2×#1062280711yescharacteristic
428C2#1308175011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#495C2
socleC22×C11C22×D8
prime radical#13070528C2
hypercenterC2×#495D11
hypocenterC11#33777
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×#495

Complements

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

NH ≅ G/Ntype
1. #13079186C2semidirect
2. #13070875C2semidirect
3. #13070847C2semidirect
4. #13070675C2semidirect
5. #13070668C2semidirect
6. #13070550C2semidirect
7. #13070545C2semidirect
8. #13070533C2semidirect
10. #13070415C2semidirect
11. C2×C11×#495C2semidirect
22. C2×#66893C22semidirect
23. C2×#66892C22semidirect
29. C4×Dic44C22semidirect
31. #10622309C22semidirect
32. C4×D88C22semidirect
34. #10622296C22semidirect
35. #10622202C22semidirect
36. #10622202C22semidirect
41. C4⋊(C11⋊C16)C22semidirect
42. C4×C11⋊C16C22semidirect
151. C2×#495D11semidirect
363. C11#33777semidirect

Maximal subgroups

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

subgroupindex
#130791862
#130708752
#130708472
#130706752
#130706682
#130705502
#130705452
#130705332
#130705282
#130704152
C2×C11×#4952
#3377711