Finite Group Databasebeta

← #14908511

Subgroups — #14908511

Order 2816.

524 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079125C211yesmaximal, characteristic, complemented
2D11×#443C211yesmaximal, characteristic
3#13070791C212yesmaximal, complemented
4#13070790C212yesmaximal, complemented
5#13070788C211yesmaximal, characteristic, complemented
6#13070787C211yesmaximal, characteristic, complemented
7#13070784C211yesmaximal, characteristic, complemented
8#13070387C212yesmaximal, complemented
9D11×#364C211yesmaximal, characteristic, complemented
10#13070350C212yesmaximal
11C11×#2230C211yesmaximal, characteristic, complemented
12D11×#135C2211yescharacteristic
13D11×#131—21no—
14#10623259—21no—
15C11×#498C2211yescharacteristic, complemented
16C11×#443C2211yescharacteristic
17#10622809C2211yescharacteristic
18#10622757—21no—
19#10622691—21no—
20D11×M32C2212yes—
21#10622508C2211yescharacteristic
22D11×#108C2211yescharacteristic
23#10622473—21no—
24#10622473C2212yes—
25#10622471—21no—
26#10622471C2212yescomplemented
27#10622437—21no—
28D11×#104—21no—
29#10622313C2211yescharacteristic
30C4×C8×D11C2211yescharacteristic
31#10622293C2211yescharacteristic, complemented
32C11×#365C2212yescomplemented
33C11×#364C2211yescharacteristic, complemented
34C11×#360C2212yes—
35#10622204C2212yes—
36#10622156C2212yes—
37#10622151C2212yescomplemented
38#10622149C2212yescomplemented
39#10622132C2212yescomplemented
40#10622126C2212yes—
41#10622125C2212yescomplemented
42#10622101C2211yescharacteristic, complemented
43#41×D11—21no—
44C11×#135C2311yescharacteristic
45C11×#131—21no—
46C11×C4⋊Q8—21no—
47#67003—21no—
48#67001—21no—
49#66999—41no—
50Q8×Dic11—41no—
51#66972Q811yescharacteristic, complemented
52Q16×D11Q811yescharacteristic, complemented
53#66969—21no—
54SD16×D11—21no—
55#66965Q811yescharacteristic, complemented
56D8×D11Q811yescharacteristic, complemented
57#66960—21no—
58#66960—41no—
59M16×D11—21no—
60M16×D11—41no—
61#66957C2311yescharacteristic
62#66954—21no—
63#66954—41no—
64C2×C8×D11—41no—
65C2×C8×D11D411yescharacteristic
66C2×C8×D11C2311yescharacteristic
67#66950—41no—
68#66945—22no—
69#66943—22no—
70#66940—41no—
71C42×D11D411yescharacteristic
72#66922—21no—
73C11×M32C2312yes—
74C11×#108C2311yescharacteristic
75C11×#106—21no—
76C11×#106C2312yes—
77C11×#104—21no—
78C4×C8×C11C2311yescharacteristic
79#66901—21no—
80#66889—21no—
81#66886—21no—
82#66883C2311yescharacteristic
83#66881—21no—
84#66881C2312yes—
85C8×Dic11D411yescharacteristic
86C8×Dic11C2311yescharacteristic
87#66876C2312yes—
88#66871—22no—
89#66871—22no—
90#66869—21no—
91C4×C11⋊C8D411yescharacteristic
92#66862—22no—
93C16×D11—22no—
94#33637—111nomaximal, Sylow
95C11×#41—21no—
96C2×Q8×C11—41no—
97#4343—21no—
98Q8×D11—21no—
99#4341—21no—
100#4341—41no—
101D4×D11—21no—
102D4×D11—41no—
103#4339—21no—
104#4339—41no—
105C2×C4×D11—21no—
106C2×C4×D11—41no—
107C2×C4×D11C2×D411yescharacteristic
108C2×Dic22—41no—
109C11×Q16C2×Q811yescharacteristic
110C11×SD16—21no—
111C11×D8C2×Q811yescharacteristic
112C11×M16—21no—
113C11×M16—41no—
114C2×C8×C11—41no—
115C2×C8×C11C2×D411yescharacteristic
116C2×C8×C11C2411yescharacteristic
117C11×C4⋊C4—22no—
118C11×C4⋊C4—41no—
119C42×C11C2×D411yescharacteristic
120#4326—21no—
121#4325—21no—
122#4324—21no—
123#4323—21no—
124(C2×D11)⋊C4—42no—
125C4⋊Dic11—22no—
126C4⋊Dic11—41no—
127C4⋊Dic11—42no—
128Dic11⋊C4—42no—
129C4×Dic11—21no—
130C4×Dic11—42no—
131C4×Dic11C2×D411yescharacteristic
132#4318—21no—
133#4318—41no—
134C2×C11⋊C8—41no—
135C2×C11⋊C8C2×D411yescharacteristic
136C2×C11⋊C8C2×D411yescharacteristic
137Dic44C2×Q811yescharacteristic
138D88C2×Q811yescharacteristic
139#4314—21no—
140#4313—41no—
141#4313—41no—
142#4313—41no—
143C8×D11—41no—
144C8×D11—41no—
145C8×D11—41no—
146C8×D11SD1611yescharacteristic
147C8×D11SD1611yescharacteristic
148C8×D11SD1611yescharacteristic
149C8×D11SD1611yescharacteristic
150C8×D11C2×Q811yescharacteristic
151C8×D11C2×Q811yescharacteristic
152C8×D11#4111yescharacteristic
153C8×D11#4111yescharacteristic
154C11×C16—22no—
155C11⋊C16—22no—
156#3160—111no—
157C2×#443—111no—
158#2231—112no—
159#2231—112no—
160#2230—111no—
161#2230—111no—
162#2230—111no—
163#2230D1111yescharacteristic, complemented
164#2155—112no—
165C2×#364—111no—
166#2145—112no—
167C22×D11—41no—
168C22×D11AGL(1,ℤ/8)11yescharacteristic
169Q8×C11—21no—
170Q8×C11—82no—
171D4×C11—21no—
172D4×C11—41no—
173C2×C4×C11—21no—
174C2×C4×C11—41no—
175C2×C4×C11—42no—
176C2×C4×C11C22×D411yescharacteristic
177C22⋊D11—41no—
178C22⋊D11—41no—
179C22⋊D11—41no—
180C2×Dic11—21no—
181C2×Dic11—41no—
182C2×Dic11—42no—
183C2×Dic11AGL(1,ℤ/8)11yescharacteristic
184D44—21no—
185D44—41no—
186C4×D11—42no—
187C4×D11—41no—
188C4×D11—41no—
189C4×D11—41no—
190C4×D11C22⋊Q811yescharacteristic
191C4×D11C22⋊Q811yescharacteristic
192C4×D11C2×SD1611yescharacteristic
193C4×D11C2×SD1611yescharacteristic
194Dic22—21no—
195Dic22—41no—
196Dic22—82no—
197C8×C11—41no—
198C8×C11C2×SD1611yescharacteristic
199C8×C11C2×SD1611yescharacteristic
200C8×C11C22×Q811yescharacteristic
201C8×C11C2×#4111yescharacteristic
202C11⋊C8—41no—
203C11⋊C8C22⋊Q811yescharacteristic
204C11⋊C8C22⋊Q811yescharacteristic
205C11⋊C8C2×SD1611yescharacteristic
206C11⋊C8C2×SD1611yescharacteristic
207C2×#135—111no—
208C2×#131—221no—
209#533—221no—
210C2×M32—112no—
211#500—221no—
212#499—112no—
213#499—221no—
214#498—111no—
215#498C2×D1111yescharacteristic, complemented
216#443—111no—
217#443—111no—
218#443—111no—
219#443—221no—
220#443—221no—
221#443C2×D1111yescharacteristic
222C2×#108—111no—
223#427—112no—
224#427—221no—
225C2×#104—221no—
226C2×C4×C8—111no—
227#365—112no—
228#365—112no—
229#365—112no—
230#365C2×D1112yescomplemented
231#364—112no—
232#364—111no—
233#364C2×D1111yescharacteristic, complemented
234#360—112no—
235#360—112no—
236#360—112no—
237#360C2×D1112yes—
238C22×C11—41no—
239C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
240C2×D11—41no—
241C2×D11—41no—
242C2×D11—82no—
243C2×D11#47611yescharacteristic
244C2×D11#47611yescharacteristic
245C4×C11—22no—
246C4×C11—41no—
247C4×C11—82no—
248C4×C11C2×C22⋊Q811yescharacteristic
249C4×C11C22×SD1611yescharacteristic
250Dic11—41no—
251Dic11—41no—
252Dic11—82no—
253Dic11#47611yescharacteristic
254Dic11#47611yescharacteristic
255C2×#41—221no—
256#135—111no—
257#135—111no—
258#135—111no—
259#135—221no—
260#135—221no—
261#135C22×D1111yescharacteristic
262C2×Q16—111no—
263C2×SD16—221no—
264C2×D8—111no—
265#131—21no—
266#131—221no—
267#131—221no—
268#131—221no—
269#131—441no—
270#131—441no—
271C2×M16—221no—
272C2×M16—441no—
273C22×C8—111no—
274C22×C8—111no—
275C22×C8—441no—
276C4⋊Q8—21no—
277C4⋊Q8—221no—
278#125—222no—
279C22⋊Q8—441no—
280C22⋊Q8—441no—
281C4×Q8—441no—
282C4×Q8—441no—
283#117—222no—
284C2×C42—111no—
285M32—112no—
286M32—222no—
287M32C22×D1112yes—
288C2×C16—222no—
289#108—111no—
290#108—221no—
291#108C22×D1111yescharacteristic
292#107—222no—
293#107—222no—
294#106—21no—
295#106—112no—
296#106—221no—
297#106C22×D1112yes—
298#104—21no—
299#104—221no—
300#104—221no—
301#104—221no—
302C4×C8—111no—
303C4×C8—111no—
304C4×C8—111no—
305C4×C8C22×D1111yescharacteristic
306C2×C11—21no—
307C2×C11—81no—
308C2×C11C2×#47611yescharacteristic
309D11—21no—
310D11—21no—
311D11—81no—
312#41—21no—
313#41—221no—
314#41—221no—
315#41—221no—
316#41—441no—
317#41—441no—
318C2×Q8—41no—
319C2×Q8—221no—
320C2×Q8—441no—
321C2×D4—221no—
322C2×D4—441no—
323C22×C4—111no—
324C22×C4—221no—
325C22×C4—441no—
326Q16—111no—
327Q16—221no—
328Q16Q8×D1111yescharacteristic
329SD16—21no—
330SD16—221no—
331SD16—221no—
332SD16—221no—
333D8—111no—
334D8—221no—
335D8Q8×D1111yescharacteristic
336M16—21no—
337M16—41no—
338M16—221no—
339M16—441no—
340M16—441no—
341M16—441no—
342M16—441no—
343C2×C8—41no—
344C2×C8—111no—
345C2×C8—111no—
346C2×C8—111no—
347C2×C8—111no—
348C2×C8—111no—
349C2×C8—111no—
350C2×C8—111no—
351C2×C8—111no—
352C2×C8—111no—
353C2×C8—111no—
354C2×C8—441no—
355C2×C8—441no—
356C2×C8—441no—
357C2×C8—441no—
358C2×C8D4×D1111yescharacteristic
359C2×C8C23×D1111yescharacteristic
360C4⋊C4—22no—
361C4⋊C4—41no—
362C4⋊C4—222no—
363C4⋊C4—441no—
364C4⋊C4—442no—
365C4⋊C4—442no—
366C22⋊C4—442no—
367C42—111no—
368C42—221no—
369C42—442no—
370C42D4×D1111yescharacteristic
371C16—22no—
372C16—222no—
373C11#3363711yescharacteristic, complemented, Sylow
374C23—111no—
375C23—441no—
376Q8—21no—
377Q8—82no—
378Q8—221no—
379Q8—441no—
380Q8—882no—
381D4—21no—
382D4—41no—
383D4—221no—
384D4—441no—
385D4—441no—
386D4—441no—
387D4—441no—
388C2×C4—21no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—111no—
392C2×C4—111no—
393C2×C4—111no—
394C2×C4—111no—
395C2×C4—111no—
396C2×C4—221no—
397C2×C4—442no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4—441no—
401C2×C4—441no—
402C2×C4—442no—
403C2×C4C2×D4×D1111yescharacteristic
404C8—41no—
405C8—111no—
406C8—111no—
407C8—111no—
408C8—111no—
409C8—441no—
410C8SD16×D1111yescharacteristic
411C8SD16×D1111yescharacteristic
412C8C2×Q8×D1111yescharacteristic
413C8#41×D1111yescharacteristic
414C22—41no—
415C22—111no—
416C22—111no—
417C22—441no—
418C22—441no—
419C22—882no—
420C22D11×AGL(1,ℤ/8)11yescharacteristic
421C4—22no—
422C4—41no—
423C4—82no—
424C4—111no—
425C4—111no—
426C4—441no—
427C4—441no—
428C4—882no—
429C4D11×C22⋊Q811yescharacteristic
430C4C2×SD16×D1111yescharacteristic
431C2—21no—
432C2—81no—
433C2—221no—
434C2—221no—
435C2—881no—
436C2D11×#47611yescharacteristic
subgroupG/H
centerC2D11×#476
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2230C2
socleC2×C11C2×#476
prime radicalD11×#135C22
hypercenter#2230D11
hypocenterC11#33637
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2230

Complements

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

NH ≅ G/Ntype
1. #13079125C2semidirect
3. #13070791C2semidirect
4. #13070790C2semidirect
5. #13070788C2semidirect
6. #13070787C2semidirect
7. #13070784C2semidirect
8. #13070387C2semidirect
9. D11×#364C2semidirect
11. C11×#2230C2semidirect
15. C11×#498C22semidirect
26. #10622471C22semidirect
31. #10622293C22semidirect
32. C11×#365C22semidirect
33. C11×#364C22semidirect
37. #10622151C22semidirect
38. #10622149C22semidirect
39. #10622132C22semidirect
41. #10622125C22semidirect
42. #10622101C22semidirect
51. #66972Q8semidirect
52. Q16×D11Q8semidirect
55. #66965Q8semidirect
56. D8×D11Q8semidirect
163. #2230D11semidirect
215. #498C2×D11semidirect
230. #365C2×D11semidirect
233. #364C2×D11semidirect
373. C11#33637semidirect

Maximal subgroups

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

subgroupindex
#130791252
D11×#4432
#130707912
#130707902
#130707882
#130707872
#130707842
#130703872
D11×#3642
#130703502
C11×#22302
#3363711