Finite Group Databasebeta

← #14910550

Subgroups — #14910550

Order 2816.

652 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#13081759C212yesmaximal, complemented
2#13080421C211yesmaximal, characteristic, complemented
3#13080416C211yesmaximal, characteristic, complemented
4#13070872C211yesmaximal, characteristic, complemented
5#13070747C212yesmaximal, complemented
6#13070697C211yesmaximal, characteristic, complemented
7#13070692C211yesmaximal, characteristic, complemented
8#13070588C212yesmaximal, complemented
9#13070581C212yesmaximal, complemented
10#13070454C211yesmaximal, characteristic, complemented
11C11×#2178C211yesmaximal, characteristic, complemented
12#10623302C2212yescomplemented
13#10623300C2212yes—
14#10623284—21no—
15#10623283—21no—
16C11×#508C2211yescharacteristic
17C11×#443C2211yescharacteristic
18C11×#443C2211yescharacteristic, complemented
19#10622808C2212yes—
20#10622806C2212yescomplemented
21#10622756—21no—
22#10622755—21no—
23#10622531—22no—
24#10622529—22no—
25D11×SD32—22no—
26#10622524—22no—
27C2×#66864C2212yescomplemented
28C2×#66864C2212yescomplemented
29#10622514C2212yescomplemented
30#10622510C2212yes—
31#10622509C2212yescomplemented
32#10622439—22no—
33#10622435—22no—
34#10622313C2211yescharacteristic
35#10622312C2211yescharacteristic, complemented
36#10622308C2211yescharacteristic
37C11×#368C2211yescharacteristic, complemented
38C11×#359C2211yescharacteristic
39C11×#359C2211yescharacteristic, complemented
40C4×C11×C16C2211yescharacteristic, complemented
41#10622146C2212yescomplemented
42#10622134C2212yescomplemented
43#10622133C2212yescomplemented
44#10622101C2211yescharacteristic, complemented
45#67043—22no—
46#67042—22no—
47C11×#135C2311yescharacteristic
48C11×#135C2311yescharacteristic
49C11×#131—21no—
50C11×#131—21no—
51#67004—22no—
52#67002—22no—
53#66972—22no—
54Q16×D11—22no—
55#66968—42no—
56#66967—42no—
57#66965—22no—
58D8×D11—22no—
59#66962—22no—
60#66962—42no—
61#66961—22no—
62#66961—42no—
63C2×Dic44—21no—
64C2×Dic44—41no—
65C2×Dic44C2312yes—
66#66957—41no—
67#66957—41no—
68#66957D411yescharacteristic
69C2×D88—21no—
70C2×D88—41no—
71C2×D88C2312yes—
72#66954C2312yes—
73#66927—21no—
74#66922—21no—
75C11×Q32D411yescharacteristic, complemented
76C11×SD32D411yescharacteristic, complemented
77C11×SD32D411yescharacteristic, complemented
78C11×D16D411yescharacteristic, complemented
79C2×C11×C16C2311yescharacteristic
80C2×C11×C16C2311yescharacteristic
81C11×#108C2311yescharacteristic
82C11×#108C2311yescharacteristic
83C11×#104—21no—
84C11×#104—21no—
85C4×C8×C11C2311yescharacteristic
86#66893—22no—
87#66892—22no—
88#66891—22no—
89#66890—22no—
90#66888—22no—
91#66887—22no—
92#66883D411yescharacteristic
93#66876C2312yes—
94#66869D412yes—
95#66864—22no—
96#66864—22no—
97#66864—42no—
98#66862—22no—
99C16×D11—22no—
100#33856—111nomaximal, Sylow
101C11×#41—21no—
102C11×#41—21no—
103#4343—42no—
104Q8×D11—42no—
105#4341—42no—
106#4341—82no—
107D4×D11—42no—
108D4×D11—82no—
109#4339—42no—
110#4339—42no—
111#4339C2×D412yes—
112C2×D44—22no—
113C2×D44—42no—
114C2×D44—81no—
115C2×Dic22—22no—
116C2×Dic22—42no—
117C11×Q16C2×D411yescharacteristic
118C11×Q16C2×D411yescharacteristic
119C11×SD16—21no—
120C11×SD16—21no—
121C11×D8C2×D411yescharacteristic
122C11×D8C2×D411yescharacteristic
123C11×M16—21no—
124C11×M16—21no—
125C11×M16—41no—
126C11×M16—41no—
127C2×C8×C11—41no—
128C2×C8×C11—41no—
129C2×C8×C11C2×D411yescharacteristic
130C2×C8×C11C2411yescharacteristic
131C42×C11C2×D411yescharacteristic
132#4326—42no—
133#4325—42no—
134#4324—42no—
135#4323—42no—
136C4⋊Dic11—81no—
137#4318C2×D412yes—
138Dic44—22no—
139Dic44—22no—
140Dic44—42no—
141Dic44—41no—
142Dic44—41no—
143Dic44D811yescharacteristic
144D88—22no—
145D88—22no—
146D88—42no—
147D88—41no—
148D88—41no—
149D88D811yescharacteristic
150#4314—42no—
151#4314—42no—
152#4314D812yes—
153#4313—22no—
154C8×D11—22no—
155C11×C16—21no—
156C11×C16C2×D411yescharacteristic
157C11×C16C2×D411yescharacteristic
158C11⋊C16—22no—
159#3416—112no—
160#3293—111no—
161#3292—111no—
162#2248—111no—
163#2223—112no—
164#2214—111no—
165#2213—111no—
166#2194—112no—
167#2193—112no—
168#2178D1111yescharacteristic, complemented
169#2170—111no—
170C22×D11—42no—
171C22×D11—82no—
172Q8×C11—21no—
173Q8×C11—21no—
174D4×C11—21no—
175D4×C11—21no—
176D4×C11—41no—
177D4×C11—41no—
178C2×C4×C11—21no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11C22×D411yescharacteristic
182C22⋊D11—22no—
183C22⋊D11—82no—
184C22⋊D11—82no—
185C2×Dic11—42no—
186C2×Dic11—82no—
187D44—42no—
188D44—42no—
189D44—82no—
190D44—162no—
191D44C2×D812yes—
192C4×D11—22no—
193C4×D11—82no—
194C4×D11—82no—
195Dic22—42no—
196Dic22—42no—
197Dic22—82no—
198Dic22C2×D812yes—
199C8×C11—41no—
200C8×C11—41no—
201C8×C11C2×D811yescharacteristic
202C8×C11C2×D811yescharacteristic
203C8×C11C22×D411yescharacteristic
204C8×C11H(5,𝔽2)11yescharacteristic
205C11⋊C8—22no—
206#578—112no—
207#578—221no—
208#576—112no—
209#576—221no—
210#510—112no—
211#510—222no—
212#509—112no—
213#509—222no—
214#508—222no—
215#508C2×D1111yescharacteristic
216C2×SD32—112no—
217C2×SD32—112no—
218C2×SD32—222no—
219#504—112no—
220#494—111no—
221#493—111no—
222#473—112no—
223#473—221no—
224#472—112no—
225#472—221no—
226#456—222no—
227#453—222no—
228#443—111no—
229#443C2×D1111yescharacteristic
230#443C2×D1111yescharacteristic, complemented
231#368C2×D1111yescharacteristic, complemented
232#364—111no—
233#362—112no—
234#361—112no—
235#359C2×D1111yescharacteristic
236#359C2×D1111yescharacteristic, complemented
237#350—112no—
238C4×C16C2×D1111yescharacteristic, complemented
239C22×C11—41no—
240C22×C11—41no—
241C22×C11#57611yescharacteristic
242C2×D11—22no—
243C2×D11—82no—
244C2×D11—162no—
245C2×D11—322no—
246C4×C11—22no—
247C4×C11—41no—
248C4×C11—41no—
249C4×C11D4211yescharacteristic
250C4×C11C22×D811yescharacteristic
251Dic11—22no—
252Dic11—82no—
2532−1+4—222no—
254H(5,𝔽2)—222no—
255#137—222no—
256#137—222no—
257#137—442no—
258#137—442no—
259AGL(1,ℤ/8)—222no—
260AGL(1,ℤ/8)—222no—
261AGL(1,ℤ/8)—442no—
262AGL(1,ℤ/8)—442no—
263#135—111no—
264#135—222no—
265#135—222no—
266#135—441no—
267#135—441no—
268#135C22×D1111yescharacteristic
269#135C22×D1111yescharacteristic
270C2×Q16—112no—
271C2×Q16—222no—
272C2×Q16—221no—
273C2×Q16—441no—
274C2×D8—112no—
275C2×D8—222no—
276C2×D8—221no—
277C2×D8—441no—
278#131—21no—
279#131—21no—
280#131—112no—
281C4⋊Q8—221no—
282#127—221no—
283Q32—222no—
284Q32D4411yescharacteristic, complemented
285SD32—222no—
286SD32—222no—
287SD32—222no—
288SD32—222no—
289SD32—442no—
290SD32D4411yescharacteristic, complemented
291SD32D4411yescharacteristic, complemented
292D16—222no—
293D16D4411yescharacteristic, complemented
294M32—112no—
295M32—222no—
296C2×C16—222no—
297C2×C16C22×D1111yescharacteristic
298C2×C16C22×D1111yescharacteristic
299#108—111no—
300#108C22×D1111yescharacteristic
301#108C22×D1111yescharacteristic
302#104—21no—
303#104—21no—
304#104—112no—
305#101—222no—
306#100—222no—
307C4×C8C22×D1111yescharacteristic
308C2×C11—21no—
309C2×C11—81no—
310C2×C11—81no—
311C2×C11D4×D811yescharacteristic
312D11—42no—
313D11—162no—
314#41—21no—
315#41—21no—
316#41—112no—
317#41—442no—
318#41—442no—
319#41—442no—
320#41—442no—
321#41—882no—
322C2×Q8—222no—
323C2×Q8—442no—
324C2×Q8—442no—
325C2×D4—222no—
326C2×D4—442no—
327C2×D4—442no—
328C2×D4—881no—
329C2×D4—882no—
330Q16—111no—
331Q16—222no—
332Q16—222no—
333Q16—442no—
334Q16—442no—
335Q16—441no—
336Q16—441no—
337Q16C2×D4411yescharacteristic
338Q16C2×D4411yescharacteristic
339SD16—21no—
340SD16—21no—
341SD16—112no—
342SD16—442no—
343SD16—442no—
344SD16—442no—
345SD16—442no—
346D8—111no—
347D8—222no—
348D8—222no—
349D8—442no—
350D8—442no—
351D8—441no—
352D8—441no—
353D8C2×D4411yescharacteristic
354D8C2×D4411yescharacteristic
355M16—21no—
356M16—21no—
357M16—41no—
358M16—41no—
359M16—112no—
360M16—222no—
361C2×C8—41no—
362C2×C8—41no—
363C2×C8—222no—
364C2×C8D4×D1111yescharacteristic
365C2×C8C23×D1111yescharacteristic
366C4⋊C4—881no—
367C42D4×D1111yescharacteristic
368C16—21no—
369C16—222no—
370C16C2×D4411yescharacteristic
371C16C2×D4411yescharacteristic
372C11#3385611yescharacteristic, complemented, Sylow
373C23—442no—
374C23—882no—
375Q8—21no—
376Q8—21no—
377Q8—112no—
378Q8—442no—
379Q8—442no—
380Q8—882no—
381D4—21no—
382D4—21no—
383D4—41no—
384D4—41no—
385D4—112no—
386D4—222no—
387D4—442no—
388D4—442no—
389D4—882no—
390D4—882no—
391D4—882no—
392D4—1762no—
393C2×C4—21no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—222no—
397C2×C4—442no—
398C2×C4—882no—
399C2×C4—882no—
400C2×C4—882no—
401C2×C4C2×D4×D1111yescharacteristic
402C8—41no—
403C8—41no—
404C8—222no—
405C8D8×D1111yescharacteristic
406C8D8×D1111yescharacteristic
407C8C22×D4411yescharacteristic
408C8#6704211yescharacteristic
409C22—41no—
410C22—41no—
411C22—222no—
412C22—882no—
413C22—3522no—
414C22—1762no—
415C22#1062330011yescharacteristic
416C4—22no—
417C4—41no—
418C4—41no—
419C4—222no—
420C4—882no—
421C4D4×D4411yescharacteristic
422C4C2×D8×D1111yescharacteristic
423C2—21no—
424C2—81no—
425C2—81no—
426C2—442no—
427C2—1762no—
428C2D8×D4411yescharacteristic
subgroupG/H
centerC2D8×D44
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2178C2
socleC2×C11D4×D8
hypercenter#2178D11
hypocenterC11#33856
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2178

Complements

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

NH ≅ G/Ntype
1. #13081759C2semidirect
2. #13080421C2semidirect
3. #13080416C2semidirect
4. #13070872C2semidirect
5. #13070747C2semidirect
6. #13070697C2semidirect
7. #13070692C2semidirect
8. #13070588C2semidirect
9. #13070581C2semidirect
10. #13070454C2semidirect
11. C11×#2178C2semidirect
12. #10623302C22semidirect
18. C11×#443C22semidirect
20. #10622806C22semidirect
27. C2×#66864C22semidirect
28. C2×#66864C22semidirect
29. #10622514C22semidirect
31. #10622509C22semidirect
35. #10622312C22semidirect
37. C11×#368C22semidirect
39. C11×#359C22semidirect
40. C4×C11×C16C22semidirect
41. #10622146C22semidirect
42. #10622134C22semidirect
43. #10622133C22semidirect
44. #10622101C22semidirect
75. C11×Q32D4semidirect
76. C11×SD32D4semidirect
77. C11×SD32D4semidirect
78. C11×D16D4semidirect
168. #2178D11semidirect
230. #443C2×D11semidirect
231. #368C2×D11semidirect
236. #359C2×D11semidirect
238. C4×C16C2×D11semidirect
284. Q32D44semidirect
290. SD32D44semidirect
291. SD32D44semidirect
293. D16D44semidirect
372. C11#33856semidirect

Maximal subgroups

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

subgroupindex
#130817592
#130804212
#130804162
#130708722
#130707472
#130706972
#130706922
#130705882
#130705812
#130704542
C11×#21782
#3385611