Finite Group Databasebeta

← #14910545

Subgroups — #14910545

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#13081763C212yesmaximal, complemented
2#13080421C211yesmaximal, characteristic, complemented
3#13070871C211yesmaximal, characteristic, complemented
4#13070744C212yesmaximal, complemented
5#13070697C211yesmaximal, characteristic, complemented
6#13070689C211yesmaximal, characteristic, complemented
7#13070587C212yesmaximal, complemented
8#13070578C212yesmaximal, complemented
9#13070495C211yesmaximal, characteristic, complemented
10#13070453C211yesmaximal, characteristic, complemented
11C11×#3292C211yesmaximal, characteristic, complemented
12C11×#576—21no—
13C11×#576C2212yes—
14#10623302—21no—
15#10623284C2212yescomplemented
16C11×#493C2211yescharacteristic
17C11×#472—21no—
18C11×#472C2212yes—
19C11×#453—22no—
20C11×#443C2211yescharacteristic
21C11×#443C2211yescharacteristic
22#10622808—22no—
23#10622808C2212yes—
24#10622807—22no—
25#10622807C2211yescharacteristic
26C2×#66891—22no—
27C2×#66891C2212yescomplemented
28C2×#66891C2212yescomplemented
29#10622760—22no—
30#10622760C2212yescomplemented
31#10622756C2212yescomplemented
32#10622753C2212yescomplemented
33#10622509—21no—
34#10622439—22no—
35#10622313C2211yescharacteristic, complemented
36#10622312C2211yescharacteristic, complemented
37#10622205C2211yescharacteristic
38#10622201C2212yescomplemented
39#10622199C2212yescomplemented
40#10622135C2211yescharacteristic, complemented
41#10622134C2212yescomplemented
42#10622131C2211yescharacteristic, complemented
43#10622101C2211yescharacteristic, complemented
44C4×C11⋊C16C2211yescharacteristic, complemented
45C11×H(5,𝔽2)—22no—
46#67043—22no—
47C11×AGL(1,ℤ/8)—22no—
48C11×AGL(1,ℤ/8)—22no—
49C11×AGL(1,ℤ/8)—42no—
50C11×AGL(1,ℤ/8)—42no—
51C11×#135—22no—
52C11×#135—41no—
53C11×#135D411yescharacteristic
54C11×#135C2311yescharacteristic
55C2×C11×D8—22no—
56C2×C11×D8—21no—
57C2×C11×D8—41no—
58C2×C11×D8C2312yes—
59C11×#131—21no—
60C11×#131C2312yes—
61C11×#127—21no—
62#67004—22no—
63Q16×D11—41no—
64#66968—42no—
65#66965—41no—
66#66962—22no—
67#66962—42no—
68C2×Dic44—22no—
69C2×Dic44—21no—
70C2×Dic44C2312yes—
71#66957—22no—
72#66957C2311yescharacteristic
73#66954—21no—
74#66922—21no—
75C11×#108D411yescharacteristic
76C11×#108C2311yescharacteristic
77C11×#104—21no—
78C11×#104D412yes—
79C11×#100—22no—
80C4×C8×C11C2311yescharacteristic
81#66893—22no—
82#66893D411yescharacteristic, complemented
83#66892D411yescharacteristic, complemented
84#66891—22no—
85#66891—22no—
86#66891—22no—
87#66891—22no—
88#66891—42no—
89#66891D411yescharacteristic, complemented
90#66890—22no—
91#66890D411yescharacteristic, complemented
92#66888—22no—
93#66883C2311yescharacteristic
94#66876—22no—
95#66876C2312yes—
96C2×C11⋊C16—22no—
97C2×C11⋊C16C2311yescharacteristic
98C2×C11⋊C16C2311yescharacteristic
99#66869—21no—
100#33856—111nomaximal, Sylow
101C11×#41—21no—
102C11×#41—42no—
103C11×#41—42no—
104C11×#41C2×D412yes—
105C2×D4×C11—22no—
106C2×D4×C11—42no—
107C2×D4×C11—42no—
108C2×D4×C11—81no—
109C2×D4×C11—82no—
110Q8×D11—42no—
111#4341—42no—
112#4341—82no—
113#4339—21no—
114#4339—42no—
115C2×Dic22—22no—
116C2×Dic22—42no—
117C11×Q16D811yescharacteristic
118C11×Q16C2×D411yescharacteristic
119C11×SD16—21no—
120C11×SD16—42no—
121C11×SD16—42no—
122C11×SD16D812yes—
123C11×D8—22no—
124C11×D8—22no—
125C11×D8—42no—
126C11×D8—41no—
127C11×D8—41no—
128C11×D8—42no—
129C11×D8D811yescharacteristic
130C11×D8C2×D411yescharacteristic
131C11×M16—22no—
132C11×M16—21no—
133C11×M16—41no—
134C11×M16C2×D412yes—
135C2×C8×C11—22no—
136C2×C8×C11—41no—
137C2×C8×C11C2×D411yescharacteristic
138C2×C8×C11C2411yescharacteristic
139C42×C11C2×D411yescharacteristic
140#4326—42no—
141#4324—42no—
142C4⋊Dic11—81no—
143#4318—21no—
144Dic44—22no—
145Dic44—22no—
146Dic44—42no—
147Dic44—41no—
148Dic44—41no—
149Dic44C2×D411yescharacteristic
150D88C2×D411yescharacteristic
151#4314—21no—
152#4314—42no—
153#4313—41no—
154C8×D11—41no—
155C11⋊C16—22no—
156C11⋊C16—21no—
157C11⋊C16C2×D411yescharacteristic
158C11⋊C16C2×D411yescharacteristic
159#3416—112no—
160#3293—111no—
161#3292D1111yescharacteristic, complemented
162#2248—111no—
163#2223—112no—
164#2214—111no—
165#2213—111no—
166#2194—112no—
167#2193—112no—
168#2178—111no—
169#2170—111no—
170C23×C11—42no—
171C23×C11—82no—
172Q8×C11—21no—
173Q8×C11C2×D812yes—
174D4×C11—22no—
175D4×C11—21no—
176D4×C11—41no—
177D4×C11—42no—
178D4×C11—42no—
179D4×C11—82no—
180D4×C11—82no—
181D4×C11—162no—
182D4×C11C2×D812yes—
183C2×C4×C11—21no—
184C2×C4×C11—22no—
185C2×C4×C11—41no—
186C2×C4×C11—82no—
187C2×C4×C11C22×D411yescharacteristic
188C22⋊D11—41no—
189C22⋊D11—82no—
190C2×Dic11—42no—
191C2×Dic11—82no—
192D44—21no—
193C4×D11—41no—
194C4×D11—82no—
195Dic22—21no—
196Dic22—42no—
197Dic22—42no—
198Dic22—82no—
199C8×C11—22no—
200C8×C11—41no—
201C8×C11C2×D811yescharacteristic
202C8×C11C2×D811yescharacteristic
203C8×C11C22×D411yescharacteristic
204C8×C11H(5,𝔽2)11yescharacteristic
205C11⋊C8—41no—
206#578—112no—
207#578—221no—
208#576—21no—
209#576C2×D1112yes—
210#510—112no—
211#510—222no—
212#509—112no—
213#509—222no—
214#508—111no—
215#508—222no—
216C2×SD32—112no—
217C2×SD32—112no—
218C2×SD32—222no—
219#504—112no—
220#494—111no—
221#493C2×D1111yescharacteristic
222#473—112no—
223#473—221no—
224#472—21no—
225#472C2×D1112yes—
226#456—222no—
227#453—22no—
228#443—111no—
229#443C2×D1111yescharacteristic
230#443C2×D1111yescharacteristic
231#368—111no—
232#364—111no—
233#362—112no—
234#361—112no—
235#359—111no—
236#359—111no—
237#350—112no—
238C4×C16—111no—
239C22×C11—22no—
240C22×C11—41no—
241C22×C11—82no—
242C22×C11—162no—
243C22×C11—322no—
244C22×C11#57611yescharacteristic
245C2×D11—41no—
246C4×C11—22no—
247C4×C11—22no—
248C4×C11—41no—
249C4×C11D4211yescharacteristic
250C4×C11C22×D811yescharacteristic
251Dic11—41no—
252Dic11—82no—
2532−1+4—222no—
254H(5,𝔽2)—22no—
255#137—222no—
256#137—222no—
257#137—442no—
258#137—442no—
259AGL(1,ℤ/8)—22no—
260AGL(1,ℤ/8)—22no—
261AGL(1,ℤ/8)—42no—
262AGL(1,ℤ/8)—42no—
263#135—22no—
264#135—41no—
265#135—111no—
266#135—222no—
267#135—441no—
268#135C22⋊D1111yescharacteristic
269#135C22×D1111yescharacteristic
270C2×Q16—112no—
271C2×Q16—222no—
272C2×Q16—221no—
273C2×Q16—441no—
274C2×D8—22no—
275C2×D8—21no—
276C2×D8—41no—
277C2×D8C22×D1112yes—
278#131—21no—
279#131—221no—
280#131C22×D1112yes—
281C4⋊Q8—221no—
282#127—21no—
283Q32—111no—
284Q32—222no—
285SD32—111no—
286SD32—111no—
287SD32—222no—
288SD32—222no—
289SD32—222no—
290SD32—222no—
291SD32—442no—
292D16—111no—
293D16—222no—
294M32—112no—
295M32—222no—
296C2×C16—111no—
297C2×C16—111no—
298C2×C16—222no—
299#108—111no—
300#108C22⋊D1111yescharacteristic
301#108C22×D1111yescharacteristic
302#104—21no—
303#104—221no—
304#104C22⋊D1112yes—
305#101—222no—
306#100—22no—
307C4×C8C22×D1111yescharacteristic
308C2×C11—21no—
309C2×C11—42no—
310C2×C11—81no—
311C2×C11—162no—
312C2×C11D4×D811yescharacteristic
313D11—81no—
314#41—21no—
315#41—42no—
316#41—42no—
317#41—221no—
318#41—442no—
319#41—442no—
320#41—882no—
321#41C2×C22⋊D1112yes—
322C2×Q8—222no—
323C2×Q8—442no—
324C2×Q8—442no—
325C2×D4—22no—
326C2×D4—42no—
327C2×D4—42no—
328C2×D4—81no—
329C2×D4—82no—
330Q16—111no—
331Q16—222no—
332Q16—222no—
333Q16—442no—
334Q16—442no—
335Q16—441no—
336Q16—441no—
337Q16#432311yescharacteristic
338Q16D4×D1111yescharacteristic
339SD16—21no—
340SD16—42no—
341SD16—42no—
342SD16—221no—
343SD16—442no—
344SD16—442no—
345SD16#432312yes—
346D8—22no—
347D8—22no—
348D8—42no—
349D8—42no—
350D8—41no—
351D8—41no—
352D8—111no—
353D8#432311yescharacteristic
354D8D4×D1111yescharacteristic
355M16—22no—
356M16—21no—
357M16—41no—
358M16—221no—
359M16—441no—
360M16C2×C22⋊D1112yes—
361C2×C8—22no—
362C2×C8—41no—
363C2×C8—441no—
364C2×C8C2×C22⋊D1111yescharacteristic
365C2×C8C23×D1111yescharacteristic
366C4⋊C4—881no—
367C42C2×C22⋊D1111yescharacteristic
368C16—111no—
369C16—111no—
370C16—222no—
371C16—221no—
372C11#3385611yescharacteristic, complemented, Sylow
373C23—42no—
374C23—82no—
375Q8—21no—
376Q8—221no—
377Q8—442no—
378Q8—442no—
379Q8—882no—
380Q8C2×#432312yes—
381D4—22no—
382D4—21no—
383D4—41no—
384D4—42no—
385D4—42no—
386D4—82no—
387D4—82no—
388D4—162no—
389D4—221no—
390D4—441no—
391D4—882no—
392D4C2×#432312yes—
393C2×C4—21no—
394C2×C4—22no—
395C2×C4—41no—
396C2×C4—82no—
397C2×C4—441no—
398C2×C4—442no—
399C2×C4—882no—
400C2×C4—882no—
401C2×C4C22×C22⋊D1111yescharacteristic
402C8—22no—
403C8—41no—
404C8—441no—
405C8C2×#432311yescharacteristic
406C8C2×#432311yescharacteristic
407C8C2×D4×D1111yescharacteristic
408C8#6703711yescharacteristic
409C22—22no—
410C22—41no—
411C22—82no—
412C22—162no—
413C22—322no—
414C22—441no—
415C22#1062336611yescharacteristic
416C4—22no—
417C4—22no—
418C4—41no—
419C4—441no—
420C4—882no—
421C4C22×#432311yescharacteristic
422C4D4×C22⋊D1111yescharacteristic
423C2—21no—
424C2—42no—
425C2—81no—
426C2—162no—
427C2—881no—
428C2D4×#432311yescharacteristic
subgroupG/H
centerC2D4×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3292C2
socleC2×C11D4×D8
hypercenter#3292D11
hypocenterC11#33856
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443 ◁ #3292

Complements

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

NH ≅ G/Ntype
1. #13081763C2semidirect
2. #13080421C2semidirect
3. #13070871C2semidirect
4. #13070744C2semidirect
5. #13070697C2semidirect
6. #13070689C2semidirect
7. #13070587C2semidirect
8. #13070578C2semidirect
9. #13070495C2semidirect
10. #13070453C2semidirect
11. C11×#3292C2semidirect
15. #10623284C22semidirect
27. C2×#66891C22semidirect
28. C2×#66891C22semidirect
30. #10622760C22semidirect
31. #10622756C22semidirect
32. #10622753C22semidirect
35. #10622313C22semidirect
36. #10622312C22semidirect
38. #10622201C22semidirect
39. #10622199C22semidirect
40. #10622135C22semidirect
41. #10622134C22semidirect
42. #10622131C22semidirect
43. #10622101C22semidirect
44. C4×C11⋊C16C22semidirect
82. #66893D4semidirect
83. #66892D4semidirect
89. #66891D4semidirect
91. #66890D4semidirect
161. #3292D11semidirect
372. C11#33856semidirect

Maximal subgroups

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

subgroupindex
#130817632
#130804212
#130708712
#130707442
#130706972
#130706892
#130705872
#130705782
#130704952
#130704532
C11×#32922
#3385611