Finite Group Databasebeta

← #14908174

Subgroups — #14908174

Order 2816.

706 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081750C211yesmaximal, characteristic, complemented
2C2×#10622806C211yesmaximal, characteristic, complemented
3#13079102C211yesmaximal, characteristic, complemented
4#13070692C214yesmaximal, complemented
5#13070685C214yesmaximal, complemented
6#13070382C211yesmaximal, characteristic, complemented
7#13070363C211yesmaximal, characteristic, complemented
8C2×#10622133C211yesmaximal, characteristic, complemented
9C11×#2957C211yesmaximal, characteristic, complemented
10C2×C11×#135C2211yescharacteristic
11C11×#568—21no—
12C2×#66961—21no—
13C2×#66957C2211yescharacteristic
14C22×D88C2211yescharacteristic
15#10623056—21no—
16C11×#444—22no—
17C11×#443C2214yescomplemented
18C2×C11×#108C2211yescharacteristic
19C11×#421—21no—
20C11×#405C2211yescharacteristic
21#10622808C2212yescomplemented
22#10622807—22no—
23#10622806—22no—
24#10622806C2214yes—
25#10622806C2212yescomplemented
26#10622792—21no—
27C2×#66892—21no—
28#10622760—21no—
29C2×#66890—21no—
30C2×#66876C2211yescharacteristic
31C2×#66876C2211yescharacteristic
32#10622325—22no—
33#10622309C2212yescomplemented
34#10622308C2212yescomplemented
35#10622134C2212yescomplemented
36#10622133C2214yescomplemented
37#10622133C2212yescomplemented
38#10622101C2214yescomplemented
39C2×C11×#41—21no—
40C2×#4339—21no—
41C22×D44—21no—
42C11×#135—21no—
43C11×#135—21no—
44C11×#135D412yescomplemented
45C11×#135C2312yes—
46C2×C11×Q16D411yescharacteristic, complemented
47C2×C11×SD16—21no—
48C2×C11×D8D411yescharacteristic, complemented
49C11×#131—24no—
50C11×#131—42no—
51C2×C11×M16—21no—
52C2×C11×M16—42no—
53C2×C11×M16D411yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C11×#117D411yescharacteristic
56#66961—42no—
57#66961—42no—
58C2×Dic44C2311yescharacteristic
59#66957—21no—
60#66957—21no—
61#66957—21no—
62#66957—21no—
63C2×D88—21no—
64C2×D88—21no—
65C2×D88—21no—
66C2×D88—21no—
67C2×D88—21no—
68C2×D88—22no—
69C2×D88C2312yes—
70C2×D88C2311yescharacteristic
71C2×#4314—21no—
72C2×#4314—22no—
73#66948—42no—
74#66935—42no—
75#66928—22no—
76#66927—22no—
77C11×#108—21no—
78C11×#108C2312yes—
79C11×#104—24no—
80C11×#97D412yes—
81C4×C8×C11C2312yes—
82#66893—22no—
83#66892—24no—
84#66892—22no—
85#66891—22no—
86#66890—24no—
87#66890—22no—
88#66876—21no—
89#66876—21no—
90#66876C2312yes—
91#66876C2312yes—
92C2×C11⋊C16—21no—
93C2×C11⋊C16—21no—
94#33595—111nomaximal, Sylow
95C23×D11—41no—
96C11×#41—22no—
97C11×#41—22no—
98C11×#41—41no—
99C11×#41—41no—
100C2×Q8×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11C2×D411yescharacteristic
105C2×C22⋊D11—41no—
106#4339—41no—
107#4339—41no—
108#4339—41no—
109#4339—41no—
110C2×D44—21no—
111C2×D44—22no—
112C2×D44—44no—
113C2×D44—41no—
114C2×D44—41no—
115C2×D44—41no—
116C2×D44—41no—
117C2×D44—41no—
118C2×C4×D11—41no—
119C2×Dic22—21no—
120C11×Q16—21no—
121C11×Q16C2×D412yes—
122C11×SD16—22no—
123C11×SD16—22no—
124C11×D8—21no—
125C11×D8C2×D412yes—
126C11×M16—22no—
127C11×M16—44no—
128C11×M16—41no—
129C11×M16D812yes—
130C11×M16D812yes—
131C2×C8×C11—44no—
132C2×C8×C11—41no—
133C2×C8×C11C2×D411yescharacteristic
134C2×C8×C11C2×D411yescharacteristic
135C2×C8×C11C2×D411yescharacteristic
136C2×C8×C11C2×D412yes—
137C2×C8×C11#4111yescharacteristic
138C2×C8×C11#4111yescharacteristic
139C2×C8×C11C2411yescharacteristic
140C11×C4⋊C4—21no—
141C11×C22⋊C4—21no—
142C42×C11C2×D412yes—
143(C2×D11)⋊C4—44no—
144Dic44—21no—
145Dic44—21no—
146D88—22no—
147D88—21no—
148D88—22no—
149D88—21no—
150D88—41no—
151D88—41no—
152D88—44no—
153#4314—41no—
154#4314—41no—
155#4314—44no—
156C11⋊C16—22no—
157C11⋊C16—22no—
158#3414—111no—
159C2×#509—111no—
160#3155—111no—
161#2957D1111yescharacteristic, complemented
162#2213—114no—
163#2212—114no—
164#2153—111no—
165#2148—111no—
166C2×#361—111no—
167C23×C11—41no—
168C23×C11AGL(1,ℤ/8)11yescharacteristic
169C22×D11—42no—
170C22×D11—41no—
171C22×D11—81no—
172C22×D11—81no—
173C22×D11—162no—
174Q8×C11—22no—
175Q8×C11—41no—
176D4×C11—22no—
177D4×C11—42no—
178D4×C11—42no—
179D4×C11—41no—
180C2×C4×C11—22no—
181C2×C4×C11—41no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11C2×D811yescharacteristic
187C2×C4×C11C2×D811yescharacteristic
188C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
189C2×C4×C11C22×D411yescharacteristic
190C22⋊D11—81no—
191C22⋊D11—81no—
192C2×Dic11—41no—
193D44—41no—
194D44—42no—
195D44—42no—
196D44—41no—
197D44—81no—
198D44—81no—
199D44—164no—
200C4×D11—81no—
201C4×D11—81no—
202Dic22—41no—
203Dic22—41no—
204C8×C11—42no—
205C8×C11#12111yescharacteristic
206C8×C11#12111yescharacteristic
207C8×C11C2×D814yes—
208C8×C11C22×D411yescharacteristic
209C8×C11C2×#4111yescharacteristic
210C2×AGL(1,ℤ/8)—221no—
211C2×#135—111no—
212C2×#135C2×D1111yescharacteristic
213C22×D8—111no—
214#568—21no—
215#535—221no—
216#510—112no—
217#510—221no—
218#509—114no—
219#509—112no—
220#509—222no—
221#509—221no—
222#508—222no—
223C2×SD32—221no—
224C2×D16—221no—
225C2×M32—111no—
226C2×M32—111no—
227#496—222no—
228#495—112no—
229#493—112no—
230#444—22no—
231#443C2×D1114yescomplemented
232C2×#108C2×D1111yescharacteristic
233#421—21no—
234#405C2×D1111yescharacteristic
235#364—114no—
236#362—112no—
237#361—114no—
238#361—112no—
239C22×C11—41no—
240C22×C11—42no—
241C22×C11—161no—
242C22×C11#45911yescharacteristic
243C22×C11#45911yescharacteristic
244C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
245C2×D11—84no—
246C2×D11—82no—
247C2×D11—82no—
248C2×D11—81no—
249C2×D11—162no—
250C2×D11—162no—
251C4×C11—42no—
252C4×C11—42no—
253C4×C11#45911yescharacteristic
254C4×C11#45911yescharacteristic
255C4×C11C2×#12111yescharacteristic
256C4×C11C22×D811yescharacteristic
257Dic11—81no—
258C2×#41—21no—
259C2×#41—221no—
260C22×D4—221no—
261AGL(1,ℤ/8)—442no—
262AGL(1,ℤ/8)—442no—
263#135—21no—
264#135—21no—
265#135—221no—
266#135—221no—
267#135—221no—
268#135—221no—
269#135D4412yescomplemented
270#135C22×D1112yes—
271C2×Q16—111no—
272C2×Q16D4411yescharacteristic, complemented
273C2×SD16—21no—
274C2×SD16—221no—
275C2×SD16—222no—
276C2×D8—112no—
277C2×D8—111no—
278C2×D8—221no—
279C2×D8—221no—
280C2×D8—221no—
281C2×D8—221no—
282C2×D8—221no—
283C2×D8—222no—
284C2×D8D4411yescharacteristic, complemented
285#131—24no—
286#131—42no—
287C2×M16—21no—
288C2×M16—42no—
289C2×M16C22⋊D1111yescharacteristic
290C22×C8C22×D1111yescharacteristic
291#127—222no—
292#124—222no—
293#121—442no—
294#120—442no—
295#117C22⋊D1111yescharacteristic
296Q32—222no—
297SD32—224no—
298SD32—222no—
299SD32—222no—
300D16—224no—
301D16—222no—
302M32—112no—
303M32—112no—
304M32—221no—
305M32—221no—
306C2×C16—221no—
307C2×C16—221no—
308#108—21no—
309#108C22×D1112yes—
310#104—24no—
311#97C22⋊D1112yes—
312C4×C8C22×D1112yes—
313C2×C11—21no—
314C2×C11—21no—
315C2×C11—21no—
316C2×C11—82no—
317C2×C11C2×#45911yescharacteristic
318D11—161no—
319D11—162no—
320C24—441no—
321#41—22no—
322#41—22no—
323#41—41no—
324#41—41no—
325#41—441no—
326#41—441no—
327#41—441no—
328#41—441no—
329C2×Q8—21no—
330C2×Q8—221no—
331C2×D4—21no—
332C2×D4—41no—
333C2×D4—222no—
334C2×D4—221no—
335C2×D4—444no—
336C2×D4—441no—
337C2×D4—441no—
338C2×D4—441no—
339C2×D4—441no—
340C2×D4—441no—
341C2×D4—441no—
342C22×C4—41no—
343C22×C4—441no—
344C22×C4C2×C22⋊D1111yescharacteristic
345Q16—21no—
346Q16—221no—
347Q16—221no—
348Q16C2×D4412yes—
349SD16—22no—
350SD16—22no—
351SD16—441no—
352SD16—441no—
353SD16—444no—
354D8—21no—
355D8—222no—
356D8—221no—
357D8—222no—
358D8—221no—
359D8—441no—
360D8—441no—
361D8—444no—
362D8C2×D4412yes—
363M16—22no—
364M16—41no—
365M16—44no—
366M16#432312yes—
367M16#432312yes—
368C2×C8—41no—
369C2×C8—44no—
370C2×C8C2×D4411yescharacteristic
371C2×C8C2×D4411yescharacteristic
372C2×C8#433911yescharacteristic
373C2×C8#433911yescharacteristic
374C2×C8C2×C22⋊D1111yescharacteristic
375C2×C8C2×C22⋊D1112yes—
376C2×C8C23×D1111yescharacteristic
377C4⋊C4—21no—
378C22⋊C4—21no—
379C22⋊C4—444no—
380C42C2×C22⋊D1112yes—
381C16—222no—
382C16—222no—
383C11#3359511yescharacteristic, complemented, Sylow
384C23—41no—
385C23—442no—
386C23—441no—
387C23—881no—
388C23—881no—
389C23—1762no—
390C23#6700211yescharacteristic
391Q8—22no—
392Q8—41no—
393Q8—441no—
394Q8—441no—
395D4—22no—
396D4—42no—
397D4—42no—
398D4—41no—
399D4—442no—
400D4—441no—
401D4—441no—
402D4—442no—
403D4—881no—
404D4—881no—
405D4—881no—
406D4—881no—
407D4—1764no—
408C2×C4—22no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—441no—
413C2×C4—881no—
414C2×C4—881no—
415C2×C4#6698311yescharacteristic
416C2×C4#6698311yescharacteristic
417C2×C4C2×#432311yescharacteristic
418C2×C4C2×#432311yescharacteristic
419C2×C4#6700211yescharacteristic
420C2×C4C22×C22⋊D1111yescharacteristic
421C8—42no—
422C8#6698311yescharacteristic
423C8#6698311yescharacteristic
424C8C2×#432314yes—
425C8C22×D4411yescharacteristic
426C8C2×#433911yescharacteristic
427C22—41no—
428C22—42no—
429C22—161no—
430C22—882no—
431C22—884no—
432C22—881no—
433C22—882no—
434C22—1762no—
435C22—1762no—
436C22#1062262811yescharacteristic
437C22#1062262811yescharacteristic
438C22C2×#6700211yescharacteristic
439C4—42no—
440C4—42no—
441C4—881no—
442C4#1062262811yescharacteristic
443C4#1062262811yescharacteristic
444C4C2×#6698311yescharacteristic
445C4C22×#432311yescharacteristic
446C2—21no—
447C2—21no—
448C2—21no—
449C2—82no—
450C2—1762no—
451C2—1761no—
452C2C2×#1062262811yescharacteristic
subgroupG/H
centerC2C2×#10622628
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2957C2
socleC2×C11C2×#459
hypercenter#2957D11
hypocenterC11#33595
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ #405 ◁ #2957

Complements

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

NH ≅ G/Ntype
1. #13081750C2semidirect
2. C2×#10622806C2semidirect
3. #13079102C2semidirect
4. #13070692C2semidirect
5. #13070685C2semidirect
6. #13070382C2semidirect
7. #13070363C2semidirect
8. C2×#10622133C2semidirect
9. C11×#2957C2semidirect
17. C11×#443C22semidirect
21. #10622808C22semidirect
25. #10622806C22semidirect
33. #10622309C22semidirect
34. #10622308C22semidirect
35. #10622134C22semidirect
36. #10622133C22semidirect
37. #10622133C22semidirect
38. #10622101C22semidirect
44. C11×#135D4semidirect
46. C2×C11×Q16D4semidirect
48. C2×C11×D8D4semidirect
161. #2957D11semidirect
231. #443C2×D11semidirect
269. #135D44semidirect
272. C2×Q16D44semidirect
284. C2×D8D44semidirect
383. C11#33595semidirect

Maximal subgroups

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

subgroupindex
#130817502
C2×#106228062
#130791022
#130706922
#130706852
#130703822
#130703632
C2×#106221332
C11×#29572
#3359511