Finite Group Databasebeta

← #14908183

Subgroups — #14908183

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081750C211yesmaximal, characteristic
2C2×#10622808C211yesmaximal, characteristic, complemented
3#13079110C211yesmaximal, characteristic, complemented
4#13070697C214yesmaximal, complemented
5#13070685C214yesmaximal, complemented
6#13070382C211yesmaximal, characteristic, complemented
7#13070363C211yesmaximal, characteristic, complemented
8C2×#10622134C211yesmaximal, characteristic, complemented
9C11×#2957C211yesmaximal, characteristic, complemented
10C2×C11×#135C2211yescharacteristic
11C11×#568—21no—
12C2×#66962—21no—
13C22×Dic44C2211yescharacteristic
14C2×#66957C2211yescharacteristic
15#10623057—21no—
16C11×#444—22no—
17C11×#443C2214yes—
18C2×C11×#108C2211yescharacteristic
19C11×#421—21no—
20C11×#405C2211yescharacteristic
21#10622808—22no—
22#10622808C2214yes—
23#10622808C2212yes—
24#10622807—22no—
25#10622806C2212yes—
26C2×#66893—21no—
27#10622792—21no—
28C2×#66891—21no—
29#10622760—21no—
30C2×#66876C2211yescharacteristic
31C2×#66876C2211yescharacteristic
32#10622328—22no—
33#10622312C2212yescomplemented
34#10622309C2212yescomplemented
35#10622134C2214yescomplemented
36#10622134C2212yescomplemented
37#10622133C2212yescomplemented
38#10622101C2214yescomplemented
39C2×C11×#41—21no—
40C2×#4339—21no—
41C22×Dic22—21no—
42C11×#135—21no—
43C11×#135—21no—
44C11×#135D412yes—
45C11×#135C2312yes—
46C2×C11×Q16D411yescharacteristic
47C2×C11×SD16—21no—
48C2×C11×D8D411yescharacteristic
49C11×#131—24no—
50C11×#131—42no—
51C2×C11×M16—21no—
52C2×C11×M16—42no—
53C2×C11×M16D411yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C11×#117D411yescharacteristic
56#66962—42no—
57#66962—42no—
58C2×Dic44—21no—
59C2×Dic44—21no—
60C2×Dic44—21no—
61C2×Dic44—21no—
62C2×Dic44—21no—
63C2×Dic44—22no—
64C2×Dic44C2311yescharacteristic
65C2×Dic44C2312yes—
66#66957—21no—
67#66957—21no—
68#66957—21no—
69#66957—21no—
70C2×D88C2311yescharacteristic
71C2×#4314—21no—
72C2×#4314—22no—
73#66950—42no—
74#66939—42no—
75#66928—22no—
76#66922—22no—
77C11×#108—21no—
78C11×#108C2312yes—
79C11×#104—24no—
80C11×#97D412yes—
81C4×C8×C11C2312yes—
82#66893—22no—
83#66893—24no—
84#66892—22no—
85#66891—22no—
86#66891—24no—
87#66890—22no—
88#66876—21no—
89#66876—21no—
90#66876C2312yes—
91#66876C2312yes—
92C2×C11⋊C16—21no—
93C2×C11⋊C16—21no—
94#33596—111nomaximal, Sylow
95C11×#41—22no—
96C11×#41—22no—
97C11×#41—41no—
98C11×#41—41no—
99C2×Q8×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11C2×D411yescharacteristic
104C2×C22⋊D11—41no—
105C22×Dic11—41no—
106#4339—41no—
107#4339—41no—
108#4339—41no—
109#4339—41no—
110C2×D44—21no—
111C2×C4×D11—41no—
112C2×Dic22—21no—
113C2×Dic22—22no—
114C2×Dic22—41no—
115C2×Dic22—41no—
116C2×Dic22—41no—
117C2×Dic22—41no—
118C2×Dic22—41no—
119C11×Q16—21no—
120C11×Q16C2×D412yes—
121C11×SD16—22no—
122C11×SD16—22no—
123C11×D8—21no—
124C11×D8C2×D412yes—
125C11×M16—22no—
126C11×M16—44no—
127C11×M16—41no—
128C11×M16D812yes—
129C11×M16D812yes—
130C2×C8×C11—44no—
131C2×C8×C11—41no—
132C2×C8×C11C2×D411yescharacteristic
133C2×C8×C11C2×D411yescharacteristic
134C2×C8×C11C2×D411yescharacteristic
135C2×C8×C11C2×D412yes—
136C2×C8×C11#4111yescharacteristic
137C2×C8×C11#4111yescharacteristic
138C2×C8×C11C2411yescharacteristic
139C11×C4⋊C4—21no—
140C11×C22⋊C4—21no—
141C42×C11C2×D412yes—
142(C2×D11)⋊C4—44no—
143C4⋊Dic11—44no—
144Dic44—21no—
145Dic44—22no—
146Dic44—21no—
147Dic44—22no—
148Dic44—41no—
149Dic44—41no—
150Dic44—44no—
151D88—21no—
152D88—21no—
153#4314—41no—
154#4314—41no—
155#4314—44no—
156C11⋊C16—22no—
157C11⋊C16—22no—
158#3414—111no—
159C2×#510—111no—
160#3156—111no—
161#2957D1111yescharacteristic, complemented
162#2214—114no—
163#2212—114no—
164#2153—111no—
165#2148—111no—
166C2×#362—111no—
167C23×C11—41no—
168C23×C11AGL(1,ℤ/8)11yescharacteristic
169C22×D11—41no—
170Q8×C11—22no—
171Q8×C11—41no—
172D4×C11—22no—
173D4×C11—42no—
174D4×C11—42no—
175D4×C11—41no—
176C2×C4×C11—22no—
177C2×C4×C11—41no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11C2×D811yescharacteristic
183C2×C4×C11C2×D811yescharacteristic
184C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C11C22×D411yescharacteristic
186C22⋊D11—81no—
187C22⋊D11—81no—
188C2×Dic11—41no—
189C2×Dic11—42no—
190C2×Dic11—81no—
191C2×Dic11—81no—
192D44—41no—
193D44—41no—
194C4×D11—81no—
195C4×D11—81no—
196Dic22—41no—
197Dic22—42no—
198Dic22—42no—
199Dic22—41no—
200Dic22—81no—
201Dic22—81no—
202C8×C11—42no—
203C8×C11#12111yescharacteristic
204C8×C11#12111yescharacteristic
205C8×C11C2×D814yes—
206C8×C11C22×D411yescharacteristic
207C8×C11C2×#4111yescharacteristic
208C2×#137—221no—
209C2×#135—111no—
210C2×#135C2×D1111yescharacteristic
211C22×Q16—111no—
212#568—21no—
213#536—221no—
214#510—114no—
215#510—112no—
216#510—222no—
217#510—221no—
218#509—112no—
219#509—221no—
220#508—222no—
221C2×Q32—221no—
222C2×SD32—221no—
223C2×M32—111no—
224C2×M32—111no—
225#497—222no—
226#495—112no—
227#494—112no—
228#444—22no—
229#443C2×D1114yes—
230C2×#108C2×D1111yescharacteristic
231#421—21no—
232#405C2×D1111yescharacteristic
233#364—114no—
234#362—114no—
235#362—112no—
236#361—112no—
237C22×C11—41no—
238C22×C11—42no—
239C22×C11—161no—
240C22×C11#45911yescharacteristic
241C22×C11#45911yescharacteristic
242C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
243C2×D11—82no—
244C2×D11—81no—
245C4×C11—42no—
246C4×C11—42no—
247C4×C11#45911yescharacteristic
248C4×C11#45911yescharacteristic
249C4×C11C2×#12111yescharacteristic
250C4×C11C22×D811yescharacteristic
251Dic11—82no—
252Dic11—81no—
253C2×#41—21no—
254C2×#41—221no—
255C22×Q8—221no—
256#137—442no—
257#137—442no—
258#135—21no—
259#135—21no—
260#135—221no—
261#135—221no—
262#135—221no—
263#135—221no—
264#135D4412yes—
265#135C22×D1112yes—
266C2×Q16—112no—
267C2×Q16—111no—
268C2×Q16—221no—
269C2×Q16—221no—
270C2×Q16—221no—
271C2×Q16—221no—
272C2×Q16—221no—
273C2×Q16—222no—
274C2×Q16D4411yescharacteristic
275C2×SD16—21no—
276C2×SD16—221no—
277C2×SD16—222no—
278C2×D8—111no—
279C2×D8D4411yescharacteristic
280#131—24no—
281#131—42no—
282C2×M16—21no—
283C2×M16—42no—
284C2×M16C22⋊D1111yescharacteristic
285C22×C8C22×D1111yescharacteristic
286C4⋊Q8—222no—
287#124—222no—
288#123—442no—
289C22⋊Q8—442no—
290#117C22⋊D1111yescharacteristic
291Q32—224no—
292Q32—222no—
293SD32—222no—
294SD32—224no—
295SD32—222no—
296D16—222no—
297M32—112no—
298M32—112no—
299M32—221no—
300M32—221no—
301C2×C16—221no—
302C2×C16—221no—
303#108—21no—
304#108C22×D1112yes—
305#104—24no—
306#97C22⋊D1112yes—
307C4×C8C22×D1112yes—
308C2×C11—21no—
309C2×C11—21no—
310C2×C11—21no—
311C2×C11—82no—
312C2×C11C2×#45911yescharacteristic
313D11—161no—
314#41—22no—
315#41—22no—
316#41—41no—
317#41—41no—
318#41—441no—
319#41—441no—
320#41—441no—
321#41—441no—
322C2×Q8—21no—
323C2×Q8—222no—
324C2×Q8—221no—
325C2×Q8—441no—
326C2×Q8—441no—
327C2×Q8—441no—
328C2×Q8—441no—
329C2×Q8—441no—
330C2×D4—21no—
331C2×D4—41no—
332C2×D4—221no—
333C2×D4—441no—
334C22×C4—41no—
335C22×C4—441no—
336C22×C4—441no—
337C22×C4C2×C22⋊D1111yescharacteristic
338Q16—21no—
339Q16—222no—
340Q16—221no—
341Q16—222no—
342Q16—221no—
343Q16—441no—
344Q16—441no—
345Q16—444no—
346Q16C2×D4412yes—
347SD16—22no—
348SD16—22no—
349SD16—441no—
350SD16—441no—
351SD16—444no—
352D8—21no—
353D8—221no—
354D8—221no—
355D8C2×D4412yes—
356M16—22no—
357M16—41no—
358M16—44no—
359M16#432312yes—
360M16#432312yes—
361C2×C8—41no—
362C2×C8—44no—
363C2×C8C2×D4411yescharacteristic
364C2×C8C2×D4411yescharacteristic
365C2×C8#433911yescharacteristic
366C2×C8#433911yescharacteristic
367C2×C8C2×C22⋊D1111yescharacteristic
368C2×C8C2×C22⋊D1112yes—
369C2×C8C23×D1111yescharacteristic
370C4⋊C4—21no—
371C4⋊C4—444no—
372C22⋊C4—21no—
373C22⋊C4—444no—
374C42C2×C22⋊D1112yes—
375C16—222no—
376C16—222no—
377C11#3359611yescharacteristic, complemented, Sylow
378C23—41no—
379C23—441no—
380C23#6700211yescharacteristic
381Q8—22no—
382Q8—41no—
383Q8—441no—
384Q8—442no—
385Q8—442no—
386Q8—441no—
387Q8—881no—
388Q8—881no—
389D4—22no—
390D4—42no—
391D4—42no—
392D4—41no—
393D4—441no—
394D4—441no—
395D4—881no—
396D4—881no—
397C2×C4—22no—
398C2×C4—41no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—442no—
402C2×C4—441no—
403C2×C4—881no—
404C2×C4—881no—
405C2×C4—881no—
406C2×C4—881no—
407C2×C4#6698311yescharacteristic
408C2×C4#6698311yescharacteristic
409C2×C4C2×#432311yescharacteristic
410C2×C4C2×#432311yescharacteristic
411C2×C4#6700211yescharacteristic
412C2×C4C22×C22⋊D1111yescharacteristic
413C8—42no—
414C8#6698311yescharacteristic
415C8#6698311yescharacteristic
416C8C2×#432314yes—
417C8C22×D4411yescharacteristic
418C8C2×#433911yescharacteristic
419C22—41no—
420C22—42no—
421C22—161no—
422C22—882no—
423C22—881no—
424C22#1062262811yescharacteristic
425C22#1062262811yescharacteristic
426C22C2×#6700211yescharacteristic
427C4—42no—
428C4—42no—
429C4—881no—
430C4—882no—
431C4#1062262811yescharacteristic
432C4#1062262811yescharacteristic
433C4C2×#6698311yescharacteristic
434C4C22×#432311yescharacteristic
435C2—21no—
436C2—21no—
437C2—21no—
438C2—82no—
439C2—1761no—
440C2C2×#1062262811yescharacteristic
subgroupG/H
centerC2C2×#10622628
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2957C2
socleC2×C11C2×#459
prime radical#13081750C2
hypercenter#2957D11
hypocenterC11#33596
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
2. C2×#10622808C2semidirect
3. #13079110C2semidirect
4. #13070697C2semidirect
5. #13070685C2semidirect
6. #13070382C2semidirect
7. #13070363C2semidirect
8. C2×#10622134C2semidirect
9. C11×#2957C2semidirect
33. #10622312C22semidirect
34. #10622309C22semidirect
35. #10622134C22semidirect
36. #10622134C22semidirect
37. #10622133C22semidirect
38. #10622101C22semidirect
161. #2957D11semidirect
377. C11#33596semidirect

Maximal subgroups

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

subgroupindex
#130817502
C2×#106228082
#130791102
#130706972
#130706852
#130703822
#130703632
C2×#106221342
C11×#29572
#3359611