Finite Group Databasebeta

← #14908179

Subgroups — #14908179

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×#10622792C211yesmaximal, characteristic, complemented
3#13077534C211yesmaximal, characteristic, complemented
4#13070694C214yesmaximal, complemented
5#13070682C214yesmaximal, complemented
6#13070382C211yesmaximal, characteristic, complemented
7#13070365C211yesmaximal, characteristic, complemented
8C2×#10622203C211yesmaximal, characteristic, complemented
9C11×#3156C211yesmaximal, characteristic, complemented
10C2×C11×#137—21no—
11C2×C11×#135C2211yescharacteristic
12C22×C11×Q16C2211yescharacteristic
13C11×#536—21no—
14#10623276—21no—
15C2×#66957C2211yescharacteristic
16C11×#497—22no—
17C11×#495C2212yescomplemented
18C11×#494C2212yescomplemented
19C11×#405C2211yescharacteristic
20#10622808—21no—
21#10622807—22no—
22#10622806—21no—
23C2×#66893—21no—
24#10622792—22no—
25#10622792C2214yes—
26#10622792C2212yes—
27C2×#66892—21no—
28#10622760C2212yes—
29C2×#66883C2211yescharacteristic
30C2×#66876C2211yescharacteristic
31C2×#66876C2211yescharacteristic
32#10622618—21no—
33#10622330—22no—
34#10622313C2214yes—
35#10622203C2214yescomplemented
36#10622203C2212yescomplemented
37#10622201C2212yescomplemented
38#10622101C2214yescomplemented
39C2×C11×#41—21no—
40C22×Q8×C11—21no—
41C2×#4339—21no—
42C11×#137—42no—
43C11×#137—42no—
44C11×#135—21no—
45C11×#135—21no—
46C11×#135—21no—
47C11×#135—21no—
48C2×C11×Q16—21no—
49C2×C11×Q16—21no—
50C2×C11×Q16—22no—
51C2×C11×Q16—21no—
52C2×C11×Q16—21no—
53C2×C11×Q16—21no—
54C2×C11×Q16C2311yescharacteristic
55C2×C11×Q16C2312yes—
56C2×C11×SD16—22no—
57C2×C11×SD16—21no—
58C2×C11×D8C2311yescharacteristic
59C2×C11×M16D411yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C11×C4⋊Q8—22no—
62C11×#124—22no—
63C11×#123—42no—
64C11×C22⋊Q8—42no—
65C11×#117D411yescharacteristic
66C2×#4318—21no—
67#66960—42no—
68M16×D11—42no—
69C2×Dic44D411yescharacteristic
70#66957—21no—
71#66957—21no—
72#66957D412yes—
73#66957C2312yes—
74C2×D88D411yescharacteristic
75C2×#4314—21no—
76#66954—24no—
77C11×#97D412yes—
78C4×C8×C11C2312yes—
79#66893—24no—
80#66893—22no—
81#66892—24no—
82#66892—22no—
83#66891—22no—
84#66890—22no—
85#66883—21no—
86#66883C2312yes—
87#66876—21no—
88#66876—21no—
89#66876C2312yes—
90#66876C2312yes—
91C2×C11⋊C16—21no—
92C2×C11⋊C16—21no—
93#66869—24no—
94#33596—111nomaximal, Sylow
95C11×#41—41no—
96C11×#41—41no—
97C11×#41—41no—
98C11×#41—41no—
99C2×Q8×C11—22no—
100C2×Q8×C11—21no—
101C2×Q8×C11—41no—
102C2×Q8×C11—41no—
103C2×Q8×C11—41no—
104C2×Q8×C11—41no—
105C2×Q8×C11—41no—
106C2×D4×C11—21no—
107C2×D4×C11—41no—
108C22×C4×C11—41no—
109C22×C4×C11—41no—
110C22×C4×C11C2×D411yescharacteristic
111C2×C22⋊D11—41no—
112#4339—22no—
113#4339—22no—
114#4339—41no—
115#4339—41no—
116C2×D44—21no—
117C2×C4×D11—41no—
118C2×Dic22—21no—
119C11×Q16—22no—
120C11×Q16—21no—
121C11×Q16—22no—
122C11×Q16—21no—
123C11×Q16—41no—
124C11×Q16—41no—
125C11×Q16—44no—
126C11×SD16—41no—
127C11×SD16—41no—
128C11×SD16—44no—
129C11×D8—21no—
130C11×D8—21no—
131C11×M16D812yes—
132C11×M16D812yes—
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×C4⋊C4—44no—
142C11×C22⋊C4—21no—
143C11×C22⋊C4—44no—
144C42×C11C2×D412yes—
145#4318—22no—
146#4318—41no—
147C2×C11⋊C8—41no—
148Dic44—21no—
149Dic44C2×D412yes—
150D88—21no—
151D88C2×D412yes—
152#4314—22no—
153#4314—22no—
154#4313—44no—
155C8×D11—44no—
156C11⋊C16—22no—
157C11⋊C16—22no—
158#3414—111no—
159C2×#510—111no—
160#3156D1111yescharacteristic, complemented
161#2957—111no—
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—41no—
171Q8×C11—42no—
172Q8×C11—42no—
173Q8×C11—41no—
174Q8×C11—81no—
175Q8×C11—81no—
176D4×C11—41no—
177D4×C11—41no—
178D4×C11—81no—
179D4×C11—81no—
180C2×C4×C11—22no—
181C2×C4×C11—42no—
182C2×C4×C11—41no—
183C2×C4×C11—81no—
184C2×C4×C11—81no—
185C2×C4×C11—81no—
186C2×C4×C11—81no—
187C2×C4×C11#12111yescharacteristic
188C2×C4×C11#12111yescharacteristic
189C2×C4×C11C2×D811yescharacteristic
190C2×C4×C11C2×D811yescharacteristic
191C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C11C22×D411yescharacteristic
193C22⋊D11—42no—
194C22⋊D11—42no—
195C2×Dic11—41no—
196D44—22no—
197D44—41no—
198C4×D11—42no—
199C4×D11—42no—
200Dic22—22no—
201Dic22—41no—
202C8×C11#12111yescharacteristic
203C8×C11#12111yescharacteristic
204C8×C11C2×D814yes—
205C8×C11C22×D411yescharacteristic
206C8×C11C2×#4111yescharacteristic
207C11⋊C8—42no—
208C2×#137—21no—
209C2×#135—111no—
210C2×#135C2×D1111yescharacteristic
211C22×Q16C2×D1111yescharacteristic
212#568—221no—
213#536—21no—
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—22no—
226#495C2×D1112yescomplemented
227#494C2×D1112yescomplemented
228#444—222no—
229#443—114no—
230C2×#108—111no—
231#421—221no—
232#405C2×D1111yescharacteristic
233#364—114no—
234#362—114no—
235#362—112no—
236#361—112no—
237C22×C11—41no—
238C22×C11—82no—
239C22×C11—81no—
240C22×C11#45911yescharacteristic
241C22×C11#45911yescharacteristic
242C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
243C2×D11—42no—
244C2×D11—161no—
245C4×C11—42no—
246C4×C11—81no—
247C4×C11—82no—
248C4×C11#45911yescharacteristic
249C4×C11#45911yescharacteristic
250C4×C11C2×#12111yescharacteristic
251C4×C11C22×D811yescharacteristic
252Dic11—42no—
253C2×#41—21no—
254C2×#41—221no—
255C22×Q8—21no—
256#137—42no—
257#137—42no—
258#135—21no—
259#135—21no—
260#135—21no—
261#135—21no—
262#135—112no—
263#135—112no—
264#135—221no—
265#135—221no—
266C2×Q16—21no—
267C2×Q16—21no—
268C2×Q16—21no—
269C2×Q16—21no—
270C2×Q16—21no—
271C2×Q16—22no—
272C2×Q16—111no—
273C2×Q16C22×D1112yes—
274C2×Q16C22×D1111yescharacteristic
275C2×SD16—21no—
276C2×SD16—22no—
277C2×SD16—221no—
278C2×D8—111no—
279C2×D8C22×D1111yescharacteristic
280#131—224no—
281#131—442no—
282C2×M16—221no—
283C2×M16—442no—
284C2×M16C22⋊D1111yescharacteristic
285C22×C8C22×D1111yescharacteristic
286C4⋊Q8—22no—
287#124—22no—
288#123—42no—
289C22⋊Q8—42no—
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—112no—
304#108—221no—
305#104—224no—
306#97C22⋊D1112yes—
307C4×C8C22×D1112yes—
308C2×C11—21no—
309C2×C11—21no—
310C2×C11—21no—
311C2×C11—161no—
312C2×C11C2×#45911yescharacteristic
313D11—82no—
314#41—41no—
315#41—41no—
316#41—41no—
317#41—41no—
318#41—222no—
319#41—222no—
320#41—441no—
321#41—441no—
322C2×Q8—22no—
323C2×Q8—21no—
324C2×Q8—41no—
325C2×Q8—41no—
326C2×Q8—41no—
327C2×Q8—41no—
328C2×Q8—41no—
329C2×Q8—221no—
330C2×D4—21no—
331C2×D4—41no—
332C2×D4—221no—
333C2×D4—441no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—441no—
337C22×C4C2×C22⋊D1111yescharacteristic
338Q16—22no—
339Q16—21no—
340Q16—22no—
341Q16—21no—
342Q16—44no—
343Q16—41no—
344Q16—41no—
345Q16—112no—
346Q16—221no—
347SD16—44no—
348SD16—41no—
349SD16—41no—
350SD16—222no—
351SD16—222no—
352D8—21no—
353D8—21no—
354D8—112no—
355D8—221no—
356M16—222no—
357M16—441no—
358M16—444no—
359M16#432312yes—
360M16#432312yes—
361C2×C8—441no—
362C2×C8—444no—
363C2×C8D4×D1111yescharacteristic
364C2×C8D4×D1111yescharacteristic
365C2×C8#434111yescharacteristic
366C2×C8#434111yescharacteristic
367C2×C8C2×C22⋊D1112yes—
368C2×C8C2×C22⋊D1111yescharacteristic
369C2×C8C23×D1111yescharacteristic
370C4⋊C4—21no—
371C4⋊C4—44no—
372C22⋊C4—21no—
373C22⋊C4—44no—
374C42C2×C22⋊D1112yes—
375C16—222no—
376C16—222no—
377C11#3359611yescharacteristic, complemented, Sylow
378C23—41no—
379C23—441no—
380C23#6698511yescharacteristic
381Q8—42no—
382Q8—41no—
383Q8—41no—
384Q8—42no—
385Q8—81no—
386Q8—81no—
387Q8—222no—
388Q8—441no—
389D4—41no—
390D4—41no—
391D4—81no—
392D4—81no—
393D4—222no—
394D4—442no—
395D4—442no—
396D4—441no—
397C2×C4—22no—
398C2×C4—42no—
399C2×C4—41no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—441no—
405C2×C4—442no—
406C2×C4—442no—
407C2×C4C2×#432311yescharacteristic
408C2×C4C2×#432311yescharacteristic
409C2×C4#6698511yescharacteristic
410C2×C4#6699111yescharacteristic
411C2×C4#6699111yescharacteristic
412C2×C4C22×C22⋊D1111yescharacteristic
413C8—442no—
414C8C2×#432314yes—
415C8#6699111yescharacteristic
416C8#6699111yescharacteristic
417C8C2×D4×D1111yescharacteristic
418C8C2×#434111yescharacteristic
419C22—41no—
420C22—82no—
421C22—81no—
422C22—442no—
423C22—1761no—
424C22#1062268511yescharacteristic
425C22#1062268511yescharacteristic
426C22C2×#6698511yescharacteristic
427C4—42no—
428C4—81no—
429C4—82no—
430C4—442no—
431C4#1062268511yescharacteristic
432C4#1062268511yescharacteristic
433C4C22×#432311yescharacteristic
434C4C2×#6699111yescharacteristic
435C2—21no—
436C2—21no—
437C2—21no—
438C2—161no—
439C2—882no—
440C2C2×#1062268511yescharacteristic
subgroupG/H
centerC2C2×#10622685
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3156C2
socleC2×C11C2×#459
prime radical#13081750C2
hypercenter#3156D11
hypocenterC11#33596
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ #405 ◁ #3156

Complements

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

NH ≅ G/Ntype
2. C2×#10622792C2semidirect
3. #13077534C2semidirect
4. #13070694C2semidirect
5. #13070682C2semidirect
6. #13070382C2semidirect
7. #13070365C2semidirect
8. C2×#10622203C2semidirect
9. C11×#3156C2semidirect
17. C11×#495C22semidirect
18. C11×#494C22semidirect
35. #10622203C22semidirect
36. #10622203C22semidirect
37. #10622201C22semidirect
38. #10622101C22semidirect
160. #3156D11semidirect
226. #495C2×D11semidirect
227. #494C2×D11semidirect
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×#106227922
#130775342
#130706942
#130706822
#130703822
#130703652
C2×#106222032
C11×#31562
#3359611