Finite Group Databasebeta

← #14648478

Subgroups — #14648478

Order 2816.

516 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078676C211yesmaximal, characteristic
2#13069443C211yesmaximal, characteristic, complemented
3C4×#66901C211yesmaximal, characteristic, complemented
4#13067032C211yesmaximal, characteristic, complemented
5#13066505C211yesmaximal, characteristic, complemented
6#13066448C211yesmaximal, characteristic, complemented
7C11×#2990C211yesmaximal, characteristic, complemented
8C4×C11×#41C2211yescharacteristic
9#10623008C2211yescharacteristic
10C11×#446—21no—
11C11×#435—22no—
12C8×D4×C11—21no—
13C11×#432—21no—
14C11×#431C2211yescharacteristic
15C11×#423C2211yescharacteristic
16C2×C11×C4⋊C8—21no—
17#10622851—21no—
18C2×#66901—21no—
19C2×#66889—22no—
20#10622640C411yescharacteristic, complemented
21C4×#4325—21no—
22#10622634C411yescharacteristic, complemented
23#10622628C411yescharacteristic, complemented
24C4×#4323—21no—
25#10622621C411yescharacteristic, complemented
26#10622616—21no—
27C42×Dic11C2211yescharacteristic
28#10622538C2211yescharacteristic
29C4×#4318C2211yescharacteristic
30#10622170—21no—
31#10622121—21no—
32#10622121—21no—
33C2×C11×#41D411yescharacteristic
34C2×#4339—21no—
35C2×C11×M16D412yes—
36C22×C8×C11—22no—
37C4×Q8×C11C2×C411yescharacteristic
38C4×Q8×C11D411yescharacteristic
39C4×D4×C11—21no—
40C4×D4×C11—21no—
41C4×D4×C11C2×C411yescharacteristic
42C4×D4×C11D411yescharacteristic
43C11×#117—21no—
44C11×#117D411yescharacteristic
45C2×C42×C11—21no—
46C2×C42×C11C2311yescharacteristic
47C2×#4325—21no—
48C2×#4323—21no—
49#66983—21no—
50#66983—21no—
51C2×C4×Dic11—21no—
52C2×C4×Dic11—21no—
53C2×C4×Dic11—21no—
54C2×#4318—21no—
55#66928—21no—
56#66927C2×C411yescharacteristic
57C4×D44—21no—
58C4×D44—21no—
59#66922C2×C411yescharacteristic
60C11×C4⋊C8—22no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8D411yescharacteristic
64C11×C4⋊C8D411yescharacteristic
65C11×C22⋊C8—22no—
66C11×C22⋊C8—21no—
67C11×#97—22no—
68C4×C8×C11—21no—
69#66901—24no—
70#66899—21no—
71#66896—21no—
72C22⋊(C11⋊C8)—21no—
73#66889—44no—
74#66873—21no—
75#66873—21no—
76#66872—21no—
77#66871—21no—
78C4⋊(C11⋊C8)C2×C411yescharacteristic
79C4⋊(C11⋊C8)C2×C411yescharacteristic
80#66867—21no—
81C4×C11⋊C8—21no—
82C4×C11⋊C8—21no—
83#8969—111nomaximal, Sylow
84C11×#41—22no—
85C11×#41—41no—
86C2×Q8×C11C22⋊C411yescharacteristic
87C2×D4×C11—21no—
88C2×D4×C11C22⋊C411yescharacteristic
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C2×C22⋊D11—41no—
96C22×Dic11—41no—
97#4339—42no—
98#4339—42no—
99C2×D44—21no—
100C2×D44—21no—
101C2×D44—21no—
102C2×C4×D11—41no—
103C2×Dic22—21no—
104C11×M16—42no—
105C2×C8×C11—21no—
106C2×C8×C11—21no—
107C2×C8×C11—22no—
108C2×C8×C11—82no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4C22⋊C411yescharacteristic
112C11×C4⋊C4C22⋊C411yescharacteristic
113C11×C22⋊C4—21no—
114C11×C22⋊C4—21no—
115C11×C22⋊C4—21no—
116C42×C11—21no—
117C42×C11—21no—
118C42×C11—21no—
119C42×C11C22×C411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C42×C11#4111yescharacteristic
123#4325—42no—
124#4323—42no—
125(C2×D11)⋊C4—41no—
126(C2×D11)⋊C4—41no—
127C4⋊Dic11—21no—
128C4⋊Dic11—21no—
129C4×Dic11—22no—
130C4×Dic11—22no—
131C4×Dic11—22no—
132C4×Dic11—41no—
133C4×Dic11—41no—
134C4×Dic11—41no—
135#4318—22no—
136#4318—41no—
137C2×C11⋊C8—21no—
138C2×C11⋊C8—21no—
139C2×C11⋊C8—41no—
140#3106—111no—
141#2990D1111yescharacteristic, complemented
142#1962—111no—
143C4×#104—111no—
144#1484—111no—
145#1299—111no—
146#1276—111no—
147C23×C11—21no—
148C23×C11#12111yescharacteristic
149C22×D11—41no—
150Q8×C11—21no—
151Q8×C11—21no—
152D4×C11—21no—
153D4×C11—42no—
154D4×C11#10412yescomplemented
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—42no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11C2×C22⋊C411yescharacteristic
170C2×C4×C11C4×D411yescharacteristic
171C2×C4×C11C4×D411yescharacteristic
172C2×C4×C11#12011yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12311yescharacteristic
175C22⋊D11—82no—
176C2×Dic11—42no—
177C2×Dic11—42no—
178C2×Dic11—42no—
179C2×Dic11—41no—
180D44—42no—
181D44—41no—
182D44—41no—
183D44—41no—
184D44—41no—
185C4×D11—81no—
186C4×D11—81no—
187Dic22—42no—
188C8×C11—41no—
189C8×C11—42no—
190C8×C11—41no—
191C11⋊C8—42no—
192C11⋊C8—41no—
193C11⋊C8—41no—
194#532—111no—
195C4×#41C2×D1111yescharacteristic
196#482—221no—
197#477—111no—
198#476—111no—
199#460—111no—
200#459—111no—
201#449—221no—
202#446—21no—
203C4×SD16—221no—
204C4×D8—221no—
205#435—22no—
206C8×D4—21no—
207#432—21no—
208#431—111no—
209#431C2×D1111yescharacteristic
210#423C2×D1111yescharacteristic
211C2×C4⋊C8—21no—
212C2×#104—221no—
213C2×#104—222no—
214C4×M16—111no—
215C43—111no—
216#339—221no—
217D4⋊C8—221no—
218D4⋊C8—221no—
219C22×C11—21no—
220C22×C11—22no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—41no—
224C22×C11—41no—
225C22×C11#38611yescharacteristic
226C2×D11—81no—
227C2×D11—81no—
228C2×D11—81no—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—41no—
233C4×C11—41no—
234C4×C11—41no—
235C4×C11C2×#10411yescharacteristic
236C4×C11#42111yescharacteristic
237C4×C11#44311yescharacteristic
238C4×C11#44411yescharacteristic
239C4×C11#45311yescharacteristic
240C4×C11#45411yescharacteristic
241Dic11—44no—
242Dic11—81no—
243C2×#41—221no—
244C2×#41D4411yescharacteristic
245C2×SD16—221no—
246C2×D8—221no—
247C2×M16—221no—
248C2×M16C22⋊D1112yes—
249C22×C8—22no—
250C4⋊Q8—111no—
251#127—111no—
252#124—221no—
253#121—221no—
254#121—221no—
255C4×Q8C4×D1111yescharacteristic
256C4×Q8C22⋊D1111yescharacteristic
257C4×D4—21no—
258C4×D4—21no—
259C4×D4—221no—
260C4×D4—221no—
261C4×D4C4×D1111yescharacteristic
262C4×D4C22⋊D1111yescharacteristic
263#117—21no—
264#117D4411yescharacteristic
265C2×C42—21no—
266C2×C42—221no—
267C2×C42—221no—
268C2×C42—221no—
269C2×C42C22×D1111yescharacteristic
270#107—221no—
271#106—221no—
272C4⋊C8—22no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8—111no—
276C4⋊C8—111no—
277C4⋊C8C22⋊D1111yescharacteristic
278C4⋊C8C22⋊D1111yescharacteristic
279#104—224no—
280#104—444no—
281#103—221no—
282#102—221no—
283#102—221no—
284#102—221no—
285C22⋊C8—22no—
286C22⋊C8—21no—
287C22⋊C8—221no—
288#97—22no—
289#97—221no—
290C4×C8—21no—
291C4×C8—221no—
292C4×C8—221no—
293C2×C11—41no—
294C2×C11—42no—
295C2×C11#187111yescharacteristic
296C2×C11#187611yescharacteristic
297C2×C11#188311yescharacteristic
298D11—161no—
299#41—22no—
300#41—41no—
301#41—442no—
302#41—442no—
303C2×Q8—221no—
304C2×Q8(C2×D11)⋊C411yescharacteristic
305C2×D4—21no—
306C2×D4—221no—
307C2×D4—221no—
308C2×D4—221no—
309C2×D4—441no—
310C2×D4(C2×D11)⋊C411yescharacteristic
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—441no—
315C22×C4—441no—
316C22×C4C2×D4411yescharacteristic
317C22×C4#433911yescharacteristic
318C22×C4C2×C22⋊D1111yescharacteristic
319SD16—442no—
320D8—442no—
321M16—42no—
322M16—222no—
323M16—441no—
324C2×C8—21no—
325C2×C8—21no—
326C2×C8—22no—
327C2×C8—82no—
328C2×C8—221no—
329C2×C8—221no—
330C2×C8—441no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—221no—
334C4⋊C4—221no—
335C4⋊C4(C2×D11)⋊C411yescharacteristic
336C4⋊C4(C2×D11)⋊C411yescharacteristic
337C22⋊C4—21no—
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—441no—
341C22⋊C4—441no—
342C42—21no—
343C42—21no—
344C42—21no—
345C42—222no—
346C42—222no—
347C42—222no—
348C42—441no—
349C42—441no—
350C42—441no—
351C42C2×C4×D1111yescharacteristic
352C42#433911yescharacteristic
353C42C2×C22⋊D1111yescharacteristic
354C42C2×C22⋊D1111yescharacteristic
355C11#896911yescharacteristic, complemented, Sylow
356C23—21no—
357C23—441no—
358C23#6698311yescharacteristic
359Q8—21no—
360Q8—21no—
361Q8—442no—
362D4—21no—
363D4—42no—
364D4—442no—
365D4—441no—
366D4—441no—
367D4—441no—
368D4—441no—
369D4—882no—
370D4#6688912yescomplemented
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—442no—
386C2×C4—442no—
387C2×C4—442no—
388C2×C4—441no—
389C2×C4—881no—
390C2×C4—881no—
391C2×C4C2×(C2×D11)⋊C411yescharacteristic
392C2×C4C4×C22⋊D1111yescharacteristic
393C2×C4C4×C22⋊D1111yescharacteristic
394C2×C4#6698211yescharacteristic
395C2×C4#6698311yescharacteristic
396C2×C4#6700611yescharacteristic
397C8—41no—
398C8—42no—
399C8—41no—
400C8—442no—
401C8—441no—
402C8—441no—
403C22—21no—
404C22—22no—
405C22—21no—
406C22—21no—
407C22—41no—
408C22—41no—
409C22—881no—
410C22—881no—
411C22—881no—
412C22#1062282611yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—41no—
417C4—41no—
418C4—41no—
419C4—444no—
420C4—881no—
421C4C2×#6688911yescharacteristic
422C4#1062275211yescharacteristic
423C4#1062275711yescharacteristic
424C4#1062275811yescharacteristic
425C4#1062285411yescharacteristic
426C4#1062285811yescharacteristic
427C2—41no—
428C2—42no—
429C2—1761no—
430C2#1306891811yescharacteristic
431C2#1306894311yescharacteristic
432C2#1306899211yescharacteristic
subgroupG/H
centerC2×C4#67006
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2990C2
socleC22×C11#386
prime radical#13078676C2
cosocleC2×C42×C11C23
hypercenter#2990D11
hypocenterC11#8969
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2990

Complements

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

NH ≅ G/Ntype
2. #13069443C2semidirect
3. C4×#66901C2semidirect
4. #13067032C2semidirect
5. #13066505C2semidirect
6. #13066448C2semidirect
7. C11×#2990C2semidirect
20. #10622640C4semidirect
22. #10622634C4semidirect
23. #10622628C4semidirect
25. #10622621C4semidirect
141. #2990D11semidirect
154. D4×C11#104semidirect
355. C11#8969semidirect
370. D4#66889semidirect

Maximal subgroups

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

subgroupindex
#130786762
#130694432
C4×#669012
#130670322
#130665052
#130664482
C11×#29902
#896911