Finite Group Databasebeta

← #14909513

Subgroups — #14909513

Order 2816.

646 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078195C211yesmaximal, characteristic, complemented
2C2×#10622770C211yesmaximal, characteristic, complemented
3#13070819C211yesmaximal, characteristic, complemented
4#13070805C212yesmaximal, complemented
5#13070799C211yesmaximal, characteristic, complemented
6#13070711C212yesmaximal, complemented
7#13070699C212yesmaximal, complemented
8#13070545C211yesmaximal, characteristic, complemented
9#13070536C212yesmaximal, complemented
10D11×C22⋊C16C211yesmaximal, characteristic, complemented
11C11×#2184C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13C2×#66991—21no—
14C2×#66965C2211yescharacteristic, complemented
15C22×C8×D11C2211yescharacteristic
16#10623137—21no—
17C2×C11×D16C2212yescomplemented
18C11×#466C2211yescharacteristic
19C2×#66896—21no—
20#10622770—21no—
21#10622770—21no—
22#10622770C2212yes—
23#10622770C2212yes—
24#10622770C2211yescharacteristic, complemented
25C2×#66891C2212yescomplemented
26#10622729C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28#10622654—21no—
29C2×C16×D11C2212yescomplemented
30#10622500C2211yescharacteristic, complemented
31#10622493C2211yescharacteristic, complemented
32#10622391—21no—
33#10622385—21no—
34C11×#357C2212yescomplemented
35C11×C22⋊C16C2211yescharacteristic
36#10622200C2212yescomplemented
37#10622200C2212yescomplemented
38C22⋊(C11⋊C16)C2211yescharacteristic
39(C2×D11)⋊C16C2212yescomplemented
40#10622142C2212yescomplemented
41#10622141C2212yescomplemented
42#10622128C2212yescomplemented
43C22×D4×C11—21no—
44C22×C22⋊D11—41no—
45C2×#4341—21no—
46C22×C4×D11D411yescharacteristic
47C2×C11×D8—21no—
48C2×C11×D8—42no—
49C2×C11×D8C2311yescharacteristic
50C2×C11×D8C2312yes—
51C22×C8×C11C2311yescharacteristic
52C11×#121—21no—
53C2×C22⋊Dic11—41no—
54#66991—22no—
55#66991—22no—
56#66991—21no—
57#66991—41no—
58#66991—41no—
59#66990—41no—
60D4×Dic11—41no—
61C2×#4324—21no—
62C2×C4⋊Dic11—21no—
63#66977—21no—
64C22×C11⋊C8D411yescharacteristic
65#66965—42no—
66C2×Dic44C2311yescharacteristic
67C2×C8×D11—42no—
68C2×C8×D11D411yescharacteristic
69C2×C8×D11D411yescharacteristic
70C2×C8×D11C2311yescharacteristic
71C2×C8×D11C2311yescharacteristic
72#66950—21no—
73#66945—21no—
74#66936—41no—
75(C22⋊D11)⋊C4—41no—
76C11×D16—42no—
77C2×C11×C16C2312yes—
78C11×#107C2311yescharacteristic
79C11×#102—21no—
80#66896—22no—
81#66896—22no—
82#66896—21no—
83#66891—42no—
84#66882—21no—
85#66882C2311yescharacteristic
86#66882C2312yes—
87#66880—21no—
88C2×C11⋊C16C2312yes—
89#66874—21no—
90#66872—21no—
91C16×D11—42no—
92#33754—111nomaximal, Sylow
93C24×C11—41no—
94C23×D11D811yescharacteristic
95C2×D4×C11—22no—
96C2×D4×C11—21no—
97C2×D4×C11—42no—
98C2×D4×C11—42no—
99C2×D4×C11—41no—
100C2×D4×C11—41no—
101C22×C4×C11C2×D411yescharacteristic
102C2×C22⋊D11—41no—
103C2×C22⋊D11—41no—
104C2×C22⋊D11—42no—
105C2×C22⋊D11—42no—
106C2×C22⋊D11—84no—
107C22×Dic11—41no—
108C22×Dic11—41no—
109C22×Dic11D811yescharacteristic
110#4341—42no—
111#4341—42no—
112C2×C4×D11—41no—
113C2×C4×D11—41no—
114C2×C4×D11D811yescharacteristic
115C2×C4×D11D811yescharacteristic
116C2×C4×D11C2×D411yescharacteristic
117C2×C4×D11C2×D411yescharacteristic
118C2×Dic22—21no—
119C11×D8—22no—
120C11×D8—22no—
121C11×D8—22no—
122C11×D8—42no—
123C2×C8×C11—22no—
124C2×C8×C11C2×D411yescharacteristic
125C2×C8×C11C2411yescharacteristic
126C11×C4⋊C4—21no—
127C11×C22⋊C4—41no—
128C22⋊Dic11—41no—
129C22⋊Dic11—42no—
130C22⋊Dic11—42no—
131C22⋊Dic11—41no—
132#4324—42no—
133(C2×D11)⋊C4—41no—
134(C2×D11)⋊C4—41no—
135C4⋊Dic11—21no—
136C4⋊Dic11—22no—
137C4⋊Dic11—41no—
138C4⋊Dic11—41no—
139Dic11⋊C4—41no—
140C4×Dic11—41no—
141C2×C11⋊C8—41no—
142C2×C11⋊C8C2×D411yescharacteristic
143C2×C11⋊C8C2×D411yescharacteristic
144Dic44—22no—
145C8×D11—22no—
146C8×D11—22no—
147C8×D11—41no—
148C8×D11—41no—
149C11×C16—22no—
150C11⋊C16—22no—
151#3050—111no—
152C2×#466—111no—
153#2236—111no—
154#2234—112no—
155#2233—111no—
156#2217—112no—
157#2215—112no—
158#2187—111no—
159#2186—112no—
160#2184D1111yescharacteristic, complemented
161C2×C22⋊C16—111no—
162C23×C11—42no—
163C23×C11—41no—
164C23×C11—82no—
165C23×C11—82no—
166C23×C11—82no—
167C23×C11C2×D811yescharacteristic
168C22×D11—22no—
169C22×D11—22no—
170C22×D11—41no—
171C22×D11C2×D811yescharacteristic
172C22×D11C2×D811yescharacteristic
173D4×C11—41no—
174D4×C11—42no—
175D4×C11—41no—
176D4×C11—42no—
177D4×C11—82no—
178D4×C11—82no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—41no—
182C2×C4×C11C2×D811yescharacteristic
183C2×C4×C11C22×D411yescharacteristic
184C22⋊D11—82no—
185C22⋊D11—84no—
186C22⋊D11—82no—
187C22⋊D11—84no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191C2×Dic11—42no—
192C2×Dic11—82no—
193C2×Dic11—82no—
194C2×Dic11C2×D811yescharacteristic
195C2×Dic11C2×D811yescharacteristic
196C4×D11—21no—
197C4×D11—21no—
198C4×D11—21no—
199C4×D11—21no—
200C4×D11—41no—
201C4×D11—41no—
202Dic22—41no—
203Dic22—41no—
204C8×C11—21no—
205C8×C11H(5,𝔽2)12yes—
206C11⋊C8—21no—
207C11⋊C8—21no—
208C2×#135—111no—
209C22×D8C2×D1111yescharacteristic
210C23×C8—111no—
211#525—221no—
212C2×#121—221no—
213C2×SD32—112no—
214C2×D16C2×D1112yescomplemented
215C22×C16—112no—
216#467—111no—
217#467—111no—
218#466—112no—
219#466—112no—
220#466—111no—
221#466—221no—
222#466—221no—
223#466C2×D1111yescharacteristic
224#465—221no—
225#465—221no—
226#427—111no—
227C2×#107—111no—
228#416—221no—
229C2×#102—221no—
230#367—112no—
231#366—112no—
232#358—112no—
233#357—112no—
234#357—112no—
235#357C2×D1112yescomplemented
236C22⋊C16—111no—
237C22⋊C16—112no—
238C22⋊C16C2×D1111yescharacteristic
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—81no—
242C22×C11—82no—
243C22×C11—82no—
244C22×C11—81no—
245C22×C11—82no—
246C22×C11—81no—
247C22×C11—164no—
248C22×C11#50812yes—
249C22×C11C22×D811yescharacteristic
250C2×D11—21no—
251C2×D11—21no—
252C2×D11—21no—
253C2×D11—21no—
254C2×D11—21no—
255C2×D11—44no—
256C2×D11#50912yes—
257C4×C11—21no—
258C4×C11—81no—
259C4×C11#53411yescharacteristic
260C4×C11#57511yescharacteristic
261Dic11—21no—
262Dic11—21no—
263Dic11—82no—
264Dic11—81no—
265Dic11—81no—
266C2×#41—221no—
267C22×D4—21no—
268C22×D4—441no—
269C23×C4—111no—
270#135—442no—
271C2×Q16—111no—
272C2×SD16—221no—
273C2×D8—21no—
274C2×D8—42no—
275C2×D8C22×D1112yes—
276C2×D8C22×D1111yescharacteristic
277C22×C8—111no—
278C22×C8—111no—
279C22×C8—111no—
280C22×C8—111no—
281C22×C8—111no—
282C22×C8—442no—
283C22×C8C22×D1111yescharacteristic
284#123—441no—
285C22⋊Q8—221no—
286C22⋊Q8—221no—
287#121—21no—
288#121—222no—
289#121—222no—
290#121—221no—
291#121—441no—
292#121—441no—
293#120—441no—
294C4×D4—441no—
295C4×D4—441no—
296#117—221no—
297C2×C4⋊C4—221no—
298C2×C22⋊C4—441no—
299SD32—442no—
300D16—42no—
301C2×C16—112no—
302C2×C16—442no—
303C2×C16C22×D1112yes—
304#107—111no—
305#107—112no—
306#107—221no—
307#107C22×D1111yescharacteristic
308#106—221no—
309#103—221no—
310#103—221no—
311#102—21no—
312#102—222no—
313#102—222no—
314#102—221no—
315C2×C11—22no—
316C2×C11—161no—
317C2×C11—162no—
318C2×C11#318611yescharacteristic
319C2×C11C2×#50811yescharacteristic
320C2×C11C2×#50911yescharacteristic
321D11—22no—
322D11—41no—
323C24—41no—
324C24—111no—
325#41—442no—
326#41—442no—
327C2×Q8—221no—
328C2×D4—21no—
329C2×D4—22no—
330C2×D4—42no—
331C2×D4—42no—
332C2×D4—41no—
333C2×D4—41no—
334C2×D4—441no—
335C2×D4—441no—
336C2×D4—442no—
337C2×D4—442no—
338C2×D4—884no—
339C22×C4—111no—
340C22×C4—111no—
341C22×C4—111no—
342C22×C4—111no—
343C22×C4—111no—
344C22×C4—441no—
345C22×C4—441no—
346C22×C4—441no—
347C22×C4—441no—
348C22×C4D4×D1111yescharacteristic
349Q16—222no—
350SD16—442no—
351D8—22no—
352D8—22no—
353D8—22no—
354D8—42no—
355C2×C8—22no—
356C2×C8—111no—
357C2×C8—111no—
358C2×C8—222no—
359C2×C8—222no—
360C2×C8—441no—
361C2×C8—441no—
362C2×C8—441no—
363C2×C8D4×D1111yescharacteristic
364C2×C8C23×D1111yescharacteristic
365C4⋊C4—21no—
366C4⋊C4—222no—
367C4⋊C4—221no—
368C4⋊C4—441no—
369C4⋊C4—441no—
370C4⋊C4—441no—
371C22⋊C4—41no—
372C22⋊C4—441no—
373C22⋊C4—441no—
374C22⋊C4—442no—
375C22⋊C4—442no—
376C22⋊C4—441no—
377C22⋊C4—441no—
378C42—441no—
379C16—22no—
380C16—222no—
381C11#3375411yescharacteristic, complemented, Sylow
382C23—41no—
383C23—42no—
384C23—82no—
385C23—82no—
386C23—82no—
387C23—111no—
388C23—111no—
389C23—222no—
390C23—222no—
391C23—441no—
392C23D8×D1111yescharacteristic
393Q8—441no—
394Q8—441no—
395D4—42no—
396D4—41no—
397D4—42no—
398D4—41no—
399D4—82no—
400D4—82no—
401D4—884no—
402D4—882no—
403D4—884no—
404D4—882no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—111no—
409C2×C4—111no—
410C2×C4—221no—
411C2×C4—221no—
412C2×C4—221no—
413C2×C4—221no—
414C2×C4—441no—
415C2×C4—441no—
416C2×C4—441no—
417C2×C4—441no—
418C2×C4—442no—
419C2×C4—441no—
420C2×C4—882no—
421C2×C4—882no—
422C2×C4D8×D1111yescharacteristic
423C2×C4C2×D4×D1111yescharacteristic
424C8—21no—
425C8—221no—
426C8—221no—
427C8#6703712yes—
428C22—21no—
429C22—21no—
430C22—81no—
431C22—82no—
432C22—81no—
433C22—82no—
434C22—82no—
435C22—81no—
436C22—112no—
437C22—164no—
438C22—221no—
439C22—221no—
440C22—221no—
441C22—221no—
442C22—221no—
443C22—444no—
444C22#1062252512yes—
445C22C2×D8×D1111yescharacteristic
446C4—21no—
447C4—81no—
448C4—221no—
449C4—221no—
450C4—881no—
451C4—882no—
452C4—881no—
453C4#1062312011yescharacteristic
454C4#1062330411yescharacteristic
455C2—22no—
456C2—162no—
457C2—161no—
458C2—222no—
459C2—441no—
460C2#1307936511yescharacteristic
461C2C2×#1062252511yescharacteristic
462C2D11×#50911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2184C2
socleC22×C11C22×D8
hypercenter#2184D11
hypocenterC11#33754
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2184

Complements

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

NH ≅ G/Ntype
1. #13078195C2semidirect
2. C2×#10622770C2semidirect
3. #13070819C2semidirect
4. #13070805C2semidirect
5. #13070799C2semidirect
6. #13070711C2semidirect
7. #13070699C2semidirect
8. #13070545C2semidirect
9. #13070536C2semidirect
10. D11×C22⋊C16C2semidirect
11. C11×#2184C2semidirect
14. C2×#66965C22semidirect
17. C2×C11×D16C22semidirect
24. #10622770C22semidirect
25. C2×#66891C22semidirect
29. C2×C16×D11C22semidirect
30. #10622500C22semidirect
31. #10622493C22semidirect
34. C11×#357C22semidirect
36. #10622200C22semidirect
37. #10622200C22semidirect
39. (C2×D11)⋊C16C22semidirect
40. #10622142C22semidirect
41. #10622141C22semidirect
42. #10622128C22semidirect
160. #2184D11semidirect
214. C2×D16C2×D11semidirect
235. #357C2×D11semidirect
381. C11#33754semidirect

Maximal subgroups

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

subgroupindex
#130781952
C2×#106227702
#130708192
#130708052
#130707992
#130707112
#130706992
#130705452
#130705362
D11×C22⋊C162
C11×#21842
#3375411