Finite Group Databasebeta

← #14909565

Subgroups — #14909565

Order 2816.

640 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#13078197C211yesmaximal, characteristic, complemented
2#13070813C211yesmaximal, characteristic, complemented
3#13070804C212yesmaximal, complemented
4#13070796C211yesmaximal, characteristic, complemented
5#13070727C212yesmaximal, complemented
6#13070717C212yesmaximal, complemented
7#13070545C211yesmaximal, characteristic, complemented
8#13070537C212yesmaximal, complemented
9#13070528C211yesmaximal, characteristic, complemented
10#13070227C211yesmaximal, characteristic, complemented
11C2×C11×#466C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C11×#121—21no—
15#10623322—21no—
16C2×#66957C2211yescharacteristic, complemented
17C11×#466—21no—
18C11×#466—21no—
19C11×#466C2212yes—
20C11×#466C2212yes—
21C2×C11×#107C2211yescharacteristic
22C2×C11×#102—21no—
23C2×#66891C2212yescomplemented
24C2×#66890C2212yescomplemented
25#10622729C2211yescharacteristic
26#10622729C2211yescharacteristic, complemented
27#10622728C2211yescharacteristic
28#10622728C2211yescharacteristic, complemented
29#10622727—21no—
30#10622727—21no—
31#10622726—21no—
32#10622719C2211yescharacteristic, complemented
33C2×#66876C2212yescomplemented
34#10622200C2212yescomplemented
35#10622200C2212yescomplemented
36C22⋊(C11⋊C16)C2211yescharacteristic
37C22⋊(C11⋊C16)C2211yescharacteristic
38C22⋊(C11⋊C16)C2212yescomplemented
39#10622130C2212yescomplemented
40#10622129C2212yescomplemented
41#10622128C2212yescomplemented
42#10622127C2212yescomplemented
43C22×D4×C11—21no—
44C22×D4×C11—41no—
45C23×C4×C11D411yescharacteristic
46C2×#4339—21no—
47C2×C11×D8—21no—
48C2×C11×D8—42no—
49C2×C11×D8C2312yes—
50C22×C8×C11—42no—
51C22×C8×C11D411yescharacteristic
52C22×C8×C11D411yescharacteristic
53C22×C8×C11D411yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2311yescharacteristic
56C22×C8×C11C2311yescharacteristic
57C11×#121—22no—
58C11×#121—22no—
59C11×#121—41no—
60C11×#121—41no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C22⋊C4—41no—
63#67006—41no—
64#66983—21no—
65#66983—21no—
66#66982—41no—
67C4×C22⋊D11—41no—
68C4×C22⋊D11—41no—
69#66979—21no—
70#66977—21no—
71#66977—21no—
72C2×Dic44C2311yescharacteristic
73#66957—42no—
74C2×D88C2311yescharacteristic
75C2×#4314—21no—
76C11×#107—21no—
77C11×#107C2312yes—
78C11×#102—22no—
79C11×#102—22no—
80#66891—42no—
81#66890—42no—
82#66885—21no—
83#66885—21no—
84#66882C2311yescharacteristic
85#66882C2311yescharacteristic
86#66881—21no—
87#66880—21no—
88#66880—21no—
89#66876—42no—
90C2×C11⋊C16C2312yes—
91C2×C11⋊C16C2312yes—
92#33760—111nomaximal, Sylow
93C24×C11—41no—
94C24×C11D811yescharacteristic
95C2×D4×C11—22no—
96C2×D4×C11—42no—
97C2×D4×C11—42no—
98C2×D4×C11—42no—
99C2×D4×C11—42no—
100C2×D4×C11—41no—
101C2×D4×C11—84no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11D811yescharacteristic
106C22×C4×C11D811yescharacteristic
107C22×C4×C11D811yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C2×C22⋊D11—41no—
112C2×C22⋊D11—41no—
113C2×C22⋊D11—41no—
114#4339—42no—
115#4339—42no—
116C2×D44—21no—
117C2×C4×D11—41no—
118C2×Dic22—21no—
119C11×D8—22no—
120C11×D8—22no—
121C11×D8—42no—
122C2×C8×C11—22no—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11—41no—
126C2×C8×C11—41no—
127C2×C8×C11—41no—
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2×D411yescharacteristic
130C2×C8×C11C2×D411yescharacteristic
131C2×C8×C11C2411yescharacteristic
132C11×C4⋊C4—22no—
133C11×C4⋊C4—41no—
134C11×C22⋊C4—42no—
135C11×C22⋊C4—42no—
136C22⋊Dic11—41no—
137C22⋊Dic11—41no—
138C22⋊Dic11—41no—
139(C2×D11)⋊C4—41no—
140(C2×D11)⋊C4—41no—
141C4⋊Dic11—21no—
142C4⋊Dic11—21no—
143Dic11⋊C4—41no—
144Dic11⋊C4—41no—
145C4×Dic11—41no—
146Dic44—22no—
147D88—22no—
148#4314—42no—
149C11⋊C16—22no—
150C11⋊C16—22no—
151#3050—111no—
152C2×#466D1111yescharacteristic, complemented
153#2235—111no—
154#2234—112no—
155#2232—111no—
156#2220—112no—
157#2218—112no—
158#2187—111no—
159#2186—112no—
160#2184—111no—
161#2112—111no—
162C23×C11—22no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11—42no—
166C23×C11—82no—
167C23×C11—82no—
168C23×C11—82no—
169C23×C11C2×D811yescharacteristic
170C23×C11C2×D811yescharacteristic
171C23×C11C2×D811yescharacteristic
172C22×D11—41no—
173D4×C11—42no—
174D4×C11—42no—
175D4×C11—82no—
176D4×C11—84no—
177D4×C11—84no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—42no—
188C2×C4×C11—82no—
189C2×C4×C11C2×D811yescharacteristic
190C2×C4×C11C2×D811yescharacteristic
191C2×C4×C11C2×D811yescharacteristic
192C2×C4×C11C22×D411yescharacteristic
193C22⋊D11—82no—
194C22⋊D11—82no—
195C22⋊D11—82no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199D44—41no—
200D44—41no—
201C4×D11—82no—
202Dic22—41no—
203Dic22—41no—
204C8×C11—21no—
205C8×C11—21no—
206C8×C11—21no—
207C8×C11H(5,𝔽2)12yes—
208C2×#135—111no—
209C22×D8C2×D1111yescharacteristic
210C23×C8C2×D1111yescharacteristic
211#525—221no—
212C2×#121—21no—
213C2×SD32—112no—
214C2×D16—112no—
215C2×M32—112no—
216#467—111no—
217#467—111no—
218#466—21no—
219#466—21no—
220#466—111no—
221#466—111no—
222#466C2×D1112yes—
223#466C2×D1112yes—
224#465—221no—
225#465—221no—
226#427—111no—
227C2×#107C2×D1111yescharacteristic
228#416—221no—
229C2×#102—21no—
230#367—112no—
231#366—112no—
232#358—112no—
233#357—112no—
234#357—112no—
235#357—112no—
236C22⋊C16—111no—
237C22⋊C16—112no—
238C22⋊C16—111no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—21no—
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—21no—
247C22×C11—44no—
248C22×C11—82no—
249C22×C11—82no—
250C22×C11—82no—
251C22×C11—164no—
252C22×C11#50912yes—
253C22×C11C22×D811yescharacteristic
254C2×D11—81no—
255C2×D11—81no—
256C2×D11—81no—
257C4×C11—21no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—82no—
261C4×C11#53411yescharacteristic
262C4×C11#57511yescharacteristic
263Dic11—81no—
264Dic11—81no—
265Dic11—81no—
266C2×#41—221no—
267C22×D4—21no—
268C22×D4—41no—
269C23×C4C22⋊D1111yescharacteristic
270#135—442no—
271C2×Q16—111no—
272C2×SD16—221no—
273C2×D8—21no—
274C2×D8—42no—
275C2×D8—111no—
276C2×D8C22×D1112yes—
277C22×C8—42no—
278C22×C8C22⋊D1111yescharacteristic
279C22×C8C22⋊D1111yescharacteristic
280C22×C8C22⋊D1111yescharacteristic
281C22×C8C22×D1111yescharacteristic
282C22×C8C22×D1111yescharacteristic
283C22×C8C22×D1111yescharacteristic
284#123—441no—
285C22⋊Q8—221no—
286C22⋊Q8—221no—
287#121—22no—
288#121—22no—
289#121—41no—
290#121—41no—
291#121—221no—
292#121—221no—
293#120—441no—
294C4×D4—441no—
295C4×D4—441no—
296#117—221no—
297C2×C4⋊C4—21no—
298C2×C22⋊C4—41no—
299SD32—442no—
300D16—442no—
301M32—442no—
302C2×C16—112no—
303C2×C16—112no—
304#107—21no—
305#107—111no—
306#107—111no—
307#107C22×D1112yes—
308#106—221no—
309#103—221no—
310#103—221no—
311#102—22no—
312#102—22no—
313#102—221no—
314#102—221no—
315C2×C11—22no—
316C2×C11—41no—
317C2×C11—41no—
318C2×C11—162no—
319C2×C11#318611yescharacteristic
320C2×C11C2×#50911yescharacteristic
321C2×C11#341411yescharacteristic
322D11—161no—
323C24—41no—
324C24#432311yescharacteristic
325#41—442no—
326#41—442no—
327C2×Q8—221no—
328C2×D4—22no—
329C2×D4—42no—
330C2×D4—42no—
331C2×D4—42no—
332C2×D4—42no—
333C2×D4—41no—
334C2×D4—84no—
335C2×D4—221no—
336C2×D4—441no—
337C2×D4—441no—
338C2×D4—441no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—441no—
343C22×C4#432311yescharacteristic
344C22×C4#432311yescharacteristic
345C22×C4#432311yescharacteristic
346C22×C4C2×C22⋊D1111yescharacteristic
347C22×C4C2×C22⋊D1111yescharacteristic
348C22×C4C2×C22⋊D1111yescharacteristic
349Q16—222no—
350SD16—442no—
351D8—22no—
352D8—22no—
353D8—42no—
354D8—222no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—41no—
359C2×C8—41no—
360C2×C8—41no—
361C2×C8C2×C22⋊D1111yescharacteristic
362C2×C8C2×C22⋊D1111yescharacteristic
363C2×C8C2×C22⋊D1111yescharacteristic
364C2×C8C23×D1111yescharacteristic
365C4⋊C4—22no—
366C4⋊C4—41no—
367C4⋊C4—221no—
368C4⋊C4—221no—
369C4⋊C4—441no—
370C4⋊C4—441no—
371C22⋊C4—42no—
372C22⋊C4—42no—
373C22⋊C4—441no—
374C22⋊C4—441no—
375C22⋊C4—441no—
376C22⋊C4—441no—
377C22⋊C4—441no—
378C42—441no—
379C16—222no—
380C16—222no—
381C11#3376011yescharacteristic, complemented, Sylow
382C23—22no—
383C23—41no—
384C23—41no—
385C23—42no—
386C23—82no—
387C23—82no—
388C23—82no—
389C23—441no—
390C23C2×#432311yescharacteristic
391C23C2×#432311yescharacteristic
392C23C2×#432311yescharacteristic
393Q8—441no—
394Q8—441no—
395D4—42no—
396D4—42no—
397D4—82no—
398D4—84no—
399D4—84no—
400D4—441no—
401D4—441no—
402D4—882no—
403D4—882no—
404D4—882no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—42no—
415C2×C4—82no—
416C2×C4—441no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—882no—
420C2×C4C2×#432311yescharacteristic
421C2×C4C2×#432311yescharacteristic
422C2×C4C2×#432311yescharacteristic
423C2×C4C22×C22⋊D1111yescharacteristic
424C8—21no—
425C8—21no—
426C8—21no—
427C8#6703712yes—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—44no—
437C22—82no—
438C22—82no—
439C22—82no—
440C22—164no—
441C22—881no—
442C22—881no—
443C22—881no—
444C22#1062276012yes—
445C22C22×#432311yescharacteristic
446C4—21no—
447C4—21no—
448C4—21no—
449C4—82no—
450C4—881no—
451C4—881no—
452C4—881no—
453C4#1062333511yescharacteristic
454C4#1062335311yescharacteristic
455C2—22no—
456C2—41no—
457C2—41no—
458C2—162no—
459C2—1761no—
460C2#1307936411yescharacteristic
461C2C2×#1062276011yescharacteristic
462C2#1308175011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#466C2
socleC22×C11C22×D8
hypercenterC2×#466D11
hypocenterC11#33760
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. #13078197C2semidirect
2. #13070813C2semidirect
3. #13070804C2semidirect
4. #13070796C2semidirect
5. #13070727C2semidirect
6. #13070717C2semidirect
7. #13070545C2semidirect
8. #13070537C2semidirect
9. #13070528C2semidirect
10. #13070227C2semidirect
11. C2×C11×#466C2semidirect
16. C2×#66957C22semidirect
23. C2×#66891C22semidirect
24. C2×#66890C22semidirect
26. #10622729C22semidirect
28. #10622728C22semidirect
32. #10622719C22semidirect
33. C2×#66876C22semidirect
34. #10622200C22semidirect
35. #10622200C22semidirect
38. C22⋊(C11⋊C16)C22semidirect
39. #10622130C22semidirect
40. #10622129C22semidirect
41. #10622128C22semidirect
42. #10622127C22semidirect
152. C2×#466D11semidirect
381. C11#33760semidirect

Maximal subgroups

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

subgroupindex
#130781972
#130708132
#130708042
#130707962
#130707272
#130707172
#130705452
#130705372
#130705282
#130702272
C2×C11×#4662
#3376011