Finite Group Databasebeta

← #14909339

Subgroups — #14909339

Order 2816.

554 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079190C211yesmaximal, characteristic, complemented
2#13079181C211yesmaximal, characteristic, complemented
3#13070901C211yesmaximal, characteristic, complemented
4#13070879C211yesmaximal, characteristic, complemented
5#13070856C211yesmaximal, characteristic, complemented
6#13070851C211yesmaximal, characteristic, complemented
7#13070729C211yesmaximal, characteristic, complemented
8#13070727C211yesmaximal, characteristic, complemented
9#13070717C211yesmaximal, characteristic, complemented
10#13070471C211yesmaximal, characteristic, complemented
11#13070467C211yesmaximal, characteristic, complemented
12D16×Dic11C211yesmaximal, characteristic, complemented
13#13070460C211yesmaximal, characteristic, complemented
14M32×Dic11C211yesmaximal, characteristic, complemented
15C11×#2218C211yesmaximal, characteristic, complemented
16#10623131—21no—
17#10623127—21no—
18C2×C11×D16C2211yescharacteristic
19C2×C11×M32C2211yescharacteristic
20C11×#466C2211yescharacteristic
21C11×#466C2211yescharacteristic
22#10622768C2211yescharacteristic
23#10622764C2211yescharacteristic
24D8×Dic11C2211yescharacteristic
25D8×Dic11C2211yescharacteristic
26C2×#66891C2211yescharacteristic
27C2×#66890C2211yescharacteristic
28#10622729C2211yescharacteristic
29#10622728C2211yescharacteristic
30C2×C8×Dic11C2211yescharacteristic
31C2×#66876C2211yescharacteristic
32#10622654—21no—
33#10622651—21no—
34C2×#66864C2211yescharacteristic
35#10622491C2211yescharacteristic
36#10622487C2211yescharacteristic
37#10622486C2211yescharacteristic
38#10622485C2211yescharacteristic
39#10622381—21no—
40#10622373—21no—
41#10622371—21no—
42#10622369—21no—
43C11×#367C2211yescharacteristic
44C11×#357C2211yescharacteristic
45C11×#357C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622200C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622142C2211yescharacteristic
50#10622141C2211yescharacteristic
51#10622140C2211yescharacteristic
52#10622140C2211yescharacteristic
53C16×Dic11C2211yescharacteristic
54C16×Dic11C2211yescharacteristic
55#10622130C2211yescharacteristic
56#10622129C2211yescharacteristic
57#10622128C2211yescharacteristic
58#10622127C2211yescharacteristic
59C2×#4341—41no—
60C2×C11×D8C2311yescharacteristic
61C2×C11×D8C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C11×#121—21no—
64C11×#121—21no—
65#66993—21no—
66#66992—41no—
67#66989—21no—
68#66988—41no—
69D4×Dic11—21no—
70D4×Dic11—21no—
71D4×Dic11—41no—
72C2×#4324—21no—
73C2×#4323—21no—
74#66983—21no—
75#66977—21no—
76C2×C4×Dic11D411yescharacteristic
77C22×C11⋊C8D411yescharacteristic
78C2×Dic44C2311yescharacteristic
79C2×D88C2311yescharacteristic
80#66946—21no—
81#66943—21no—
82#66941—21no—
83#66940—21no—
84#66938—41no—
85(C22⋊D11)⋊C4—41no—
86#66932—41no—
87#66930—41no—
88C11×D16—22no—
89C11×M32—22no—
90C2×C11×C16C2311yescharacteristic
91C2×C11×C16C2311yescharacteristic
92C11×#107C2311yescharacteristic
93C11×#107C2311yescharacteristic
94C11×#102—21no—
95C11×#102—21no—
96#66896—21no—
97#66896—21no—
98#66891—22no—
99#66890—22no—
100#66885—21no—
101#66882C2311yescharacteristic
102#66882C2311yescharacteristic
103#66880—21no—
104C8×Dic11D411yescharacteristic
105C8×Dic11D411yescharacteristic
106C8×Dic11C2311yescharacteristic
107C8×Dic11C2311yescharacteristic
108#66876—22no—
109C2×C11⋊C16C2311yescharacteristic
110C2×C11⋊C16C2311yescharacteristic
111#66874—21no—
112#66873—21no—
113#66872—21no—
114#66871—21no—
115#66864—22no—
116#33737—111nomaximal, Sylow
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—41no—
120C2×D4×C11—41no—
121C22×C4×C11C2×D411yescharacteristic
122C2×C22⋊D11—41no—
123C2×C22⋊D11—41no—
124C2×C22⋊D11—41no—
125C22×Dic11—41no—
126C22×Dic11—41no—
127C22×Dic11D811yescharacteristic
128C22×Dic11D811yescharacteristic
129#4341—84no—
130C2×D44—21no—
131C2×C4×D11—41no—
132C2×Dic22—21no—
133C2×Dic22—41no—
134C11×D8—21no—
135C11×D8—21no—
136C11×D8—21no—
137C11×D8—21no—
138C2×C8×C11—21no—
139C2×C8×C11—21no—
140C2×C8×C11C2×D411yescharacteristic
141C2×C8×C11C2411yescharacteristic
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C22⋊C4—41no—
145C11×C22⋊C4—41no—
146C22⋊Dic11—41no—
147C22⋊Dic11—41no—
148C22⋊Dic11—41no—
149C22⋊Dic11—41no—
150C22⋊Dic11—41no—
151#4324—42no—
152#4323—42no—
153(C2×D11)⋊C4—41no—
154(C2×D11)⋊C4—41no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157C4⋊Dic11—41no—
158Dic11⋊C4—41no—
159Dic11⋊C4—41no—
160Dic11⋊C4—41no—
161Dic11⋊C4—41no—
162C4×Dic11—41no—
163C4×Dic11D811yescharacteristic
164C4×Dic11D811yescharacteristic
165C4×Dic11C2×D411yescharacteristic
166C4×Dic11C2×D411yescharacteristic
167C2×C11⋊C8—22no—
168C2×C11⋊C8C2×D411yescharacteristic
169C2×C11⋊C8C2×D411yescharacteristic
170Dic44—21no—
171Dic44—21no—
172D88—21no—
173D88—21no—
174C11×C16—21no—
175C11×C16#4112yescomplemented
176C11⋊C16—21no—
177C11⋊C16#4112yescomplemented
178#3169—111no—
179#3168—111no—
180#2255—111no—
181#2250—111no—
182#2244—111no—
183#2243—111no—
184#2220—111no—
185#2220—111no—
186#2218—111no—
187#2218D1111yescharacteristic, complemented
188C4×SD32—111no—
189C4×SD32—111no—
190C4×D16—111no—
191C4×D16—111no—
192C4×M32—111no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11C2×D811yescharacteristic
196C22×D11—41no—
197D4×C11—41no—
198D4×C11—41no—
199D4×C11—41no—
200D4×C11—41no—
201D4×C11—82no—
202D4×C11—82no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11C2×D811yescharacteristic
208C2×C4×C11C22×D411yescharacteristic
209C22⋊D11—82no—
210C22⋊D11—82no—
211C22⋊D11—82no—
212C2×Dic11—22no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—82no—
218C2×Dic11—82no—
219C2×Dic11C2×D811yescharacteristic
220C2×Dic11C2×D811yescharacteristic
221C2×Dic11C2×D811yescharacteristic
222C2×Dic11C2×D811yescharacteristic
223D44—41no—
224D44—41no—
225C4×D11—82no—
226Dic22—41no—
227Dic22—41no—
228Dic22—82no—
229C8×C11—21no—
230C8×C11C2×#4111yescharacteristic
231C8×C11C2×#4111yescharacteristic
232C11⋊C8—21no—
233C11⋊C8#13512yes—
234#532—221no—
235#529—221no—
236C2×SD32—111no—
237C2×SD32—111no—
238C2×D16—111no—
239C2×D16C2×D1111yescharacteristic
240C2×M32—111no—
241C2×M32C2×D1111yescharacteristic
242#500—111no—
243#499—111no—
244#495—111no—
245#493—111no—
246#488—221no—
247#486—221no—
248#467—111no—
249#466—111no—
250#466—221no—
251#466C2×D1111yescharacteristic
252#466C2×D1111yescharacteristic
253#465—221no—
254C4×Q16—111no—
255C4×SD16—221no—
256C4×D8—111no—
257C4×D8—111no—
258C4×D8—111no—
259C4×D8—221no—
260C2×C4×C8—111no—
261#367—111no—
262#367C2×D1111yescharacteristic
263#366—111no—
264#366—111no—
265#358—111no—
266#358—111no—
267#357—111no—
268#357—111no—
269#357—111no—
270#357—111no—
271#357C2×D1111yescharacteristic
272#357C2×D1111yescharacteristic
273#346—111no—
274#346—111no—
275C4×C16—111no—
276C4×C16—111no—
277C22×C11—21no—
278C22×C11—21no—
279C22×C11—21no—
280C22×C11—81no—
281C22×C11—81no—
282C22×C11—81no—
283C22×C11—81no—
284C22×C11—81no—
285C22×C11—81no—
286C22×C11C22×D811yescharacteristic
287C2×D11—81no—
288C2×D11—81no—
289C2×D11—81no—
290C4×C11—21no—
291C4×C11—81no—
292C4×C11—81no—
293C4×C11#53211yescharacteristic
294C4×C11C2×#13511yescharacteristic
295Dic11—21no—
296Dic11—21no—
297Dic11—21no—
298Dic11—81no—
299Dic11—81no—
300Dic11—81no—
301Dic11#50912yes—
302C2×#41—441no—
303C2×Q16—111no—
304C2×SD16—221no—
305C2×D8—111no—
306C2×D8—221no—
307C2×D8C22×D1111yescharacteristic
308C2×D8C22×D1111yescharacteristic
309C22×C8—111no—
310C22×C8C22×D1111yescharacteristic
311C4⋊Q8—221no—
312#127—221no—
313#126—441no—
314#125—221no—
315#124—221no—
316#124—441no—
317#123—441no—
318C22⋊Q8—221no—
319#121—21no—
320#121—21no—
321#121—221no—
322#121—441no—
323C4×Q8—221no—
324C4×D4—221no—
325C4×D4—221no—
326C4×D4—221no—
327C4×D4—441no—
328C4×D4—441no—
329#117—441no—
330C2×C42—111no—
331SD32—222no—
332SD32—222no—
333D16—22no—
334D16—222no—
335M32—22no—
336M32—222no—
337C2×C16—111no—
338C2×C16—111no—
339C2×C16C22×D1111yescharacteristic
340C2×C16C22×D1111yescharacteristic
341#107—111no—
342#107—111no—
343#107—221no—
344#107C22×D1111yescharacteristic
345#107C22×D1111yescharacteristic
346#106—221no—
347#103—221no—
348#103—221no—
349#102—21no—
350#102—21no—
351#102—221no—
352#102—221no—
353#102—221no—
354#102—221no—
355C4×C8—111no—
356C4×C8—111no—
357C4×C8—111no—
358C4×C8—111no—
359C2×C11—41no—
360C2×C11—161no—
361C2×C11—161no—
362C2×C11#316911yescharacteristic
363C2×C11C2×#50911yescharacteristic
364C2×C11#341411yescharacteristic
365D11—161no—
366#41—884no—
367C2×Q8—221no—
368C2×Q8—441no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—221no—
374C2×D4—441no—
375C2×D4—441no—
376C2×D4—441no—
377C22×C4—111no—
378C22×C4—111no—
379C22×C4—441no—
380C22×C4—441no—
381C22×C4—441no—
382C22×C4D4×D1111yescharacteristic
383Q16—221no—
384Q16—221no—
385SD16—442no—
386D8—21no—
387D8—21no—
388D8—21no—
389D8—21no—
390D8—221no—
391D8—221no—
392D8—442no—
393C2×C8—21no—
394C2×C8—21no—
395C2×C8—111no—
396C2×C8—111no—
397C2×C8—222no—
398C2×C8D4×D1111yescharacteristic
399C2×C8C23×D1111yescharacteristic
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—221no—
403C4⋊C4—221no—
404C4⋊C4—441no—
405C4⋊C4—441no—
406C4⋊C4—441no—
407C4⋊C4—441no—
408C4⋊C4—441no—
409C22⋊C4—41no—
410C22⋊C4—41no—
411C22⋊C4—441no—
412C22⋊C4—441no—
413C22⋊C4—441no—
414C22⋊C4—441no—
415C22⋊C4—441no—
416C22⋊C4—441no—
417C22⋊C4—441no—
418C42—111no—
419C42—111no—
420C42—111no—
421C42—111no—
422C42—441no—
423C16—21no—
424C16—112no—
425C16—221no—
426C16#434112yescomplemented
427C11#3373711yescharacteristic, complemented, Sylow
428C23—41no—
429C23—41no—
430C23—441no—
431C23D8×D1111yescharacteristic
432Q8—441no—
433Q8—441no—
434Q8—882no—
435D4—41no—
436D4—41no—
437D4—41no—
438D4—41no—
439D4—82no—
440D4—82no—
441D4—441no—
442D4—441no—
443D4—882no—
444D4—882no—
445D4—882no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—111no—
451C2×C4—111no—
452C2×C4—111no—
453C2×C4—111no—
454C2×C4—222no—
455C2×C4—441no—
456C2×C4—441no—
457C2×C4—441no—
458C2×C4—441no—
459C2×C4—882no—
460C2×C4—882no—
461C2×C4—882no—
462C2×C4D8×D1111yescharacteristic
463C2×C4C2×D4×D1111yescharacteristic
464C8—21no—
465C8—112no—
466C8—221no—
467C8C2×#434111yescharacteristic
468C8#41×D1111yescharacteristic
469C22—21no—
470C22—21no—
471C22—21no—
472C22—81no—
473C22—81no—
474C22—81no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22—881no—
479C22—881no—
480C22—881no—
481C22C2×D8×D1111yescharacteristic
482C4—21no—
483C4—81no—
484C4—81no—
485C4—112no—
486C4—221no—
487C4—221no—
488C4—221no—
489C4—881no—
490C4—881no—
491C4—881no—
492C4#1062312711yescharacteristic
493C4D11×#13511yescharacteristic
494C2—41no—
495C2—161no—
496C2—161no—
497C2—1761no—
498C2#1307919011yescharacteristic
499C2D11×#50911yescharacteristic
500C2#1308174811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2218C2
socleC22×C11C22×D8
hypercenter#2218D11
hypocenterC11#33737
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2218

Complements

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

NH ≅ G/Ntype
1. #13079190C2semidirect
2. #13079181C2semidirect
3. #13070901C2semidirect
4. #13070879C2semidirect
5. #13070856C2semidirect
6. #13070851C2semidirect
7. #13070729C2semidirect
8. #13070727C2semidirect
9. #13070717C2semidirect
10. #13070471C2semidirect
11. #13070467C2semidirect
12. D16×Dic11C2semidirect
13. #13070460C2semidirect
14. M32×Dic11C2semidirect
15. C11×#2218C2semidirect
175. C11×C16#41semidirect
177. C11⋊C16#41semidirect
187. #2218D11semidirect
426. C16#4341semidirect
427. C11#33737semidirect

Maximal subgroups

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

subgroupindex
#130791902
#130791812
#130709012
#130708792
#130708562
#130708512
#130707292
#130707272
#130707172
#130704712
#130704672
D16×Dic112
#130704602
M32×Dic112
C11×#22182
#3373711