Finite Group Databasebeta

← #14910619

Subgroups — #14910619

Order 2816.

568 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080984C211yesmaximal, characteristic, complemented
2#13080295C211yesmaximal, characteristic
3#13070849C211yesmaximal, characteristic, complemented
4#13070812C211yesmaximal, characteristic, complemented
5#13070807C211yesmaximal, characteristic, complemented
6#13070775C211yesmaximal, characteristic, complemented
7#13070712C211yesmaximal, characteristic, complemented
8#13070706C211yesmaximal, characteristic, complemented
9#13070681C211yesmaximal, characteristic, complemented
10#13070556C211yesmaximal, characteristic, complemented
11#13070546C211yesmaximal, characteristic, complemented
12#13070471C211yesmaximal, characteristic, complemented
13C16×C22⋊D11C211yesmaximal, characteristic, complemented
14D11×#357C211yesmaximal, characteristic, complemented
15C11×#2138C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic
17#10623360—21no—
18C2×D8×D11C2211yescharacteristic
19#10623060—21no—
20C22×C11×C16C2211yescharacteristic, complemented
21C11×#427C2211yescharacteristic, complemented
22#10622851—21no—
23#10622804C2211yescharacteristic
24#10622801C2211yescharacteristic
25C2×#66893C2211yescharacteristic, complemented
26#10622782—21no—
27#10622778—21no—
28D8×Dic11C2211yescharacteristic
29C2×#66891C2211yescharacteristic
30#10622729C2211yescharacteristic, complemented
31#10622728C2211yescharacteristic
32C8×C22⋊D11C2211yescharacteristic
33#10622609—21no—
34C2×#66864C2211yescharacteristic
35C2×C16×D11C2211yescharacteristic
36#10622500C2211yescharacteristic
37D11×#107C2211yescharacteristic
38#10622491C2211yescharacteristic, complemented
39#10622486C2211yescharacteristic, complemented
40#10622475—21no—
41#10622470—21no—
42C11×#358C2211yescharacteristic, complemented
43C11×#358C2211yescharacteristic, complemented
44C11×#357C2211yescharacteristic
45C11×#357C2211yescharacteristic
46#10622202C2211yescharacteristic, complemented
47#10622200C2211yescharacteristic
48C22⋊(C11⋊C16)C2211yescharacteristic, complemented
49#10622147C2211yescharacteristic
50(C2×D11)⋊C16C2211yescharacteristic
51#10622143C2211yescharacteristic, complemented
52#10622141C2211yescharacteristic, complemented
53Dic11⋊C16C2211yescharacteristic, complemented
54C16×Dic11C2211yescharacteristic, complemented
55#10622129C2211yescharacteristic
56#10622129C2211yescharacteristic
57#10622128C2211yescharacteristic, complemented
58#10622127C2211yescharacteristic, complemented
59C2×C11×#41—21no—
60C2×D4×D11—21no—
61C11×#135—22no—
62C11×#135—41no—
63C2×C11×Q16C2311yescharacteristic
64C2×C11×SD16—21no—
65C2×C11×D8C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×#117—21no—
68#67000—21no—
69#66999—21no—
70C2×#4325—21no—
71#66992—41no—
72#66990—41no—
73D4×Dic11—21no—
74C2×#4323—21no—
75#66983—21no—
76#66982—41no—
77C4×C22⋊D11D411yescharacteristic
78C2×(C2×D11)⋊C4—41no—
79#66977—21no—
80D8×D11—22no—
81D8×D11—41no—
82C2×Dic44C2311yescharacteristic
83C2×D88C2311yescharacteristic
84C2×C8×D11C2311yescharacteristic
85#66950—21no—
86C4⋊C4×D11—21no—
87#66943—21no—
88#66940—21no—
89#66936—41no—
90#66932—41no—
91#66925—41no—
92#66923—41no—
93C2×C11×C16—41no—
94C2×C11×C16C2311yescharacteristic
95C2×C11×C16C2311yescharacteristic
96C11×#107C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#106—21no—
99#66899—21no—
100#66896—21no—
101C22⋊(C11⋊C8)D411yescharacteristic
102#66893—41no—
103#66891—22no—
104#66885—21no—
105(C2×D11)⋊C8D411yescharacteristic
106#66882C2311yescharacteristic
107#66882C2311yescharacteristic
108#66880—21no—
109Dic11⋊C8D411yescharacteristic
110C8×Dic11C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113#66874—21no—
114#66874—21no—
115#66872—21no—
116#66871—21no—
117#66864—41no—
118C16×D11—41no—
119#33863—111nomaximal, Sylow
120C23×D11—41no—
121C11×#41—42no—
122C11×#41—81no—
123C2×Q8×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—41no—
126C22×C4×C11—41no—
127C22×C4×C11C2×D411yescharacteristic
128C2×C22⋊D11—41no—
129C2×C22⋊D11—41no—
130C2×C22⋊D11D811yescharacteristic
131C22×Dic11—41no—
132D4×D11—42no—
133D4×D11—81no—
134C2×D44—21no—
135C2×C4×D11—41no—
136C2×C4×D11C2×D411yescharacteristic
137C2×Dic22—21no—
138C11×Q16—21no—
139C11×Q16—21no—
140C11×SD16—42no—
141C11×D8—21no—
142C11×D8#4112yes—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11C2×D411yescharacteristic
146C2×C8×C11C2411yescharacteristic
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C22⋊C4—41no—
150C42×C11—41no—
151C22⋊Dic11—41no—
152C22⋊Dic11—41no—
153C22⋊Dic11D811yescharacteristic
154#4325—81no—
155#4323—42no—
156(C2×D11)⋊C4—41no—
157(C2×D11)⋊C4—41no—
158(C2×D11)⋊C4—41no—
159(C2×D11)⋊C4—41no—
160(C2×D11)⋊C4—41no—
161(C2×D11)⋊C4D811yescharacteristic
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164C4⋊Dic11—41no—
165C4⋊Dic11—41no—
166Dic11⋊C4—41no—
167Dic11⋊C4—41no—
168Dic11⋊C4—41no—
169Dic11⋊C4—41no—
170Dic11⋊C4—41no—
171Dic11⋊C4D811yescharacteristic
172C4×Dic11—41no—
173C4×Dic11C2×D411yescharacteristic
174C2×C11⋊C8C2×D411yescharacteristic
175C2×C11⋊C8C2×D411yescharacteristic
176Dic44—21no—
177Dic44—21no—
178D88—21no—
179D88—21no—
180C8×D11—21no—
181C8×D11—21no—
182C11×C16—21no—
183C11×C16—21no—
184C11⋊C16—21no—
185C11⋊C16—21no—
186#3336—111no—
187#3280—111no—
188#2242—111no—
189#2235—111no—
190#2234—111no—
191#2228—111no—
192#2217—111no—
193#2216—111no—
194#2211—111no—
195#2189—111no—
196#2187—111no—
197C4×SD32—111no—
198D4×C16—111no—
199#2138D1111yescharacteristic, complemented
200C2×#357—111no—
201C23×C11—41no—
202C23×C11C2×D811yescharacteristic
203C22×D11—41no—
204C22×D11—82no—
205C22×D11—82no—
206C22×D11—161no—
207C22×D11C2×D811yescharacteristic
208Q8×C11—41no—
209Q8×C11—41no—
210D4×C11—22no—
211D4×C11—41no—
212D4×C11—82no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—82no—
219C2×C4×C11C2×D811yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C22⋊D11—22no—
222C22⋊D11—82no—
223C22⋊D11—161no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—161no—
228C2×Dic11C2×D811yescharacteristic
229C2×Dic11C2×D811yescharacteristic
230C2×Dic11C2×D811yescharacteristic
231D44—41no—
232D44—41no—
233C4×D11—21no—
234C4×D11—21no—
235C4×D11—82no—
236Dic22—41no—
237Dic22—41no—
238C8×C11—21no—
239C8×C11C2×#4111yescharacteristic
240C8×C11H(5,𝔽2)11yescharacteristic
241C11⋊C8—21no—
242C11⋊C8—21no—
243C2×#135C2×D1111yescharacteristic
244C22×D8—111no—
245#552—221no—
246#546—221no—
247C2×Q32—111no—
248C2×SD32—111no—
249C2×SD32—111no—
250C22×C16—111no—
251C22×C16C2×D1111yescharacteristic, complemented
252#499—111no—
253#495—111no—
254#485—221no—
255#483—221no—
256#479—221no—
257#467—111no—
258#467—111no—
259#467—111no—
260#466—111no—
261#463—221no—
262#450—221no—
263#449—221no—
264C4×Q16—111no—
265C4×D8—111no—
266C8×D4—111no—
267#427C2×D1111yescharacteristic, complemented
268C2×#107—111no—
269#367—111no—
270#367—111no—
271#366—111no—
272C4⋊C16—111no—
273#358—111no—
274#358—111no—
275#358C2×D1111yescharacteristic, complemented
276#358C2×D1111yescharacteristic, complemented
277#357—111no—
278#357—111no—
279#357—111no—
280#357—111no—
281#357C2×D1111yescharacteristic
282#357C2×D1111yescharacteristic
283C22⋊C16—111no—
284C22⋊C16—111no—
285C4×C16—111no—
286C22×C11—21no—
287C22×C11—21no—
288C22×C11—21no—
289C22×C11—42no—
290C22×C11—81no—
291C22×C11—81no—
292C22×C11C22×D811yescharacteristic
293C2×D11—21no—
294C2×D11—21no—
295C2×D11—81no—
296C2×D11—81no—
297C2×D11—81no—
298C2×D11—164no—
299C2×D11#50812yes—
300C4×C11—21no—
301C4×C11—81no—
302C4×C11—81no—
303C4×C11—81no—
304C4×C11#54611yescharacteristic
305C4×C11#57711yescharacteristic
306Dic11—21no—
307Dic11—21no—
308Dic11—21no—
309Dic11—81no—
310Dic11—81no—
311Dic11—81no—
312C2×#41—21no—
313C22×D4—221no—
314#135—22no—
315#135—41no—
316C2×Q16—111no—
317C2×Q16C22×D1111yescharacteristic
318C2×SD16—21no—
319C2×SD16—221no—
320C2×D8—111no—
321C2×D8—221no—
322C2×D8—222no—
323C2×D8—441no—
324C2×D8C22×D1111yescharacteristic
325C22×C8—111no—
326C22×C8C22×D1111yescharacteristic
327#126—441no—
328#125—221no—
329#125—441no—
330#124—221no—
331#123—441no—
332#123—441no—
333C22⋊Q8—221no—
334C22⋊Q8—221no—
335C22⋊Q8—221no—
336#121—221no—
337#121—441no—
338#120—441no—
339C4×Q8—221no—
340C4×D4—111no—
341C4×D4—221no—
342#117—21no—
343#117—441no—
344C2×C4⋊C4—221no—
345C2×C22⋊C4—441no—
346Q32—441no—
347SD32—222no—
348SD32—441no—
349C2×C16—41no—
350C2×C16—111no—
351C2×C16—111no—
352C2×C16—441no—
353C2×C16C22×D1111yescharacteristic
354C2×C16C22×D1111yescharacteristic
355#107—111no—
356#107—111no—
357#107—221no—
358#107C22×D1111yescharacteristic
359#107C22×D1111yescharacteristic
360#106—21no—
361#106—221no—
362C4⋊C8—111no—
363#103—221no—
364#103—221no—
365#103—221no—
366#103—221no—
367#102—221no—
368#102—221no—
369C22⋊C8—111no—
370C22⋊C8—111no—
371C4×C8—111no—
372C2×C11—41no—
373C2×C11—82no—
374C2×C11#329411yescharacteristic
375C2×C11C2×#50811yescharacteristic
376C2×C11#341611yescharacteristic
377D11—22no—
378D11—161no—
379C24—441no—
380#41—42no—
381#41—81no—
382C2×Q8—21no—
383C2×Q8—221no—
384C2×D4—21no—
385C2×D4—41no—
386C2×D4—111no—
387C2×D4—221no—
388C2×D4—441no—
389C2×D4—442no—
390C2×D4—441no—
391C2×D4—881no—
392C22×C4—41no—
393C22×C4—111no—
394C22×C4—441no—
395C22×C4—441no—
396C22×C4D4×D1111yescharacteristic
397Q16—21no—
398Q16—21no—
399Q16—221no—
400Q16—221no—
401SD16—42no—
402SD16—881no—
403D8—21no—
404D8—221no—
405D8—221no—
406D8—442no—
407D8#433912yes—
408C2×C8—21no—
409C2×C8—21no—
410C2×C8—111no—
411C2×C8—111no—
412C2×C8—221no—
413C2×C8—221no—
414C2×C8D4×D1111yescharacteristic
415C2×C8C23×D1111yescharacteristic
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—111no—
419C4⋊C4—221no—
420C4⋊C4—221no—
421C4⋊C4—441no—
422C4⋊C4—441no—
423C4⋊C4—441no—
424C4⋊C4—441no—
425C4⋊C4—441no—
426C4⋊C4—441no—
427C4⋊C4—441no—
428C22⋊C4—41no—
429C22⋊C4—111no—
430C22⋊C4—111no—
431C22⋊C4—441no—
432C22⋊C4—441no—
433C22⋊C4—441no—
434C22⋊C4—441no—
435C22⋊C4—441no—
436C22⋊C4—441no—
437C22⋊C4—441no—
438C42—41no—
439C42—111no—
440C42—441no—
441C16—21no—
442C16—21no—
443C16—221no—
444C16—221no—
445C11#3386311yescharacteristic, complemented, Sylow
446C23—41no—
447C23—111no—
448C23—441no—
449C23—882no—
450C23—882no—
451C23—1761no—
452C23D8×D1111yescharacteristic
453Q8—41no—
454Q8—41no—
455Q8—441no—
456Q8—441no—
457D4—22no—
458D4—41no—
459D4—82no—
460D4—222no—
461D4—441no—
462D4—441no—
463D4—882no—
464D4—1761no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—82no—
471C2×C4—111no—
472C2×C4—111no—
473C2×C4—111no—
474C2×C4—221no—
475C2×C4—221no—
476C2×C4—441no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—882no—
480C2×C4—1761no—
481C2×C4D8×D1111yescharacteristic
482C2×C4C2×D4×D1111yescharacteristic
483C8—21no—
484C8—221no—
485C8—221no—
486C8C2×#433911yescharacteristic
487C8#6703711yescharacteristic
488C22—21no—
489C22—21no—
490C22—21no—
491C22—42no—
492C22—81no—
493C22—81no—
494C22—112no—
495C22—221no—
496C22—221no—
497C22—881no—
498C22—881no—
499C22—881no—
500C22—1764no—
501C22C2×D8×D1111yescharacteristic
502C4—21no—
503C4—81no—
504C4—81no—
505C4—81no—
506C4—221no—
507C4—221no—
508C4—221no—
509C4—881no—
510C4—881no—
511C4—881no—
512C4#1062302111yescharacteristic
513C4#1062329311yescharacteristic
514C2—41no—
515C2—82no—
516C2—222no—
517C2—1761no—
518C2#1308042511yescharacteristic
519C2D11×#50811yescharacteristic
520C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2138C2
socleC22×C11C22×D8
prime radical#13080295C2
hypercenter#2138D11
hypocenterC11#33863
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2138

Complements

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

NH ≅ G/Ntype
1. #13080984C2semidirect
3. #13070849C2semidirect
4. #13070812C2semidirect
5. #13070807C2semidirect
6. #13070775C2semidirect
7. #13070712C2semidirect
8. #13070706C2semidirect
9. #13070681C2semidirect
10. #13070556C2semidirect
11. #13070546C2semidirect
12. #13070471C2semidirect
13. C16×C22⋊D11C2semidirect
14. D11×#357C2semidirect
15. C11×#2138C2semidirect
20. C22×C11×C16C22semidirect
21. C11×#427C22semidirect
25. C2×#66893C22semidirect
30. #10622729C22semidirect
38. #10622491C22semidirect
39. #10622486C22semidirect
42. C11×#358C22semidirect
43. C11×#358C22semidirect
46. #10622202C22semidirect
48. C22⋊(C11⋊C16)C22semidirect
51. #10622143C22semidirect
52. #10622141C22semidirect
53. Dic11⋊C16C22semidirect
54. C16×Dic11C22semidirect
57. #10622128C22semidirect
58. #10622127C22semidirect
199. #2138D11semidirect
251. C22×C16C2×D11semidirect
267. #427C2×D11semidirect
275. #358C2×D11semidirect
276. #358C2×D11semidirect
445. C11#33863semidirect

Maximal subgroups

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

subgroupindex
#130809842
#130802952
#130708492
#130708122
#130708072
#130707752
#130707122
#130707062
#130706812
#130705562
#130705462
#130704712
C16×C22⋊D112
D11×#3572
C11×#21382
#3386311