Finite Group Databasebeta

← #14910823

Subgroups — #14910823

Order 2816.

562 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#13081043C211yesmaximal, characteristic, complemented
2#13080295C211yesmaximal, characteristic
3#13070854C211yesmaximal, characteristic, complemented
4#13070823C211yesmaximal, characteristic, complemented
5#13070808C211yesmaximal, characteristic, complemented
6#13070761C211yesmaximal, characteristic, complemented
7#13070721C211yesmaximal, characteristic, complemented
8#13070714C211yesmaximal, characteristic, complemented
9#13070680C211yesmaximal, characteristic, complemented
10#13070543C211yesmaximal, characteristic, complemented
11#13070481C211yesmaximal, characteristic, complemented
12#13070438C211yesmaximal, characteristic, complemented
13#13070330C211yesmaximal, characteristic, complemented
14#13070323C211yesmaximal, characteristic, complemented
15C11×#2189C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic
17#10623360—21no—
18C2×D8×D11C2211yescharacteristic
19#10623172—21no—
20C2×C11×Q32C2211yescharacteristic, complemented
21C2×C11×SD32C2211yescharacteristic
22C11×#467C2211yescharacteristic, complemented
23#10622851—21no—
24#10622804C2211yescharacteristic
25#10622801C2211yescharacteristic
26#10622801C2211yescharacteristic
27Q16×Dic11C2211yescharacteristic, complemented
28C2×#66892C2211yescharacteristic
29#10622782—21no—
30#10622778—21no—
31D8×Dic11C2211yescharacteristic
32#10622728C2211yescharacteristic
33C8×C22⋊D11C2211yescharacteristic
34#10622719C2211yescharacteristic, complemented
35C22×C11⋊C16C2211yescharacteristic, complemented
36#10622658—21no—
37C2×#66862C2211yescharacteristic
38#10622493C2211yescharacteristic
39#10622487C2211yescharacteristic, complemented
40#10622428—21no—
41#10622404—21no—
42C11×#358C2211yescharacteristic, complemented
43C11×#357C2211yescharacteristic
44C11×C22⋊C16C2211yescharacteristic, complemented
45#10622202C2211yescharacteristic, complemented
46#10622202C2211yescharacteristic, complemented
47#10622202C2211yescharacteristic, complemented
48#10622200C2211yescharacteristic
49#10622200C2211yescharacteristic
50#10622147C2211yescharacteristic
51#10622147C2211yescharacteristic
52(C2×D11)⋊C16C2211yescharacteristic
53#10622143C2211yescharacteristic, complemented
54#10622142C2211yescharacteristic, complemented
55#10622140C2211yescharacteristic, complemented
56Dic11⋊C16C2211yescharacteristic, complemented
57#10622129C2211yescharacteristic
58#10622128C2211yescharacteristic, complemented
59C2×C11×#41—21no—
60C2×D4×D11—21no—
61C11×#135—22no—
62C11×#135—41no—
63C2×C11×Q16C2311yescharacteristic
64C2×C11×Q16C2311yescharacteristic
65C2×C11×SD16—21no—
66C2×C11×D8C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×C22⋊Q8—21no—
69#67000—21no—
70#66999—21no—
71#66999—21no—
72Q8×Dic11—21no—
73C2×#4325—21no—
74#66992—41no—
75#66990—41no—
76D4×Dic11—21no—
77C2×#4323—21no—
78#66983—21no—
79#66982—41no—
80C4×C22⋊D11D411yescharacteristic
81C2×(C2×D11)⋊C4—41no—
82#66979—21no—
83D8×D11—22no—
84D8×D11—41no—
85C2×D88C2311yescharacteristic
86C2×C8×D11C2311yescharacteristic
87#66951—41no—
88#66945—21no—
89#66941—21no—
90#66940—41no—
91#66938—41no—
92#66932—41no—
93C11×Q32—41no—
94C11×SD32—22no—
95C2×C11×C16C2311yescharacteristic
96C2×C11×C16C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#103—21no—
99#66899—21no—
100#66899—21no—
101#66899—21no—
102#66896—21no—
103C22⋊(C11⋊C8)D411yescharacteristic
104#66892—41no—
105#66885—21no—
106(C2×D11)⋊C8D411yescharacteristic
107#66882C2311yescharacteristic
108#66882C2311yescharacteristic
109#66882C2311yescharacteristic
110#66881—21no—
111Dic11⋊C8D411yescharacteristic
112C8×Dic11C2311yescharacteristic
113C2×C11⋊C16—41no—
114C2×C11⋊C16C2311yescharacteristic
115C2×C11⋊C16C2311yescharacteristic
116#66872—21no—
117#66871—21no—
118#66862—41no—
119#33878—111nomaximal, Sylow
120C23×D11—41no—
121C11×#41—42no—
122C11×#41—81no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—41no—
127C22×C4×C11—41no—
128C22×C4×C11C2×D411yescharacteristic
129C2×C22⋊D11—41no—
130C2×C22⋊D11—41no—
131C2×C22⋊D11D811yescharacteristic
132C22×Dic11—41no—
133D4×D11—42no—
134D4×D11—81no—
135C2×D44—21no—
136C2×C4×D11C2×D411yescharacteristic
137C2×Dic22—41no—
138C11×Q16—21no—
139C11×Q16—21no—
140C11×Q16—21no—
141C11×Q16—21no—
142C11×SD16—42no—
143C11×D8—21no—
144C11×D8#4112yes—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11C2×D411yescharacteristic
148C2×C8×C11C2411yescharacteristic
149C11×C4⋊C4—21no—
150C11×C4⋊C4—41no—
151C11×C22⋊C4—41no—
152C22⋊Dic11—41no—
153C22⋊Dic11—41no—
154C22⋊Dic11D811yescharacteristic
155#4325—81no—
156#4323—42no—
157(C2×D11)⋊C4—41no—
158(C2×D11)⋊C4—41no—
159(C2×D11)⋊C4—41no—
160(C2×D11)⋊C4—41no—
161(C2×D11)⋊C4—41no—
162(C2×D11)⋊C4—41no—
163(C2×D11)⋊C4D811yescharacteristic
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11—41no—
168Dic11⋊C4—41no—
169Dic11⋊C4—41no—
170Dic11⋊C4—41no—
171Dic11⋊C4D811yescharacteristic
172C4×Dic11—41no—
173C4×Dic11—41no—
174C4×Dic11—41no—
175C4×Dic11C2×D411yescharacteristic
176C2×C11⋊C8C2×D411yescharacteristic
177C2×C11⋊C8C2×D411yescharacteristic
178D88—21no—
179D88—21no—
180C8×D11—21no—
181C8×D11—21no—
182C11×C16—21no—
183C11×C16—21no—
184C11⋊C16—21no—
185C11⋊C16—21no—
186#3342—111no—
187#3280—111no—
188#2243—111no—
189#2237—111no—
190#2234—111no—
191#2226—111no—
192#2219—111no—
193#2217—111no—
194#2211—111no—
195#2189D1111yescharacteristic, complemented
196#2187—111no—
197#2175—111no—
198#2168—111no—
199#2140—111no—
200#2138—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—
210Q8×C11—41no—
211Q8×C11—41no—
212D4×C11—22no—
213D4×C11—41no—
214D4×C11—82no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—82no—
221C2×C4×C11C2×D811yescharacteristic
222C2×C4×C11C22×D411yescharacteristic
223C22⋊D11—41no—
224C22⋊D11—82no—
225C22⋊D11—161no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—161no—
230C2×Dic11C2×D811yescharacteristic
231C2×Dic11C2×D811yescharacteristic
232C2×Dic11C2×D811yescharacteristic
233D44—41no—
234D44—41no—
235C4×D11—21no—
236C4×D11—21no—
237Dic22—82no—
238C8×C11—21no—
239C8×C11C2×#4111yescharacteristic
240C8×C11H(5,𝔽2)11yescharacteristic
241C11⋊C8—21no—
242C11⋊C8—21no—
243C2×#135C2×D1111yescharacteristic
244C22×D8—111no—
245#556—221no—
246#546—221no—
247C2×Q32C2×D1111yescharacteristic, complemented
248C2×SD32—111no—
249C2×SD32C2×D1111yescharacteristic
250C2×M32—111no—
251C22×C16—111no—
252#500—111no—
253#495—111no—
254#485—221no—
255#485—221no—
256#475—221no—
257#467—111no—
258#467—111no—
259#467C2×D1111yescharacteristic, complemented
260#466—111no—
261#463—221no—
262#450—221no—
263#449—221no—
264C4×Q16—111no—
265C4×D8—111no—
266C8×D4—111no—
267#427—111no—
268#427—111no—
269#367—111no—
270#367—111no—
271#366—111no—
272C4⋊C16—111no—
273#358—111no—
274#358—111no—
275#358—111no—
276#358C2×D1111yescharacteristic, complemented
277#357—111no—
278#357—111no—
279#357—111no—
280#357—111no—
281#357—111no—
282#357C2×D1111yescharacteristic
283C22⋊C16—111no—
284C22⋊C16C2×D1111yescharacteristic, complemented
285#346—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—21no—
296C2×D11—81no—
297C2×D11—81no—
298C2×D11—81no—
299C2×D11—164no—
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×Q16C22×D1111yescharacteristic
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
327C4⋊Q8—221no—
328#126—441no—
329#126—441no—
330#124—221no—
331#124—441no—
332#123—441no—
333C22⋊Q8—21no—
334C22⋊Q8—221no—
335C22⋊Q8—221no—
336#121—221no—
337#121—441no—
338#120—441no—
339C4×Q8—221no—
340C4×Q8—441no—
341C4×D4—111no—
342C4×D4—221no—
343#117—221no—
344#117—221no—
345C2×C22⋊C4—441no—
346Q32—41no—
347SD32—22no—
348SD32—441no—
349M32—441no—
350C2×C16—111no—
351C2×C16—111no—
352C2×C16—441no—
353C2×C16C22×D1111yescharacteristic
354C2×C16C22×D1111yescharacteristic
355#107—111no—
356#107—111no—
357#107—111no—
358#107—221no—
359#107C22×D1111yescharacteristic
360#106—221no—
361#106—221no—
362C4⋊C8—111no—
363#103—21no—
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×C11#341411yescharacteristic
376C2×C11#341611yescharacteristic
377D11—41no—
378D11—161no—
379C24—441no—
380#41—42no—
381#41—81no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—441no—
385C2×D4—21no—
386C2×D4—41no—
387C2×D4—111no—
388C2×D4—221no—
389C2×D4—441no—
390C2×D4—442no—
391C2×D4—441no—
392C2×D4—881no—
393C22×C4—41no—
394C22×C4—111no—
395C22×C4—441no—
396C22×C4D4×D1111yescharacteristic
397Q16—21no—
398Q16—21no—
399Q16—21no—
400Q16—21no—
401SD16—42no—
402SD16—881no—
403D8—21no—
404D8—221no—
405D8—221no—
406D8—442no—
407D8#434112yes—
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—41no—
418C4⋊C4—111no—
419C4⋊C4—221no—
420C4⋊C4—221no—
421C4⋊C4—221no—
422C4⋊C4—441no—
423C4⋊C4—441no—
424C4⋊C4—441no—
425C4⋊C4—441no—
426C22⋊C4—41no—
427C22⋊C4—111no—
428C22⋊C4—111no—
429C22⋊C4—441no—
430C22⋊C4—441no—
431C22⋊C4—441no—
432C22⋊C4—441no—
433C22⋊C4—441no—
434C22⋊C4—441no—
435C22⋊C4—441no—
436C22⋊C4—441no—
437C42—111no—
438C42—441no—
439C42—441no—
440C42—441no—
441C16—21no—
442C16—21no—
443C16—221no—
444C16—221no—
445C11#3387811yescharacteristic, complemented, Sylow
446C23—41no—
447C23—111no—
448C23—441no—
449C23—882no—
450C23—882no—
451C23—1761no—
452C23D8×D1111yescharacteristic
453Q8—41no—
454Q8—41no—
455Q8—41no—
456Q8—41no—
457Q8—882no—
458D4—22no—
459D4—41no—
460D4—82no—
461D4—441no—
462D4—441no—
463D4—441no—
464D4—882no—
465D4—1761no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—82no—
472C2×C4—111no—
473C2×C4—111no—
474C2×C4—111no—
475C2×C4—221no—
476C2×C4—221no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4—1761no—
481C2×C4D8×D1111yescharacteristic
482C2×C4C2×D4×D1111yescharacteristic
483C8—21no—
484C8—221no—
485C8—221no—
486C8C2×#434111yescharacteristic
487C8#6703711yescharacteristic
488C22—21no—
489C22—21no—
490C22—21no—
491C22—42no—
492C22—81no—
493C22—81no—
494C22—221no—
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#1062312211yescharacteristic
513C4#1062330611yescharacteristic
514C2—41no—
515C2—82no—
516C2—441no—
517C2—1761no—
518C2#1308042211yescharacteristic
519C2#1308174911yescharacteristic
520C2#1308176111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2189C2
socleC22×C11C22×D8
prime radical#13080295C2
hypercenter#2189D11
hypocenterC11#33878
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2189

Complements

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

NH ≅ G/Ntype
1. #13081043C2semidirect
3. #13070854C2semidirect
4. #13070823C2semidirect
5. #13070808C2semidirect
6. #13070761C2semidirect
7. #13070721C2semidirect
8. #13070714C2semidirect
9. #13070680C2semidirect
10. #13070543C2semidirect
11. #13070481C2semidirect
12. #13070438C2semidirect
13. #13070330C2semidirect
14. #13070323C2semidirect
15. C11×#2189C2semidirect
20. C2×C11×Q32C22semidirect
22. C11×#467C22semidirect
27. Q16×Dic11C22semidirect
34. #10622719C22semidirect
35. C22×C11⋊C16C22semidirect
39. #10622487C22semidirect
42. C11×#358C22semidirect
44. C11×C22⋊C16C22semidirect
45. #10622202C22semidirect
46. #10622202C22semidirect
47. #10622202C22semidirect
53. #10622143C22semidirect
54. #10622142C22semidirect
55. #10622140C22semidirect
56. Dic11⋊C16C22semidirect
58. #10622128C22semidirect
195. #2189D11semidirect
247. C2×Q32C2×D11semidirect
259. #467C2×D11semidirect
276. #358C2×D11semidirect
284. C22⋊C16C2×D11semidirect
445. C11#33878semidirect

Maximal subgroups

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

subgroupindex
#130810432
#130802952
#130708542
#130708232
#130708082
#130707612
#130707212
#130707142
#130706802
#130705432
#130704812
#130704382
#130703302
#130703232
C11×#21892
#3387811