Finite Group Databasebeta

← #14908616

Subgroups — #14908616

Order 2816.

588 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078259C211yesmaximal, characteristic
2#13077212C211yesmaximal, characteristic, complemented
3#13070809C211yesmaximal, characteristic, complemented
4#13070808C211yesmaximal, characteristic, complemented
5#13070806C211yesmaximal, characteristic, complemented
6#13070804C211yesmaximal, characteristic, complemented
7#13070803C211yesmaximal, characteristic, complemented
8#13070796C211yesmaximal, characteristic, complemented
9#13070795C211yesmaximal, characteristic, complemented
10#13070403C211yesmaximal, characteristic, complemented
11#13070399C211yesmaximal, characteristic, complemented
12#13070330C211yesmaximal, characteristic, complemented
13D11×#357C211yesmaximal, characteristic, complemented
14#13070228C211yesmaximal, characteristic, complemented
15C11×#2233C211yesmaximal, characteristic, complemented
16C2×D8×D11C2211yescharacteristic
17C2×#66954C2211yescharacteristic
18#10623138—21no—
19#10623035—21no—
20C11×#466C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic, complemented
22#10622770C2211yescharacteristic
23#10622728C2211yescharacteristic
24#10622719C2211yescharacteristic, complemented
25#10622652—21no—
26#10622577—21no—
27C2×#66862C2211yescharacteristic
28C2×C16×D11C2211yescharacteristic
29#10622496C2211yescharacteristic
30#10622494—21no—
31#10622494—21no—
32#10622493C2211yescharacteristic
33#10622493C2211yescharacteristic
34#10622493C2211yescharacteristic, complemented
35D11×#107C2211yescharacteristic
36D11×#107C2211yescharacteristic, complemented
37#10622395—21no—
38#10622383—21no—
39C11×#367C2211yescharacteristic, complemented
40C11×#367C2211yescharacteristic, complemented
41C11×#357C2211yescharacteristic
42C11×#357C2211yescharacteristic
43C11×C22⋊C16C2211yescharacteristic, complemented
44#10622200C2211yescharacteristic
45#10622200C2211yescharacteristic
46C22⋊(C11⋊C16)C2211yescharacteristic, complemented
47#10622147C2211yescharacteristic
48#10622147C2211yescharacteristic
49(C2×D11)⋊C16C2211yescharacteristic, complemented
50(C2×D11)⋊C16C2211yescharacteristic, complemented
51#10622143C2211yescharacteristic, complemented
52#10622142C2211yescharacteristic, complemented
53#10622129C2211yescharacteristic
54#10622129C2211yescharacteristic
55#10622128C2211yescharacteristic, complemented
56#10622127C2211yescharacteristic, complemented
57#10622127C2211yescharacteristic, complemented
58#10622127C2211yescharacteristic, complemented
59C2×D4×D11—21no—
60C2×#4339D411yescharacteristic
61C2×C11×D8C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C11×#121—21no—
64C2×C11×C4⋊C4—21no—
65#66993—41no—
66#66991—21no—
67#66990—41no—
68C2×#4323—21no—
69#66983—21no—
70C4×C22⋊D11—41no—
71C4×C22⋊D11—41no—
72#66979—21no—
73C2×#4318D411yescharacteristic
74D8×D11—22no—
75D8×D11—22no—
76C2×D88C2311yescharacteristic
77#66954—22no—
78#66954—22no—
79C2×#4313D411yescharacteristic
80C2×#4313D411yescharacteristic
81C2×C8×D11C2311yescharacteristic
82C2×C8×D11C2311yescharacteristic
83#66948—21no—
84#66946—41no—
85#66945—21no—
86#66945—21no—
87#66945—21no—
88C4⋊C4×D11—21no—
89C4⋊C4×D11—21no—
90#66940—41no—
91#66938—41no—
92#66935—41no—
93C2×C11×C16C2311yescharacteristic
94C2×C11×C16C2311yescharacteristic
95C11×#107—21no—
96C11×#107C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#107C2311yescharacteristic
99C11×#102—21no—
100#66896—21no—
101#66885—21no—
102#66882C2311yescharacteristic
103#66882C2311yescharacteristic
104#66882C2311yescharacteristic
105#66881—21no—
106C2×C11⋊C16C2311yescharacteristic
107C2×C11⋊C16C2311yescharacteristic
108#66873—21no—
109#66872—21no—
110#66872—21no—
111#66872—21no—
112#66871—21no—
113#66871—21no—
114#66862—22no—
115C16×D11—22no—
116#33650—111nomaximal, Sylow
117C23×D11—41no—
118C2×D4×C11—21no—
119C2×D4×C11—41no—
120C22×C4×C11—41no—
121C22×C4×C11C2×D411yescharacteristic
122C2×C22⋊D11—41no—
123C2×C22⋊D11—41no—
124C2×C22⋊D11—41no—
125C2×C22⋊D11D811yescharacteristic
126C2×C22⋊D11D811yescharacteristic
127D4×D11—42no—
128D4×D11—42no—
129#4339—22no—
130#4339—22no—
131C2×D44—21no—
132C2×D44—41no—
133C2×D44D811yescharacteristic
134C2×C4×D11—41no—
135C2×C4×D11—41no—
136C2×C4×D11C2×D411yescharacteristic
137C2×C4×D11C2×D411yescharacteristic
138C2×Dic22D811yescharacteristic
139C11×D8—21no—
140C11×D8—21no—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11C2×D411yescharacteristic
144C2×C8×C11C2411yescharacteristic
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—41no—
149C11×C22⋊C4—41no—
150C22⋊Dic11—41no—
151C22⋊Dic11—41no—
152#4323—42no—
153(C2×D11)⋊C4—41no—
154(C2×D11)⋊C4—41no—
155(C2×D11)⋊C4—41no—
156(C2×D11)⋊C4—41no—
157(C2×D11)⋊C4—41no—
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161Dic11⋊C4—41no—
162Dic11⋊C4—41no—
163C4×Dic11—41no—
164C4×Dic11—41no—
165C4×Dic11—41no—
166C4×Dic11—41no—
167#4318—22no—
168C2×C11⋊C8C2×D411yescharacteristic
169C2×C11⋊C8C2×D411yescharacteristic
170D88—21no—
171D88—21no—
172#4313—22no—
173#4313—22no—
174C8×D11—21no—
175C8×D11—21no—
176C8×D11#4112yes—
177C8×D11#4112yes—
178C11×C16—21no—
179C11×C16—21no—
180C11⋊C16—21no—
181C11⋊C16—21no—
182#3058—111no—
183#2913—111no—
184#2234—111no—
185#2234—111no—
186#2234—111no—
187#2234—111no—
188#2233—111no—
189#2233D1111yescharacteristic, complemented
190#2232—111no—
191#2232—111no—
192#2159—111no—
193#2158—111no—
194#2140—111no—
195C2×#357—111no—
196#2113—111no—
197C23×C11—41no—
198C23×C11C2×D811yescharacteristic
199C22×D11—41no—
200C22×D11—82no—
201C22×D11—161no—
202C22×D11—161no—
203C22×D11C2×D811yescharacteristic
204C22×D11C2×D811yescharacteristic
205D4×C11—41no—
206D4×C11—41no—
207D4×C11—161no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—161no—
214C2×C4×C11C2×D811yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C22⋊D11—22no—
217C22⋊D11—22no—
218C22⋊D11—82no—
219C22⋊D11—161no—
220C22⋊D11—161no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11C2×D811yescharacteristic
225C2×Dic11C2×D811yescharacteristic
226D44—22no—
227D44—41no—
228D44—41no—
229D44—161no—
230C4×D11—21no—
231C4×D11—21no—
232C4×D11—161no—
233C4×D11—161no—
234C4×D11#12312yes—
235C4×D11#13712yes—
236Dic22—22no—
237C8×C11—21no—
238C8×C11C2×#4111yescharacteristic
239C8×C11C2×#4111yescharacteristic
240C11⋊C8—21no—
241C11⋊C8#12312yes—
242C22×D8—111no—
243C2×#131—111no—
244#535—221no—
245#520—221no—
246C2×M32—111no—
247C22×C16—111no—
248#469—221no—
249#469—221no—
250#466—111no—
251#466—111no—
252#466—111no—
253#466C2×D1111yescharacteristic
254#428—221no—
255#428—221no—
256#428—221no—
257#427—111no—
258#427—111no—
259#427—111no—
260#427—111no—
261C2×#107—111no—
262C2×#107—111no—
263C2×#107C2×D1111yescharacteristic, complemented
264#418—221no—
265#367—111no—
266#367—111no—
267#367C2×D1111yescharacteristic, complemented
268#367C2×D1111yescharacteristic, complemented
269#366—111no—
270#366—111no—
271#366—111no—
272#366—111no—
273#357—111no—
274#357—111no—
275#357—111no—
276#357—111no—
277#357—111no—
278#357—111no—
279#357C2×D1111yescharacteristic
280#357C2×D1111yescharacteristic
281C22⋊C16—111no—
282C22⋊C16—111no—
283C22⋊C16—111no—
284C22⋊C16C2×D1111yescharacteristic, complemented
285C22×C11—21no—
286C22×C11—21no—
287C22×C11—21no—
288C22×C11—81no—
289C22×C11—81no—
290C22×C11—81no—
291C22×C11C22×D811yescharacteristic
292C2×D11—21no—
293C2×D11—21no—
294C2×D11—21no—
295C2×D11—21no—
296C2×D11—21no—
297C2×D11—81no—
298C2×D11—81no—
299C2×D11—81no—
300C2×D11—164no—
301C2×D11#48012yes—
302C4×C11—21no—
303C4×C11—81no—
304C4×C11—81no—
305C4×C11—81no—
306C4×C11C2×#12311yescharacteristic
307C4×C11C2×#13711yescharacteristic
308Dic11—21no—
309Dic11—81no—
310Dic11—81no—
311Dic11—81no—
312Dic11#48012yes—
313C2×#41—111no—
314C22×D4—221no—
315C2×D8—111no—
316C2×D8—222no—
317C2×D8—222no—
318C2×D8—221no—
319C2×D8C22×D1111yescharacteristic
320#131—222no—
321#131—222no—
322C2×M16—111no—
323C2×M16—111no—
324C2×M16—111no—
325C22×C8—111no—
326C22×C8—111no—
327C22×C8C22×D1111yescharacteristic
328#127—441no—
329#124—441no—
330#121—21no—
331#121—221no—
332#121—221no—
333#121—221no—
334#120—441no—
335#120—441no—
336C4×Q8—441no—
337C4×D4—441no—
338C4×D4—441no—
339C4×D4—441no—
340#117—221no—
341#117—221no—
342#117—221no—
343#117—221no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—221no—
346C2×C4⋊C4—221no—
347M32—222no—
348C2×C16—111no—
349C2×C16—111no—
350C2×C16—222no—
351C2×C16C22×D1111yescharacteristic
352C2×C16C22×D1111yescharacteristic
353#107—21no—
354#107—111no—
355#107—111no—
356#107—111no—
357#107—221no—
358#107—221no—
359#107C22×D1111yescharacteristic
360#107C22×D1111yescharacteristic
361#107C22×D1111yescharacteristic
362#106—221no—
363#106—221no—
364#106—221no—
365#106—221no—
366#102—21no—
367#102—221no—
368#102—221no—
369#102—221no—
370C2×C11—41no—
371C2×C11—161no—
372C2×C11C2×#48011yescharacteristic
373C2×C11#341511yescharacteristic
374C2×C11#341611yescharacteristic
375D11—22no—
376D11—41no—
377D11—161no—
378C24—441no—
379#41—222no—
380#41—222no—
381C2×Q8—111no—
382C2×D4—21no—
383C2×D4—41no—
384C2×D4—111no—
385C2×D4—111no—
386C2×D4—111no—
387C2×D4—221no—
388C2×D4—441no—
389C2×D4—442no—
390C2×D4—442no—
391C2×D4—441no—
392C2×D4—441no—
393C2×D4—441no—
394C22×C4—41no—
395C22×C4—111no—
396C22×C4—111no—
397C22×C4—441no—
398C22×C4—441no—
399C22×C4D4×D1111yescharacteristic
400D8—21no—
401D8—21no—
402D8—221no—
403D8—221no—
404D8—442no—
405M16—222no—
406M16—222no—
407M16—222no—
408C2×C8—21no—
409C2×C8—21no—
410C2×C8—111no—
411C2×C8—112no—
412C2×C8—112no—
413C2×C8—111no—
414C2×C8—221no—
415C2×C8—221no—
416C2×C8D4×D1111yescharacteristic
417C2×C8C23×D1111yescharacteristic
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—41no—
422C4⋊C4—221no—
423C4⋊C4—221no—
424C4⋊C4—221no—
425C4⋊C4—441no—
426C4⋊C4—441no—
427C22⋊C4—41no—
428C22⋊C4—441no—
429C22⋊C4—441no—
430C22⋊C4—441no—
431C22⋊C4—441no—
432C22⋊C4—441no—
433C22⋊C4—441no—
434C22⋊C4—441no—
435C42—441no—
436C42—441no—
437C42—441no—
438C42—441no—
439C16—21no—
440C16—21no—
441C16—221no—
442C16—221no—
443C11#3365011yescharacteristic, complemented, Sylow
444C23—41no—
445C23—111no—
446C23—111no—
447C23—441no—
448C23—882no—
449C23—1761no—
450C23—1761no—
451C23D8×D1111yescharacteristic
452Q8—222no—
453D4—41no—
454D4—41no—
455D4—161no—
456D4—222no—
457D4—222no—
458D4—222no—
459D4—441no—
460D4—441no—
461D4—882no—
462D4—1761no—
463D4—1761no—
464D4—1761no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—111no—
471C2×C4—112no—
472C2×C4—112no—
473C2×C4—111no—
474C2×C4—161no—
475C2×C4—221no—
476C2×C4—221no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4—1761no—
481C2×C4—1761no—
482C2×C4D8×D1111yescharacteristic
483C2×C4C2×D4×D1111yescharacteristic
484C8—21no—
485C8—112no—
486C8—221no—
487C8#41×D1111yescharacteristic
488C8#41×D1111yescharacteristic
489C22—21no—
490C22—21no—
491C22—21no—
492C22—81no—
493C22—81no—
494C22—81no—
495C22—112no—
496C22—221no—
497C22—221no—
498C22—221no—
499C22—221no—
500C22—221no—
501C22—881no—
502C22—881no—
503C22—881no—
504C22—1764no—
505C22C2×D8×D1111yescharacteristic
506C4—21no—
507C4—81no—
508C4—81no—
509C4—81no—
510C4—112no—
511C4—221no—
512C4—881no—
513C4—881no—
514C4—881no—
515C4D11×#12311yescharacteristic
516C4D11×#13711yescharacteristic
517C2—41no—
518C2—161no—
519C2—222no—
520C2—441no—
521C2—1761no—
522C2D11×#48011yescharacteristic
523C2#1308175611yescharacteristic
524C2#1308175811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2233C2
socleC22×C11C22×D8
prime radical#13078259C2
hypercenter#2233D11
hypocenterC11#33650
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2233

Complements

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

NH ≅ G/Ntype
2. #13077212C2semidirect
3. #13070809C2semidirect
4. #13070808C2semidirect
5. #13070806C2semidirect
6. #13070804C2semidirect
7. #13070803C2semidirect
8. #13070796C2semidirect
9. #13070795C2semidirect
10. #13070403C2semidirect
11. #13070399C2semidirect
12. #13070330C2semidirect
13. D11×#357C2semidirect
14. #13070228C2semidirect
15. C11×#2233C2semidirect
21. C2×C11×#107C22semidirect
24. #10622719C22semidirect
34. #10622493C22semidirect
36. D11×#107C22semidirect
39. C11×#367C22semidirect
40. C11×#367C22semidirect
43. C11×C22⋊C16C22semidirect
46. C22⋊(C11⋊C16)C22semidirect
49. (C2×D11)⋊C16C22semidirect
50. (C2×D11)⋊C16C22semidirect
51. #10622143C22semidirect
52. #10622142C22semidirect
55. #10622128C22semidirect
56. #10622127C22semidirect
57. #10622127C22semidirect
58. #10622127C22semidirect
189. #2233D11semidirect
263. C2×#107C2×D11semidirect
267. #367C2×D11semidirect
268. #367C2×D11semidirect
284. C22⋊C16C2×D11semidirect
443. C11#33650semidirect

Maximal subgroups

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

subgroupindex
#130782592
#130772122
#130708092
#130708082
#130708062
#130708042
#130708032
#130707962
#130707952
#130704032
#130703992
#130703302
D11×#3572
#130702282
C11×#22332
#3365011