Finite Group Databasebeta

← #14908092

Subgroups — #14908092

Order 2816.

716 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622527C211yesmaximal, characteristic
2C2×D11×SD32C211yesmaximal, characteristic, complemented
3#13079104C211yesmaximal, characteristic, complemented
4#13077463C211yesmaximal, characteristic, complemented
5#13070674C211yesmaximal, characteristic, complemented
6#13070673C211yesmaximal, characteristic, complemented
7#13070672C211yesmaximal, characteristic, complemented
8#13070671C211yesmaximal, characteristic, complemented
9#13070660C211yesmaximal, characteristic, complemented
10#13070659C211yesmaximal, characteristic, complemented
11#13070658C211yesmaximal, characteristic, complemented
12#13070373C211yesmaximal, characteristic, complemented
13#13070334C211yesmaximal, characteristic, complemented
14#13070322C211yesmaximal, characteristic, complemented
15C11×#2208C211yesmaximal, characteristic, complemented
16C2×#66972C2211yescharacteristic
17C2×#66971—21no—
18C2×Q16×D11C2211yescharacteristic
19C2×D8×D11C2211yescharacteristic
20#10623255—21no—
21#10623076—21no—
22C2×C11×SD32C2211yescharacteristic
23C2×C11×SD32C2211yescharacteristic
24C11×#494C2211yescharacteristic, complemented
25C4×C11×D8C2211yescharacteristic
26#10622804C2211yescharacteristic, complemented
27#10622803—21no—
28#10622794C2211yescharacteristic, complemented
29C2×#66892C2211yescharacteristic
30C2×#66892C2211yescharacteristic
31D8×Dic11C2211yescharacteristic
32C2×#66891C2211yescharacteristic
33C2×#66890C2211yescharacteristic
34#10622699—21no—
35#10622627—21no—
36#10622527—24no—
37D11×SD32—24no—
38C2×#66864C2211yescharacteristic
39C2×D176C2211yescharacteristic
40C2×#66862C2211yescharacteristic
41C2×C16×D11C2211yescharacteristic
42#10622493C2211yescharacteristic
43#10622485C2211yescharacteristic
44#10622398—21no—
45#10622383—21no—
46#10622309C2211yescharacteristic, complemented
47C4×D88C2211yescharacteristic
48#10622302C2211yescharacteristic
49C11×C4⋊C16C2211yescharacteristic, complemented
50C11×#358C2211yescharacteristic, complemented
51C11×#358C2211yescharacteristic, complemented
52#10622202C2211yescharacteristic, complemented
53#10622202C2211yescharacteristic, complemented
54#10622147C2211yescharacteristic, complemented
55#10622141C2211yescharacteristic, complemented
56Dic11⋊C16C2211yescharacteristic, complemented
57Dic11⋊C16C2211yescharacteristic, complemented
58#10622130C2211yescharacteristic, complemented
59#10622129C2211yescharacteristic, complemented
60C4⋊(C11⋊C16)C2211yescharacteristic, complemented
61C2×#4343—21no—
62C2×Q8×D11—21no—
63C2×D4×D11—21no—
64C2×C11×Q16—21no—
65C2×C11×Q16C2311yescharacteristic
66C2×C11×Q16C2311yescharacteristic
67C2×C11×D8C2311yescharacteristic
68C11×C4⋊Q8—21no—
69C4×D4×C11—21no—
70#67000—21no—
71#66997—21no—
72C2×#4326—21no—
73C2×#4326—21no—
74C2×#4325—21no—
75C2×#4325—21no—
76D4×Dic11—21no—
77C2×#4323—21no—
78C4×C22⋊D11—41no—
79C2×(C2×D11)⋊C4—41no—
80#66972—22no—
81#66972—22no—
82#66971—44no—
83Q16×D11—22no—
84Q16×D11—22no—
85D8×D11—22no—
86D8×D11D414yes—
87C2×Dic44C2311yescharacteristic
88C2×D88C2311yescharacteristic
89C2×D88C2311yescharacteristic
90C2×#4314—21no—
91C2×#4313D411yescharacteristic
92C2×C8×D11C2311yescharacteristic
93#66949—41no—
94#66949—41no—
95#66947—41no—
96#66947—41no—
97#66946—21no—
98#66945—21no—
99(C22⋊D11)⋊C4—41no—
100C22⋊C4×D11—41no—
101#66928—21no—
102C4×D44—21no—
103#66925D411yescharacteristic
104C11×SD32—22no—
105C11×SD32—22no—
106C2×C11×C16C2311yescharacteristic
107C2×C11×C16C2311yescharacteristic
108C11×#107C2311yescharacteristic
109C11×#102—21no—
110C4×C8×C11C2311yescharacteristic
111#66896—21no—
112#66892—22no—
113#66892—22no—
114#66891—22no—
115#66890—22no—
116#66885—21no—
117#66882C2311yescharacteristic
118#66879D411yescharacteristic
119C8×Dic11C2311yescharacteristic
120C2×C11⋊C16C2311yescharacteristic
121C2×C11⋊C16C2311yescharacteristic
122#66873—21no—
123#66872—21no—
124#66867D411yescharacteristic
125#66864—22no—
126D176—22no—
127#66862—22no—
128C16×D11—22no—
129#33586—111nomaximal, Sylow
130C23×D11—41no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×D4×C11—21no—
134C22×C4×C11—41no—
135C2×C22⋊D11—41no—
136C22×Dic11—41no—
137#4343—42no—
138#4343—42no—
139Q8×D11—42no—
140Q8×D11—42no—
141D4×D11—24no—
142D4×D11—42no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—41no—
146C2×C4×D11—41no—
147C2×C4×D11—41no—
148C2×C4×D11—41no—
149C2×C4×D11—41no—
150C2×C4×D11C2×D411yescharacteristic
151C2×Dic22—21no—
152C2×Dic22—41no—
153C11×Q16—21no—
154C11×Q16—21no—
155C11×Q16—21no—
156C11×Q16—21no—
157C11×Q16—42no—
158C11×D8—21no—
159C11×D8C2×D412yes—
160C2×C8×C11C2×D411yescharacteristic
161C2×C8×C11C2411yescharacteristic
162C11×C4⋊C4—21no—
163C11×C4⋊C4—41no—
164C11×C4⋊C4—41no—
165C11×C22⋊C4—41no—
166C42×C11C2×D411yescharacteristic
167C22⋊Dic11—41no—
168#4326—42no—
169#4326—42no—
170#4325—42no—
171#4325—42no—
172#4323—24no—
173(C2×D11)⋊C4—41no—
174(C2×D11)⋊C4—41no—
175(C2×D11)⋊C4—41no—
176(C2×D11)⋊C4—41no—
177(C2×D11)⋊C4—41no—
178(C2×D11)⋊C4—41no—
179(C2×D11)⋊C4—41no—
180(C2×D11)⋊C4D811yescharacteristic
181(C2×D11)⋊C4D811yescharacteristic
182C4⋊Dic11—21no—
183Dic11⋊C4—41no—
184Dic11⋊C4—41no—
185Dic11⋊C4D811yescharacteristic
186Dic11⋊C4D811yescharacteristic
187C4×Dic11—41no—
188C4×Dic11C2×D411yescharacteristic
189C2×C11⋊C8C2×D411yescharacteristic
190C2×C11⋊C8C2×D411yescharacteristic
191Dic44—21no—
192Dic44—21no—
193D88—21no—
194D88—21no—
195D88—21no—
196D88C2×D412yes—
197#4314—42no—
198#4313—22no—
199C8×D11C2×D412yes—
200C8×D11#4112yes—
201C11×C16—21no—
202C11×C16—21no—
203C11⋊C16—21no—
204C11⋊C16—21no—
205C2×#509—111no—
206C22×SD32—111no—
207#3156—111no—
208#2948—111no—
209#2210—111no—
210#2210—111no—
211#2210—111no—
212#2210—111no—
213#2208—111no—
214#2208—111no—
215#2208—111no—
216#2208D1111yescharacteristic, complemented
217#2151—111no—
218#2141—111no—
219#2138—111no—
220C23×C11—41no—
221C22×D11—41no—
222C22×D11—44no—
223C22×D11—41no—
224C22×D11—161no—
225C22×D11—161no—
226C22×D11C2×D811yescharacteristic
227Q8×C11—41no—
228Q8×C11—41no—
229Q8×C11—41no—
230Q8×C11—41no—
231D4×C11—22no—
232D4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—161no—
237C2×C4×C11C2×D811yescharacteristic
238C2×C4×C11C2×D811yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C22⋊D11—44no—
241C2×Dic11—41no—
242C2×Dic11—41no—
243C2×Dic11—161no—
244C2×Dic11C2×D811yescharacteristic
245C2×Dic11C2×D811yescharacteristic
246C2×Dic11C2×D811yescharacteristic
247D44—22no—
248D44—41no—
249D44—41no—
250D44—41no—
251D44—82no—
252C4×D11—82no—
253C4×D11—82no—
254C4×D11—161no—
255C4×D11—161no—
256C4×D11#12112yes—
257C4×D11AGL(1,ℤ/8)12yes—
258Dic22—41no—
259Dic22—41no—
260Dic22—82no—
261C8×C11—21no—
262C8×C11C22×D411yescharacteristic
263C8×C11C2×#4111yescharacteristic
264C11⋊C8—21no—
265C11⋊C8#12112yes—
266C2×#137—221no—
267C2×#135—111no—
268C22×Q16—111no—
269C22×D8—111no—
270#536—221no—
271#518—221no—
272#509—224no—
273C2×SD32—111no—
274C2×SD32—111no—
275C2×SD32—111no—
276C2×SD32—111no—
277C2×SD32—224no—
278C2×SD32C2×D1111yescharacteristic
279C2×SD32C2×D1111yescharacteristic
280C2×D16—111no—
281C2×D16—111no—
282C2×M32—111no—
283C22×C16—111no—
284#497—221no—
285#497—221no—
286#495—111no—
287#495—111no—
288#494—111no—
289#494C2×D1111yescharacteristic, complemented
290#442—221no—
291#442—221no—
292C4×D8—111no—
293C4×D8—111no—
294C4×D8—111no—
295C4×D8C2×D1111yescharacteristic
296#427—111no—
297#418—221no—
298#405—111no—
299C4⋊C16—111no—
300C4⋊C16—111no—
301C4⋊C16—111no—
302C4⋊C16C2×D1111yescharacteristic, complemented
303#358—111no—
304#358—111no—
305#358—111no—
306#358—111no—
307#358C2×D1111yescharacteristic, complemented
308#358C2×D1111yescharacteristic, complemented
309#357—111no—
310#357—111no—
311C22×C11—42no—
312C22×C11—81no—
313C22×C11—81no—
314C22×C11C22×D811yescharacteristic
315C2×D11—21no—
316C2×D11—21no—
317C2×D11—42no—
318C2×D11—81no—
319C2×D11—81no—
320C2×D11—81no—
321C2×D11—81no—
322C2×D11—81no—
323C2×D11—164no—
324C2×D11#45912yes—
325C4×C11—21no—
326C4×C11—21no—
327C4×C11—81no—
328C4×C11—81no—
329C4×C11—81no—
330C4×C11C2×#12111yescharacteristic
331C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
332Dic11—21no—
333Dic11—21no—
334Dic11—81no—
335Dic11—81no—
336Dic11#45912yes—
337C2×#41—221no—
338C22×Q8—221no—
339C22×D4—221no—
340#137—444no—
341#135—222no—
342#135—222no—
343C2×Q16—21no—
344C2×Q16—111no—
345C2×Q16—222no—
346C2×Q16—222no—
347C2×Q16—221no—
348C2×Q16—221no—
349C2×Q16C22×D1111yescharacteristic
350C2×Q16C22×D1111yescharacteristic
351C2×SD16—221no—
352C2×SD16—221no—
353C2×SD16—221no—
354C2×D8—114no—
355C2×D8—111no—
356C2×D8—111no—
357C2×D8—222no—
358C2×D8—221no—
359C2×D8C22×D1111yescharacteristic
360C2×M16—111no—
361C22×C8—111no—
362C4⋊Q8—21no—
363C4⋊Q8—221no—
364#124—221no—
365#124—221no—
366#123—441no—
367#123—441no—
368C22⋊Q8—441no—
369C22⋊Q8—441no—
370C4×D4—21no—
371C4×D4—221no—
372C4×D4—221no—
373C4×D4—221no—
374C4×D4—441no—
375C4×D4—441no—
376#117—111no—
377#117—221no—
378C2×C22⋊C4—441no—
379C2×C22⋊C4—441no—
380SD32—22no—
381SD32—22no—
382SD32—222no—
383SD32—222no—
384SD32—222no—
385SD32—222no—
386D16—222no—
387D16—222no—
388M32—222no—
389C2×C16—111no—
390C2×C16—111no—
391C2×C16—222no—
392C2×C16C22×D1111yescharacteristic
393C2×C16C22×D1111yescharacteristic
394#107—111no—
395#107C22×D1111yescharacteristic
396#106—221no—
397#102—21no—
398#102—221no—
399#102—221no—
400#102—221no—
401#97—111no—
402#97—111no—
403C4×C8—111no—
404C4×C8C22×D1111yescharacteristic
405C2×C11—82no—
406C2×C11C2×#45911yescharacteristic
407C2×C11#341611yescharacteristic
408C2×C11#341611yescharacteristic
409D11—22no—
410D11—82no—
411D11—161no—
412C24—441no—
413#41—442no—
414#41—442no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—221no—
418C2×Q8—441no—
419C2×Q8—442no—
420C2×Q8—442no—
421C2×D4—21no—
422C2×D4—224no—
423C2×D4—221no—
424C2×D4—221no—
425C2×D4—441no—
426C2×D4—442no—
427C2×D4—441no—
428C22×C4—41no—
429C22×C4—111no—
430C22×C4—441no—
431C22×C4—441no—
432C22×C4—441no—
433C22×C4—441no—
434C22×C4—441no—
435Q16—21no—
436Q16—21no—
437Q16—21no—
438Q16—21no—
439Q16—42no—
440Q16—221no—
441Q16—221no—
442Q16—442no—
443Q16—442no—
444SD16—442no—
445SD16—442no—
446SD16—442no—
447D8—21no—
448D8—112no—
449D8—224no—
450D8—221no—
451D8—221no—
452D8—221no—
453D8D4×D1112yes—
454M16—222no—
455C2×C8—111no—
456C2×C8—112no—
457C2×C8—112no—
458C2×C8—111no—
459C2×C8D4×D1111yescharacteristic
460C2×C8C23×D1111yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—111no—
465C4⋊C4—111no—
466C4⋊C4—221no—
467C4⋊C4—441no—
468C4⋊C4—441no—
469C22⋊C4—41no—
470C22⋊C4—111no—
471C22⋊C4—111no—
472C22⋊C4—441no—
473C22⋊C4—441no—
474C22⋊C4—441no—
475C22⋊C4—441no—
476C22⋊C4—441no—
477C22⋊C4—441no—
478C22⋊C4—441no—
479C22⋊C4—441no—
480C42—111no—
481C42—441no—
482C42D4×D1111yescharacteristic
483C16—21no—
484C16—21no—
485C16—221no—
486C16—221no—
487C11#3358611yescharacteristic, complemented, Sylow
488C23—41no—
489C23—111no—
490C23—444no—
491C23—441no—
492C23—441no—
493C23—1761no—
494C23—1761no—
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—441no—
500Q8—441no—
501Q8—882no—
502D4—22no—
503D4—41no—
504D4—222no—
505D4—444no—
506D4—441no—
507D4—441no—
508D4—441no—
509D4—882no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—111no—
514C2×C4—112no—
515C2×C4—112no—
516C2×C4—111no—
517C2×C4—111no—
518C2×C4—161no—
519C2×C4—441no—
520C2×C4—441no—
521C2×C4—882no—
522C2×C4—882no—
523C2×C4—1761no—
524C2×C4—1761no—
525C2×C4—1761no—
526C2×C4D8×D1111yescharacteristic
527C2×C4D8×D1111yescharacteristic
528C2×C4C2×D4×D1111yescharacteristic
529C8—21no—
530C8—112no—
531C8—221no—
532C8C2×D4×D1111yescharacteristic
533C8#41×D1111yescharacteristic
534C22—42no—
535C22—81no—
536C22—81no—
537C22—112no—
538C22—221no—
539C22—221no—
540C22—442no—
541C22—881no—
542C22—881no—
543C22—881no—
544C22—881no—
545C22—881no—
546C22—1764no—
547C22C2×D8×D1111yescharacteristic
548C4—21no—
549C4—21no—
550C4—81no—
551C4—81no—
552C4—81no—
553C4—112no—
554C4—221no—
555C4—221no—
556C4—881no—
557C4—881no—
558C4D11×#12111yescharacteristic
559C4D11×AGL(1,ℤ/8)11yescharacteristic
560C2—82no—
561C2—222no—
562C2—882no—
563C2—1761no—
564C2D11×#45911yescharacteristic
565C2#1308175811yescharacteristic
566C2#1308176111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2208C2
socleC22×C11C22×D8
prime radicalC2×#10622527C2
hypercenter#2208D11
hypocenterC11#33586
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2208

Complements

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

NH ≅ G/Ntype
2. C2×D11×SD32C2semidirect
3. #13079104C2semidirect
4. #13077463C2semidirect
5. #13070674C2semidirect
6. #13070673C2semidirect
7. #13070672C2semidirect
8. #13070671C2semidirect
9. #13070660C2semidirect
10. #13070659C2semidirect
11. #13070658C2semidirect
12. #13070373C2semidirect
13. #13070334C2semidirect
14. #13070322C2semidirect
15. C11×#2208C2semidirect
24. C11×#494C22semidirect
26. #10622804C22semidirect
28. #10622794C22semidirect
46. #10622309C22semidirect
49. C11×C4⋊C16C22semidirect
50. C11×#358C22semidirect
51. C11×#358C22semidirect
52. #10622202C22semidirect
53. #10622202C22semidirect
54. #10622147C22semidirect
55. #10622141C22semidirect
56. Dic11⋊C16C22semidirect
57. Dic11⋊C16C22semidirect
58. #10622130C22semidirect
59. #10622129C22semidirect
60. C4⋊(C11⋊C16)C22semidirect
216. #2208D11semidirect
289. #494C2×D11semidirect
302. C4⋊C16C2×D11semidirect
307. #358C2×D11semidirect
308. #358C2×D11semidirect
487. C11#33586semidirect

Maximal subgroups

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

subgroupindex
C2×#106225272
C2×D11×SD322
#130791042
#130774632
#130706742
#130706732
#130706722
#130706712
#130706602
#130706592
#130706582
#130703732
#130703342
#130703222
C11×#22082
#3358611