Finite Group Databasebeta

← #14908101

Subgroups — #14908101

Order 2816.

712 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×#10622528C211yesmaximal, characteristic, complemented
2C2×D11×SD32C211yesmaximal, characteristic, complemented
3#13079096C211yesmaximal, characteristic
4#13077479C211yesmaximal, characteristic, complemented
5#13070679C211yesmaximal, characteristic, complemented
6#13070678C211yesmaximal, characteristic, complemented
7#13070677C211yesmaximal, characteristic, complemented
8#13070676C211yesmaximal, characteristic, complemented
9#13070655C211yesmaximal, characteristic, complemented
10#13070654C211yesmaximal, characteristic, complemented
11#13070653C211yesmaximal, characteristic, complemented
12#13070373C211yesmaximal, characteristic, complemented
13#13070330C211yesmaximal, characteristic, complemented
14#13070320C211yesmaximal, characteristic, complemented
15C11×#2207C211yesmaximal, characteristic, complemented
16C2×Q16×D11C2211yescharacteristic
17C2×#66965C2211yescharacteristic
18C2×#66964—21no—
19C2×D8×D11C2211yescharacteristic
20#10623246—21no—
21#10623103—21no—
22C2×C11×SD32C2211yescharacteristic
23C2×C11×SD32C2211yescharacteristic, complemented
24C11×#493C2211yescharacteristic
25C4×C11×Q16C2211yescharacteristic, complemented
26Q16×Dic11C2211yescharacteristic, complemented
27C2×#66893C2211yescharacteristic, complemented
28C2×#66892C2211yescharacteristic
29#10622768C2211yescharacteristic
30#10622767—21no—
31#10622764C2211yescharacteristic
32C2×#66891C2211yescharacteristic
33C2×#66891C2211yescharacteristic, complemented
34#10622687—21no—
35#10622643—21no—
36#10622528—24no—
37D11×SD32—24no—
38C2×Dic88C2211yescharacteristic, complemented
39C2×#66864C2211yescharacteristic
40C2×#66862C2211yescharacteristic
41C2×C16×D11C2211yescharacteristic
42#10622493C2211yescharacteristic
43#10622486C2211yescharacteristic, complemented
44#10622415—21no—
45#10622402—21no—
46C4×Dic44C2211yescharacteristic, complemented
47#10622309C2211yescharacteristic
48#10622302C2211yescharacteristic
49C11×C4⋊C16C2211yescharacteristic, complemented
50C11×#357C2211yescharacteristic
51C11×#357C2211yescharacteristic, complemented
52#10622200C2211yescharacteristic
53#10622200C2211yescharacteristic, complemented
54#10622147C2211yescharacteristic
55#10622141C2211yescharacteristic, complemented
56Dic11⋊C16C2211yescharacteristic, complemented
57Dic11⋊C16C2211yescharacteristic, complemented
58#10622130C2211yescharacteristic, complemented
59#10622129C2211yescharacteristic
60C4⋊(C11⋊C16)C2211yescharacteristic, complemented
61C2×Q8×D11—21no—
62C2×#4341—21no—
63C2×D4×D11—21no—
64C2×C11×Q16C2311yescharacteristic
65C2×C11×D8—21no—
66C2×C11×D8C2311yescharacteristic
67C2×C11×D8C2311yescharacteristic
68C11×#127—21no—
69C4×Q8×C11—21no—
70Q8×Dic11—21no—
71C2×#4326—21no—
72#66993—21no—
73#66992—41no—
74#66992—41no—
75#66990—41no—
76#66990—41no—
77#66989—21no—
78C2×#4324—21no—
79C2×#4324—21no—
80C2×#4323—21no—
81C2×#4323—21no—
82Q16×D11—22no—
83Q16×D11D414yescomplemented
84#66965—22no—
85#66965—22no—
86#66964—44no—
87D8×D11—22no—
88D8×D11—22no—
89C2×Dic44C2311yescharacteristic
90C2×Dic44C2311yescharacteristic
91C2×D88C2311yescharacteristic
92C2×#4314—21no—
93C2×#4313D411yescharacteristic
94C2×C8×D11C2311yescharacteristic
95#66945—21no—
96#66945—41no—
97#66940—21no—
98#66940—41no—
99#66928—21no—
100#66925—41no—
101#66925D411yescharacteristic
102C4×Dic22—21no—
103C4×Dic22—41no—
104C11×SD32—22no—
105C11×SD32—22no—
106C2×C11×C16C2311yescharacteristic
107C2×C11×C16C2311yescharacteristic
108C11×#107C2311yescharacteristic
109C11×#103—21no—
110C4×C8×C11C2311yescharacteristic
111#66899—21no—
112#66893—22no—
113#66892—22no—
114#66891—22no—
115#66891—22no—
116#66882C2311yescharacteristic
117#66880—21no—
118#66879D411yescharacteristic
119C8×Dic11C2311yescharacteristic
120C2×C11⋊C16C2311yescharacteristic
121C2×C11⋊C16C2311yescharacteristic
122#66874—21no—
123#66872—21no—
124#66867D411yescharacteristic
125Dic88—22no—
126#66864—22no—
127#66862—22no—
128C16×D11—22no—
129#33587—111nomaximal, Sylow
130C23×D11—41no—
131C2×Q8×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—41no—
135C2×D4×C11—41no—
136C2×C22⋊D11—41no—
137C2×C22⋊D11—41no—
138C2×C22⋊D11—41no—
139C2×C22⋊D11—41no—
140C22×Dic11—41no—
141Q8×D11—24no—
142Q8×D11—42no—
143#4341—42no—
144#4341—42no—
145D4×D11—42no—
146D4×D11—42no—
147C2×D44—21no—
148C2×C4×D11—41no—
149C2×C4×D11C2×D411yescharacteristic
150C2×Dic22—21no—
151C2×Dic22—21no—
152C2×Dic22—41no—
153C11×Q16—21no—
154C11×Q16C2×D412yes—
155C11×D8—21no—
156C11×D8—21no—
157C11×D8—21no—
158C11×D8—21no—
159C11×D8—42no—
160C2×C8×C11C2×D411yescharacteristic
161C2×C8×C11C2411yescharacteristic
162C11×C4⋊C4—21no—
163C11×C4⋊C4—41no—
164C42×C11—41no—
165C42×C11C2×D411yescharacteristic
166C22⋊Dic11—41no—
167C22⋊Dic11—41no—
168#4326—24no—
169#4324—42no—
170#4324—42no—
171#4323—42no—
172#4323—42no—
173(C2×D11)⋊C4—41no—
174(C2×D11)⋊C4—41no—
175(C2×D11)⋊C4—41no—
176(C2×D11)⋊C4D811yescharacteristic
177(C2×D11)⋊C4D811yescharacteristic
178C4⋊Dic11—21no—
179C4⋊Dic11—41no—
180Dic11⋊C4—41no—
181Dic11⋊C4—41no—
182Dic11⋊C4D811yescharacteristic
183Dic11⋊C4D811yescharacteristic
184C4×Dic11—41no—
185C4×Dic11—41no—
186C4×Dic11—41no—
187C4×Dic11—41no—
188C4×Dic11C2×D411yescharacteristic
189C2×C11⋊C8C2×D411yescharacteristic
190C2×C11⋊C8C2×D411yescharacteristic
191Dic44—21no—
192Dic44—21no—
193Dic44—21no—
194Dic44C2×D412yes—
195D88—21no—
196D88—21no—
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×#510—111no—
206C22×SD32—111no—
207#3155—111no—
208#2950—111no—
209#2211—111no—
210#2211—111no—
211#2211—111no—
212#2211—111no—
213#2207—111no—
214#2207—111no—
215#2207—111no—
216#2207D1111yescharacteristic, complemented
217#2151—111no—
218#2140—111no—
219#2138—111no—
220C23×C11—41no—
221C23×C11—41no—
222C22×D11—41no—
223C22×D11—82no—
224C22×D11—161no—
225C22×D11—161no—
226C22×D11C2×D811yescharacteristic
227Q8×C11—22no—
228Q8×C11—41no—
229D4×C11—41no—
230D4×C11—41no—
231D4×C11—41no—
232D4×C11—41no—
233D4×C11—161no—
234D4×C11—161no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11C2×D811yescharacteristic
238C2×C4×C11C2×D811yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C22⋊D11—82no—
241C22⋊D11—82no—
242C22⋊D11—161no—
243C22⋊D11—161no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—82no—
248C2×Dic11C2×D811yescharacteristic
249C2×Dic11C2×D811yescharacteristic
250C2×Dic11C2×D811yescharacteristic
251D44—41no—
252D44—41no—
253C4×D11—44no—
254C4×D11#12112yes—
255C4×D11AGL(1,ℤ/8)12yes—
256Dic22—22no—
257Dic22—41no—
258Dic22—44no—
259Dic22—41no—
260Dic22—41no—
261C8×C11—21no—
262C8×C11C22×D411yescharacteristic
263C8×C11C2×#4111yescharacteristic
264C11⋊C8—21no—
265C11⋊C8#12112yes—
266C2×AGL(1,ℤ/8)—221no—
267C2×#135—111no—
268C22×Q16—111no—
269C22×D8—111no—
270#535—221no—
271#519—221no—
272#510—224no—
273C2×Q32—111no—
274C2×Q32—111no—
275C2×SD32—111no—
276C2×SD32—111no—
277C2×SD32—111no—
278C2×SD32—111no—
279C2×SD32—224no—
280C2×SD32C2×D1111yescharacteristic
281C2×SD32C2×D1111yescharacteristic, complemented
282C2×M32—111no—
283C22×C16—111no—
284#496—221no—
285#496—221no—
286#495—111no—
287#495—111no—
288#493—111no—
289#493C2×D1111yescharacteristic
290#441—221no—
291#441—221no—
292C4×Q16—111no—
293C4×Q16—111no—
294C4×Q16—111no—
295C4×Q16C2×D1111yescharacteristic, complemented
296#427—111no—
297#419—221no—
298#405—111no—
299C4⋊C16—111no—
300C4⋊C16—111no—
301C4⋊C16—111no—
302C4⋊C16C2×D1111yescharacteristic, complemented
303#358—111no—
304#358—111no—
305#357—111no—
306#357—111no—
307#357—111no—
308#357—111no—
309#357C2×D1111yescharacteristic
310#357C2×D1111yescharacteristic, complemented
311C22×C11—81no—
312C22×C11—81no—
313C22×C11—81no—
314C22×C11—81no—
315C22×C11—81no—
316C22×C11—81no—
317C22×C11C22×D811yescharacteristic
318C2×D11—21no—
319C2×D11—21no—
320C2×D11—81no—
321C2×D11—81no—
322C2×D11—81no—
323C2×D11—164no—
324C2×D11#45912yes—
325C4×C11—21no—
326C4×C11—21no—
327C4×C11—42no—
328C4×C11—81no—
329C4×C11C2×#12111yescharacteristic
330C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
331Dic11—21no—
332Dic11—21no—
333Dic11—42no—
334Dic11—81no—
335Dic11—81no—
336Dic11#45912yes—
337C2×#41—221no—
338C22×Q8—221no—
339C22×D4—221no—
340AGL(1,ℤ/8)—444no—
341#135—222no—
342#135—222no—
343C2×Q16—114no—
344C2×Q16—111no—
345C2×Q16—111no—
346C2×Q16—222no—
347C2×Q16—221no—
348C2×Q16C22×D1111yescharacteristic
349C2×SD16—221no—
350C2×SD16—221no—
351C2×SD16—221no—
352C2×D8—21no—
353C2×D8—111no—
354C2×D8—222no—
355C2×D8—222no—
356C2×D8—221no—
357C2×D8—221no—
358C2×D8C22×D1111yescharacteristic
359C2×D8C22×D1111yescharacteristic
360C2×M16—111no—
361C22×C8—111no—
362#127—21no—
363#127—221no—
364#124—221no—
365#124—221no—
366#121—441no—
367#121—441no—
368#120—441no—
369#120—441no—
370C4×Q8—21no—
371C4×Q8—221no—
372C4×Q8—221no—
373C4×Q8—221no—
374C4×Q8—441no—
375C4×Q8—441no—
376#117—111no—
377#117—221no—
378#117—441no—
379#117—441no—
380Q32—222no—
381Q32—222no—
382SD32—22no—
383SD32—22no—
384SD32—222no—
385SD32—222no—
386SD32—222no—
387SD32—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#103—21no—
398#103—221no—
399#103—221no—
400#103—221no—
401#97—111no—
402#97—111no—
403C4×C8—111no—
404C4×C8C22×D1111yescharacteristic
405C2×C11—161no—
406C2×C11—161no—
407C2×C11C2×#45911yescharacteristic
408C2×C11#341611yescharacteristic
409C2×C11#341611yescharacteristic
410D11—22no—
411D11—161no—
412C24—441no—
413#41—442no—
414#41—442no—
415C2×Q8—21no—
416C2×Q8—224no—
417C2×Q8—221no—
418C2×Q8—221no—
419C2×Q8—441no—
420C2×Q8—442no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—221no—
426C2×D4—442no—
427C2×D4—442no—
428C2×D4—441no—
429C2×D4—441no—
430C2×D4—441no—
431C2×D4—441no—
432C22×C4—111no—
433C22×C4—441no—
434C22×C4—441no—
435Q16—21no—
436Q16—112no—
437Q16—224no—
438Q16—221no—
439Q16—221no—
440Q16—221no—
441Q16D4×D1112yes—
442SD16—442no—
443SD16—442no—
444SD16—442no—
445D8—21no—
446D8—21no—
447D8—21no—
448D8—21no—
449D8—42no—
450D8—221no—
451D8—221no—
452D8—442no—
453D8—442no—
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—111no—
464C4⋊C4—111no—
465C4⋊C4—221no—
466C4⋊C4—441no—
467C4⋊C4—441no—
468C4⋊C4—441no—
469C22⋊C4—111no—
470C22⋊C4—111no—
471C22⋊C4—441no—
472C22⋊C4—441no—
473C22⋊C4—441no—
474C22⋊C4—441no—
475C22⋊C4—441no—
476C42—41no—
477C42—111no—
478C42—441no—
479C42—441no—
480C42—441no—
481C42—441no—
482C42D4×D1111yescharacteristic
483C16—21no—
484C16—21no—
485C16—221no—
486C16—221no—
487C11#3358711yescharacteristic, complemented, Sylow
488C23—41no—
489C23—41no—
490C23—111no—
491C23—441no—
492C23—882no—
493C23—1761no—
494C23—1761no—
495Q8—22no—
496Q8—41no—
497Q8—222no—
498Q8—444no—
499Q8—441no—
500Q8—441no—
501Q8—441no—
502D4—41no—
503D4—41no—
504D4—41no—
505D4—41no—
506D4—161no—
507D4—161no—
508D4—441no—
509D4—441no—
510D4—882no—
511D4—882no—
512D4—1761no—
513D4—1761no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—111no—
517C2×C4—112no—
518C2×C4—112no—
519C2×C4—111no—
520C2×C4—111no—
521C2×C4—444no—
522C2×C4—441no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4—882no—
526C2×C4D8×D1111yescharacteristic
527C2×C4D8×D1111yescharacteristic
528C2×C4C2×D4×D1111yescharacteristic
529C8—21no—
530C8—112no—
531C8—221no—
532C8C2×D4×D1111yescharacteristic
533C8#41×D1111yescharacteristic
534C22—81no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22—112no—
541C22—221no—
542C22—221no—
543C22—881no—
544C22—881no—
545C22—881no—
546C22—1764no—
547C22C2×D8×D1111yescharacteristic
548C4—21no—
549C4—21no—
550C4—42no—
551C4—81no—
552C4—112no—
553C4—221no—
554C4—221no—
555C4—442no—
556C4—881no—
557C4—881no—
558C4D11×#12111yescharacteristic
559C4D11×AGL(1,ℤ/8)11yescharacteristic
560C2—161no—
561C2—161no—
562C2—222no—
563C2—1761no—
564C2D11×#45911yescharacteristic
565C2#1308175811yescharacteristic
566C2#1308176211yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2207C2
socleC22×C11C22×D8
prime radical#13079096C2
hypercenter#2207D11
hypocenterC11#33587
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2207

Complements

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

NH ≅ G/Ntype
1. C2×#10622528C2semidirect
2. C2×D11×SD32C2semidirect
4. #13077479C2semidirect
5. #13070679C2semidirect
6. #13070678C2semidirect
7. #13070677C2semidirect
8. #13070676C2semidirect
9. #13070655C2semidirect
10. #13070654C2semidirect
11. #13070653C2semidirect
12. #13070373C2semidirect
13. #13070330C2semidirect
14. #13070320C2semidirect
15. C11×#2207C2semidirect
23. C2×C11×SD32C22semidirect
25. C4×C11×Q16C22semidirect
26. Q16×Dic11C22semidirect
27. C2×#66893C22semidirect
33. C2×#66891C22semidirect
38. C2×Dic88C22semidirect
43. #10622486C22semidirect
46. C4×Dic44C22semidirect
49. C11×C4⋊C16C22semidirect
51. C11×#357C22semidirect
53. #10622200C22semidirect
55. #10622141C22semidirect
56. Dic11⋊C16C22semidirect
57. Dic11⋊C16C22semidirect
58. #10622130C22semidirect
60. C4⋊(C11⋊C16)C22semidirect
83. Q16×D11D4semidirect
216. #2207D11semidirect
281. C2×SD32C2×D11semidirect
295. C4×Q16C2×D11semidirect
302. C4⋊C16C2×D11semidirect
310. #357C2×D11semidirect
487. C11#33587semidirect

Maximal subgroups

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

subgroupindex
C2×#106225282
C2×D11×SD322
#130790962
#130774792
#130706792
#130706782
#130706772
#130706762
#130706552
#130706542
#130706532
#130703732
#130703302
#130703202
C11×#22072
#3358711