Finite Group Databasebeta

← #14907137

Subgroups — #14907137

Order 2816.

682 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×SD32C211yesmaximal, characteristic
2#13077479C211yesmaximal, characteristic, complemented
3#13077463C211yesmaximal, characteristic
4#13070483C211yesmaximal, characteristic, complemented
5#13070480C211yesmaximal, characteristic, complemented
6#13070478C211yesmaximal, characteristic, complemented
7#13070477C211yesmaximal, characteristic, complemented
8C4×#66864C211yesmaximal, characteristic, complemented
9SD32×Dic11C211yesmaximal, characteristic, complemented
10#13070467C211yesmaximal, characteristic, complemented
11#13070399C211yesmaximal, characteristic, complemented
12#13070334C211yesmaximal, characteristic, complemented
13#13070330C211yesmaximal, characteristic
14#13070211C211yesmaximal, characteristic, complemented
15C4×C11×SD32C211yesmaximal, characteristic, complemented
16C2×Q16×D11C2211yescharacteristic
17C2×D8×D11C2211yescharacteristic
18#10623103—21no—
19#10623076—21no—
20C2×C11×SD32C2211yescharacteristic
21C4×C11×Q16C2211yescharacteristic, complemented
22C4×C11×D8C2211yescharacteristic
23Q16×Dic11C2211yescharacteristic, complemented
24C2×#66892C2211yescharacteristic
25D8×Dic11C2211yescharacteristic
26C2×#66891C2211yescharacteristic
27#10622643—21no—
28#10622627—21no—
29D11×SD32C418yescomplemented
30C2×#66864C2211yescharacteristic
31C2×#66862C2211yescharacteristic
32C2×C16×D11C2211yescharacteristic
33#10622493C2211yescharacteristic
34#10622493C2211yescharacteristic
35#10622486C2211yescharacteristic, complemented
36#10622485C2211yescharacteristic
37#10622415—21no—
38#10622402—21no—
39#10622398—21no—
40#10622383—21no—
41C4×Dic44C2211yescharacteristic, complemented
42C4×D88C2211yescharacteristic
43#10622302C2211yescharacteristic
44C11×#367C2211yescharacteristic, complemented
45C11×#358C2211yescharacteristic, complemented
46C11×#357C2211yescharacteristic
47C4×C11×C16C2211yescharacteristic, complemented
48#10622202C2211yescharacteristic, complemented
49#10622200C2211yescharacteristic
50#10622147C2211yescharacteristic
51#10622143C2211yescharacteristic, complemented
52#10622141C2211yescharacteristic, complemented
53#10622140C2211yescharacteristic, complemented
54C16×Dic11C2211yescharacteristic, complemented
55#10622130C2211yescharacteristic, complemented
56#10622129C2211yescharacteristic
57#10622127C2211yescharacteristic, complemented
58#10622127C2211yescharacteristic, complemented
59#10622099C2211yescharacteristic, complemented
60C2×Q8×D11—21no—
61C2×D4×D11—21no—
62C2×C11×Q16C2311yescharacteristic
63C2×C11×D8C2311yescharacteristic
64C4×Q8×C11—21no—
65C4×D4×C11—21no—
66Q8×Dic11—21no—
67C2×#4326—21no—
68D4×Dic11—21no—
69C2×#4323—21no—
70C4×C22⋊D11—41no—
71C2×(C2×D11)⋊C4—41no—
72Q16×D11—22no—
73Q16×D11C2×C414yescomplemented
74D8×D11—22no—
75D8×D11C2×C414yes—
76C2×Dic44C2311yescharacteristic
77C2×D88C2311yescharacteristic
78C2×#4313D411yescharacteristic
79C2×C8×D11C2311yescharacteristic
80#66946—21no—
81#66945—21no—
82#66945—21no—
83#66945—41no—
84#66940—21no—
85#66940—41no—
86(C22⋊D11)⋊C4—41no—
87C22⋊C4×D11—41no—
88C4×D44—21no—
89#66925—41no—
90#66925D411yescharacteristic
91C4×Dic22—21no—
92C4×Dic22—41no—
93C11×SD32C2×C414yescomplemented
94C2×C11×C16C2311yescharacteristic
95C2×C11×C16C2311yescharacteristic
96C11×#107C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#103—21no—
99C11×#102—21no—
100C4×C8×C11C2311yescharacteristic
101#66899—21no—
102#66896—21no—
103#66892C2×C414yescomplemented
104#66891C2×C414yescomplemented
105#66885—21no—
106#66882C2311yescharacteristic
107#66882C2311yescharacteristic
108#66880—21no—
109#66879D411yescharacteristic
110C8×Dic11C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113#66874—21no—
114#66873—21no—
115#66872—21no—
116#66872—21no—
117#66867D411yescharacteristic
118#66864C2×C414yescomplemented
119#66862—22no—
120C16×D11C2×C414yescomplemented
121#33457—111nomaximal, Sylow
122C23×D11—41no—
123C2×Q8×C11—21no—
124C2×D4×C11—21no—
125C22×C4×C11—41no—
126C2×C22⋊D11—41no—
127C22×Dic11—41no—
128Q8×D11—24no—
129Q8×D11—42no—
130D4×D11—24no—
131D4×D11—42no—
132C2×D44—21no—
133C2×C4×D11—41no—
134C2×C4×D11—41no—
135C2×C4×D11—41no—
136C2×C4×D11C2×D411yescharacteristic
137C2×Dic22—21no—
138C2×Dic22—41no—
139C11×Q16—21no—
140C11×Q16C22×C412yes—
141C11×D8—21no—
142C11×D8C22×C412yes—
143C2×C8×C11C2×D411yescharacteristic
144C2×C8×C11C2411yescharacteristic
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—41no—
148C11×C22⋊C4—41no—
149C42×C11—41no—
150C42×C11C2×D411yescharacteristic
151C22⋊Dic11—41no—
152#4326—24no—
153#4323—24no—
154(C2×D11)⋊C4—41no—
155(C2×D11)⋊C4—41no—
156(C2×D11)⋊C4—41no—
157(C2×D11)⋊C4—41no—
158(C2×D11)⋊C4D811yescharacteristic
159(C2×D11)⋊C4D811yescharacteristic
160C4⋊Dic11—21no—
161C4⋊Dic11—21no—
162C4⋊Dic11—41no—
163Dic11⋊C4—41no—
164Dic11⋊C4—41no—
165Dic11⋊C4D811yescharacteristic
166Dic11⋊C4D811yescharacteristic
167C4×Dic11—41no—
168C4×Dic11—41no—
169C4×Dic11—41no—
170C4×Dic11—41no—
171C4×Dic11—41no—
172C4×Dic11C2×D411yescharacteristic
173C2×C11⋊C8C2×D411yescharacteristic
174C2×C11⋊C8C2×D411yescharacteristic
175Dic44—21no—
176Dic44C22×C412yes—
177D88—21no—
178D88C22×C412yes—
179#4313—22no—
180C8×D11C22×C412yes—
181C8×D11#4112yes—
182C11×C16—21no—
183C11×C16C22×C412yes—
184C11⋊C16—21no—
185C11⋊C16C22×C412yes—
186C22×SD32—111no—
187#2950—111no—
188#2948—111no—
189#2175—111no—
190#2175—111no—
191#2175—111no—
192#2175—111no—
193C4×SD32—111no—
194C4×SD32—111no—
195C4×SD32—111no—
196C4×SD32D1111yescharacteristic, complemented
197#2158—111no—
198#2141—111no—
199#2140—111no—
200#2108—111no—
201C23×C11—41no—
202C22×D11—41no—
203C22×D11—44no—
204C22×D11—161no—
205C22×D11—161no—
206C22×D11C2×D811yescharacteristic
207Q8×C11—22no—
208Q8×C11—41no—
209D4×C11—22no—
210D4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—161no—
215C2×C4×C11C2×D811yescharacteristic
216C2×C4×C11C2×D811yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C22⋊D11—44no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—161no—
223C2×Dic11C2×D811yescharacteristic
224C2×Dic11C2×D811yescharacteristic
225C2×Dic11C2×D811yescharacteristic
226D44—22no—
227D44—41no—
228C4×D11—44no—
229C4×D11—161no—
230C4×D11—161no—
231C4×D11C4×D412yes—
232C4×D11#13512yes—
233Dic22—22no—
234Dic22—41no—
235Dic22—44no—
236C8×C11—21no—
237C8×C11C23×C411yescharacteristic
238C8×C11C2×#4111yescharacteristic
239C11⋊C8—21no—
240C11⋊C8C4×D412yes—
241C22×Q16—111no—
242C22×D8—111no—
243#519—221no—
244#518—221no—
245C2×SD32—111no—
246C2×SD32—111no—
247C2×SD32—118no—
248C2×SD32—111no—
249C2×SD32C2×D1111yescharacteristic
250C2×M32—111no—
251C22×C16—111no—
252#442—221no—
253#442—221no—
254#441—221no—
255#441—221no—
256C4×Q16—111no—
257C4×Q16—111no—
258C4×Q16—111no—
259C4×Q16C2×D1111yescharacteristic, complemented
260C4×D8—111no—
261C4×D8—111no—
262C4×D8—111no—
263C4×D8C2×D1111yescharacteristic
264#427—111no—
265#427—111no—
266#419—221no—
267#418—221no—
268#405—111no—
269#367—111no—
270#367C2×D1111yescharacteristic, complemented
271#366—111no—
272#366—111no—
273#358—111no—
274#358—111no—
275#358—111no—
276#358C2×D1111yescharacteristic, complemented
277#357—111no—
278#357—111no—
279#357—111no—
280#357C2×D1111yescharacteristic
281#346—111no—
282#346—111no—
283C4×C16—111no—
284C4×C16C2×D1111yescharacteristic, complemented
285C22×C11—42no—
286C22×C11—81no—
287C22×C11—81no—
288C22×C11C22×D811yescharacteristic
289C2×D11—21no—
290C2×D11—21no—
291C2×D11—42no—
292C2×D11—81no—
293C2×D11—81no—
294C2×D11—164no—
295C2×D11C4×D812yes—
296C4×C11—21no—
297C4×C11—21no—
298C4×C11—42no—
299C4×C11—81no—
300C4×C11—81no—
301C4×C11C2×C4×D411yescharacteristic
302C4×C11C2×#13511yescharacteristic
303Dic11—21no—
304Dic11—21no—
305Dic11—42no—
306Dic11—81no—
307Dic11—81no—
308Dic11C4×D812yes—
309C22×Q8—221no—
310C22×D4—221no—
311C2×Q16—114no—
312C2×Q16—111no—
313C2×Q16—222no—
314C2×Q16—221no—
315C2×Q16C22×D1111yescharacteristic
316C2×D8—114no—
317C2×D8—111no—
318C2×D8—222no—
319C2×D8—221no—
320C2×D8C22×D1111yescharacteristic
321C2×M16—111no—
322C22×C8—111no—
323C4×Q8—21no—
324C4×Q8—221no—
325C4×Q8—221no—
326C4×Q8—221no—
327C4×Q8—441no—
328C4×Q8—441no—
329C4×D4—21no—
330C4×D4—221no—
331C4×D4—221no—
332C4×D4—221no—
333C4×D4—441no—
334C4×D4—441no—
335#117—111no—
336#117—221no—
337#117—221no—
338#117—441no—
339#117—441no—
340C2×C22⋊C4—441no—
341C2×C22⋊C4—441no—
342SD32—114no—
343SD32—114no—
344SD32—114no—
345SD32C4×D1114yescomplemented
346M32—222no—
347C2×C16—111no—
348C2×C16—114no—
349C2×C16—111no—
350C2×C16C22×D1111yescharacteristic
351C2×C16C22×D1111yescharacteristic
352#107—111no—
353#107—111no—
354#107C22×D1111yescharacteristic
355#107C22×D1111yescharacteristic
356#106—221no—
357#106—221no—
358#103—21no—
359#103—221no—
360#103—221no—
361#103—221no—
362#102—21no—
363#102—221no—
364#102—221no—
365#102—221no—
366#97—111no—
367#97—111no—
368C4×C8—111no—
369C4×C8C22×D1111yescharacteristic
370C2×C11—82no—
371C2×C11C2×C4×D811yescharacteristic
372C2×C11#341611yescharacteristic
373C2×C11#341611yescharacteristic
374D11—22no—
375D11—82no—
376C24—441no—
377C2×Q8—21no—
378C2×Q8—224no—
379C2×Q8—221no—
380C2×Q8—441no—
381C2×Q8—442no—
382C2×D4—21no—
383C2×D4—224no—
384C2×D4—221no—
385C2×D4—442no—
386C2×D4—441no—
387C22×C4—41no—
388C22×C4—111no—
389C22×C4—441no—
390C22×C4—441no—
391C22×C4—441no—
392C22×C4—441no—
393Q16—21no—
394Q16—112no—
395Q16—224no—
396Q16—221no—
397Q16C2×C4×D1112yes—
398D8—21no—
399D8—112no—
400D8—224no—
401D8—221no—
402D8C2×C4×D1112yes—
403M16—222no—
404C2×C8—111no—
405C2×C8—112no—
406C2×C8—112no—
407C2×C8—111no—
408C2×C8D4×D1111yescharacteristic
409C2×C8C23×D1111yescharacteristic
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—41no—
413C4⋊C4—111no—
414C4⋊C4—111no—
415C4⋊C4—221no—
416C4⋊C4—221no—
417C4⋊C4—441no—
418C4⋊C4—441no—
419C4⋊C4—441no—
420C22⋊C4—41no—
421C22⋊C4—111no—
422C22⋊C4—111no—
423C22⋊C4—441no—
424C22⋊C4—441no—
425C22⋊C4—441no—
426C22⋊C4—441no—
427C22⋊C4—441no—
428C42—41no—
429C42—111no—
430C42—441no—
431C42—441no—
432C42—441no—
433C42—441no—
434C42—441no—
435C42D4×D1111yescharacteristic
436C16—21no—
437C16—112no—
438C16—221no—
439C16C2×C4×D1112yes—
440C11#3345711yescharacteristic, complemented, Sylow
441C23—41no—
442C23—111no—
443C23—444no—
444C23—441no—
445C23—1761no—
446C23—1761no—
447Q8—22no—
448Q8—41no—
449Q8—222no—
450Q8—444no—
451Q8—441no—
452D4—22no—
453D4—41no—
454D4—222no—
455D4—444no—
456D4—441no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—111no—
461C2×C4—112no—
462C2×C4—112no—
463C2×C4—111no—
464C2×C4—111no—
465C2×C4—161no—
466C2×C4—444no—
467C2×C4—441no—
468C2×C4—441no—
469C2×C4—441no—
470C2×C4—1761no—
471C2×C4—1761no—
472C2×C4—1761no—
473C2×C4D8×D1111yescharacteristic
474C2×C4D8×D1111yescharacteristic
475C2×C4C2×D4×D1111yescharacteristic
476C8—21no—
477C8—112no—
478C8—221no—
479C8C22×C4×D1111yescharacteristic
480C8#41×D1111yescharacteristic
481C22—42no—
482C22—81no—
483C22—81no—
484C22—112no—
485C22—221no—
486C22—221no—
487C22—442no—
488C22—881no—
489C22—881no—
490C22—1764no—
491C22C2×D8×D1111yescharacteristic
492C4—21no—
493C4—21no—
494C4—42no—
495C4—81no—
496C4—81no—
497C4—112no—
498C4—221no—
499C4—221no—
500C4—442no—
501C4—881no—
502C4—881no—
503C4C4×D4×D1111yescharacteristic
504C4D11×#13511yescharacteristic
505C2—82no—
506C2—222no—
507C2—882no—
508C2C4×D8×D1111yescharacteristic
509C2#1308175811yescharacteristic
510C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC4×C11×SD32C2
socleC22×C11C22×D8
prime radicalC2×D8×D11C22
cosocleC2×C8×C11C24
hypercenterC4×SD32D11
hypocenterC11#33457
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×SD32

Complements

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

NH ≅ G/Ntype
2. #13077479C2semidirect
4. #13070483C2semidirect
5. #13070480C2semidirect
6. #13070478C2semidirect
7. #13070477C2semidirect
8. C4×#66864C2semidirect
9. SD32×Dic11C2semidirect
10. #13070467C2semidirect
11. #13070399C2semidirect
12. #13070334C2semidirect
14. #13070211C2semidirect
15. C4×C11×SD32C2semidirect
21. C4×C11×Q16C22semidirect
23. Q16×Dic11C22semidirect
29. D11×SD32C4semidirect
35. #10622486C22semidirect
41. C4×Dic44C22semidirect
44. C11×#367C22semidirect
45. C11×#358C22semidirect
47. C4×C11×C16C22semidirect
48. #10622202C22semidirect
51. #10622143C22semidirect
52. #10622141C22semidirect
53. #10622140C22semidirect
54. C16×Dic11C22semidirect
55. #10622130C22semidirect
57. #10622127C22semidirect
58. #10622127C22semidirect
59. #10622099C22semidirect
73. Q16×D11C2×C4semidirect
93. C11×SD32C2×C4semidirect
103. #66892C2×C4semidirect
104. #66891C2×C4semidirect
118. #66864C2×C4semidirect
120. C16×D11C2×C4semidirect
196. C4×SD32D11semidirect
259. C4×Q16C2×D11semidirect
270. #367C2×D11semidirect
276. #358C2×D11semidirect
284. C4×C16C2×D11semidirect
345. SD32C4×D11semidirect
440. C11#33457semidirect

Maximal subgroups

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

subgroupindex
C2×D11×SD322
#130774792
#130774632
#130704832
#130704802
#130704782
#130704772
C4×#668642
SD32×Dic112
#130704672
#130703992
#130703342
#130703302
#130702112
C4×C11×SD322
#3345711