Finite Group Databasebeta

← #14907094

Subgroups — #14907094

Order 2816.

738 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622524C211yesmaximal, characteristic
2C4×#66965C211yesmaximal, characteristic, complemented
3C4×D8×D11C211yesmaximal, characteristic, complemented
4#13070490C211yesmaximal, characteristic, complemented
5#13070482C211yesmaximal, characteristic, complemented
6#13070480C211yesmaximal, characteristic, complemented
7#13070471C211yesmaximal, characteristic, complemented
8#13070467C211yesmaximal, characteristic, complemented
9D16×Dic11C211yesmaximal, characteristic, complemented
10#13070460C211yesmaximal, characteristic, complemented
11#13070403C211yesmaximal, characteristic, complemented
12#13070330C211yesmaximal, characteristic, complemented
13#13070325C211yesmaximal, characteristic, complemented
14#13070209C211yesmaximal, characteristic, complemented
15C11×#2177C211yesmaximal, characteristic, complemented
16C2×#66965C2211yescharacteristic
17C2×D8×D11C2211yescharacteristic
18C4×D4×D11—21no—
19C4×#4341—21no—
20C2×C11×D16C2211yescharacteristic
21C4×C11×D8C2211yescharacteristic
22C4×C11×D8C2211yescharacteristic, complemented
23D8×Dic11C2211yescharacteristic
24D8×Dic11C2211yescharacteristic, complemented
25C2×#66891C2211yescharacteristic
26C2×#66890C2211yescharacteristic
27C4×#4324—21no—
28C4×#4323—21no—
29#10622524C418yescomplemented
30C2×#66864C2211yescharacteristic
31C2×#66862C2211yescharacteristic
32C2×#66862C2211yescharacteristic
33#10622493C2211yescharacteristic
34D11×#107C2211yescharacteristic
35#10622486C2211yescharacteristic, complemented
36#10622485C2211yescharacteristic
37#10622385—21no—
38D11×#102—21no—
39#10622371—21no—
40#10622369—21no—
41C4×Dic44C2211yescharacteristic, complemented
42C4×D88C2211yescharacteristic
43C4×C8×D11C2211yescharacteristic
44C11×#367C2211yescharacteristic, complemented
45C11×#357C2211yescharacteristic
46C11×#357C2211yescharacteristic, complemented
47C11×#346C2211yescharacteristic, complemented
48#10622200C2211yescharacteristic
49#10622200C2211yescharacteristic, complemented
50#10622147C2211yescharacteristic
51#10622142C2211yescharacteristic, complemented
52#10622141C2211yescharacteristic, complemented
53C16×Dic11C2211yescharacteristic, complemented
54C16×Dic11C2211yescharacteristic, complemented
55#10622130C2211yescharacteristic, complemented
56#10622129C2211yescharacteristic
57#10622128C2211yescharacteristic, complemented
58#10622127C2211yescharacteristic, complemented
59#10622099C2211yescharacteristic, complemented
60C2×#4341—21no—
61C2×D4×D11—21no—
62C22×C4×D11—41no—
63C2×C11×D8C2311yescharacteristic
64C2×C11×D8C2311yescharacteristic
65C4×D4×C11—21no—
66C4×D4×C11—21no—
67D4×Dic11—21no—
68D4×Dic11—21no—
69C2×#4324—21no—
70C2×#4323—21no—
71C4×C22⋊D11—41no—
72C4×C22⋊D11—41no—
73C2×C4×Dic11—41no—
74#66965—22no—
75#66965C2×C414yescomplemented
76D8×D11—22no—
77D8×D11C2×C414yescomplemented
78C2×Dic44C2311yescharacteristic
79C2×D88C2311yescharacteristic
80C2×C8×D11D411yescharacteristic
81C2×C8×D11C2311yescharacteristic
82#66946—21no—
83#66945—21no—
84C4⋊C4×D11—21no—
85#66940—21no—
86(C22⋊D11)⋊C4—41no—
87(C22⋊D11)⋊C4—41no—
88C22⋊C4×D11—41no—
89#66930—41no—
90C4×D44—21no—
91C42×D11D411yescharacteristic
92C4×Dic22—21no—
93C11×D16C2×C414yescomplemented
94C2×C11×C16C2311yescharacteristic
95C2×C11×C16C2311yescharacteristic
96C11×#107C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#102—21no—
99C11×#102—21no—
100C4×C8×C11C2311yescharacteristic
101#66896—21no—
102#66896—21no—
103#66891C2×C414yescomplemented
104#66890C2×C414yescomplemented
105#66885—21no—
106#66882C2311yescharacteristic
107#66882C2311yescharacteristic
108#66880—21no—
109C8×Dic11D411yescharacteristic
110C8×Dic11C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113#66874—21no—
114#66873—21no—
115#66872—21no—
116#66871—21no—
117C4×C11⋊C8D411yescharacteristic
118#66864C2×C414yescomplemented
119#66862—22no—
120#66862C2×C414yescomplemented
121C4×#509—111nomaximal, Sylow
122C23×D11—41no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C22×C4×C11—41no—
126C22×C4×C11—41no—
127C2×C22⋊D11—41no—
128C2×C22⋊D11—41no—
129C22×Dic11—41no—
130C22×Dic11—41no—
131C22×Dic11—41no—
132#4341—24no—
133#4341—42no—
134D4×D11—24no—
135D4×D11—42no—
136C2×D44—21no—
137C2×C4×D11—41no—
138C2×C4×D11—41no—
139C2×C4×D11—41no—
140C2×C4×D11—84no—
141C2×C4×D11D811yescharacteristic
142C2×C4×D11D811yescharacteristic
143C2×C4×D11C2×D411yescharacteristic
144C2×Dic22—21no—
145C11×D8—21no—
146C11×D8—21no—
147C11×D8C22×C412yes—
148C11×D8C22×C412yescomplemented
149C2×C8×C11C2×D411yescharacteristic
150C2×C8×C11C2411yescharacteristic
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C22⋊C4—41no—
154C11×C22⋊C4—41no—
155C42×C11C2×D411yescharacteristic
156C22⋊Dic11—41no—
157C22⋊Dic11—41no—
158#4324—24no—
159#4323—24no—
160(C2×D11)⋊C4—41no—
161(C2×D11)⋊C4—41no—
162(C2×D11)⋊C4—41no—
163C4⋊Dic11—21no—
164C4⋊Dic11—21no—
165Dic11⋊C4—41no—
166Dic11⋊C4—41no—
167Dic11⋊C4—41no—
168C4×Dic11—41no—
169C4×Dic11—41no—
170C4×Dic11—41no—
171C4×Dic11D811yescharacteristic
172C4×Dic11D811yescharacteristic
173C4×Dic11C2×D411yescharacteristic
174C2×C11⋊C8C2×D411yescharacteristic
175C2×C11⋊C8C2×D411yescharacteristic
176Dic44—21no—
177Dic44C22×C412yescomplemented
178D88—21no—
179D88C22×C412yes—
180C8×D11—22no—
181C8×D11C22×C412yes—
182C8×D11#4112yes—
183C11×C16—21no—
184C11×C16C22×C412yescomplemented
185C11⋊C16—21no—
186C11⋊C16C22×C412yescomplemented
187C2×#509—111no—
188C4×#135—111no—
189C2×C4×D8—111no—
190#2177—111no—
191#2177D1111yescharacteristic, complemented
192#2175—111no—
193#2175—111no—
194C4×SD32—111no—
195C4×SD32—111no—
196C4×D16—111no—
197C4×D16—111no—
198#2159—111no—
199#2140—111no—
200#2139—111no—
201C4×M32—111no—
202C23×C11—41no—
203C23×C11—41no—
204C22×D11—41no—
205C22×D11—44no—
206C22×D11—82no—
207C22×D11—82no—
208C22×D11C2×D811yescharacteristic
209D4×C11—22no—
210D4×C11—22no—
211D4×C11—41no—
212D4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—82no—
216C2×C4×C11—82no—
217C2×C4×C11C2×D811yescharacteristic
218C2×C4×C11C2×D811yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C22⋊D11—44no—
221C22⋊D11—44no—
222C2×Dic11—41no—
223C2×Dic11—44no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—82no—
227C2×Dic11—82no—
228C2×Dic11C2×D811yescharacteristic
229C2×Dic11C2×D811yescharacteristic
230C2×Dic11C2×D811yescharacteristic
231D44—22no—
232D44—41no—
233C4×D11—22no—
234C4×D11—41no—
235C4×D11—82no—
236C4×D11—82no—
237C4×D11—82no—
238C4×D11C4×D412yes—
239C4×D11#13512yes—
240Dic22—22no—
241Dic22—41no—
242C8×C11—21no—
243C8×C11C23×C411yescharacteristic
244C8×C11C2×#4111yescharacteristic
245C11⋊C8—21no—
246C11⋊C8C4×D412yes—
247C2×#135—111no—
248C22×D8—111no—
249C4×#41—221no—
250C2×C4×D4—221no—
251#509—118no—
252C2×SD32—111no—
253C2×SD32—111no—
254C2×D16—111no—
255C2×D16C2×D1111yescharacteristic
256C2×M32—111no—
257C2×M32—111no—
258C4×Q16—111no—
259C4×Q16—111no—
260C4×SD16—221no—
261C4×SD16—221no—
262C4×D8—111no—
263C4×D8—111no—
264C4×D8—111no—
265C4×D8—111no—
266C4×D8—221no—
267C4×D8—221no—
268C4×D8C2×D1111yescharacteristic
269C4×D8C2×D1111yescharacteristic, complemented
270#427—111no—
271C2×#107—111no—
272#416—221no—
273C2×#102—221no—
274C2×C4×C8—111no—
275#367—111no—
276#367C2×D1111yescharacteristic, complemented
277#366—111no—
278#366—111no—
279#358—111no—
280#358—111no—
281#357—111no—
282#357—111no—
283#357—111no—
284#357—111no—
285#357C2×D1111yescharacteristic
286#357C2×D1111yescharacteristic, complemented
287#346—111no—
288#346C2×D1111yescharacteristic, complemented
289C4×C16—111no—
290C4×C16—111no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—81no—
294C22×C11—81no—
295C22×C11—81no—
296C22×C11—81no—
297C22×C11C22×D811yescharacteristic
298C2×D11—21no—
299C2×D11—21no—
300C2×D11—42no—
301C2×D11—88no—
302C2×D11—81no—
303C2×D11—81no—
304C2×D11C4×D812yes—
305C4×C11—21no—
306C4×C11—21no—
307C4×C11—81no—
308C4×C11—81no—
309C4×C11C2×C4×D411yescharacteristic
310C4×C11C2×#13511yescharacteristic
311Dic11—21no—
312Dic11—42no—
313Dic11—81no—
314Dic11—81no—
315Dic11C4×D812yes—
316Dic11#50912yescomplemented
317C2×#41—221no—
318C22×D4—221no—
319C23×C4—441no—
320#135—114no—
321#135—222no—
322C2×Q16—111no—
323C2×SD16—221no—
324C2×D8—114no—
325C2×D8—111no—
326C2×D8—222no—
327C2×D8—221no—
328C2×D8C22×D1111yescharacteristic
329C2×D8C22×D1111yescharacteristic
330C22×C8—111no—
331C22×C8—111no—
332C4×Q8—221no—
333C4×Q8—221no—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4—221no—
337C4×D4—221no—
338C4×D4—221no—
339C4×D4—221no—
340C4×D4—441no—
341C4×D4—441no—
342C4×D4—441no—
343C4×D4—441no—
344#117—221no—
345#117—441no—
346C2×C4⋊C4—221no—
347C2×C22⋊C4—441no—
348C2×C42—111no—
349C2×C42—441no—
350SD32—114no—
351SD32—114no—
352D16—114no—
353D16C4×D1114yescomplemented
354M32—114no—
355M32—222no—
356C2×C16—111no—
357C2×C16—111no—
358C2×C16C22×D1111yescharacteristic
359C2×C16C22×D1111yescharacteristic
360#107—111no—
361#107—111no—
362#107—221no—
363#107C22×D1111yescharacteristic
364#107C22×D1111yescharacteristic
365#106—221no—
366#103—221no—
367#103—221no—
368#102—21no—
369#102—21no—
370#102—221no—
371#102—221no—
372#102—221no—
373#102—221no—
374C4×C8—111no—
375C4×C8—111no—
376C4×C8—111no—
377C4×C8C22×D1111yescharacteristic
378C2×C11—82no—
379C2×C11—82no—
380C2×C11C2×C4×D811yescharacteristic
381C2×C11C2×#50911yescharacteristic
382C2×C11#341411yescharacteristic
383D11—22no—
384D11—82no—
385C24—441no—
386#41—224no—
387#41—442no—
388C2×Q8—221no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—224no—
392C2×D4—221no—
393C2×D4—442no—
394C2×D4—441no—
395C2×D4—441no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—111no—
399C22×C4—111no—
400C22×C4—111no—
401C22×C4—441no—
402C22×C4—441no—
403C22×C4—441no—
404C22×C4—441no—
405C22×C4—441no—
406C22×C4—441no—
407C22×C4—884no—
408Q16—112no—
409Q16—221no—
410SD16—224no—
411D8—21no—
412D8—21no—
413D8—112no—
414D8—224no—
415D8—221no—
416D8C2×C4×D1112yes—
417D8C2×C4×D1112yescomplemented
418C2×C8—111no—
419C2×C8—112no—
420C2×C8—112no—
421C2×C8—111no—
422C2×C8—222no—
423C2×C8D4×D1111yescharacteristic
424C2×C8C23×D1111yescharacteristic
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—221no—
428C4⋊C4—221no—
429C4⋊C4—441no—
430C4⋊C4—441no—
431C4⋊C4—441no—
432C22⋊C4—41no—
433C22⋊C4—41no—
434C22⋊C4—441no—
435C22⋊C4—441no—
436C22⋊C4—441no—
437C22⋊C4—441no—
438C22⋊C4—441no—
439C42—111no—
440C42—111no—
441C42—111no—
442C42—441no—
443C42—441no—
444C42—441no—
445C42D4×D1111yescharacteristic
446C16—21no—
447C16—112no—
448C16—221no—
449C16C2×C4×D1112yescomplemented
450C11C4×#50911yescharacteristic, complemented, Sylow
451C23—41no—
452C23—41no—
453C23—111no—
454C23—444no—
455C23—441no—
456C23—882no—
457C23—882no—
458Q8—222no—
459Q8—441no—
460D4—22no—
461D4—22no—
462D4—41no—
463D4—41no—
464D4—222no—
465D4—444no—
466D4—444no—
467D4—441no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—82no—
471C2×C4—82no—
472C2×C4—111no—
473C2×C4—111no—
474C2×C4—112no—
475C2×C4—112no—
476C2×C4—111no—
477C2×C4—222no—
478C2×C4—441no—
479C2×C4—444no—
480C2×C4—441no—
481C2×C4—441no—
482C2×C4—441no—
483C2×C4—882no—
484C2×C4—882no—
485C2×C4—882no—
486C2×C4—882no—
487C2×C4—882no—
488C2×C4D8×D1111yescharacteristic
489C2×C4D8×D1111yescharacteristic
490C2×C4C2×D4×D1111yescharacteristic
491C8—21no—
492C8—112no—
493C8—221no—
494C8C22×C4×D1111yescharacteristic
495C8#41×D1111yescharacteristic
496C22—42no—
497C22—42no—
498C22—81no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22—112no—
503C22—221no—
504C22—221no—
505C22—442no—
506C22—888no—
507C22—881no—
508C22—881no—
509C22C2×D8×D1111yescharacteristic
510C4—21no—
511C4—21no—
512C4—81no—
513C4—81no—
514C4—112no—
515C4—112no—
516C4—221no—
517C4—442no—
518C4—881no—
519C4—881no—
520C4C4×D4×D1111yescharacteristic
521C4D11×#13511yescharacteristic
522C2—82no—
523C2—82no—
524C2—222no—
525C2—882no—
526C2C4×D8×D1111yescharacteristic
527C2D11×#50911yescharacteristic
528C2#1308174811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC11×#2177C2
socleC22×C11C22×D8
prime radicalC2×#10622524C2
cosocleC2×C8×C11C24
hypercenter#2177D11
hypocenterC11C4×#509
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2177

Complements

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

NH ≅ G/Ntype
2. C4×#66965C2semidirect
3. C4×D8×D11C2semidirect
4. #13070490C2semidirect
5. #13070482C2semidirect
6. #13070480C2semidirect
7. #13070471C2semidirect
8. #13070467C2semidirect
9. D16×Dic11C2semidirect
10. #13070460C2semidirect
11. #13070403C2semidirect
12. #13070330C2semidirect
13. #13070325C2semidirect
14. #13070209C2semidirect
15. C11×#2177C2semidirect
22. C4×C11×D8C22semidirect
24. D8×Dic11C22semidirect
29. #10622524C4semidirect
35. #10622486C22semidirect
41. C4×Dic44C22semidirect
44. C11×#367C22semidirect
46. C11×#357C22semidirect
47. C11×#346C22semidirect
49. #10622200C22semidirect
51. #10622142C22semidirect
52. #10622141C22semidirect
53. C16×Dic11C22semidirect
54. C16×Dic11C22semidirect
55. #10622130C22semidirect
57. #10622128C22semidirect
58. #10622127C22semidirect
59. #10622099C22semidirect
75. #66965C2×C4semidirect
77. D8×D11C2×C4semidirect
93. C11×D16C2×C4semidirect
103. #66891C2×C4semidirect
104. #66890C2×C4semidirect
118. #66864C2×C4semidirect
120. #66862C2×C4semidirect
148. C11×D8C22×C4semidirect
177. Dic44C22×C4semidirect
184. C11×C16C22×C4semidirect
186. C11⋊C16C22×C4semidirect
191. #2177D11semidirect
269. C4×D8C2×D11semidirect
276. #367C2×D11semidirect
286. #357C2×D11semidirect
288. #346C2×D11semidirect
316. Dic11#509semidirect
353. D16C4×D11semidirect
417. D8C2×C4×D11semidirect
449. C16C2×C4×D11semidirect
450. C11C4×#509semidirect

Maximal subgroups

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

subgroupindex
C2×#106225242
C4×#669652
C4×D8×D112
#130704902
#130704822
#130704802
#130704712
#130704672
D16×Dic112
#130704602
#130704032
#130703302
#130703252
#130702092
C11×#21772
C4×#50911