Finite Group Databasebeta

← #13077918

Subgroups — #13077918

Order 1408.

764 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#67042C211yesmaximal, characteristic, complemented
2C2×#66969C211yesmaximal, characteristic, complemented
3C2×#66964C211yesmaximal, characteristic, complemented
4#10623139C211yesmaximal, characteristic, complemented
5C11×#449C211yesmaximal, characteristic, complemented
6#10622852C211yesmaximal, characteristic, complemented
7#10622785C211yesmaximal, characteristic, complemented
8#10622769C211yesmaximal, characteristic, complemented
9#10622649C211yesmaximal, characteristic, complemented
10#10622423C211yesmaximal, characteristic, complemented
11#10622416C211yesmaximal, characteristic, complemented
12#10622389C211yesmaximal, characteristic, complemented
13D11×#102C211yesmaximal, characteristic, complemented
14#10622344C211yesmaximal, characteristic, complemented
15#10622340C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17#67042—24no—
18#67042—24no—
19C2×#4343C2211yescharacteristic
20C2×#4343C2211yescharacteristic
21C2×#4341C2211yescharacteristic, complemented
22C2×D4×D11—21no—
23C2×D4×D11—21no—
24C2×D4×D11C2211yescharacteristic
25C2×D4×D11C2211yescharacteristic
26C2×#4339—21no—
27C2×#4339C2211yescharacteristic
28C22×D44—21no—
29C22×D44C2211yescharacteristic
30C2×C11×SD16C2211yescharacteristic, complemented
31C2×C11×D8C2211yescharacteristic, complemented
32C11×#121C2211yescharacteristic, complemented
33C2×#4326C2211yescharacteristic, complemented
34#66992—21no—
35#66991—21no—
36#66991C2211yescharacteristic, complemented
37C2×#4324C2211yescharacteristic, complemented
38C2×#4323C2211yescharacteristic, complemented
39C2×#4323C2211yescharacteristic, complemented
40#66977C2211yescharacteristic, complemented
41#66969—24no—
42#66964—24no—
43C2×#4314C2211yescharacteristic, complemented
44C2×#4314C2211yescharacteristic, complemented
45C2×#4313C2211yescharacteristic, complemented
46C2×C8×D11C2211yescharacteristic, complemented
47#66950C2211yescharacteristic, complemented
48C4⋊C4×D11C2211yescharacteristic, complemented
49#66937—21no—
50#66931—21no—
51C11×#103C2211yescharacteristic, complemented
52C11×#102C2211yescharacteristic, complemented
53C11×C22⋊C8C2211yescharacteristic, complemented
54#66899C2211yescharacteristic, complemented
55#66896C2211yescharacteristic, complemented
56C22⋊(C11⋊C8)C2211yescharacteristic, complemented
57#66885C2211yescharacteristic, complemented
58#66885C2211yescharacteristic, complemented
59(C2×D11)⋊C8C2211yescharacteristic, complemented
60(C2×D11)⋊C8C2211yescharacteristic, complemented
61#66873C2211yescharacteristic, complemented
62#66873C2211yescharacteristic, complemented
63C23×D11—21no—
64C23×D11—21no—
65C23×D11—21no—
66C11×#41—22no—
67C11×#41—22no—
68C2×Q8×C11C2311yescharacteristic
69C2×D4×C11—21no—
70C2×D4×C11—21no—
71C2×D4×C11C2311yescharacteristic
72C2×D4×C11C2311yescharacteristic
73C22×C4×C11—21no—
74C22×C4×C11C2311yescharacteristic
75C2×C22⋊D11—21no—
76C2×C22⋊D11—21no—
77C2×C22⋊D11—21no—
78C2×C22⋊D11—21no—
79C2×C22⋊D11D411yescharacteristic
80C2×C22⋊D11D411yescharacteristic
81C22×Dic11—21no—
82#4343—22no—
83#4343—22no—
84#4343—22no—
85#4343D414yescomplemented
86#4341—22no—
87#4341—22no—
88D4×D11—28no—
89D4×D11—28no—
90D4×D11—22no—
91D4×D11—22no—
92D4×D11—22no—
93D4×D11D414yescomplemented
94#4339—28no—
95#4339—22no—
96#4339—22no—
97C2×D44—28no—
98C2×D44—22no—
99C2×D44—22no—
100C2×D44—21no—
101C2×D44—21no—
102C2×D44—21no—
103C2×D44D411yescharacteristic
104C2×D44C2311yescharacteristic
105C2×D44C2311yescharacteristic
106C2×C4×D11—21no—
107C2×C4×D11—21no—
108C2×C4×D11—21no—
109C2×C4×D11C2311yescharacteristic
110C2×C4×D11C2311yescharacteristic
111C2×Dic22D411yescharacteristic
112C2×Dic22C2311yescharacteristic
113C11×SD16—22no—
114C11×D8—22no—
115C2×C8×C11C2311yescharacteristic
116C2×C8×C11C2311yescharacteristic
117C11×C4⋊C4C2311yescharacteristic
118C11×C22⋊C4—21no—
119C22⋊Dic11—21no—
120C22⋊Dic11—21no—
121#4326—22no—
122#4324—22no—
123#4323—22no—
124#4323—22no—
125(C2×D11)⋊C4—21no—
126C4⋊Dic11—21no—
127C4⋊Dic11C2311yescharacteristic
128Dic11⋊C4—21no—
129Dic11⋊C4—21no—
130C2×C11⋊C8C2311yescharacteristic
131C2×C11⋊C8C2311yescharacteristic
132#4314—22no—
133#4314—22no—
134#4313—22no—
135C8×D11—22no—
136#3012—111nomaximal, Sylow
137C23×C11—21no—
138C23×C11—21no—
139C23×C11C2×D411yescharacteristic
140C22×D11—21no—
141C22×D11—21no—
142C22×D11—24no—
143C22×D11—24no—
144C22×D11—24no—
145C22×D11—81no—
146C22×D11—81no—
147C22×D11—81no—
148C22×D11—81no—
149C22×D11—81no—
150C22×D11—81no—
151C22×D11C2×D411yescharacteristic
152C22×D11C2×D411yescharacteristic
153Q8×C11—21no—
154Q8×C11C2×D412yes—
155D4×C11—24no—
156D4×C11—21no—
157D4×C11—21no—
158D4×C11—21no—
159D4×C11—81no—
160D4×C11C2×D412yes—
161C2×C4×C11—24no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11C2×D411yescharacteristic
167C2×C4×C11C2411yescharacteristic
168C22⋊D11—24no—
169C22⋊D11—22no—
170C22⋊D11—22no—
171C22⋊D11—24no—
172C22⋊D11—42no—
173C22⋊D11—81no—
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—42no—
177C2×Dic11C2×D411yescharacteristic
178C2×Dic11C2×D411yescharacteristic
179D44—24no—
180D44—24no—
181D44—22no—
182D44—24no—
183D44—21no—
184D44—21no—
185D44C2×D412yes—
186D44C2×D412yes—
187C4×D11—24no—
188C4×D11—21no—
189C4×D11—21no—
190C4×D11—24no—
191C4×D11—81no—
192C4×D11C2×D412yes—
193C4×D11C2×D412yes—
194Dic22—22no—
195Dic22—21no—
196Dic22—21no—
197C8×C11—21no—
198C8×C11—21no—
199C11⋊C8—21no—
200C11⋊C8—21no—
201C2×H(5,𝔽2)—111no—
202C2×AGL(1,ℤ/8)—111no—
203C2×#135—111no—
204#537—111no—
205#452—111no—
206#452—111no—
207#450—111no—
208#450—111no—
209#449—111no—
210#449D1111yescharacteristic, complemented
211#447—111no—
212#447—111no—
213#417—111no—
214C2×#102—111no—
215#408—111no—
216C22×C11—21no—
217C22×C11—22no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—41no—
221C22×C11—41no—
222C22×C11—41no—
223C22×C11—41no—
224C22×C11—41no—
225C22×C11C22×D411yescharacteristic
226C2×D11—21no—
227C2×D11—21no—
228C2×D11—22no—
229C2×D11—22no—
230C2×D11—21no—
231C2×D11—21no—
232C2×D11—21no—
233C2×D11—41no—
234C2×D11—41no—
235C2×D11—41no—
236C2×D11—41no—
237C2×D11—84no—
238C2×D11—84no—
239C2×D11—84no—
240C2×D11#12012yes—
241C4×C11—21no—
242C4×C11—22no—
243C4×C11—41no—
244C4×C11C22×D411yescharacteristic
245C4×C11C22×D411yescharacteristic
246Dic11—21no—
247Dic11—41no—
248Dic11—41no—
249Dic11#12012yes—
250H(5,𝔽2)—224no—
251H(5,𝔽2)—224no—
252C2×#41—111no—
253C2×#41—111no—
254C2×#41—111no—
255C2×#41—111no—
256C2×#41—221no—
257C2×#41C2×D1111yescharacteristic
258C22×D4—111no—
259C22×D4—111no—
260C22×D4—111no—
261C22×D4—221no—
262C22×D4—221no—
263C22×D4—221no—
264AGL(1,ℤ/8)—224no—
265#135—224no—
266C2×Q16—111no—
267C2×SD16—111no—
268C2×SD16—111no—
269C2×SD16—111no—
270C2×SD16C2×D1111yescharacteristic, complemented
271C2×D8—111no—
272C2×D8—111no—
273C2×D8C2×D1111yescharacteristic, complemented
274C2×M16—111no—
275C22×C8—111no—
276C22⋊Q8—111no—
277C22⋊Q8—111no—
278C22⋊Q8—221no—
279#121—111no—
280#121—221no—
281#121—221no—
282#121—221no—
283#121C2×D1111yescharacteristic, complemented
284C2×C4⋊C4—111no—
285#103—111no—
286#103C2×D1111yescharacteristic, complemented
287#102—111no—
288#102—111no—
289#102—111no—
290#102—111no—
291#102—111no—
292#102C2×D1111yescharacteristic, complemented
293C22⋊C8—111no—
294C22⋊C8—111no—
295C22⋊C8—111no—
296C22⋊C8C2×D1111yescharacteristic, complemented
297C2×C11—41no—
298C2×C11—42no—
299C2×C11—81no—
300C2×C11C2×#12011yescharacteristic
301C2×C11#57611yescharacteristic
302C2×C11#57711yescharacteristic
303D11—22no—
304D11—41no—
305D11—42no—
306D11—42no—
307C24—221no—
308C24—221no—
309C24—221no—
310#41—22no—
311#41—22no—
312#41—114no—
313#41—222no—
314#41—222no—
315#41—228no—
316#41—222no—
317#41—222no—
318#41—222no—
319#41—222no—
320#41—222no—
321C2×Q8—111no—
322C2×Q8—111no—
323C2×Q8C22×D1111yescharacteristic
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—114no—
327C2×D4—111no—
328C2×D4—111no—
329C2×D4—111no—
330C2×D4—111no—
331C2×D4—111no—
332C2×D4—222no—
333C2×D4—222no—
334C2×D4—221no—
335C2×D4—221no—
336C2×D4—228no—
337C2×D4—222no—
338C2×D4—221no—
339C2×D4—221no—
340C2×D4—222no—
341C2×D4—228no—
342C2×D4—228no—
343C2×D4—222no—
344C2×D4—221no—
345C2×D4—221no—
346C2×D4—221no—
347C2×D4C22×D1111yescharacteristic
348C2×D4C22×D1111yescharacteristic
349C22×C4—21no—
350C22×C4—111no—
351C22×C4—111no—
352C22×C4—221no—
353C22×C4—221no—
354C22×C4—221no—
355C22×C4—221no—
356C22×C4C22×D1111yescharacteristic
357Q16—222no—
358SD16—22no—
359SD16—222no—
360SD16—222no—
361SD16—222no—
362D8—22no—
363D8—222no—
364D8—222no—
365M16—222no—
366C2×C8—111no—
367C2×C8—111no—
368C2×C8—222no—
369C2×C8C22×D1111yescharacteristic
370C2×C8C22×D1111yescharacteristic
371C4⋊C4—111no—
372C4⋊C4—221no—
373C4⋊C4—221no—
374C4⋊C4—221no—
375C4⋊C4C22×D1111yescharacteristic
376C22⋊C4—21no—
377C22⋊C4—221no—
378C22⋊C4—221no—
379C22⋊C4—221no—
380C11#301211yescharacteristic, complemented, Sylow
381C23—21no—
382C23—21no—
383C23—111no—
384C23—111no—
385C23—224no—
386C23—224no—
387C23—224no—
388C23—221no—
389C23—221no—
390C23—881no—
391C23—881no—
392C23—881no—
393C23—881no—
394C23—881no—
395C23—881no—
396C23D4×D1111yescharacteristic
397Q8—21no—
398Q8—222no—
399Q8—221no—
400Q8—221no—
401Q8D4×D1112yes—
402D4—24no—
403D4—21no—
404D4—21no—
405D4—21no—
406D4—81no—
407D4—112no—
408D4—112no—
409D4—222no—
410D4—224no—
411D4—224no—
412D4—224no—
413D4—222no—
414D4—224no—
415D4—222no—
416D4—224no—
417D4—221no—
418D4—221no—
419D4—442no—
420D4—881no—
421D4D4×D1112yes—
422C2×C4—24no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—111no—
428C2×C4—112no—
429C2×C4—112no—
430C2×C4—111no—
431C2×C4—224no—
432C2×C4—224no—
433C2×C4—221no—
434C2×C4—221no—
435C2×C4—221no—
436C2×C4—221no—
437C2×C4—442no—
438C2×C4—881no—
439C2×C4D4×D1111yescharacteristic
440C2×C4C23×D1111yescharacteristic
441C8—21no—
442C8—21no—
443C8—221no—
444C8—221no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—22no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—112no—
455C22—221no—
456C22—221no—
457C22—221no—
458C22—221no—
459C22—222no—
460C22—222no—
461C22—221no—
462C22—441no—
463C22—441no—
464C22—441no—
465C22—441no—
466C22—884no—
467C22—884no—
468C22—884no—
469C22C2×D4×D1111yescharacteristic
470C4—21no—
471C4—22no—
472C4—41no—
473C4—112no—
474C4—221no—
475C4—441no—
476C4—441no—
477C4C2×D4×D1111yescharacteristic
478C4C2×D4×D1111yescharacteristic
479C2—41no—
480C2—42no—
481C2—81no—
482C2—222no—
483C2—441no—
484C2—442no—
485C2—442no—
486C2D11×#12011yescharacteristic
487C2#1062330111yescharacteristic
488C2#1062330511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#449C2
socleC22×C11C22×D4
hypercenter#449D11
hypocenterC11#3012
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#67042C2semidirect
2. C2×#66969C2semidirect
3. C2×#66964C2semidirect
4. #10623139C2semidirect
5. C11×#449C2semidirect
6. #10622852C2semidirect
7. #10622785C2semidirect
8. #10622769C2semidirect
9. #10622649C2semidirect
10. #10622423C2semidirect
11. #10622416C2semidirect
12. #10622389C2semidirect
13. D11×#102C2semidirect
14. #10622344C2semidirect
15. #10622340C2semidirect
21. C2×#4341C22semidirect
30. C2×C11×SD16C22semidirect
31. C2×C11×D8C22semidirect
32. C11×#121C22semidirect
33. C2×#4326C22semidirect
36. #66991C22semidirect
37. C2×#4324C22semidirect
38. C2×#4323C22semidirect
39. C2×#4323C22semidirect
40. #66977C22semidirect
43. C2×#4314C22semidirect
44. C2×#4314C22semidirect
45. C2×#4313C22semidirect
46. C2×C8×D11C22semidirect
47. #66950C22semidirect
48. C4⋊C4×D11C22semidirect
51. C11×#103C22semidirect
52. C11×#102C22semidirect
53. C11×C22⋊C8C22semidirect
54. #66899C22semidirect
55. #66896C22semidirect
56. C22⋊(C11⋊C8)C22semidirect
57. #66885C22semidirect
58. #66885C22semidirect
59. (C2×D11)⋊C8C22semidirect
60. (C2×D11)⋊C8C22semidirect
61. #66873C22semidirect
62. #66873C22semidirect
85. #4343D4semidirect
93. D4×D11D4semidirect
210. #449D11semidirect
270. C2×SD16C2×D11semidirect
273. C2×D8C2×D11semidirect
283. #121C2×D11semidirect
286. #103C2×D11semidirect
292. #102C2×D11semidirect
296. C22⋊C8C2×D11semidirect
380. C11#3012semidirect

Maximal subgroups

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

subgroupindex
C2×#670422
C2×#669692
C2×#669642
#106231392
C11×#4492
#106228522
#106227852
#106227692
#106226492
#106224232
#106224162
#106223892
D11×#1022
#106223442
#106223402
#301211