Finite Group Databasebeta

← #471×D61 #21455514

Subgroups — #471×D61 #21455514

Order 7808.

468 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#137×D61C211yesmaximal, characteristic, complemented
2AGL(1,ℤ/8)×D61C211yesmaximal, characteristic
3C2×SD16×D61C211yesmaximal, characteristic, complemented
4#131×D61C211yesmaximal, characteristic, complemented
5#16840028C211yesmaximal, characteristic, complemented
6#16840027C211yesmaximal, characteristic, complemented
7#16840026C211yesmaximal, characteristic, complemented
8#16840025C211yesmaximal, characteristic, complemented
9#16840024C211yesmaximal, characteristic, complemented
10#16840023C211yesmaximal, characteristic, complemented
11#16840022C211yesmaximal, characteristic, complemented
12#108×D61C211yesmaximal, characteristic, complemented
13#101×D61C211yesmaximal, characteristic, complemented
14#100×D61C211yesmaximal, characteristic, complemented
15C61×#471C211yesmaximal, characteristic, complemented
16#41×D61C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic
18C2×D4×D61C2211yescharacteristic
19#14519810C2211yescharacteristic, complemented
20#14519809—21no—
21#14519808C2211yescharacteristic, complemented
22#14519807C2211yescharacteristic, complemented
23#14519806—21no—
24#14519805C2211yescharacteristic
25#14519804—21no—
26#14519803C2211yescharacteristic
27#14519802C2211yescharacteristic
28#14519801—21no—
29Q16×D61—21no—
30C2×#11758190C2211yescharacteristic, complemented
31C2×#11758200C2211yescharacteristic, complemented
32C2×#11758201C2211yescharacteristic, complemented
33SD16×D61—21no—
34SD16×D61—21no—
35SD16×D61—21no—
36SD16×D61—21no—
37SD16×D61—21no—
38SD16×D61—21no—
39D8×D61—21no—
40#14519785—21no—
41#14519785C2211yescharacteristic, complemented
42#14519784C2211yescharacteristic, complemented
43#14519783—21no—
44#14519783C2211yescharacteristic, complemented
45M16×D61—21no—
46M16×D61C2211yescharacteristic
47M16×D61C2211yescharacteristic
48M16×D61C2211yescharacteristic
49C2×C8×D61—21no—
50C2×C8×D61C2211yescharacteristic
51#14519713C2211yescharacteristic, complemented
52#14519712C2211yescharacteristic, complemented
53#14519712C2211yescharacteristic, complemented
54#14519696C2211yescharacteristic, complemented
55#14519695C2211yescharacteristic, complemented
56#14519695C2211yescharacteristic, complemented
57#14519694C2211yescharacteristic, complemented
58#14519693C2211yescharacteristic, complemented
59#14519693C2211yescharacteristic, complemented
60#137×C61C2211yescharacteristic, complemented
61AGL(1,ℤ/8)×C61C2211yescharacteristic
62C2×SD16×C61C2211yescharacteristic, complemented
63#131×C61C2211yescharacteristic, complemented
64#108×C61C2211yescharacteristic, complemented
65#101×C61C2211yescharacteristic, complemented
66#100×C61C2211yescharacteristic, complemented
67C23×D61—21no—
68#41×C61C2311yescharacteristic
69C2×Q8×C61C2311yescharacteristic
70C2×D4×C61C2311yescharacteristic
71C2×C22⋊D61—21no—
72#11758226D411yescharacteristic
73Q8×D61—21no—
74Q8×D61—21no—
75Q8×D61—21no—
76Q8×D61—21no—
77Q8×D61D411yescharacteristic
78#11758224—21no—
79#11758224D411yescharacteristic
80D4×D61—21no—
81D4×D61—21no—
82D4×D61—21no—
83D4×D61—21no—
84D4×D61—21no—
85D4×D61D411yescharacteristic
86#11758222—21no—
87#11758222C2311yescharacteristic
88C2×D244C2311yescharacteristic
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61C2311yescharacteristic
92C2×Dic122—21no—
93C2×Dic122C2311yescharacteristic
94Q16×C61—21no—
95SD16×C61—21no—
96SD16×C61—21no—
97SD16×C61—21no—
98SD16×C61—21no—
99D8×C61—21no—
100M16×C61—21no—
101M16×C61C2311yescharacteristic
102M16×C61C2311yescharacteristic
103M16×C61C2311yescharacteristic
104C2×C8×C61—21no—
105C2×C8×C61C2311yescharacteristic
106#11758202—21no—
107#11758202—21no—
108#11758201—21no—
109#11758201—21no—
110#11758201—21no—
111#11758201—21no—
112#11758200—21no—
113#11758200—21no—
114#11758200—21no—
115#11758200—21no—
116#11758199—21no—
117#11758199—21no—
118#11758194—21no—
119#11758194C2311yescharacteristic
120#11758194C2311yescharacteristic
121#11758194C2311yescharacteristic
122C2×#92418—21no—
123C2×#92418C2311yescharacteristic
124Dic244—21no—
125D488—21no—
126#11758190—21no—
127#11758190—21no—
128#11758190—21no—
129#11758190—21no—
130#11758189—21no—
131#11758189—21no—
132#11758189—21no—
133#11758189—21no—
134#11758189—21no—
135C8×D61—21no—
136C8×D61—21no—
137C8×D61—21no—
138C8×D61—21no—
139C8×D61—21no—
140C8×D61D411yescharacteristic
141C8×D61D411yescharacteristic
142C8×D61D411yescharacteristic
143C8×D61D411yescharacteristic
144C23×C61—21no—
145C22×D61—21no—
146C22×D61—21no—
147C22×D61—41no—
148C22×D61—41no—
149C22×D61—82no—
150C22×D61#4111yescharacteristic
151Q8×C61—21no—
152Q8×C61—21no—
153Q8×C61C2×D411yescharacteristic
154D4×C61—21no—
155D4×C61—21no—
156D4×C61—21no—
157D4×C61C2×D411yescharacteristic
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61C2411yescharacteristic
161C22⋊D61—21no—
162C22⋊D61—21no—
163C22⋊D61—21no—
164C22⋊D61—41no—
165C22⋊D61—41no—
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61#4111yescharacteristic
169D244—21no—
170D244—21no—
171D244—21no—
172D244C2×D411yescharacteristic
173C4×D61—21no—
174C4×D61—21no—
175C4×D61—21no—
176C4×D61—41no—
177C4×D61—41no—
178C4×D61C2×D411yescharacteristic
179C4×D61C2×D411yescharacteristic
180C4×D61C2×D411yescharacteristic
181C4×D61C2×D411yescharacteristic
182Dic122—21no—
183Dic122—21no—
184Dic122—21no—
185Dic122—41no—
186Dic122—41no—
187Dic122C2×D411yescharacteristic
188C8×C61—21no—
189C8×C61—21no—
190C8×C61—21no—
191C8×C61C2×D411yescharacteristic
192C8×C61C2×D411yescharacteristic
193#92418—21no—
194#92418—21no—
195#92418—21no—
196#92418C2×D411yescharacteristic
197#92418C2×D411yescharacteristic
198C22×C61—21no—
199C22×C61—41no—
200C22×C61—81no—
201C22×C61C2×#4111yescharacteristic
202C2×D61—22no—
203C2×D61—21no—
204C2×D61—42no—
205C2×D61—41no—
206C2×D61—82no—
207C2×D61—82no—
208C2×D61—81no—
209C2×D61#12111yescharacteristic
210C2×D61#12111yescharacteristic
211C4×C61—21no—
212C4×C61—41no—
213C4×C61C22×D411yescharacteristic
214C4×C61C22×D411yescharacteristic
215Dic61—21no—
216Dic61—41no—
217Dic61#12111yescharacteristic
218Dic61#12111yescharacteristic
219C2×#471—611nomaximal, Sylow
220C2×C61—21no—
221C2×C61—41no—
222C2×C61—81no—
223C2×C61C2×#12111yescharacteristic
224D61—21no—
225D61—41no—
226D61—81no—
227D61#47112yesdirect product factor
228C2×#137—611no—
229C2×AGL(1,ℤ/8)—611no—
230C22×SD16—611no—
231C2×#131—611no—
232#471—611no—
233#471—611no—
234#471—611no—
235#471—611no—
236#471—611no—
237#471—611no—
238#471—611no—
239#471D6111yescharacteristic, direct product factor
240C2×#108—611no—
241C2×#101—611no—
242C2×#100—611no—
243C61C2×#47111yescharacteristic, complemented, Sylow
244C2×#41—611no—
245C22×Q8—611no—
246C22×D4—611no—
247#137—611no—
248#137—611no—
249#137—611no—
250#137—1221no—
251#137—1221no—
252#137C2×D6111yescharacteristic, complemented
253AGL(1,ℤ/8)—611no—
254AGL(1,ℤ/8)—611no—
255AGL(1,ℤ/8)—611no—
256AGL(1,ℤ/8)—1221no—
257AGL(1,ℤ/8)—1221no—
258AGL(1,ℤ/8)C2×D6111yescharacteristic
259C2×Q16—1221no—
260C2×SD16—611no—
261C2×SD16—611no—
262C2×SD16—611no—
263C2×SD16—1221no—
264C2×SD16—1221no—
265C2×SD16—1221no—
266C2×SD16—1221no—
267C2×SD16—1221no—
268C2×SD16—1221no—
269C2×SD16C2×D6111yescharacteristic, complemented
270C2×D8—1221no—
271#131—611no—
272#131—611no—
273#131—611no—
274#131—1221no—
275#131—1221no—
276#131C2×D6111yescharacteristic, complemented
277C2×M16—611no—
278C2×M16—611no—
279C2×M16—611no—
280C2×M16—1221no—
281C22×C8—611no—
282C22×C8—1221no—
283#108—611no—
284#108—611no—
285#108—611no—
286#108C2×D6111yescharacteristic, complemented
287#101—611no—
288#101—611no—
289#101—611no—
290#101C2×D6111yescharacteristic, complemented
291#100—611no—
292#100—611no—
293#100—611no—
294#100C2×D6111yescharacteristic, complemented
295C24—1221no—
296#41—611no—
297#41—611no—
298#41—611no—
299#41—1221no—
300#41—1221no—
301#41C22×D6111yescharacteristic
302C2×Q8—611no—
303C2×Q8—611no—
304C2×Q8—1221no—
305C2×Q8—1221no—
306C2×Q8—1221no—
307C2×Q8—1221no—
308C2×Q8—1221no—
309C2×Q8C22×D6111yescharacteristic
310C2×D4—611no—
311C2×D4—611no—
312C2×D4—1221no—
313C2×D4—1221no—
314C2×D4—1221no—
315C2×D4—1221no—
316C2×D4—1221no—
317C2×D4—1221no—
318C2×D4C22×D6111yescharacteristic
319C22×C4—611no—
320C22×C4—1221no—
321C22×C4—1221no—
322Q16—21no—
323Q16—1221no—
324Q16—1221no—
325Q16—1221no—
326SD16—21no—
327SD16—21no—
328SD16—21no—
329SD16—21no—
330SD16—1221no—
331SD16—1221no—
332SD16—1221no—
333SD16—1221no—
334SD16—1221no—
335SD16—1221no—
336SD16—1221no—
337SD16—1221no—
338SD16—1221no—
339SD16—1221no—
340SD16—1221no—
341SD16—1221no—
342D8—21no—
343D8—1221no—
344D8—1221no—
345D8—1221no—
346M16—21no—
347M16—611no—
348M16—611no—
349M16—611no—
350M16—1221no—
351M16—1221no—
352M16—1221no—
353M16—1221no—
354M16—1221no—
355M16—1221no—
356M16C22×D6111yescharacteristic
357M16C22×D6111yescharacteristic
358M16C22×D6111yescharacteristic
359C2×C8—21no—
360C2×C8—611no—
361C2×C8—611no—
362C2×C8—611no—
363C2×C8—611no—
364C2×C8—611no—
365C2×C8—1221no—
366C2×C8—1221no—
367C2×C8—1221no—
368C2×C8—1221no—
369C2×C8—1221no—
370C2×C8—1221no—
371C2×C8C22×D6111yescharacteristic
372C23—21no—
373C23—611no—
374C23—1221no—
375C23—1221no—
376C23—4882no—
377C23—2441no—
378C23—2441no—
379Q8—21no—
380Q8—21no—
381Q8—611no—
382Q8—1221no—
383Q8—1221no—
384Q8—1221no—
385Q8—2441no—
386Q8—2441no—
387Q8D4×D6111yescharacteristic
388D4—21no—
389D4—21no—
390D4—21no—
391D4—611no—
392D4—1221no—
393D4—1221no—
394D4—1221no—
395D4—1221no—
396D4—1221no—
397D4—1221no—
398D4—2441no—
399D4—2441no—
400D4D4×D6111yescharacteristic
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—611no—
404C2×C4—611no—
405C2×C4—611no—
406C2×C4—611no—
407C2×C4—611no—
408C2×C4—1221no—
409C2×C4—1221no—
410C2×C4—1221no—
411C2×C4—1221no—
412C2×C4—1221no—
413C2×C4—2441no—
414C2×C4—2441no—
415C2×C4C23×D6111yescharacteristic
416C8—21no—
417C8—21no—
418C8—21no—
419C8—611no—
420C8—611no—
421C8—1221no—
422C8—1221no—
423C8—1221no—
424C8D4×D6111yescharacteristic
425C8D4×D6111yescharacteristic
426C22—21no—
427C22—41no—
428C22—81no—
429C22—611no—
430C22—611no—
431C22—1222no—
432C22—1221no—
433C22—4881no—
434C22—4882no—
435C22—4882no—
436C22—2442no—
437C22—2441no—
438C22#41×D6111yescharacteristic
439C4—21no—
440C4—41no—
441C4—611no—
442C4—611no—
443C4—1221no—
444C4—2441no—
445C4C2×D4×D6111yescharacteristic
446C4C2×D4×D6111yescharacteristic
447C2—21no—
448C2—41no—
449C2—81no—
450C2—612no—
451C2—1221no—
452C2—4881no—
453C2—2441no—
454C2#121×D6111yescharacteristic
subgroupG/H
centerC2#121×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#471C2
socleC2×C61C2×#121
hypercenter#471D61
hypocenterC61C2×#471
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #137×D61C2semidirect
3. C2×SD16×D61C2semidirect
4. #131×D61C2semidirect
5. #16840028C2semidirect
6. #16840027C2semidirect
7. #16840026C2semidirect
8. #16840025C2semidirect
9. #16840024C2semidirect
10. #16840023C2semidirect
11. #16840022C2semidirect
12. #108×D61C2semidirect
13. #101×D61C2semidirect
14. #100×D61C2semidirect
15. C61×#471C2semidirect
19. #14519810C22semidirect
21. #14519808C22semidirect
22. #14519807C22semidirect
30. C2×#11758190C22semidirect
31. C2×#11758200C22semidirect
32. C2×#11758201C22semidirect
41. #14519785C22semidirect
42. #14519784C22semidirect
44. #14519783C22semidirect
51. #14519713C22semidirect
52. #14519712C22semidirect
53. #14519712C22semidirect
54. #14519696C22semidirect
55. #14519695C22semidirect
56. #14519695C22semidirect
57. #14519694C22semidirect
58. #14519693C22semidirect
59. #14519693C22semidirect
60. #137×C61C22semidirect
62. C2×SD16×C61C22semidirect
63. #131×C61C22semidirect
64. #108×C61C22semidirect
65. #101×C61C22semidirect
66. #100×C61C22semidirect
227. D61#471direct (N × H)
239. #471D61direct (N × H)
243. C61C2×#471semidirect
252. #137C2×D61semidirect
269. C2×SD16C2×D61semidirect
276. #131C2×D61semidirect
286. #108C2×D61semidirect
290. #101C2×D61semidirect
294. #100C2×D61semidirect