Finite Group Databasebeta

← #21455545

Subgroups — #21455545

Order 7808.

466 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840558C211yesmaximal, characteristic, complemented
2C2×#14519801C211yesmaximal, characteristic, complemented
3AGL(1,ℤ/8)×D61C211yesmaximal, characteristic, complemented
4#16840527C211yesmaximal, characteristic, complemented
5#16840031C211yesmaximal, characteristic, complemented
6#16840030C211yesmaximal, characteristic, complemented
7#16840029C211yesmaximal, characteristic, complemented
8#16840026C211yesmaximal, characteristic, complemented
9#16840025C211yesmaximal, characteristic, complemented
10#16840024C211yesmaximal, characteristic, complemented
11#16840023C211yesmaximal, characteristic, complemented
12#16839809C211yesmaximal, characteristic, complemented
13#16839743C211yesmaximal, characteristic, complemented
14#100×D61C211yesmaximal, characteristic, complemented
15C61×#472C211yesmaximal, characteristic, complemented
16C2×#11758224C2211yescharacteristic
17#41×D61C2211yescharacteristic
18C2×D4×D61C2211yescharacteristic
19#14519810C2211yescharacteristic, complemented
20#14519807C2211yescharacteristic, complemented
21#14519806—21no—
22#14519805C2211yescharacteristic
23#14519804—21no—
24#14519803C2211yescharacteristic
25#14519803C2211yescharacteristic, complemented
26#14519802C2211yescharacteristic
27#14519801—21no—
28#14519801—21no—
29#14519801—21no—
30#14519801—21no—
31#14519801—21no—
32#14519801—21no—
33#14519798—21no—
34#14519796—21no—
35C2×#11758190C2211yescharacteristic, complemented
36C2×#11758200C2211yescharacteristic, complemented
37SD16×D61—21no—
38C2×#11758199C2211yescharacteristic, complemented
39D8×D61—21no—
40#14519785—21no—
41#14519785C2211yescharacteristic, complemented
42#14519784C2211yescharacteristic, complemented
43#14519783—21no—
44#14519783C2211yescharacteristic, complemented
45C2×#11758189—21no—
46C2×#11758189C2211yescharacteristic
47M16×D61—21no—
48M16×D61C2211yescharacteristic
49M16×D61C2211yescharacteristic
50M16×D61C2211yescharacteristic
51#14519713C2211yescharacteristic, complemented
52#14519712C2211yescharacteristic, complemented
53#14519712C2211yescharacteristic, complemented
54#14519695C2211yescharacteristic, complemented
55#14519695C2211yescharacteristic, complemented
56#14519694C2211yescharacteristic, complemented
57#14519694C2211yescharacteristic, complemented
58#14519693C2211yescharacteristic, complemented
59#14519693C2211yescharacteristic, complemented
60AGL(1,ℤ/8)×C61C2211yescharacteristic
61AGL(1,ℤ/8)×C61C2211yescharacteristic, complemented
62C2×D8×C61C2211yescharacteristic, complemented
63#131×C61C2211yescharacteristic, complemented
64#108×C61C2211yescharacteristic, complemented
65#100×C61C2211yescharacteristic, complemented
66#100×C61C2211yescharacteristic, complemented
67C23×D61—21no—
68#41×C61C2311yescharacteristic
69C2×D4×C61C2311yescharacteristic
70C2×D4×C61C2311yescharacteristic
71C2×C22⋊D61—21no—
72C2×C22⋊D61—21no—
73C22×Dic61—21no—
74#11758226D411yescharacteristic
75Q8×D61D411yescharacteristic
76#11758224—21no—
77#11758224—21no—
78#11758224—21no—
79#11758224—21no—
80#11758224—21no—
81#11758224D411yescharacteristic
82D4×D61—21no—
83D4×D61—21no—
84D4×D61—21no—
85D4×D61—21no—
86D4×D61—21no—
87D4×D61D411yescharacteristic
88#11758222—21no—
89#11758222C2311yescharacteristic
90C2×D244C2311yescharacteristic
91C2×C4×D61—21no—
92C2×C4×D61C2311yescharacteristic
93C2×Dic122C2311yescharacteristic
94SD16×C61—21no—
95SD16×C61—21no—
96D8×C61—21no—
97D8×C61—21no—
98D8×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#11758201—21no—
108#11758200—21no—
109#11758200—21no—
110#11758200—21no—
111#11758200—21no—
112#11758200—21no—
113#11758199—21no—
114#11758199—21no—
115#11758199—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—
135#11758189D411yescharacteristic
136#11758189D411yescharacteristic
137#11758189D411yescharacteristic
138#11758189D411yescharacteristic
139C8×D61—21no—
140C8×D61—21no—
141C8×D61—21no—
142C8×D61—21no—
143C8×D61—21no—
144C23×C61—21no—
145C23×C61—21no—
146C22×D61—21no—
147C22×D61—21no—
148C22×D61—41no—
149C22×D61—41no—
150C22×D61—82no—
151C22×D61#4111yescharacteristic
152Q8×C61C2×D411yescharacteristic
153D4×C61—21no—
154D4×C61—21no—
155D4×C61—21no—
156D4×C61—21no—
157D4×C61—21no—
158D4×C61C2×D411yescharacteristic
159C2×C4×C61—21no—
160C2×C4×C61C2411yescharacteristic
161C22⋊D61—21no—
162C22⋊D61—21no—
163C22⋊D61—21no—
164C22⋊D61—41no—
165C22⋊D61—41no—
166C22⋊D61—41no—
167C22⋊D61—41no—
168C2×Dic61—21no—
169C2×Dic61—21no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61#4111yescharacteristic
173D244—21no—
174D244—21no—
175D244—21no—
176D244C2×D411yescharacteristic
177C4×D61—21no—
178C4×D61—21no—
179C4×D61—21no—
180C4×D61C2×D411yescharacteristic
181C4×D61C2×D411yescharacteristic
182C4×D61C2×D411yescharacteristic
183C4×D61C2×D411yescharacteristic
184Dic122—21no—
185Dic122—21no—
186Dic122—21no—
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—41no—
201C22×C61—81no—
202C22×C61—81no—
203C22×C61C2×#4111yescharacteristic
204C2×D61—21no—
205C2×D61—41no—
206C2×D61—41no—
207C2×D61—81no—
208C2×D61—82no—
209C2×D61—82no—
210C2×D61—81no—
211C2×D61#12111yescharacteristic
212C2×D61#12111yescharacteristic
213C4×C61—21no—
214C4×C61C22×D411yescharacteristic
215C4×C61C22×D411yescharacteristic
216Dic61—21no—
217Dic61—41no—
218Dic61#12111yescharacteristic
219Dic61#12111yescharacteristic
220#3068—611nomaximal, Sylow
221C2×C61—21no—
222C2×C61—41no—
223C2×C61—81no—
224C2×C61—81no—
225C2×C61C2×#12111yescharacteristic
226D61—21no—
227D61—21no—
228D61—41no—
229D61—81no—
230#575—611no—
231C2×AGL(1,ℤ/8)—611no—
232C2×AGL(1,ℤ/8)—611no—
233#568—611no—
234#472—611no—
235#472—611no—
236#472—611no—
237#472D6111yescharacteristic, complemented
238#471—611no—
239#471—611no—
240#471—611no—
241#471—611no—
242#430—611no—
243#413—611no—
244C2×#100—611no—
245C61#306811yescharacteristic, complemented, Sylow
246C2×#41—611no—
247C2×#41—611no—
248C22×D4—611no—
249#137—611no—
250#137—611no—
251#137—1221no—
252AGL(1,ℤ/8)—611no—
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)—1221no—
259AGL(1,ℤ/8)—1221no—
260AGL(1,ℤ/8)—1221no—
261AGL(1,ℤ/8)—1221no—
262AGL(1,ℤ/8)—1221no—
263AGL(1,ℤ/8)C2×D6111yescharacteristic
264AGL(1,ℤ/8)C2×D6111yescharacteristic, complemented
265#135—1221no—
266#135—1221no—
267C2×SD16—611no—
268C2×SD16—611no—
269C2×SD16—1221no—
270C2×D8—611no—
271C2×D8—1221no—
272C2×D8C2×D6111yescharacteristic, complemented
273#131—611no—
274#131—611no—
275#131—611no—
276#131—1221no—
277#131—1221no—
278#131C2×D6111yescharacteristic, complemented
279C2×M16—611no—
280C2×M16—611no—
281C2×M16—611no—
282C2×M16—611no—
283C2×M16—1221no—
284C2×M16—1221no—
285#108—611no—
286#108—611no—
287#108—611no—
288#108C2×D6111yescharacteristic, complemented
289#101—611no—
290#101—611no—
291#100—611no—
292#100—611no—
293#100—611no—
294#100—611no—
295#100C2×D6111yescharacteristic, complemented
296#100C2×D6111yescharacteristic, complemented
297C24—1221no—
298#41—611no—
299#41—611no—
300#41—611no—
301#41—1221no—
302#41—1221no—
303#41—1221no—
304#41—1221no—
305#41—1221no—
306#41—1221no—
307#41C22×D6111yescharacteristic
308C2×Q8—611no—
309C2×Q8—611no—
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×D4—1221no—
319C2×D4C22×D6111yescharacteristic
320C2×D4C22×D6111yescharacteristic
321C22×C4—611no—
322C22×C4—1221no—
323C22×C4—1221no—
324Q16—1221no—
325Q16—1221no—
326SD16—21no—
327SD16—21no—
328SD16—1221no—
329SD16—1221no—
330SD16—1221no—
331SD16—1221no—
332SD16—1221no—
333SD16—1221no—
334SD16—1221no—
335SD16—1221no—
336SD16—1221no—
337SD16—1221no—
338D8—21no—
339D8—21no—
340D8—21no—
341D8—21no—
342D8—1221no—
343D8—1221no—
344D8—1221no—
345D8—1221no—
346D8—1221no—
347D8—1221no—
348M16—21no—
349M16—611no—
350M16—611no—
351M16—611no—
352M16—611no—
353M16—611no—
354M16—611no—
355M16—611no—
356M16—1221no—
357M16—1221no—
358M16—1221no—
359M16—1221no—
360M16—1221no—
361M16—1221no—
362M16C22×D6111yescharacteristic
363M16C22×D6111yescharacteristic
364M16C22×D6111yescharacteristic
365C2×C8—21no—
366C2×C8—611no—
367C2×C8—1221no—
368C2×C8—1221no—
369C2×C8—1221no—
370C2×C8—1221no—
371C2×C8—1221no—
372C2×C8—1221no—
373C2×C8C22×D6111yescharacteristic
374C23—21no—
375C23—21no—
376C23—611no—
377C23—1221no—
378C23—1221no—
379C23—4882no—
380C23—2441no—
381C23—2441no—
382Q8—611no—
383Q8—1221no—
384Q8—1221no—
385Q8—1221no—
386Q8D4×D6111yescharacteristic
387D4—21no—
388D4—21no—
389D4—21no—
390D4—21no—
391D4—21no—
392D4—611no—
393D4—1221no—
394D4—1221no—
395D4—1221no—
396D4—1221no—
397D4—1221no—
398D4—1221no—
399D4—2441no—
400D4—2441no—
401D4—2441no—
402D4—2441no—
403D4D4×D6111yescharacteristic
404C2×C4—21no—
405C2×C4—611no—
406C2×C4—611no—
407C2×C4—611no—
408C2×C4—611no—
409C2×C4—611no—
410C2×C4—1221no—
411C2×C4—1221no—
412C2×C4—1221no—
413C2×C4—1221no—
414C2×C4—1221no—
415C2×C4—2441no—
416C2×C4—2441no—
417C2×C4C23×D6111yescharacteristic
418C8—21no—
419C8—21no—
420C8—21no—
421C8—611no—
422C8—611no—
423C8—1221no—
424C8—1221no—
425C8—1221no—
426C8D4×D6111yescharacteristic
427C8D4×D6111yescharacteristic
428C22—21no—
429C22—41no—
430C22—41no—
431C22—81no—
432C22—81no—
433C22—611no—
434C22—611no—
435C22—1221no—
436C22—4881no—
437C22—4881no—
438C22—4882no—
439C22—4882no—
440C22—2441no—
441C22—2441no—
442C22#41×D6111yescharacteristic
443C4—21no—
444C4—611no—
445C4—611no—
446C4—1221no—
447C4—2441no—
448C4C2×D4×D6111yescharacteristic
449C4C2×D4×D6111yescharacteristic
450C2—21no—
451C2—41no—
452C2—81no—
453C2—81no—
454C2—1221no—
455C2—1221no—
456C2—4881no—
457C2—2441no—
458C2#121×D6111yescharacteristic
subgroupG/H
centerC2#121×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#472C2
socleC2×C61C2×#121
hypercenter#472D61
hypocenterC61#3068
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #472

Complements

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

NH ≅ G/Ntype
1. #16840558C2semidirect
2. C2×#14519801C2semidirect
3. AGL(1,ℤ/8)×D61C2semidirect
4. #16840527C2semidirect
5. #16840031C2semidirect
6. #16840030C2semidirect
7. #16840029C2semidirect
8. #16840026C2semidirect
9. #16840025C2semidirect
10. #16840024C2semidirect
11. #16840023C2semidirect
12. #16839809C2semidirect
13. #16839743C2semidirect
14. #100×D61C2semidirect
15. C61×#472C2semidirect
19. #14519810C22semidirect
20. #14519807C22semidirect
25. #14519803C22semidirect
35. C2×#11758190C22semidirect
36. C2×#11758200C22semidirect
38. C2×#11758199C22semidirect
41. #14519785C22semidirect
42. #14519784C22semidirect
44. #14519783C22semidirect
51. #14519713C22semidirect
52. #14519712C22semidirect
53. #14519712C22semidirect
54. #14519695C22semidirect
55. #14519695C22semidirect
56. #14519694C22semidirect
57. #14519694C22semidirect
58. #14519693C22semidirect
59. #14519693C22semidirect
61. AGL(1,ℤ/8)×C61C22semidirect
62. C2×D8×C61C22semidirect
63. #131×C61C22semidirect
64. #108×C61C22semidirect
65. #100×C61C22semidirect
66. #100×C61C22semidirect
237. #472D61semidirect
245. C61#3068semidirect
264. AGL(1,ℤ/8)C2×D61semidirect
272. C2×D8C2×D61semidirect
278. #131C2×D61semidirect
288. #108C2×D61semidirect
295. #100C2×D61semidirect
296. #100C2×D61semidirect