Finite Group Databasebeta

← #21457584

Subgroups — #21457584

Order 7808.

464 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840571C211yesmaximal, characteristic, complemented
2#16840568C211yesmaximal, characteristic, complemented
3#16840567C211yesmaximal, characteristic, complemented
4#16840566C211yesmaximal, characteristic, complemented
5#16840148C211yesmaximal, characteristic, complemented
6#16840033C211yesmaximal, characteristic, complemented
7#16840031C211yesmaximal, characteristic, complemented
8#16840028C211yesmaximal, characteristic, complemented
9#16839938C211yesmaximal, characteristic, complemented
10#16839937C211yesmaximal, characteristic, complemented
11#16839932C211yesmaximal, characteristic, complemented
12#16839928C211yesmaximal, characteristic, complemented
13#16839883C211yesmaximal, characteristic, complemented
14#16839882C211yesmaximal, characteristic, complemented
15C61×#471C211yesmaximal, characteristic, complemented
16#14519825C2211yescharacteristic, complemented
17#14519823C2211yescharacteristic
18#14519823C2211yescharacteristic, complemented
19#14519822C2211yescharacteristic, complemented
20#14519809—21no—
21#14519808C2211yescharacteristic, complemented
22#14519806—21no—
23#14519805—21no—
24#14519805—21no—
25#14519805C2211yescharacteristic
26#14519805C2211yescharacteristic, complemented
27#14519805C2211yescharacteristic, complemented
28#14519805C2211yescharacteristic, complemented
29#14519804—21no—
30#14519804—21no—
31#14519804—21no—
32#14519803C2211yescharacteristic, complemented
33#14519801—21no—
34#14519800—21no—
35#14519799—21no—
36#14519799C2211yescharacteristic
37#14519798—21no—
38#14519798—21no—
39#14519797C2211yescharacteristic
40C2×#11758201C2211yescharacteristic, complemented
41SD16×D61—21no—
42SD16×D61—21no—
43C2×D488—21no—
44C2×D488C2211yescharacteristic, complemented
45C2×#11758199C2211yescharacteristic, complemented
46D8×D61—21no—
47#14519785C2211yescharacteristic, complemented
48#14519785C2211yescharacteristic, complemented
49#14519783C2211yescharacteristic, complemented
50#14519773C2211yescharacteristic, complemented
51#14519766C2211yescharacteristic, complemented
52#14519712C2211yescharacteristic, complemented
53#14519704C2211yescharacteristic, complemented
54#14519703C2211yescharacteristic, complemented
55#14519703C2211yescharacteristic, complemented
56#14519703C2211yescharacteristic, complemented
57#14519693C2211yescharacteristic, complemented
58#14519693C2211yescharacteristic, complemented
59#14519687C2211yescharacteristic, 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
67#41×C61C2311yescharacteristic
68C2×Q8×C61C2311yescharacteristic
69C2×D4×C61C2311yescharacteristic
70C2×C22⋊D61—41no—
71C2×C22⋊D61—41no—
72#11758226—21no—
73#11758226—21no—
74#11758226—21no—
75#11758226—21no—
76Q8×D61—21no—
77Q8×D61—21no—
78#11758224—21no—
79#11758224—21no—
80D4×D61—21no—
81D4×D61—21no—
82D4×D61—21no—
83D4×D61—21no—
84D4×D61—41no—
85D4×D61—41no—
86#11758222—21no—
87#11758222—21no—
88#11758222—41no—
89#11758222C2311yescharacteristic
90#11758222C2311yescharacteristic
91#11758222C2311yescharacteristic
92C2×D244—21no—
93C2×D244—21no—
94C2×D244C2311yescharacteristic
95C2×D244C2311yescharacteristic
96Q16×C61—21no—
97SD16×C61—21no—
98SD16×C61—21no—
99SD16×C61—21no—
100SD16×C61—21no—
101D8×C61—21no—
102M16×C61—21no—
103M16×C61C2311yescharacteristic
104M16×C61C2311yescharacteristic
105M16×C61C2311yescharacteristic
106C2×C8×C61—21no—
107C2×C8×C61C2311yescharacteristic
108#11758202—21no—
109#11758202D411yescharacteristic, complemented
110#11758201—21no—
111#11758201—21no—
112#11758201—21no—
113#11758201D411yescharacteristic, complemented
114#11758200—21no—
115#11758200D411yescharacteristic, complemented
116#11758199—21no—
117#11758199—21no—
118#11758199—21no—
119#11758199D411yescharacteristic, complemented
120#11758198—41no—
121C4×Dic61C2311yescharacteristic
122#11758194C2311yescharacteristic
123C2×#92418C2311yescharacteristic
124Dic244D411yescharacteristic, complemented
125D488—21no—
126D488—21no—
127D488—21no—
128D488—21no—
129D488—21no—
130D488—21no—
131D488D411yescharacteristic, complemented
132#11758190—21no—
133#11758190—21no—
134#11758190—21no—
135#11758190—21no—
136#11758190D411yescharacteristic, complemented
137#11758190D411yescharacteristic, complemented
138#11758189—21no—
139#11758189—21no—
140#11758189—21no—
141C8×D61—21no—
142C8×D61—21no—
143C8×D61—21no—
144C23×C61—21no—
145C22×D61—21no—
146C22×D61—21no—
147C22×D61—41no—
148C22×D61—41no—
149C22×D61—41no—
150Q8×C61—21no—
151Q8×C61—21no—
152Q8×C61C2×D411yescharacteristic
153D4×C61—21no—
154D4×C61—21no—
155D4×C61—21no—
156D4×C61C2×D411yescharacteristic
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61C2411yescharacteristic
160C22⋊D61—21no—
161C22⋊D61—21no—
162C22⋊D61—21no—
163C22⋊D61—41no—
164C22⋊D61—41no—
165C22⋊D61—41no—
166C22⋊D61—41no—
167C22⋊D61—82no—
168C2×Dic61—21no—
169C2×Dic61—41no—
170D244—21no—
171D244—21no—
172D244—21no—
173D244—21no—
174D244—41no—
175D244—41no—
176D244—41no—
177D244C2×D411yescharacteristic
178D244C2×D411yescharacteristic
179D244C2×D411yescharacteristic
180C4×D61—21no—
181C4×D61—21no—
182C4×D61—21no—
183C4×D61—41no—
184C4×D61—41no—
185C4×D61—41no—
186C4×D61—41no—
187Dic122—41no—
188Dic122C2×D411yescharacteristic
189Dic122C2×D411yescharacteristic
190Dic122C2×D411yescharacteristic
191C8×C61—21no—
192C8×C61—21no—
193C8×C61—21no—
194C8×C61C2×D411yescharacteristic
195C8×C61C2×D411yescharacteristic
196#92418—21no—
197#92418C2×D411yescharacteristic
198#92418C2×D411yescharacteristic
199C22×C61—21no—
200C22×C61—41no—
201C22×C61—81no—
202C22×C61H(5,𝔽2)11yescharacteristic
203C2×D61—21no—
204C2×D61—21no—
205C2×D61—21no—
206C2×D61—41no—
207C2×D61—41no—
208C2×D61—81no—
209C2×D61—81no—
210C2×D61—161no—
211C2×D61—161no—
212C2×D61—161no—
213C4×C61—21no—
214C4×C61—41no—
215C4×C61C22×D411yescharacteristic
216C4×C61C22×D411yescharacteristic
217Dic61—21no—
218Dic61—21no—
219Dic61—21no—
220Dic61—41no—
221#3288—611nomaximal, Sylow
222C2×C61—21no—
223C2×C61—41no—
224C2×C61—81no—
225C2×C61D4211yescharacteristic
226D61—41no—
227D61—41no—
228D61—41no—
229D61—81no—
230D61—81no—
231#577—611no—
232#577—611no—
233#576—611no—
234#576—611no—
235#496—611no—
236#472—611no—
237#472—611no—
238#471—611no—
239#471D6111yescharacteristic, complemented
240#455—611no—
241#454—611no—
242#453—611no—
243#453—611no—
244#444—611no—
245#444—611no—
246C61#328811yescharacteristic, complemented, Sylow
2472−1+4—611no—
248H(5,𝔽2)—611no—
249H(5,𝔽2)—611no—
250H(5,𝔽2)—611no—
251#137—611no—
252#137—1221no—
253#137—1221no—
254#137C2×D6111yescharacteristic, complemented
255AGL(1,ℤ/8)—611no—
256AGL(1,ℤ/8)—611no—
257AGL(1,ℤ/8)—611no—
258AGL(1,ℤ/8)—611no—
259AGL(1,ℤ/8)—611no—
260AGL(1,ℤ/8)—1221no—
261AGL(1,ℤ/8)—1221no—
262AGL(1,ℤ/8)—1221no—
263AGL(1,ℤ/8)—1221no—
264AGL(1,ℤ/8)—1221no—
265AGL(1,ℤ/8)—1221no—
266AGL(1,ℤ/8)C2×D6111yescharacteristic
267#135—611no—
268#135—611no—
269#135—1221no—
270#135—1221no—
271#135—1221no—
272#135—1221no—
273C2×SD16—611no—
274C2×SD16—1221no—
275C2×SD16—1221no—
276C2×SD16C2×D6111yescharacteristic, complemented
277C2×D8—611no—
278C2×D8—611no—
279C2×D8—1221no—
280C2×D8—1221no—
281#131—611no—
282#131—611no—
283#131—611no—
284#131C2×D6111yescharacteristic, complemented
285#127—611no—
286#124—611no—
287#108—611no—
288#108C2×D6111yescharacteristic, complemented
289#104—611no—
290#104—611no—
291#104—611no—
292#104—611no—
293#101C2×D6111yescharacteristic, complemented
294#100—611no—
295#100—611no—
296#100C2×D6111yescharacteristic, complemented
297#97—611no—
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#41—1221no—
308#41—1221no—
309#41—2441no—
310#41C22×D6111yescharacteristic
311C2×Q8—1221no—
312C2×Q8—1221no—
313C2×Q8C22×D6111yescharacteristic
314C2×D4—611no—
315C2×D4—611no—
316C2×D4—1221no—
317C2×D4—1221no—
318C2×D4—1221no—
319C2×D4—1221no—
320C2×D4—1221no—
321C2×D4—1221no—
322C2×D4—2441no—
323C2×D4—2441no—
324C2×D4—2441no—
325C2×D4—2441no—
326C2×D4C22×D6111yescharacteristic
327Q16—21no—
328Q16—611no—
329Q16—611no—
330Q16—1221no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—21no—
335SD16—611no—
336SD16—611no—
337SD16—611no—
338SD16—611no—
339SD16—1221no—
340SD16—1221no—
341SD16—1221no—
342SD16—1221no—
343SD16—1221no—
344SD16—1221no—
345SD16—1221no—
346SD16—1221no—
347D8—21no—
348D8—611no—
349D8—611no—
350D8—1221no—
351D8—1221no—
352D8—1221no—
353D8—1221no—
354D8—1221no—
355D8—1221no—
356D8—1221no—
357D8—1221no—
358D8—1221no—
359M16—21no—
360M16—611no—
361M16—1221no—
362M16—1221no—
363M16—1221no—
364M16C22×D6111yescharacteristic
365M16C22×D6111yescharacteristic
366M16C22×D6111yescharacteristic
367C2×C8—21no—
368C2×C8—611no—
369C2×C8—1221no—
370C2×C8—1221no—
371C2×C8—1221no—
372C2×C8C22×D6111yescharacteristic
373C22⋊C4—2441no—
374C42—611no—
375C23—21no—
376C23—1221no—
377C23—1221no—
378C23—2441no—
379C23—2441no—
380C23—2441no—
381Q8—21no—
382Q8—21no—
383Q8—611no—
384Q8—611no—
385Q8—611no—
386Q8—2441no—
387Q8D4×D6111yescharacteristic
388D4—21no—
389D4—21no—
390D4—21no—
391D4—611no—
392D4—611no—
393D4—611no—
394D4—1221no—
395D4—1221no—
396D4—1221no—
397D4—1221no—
398D4—1221no—
399D4—1221no—
400D4—1221no—
401D4—4882no—
402D4—2441no—
403D4—2441no—
404D4—2441no—
405D4—2441no—
406D4—2441no—
407D4—2441no—
408D4—2441no—
409D4D4×D6111yescharacteristic
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—1221no—
413C2×C4—1221no—
414C2×C4—1221no—
415C2×C4—1221no—
416C2×C4—2441no—
417C2×C4—2441no—
418C2×C4—2441no—
419C2×C4—2441no—
420C2×C4—2441no—
421C2×C4C23×D6111yescharacteristic
422C8—21no—
423C8—21no—
424C8—21no—
425C8—611no—
426C8—611no—
427C8—1221no—
428C8D4×D6111yescharacteristic
429C8D4×D6111yescharacteristic
430C22—21no—
431C22—41no—
432C22—81no—
433C22—1221no—
434C22—1221no—
435C22—1221no—
436C22—9761no—
437C22—9761no—
438C22—9761no—
439C22—4881no—
440C22—4881no—
441C22—2441no—
442C22—2441no—
443C22#1451982311yescharacteristic
444C4—21no—
445C4—41no—
446C4—1221no—
447C4—1221no—
448C4—1221no—
449C4—2441no—
450C4C2×D4×D6111yescharacteristic
451C4C2×D4×D6111yescharacteristic
452C2—21no—
453C2—41no—
454C2—81no—
455C2—4881no—
456C2—4881no—
457C2—2441no—
458C2—2441no—
459C2—2441no—
460C2#1684039611yescharacteristic
subgroupG/H
centerC2#16840396
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#471C2
socleC2×C61D42
hypercenter#471D61
hypocenterC61#3288
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. #16840571C2semidirect
2. #16840568C2semidirect
3. #16840567C2semidirect
4. #16840566C2semidirect
5. #16840148C2semidirect
6. #16840033C2semidirect
7. #16840031C2semidirect
8. #16840028C2semidirect
9. #16839938C2semidirect
10. #16839937C2semidirect
11. #16839932C2semidirect
12. #16839928C2semidirect
13. #16839883C2semidirect
14. #16839882C2semidirect
15. C61×#471C2semidirect
16. #14519825C22semidirect
18. #14519823C22semidirect
19. #14519822C22semidirect
21. #14519808C22semidirect
26. #14519805C22semidirect
27. #14519805C22semidirect
28. #14519805C22semidirect
32. #14519803C22semidirect
40. C2×#11758201C22semidirect
44. C2×D488C22semidirect
45. C2×#11758199C22semidirect
47. #14519785C22semidirect
48. #14519785C22semidirect
49. #14519783C22semidirect
50. #14519773C22semidirect
51. #14519766C22semidirect
52. #14519712C22semidirect
53. #14519704C22semidirect
54. #14519703C22semidirect
55. #14519703C22semidirect
56. #14519703C22semidirect
57. #14519693C22semidirect
58. #14519693C22semidirect
59. #14519687C22semidirect
60. #137×C61C22semidirect
62. C2×SD16×C61C22semidirect
63. #131×C61C22semidirect
64. #108×C61C22semidirect
65. #101×C61C22semidirect
66. #100×C61C22semidirect
109. #11758202D4semidirect
113. #11758201D4semidirect
115. #11758200D4semidirect
119. #11758199D4semidirect
124. Dic244D4semidirect
131. D488D4semidirect
136. #11758190D4semidirect
137. #11758190D4semidirect
239. #471D61semidirect
246. C61#3288semidirect
254. #137C2×D61semidirect
276. C2×SD16C2×D61semidirect
284. #131C2×D61semidirect
288. #108C2×D61semidirect
293. #101C2×D61semidirect
296. #100C2×D61semidirect