Finite Group Databasebeta

← #21457603

Subgroups — #21457603

Order 7808.

454 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840578C211yesmaximal, characteristic, complemented
2#16840573C211yesmaximal, characteristic, complemented
3#16840571C211yesmaximal, characteristic, complemented
4#16840565C211yesmaximal, characteristic, complemented
5#16840144C211yesmaximal, characteristic, complemented
6#16840035C211yesmaximal, characteristic, complemented
7#16840031C211yesmaximal, characteristic, complemented
8#16840027C211yesmaximal, characteristic, complemented
9#16840024C211yesmaximal, characteristic, complemented
10#16839941C211yesmaximal, characteristic, complemented
11#16839936C211yesmaximal, characteristic, complemented
12#16839934C211yesmaximal, characteristic, complemented
13#16839876C211yesmaximal, characteristic, complemented
14#16839876C211yesmaximal, characteristic, complemented
15C61×#455C211yesmaximal, characteristic, complemented
16#14519825C2211yescharacteristic, complemented
17#14519824C2211yescharacteristic, complemented
18#14519823C2211yescharacteristic
19#14519810C2211yescharacteristic, complemented
20#14519809—21no—
21#14519809—21no—
22#14519807—21no—
23#14519807C2211yescharacteristic
24#14519806—21no—
25#14519805C2211yescharacteristic, complemented
26#14519804—21no—
27#14519803—21no—
28#14519803—21no—
29#14519803C2211yescharacteristic
30#14519803C2211yescharacteristic, complemented
31#14519802—21no—
32#14519802C2211yescharacteristic
33#14519800—21no—
34#14519798—21no—
35#14519797—21no—
36#14519797—21no—
37#14519797C2211yescharacteristic
38#14519797C2211yescharacteristic
39C2×#11758202C2211yescharacteristic, complemented
40Q16×D61—21no—
41C2×#11758200—21no—
42C2×#11758200C2211yescharacteristic, complemented
43C2×#11758201C2211yescharacteristic, complemented
44SD16×D61—21no—
45C2×#11758199—21no—
46C2×#11758199C2211yescharacteristic
47#14519785C2211yescharacteristic, complemented
48#14519785C2211yescharacteristic, complemented
49#14519784C2211yescharacteristic
50#14519784C2211yescharacteristic, complemented
51#14519765C2211yescharacteristic, complemented
52#14519712C2211yescharacteristic, complemented
53#14519712C2211yescharacteristic, complemented
54#14519705C2211yescharacteristic, complemented
55#14519705C2211yescharacteristic, complemented
56#14519696C2211yescharacteristic, complemented
57#14519695C2211yescharacteristic, complemented
58#14519693C2211yescharacteristic, complemented
59C4×#92418C2211yescharacteristic, complemented
60H(5,𝔽2)×C61C2211yescharacteristic
61#137×C61C2211yescharacteristic
62#137×C61C2211yescharacteristic, complemented
63#124×C61C2211yescharacteristic, complemented
64#104×C61C2211yescharacteristic
65#104×C61C2211yescharacteristic, complemented
66#100×C61C2211yescharacteristic, complemented
67#41×C61—21no—
68#41×C61—21no—
69#41×C61C2311yescharacteristic
70#41×C61C2311yescharacteristic
71C2×Q8×C61C2311yescharacteristic
72C2×D4×C61—21no—
73C2×D4×C61—21no—
74C2×D4×C61—41no—
75C2×D4×C61C2311yescharacteristic
76#11758226—21no—
77#11758226—21no—
78#11758226—21no—
79Q8×D61—21no—
80Q8×D61—21no—
81Q8×D61—21no—
82#11758224—21no—
83#11758224—41no—
84D4×D61—21no—
85D4×D61—41no—
86#11758222—21no—
87#11758222—21no—
88#11758222—41no—
89#11758222C2311yescharacteristic
90#11758222C2311yescharacteristic
91C2×D244—21no—
92C2×D244C2311yescharacteristic
93C2×Dic122—21no—
94C2×Dic122C2311yescharacteristic
95Q16×C61—21no—
96Q16×C61—21no—
97SD16×C61—21no—
98SD16×C61—21no—
99M16×C61C2311yescharacteristic
100M16×C61C2311yescharacteristic
101C22⋊C4×C61—41no—
102C42×C61C2311yescharacteristic
103#11758202—21no—
104#11758202—21no—
105#11758202—21no—
106#11758202D411yescharacteristic
107#11758202D411yescharacteristic
108#11758201—21no—
109#11758201—21no—
110#11758201—21no—
111#11758201D411yescharacteristic
112#11758201D411yescharacteristic
113#11758200—21no—
114#11758200—21no—
115#11758200—21no—
116#11758200—21no—
117#11758200—21no—
118#11758200D411yescharacteristic
119#11758200D411yescharacteristic
120#11758199—21no—
121#11758199—21no—
122#11758199—21no—
123#11758199—21no—
124#11758199—21no—
125#11758199D411yescharacteristic
126#11758199D411yescharacteristic
127#11758198—41no—
128#11758194—21no—
129#11758194—21no—
130#11758194C2311yescharacteristic
131#11758194C2311yescharacteristic
132C2×#92418—21no—
133C2×#92418—21no—
134C2×#92418C2311yescharacteristic
135C2×#92418C2311yescharacteristic
136Dic244—21no—
137D488—21no—
138#11758190—21no—
139#11758190—21no—
140#11758189—21no—
141#11758189—21no—
142C8×D61—21no—
143C8×D61—21no—
144C23×C61—21no—
145C23×C61—41no—
146C22×D61—21no—
147C22×D61—41no—
148Q8×C61—21no—
149Q8×C61—21no—
150Q8×C61C2×D411yescharacteristic
151Q8×C61C2×D411yescharacteristic
152D4×C61—21no—
153D4×C61—21no—
154D4×C61—21no—
155D4×C61—21no—
156D4×C61—41no—
157D4×C61—41no—
158D4×C61C2×D411yescharacteristic
159D4×C61C2×D411yescharacteristic
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—21no—
164C2×C4×C61—41no—
165C2×C4×C61C2411yescharacteristic
166C22⋊D61—21no—
167C22⋊D61—21no—
168C22⋊D61—41no—
169C22⋊D61—41no—
170C2×Dic61—21no—
171C2×Dic61—41no—
172D244—21no—
173D244—21no—
174D244—41no—
175D244—41no—
176D244C2×D411yescharacteristic
177D244C2×D411yescharacteristic
178C4×D61—21no—
179C4×D61—21no—
180C4×D61—41no—
181C4×D61—41no—
182C4×D61—41no—
183C4×D61—41no—
184Dic122—21no—
185Dic122—21no—
186Dic122—41no—
187Dic122—41no—
188Dic122C2×D411yescharacteristic
189Dic122C2×D411yescharacteristic
190C8×C61—21no—
191C8×C61—21no—
192#92418—21no—
193#92418—21no—
194#92418C2×D411yescharacteristic
195#92418C2×D411yescharacteristic
196#92418C2×D411yescharacteristic
197#92418C2×D411yescharacteristic
198C22×C61—21no—
199C22×C61—21no—
200C22×C61—41no—
201C22×C61—81no—
202C22×C61—161no—
203C22×C61H(5,𝔽2)11yescharacteristic
204C2×D61—21no—
205C2×D61—21no—
206C2×D61—41no—
207C2×D61—81no—
208C2×D61—161no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—41no—
212C4×C61—41no—
213C4×C61C22×D411yescharacteristic
214C4×C61C22×D411yescharacteristic
215Dic61—21no—
216Dic61—21no—
217Dic61—41no—
218#3290—611nomaximal, Sylow
219C2×C61—21no—
220C2×C61—41no—
221C2×C61—41no—
222C2×C61—81no—
223C2×C61D4211yescharacteristic
224D61—41no—
225D61—41no—
226D61—81no—
227#578—611no—
228#577—611no—
229#577—611no—
230#576—611no—
231#495—611no—
232#473—611no—
233#472—611no—
234#471—611no—
235#471—611no—
236#455—611no—
237#455D6111yescharacteristic, complemented
238#454—611no—
239#454—611no—
240#443—611no—
241#443—611no—
242C61#329011yescharacteristic, complemented, Sylow
2432−1+4—611no—
2442−1+4—611no—
245H(5,𝔽2)—611no—
246H(5,𝔽2)C2×D6111yescharacteristic
247#137—611no—
248#137—611no—
249#137—1221no—
250#137—1221no—
251#137—1221no—
252#137—1221no—
253#137C2×D6111yescharacteristic
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)—1221no—
260AGL(1,ℤ/8)—1221no—
261AGL(1,ℤ/8)—1221no—
262AGL(1,ℤ/8)—1221no—
263#135—611no—
264#135—611no—
265#135—1221no—
266#135—1221no—
267#135—1221no—
268#135—1221no—
269C2×Q16—611no—
270C2×Q16—1221no—
271C2×SD16—611no—
272C2×SD16—611no—
273C2×SD16—1221no—
274C2×SD16—1221no—
275C2×D8—611no—
276C2×D8—1221no—
277#131—611no—
278#131—611no—
279#131—611no—
280#131—611no—
281#124—611no—
282#124C2×D6111yescharacteristic, complemented
283#108—611no—
284#108—611no—
285#104—611no—
286#104—611no—
287#104C2×D6111yescharacteristic
288#104C2×D6111yescharacteristic, complemented
289#101—611no—
290#101—611no—
291#100—611no—
292#100C2×D6111yescharacteristic, complemented
293C4×C8—611no—
294#41—21no—
295#41—21no—
296#41—611no—
297#41—611no—
298#41—1221no—
299#41—1221no—
300#41—1221no—
301#41—1221no—
302#41—1221no—
303#41—1221no—
304#41—2441no—
305#41—2441no—
306#41C22×D6111yescharacteristic
307#41C22×D6111yescharacteristic
308C2×Q8—611no—
309C2×Q8—1221no—
310C2×Q8—1221no—
311C2×Q8—1221no—
312C2×Q8—1221no—
313C2×Q8C22×D6111yescharacteristic
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4—611no—
318C2×D4—1221no—
319C2×D4—1221no—
320C2×D4—2441no—
321C2×D4C22×D6111yescharacteristic
322Q16—21no—
323Q16—21no—
324Q16—611no—
325Q16—611no—
326Q16—1221no—
327Q16—1221no—
328Q16—1221no—
329Q16—1221no—
330SD16—21no—
331SD16—21no—
332SD16—611no—
333SD16—611no—
334SD16—611no—
335SD16—611no—
336SD16—1221no—
337SD16—1221no—
338SD16—1221no—
339SD16—1221no—
340SD16—1221no—
341SD16—1221no—
342SD16—1221no—
343SD16—1221no—
344SD16—1221no—
345SD16—1221no—
346D8—611no—
347D8—611no—
348D8—1221no—
349D8—1221no—
350D8—1221no—
351D8—1221no—
352D8—1221no—
353D8—1221no—
354M16—611no—
355M16—611no—
356M16—1221no—
357M16—1221no—
358M16—1221no—
359M16—1221no—
360M16C22×D6111yescharacteristic
361M16C22×D6111yescharacteristic
362C2×C8—611no—
363C2×C8—611no—
364C2×C8—1221no—
365C2×C8—1221no—
366C2×C8—1221no—
367C2×C8—1221no—
368C22⋊C4—41no—
369C22⋊C4—2441no—
370C42C22×D6111yescharacteristic
371C23—21no—
372C23—41no—
373C23—1221no—
374C23—2441no—
375Q8—21no—
376Q8—21no—
377Q8—611no—
378Q8—611no—
379Q8—1221no—
380Q8—1221no—
381Q8—2441no—
382Q8—2441no—
383Q8D4×D6111yescharacteristic
384Q8D4×D6111yescharacteristic
385D4—21no—
386D4—21no—
387D4—21no—
388D4—21no—
389D4—41no—
390D4—41no—
391D4—611no—
392D4—611no—
393D4—1221no—
394D4—1221no—
395D4—1221no—
396D4—1221no—
397D4—2441no—
398D4—2441no—
399D4—2441no—
400D4—2441no—
401D4D4×D6111yescharacteristic
402D4D4×D6111yescharacteristic
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—1221no—
409C2×C4—1221no—
410C2×C4—1221no—
411C2×C4—2441no—
412C2×C4—2441no—
413C2×C4—2441no—
414C2×C4—2441no—
415C2×C4—2441no—
416C2×C4C23×D6111yescharacteristic
417C8—21no—
418C8—21no—
419C8—611no—
420C8—611no—
421C8—611no—
422C8—611no—
423C8—1221no—
424C8—1221no—
425C22—21no—
426C22—21no—
427C22—41no—
428C22—81no—
429C22—161no—
430C22—1221no—
431C22—1221no—
432C22—9761no—
433C22—4881no—
434C22—2441no—
435C22#1451982211yescharacteristic
436C4—21no—
437C4—21no—
438C4—41no—
439C4—41no—
440C4—1221no—
441C4—1221no—
442C4—2441no—
443C4C2×D4×D6111yescharacteristic
444C4C2×D4×D6111yescharacteristic
445C2—21no—
446C2—41no—
447C2—41no—
448C2—81no—
449C2—4881no—
450C2—2441no—
451C2—2441no—
452C2#1684039411yescharacteristic
subgroupG/H
centerC2#16840394
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#455C2
socleC2×C61D42
hypercenter#455D61
hypocenterC61#3290
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #455

Complements

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

NH ≅ G/Ntype
1. #16840578C2semidirect
2. #16840573C2semidirect
3. #16840571C2semidirect
4. #16840565C2semidirect
5. #16840144C2semidirect
6. #16840035C2semidirect
7. #16840031C2semidirect
8. #16840027C2semidirect
9. #16840024C2semidirect
10. #16839941C2semidirect
11. #16839936C2semidirect
12. #16839934C2semidirect
13. #16839876C2semidirect
14. #16839876C2semidirect
15. C61×#455C2semidirect
16. #14519825C22semidirect
17. #14519824C22semidirect
19. #14519810C22semidirect
25. #14519805C22semidirect
30. #14519803C22semidirect
39. C2×#11758202C22semidirect
42. C2×#11758200C22semidirect
43. C2×#11758201C22semidirect
47. #14519785C22semidirect
48. #14519785C22semidirect
50. #14519784C22semidirect
51. #14519765C22semidirect
52. #14519712C22semidirect
53. #14519712C22semidirect
54. #14519705C22semidirect
55. #14519705C22semidirect
56. #14519696C22semidirect
57. #14519695C22semidirect
58. #14519693C22semidirect
59. C4×#92418C22semidirect
62. #137×C61C22semidirect
63. #124×C61C22semidirect
65. #104×C61C22semidirect
66. #100×C61C22semidirect
237. #455D61semidirect
242. C61#3290semidirect
254. #137C2×D61semidirect
282. #124C2×D61semidirect
288. #104C2×D61semidirect
292. #100C2×D61semidirect