Finite Group Databasebeta

← #21457610

Subgroups — #21457610

Order 7808.

460 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#16840573C211yesmaximal, characteristic, complemented
2#16840570C211yesmaximal, characteristic, complemented
3#16840569C211yesmaximal, characteristic, complemented
4#16840133C211yesmaximal, characteristic, complemented
5#16840027C211yesmaximal, characteristic, complemented
6#16840025C211yesmaximal, characteristic, complemented
7#16840023C211yesmaximal, characteristic, complemented
8#16840022C211yesmaximal, characteristic, complemented
9#16839945C211yesmaximal, characteristic, complemented
10#16839943C211yesmaximal, characteristic, complemented
11#16839930C211yesmaximal, characteristic, complemented
12#16839928C211yesmaximal, characteristic, complemented
13#16839879C211yesmaximal, characteristic, complemented
14#16839877C211yesmaximal, characteristic, complemented
15C61×#577C211yesmaximal, characteristic, complemented
16#14519824C2211yescharacteristic
17#14519823C2211yescharacteristic, complemented
18#14519809—21no—
19#14519808—21no—
20#14519808C2211yescharacteristic, complemented
21#14519807—21no—
22#14519807C2211yescharacteristic, complemented
23#14519807C2211yescharacteristic, complemented
24#14519803—21no—
25#14519803C2211yescharacteristic
26#14519802—21no—
27#14519802C2211yescharacteristic
28#14519802C2211yescharacteristic
29#14519801—21no—
30#14519798—21no—
31#14519797—21no—
32#14519797—21no—
33#14519797C2211yescharacteristic
34C2×#11758190C2211yescharacteristic, complemented
35C2×#11758200—21no—
36C2×#11758200C2211yescharacteristic, complemented
37C2×#11758201—21no—
38C2×#11758201C2211yescharacteristic, complemented
39SD16×D61—21no—
40#14519784C2211yescharacteristic, complemented
41#14519784C2211yescharacteristic, complemented
42#14519783C2211yescharacteristic, complemented
43#14519775C2211yescharacteristic, complemented
44#14519773C2211yescharacteristic
45#14519713C2211yescharacteristic, complemented
46#14519712C2211yescharacteristic, complemented
47#14519704C2211yescharacteristic, complemented
48#14519704C2211yescharacteristic, complemented
49#14519704C2211yescharacteristic, complemented
50#14519703C2211yescharacteristic, complemented
51#14519696C2211yescharacteristic, complemented
52#14519695C2211yescharacteristic, complemented
53#14519694C2211yescharacteristic, complemented
54#14519693C2211yescharacteristic, complemented
55C8×Dic61C2211yescharacteristic, complemented
562−1+4×C61C2211yescharacteristic
57H(5,𝔽2)×C61C2211yescharacteristic, complemented
58#137×C61—21no—
59#137×C61C2211yescharacteristic, complemented
60AGL(1,ℤ/8)×C61—21no—
61AGL(1,ℤ/8)×C61C2211yescharacteristic
62#135×C61—21no—
63#135×C61C2211yescharacteristic
64C2×SD16×C61—21no—
65C2×SD16×C61C2211yescharacteristic, complemented
66#131×C61C2211yescharacteristic, complemented
67#41×C61—21no—
68#41×C61—21no—
69#41×C61—21no—
70#41×C61—21no—
71#41×C61—41no—
72#41×C61C2311yescharacteristic
73#41×C61C2311yescharacteristic
74#41×C61C2311yescharacteristic
75C2×Q8×C61—21no—
76C2×Q8×C61—21no—
77C2×Q8×C61C2311yescharacteristic
78C2×D4×C61—21no—
79C2×D4×C61—21no—
80C2×D4×C61—41no—
81C2×D4×C61C2311yescharacteristic
82C2×C22⋊D61—41no—
83#11758226—21no—
84Q8×D61—21no—
85#11758224—21no—
86#11758224—41no—
87D4×D61—21no—
88D4×D61—41no—
89#11758222—21no—
90#11758222—21no—
91#11758222C2311yescharacteristic
92C2×D244—21no—
93C2×D244C2311yescharacteristic
94C2×Dic122—21no—
95C2×Dic122C2311yescharacteristic
96Q16×C61—21no—
97Q16×C61D411yescharacteristic, complemented
98SD16×C61—21no—
99SD16×C61—21no—
100SD16×C61—21no—
101SD16×C61—21no—
102SD16×C61D411yescharacteristic, complemented
103SD16×C61D411yescharacteristic, complemented
104D8×C61—21no—
105D8×C61D411yescharacteristic, complemented
106M16×C61—21no—
107M16×C61C2311yescharacteristic
108C2×C8×C61—21no—
109C2×C8×C61C2311yescharacteristic
110#11758202—21no—
111#11758202—21no—
112#11758202—21no—
113#11758202D411yescharacteristic, complemented
114#11758201—21no—
115#11758201—21no—
116#11758201—21no—
117#11758201—21no—
118#11758201—21no—
119#11758201D411yescharacteristic, complemented
120#11758200—21no—
121#11758200—21no—
122#11758200—21no—
123#11758200—21no—
124#11758200—21no—
125#11758200D411yescharacteristic, complemented
126#11758199—21no—
127#11758199—21no—
128#11758199—21no—
129#11758199D411yescharacteristic, complemented
130#11758196—41no—
131C4×Dic61C2311yescharacteristic
132#11758194—21no—
133#11758194—21no—
134#11758194C2311yescharacteristic
135#11758194C2311yescharacteristic
136#11758194C2311yescharacteristic
137C2×#92418—21no—
138C2×#92418—21no—
139C2×#92418C2311yescharacteristic
140#11758190—21no—
141#11758190—21no—
142#11758189—21no—
143C8×D61—21no—
144C23×C61—21no—
145C23×C61—41no—
146C22×D61—21no—
147C22×D61—41no—
148Q8×C61—21no—
149Q8×C61—21no—
150Q8×C61—41no—
151Q8×C61C2×D411yescharacteristic
152Q8×C61C2×D411yescharacteristic
153Q8×C61C2×D411yescharacteristic
154D4×C61—21no—
155D4×C61—21no—
156D4×C61—21no—
157D4×C61—21no—
158D4×C61—21no—
159D4×C61—41no—
160D4×C61—41no—
161D4×C61—41no—
162D4×C61C2×D411yescharacteristic
163D4×C61C2×D411yescharacteristic
164D4×C61C2×D411yescharacteristic
165C2×C4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61—21no—
168C2×C4×C61—21no—
169C2×C4×C61—41no—
170C2×C4×C61—41no—
171C2×C4×C61—41no—
172C2×C4×C61C2411yescharacteristic
173C22⋊D61—21no—
174C22⋊D61—41no—
175C22⋊D61—41no—
176C22⋊D61—82no—
177C2×Dic61—21no—
178C2×Dic61—21no—
179C2×Dic61—41no—
180D244—21no—
181D244—21no—
182D244—41no—
183D244C2×D411yescharacteristic
184C4×D61—21no—
185C4×D61—41no—
186C4×D61—41no—
187Dic122—21no—
188Dic122—21no—
189Dic122—41no—
190Dic122C2×D411yescharacteristic
191C8×C61—21no—
192C8×C61C2×D411yescharacteristic
193C8×C61C2×D411yescharacteristic
194#92418—21no—
195#92418—21no—
196#92418—21no—
197#92418C2×D411yescharacteristic
198#92418C2×D411yescharacteristic
199C22×C61—21no—
200C22×C61—21no—
201C22×C61—21no—
202C22×C61—41no—
203C22×C61—81no—
204C22×C61—161no—
205C22×C61H(5,𝔽2)11yescharacteristic
206C2×D61—21no—
207C2×D61—41no—
208C2×D61—81no—
209C2×D61—161no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—41no—
214C4×C61C22×D411yescharacteristic
215C4×C61C22×D411yescharacteristic
216Dic61—22no—
217Dic61—21no—
218Dic61—41no—
219#3291—611nomaximal, Sylow
220C2×C61—21no—
221C2×C61—41no—
222C2×C61—41no—
223C2×C61—41no—
224C2×C61—81no—
225C2×C61D4211yescharacteristic
226D61—41no—
227D61—81no—
228#577—611no—
229#577—611no—
230#577—611no—
231#577D6111yescharacteristic, complemented
232#492—611no—
233#471—611no—
234#471—611no—
235#471—611no—
236#471—611no—
237#456—611no—
238#456—611no—
239#453—611no—
240#453—611no—
241#443—611no—
242#443—611no—
243C61#329111yescharacteristic, complemented, Sylow
2442−1+4—611no—
2452−1+4C2×D6111yescharacteristic
246H(5,𝔽2)—611no—
247H(5,𝔽2)C2×D6111yescharacteristic, complemented
248#137—21no—
249#137—611no—
250#137—611no—
251#137—611no—
252#137—1221no—
253#137—1221no—
254#137—1221no—
255#137C2×D6111yescharacteristic, complemented
256AGL(1,ℤ/8)—21no—
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)C2×D6111yescharacteristic
264#135—21no—
265#135—611no—
266#135—1221no—
267#135—1221no—
268#135—1221no—
269#135C2×D6111yescharacteristic
270C2×SD16—21no—
271C2×SD16—611no—
272C2×SD16—611no—
273C2×SD16—611no—
274C2×SD16—1221no—
275C2×SD16—1221no—
276C2×SD16—1221no—
277C2×SD16C2×D6111yescharacteristic, complemented
278#131—611no—
279#131—611no—
280#131—611no—
281#131C2×D6111yescharacteristic, complemented
282C4⋊Q8—611no—
283#127—611no—
284#108—611no—
285#108—611no—
286#104—611no—
287#104—611no—
288#104—611no—
289#104—611no—
290#101—611no—
291#101—611no—
292#100—611no—
293#100—611no—
294C4×C8—611no—
295#41—21no—
296#41—21no—
297#41—21no—
298#41—21no—
299#41—41no—
300#41—611no—
301#41—1221no—
302#41—1221no—
303#41—1221no—
304#41—1221no—
305#41—2441no—
306#41C22×D6111yescharacteristic
307#41C22×D6111yescharacteristic
308#41C22×D6111yescharacteristic
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—611no—
312C2×Q8—1221no—
313C2×Q8—1221no—
314C2×Q8C22×D6111yescharacteristic
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—41no—
318C2×D4—611no—
319C2×D4—1221no—
320C2×D4—1221no—
321C2×D4—2441no—
322C2×D4—2441no—
323C2×D4C22×D6111yescharacteristic
324Q16—21no—
325Q16—611no—
326Q16—1221no—
327Q16—1221no—
328Q16—1221no—
329Q16C22⋊D6111yescharacteristic, complemented
330SD16—21no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—611no—
335SD16—611no—
336SD16—1221no—
337SD16—1221no—
338SD16—1221no—
339SD16—1221no—
340SD16—1221no—
341SD16—1221no—
342SD16—1221no—
343SD16—1221no—
344SD16—1221no—
345SD16—1221no—
346SD16—1221no—
347SD16—1221no—
348SD16C22⋊D6111yescharacteristic, complemented
349SD16C22⋊D6111yescharacteristic, complemented
350D8—21no—
351D8—611no—
352D8—1221no—
353D8—1221no—
354D8—1221no—
355D8C22⋊D6111yescharacteristic, complemented
356M16—21no—
357M16—611no—
358M16—611no—
359M16—611no—
360M16—1221no—
361M16—1221no—
362M16—1221no—
363M16C22×D6111yescharacteristic
364C2×C8—21no—
365C2×C8—611no—
366C2×C8—1221no—
367C2×C8—1221no—
368C2×C8—1221no—
369C2×C8C22×D6111yescharacteristic
370C4⋊C4—2441no—
371C42—611no—
372C23—21no—
373C23—41no—
374C23—1221no—
375C23—2441no—
376Q8—21no—
377Q8—21no—
378Q8—41no—
379Q8—611no—
380Q8—1221no—
381Q8—1221no—
382Q8—2441no—
383Q8D4×D6111yescharacteristic
384Q8C2×C22⋊D6111yescharacteristic
385Q8C2×C22⋊D6111yescharacteristic
386D4—21no—
387D4—21no—
388D4—21no—
389D4—21no—
390D4—21no—
391D4—41no—
392D4—41no—
393D4—41no—
394D4—611no—
395D4—1221no—
396D4—1221no—
397D4—1221no—
398D4—4882no—
399D4—2441no—
400D4—2441no—
401D4—2441no—
402D4D4×D6111yescharacteristic
403D4C2×C22⋊D6111yescharacteristic
404D4C2×C22⋊D6111yescharacteristic
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—1221no—
413C2×C4—1221no—
414C2×C4—1221no—
415C2×C4—2441no—
416C2×C4—2441no—
417C2×C4—2441no—
418C2×C4C23×D6111yescharacteristic
419C8—21no—
420C8—611no—
421C8—611no—
422C8—1221no—
423C8—1221no—
424C8—1221no—
425C8C2×C22⋊D6111yescharacteristic
426C8C2×C22⋊D6111yescharacteristic
427C22—21no—
428C22—21no—
429C22—21no—
430C22—41no—
431C22—81no—
432C22—161no—
433C22—1221no—
434C22—9761no—
435C22—4881no—
436C22—2441no—
437C22#1451982211yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—41no—
442C4—1222no—
443C4—1221no—
444C4—2441no—
445C4C2×D4×D6111yescharacteristic
446C4C22×C22⋊D6111yescharacteristic
447C2—21no—
448C2—41no—
449C2—41no—
450C2—41no—
451C2—81no—
452C2—4881no—
453C2—2441no—
454C2D4×C22⋊D6111yescharacteristic
subgroupG/H
centerC2D4×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#577C2
socleC2×C61D42
hypercenter#577D61
hypocenterC61#3291
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #577

Complements

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

NH ≅ G/Ntype
1. #16840573C2semidirect
2. #16840570C2semidirect
3. #16840569C2semidirect
4. #16840133C2semidirect
5. #16840027C2semidirect
6. #16840025C2semidirect
7. #16840023C2semidirect
8. #16840022C2semidirect
9. #16839945C2semidirect
10. #16839943C2semidirect
11. #16839930C2semidirect
12. #16839928C2semidirect
13. #16839879C2semidirect
14. #16839877C2semidirect
15. C61×#577C2semidirect
17. #14519823C22semidirect
20. #14519808C22semidirect
22. #14519807C22semidirect
23. #14519807C22semidirect
34. C2×#11758190C22semidirect
36. C2×#11758200C22semidirect
38. C2×#11758201C22semidirect
40. #14519784C22semidirect
41. #14519784C22semidirect
42. #14519783C22semidirect
43. #14519775C22semidirect
45. #14519713C22semidirect
46. #14519712C22semidirect
47. #14519704C22semidirect
48. #14519704C22semidirect
49. #14519704C22semidirect
50. #14519703C22semidirect
51. #14519696C22semidirect
52. #14519695C22semidirect
53. #14519694C22semidirect
54. #14519693C22semidirect
55. C8×Dic61C22semidirect
57. H(5,𝔽2)×C61C22semidirect
59. #137×C61C22semidirect
65. C2×SD16×C61C22semidirect
66. #131×C61C22semidirect
97. Q16×C61D4semidirect
102. SD16×C61D4semidirect
103. SD16×C61D4semidirect
105. D8×C61D4semidirect
113. #11758202D4semidirect
119. #11758201D4semidirect
125. #11758200D4semidirect
129. #11758199D4semidirect
231. #577D61semidirect
243. C61#3291semidirect
247. H(5,𝔽2)C2×D61semidirect
255. #137C2×D61semidirect
277. C2×SD16C2×D61semidirect
281. #131C2×D61semidirect
329. Q16C22⋊D61semidirect
348. SD16C22⋊D61semidirect
349. SD16C22⋊D61semidirect
355. D8C22⋊D61semidirect