Finite Group Databasebeta

← #21457599

Subgroups — #21457599

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#16840577C211yesmaximal, characteristic, complemented
2#16840569C211yesmaximal, characteristic, complemented
3#16840565C211yesmaximal, characteristic, complemented
4#16840143C211yesmaximal, characteristic, complemented
5#16840035C211yesmaximal, characteristic, complemented
6#16840030C211yesmaximal, characteristic, complemented
7#16840025C211yesmaximal, characteristic, complemented
8#16840022C211yesmaximal, characteristic, complemented
9#16839940C211yesmaximal, characteristic, complemented
10#16839938C211yesmaximal, characteristic, complemented
11#16839935C211yesmaximal, characteristic, complemented
12#16839933C211yesmaximal, characteristic, complemented
13#16839879C211yesmaximal, characteristic, complemented
14#16839877C211yesmaximal, characteristic, complemented
15C61×#577C211yesmaximal, characteristic, complemented
16#14519824C2211yescharacteristic, complemented
17#14519823C2211yescharacteristic
18#14519809—21no—
19#14519808—21no—
20#14519808C2211yescharacteristic, complemented
21#14519807—21no—
22#14519807C2211yescharacteristic
23#14519807C2211yescharacteristic, complemented
24#14519803—21no—
25#14519803C2211yescharacteristic
26#14519802—21no—
27#14519802C2211yescharacteristic
28#14519802C2211yescharacteristic, complemented
29#14519801—21no—
30#14519798—21no—
31#14519797—21no—
32#14519797—21no—
33#14519797C2211yescharacteristic
34C2×#11758202—21no—
35C2×#11758202C2211yescharacteristic, complemented
36C2×#11758190C2211yescharacteristic, complemented
37SD16×D61—21no—
38C2×#11758199—21no—
39C2×#11758199C2211yescharacteristic
40#14519784C2211yescharacteristic
41#14519784C2211yescharacteristic, complemented
42#14519783C2211yescharacteristic, complemented
43#14519766C2211yescharacteristic, complemented
44#14519764C2211yescharacteristic, complemented
45#14519713C2211yescharacteristic, complemented
46#14519712C2211yescharacteristic, complemented
47#14519704C2211yescharacteristic
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, complemented
57H(5,𝔽2)×C61C2211yescharacteristic
58#137×C61—21no—
59#137×C61C2211yescharacteristic
60AGL(1,ℤ/8)×C61—21no—
61AGL(1,ℤ/8)×C61C2211yescharacteristic, complemented
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
82#11758226—21no—
83Q8×D61—21no—
84#11758224—21no—
85#11758224—41no—
86D4×D61—21no—
87D4×D61—41no—
88#11758222—21no—
89#11758222—21no—
90#11758222C2311yescharacteristic
91C2×D244—21no—
92C2×D244C2311yescharacteristic
93C2×Dic122—21no—
94C2×Dic122C2311yescharacteristic
95Q16×C61—21no—
96Q16×C61D411yescharacteristic
97SD16×C61—21no—
98SD16×C61—21no—
99SD16×C61—21no—
100SD16×C61—21no—
101SD16×C61D411yescharacteristic
102SD16×C61D411yescharacteristic
103D8×C61—21no—
104D8×C61D411yescharacteristic
105M16×C61—21no—
106M16×C61C2311yescharacteristic
107C2×C8×C61—21no—
108C2×C8×C61C2311yescharacteristic
109C22⋊Dic61—41no—
110#11758202—21no—
111#11758202—21no—
112#11758202—21no—
113#11758202—21no—
114#11758202—21no—
115#11758202D411yescharacteristic
116#11758201—21no—
117#11758201—21no—
118#11758201—21no—
119#11758201D411yescharacteristic
120#11758200—21no—
121#11758200—21no—
122#11758200—21no—
123#11758200D411yescharacteristic
124#11758199—21no—
125#11758199—21no—
126#11758199—21no—
127#11758199—21no—
128#11758199—21no—
129#11758199D411yescharacteristic
130#11758198—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—
176C2×Dic61—21no—
177C2×Dic61—21no—
178C2×Dic61—41no—
179D244—21no—
180D244—21no—
181D244—41no—
182D244C2×D411yescharacteristic
183C4×D61—21no—
184C4×D61—41no—
185C4×D61—41no—
186Dic122—21no—
187Dic122—21no—
188Dic122—41no—
189Dic122C2×D411yescharacteristic
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—21no—
200C22×C61—21no—
201C22×C61—41no—
202C22×C61—81no—
203C22×C61—161no—
204C22×C61H(5,𝔽2)11yescharacteristic
205C2×D61—21no—
206C2×D61—41no—
207C2×D61—81no—
208C2×D61—161no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—41no—
213C4×C61C22×D411yescharacteristic
214C4×C61C22×D411yescharacteristic
215Dic61—21no—
216Dic61—41no—
217Dic61—41no—
218#3290—611nomaximal, Sylow
219C2×C61—21no—
220C2×C61—41no—
221C2×C61—41no—
222C2×C61—41no—
223C2×C61—81no—
224C2×C61D4211yescharacteristic
225D61—41no—
226D61—81no—
227#578—611no—
228#577—611no—
229#577D6111yescharacteristic, complemented
230#576—611no—
231#495—611no—
232#473—611no—
233#472—611no—
234#471—611no—
235#471—611no—
236#455—611no—
237#455—611no—
238#454—611no—
239#454—611no—
240#443—611no—
241#443—611no—
242C61#329011yescharacteristic, complemented, Sylow
2432−1+4—611no—
2442−1+4C2×D6111yescharacteristic, complemented
245H(5,𝔽2)—611no—
246H(5,𝔽2)C2×D6111yescharacteristic
247#137—21no—
248#137—611no—
249#137—611no—
250#137—611no—
251#137—1221no—
252#137—1221no—
253#137—1221no—
254#137C2×D6111yescharacteristic
255AGL(1,ℤ/8)—21no—
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)C2×D6111yescharacteristic, complemented
263#135—21no—
264#135—611no—
265#135—1221no—
266#135—1221no—
267#135—1221no—
268#135C2×D6111yescharacteristic
269C2×Q16—611no—
270C2×Q16—1221no—
271C2×SD16—21no—
272C2×SD16—611no—
273C2×SD16—1221no—
274C2×SD16C2×D6111yescharacteristic, complemented
275C2×D8—611no—
276C2×D8—1221no—
277#131—611no—
278#131—611no—
279#131—611no—
280#131C2×D6111yescharacteristic, complemented
281#124—611no—
282#124—611no—
283#108—611no—
284#108—611no—
285#104—611no—
286#104—611no—
287#104—611no—
288#104—611no—
289#101—611no—
290#101—611no—
291#100—611no—
292#100—611no—
293C4×C8—611no—
294#41—21no—
295#41—21no—
296#41—21no—
297#41—21no—
298#41—41no—
299#41—611no—
300#41—1221no—
301#41—1221no—
302#41—1221no—
303#41—1221no—
304#41—2441no—
305#41C22×D6111yescharacteristic
306#41C22×D6111yescharacteristic
307#41C22×D6111yescharacteristic
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—611no—
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—611no—
324Q16—1221no—
325Q16—1221no—
326Q16—1221no—
327Q16—1221no—
328Q16—1221no—
329Q16C22⋊D6111yescharacteristic
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—
344SD16C22⋊D6111yescharacteristic
345SD16C22⋊D6111yescharacteristic
346D8—21no—
347D8—611no—
348D8—1221no—
349D8—1221no—
350D8—1221no—
351D8—1221no—
352D8—1221no—
353D8C22⋊D6111yescharacteristic
354M16—21no—
355M16—611no—
356M16—611no—
357M16—611no—
358M16—1221no—
359M16—1221no—
360M16—1221no—
361M16C22×D6111yescharacteristic
362C2×C8—21no—
363C2×C8—611no—
364C2×C8—1221no—
365C2×C8—1221no—
366C2×C8—1221no—
367C2×C8C22×D6111yescharacteristic
368C22⋊C4—2441no—
369C22⋊C4—2441no—
370C42—611no—
371C23—21no—
372C23—41no—
373C23—1221no—
374C23—2441no—
375Q8—21no—
376Q8—21no—
377Q8—41no—
378Q8—611no—
379Q8—1221no—
380Q8—1221no—
381Q8—2441no—
382Q8D4×D6111yescharacteristic
383Q8C2×C22⋊D6111yescharacteristic
384Q8C2×C22⋊D6111yescharacteristic
385D4—21no—
386D4—21no—
387D4—21no—
388D4—21no—
389D4—21no—
390D4—41no—
391D4—41no—
392D4—41no—
393D4—611no—
394D4—1221no—
395D4—1221no—
396D4—1221no—
397D4—2441no—
398D4—2441no—
399D4—2441no—
400D4D4×D6111yescharacteristic
401D4C2×C22⋊D6111yescharacteristic
402D4C2×C22⋊D6111yescharacteristic
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—1221no—
411C2×C4—1221no—
412C2×C4—1221no—
413C2×C4—2441no—
414C2×C4—2441no—
415C2×C4—2441no—
416C2×C4C23×D6111yescharacteristic
417C8—21no—
418C8—611no—
419C8—611no—
420C8—1221no—
421C8—1221no—
422C8—1221no—
423C8C2×C22⋊D6111yescharacteristic
424C8C2×C22⋊D6111yescharacteristic
425C22—21no—
426C22—21no—
427C22—21no—
428C22—41no—
429C22—81no—
430C22—161no—
431C22—1221no—
432C22—9761no—
433C22—4881no—
434C22—2441no—
435C22#1451982211yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—41no—
440C4—1221no—
441C4—2441no—
442C4—2441no—
443C4C2×D4×D6111yescharacteristic
444C4C22×C22⋊D6111yescharacteristic
445C2—21no—
446C2—41no—
447C2—41no—
448C2—41no—
449C2—81no—
450C2—4881no—
451C2—2441no—
452C2D4×C22⋊D6111yescharacteristic
subgroupG/H
centerC2D4×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#577C2
socleC2×C61D42
hypercenter#577D61
hypocenterC61#3290
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. #16840577C2semidirect
2. #16840569C2semidirect
3. #16840565C2semidirect
4. #16840143C2semidirect
5. #16840035C2semidirect
6. #16840030C2semidirect
7. #16840025C2semidirect
8. #16840022C2semidirect
9. #16839940C2semidirect
10. #16839938C2semidirect
11. #16839935C2semidirect
12. #16839933C2semidirect
13. #16839879C2semidirect
14. #16839877C2semidirect
15. C61×#577C2semidirect
16. #14519824C22semidirect
20. #14519808C22semidirect
23. #14519807C22semidirect
28. #14519802C22semidirect
35. C2×#11758202C22semidirect
36. C2×#11758190C22semidirect
41. #14519784C22semidirect
42. #14519783C22semidirect
43. #14519766C22semidirect
44. #14519764C22semidirect
45. #14519713C22semidirect
46. #14519712C22semidirect
48. #14519704C22semidirect
49. #14519704C22semidirect
50. #14519703C22semidirect
51. #14519696C22semidirect
52. #14519695C22semidirect
53. #14519694C22semidirect
54. #14519693C22semidirect
55. C8×Dic61C22semidirect
56. 2−1+4×C61C22semidirect
61. AGL(1,ℤ/8)×C61C22semidirect
65. C2×SD16×C61C22semidirect
66. #131×C61C22semidirect
229. #577D61semidirect
242. C61#3290semidirect
244. 2−1+4C2×D61semidirect
262. AGL(1,ℤ/8)C2×D61semidirect
274. C2×SD16C2×D61semidirect
280. #131C2×D61semidirect