Finite Group Databasebeta

← #21457602

Subgroups — #21457602

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#16840574C211yesmaximal, characteristic, complemented
3#16840568C211yesmaximal, characteristic, complemented
4#16840566C211yesmaximal, characteristic, complemented
5#16840143C211yesmaximal, characteristic, complemented
6#16840036C211yesmaximal, characteristic, complemented
7#16840031C211yesmaximal, characteristic, complemented
8#16840026C211yesmaximal, characteristic, complemented
9#16839942C211yesmaximal, characteristic, complemented
10#16839938C211yesmaximal, characteristic, complemented
11#16839937C211yesmaximal, characteristic, complemented
12#16839933C211yesmaximal, characteristic, complemented
13#16839878C211yesmaximal, characteristic, complemented
14#16839877C211yesmaximal, characteristic, complemented
15C61×#471C211yesmaximal, characteristic, complemented
16#14519825C2211yescharacteristic, complemented
17#14519824C2211yescharacteristic, complemented
18#14519823C2211yescharacteristic
19#14519822C2211yescharacteristic
20#14519810—21no—
21#14519810C2211yescharacteristic
22#14519810C2211yescharacteristic, complemented
23#14519809—21no—
24#14519808C2211yescharacteristic
25#14519806—21no—
26#14519806—21no—
27#14519805—21no—
28#14519805C2211yescharacteristic
29#14519805C2211yescharacteristic, complemented
30#14519804—21no—
31#14519804—21no—
32#14519803C2211yescharacteristic, complemented
33#14519801—21no—
34#14519799—21no—
35#14519799C2211yescharacteristic
36#14519798—21no—
37#14519798—21no—
38#14519798—21no—
39#14519797C2211yescharacteristic
40C2×#11758202C2211yescharacteristic, complemented
41Q16×D61—21no—
42C2×#11758190—21no—
43C2×#11758190C2211yescharacteristic, complemented
44SD16×D61—21no—
45C2×#11758199C2211yescharacteristic
46D8×D61—21no—
47#14519785C2211yescharacteristic
48#14519785C2211yescharacteristic, complemented
49#14519783C2211yescharacteristic, complemented
50#14519766C2211yescharacteristic, complemented
51#14519764C2211yescharacteristic, complemented
52#14519712C2211yescharacteristic, complemented
53#14519704C2211yescharacteristic, complemented
54#14519703C2211yescharacteristic
55#14519703C2211yescharacteristic, complemented
56#14519703C2211yescharacteristic, complemented
57#14519695C2211yescharacteristic, complemented
58#14519693C2211yescharacteristic, complemented
59C8×Dic61C2211yescharacteristic, 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—
71#11758226—21no—
72#11758226—21no—
73#11758226—21no—
74Q8×D61—21no—
75Q8×D61—21no—
76Q8×D61—21no—
77#11758224—21no—
78#11758224—21no—
79#11758224—21no—
80#11758224—41no—
81D4×D61—21no—
82D4×D61—21no—
83D4×D61—21no—
84D4×D61—41no—
85#11758222—21no—
86#11758222—21no—
87#11758222—41no—
88#11758222C2311yescharacteristic
89#11758222C2311yescharacteristic
90#11758222C2311yescharacteristic
91C2×D244—21no—
92C2×D244C2311yescharacteristic
93C2×Dic122—21no—
94C2×Dic122C2311yescharacteristic
95Q16×C61—21no—
96SD16×C61—21no—
97SD16×C61—21no—
98SD16×C61—21no—
99SD16×C61—21no—
100D8×C61—21no—
101M16×C61—21no—
102M16×C61C2311yescharacteristic
103M16×C61C2311yescharacteristic
104M16×C61C2311yescharacteristic
105C2×C8×C61—21no—
106C2×C8×C61C2311yescharacteristic
107C22⋊Dic61—41no—
108#11758202—21no—
109#11758202—21no—
110#11758202—21no—
111#11758202D411yescharacteristic
112#11758201—21no—
113#11758201D411yescharacteristic
114#11758200—21no—
115#11758200D411yescharacteristic
116#11758199—21no—
117#11758199—21no—
118#11758199—21no—
119#11758199D411yescharacteristic
120#11758198—41no—
121C4×Dic61C2311yescharacteristic
122#11758194C2311yescharacteristic
123C2×#92418C2311yescharacteristic
124Dic244—21no—
125Dic244—21no—
126Dic244D411yescharacteristic
127D488—21no—
128D488—21no—
129D488D411yescharacteristic
130#11758190—21no—
131#11758190—21no—
132#11758190—21no—
133#11758190—21no—
134#11758190—21no—
135#11758190—21no—
136#11758190D411yescharacteristic
137#11758190D411yescharacteristic
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—41no—
147C22×D61—41no—
148Q8×C61—21no—
149Q8×C61—21no—
150Q8×C61C2×D411yescharacteristic
151D4×C61—21no—
152D4×C61—21no—
153D4×C61—21no—
154D4×C61C2×D411yescharacteristic
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61C2411yescharacteristic
158C22⋊D61—21no—
159C22⋊D61—21no—
160C22⋊D61—21no—
161C22⋊D61—41no—
162C22⋊D61—41no—
163C22⋊D61—41no—
164C22⋊D61—41no—
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169D244—21no—
170D244—21no—
171D244—41no—
172D244—41no—
173D244C2×D411yescharacteristic
174D244C2×D411yescharacteristic
175D244C2×D411yescharacteristic
176C4×D61—21no—
177C4×D61—21no—
178C4×D61—21no—
179C4×D61—41no—
180C4×D61—41no—
181C4×D61—41no—
182C4×D61—41no—
183Dic122—21no—
184Dic122—21no—
185Dic122—41no—
186Dic122—41no—
187Dic122C2×D411yescharacteristic
188Dic122C2×D411yescharacteristic
189Dic122C2×D411yescharacteristic
190C8×C61—21no—
191C8×C61—21no—
192C8×C61—21no—
193C8×C61C2×D411yescharacteristic
194C8×C61C2×D411yescharacteristic
195#92418—21no—
196#92418C2×D411yescharacteristic
197#92418C2×D411yescharacteristic
198C22×C61—21no—
199C22×C61—41no—
200C22×C61—81no—
201C22×C61H(5,𝔽2)11yescharacteristic
202C2×D61—21no—
203C2×D61—21no—
204C2×D61—21no—
205C2×D61—41no—
206C2×D61—81no—
207C2×D61—161no—
208C2×D61—161no—
209C4×C61—21no—
210C4×C61—41no—
211C4×C61C22×D411yescharacteristic
212C4×C61C22×D411yescharacteristic
213Dic61—21no—
214Dic61—21no—
215Dic61—21no—
216Dic61—41no—
217Dic61—41no—
218#3290—611nomaximal, Sylow
219C2×C61—21no—
220C2×C61—41no—
221C2×C61—81no—
222C2×C61D4211yescharacteristic
223D61—41no—
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#471D6111yescharacteristic, complemented
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+4—611no—
245H(5,𝔽2)—611no—
246H(5,𝔽2)—611no—
247#137—611no—
248#137—611no—
249#137—611no—
250#137—1221no—
251#137—1221no—
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)—1221no—
259AGL(1,ℤ/8)—1221no—
260AGL(1,ℤ/8)—1221no—
261AGL(1,ℤ/8)—1221no—
262AGL(1,ℤ/8)C2×D6111yescharacteristic
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—1221no—
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#108C2×D6111yescharacteristic, complemented
285#104—611no—
286#104—611no—
287#104—611no—
288#104—611no—
289#101—611no—
290#101C2×D6111yescharacteristic, complemented
291#100—611no—
292#100C2×D6111yescharacteristic, complemented
293C4×C8—611no—
294#41—611no—
295#41—611no—
296#41—611no—
297#41—1221no—
298#41—1221no—
299#41—1221no—
300#41—1221no—
301#41—1221no—
302#41—1221no—
303#41—1221no—
304#41—1221no—
305#41—2441no—
306#41—2441no—
307#41C22×D6111yescharacteristic
308C2×Q8—611no—
309C2×Q8—1221no—
310C2×Q8—1221no—
311C2×Q8—1221no—
312C2×Q8—1221no—
313C2×Q8C22×D6111yescharacteristic
314C2×D4—611no—
315C2×D4—1221no—
316C2×D4—1221no—
317C2×D4—1221no—
318C2×D4—1221no—
319C2×D4—2441no—
320C2×D4—2441no—
321C2×D4C22×D6111yescharacteristic
322Q16—21no—
323Q16—611no—
324Q16—611no—
325Q16—1221no—
326Q16—1221no—
327Q16—1221no—
328Q16—1221no—
329Q16—1221no—
330SD16—21no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—611no—
335SD16—611no—
336SD16—611no—
337SD16—611no—
338SD16—1221no—
339SD16—1221no—
340SD16—1221no—
341SD16—1221no—
342SD16—1221no—
343SD16—1221no—
344SD16—1221no—
345SD16—1221no—
346D8—21no—
347D8—611no—
348D8—611no—
349D8—1221no—
350D8—1221no—
351D8—1221no—
352D8—1221no—
353D8—1221no—
354M16—21no—
355M16—611no—
356M16—1221no—
357M16—1221no—
358M16—1221no—
359M16C22×D6111yescharacteristic
360M16C22×D6111yescharacteristic
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—1221no—
373C23—2441no—
374C23—2441no—
375Q8—21no—
376Q8—21no—
377Q8—611no—
378Q8—611no—
379Q8—611no—
380Q8—1221no—
381Q8—1221no—
382Q8—2441no—
383Q8—2441no—
384Q8D4×D6111yescharacteristic
385D4—21no—
386D4—21no—
387D4—21no—
388D4—611no—
389D4—611no—
390D4—611no—
391D4—1221no—
392D4—1221no—
393D4—1221no—
394D4—1221no—
395D4—1221no—
396D4—2441no—
397D4—2441no—
398D4—2441no—
399D4—2441no—
400D4—2441no—
401D4—2441no—
402D4D4×D6111yescharacteristic
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—1221no—
406C2×C4—1221no—
407C2×C4—1221no—
408C2×C4—1221no—
409C2×C4—1221no—
410C2×C4—2441no—
411C2×C4—2441no—
412C2×C4—2441no—
413C2×C4—2441no—
414C2×C4—2441no—
415C2×C4—2441no—
416C2×C4C23×D6111yescharacteristic
417C8—21no—
418C8—21no—
419C8—21no—
420C8—611no—
421C8—611no—
422C8—1221no—
423C8D4×D6111yescharacteristic
424C8D4×D6111yescharacteristic
425C22—21no—
426C22—41no—
427C22—81no—
428C22—1221no—
429C22—1221no—
430C22—1221no—
431C22—9761no—
432C22—9761no—
433C22—4881no—
434C22—2441no—
435C22#1451982311yescharacteristic
436C4—21no—
437C4—41no—
438C4—1221no—
439C4—1221no—
440C4—1221no—
441C4—2441no—
442C4—2441no—
443C4C2×D4×D6111yescharacteristic
444C4C2×D4×D6111yescharacteristic
445C2—21no—
446C2—41no—
447C2—81no—
448C2—4881no—
449C2—2441no—
450C2—2441no—
451C2—2441no—
452C2#1684039611yescharacteristic
subgroupG/H
centerC2#16840396
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#471C2
socleC2×C61D42
hypercenter#471D61
hypocenterC61#3290
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. #16840578C2semidirect
2. #16840574C2semidirect
3. #16840568C2semidirect
4. #16840566C2semidirect
5. #16840143C2semidirect
6. #16840036C2semidirect
7. #16840031C2semidirect
8. #16840026C2semidirect
9. #16839942C2semidirect
10. #16839938C2semidirect
11. #16839937C2semidirect
12. #16839933C2semidirect
13. #16839878C2semidirect
14. #16839877C2semidirect
15. C61×#471C2semidirect
16. #14519825C22semidirect
17. #14519824C22semidirect
22. #14519810C22semidirect
29. #14519805C22semidirect
32. #14519803C22semidirect
40. C2×#11758202C22semidirect
43. C2×#11758190C22semidirect
48. #14519785C22semidirect
49. #14519783C22semidirect
50. #14519766C22semidirect
51. #14519764C22semidirect
52. #14519712C22semidirect
53. #14519704C22semidirect
55. #14519703C22semidirect
56. #14519703C22semidirect
57. #14519695C22semidirect
58. #14519693C22semidirect
59. C8×Dic61C22semidirect
60. #137×C61C22semidirect
62. C2×SD16×C61C22semidirect
63. #131×C61C22semidirect
64. #108×C61C22semidirect
65. #101×C61C22semidirect
66. #100×C61C22semidirect
235. #471D61semidirect
242. C61#3290semidirect
254. #137C2×D61semidirect
274. C2×SD16C2×D61semidirect
280. #131C2×D61semidirect
284. #108C2×D61semidirect
290. #101C2×D61semidirect
292. #100C2×D61semidirect