Finite Group Databasebeta

← #21457617

Subgroups — #21457617

Order 7808.

476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840567C211yesmaximal, characteristic, complemented
2#16840566C212yesmaximal, complemented
3#16840563C211yesmaximal, characteristic, complemented
4#16840137C211yesmaximal, characteristic, complemented
5#16840033C211yesmaximal, characteristic, complemented
6#16840031C212yesmaximal, complemented
7#16839932C212yesmaximal, complemented
8#16839928C212yesmaximal, complemented
9#16839878C211yesmaximal, characteristic, complemented
10#16839877C211yesmaximal, characteristic, complemented
11C61×#472C211yesmaximal, characteristic, complemented
12#14519823C2212yescomplemented
13#14519822C2212yescomplemented
14#14519805—22no—
15#14519805C2212yescomplemented
16#14519805C2212yescomplemented
17#14519804—22no—
18#14519803C2212yescomplemented
19#14519801—22no—
20#14519801—22no—
21#14519799—21no—
22#14519799C2211yescharacteristic
23#14519798—22no—
24#14519797C2211yescharacteristic
25#14519796—21no—
26C2×D488—21no—
27C2×D488C2211yescharacteristic, complemented
28C2×#11758199C2212yescomplemented
29D8×D61—22no—
30D8×D61—21no—
31#14519785C2212yescomplemented
32#14519783C2211yescharacteristic, complemented
33#14519773C2212yescomplemented
34#14519712C2211yescharacteristic, complemented
35#14519704C2211yescharacteristic, complemented
36#14519703C2211yescharacteristic, complemented
37#14519703C2212yescomplemented
38#14519693C2212yescomplemented
39C8×Dic61C2211yescharacteristic, complemented
40AGL(1,ℤ/8)×C61C2212yescomplemented
41C2×D8×C61C2211yescharacteristic, complemented
42#131×C61C2211yescharacteristic, complemented
43#108×C61C2211yescharacteristic, complemented
44#100×C61C2212yescomplemented
45#41×C61C2311yescharacteristic
46C2×D4×C61C2312yes—
47C2×C22⋊D61—42no—
48C2×C22⋊D61—42no—
49#11758226—22no—
50#11758224—22no—
51#11758224—22no—
52D4×D61—22no—
53D4×D61—22no—
54D4×D61—22no—
55D4×D61—42no—
56#11758222—22no—
57#11758222C2311yescharacteristic
58#11758222C2312yes—
59C2×D244—22no—
60C2×D244C2312yes—
61SD16×C61—22no—
62D8×C61—22no—
63D8×C61—21no—
64D8×C61—21no—
65M16×C61—21no—
66M16×C61C2311yescharacteristic
67M16×C61C2312yes—
68C2×C8×C61—21no—
69C2×C8×C61C2311yescharacteristic
70#11758202D411yescharacteristic, complemented
71#11758201D411yescharacteristic, complemented
72#11758200—22no—
73#11758200D411yescharacteristic, complemented
74#11758199—22no—
75#11758199—22no—
76#11758199—22no—
77#11758199D411yescharacteristic, complemented
78C4×Dic61C2311yescharacteristic
79#11758194C2311yescharacteristic
80C2×#92418C2311yescharacteristic
81Dic244D411yescharacteristic, complemented
82D488—22no—
83D488—22no—
84D488—21no—
85D488—21no—
86D488D411yescharacteristic, complemented
87#11758190—22no—
88#11758190—22no—
89#11758190D412yescomplemented
90#11758189—21no—
91#11758189—22no—
92C8×D61—21no—
93C8×D61—22no—
94C23×C61—22no—
95C22×D61—22no—
96C22×D61—42no—
97C22×D61—42no—
98Q8×C61C2×D411yescharacteristic
99D4×C61—21no—
100D4×C61—22no—
101D4×C61—22no—
102D4×C61C2×D411yescharacteristic
103C2×C4×C61—21no—
104C2×C4×C61C2411yescharacteristic
105C22⋊D61—22no—
106C22⋊D61—21no—
107C22⋊D61—42no—
108C22⋊D61—42no—
109C22⋊D61—42no—
110C22⋊D61—84no—
111C2×Dic61—21no—
112C2×Dic61—42no—
113D244—22no—
114D244—22no—
115D244—42no—
116D244C2×D412yes—
117D244C2×D411yescharacteristic
118C4×D61—21no—
119C4×D61—22no—
120C4×D61—42no—
121Dic122C2×D411yescharacteristic
122Dic122C2×D412yes—
123C8×C61—22no—
124C8×C61—21no—
125C8×C61C2×D411yescharacteristic
126C8×C61C2×D411yescharacteristic
127#92418—21no—
128#92418C2×D411yescharacteristic
129#92418C2×D411yescharacteristic
130C22×C61—21no—
131C22×C61—42no—
132C22×C61—82no—
133C22×C61H(5,𝔽2)11yescharacteristic
134C2×D61—22no—
135C2×D61—21no—
136C2×D61—42no—
137C2×D61—82no—
138C2×D61—162no—
139C2×D61—162no—
140C4×C61—21no—
141C4×C61C22×D411yescharacteristic
142C4×C61C22×D411yescharacteristic
143Dic61—22no—
144Dic61—22no—
145Dic61—21no—
146#3292—611nomaximal, Sylow
147C2×C61—21no—
148C2×C61—41no—
149C2×C61—82no—
150C2×C61D4211yescharacteristic
151D61—42no—
152D61—41no—
153D61—82no—
154#576—612no—
155#576—611no—
156#576—611no—
157#493—611no—
158#472—611no—
159#472—612no—
160#472D6111yescharacteristic, complemented
161#453—612no—
162#453—612no—
163#443—611no—
164#443—611no—
165C61#329211yescharacteristic, complemented, Sylow
166H(5,𝔽2)—612no—
167H(5,𝔽2)—612no—
168AGL(1,ℤ/8)—612no—
169AGL(1,ℤ/8)—612no—
170AGL(1,ℤ/8)—612no—
171AGL(1,ℤ/8)—1222no—
172AGL(1,ℤ/8)—1222no—
173AGL(1,ℤ/8)—1222no—
174AGL(1,ℤ/8)—1222no—
175AGL(1,ℤ/8)C2×D6112yescomplemented
176#135—611no—
177#135—611no—
178#135—1221no—
179#135—1221no—
180#135—1222no—
181C2×D8—612no—
182C2×D8—611no—
183C2×D8—1221no—
184C2×D8—1222no—
185C2×D8—1221no—
186C2×D8C2×D6111yescharacteristic, complemented
187#131—612no—
188#131—611no—
189#131C2×D6111yescharacteristic, complemented
190#127—612no—
191#108—611no—
192#108C2×D6111yescharacteristic, complemented
193#104—611no—
194#104—612no—
195#104—611no—
196#100—612no—
197#100C2×D6112yescomplemented
198C4×C8—611no—
199#41—612no—
200#41—611no—
201#41—1222no—
202#41—1222no—
203#41—1222no—
204#41—1222no—
205#41C22×D6111yescharacteristic
206C2×D4—612no—
207C2×D4—1222no—
208C2×D4—1222no—
209C2×D4—1222no—
210C2×D4—1222no—
211C2×D4—2442no—
212C2×D4—2442no—
213C2×D4—2442no—
214C2×D4C22×D6112yes—
215Q16—611no—
216Q16—611no—
217SD16—22no—
218SD16—611no—
219SD16—611no—
220SD16—612no—
221SD16—1222no—
222SD16—1222no—
223SD16—1222no—
224D8—22no—
225D8—21no—
226D8—21no—
227D8—611no—
228D8—611no—
229D8—1222no—
230D8—1222no—
231D8—1222no—
232D8—1222no—
233D8—1222no—
234D8—1221no—
235D8—1221no—
236M16—21no—
237M16—611no—
238M16—1222no—
239M16—1221no—
240M16C22×D6112yes—
241M16C22×D6111yescharacteristic
242C2×C8—21no—
243C2×C8—611no—
244C2×C8—1222no—
245C2×C8—1221no—
246C2×C8C22×D6111yescharacteristic
247C42—611no—
248C23—22no—
249C23—1222no—
250C23—2442no—
251C23—2442no—
252Q8—611no—
253Q8—612no—
254Q8D4×D6111yescharacteristic
255D4—21no—
256D4—22no—
257D4—22no—
258D4—611no—
259D4—612no—
260D4—1222no—
261D4—1221no—
262D4—1222no—
263D4—1222no—
264D4—4884no—
265D4—2442no—
266D4—2442no—
267D4—2442no—
268D4—2442no—
269D4D4×D6111yescharacteristic
270C2×C4—21no—
271C2×C4—1221no—
272C2×C4—1222no—
273C2×C4—1221no—
274C2×C4—2442no—
275C2×C4—2442no—
276C2×C4C23×D6111yescharacteristic
277C8—21no—
278C8—22no—
279C8—611no—
280C8—611no—
281C8—1221no—
282C8D4×D6111yescharacteristic
283C8D4×D6111yescharacteristic
284C22—21no—
285C22—42no—
286C22—82no—
287C22—1222no—
288C22—1221no—
289C22—9762no—
290C22—9762no—
291C22—4882no—
292C22—2442no—
293C22#1451982311yescharacteristic
294C4—21no—
295C4—1222no—
296C4—1222no—
297C4—1221no—
298C4C2×D4×D6111yescharacteristic
299C4C2×D4×D6111yescharacteristic
300C2—21no—
301C2—41no—
302C2—82no—
303C2—4882no—
304C2—2442no—
305C2—2441no—
306C2#1684039611yescharacteristic
subgroupG/H
centerC2#16840396
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#472C2
socleC2×C61D42
hypercenter#472D61
hypocenterC61#3292
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #472

Complements

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

NH ≅ G/Ntype
1. #16840567C2semidirect
2. #16840566C2semidirect
3. #16840563C2semidirect
4. #16840137C2semidirect
5. #16840033C2semidirect
6. #16840031C2semidirect
7. #16839932C2semidirect
8. #16839928C2semidirect
9. #16839878C2semidirect
10. #16839877C2semidirect
11. C61×#472C2semidirect
12. #14519823C22semidirect
13. #14519822C22semidirect
15. #14519805C22semidirect
16. #14519805C22semidirect
18. #14519803C22semidirect
27. C2×D488C22semidirect
28. C2×#11758199C22semidirect
31. #14519785C22semidirect
32. #14519783C22semidirect
33. #14519773C22semidirect
34. #14519712C22semidirect
35. #14519704C22semidirect
36. #14519703C22semidirect
37. #14519703C22semidirect
38. #14519693C22semidirect
39. C8×Dic61C22semidirect
40. AGL(1,ℤ/8)×C61C22semidirect
41. C2×D8×C61C22semidirect
42. #131×C61C22semidirect
43. #108×C61C22semidirect
44. #100×C61C22semidirect
70. #11758202D4semidirect
71. #11758201D4semidirect
73. #11758200D4semidirect
77. #11758199D4semidirect
81. Dic244D4semidirect
86. D488D4semidirect
89. #11758190D4semidirect
160. #472D61semidirect
165. C61#3292semidirect
175. AGL(1,ℤ/8)C2×D61semidirect
186. C2×D8C2×D61semidirect
189. #131C2×D61semidirect
192. #108C2×D61semidirect
197. #100C2×D61semidirect