Finite Group Databasebeta

← #21457608

Subgroups — #21457608

Order 7808.

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

normal subgroups only

This group has 454 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#16840575C211yesmaximal, characteristic, complemented
2#16840571C212yesmaximal, complemented
3#16840567C211yesmaximal, characteristic, complemented
4#16840147C211yesmaximal, characteristic, complemented
5#16840033C211yesmaximal, characteristic, complemented
6#16840028C212yesmaximal, complemented
7#16839938C212yesmaximal, complemented
8#16839937C212yesmaximal, complemented
9#16839878C211yesmaximal, characteristic, complemented
10#16839877C211yesmaximal, characteristic, complemented
11C61×#473C211yesmaximal, characteristic, complemented
12#14519825C2212yescomplemented
13#14519823C2212yes—
14#14519809—22no—
15#14519809—22no—
16#14519808C2212yescomplemented
17#14519805—22no—
18#14519805C2212yes—
19#14519805C2212yescomplemented
20#14519804—22no—
21#14519800—22no—
22#14519800—21no—
23#14519799—21no—
24#14519799C2211yescharacteristic
25#14519797C2211yescharacteristic
26Q16×D61—21no—
27C2×#11758201C2212yescomplemented
28SD16×D61—22no—
29C2×D488—21no—
30C2×D488C2211yescharacteristic
31#14519785C2212yescomplemented
32#14519783C2211yescharacteristic, complemented
33#14519766C2212yescomplemented
34#14519712C2211yescharacteristic, complemented
35#14519704C2211yescharacteristic
36#14519703C2211yescharacteristic, complemented
37#14519703C2212yescomplemented
38#14519693C2212yescomplemented
39C8×Dic61C2211yescharacteristic, complemented
40#137×C61C2212yes—
41C2×Q16×C61C2211yescharacteristic, complemented
42#131×C61C2211yescharacteristic
43#108×C61C2211yescharacteristic, complemented
44#101×C61C2212yescomplemented
45#41×C61C2311yescharacteristic
46C2×Q8×C61C2312yes—
47#11758226—22no—
48#11758226—22no—
49#11758226—22no—
50Q8×D61—22no—
51Q8×D61—22no—
52D4×D61—22no—
53D4×D61—42no—
54#11758222—22no—
55#11758222—42no—
56#11758222C2312yes—
57#11758222C2311yescharacteristic
58C2×D244—22no—
59C2×D244C2312yes—
60Q16×C61—22no—
61Q16×C61—21no—
62Q16×C61—21no—
63SD16×C61—22no—
64M16×C61—21no—
65M16×C61C2311yescharacteristic
66M16×C61C2312yes—
67C2×C8×C61—21no—
68C2×C8×C61C2311yescharacteristic
69#11758202—22no—
70#11758202D411yescharacteristic
71#11758201—22no—
72#11758201—22no—
73#11758201—22no—
74#11758201D411yescharacteristic
75#11758200D411yescharacteristic
76#11758199D411yescharacteristic
77#11758198—42no—
78C4×Dic61C2311yescharacteristic
79#11758194C2311yescharacteristic
80C2×#92418C2311yescharacteristic
81Dic244D411yescharacteristic
82D488—22no—
83D488—22no—
84D488—21no—
85D488—21no—
86D488D411yescharacteristic
87#11758190—22no—
88#11758190—22no—
89#11758190D412yes—
90#11758189—21no—
91#11758189—22no—
92C8×D61—21no—
93C8×D61—22no—
94C22×D61—22no—
95C22×D61—42no—
96Q8×C61—22no—
97Q8×C61—22no—
98Q8×C61C2×D411yescharacteristic
99D4×C61—21no—
100D4×C61C2×D411yescharacteristic
101C2×C4×C61—21no—
102C2×C4×C61—22no—
103C2×C4×C61C2411yescharacteristic
104C22⋊D61—21no—
105C22⋊D61—22no—
106C22⋊D61—42no—
107C2×Dic61—21no—
108D244—22no—
109D244—22no—
110D244—42no—
111D244—42no—
112D244C2×D412yes—
113D244C2×D411yescharacteristic
114C4×D61—22no—
115C4×D61—21no—
116C4×D61—42no—
117C4×D61—42no—
118C4×D61—42no—
119Dic122—42no—
120Dic122C2×D411yescharacteristic
121Dic122C2×D412yes—
122C8×C61—22no—
123C8×C61—21no—
124C8×C61C2×D411yescharacteristic
125C8×C61C2×D411yescharacteristic
126#92418—21no—
127#92418C2×D411yescharacteristic
128#92418C2×D411yescharacteristic
129C22×C61—21no—
130C22×C61H(5,𝔽2)11yescharacteristic
131C2×D61—21no—
132C2×D61—22no—
133C2×D61—42no—
134C2×D61—82no—
135C2×D61—162no—
136C4×C61—21no—
137C4×C61—42no—
138C4×C61C22×D411yescharacteristic
139C4×C61C22×D411yescharacteristic
140Dic61—21no—
141Dic61—22no—
142Dic61—41no—
143#3290—611nomaximal, Sylow
144C2×C61—21no—
145C2×C61—41no—
146C2×C61D4211yescharacteristic
147D61—41no—
148D61—42no—
149D61—82no—
150#578—611no—
151#577—612no—
152#576—611no—
153#495—611no—
154#473D6111yescharacteristic, complemented
155#472—611no—
156#471—612no—
157#455—612no—
158#454—612no—
159#443—611no—
160#443—611no—
161C61#329011yescharacteristic, complemented, Sylow
1622−1+4—612no—
163H(5,𝔽2)—612no—
164#137—612no—
165#137—1222no—
166#137—1222no—
167#137C2×D6112yes—
168AGL(1,ℤ/8)—612no—
169AGL(1,ℤ/8)—612no—
170AGL(1,ℤ/8)—1222no—
171AGL(1,ℤ/8)—1222no—
172#135—611no—
173#135—611no—
174#135—1221no—
175#135—1221no—
176#135—1222no—
177C2×Q16—1221no—
178C2×Q16C2×D6111yescharacteristic, complemented
179C2×SD16—612no—
180C2×SD16—1222no—
181C2×D8—611no—
182C2×D8—1221no—
183#131—612no—
184#131—611no—
185#131C2×D6111yescharacteristic
186#124—612no—
187#108—611no—
188#108C2×D6111yescharacteristic, complemented
189#104—611no—
190#104—611no—
191#104—612no—
192#101C2×D6112yescomplemented
193#100—612no—
194C4×C8—611no—
195#41—611no—
196#41—612no—
197#41—1222no—
198#41—1222no—
199#41—1222no—
200#41—1222no—
201#41—2442no—
202#41C22×D6111yescharacteristic
203C2×Q8—1222no—
204C2×Q8—1222no—
205C2×Q8C22×D6112yes—
206C2×D4—612no—
207C2×D4—1222no—
208C2×D4—1222no—
209C2×D4—2442no—
210Q16—22no—
211Q16—21no—
212Q16—21no—
213Q16—611no—
214Q16—611no—
215Q16—1222no—
216SD16—22no—
217SD16—611no—
218SD16—611no—
219SD16—612no—
220SD16—1222no—
221SD16—1222no—
222SD16—1222no—
223SD16—1222no—
224SD16—1222no—
225D8—611no—
226D8—611no—
227D8—1222no—
228D8—1222no—
229D8—1221no—
230D8—1221no—
231M16—21no—
232M16—611no—
233M16—1222no—
234M16—1221no—
235M16C22×D6112yes—
236M16C22×D6111yescharacteristic
237C2×C8—21no—
238C2×C8—611no—
239C2×C8—1222no—
240C2×C8—1221no—
241C2×C8C22×D6111yescharacteristic
242C22⋊C4—2442no—
243C42—611no—
244C23—1222no—
245C23—2442no—
246Q8—22no—
247Q8—22no—
248Q8—611no—
249Q8—612no—
250Q8—2442no—
251Q8D4×D6111yescharacteristic
252D4—21no—
253D4—611no—
254D4—612no—
255D4—1222no—
256D4—1221no—
257D4—1222no—
258D4—1222no—
259D4—2442no—
260D4—2442no—
261D4—2442no—
262D4D4×D6111yescharacteristic
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—1222no—
266C2×C4—1221no—
267C2×C4—1221no—
268C2×C4—2442no—
269C2×C4—2442no—
270C2×C4—2442no—
271C2×C4C23×D6111yescharacteristic
272C8—21no—
273C8—22no—
274C8—611no—
275C8—611no—
276C8—1221no—
277C8D4×D6111yescharacteristic
278C8D4×D6111yescharacteristic
279C22—21no—
280C22—1221no—
281C22—1222no—
282C22—9762no—
283C22—4882no—
284C22—2442no—
285C22#1451982311yescharacteristic
286C4—21no—
287C4—42no—
288C4—1222no—
289C4—1221no—
290C4—2441no—
291C4C2×D4×D6111yescharacteristic
292C4C2×D4×D6111yescharacteristic
293C2—21no—
294C2—41no—
295C2—4882no—
296C2—2442no—
297C2—2441no—
298C2#1684039611yescharacteristic
subgroupG/H
centerC2#16840396
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#473C2
socleC2×C61D42
hypercenter#473D61
hypocenterC61#3290
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #473

Complements

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

NH ≅ G/Ntype
1. #16840575C2semidirect
2. #16840571C2semidirect
3. #16840567C2semidirect
4. #16840147C2semidirect
5. #16840033C2semidirect
6. #16840028C2semidirect
7. #16839938C2semidirect
8. #16839937C2semidirect
9. #16839878C2semidirect
10. #16839877C2semidirect
11. C61×#473C2semidirect
12. #14519825C22semidirect
16. #14519808C22semidirect
19. #14519805C22semidirect
27. C2×#11758201C22semidirect
31. #14519785C22semidirect
32. #14519783C22semidirect
33. #14519766C22semidirect
34. #14519712C22semidirect
36. #14519703C22semidirect
37. #14519703C22semidirect
38. #14519693C22semidirect
39. C8×Dic61C22semidirect
41. C2×Q16×C61C22semidirect
43. #108×C61C22semidirect
44. #101×C61C22semidirect
154. #473D61semidirect
161. C61#3290semidirect
178. C2×Q16C2×D61semidirect
188. #108C2×D61semidirect
192. #101C2×D61semidirect