Finite Group Databasebeta

← #21457615

Subgroups — #21457615

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#16840566C212yesmaximal, complemented
2#16840565C212yesmaximal, complemented
3#16840138C211yesmaximal, characteristic, complemented
4#16840031C212yesmaximal, complemented
5#16840030C212yesmaximal, complemented
6#16839931C212yesmaximal, complemented
7#16839929C211yesmaximal, characteristic, complemented
8#16839876C212yesmaximal, complemented
9C61×#453C211yesmaximal, characteristic, complemented
10#14519823C2212yescomplemented
11#14519822C2211yescharacteristic, complemented
12#14519805C2212yescomplemented
13#14519804—22no—
14#14519803—22no—
15#14519803C2212yescomplemented
16#14519802—22no—
17#14519802C2212yescomplemented
18#14519801—22no—
19#14519798—22no—
20#14519797—22no—
21#14519797C2212yes—
22C2×#11758199—22no—
23C2×#11758199C2212yescomplemented
24C2×#11758199C2212yescomplemented
25D8×D61—22no—
26#14519785C2212yescomplemented
27#14519784C2212yescomplemented
28#14519774C2211yescharacteristic, complemented
29#14519712C2212yescomplemented
30#14519705C2212yescomplemented
31#14519694C2211yescharacteristic, complemented
32#14519693C2212yescomplemented
33C4×#92418C2211yescharacteristic, complemented
34H(5,𝔽2)×C61C2211yescharacteristic, complemented
35AGL(1,ℤ/8)×C61C2212yescomplemented
36#127×C61C2211yescharacteristic, complemented
37#104×C61C2212yescomplemented
38#100×C61C2211yescharacteristic, complemented
39#41×C61—22no—
40#41×C61C2312yes—
41C2×D4×C61—22no—
42C2×D4×C61—41no—
43C2×D4×C61—41no—
44C2×D4×C61C2311yescharacteristic
45C2×D4×C61C2311yescharacteristic
46C2×C22⋊D61—41no—
47#11758226—22no—
48#11758224—22no—
49D4×D61—22no—
50D4×D61—22no—
51D4×D61—42no—
52#11758222—22no—
53#11758222C2312yes—
54C2×D244—22no—
55C2×D244—41no—
56C2×D244C2312yes—
57SD16×C61—22no—
58D8×C61—22no—
59M16×C61C2312yes—
60C42×C61C2311yescharacteristic
61#11758202D412yescomplemented
62#11758201—22no—
63#11758201D412yescomplemented
64#11758200—22no—
65#11758200D412yescomplemented
66#11758199—22no—
67#11758199—22no—
68#11758199—22no—
69#11758199—22no—
70#11758199—22no—
71#11758199—22no—
72#11758199D412yescomplemented
73#11758194—22no—
74#11758194C2312yes—
75C2×#92418—22no—
76C2×#92418C2312yes—
77D488—22no—
78#11758190—22no—
79#11758189—22no—
80C8×D61—22no—
81C23×C61—21no—
82C23×C61—21no—
83C23×C61—41no—
84C22×D61—22no—
85C22×D61—41no—
86C22×D61—42no—
87Q8×C61C2×D412yes—
88D4×C61—22no—
89D4×C61—22no—
90D4×C61—22no—
91D4×C61—42no—
92D4×C61—82no—
93D4×C61C2×D412yes—
94C2×C4×C61—21no—
95C2×C4×C61—22no—
96C2×C4×C61—41no—
97C2×C4×C61C2411yescharacteristic
98C22⋊D61—22no—
99C22⋊D61—42no—
100C22⋊D61—42no—
101C2×Dic61—41no—
102D244—22no—
103D244—22no—
104D244—42no—
105D244—82no—
106D244C2×D412yes—
107C4×D61—22no—
108C4×D61—42no—
109Dic122C2×D412yes—
110C8×C61—22no—
111#92418—22no—
112#92418C2×D412yes—
113#92418C2×D412yes—
114C22×C61—22no—
115C22×C61—41no—
116C22×C61—41no—
117C22×C61—81no—
118C22×C61—81no—
119C22×C61—161no—
120C22×C61H(5,𝔽2)11yescharacteristic
121C2×D61—22no—
122C2×D61—42no—
123C2×D61—82no—
124C2×D61—161no—
125C2×D61—162no—
126C4×C61—22no—
127C4×C61—22no—
128C4×C61C22×D412yes—
129Dic61—22no—
130#3292—611nomaximal, Sylow
131C2×C61—21no—
132C2×C61—42no—
133C2×C61—81no—
134C2×C61—81no—
135C2×C61D4211yescharacteristic
136D61—42no—
137D61—82no—
138#576—612no—
139#576—612no—
140#493—611no—
141#472—612no—
142#472—612no—
143#453—611no—
144#453—612no—
145#453D6111yescharacteristic, complemented
146#443—612no—
147C61#329211yescharacteristic, complemented, Sylow
148H(5,𝔽2)—612no—
149H(5,𝔽2)—611no—
150H(5,𝔽2)C2×D6111yescharacteristic, complemented
151AGL(1,ℤ/8)—612no—
152AGL(1,ℤ/8)—612no—
153AGL(1,ℤ/8)—612no—
154AGL(1,ℤ/8)—1222no—
155AGL(1,ℤ/8)—1222no—
156AGL(1,ℤ/8)—1222no—
157AGL(1,ℤ/8)—1222no—
158AGL(1,ℤ/8)C2×D6112yescomplemented
159#135—612no—
160#135—1222no—
161#135—1222no—
162C2×D8—612no—
163C2×D8—612no—
164C2×D8—1222no—
165C2×D8—1222no—
166#131—612no—
167#131—612no—
168#127—611no—
169#127C2×D6111yescharacteristic, complemented
170#108—612no—
171#104—612no—
172#104C2×D6112yescomplemented
173#100—611no—
174#100—612no—
175#100C2×D6111yescharacteristic, complemented
176C4×C8—611no—
177#41—22no—
178#41—612no—
179#41—1222no—
180#41—1222no—
181#41—1222no—
182#41C22×D6112yes—
183C2×D4—22no—
184C2×D4—41no—
185C2×D4—41no—
186C2×D4—612no—
187C2×D4—1222no—
188C2×D4—1222no—
189C2×D4—1222no—
190C2×D4—2441no—
191C2×D4—2442no—
192C2×D4—2441no—
193C2×D4C22×D6111yescharacteristic
194C2×D4C22×D6111yescharacteristic
195Q16—612no—
196SD16—22no—
197SD16—612no—
198SD16—612no—
199SD16—1222no—
200SD16—1222no—
201SD16—1222no—
202D8—22no—
203D8—612no—
204D8—1222no—
205D8—1222no—
206D8—1222no—
207D8—1222no—
208D8—1222no—
209D8—1222no—
210D8—1222no—
211M16—612no—
212M16—1222no—
213M16—1222no—
214M16C22×D6112yes—
215C2×C8—612no—
216C2×C8—1222no—
217C2×C8—1222no—
218C42C22×D6111yescharacteristic
219C23—21no—
220C23—21no—
221C23—41no—
222C23—1222no—
223C23—2442no—
224C23—2441no—
225Q8—612no—
226Q8D4×D6112yes—
227D4—22no—
228D4—22no—
229D4—22no—
230D4—42no—
231D4—82no—
232D4—612no—
233D4—1222no—
234D4—1222no—
235D4—1222no—
236D4—4882no—
237D4—2442no—
238D4—2442no—
239D4—2442no—
240D4D4×D6112yes—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—1222no—
245C2×C4—2442no—
246C2×C4—2441no—
247C2×C4C23×D6111yescharacteristic
248C8—22no—
249C8—612no—
250C8—612no—
251C8—1222no—
252C22—22no—
253C22—41no—
254C22—41no—
255C22—81no—
256C22—81no—
257C22—161no—
258C22—1222no—
259C22—9762no—
260C22—9761no—
261C22—4882no—
262C22—2442no—
263C22#1451982211yescharacteristic
264C4—22no—
265C4—22no—
266C4—1222no—
267C4C2×D4×D6112yes—
268C2—21no—
269C2—42no—
270C2—81no—
271C2—81no—
272C2—4882no—
273C2—2442no—
274C2#1684039411yescharacteristic
subgroupG/H
centerC2#16840394
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#453C2
socleC2×C61D42
hypercenter#453D61
hypocenterC61#3292
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #16840566C2semidirect
2. #16840565C2semidirect
3. #16840138C2semidirect
4. #16840031C2semidirect
5. #16840030C2semidirect
6. #16839931C2semidirect
7. #16839929C2semidirect
8. #16839876C2semidirect
9. C61×#453C2semidirect
10. #14519823C22semidirect
11. #14519822C22semidirect
12. #14519805C22semidirect
15. #14519803C22semidirect
17. #14519802C22semidirect
23. C2×#11758199C22semidirect
24. C2×#11758199C22semidirect
26. #14519785C22semidirect
27. #14519784C22semidirect
28. #14519774C22semidirect
29. #14519712C22semidirect
30. #14519705C22semidirect
31. #14519694C22semidirect
32. #14519693C22semidirect
33. C4×#92418C22semidirect
34. H(5,𝔽2)×C61C22semidirect
35. AGL(1,ℤ/8)×C61C22semidirect
36. #127×C61C22semidirect
37. #104×C61C22semidirect
38. #100×C61C22semidirect
61. #11758202D4semidirect
63. #11758201D4semidirect
65. #11758200D4semidirect
72. #11758199D4semidirect
145. #453D61semidirect
147. C61#3292semidirect
150. H(5,𝔽2)C2×D61semidirect
158. AGL(1,ℤ/8)C2×D61semidirect
169. #127C2×D61semidirect
172. #104C2×D61semidirect
175. #100C2×D61semidirect