Finite Group Databasebeta

← #21457614

Subgroups — #21457614

Order 7808.

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

normal subgroups only

This group has 460 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#16840573C212yesmaximal, complemented
2#16840572C212yesmaximal, complemented
3#16840134C211yesmaximal, characteristic, complemented
4#16840024C212yesmaximal, complemented
5#16840023C212yesmaximal, complemented
6#16839946C212yesmaximal, complemented
7#16839929C211yesmaximal, characteristic, complemented
8#16839876C212yesmaximal, complemented
9C61×#453C211yesmaximal, characteristic, complemented
10#14519824C2212yes—
11#14519822C2211yescharacteristic, complemented
12#14519810C2212yescomplemented
13#14519807—22no—
14#14519807C2212yescomplemented
15#14519806—22no—
16#14519803—22no—
17#14519803C2212yes—
18#14519801—22no—
19#14519797—22no—
20#14519797C2212yes—
21#14519796—22no—
22C2×#11758200—22no—
23C2×#11758200C2212yescomplemented
24C2×#11758200C2212yescomplemented
25SD16×D61—22no—
26#14519785C2212yescomplemented
27#14519784C2212yescomplemented
28#14519777C2211yescharacteristic, complemented
29#14519712C2212yescomplemented
30#14519705C2212yescomplemented
31#14519695C2212yescomplemented
32#14519694C2211yescharacteristic, complemented
33C4×#92418C2211yescharacteristic, complemented
34H(5,𝔽2)×C61C2211yescharacteristic, complemented
35AGL(1,ℤ/8)×C61C2212yes—
36#127×C61C2211yescharacteristic
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—
47Q8×D61—22no—
48#11758224—22no—
49#11758224—22no—
50#11758224—42no—
51D4×D61—22no—
52#11758222—22no—
53#11758222C2312yes—
54C2×Dic122—22no—
55C2×Dic122C2312yes—
56SD16×C61—22no—
57D8×C61—22no—
58M16×C61C2312yes—
59C42×C61C2311yescharacteristic
60#11758202—22no—
61#11758202D412yescomplemented
62#11758201D412yescomplemented
63#11758200—22no—
64#11758200—22no—
65#11758200—22no—
66#11758200—22no—
67#11758200—22no—
68#11758200—22no—
69#11758200D412yescomplemented
70#11758199—22no—
71#11758199D412yescomplemented
72C4⋊Dic61—41no—
73#11758194—22no—
74#11758194C2312yes—
75C2×#92418—22no—
76C2×#92418C2312yes—
77Dic244—22no—
78#11758190—22no—
79#11758189—22no—
80C8×D61—22no—
81C23×C61—21no—
82C23×C61—21no—
83C23×C61—41no—
84C22×D61—41no—
85Q8×C61C2×D412yes—
86D4×C61—22no—
87D4×C61—22no—
88D4×C61—22no—
89D4×C61—42no—
90D4×C61—82no—
91D4×C61C2×D412yes—
92C2×C4×C61—21no—
93C2×C4×C61—22no—
94C2×C4×C61—41no—
95C2×C4×C61C2411yescharacteristic
96C22⋊D61—22no—
97C22⋊D61—42no—
98C22⋊D61—42no—
99C2×Dic61—22no—
100C2×Dic61—41no—
101C2×Dic61—42no—
102D244C2×D412yes—
103C4×D61—22no—
104C4×D61—42no—
105Dic122—22no—
106Dic122—22no—
107Dic122—42no—
108Dic122C2×D412yes—
109C8×C61—22no—
110#92418—22no—
111#92418C2×D412yes—
112#92418C2×D412yes—
113C22×C61—22no—
114C22×C61—41no—
115C22×C61—41no—
116C22×C61—81no—
117C22×C61—81no—
118C22×C61—161no—
119C22×C61H(5,𝔽2)11yescharacteristic
120C2×D61—22no—
121C2×D61—161no—
122C4×C61—22no—
123C4×C61—22no—
124C4×C61C22×D412yes—
125Dic61—22no—
126Dic61—42no—
127#3291—611nomaximal, Sylow
128C2×C61—21no—
129C2×C61—42no—
130C2×C61—81no—
131C2×C61—81no—
132C2×C61D4211yescharacteristic
133D61—42no—
134#577—612no—
135#577—612no—
136#492—611no—
137#471—612no—
138#471—612no—
139#456—612no—
140#453—611no—
141#453D6111yescharacteristic, complemented
142#443—612no—
143C61#329111yescharacteristic, complemented, Sylow
1442−1+4—612no—
145H(5,𝔽2)—611no—
146H(5,𝔽2)C2×D6111yescharacteristic, complemented
147#137—612no—
148#137—612no—
149#137—1222no—
150#137—1222no—
151AGL(1,ℤ/8)—612no—
152AGL(1,ℤ/8)—1222no—
153AGL(1,ℤ/8)—1222no—
154AGL(1,ℤ/8)C2×D6112yes—
155#135—612no—
156#135—1222no—
157#135—1222no—
158C2×SD16—612no—
159C2×SD16—612no—
160C2×SD16—1222no—
161C2×SD16—1222no—
162#131—612no—
163#131—612no—
164C4⋊Q8—611no—
165#127C2×D6111yescharacteristic
166#108—612no—
167#104—612no—
168#104C2×D6112yescomplemented
169#101—612no—
170#100—611no—
171#100C2×D6111yescharacteristic, complemented
172C4×C8—611no—
173#41—22no—
174#41—612no—
175#41—1222no—
176#41—1222no—
177#41—1222no—
178#41—2442no—
179#41C22×D6112yes—
180C2×Q8—612no—
181C2×Q8—1222no—
182C2×Q8—1222no—
183C2×D4—22no—
184C2×D4—41no—
185C2×D4—41no—
186C2×D4—1222no—
187C2×D4—2441no—
188C2×D4C22×D6111yescharacteristic
189C2×D4C22×D6111yescharacteristic
190Q16—612no—
191Q16—1222no—
192Q16—1222no—
193SD16—22no—
194SD16—612no—
195SD16—612no—
196SD16—1222no—
197SD16—1222no—
198SD16—1222no—
199SD16—1222no—
200SD16—1222no—
201SD16—1222no—
202SD16—1222no—
203D8—22no—
204D8—612no—
205D8—1222no—
206M16—612no—
207M16—1222no—
208M16—1222no—
209M16C22×D6112yes—
210C2×C8—612no—
211C2×C8—1222no—
212C2×C8—1222no—
213C4⋊C4—2441no—
214C42C22×D6111yescharacteristic
215C23—21no—
216C23—21no—
217C23—41no—
218C23—2441no—
219Q8—612no—
220Q8—1222no—
221Q8—1222no—
222Q8—2442no—
223Q8D4×D6112yes—
224D4—22no—
225D4—22no—
226D4—22no—
227D4—42no—
228D4—82no—
229D4—612no—
230D4—1222no—
231D4—2442no—
232D4—2442no—
233D4D4×D6112yes—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—41no—
237C2×C4—1222no—
238C2×C4—1222no—
239C2×C4—2442no—
240C2×C4—2441no—
241C2×C4—2442no—
242C2×C4C23×D6111yescharacteristic
243C8—22no—
244C8—612no—
245C8—612no—
246C8—1222no—
247C22—22no—
248C22—41no—
249C22—41no—
250C22—81no—
251C22—81no—
252C22—161no—
253C22—1222no—
254C22—9761no—
255C22#1451982211yescharacteristic
256C4—22no—
257C4—22no—
258C4—1222no—
259C4—2442no—
260C4C2×D4×D6112yes—
261C2—21no—
262C2—42no—
263C2—81no—
264C2—81no—
265C2—2442no—
266C2#1684039411yescharacteristic
subgroupG/H
centerC2#16840394
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#453C2
socleC2×C61D42
hypercenter#453D61
hypocenterC61#3291
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. #16840573C2semidirect
2. #16840572C2semidirect
3. #16840134C2semidirect
4. #16840024C2semidirect
5. #16840023C2semidirect
6. #16839946C2semidirect
7. #16839929C2semidirect
8. #16839876C2semidirect
9. C61×#453C2semidirect
11. #14519822C22semidirect
12. #14519810C22semidirect
14. #14519807C22semidirect
23. C2×#11758200C22semidirect
24. C2×#11758200C22semidirect
26. #14519785C22semidirect
27. #14519784C22semidirect
28. #14519777C22semidirect
29. #14519712C22semidirect
30. #14519705C22semidirect
31. #14519695C22semidirect
32. #14519694C22semidirect
33. C4×#92418C22semidirect
34. H(5,𝔽2)×C61C22semidirect
37. #104×C61C22semidirect
38. #100×C61C22semidirect
61. #11758202D4semidirect
62. #11758201D4semidirect
69. #11758200D4semidirect
71. #11758199D4semidirect
141. #453D61semidirect
143. C61#3291semidirect
146. H(5,𝔽2)C2×D61semidirect
168. #104C2×D61semidirect
171. #100C2×D61semidirect