Finite Group Databasebeta

← #21457585

Subgroups — #21457585

Order 7808.

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

normal subgroups only

This group has 464 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#16840568C212yesmaximal, complemented
2#16840563C212yesmaximal, complemented
3#16840029C212yesmaximal, complemented
4#16840022C212yesmaximal, complemented
5#16839939C211yesmaximal, characteristic, complemented
6#16839934C211yesmaximal, characteristic, complemented
7#16839929C212yesmaximal, complemented
8#16839885C212yesmaximal, complemented
9C61×#496C211yesmaximal, characteristic, complemented
10#14519825C2211yescharacteristic, complemented
11#14519822C2211yescharacteristic
12#14519822C2212yescomplemented
13#14519808C2212yescomplemented
14#14519806—22no—
15#14519804—22no—
16#14519803C2212yes—
17#14519803C2212yescomplemented
18#14519803C2212yescomplemented
19#14519801—22no—
20#14519801—22no—
21#14519799C2212yes—
22#14519798—22no—
23#14519796—22no—
24SD16×D61—22no—
25D8×D61—22no—
26#14519783C2212yescomplemented
27#14519783C2212yescomplemented
28#14519713C2212yescomplemented
29#14519705C2212yescomplemented
30#14519705C2212yescomplemented
31#14519696C2211yescharacteristic, complemented
32#14519694C2211yescharacteristic, complemented
33#14519694C2212yescomplemented
34C2×SD16×C61C2212yescomplemented
35C2×D8×C61C2212yescomplemented
36#127×C61C2211yescharacteristic, complemented
37#124×C61C2211yescharacteristic, complemented
38#97×C61C2211yescharacteristic, complemented
39C2×Q8×C61C2311yescharacteristic
40C2×D4×C61—41no—
41C2×D4×C61C2311yescharacteristic
42C2×D4×C61C2312yes—
43C2×C22⋊D61—41no—
44C2×C22⋊D61—42no—
45#11758226—22no—
46Q8×D61—22no—
47#11758224—22no—
48#11758224—22no—
49#11758224—22no—
50D4×D61—22no—
51D4×D61—22no—
52D4×D61—22no—
53#11758222—41no—
54#11758222C2312yes—
55#11758222C2312yes—
56SD16×C61—22no—
57SD16×C61—22no—
58D8×C61—22no—
59D8×C61—22no—
60C2×C8×C61C2312yes—
61C22⋊C4×C61—41no—
62C42×C61C2311yescharacteristic
63#11758202—22no—
64#11758201—22no—
65#11758200—22no—
66#11758200—22no—
67#11758200—22no—
68#11758199—22no—
69#11758199—22no—
70#11758199—22no—
71#11758194C2312yes—
72#11758194C2312yes—
73Dic244D412yescomplemented
74D488D412yescomplemented
75#11758190D412yescomplemented
76#11758190D412yescomplemented
77#11758189—22no—
78#11758189—22no—
79C8×D61—22no—
80C8×D61—22no—
81C23×C61—21no—
82C23×C61—22no—
83C22×D61—42no—
84C22×D61—41no—
85Q8×C61—22no—
86D4×C61—22no—
87D4×C61—22no—
88D4×C61—22no—
89D4×C61—82no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61C2411yescharacteristic
93C22⋊D61—22no—
94C22⋊D61—22no—
95C22⋊D61—42no—
96C22⋊D61—42no—
97C22⋊D61—42no—
98C2×Dic61—42no—
99C2×Dic61—41no—
100D244—41no—
101D244C2×D412yes—
102D244C2×D412yes—
103C4×D61—22no—
104C4×D61—22no—
105C4×D61—42no—
106Dic122—41no—
107Dic122C2×D412yes—
108Dic122C2×D412yes—
109C8×C61C2×D412yes—
110C8×C61C2×D412yes—
111#92418—22no—
112#92418—22no—
113C22×C61—41no—
114C22×C61—42no—
115C22×C61—82no—
116C22×C61—81no—
117C22×C61H(5,𝔽2)11yescharacteristic
118C2×D61—22no—
119C2×D61—22no—
120C2×D61—162no—
121C2×D61—161no—
122C4×C61—41no—
123C4×C61—41no—
124C4×C61C22×D412yes—
125Dic61—22no—
126Dic61—22no—
127#3288—611nomaximal, Sylow
128C2×C61—21no—
129C2×C61—82no—
130C2×C61—81no—
131C2×C61D4211yescharacteristic
132D61—42no—
133D61—42no—
134#577—612no—
135#576—612no—
136#496D6111yescharacteristic, complemented
137#472—612no—
138#471—612no—
139#455—611no—
140#454—611no—
141#453—612no—
142#444—612no—
143C61#328811yescharacteristic, complemented, Sylow
1442−1+4—611no—
145H(5,𝔽2)—611no—
146H(5,𝔽2)—612no—
147#137—612no—
148#137—1222no—
149AGL(1,ℤ/8)—612no—
150AGL(1,ℤ/8)—612no—
151AGL(1,ℤ/8)—612no—
152AGL(1,ℤ/8)—1222no—
153AGL(1,ℤ/8)—1222no—
154AGL(1,ℤ/8)—1222no—
155#135—612no—
156#135—1222no—
157#135—1222no—
158C2×SD16—1222no—
159C2×SD16C2×D6112yescomplemented
160C2×D8—1222no—
161C2×D8C2×D6112yescomplemented
162#131—612no—
163#131—612no—
164#127C2×D6111yescharacteristic, complemented
165#124C2×D6111yescharacteristic, complemented
166#108—612no—
167#104—612no—
168#104—612no—
169#101—611no—
170#100—612no—
171#100—611no—
172#97C2×D6111yescharacteristic, complemented
173#41—612no—
174#41—612no—
175#41—1222no—
176#41—1222no—
177#41—1222no—
178#41—1222no—
179#41—2441no—
180C2×Q8—1222no—
181C2×Q8C22×D6111yescharacteristic
182C2×D4—41no—
183C2×D4—1222no—
184C2×D4—1222no—
185C2×D4—1222no—
186C2×D4—2441no—
187C2×D4—2442no—
188C2×D4C22×D6111yescharacteristic
189C2×D4C22×D6112yes—
190Q16—612no—
191Q16—1222no—
192SD16—22no—
193SD16—22no—
194SD16—612no—
195SD16—612no—
196SD16—1222no—
197SD16—1222no—
198SD16—1222no—
199SD16—1222no—
200D8—22no—
201D8—22no—
202D8—612no—
203D8—1222no—
204D8—1222no—
205D8—1222no—
206M16—612no—
207M16—612no—
208M16—1222no—
209M16—1222no—
210C2×C8—1222no—
211C2×C8—1222no—
212C2×C8C22×D6112yes—
213C22⋊C4—41no—
214C42C22×D6111yescharacteristic
215C23—21no—
216C23—22no—
217C23—2442no—
218C23—2441no—
219Q8—22no—
220Q8—612no—
221Q8—612no—
222Q8—2441no—
223D4—22no—
224D4—22no—
225D4—22no—
226D4—82no—
227D4—612no—
228D4—612no—
229D4—1222no—
230D4—1222no—
231D4—2441no—
232D4—2442no—
233D4—2442no—
234D4—2442no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—1222no—
238C2×C4—1222no—
239C2×C4—2442no—
240C2×C4—2441no—
241C2×C4—2442no—
242C2×C4C23×D6111yescharacteristic
243C8—1222no—
244C8—1222no—
245C8D4×D6112yes—
246C8D4×D6112yes—
247C22—41no—
248C22—42no—
249C22—82no—
250C22—81no—
251C22—1222no—
252C22—1222no—
253C22—9761no—
254C22—9762no—
255C22#1451982211yescharacteristic
256C4—41no—
257C4—41no—
258C4—1222no—
259C4—1222no—
260C4C2×D4×D6112yes—
261C2—21no—
262C2—82no—
263C2—81no—
264C2—2442no—
265C2—2442no—
266C2#1684039711yescharacteristic
subgroupG/H
centerC2#16840397
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#496C2
socleC2×C61D42
hypercenter#496D61
hypocenterC61#3288
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #16840568C2semidirect
2. #16840563C2semidirect
3. #16840029C2semidirect
4. #16840022C2semidirect
5. #16839939C2semidirect
6. #16839934C2semidirect
7. #16839929C2semidirect
8. #16839885C2semidirect
9. C61×#496C2semidirect
10. #14519825C22semidirect
12. #14519822C22semidirect
13. #14519808C22semidirect
17. #14519803C22semidirect
18. #14519803C22semidirect
26. #14519783C22semidirect
27. #14519783C22semidirect
28. #14519713C22semidirect
29. #14519705C22semidirect
30. #14519705C22semidirect
31. #14519696C22semidirect
32. #14519694C22semidirect
33. #14519694C22semidirect
34. C2×SD16×C61C22semidirect
35. C2×D8×C61C22semidirect
36. #127×C61C22semidirect
37. #124×C61C22semidirect
38. #97×C61C22semidirect
73. Dic244D4semidirect
74. D488D4semidirect
75. #11758190D4semidirect
76. #11758190D4semidirect
136. #496D61semidirect
143. C61#3288semidirect
159. C2×SD16C2×D61semidirect
161. C2×D8C2×D61semidirect
164. #127C2×D61semidirect
165. #124C2×D61semidirect
172. #97C2×D61semidirect