Finite Group Databasebeta

← #21455193

Subgroups — #21455193

Order 7808.

736 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 736 conjugacy classes of subgroups — too many to draw. Only its 145 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#16840598C211yesmaximal, characteristic, complemented
2C2×#14519805C212yesmaximal, complemented
3#16840326C211yesmaximal, characteristic, complemented
4#16839937C214yesmaximal, complemented
5#16839932C214yesmaximal, complemented
6#16839778C212yesmaximal, complemented
7C61×#413C211yesmaximal, characteristic, complemented
8#14519825C2212yescomplemented
9#14519824—22no—
10#14519823—22no—
11#14519822—22no—
12#14519822C2212yescomplemented
13C2×#11758222—22no—
14C2×#11758222C2212yes—
15#41×D61—24no—
16C22×D244C2211yescharacteristic, complemented
17#14519805—24no—
18#14519805C2218yescomplemented
19C2×#11758190—22no—
20C2×D488—22no—
21#14519773C2212yescomplemented
22#14519766C2212yescomplemented
23#14519751—22no—
24#14519745—22no—
25#14519736C2211yescharacteristic, complemented
26#14519703C2218yescomplemented
27C2×#41×C61C2211yescharacteristic
28C2×M16×C61C2212yescomplemented
29#101×C61C2212yescomplemented
30#100×C61C2212yescomplemented
31C23×D61—21no—
32#41×C61—22no—
33#41×C61—22no—
34C2×Q8×C61C2311yescharacteristic
35C2×D4×C61D412yes—
36C2×D4×C61C2311yescharacteristic
37C22×C4×C61D412yes—
38C22×C4×C61C2311yescharacteristic
39C2×C22⋊D61—24no—
40C2×C22⋊D61—22no—
41C2×C22⋊D61—24no—
42#11758226—24no—
43Q8×D61—24no—
44#11758224—28no—
45#11758224—24no—
46D4×D61—28no—
47D4×D61—24no—
48#11758222—24no—
49#11758222—24no—
50#11758222—22no—
51#11758222—24no—
52#11758222—22no—
53#11758222D414yescomplemented
54#11758222C2314yes—
55C2×D244—22no—
56C2×D244—22no—
57C2×D244—22no—
58C2×D244—21no—
59C2×D244D412yescomplemented
60C2×D244C2312yes—
61C2×C4×D61—24no—
62C2×C4×D61—22no—
63C2×Dic122—22no—
64C2×Dic122D412yescomplemented
65M16×C61—22no—
66M16×C61C2314yes—
67C2×C8×C61—22no—
68C22⋊Dic61—21no—
69#11758198—24no—
70C4⋊Dic61—21no—
71C4×Dic61C2312yes—
72D488—28no—
73#11758190—28no—
74C23×C61C2×D412yes—
75C23×C61C2×D411yescharacteristic
76C22×D61—24no—
77C22×D61—22no—
78C22×D61—22no—
79C22×D61—42no—
80C22×D61—82no—
81Q8×C61—22no—
82D4×C61—24no—
83D4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61C2×D412yes—
87C2×C4×C61C2×D411yescharacteristic
88C2×C4×C61C2×D412yes—
89C2×C4×C61C2×D412yes—
90C2×C4×C61C2411yescharacteristic
91C22⋊D61—28no—
92C22⋊D61—24no—
93C22⋊D61—24no—
94C22⋊D61—84no—
95C2×Dic61—24no—
96C2×Dic61—22no—
97C2×Dic61—22no—
98D244—24no—
99D244—22no—
100D244—24no—
101D244—41no—
102D244—41no—
103D244C2×D414yes—
104C4×D61—28no—
105C4×D61—24no—
106C4×D61—24no—
107Dic122—24no—
108Dic122—22no—
109Dic122C2×D414yes—
110C8×C61—24no—
111C22×C61—22no—
112C22×C61—41no—
113C22×C61—42no—
114C22×C61#12012yes—
115C22×C61C22×D411yescharacteristic
116C2×D61—24no—
117C2×D61—44no—
118C2×D61—42no—
119C2×D61—82no—
120C2×D61—84no—
121C2×D61—84no—
122C4×C61—22no—
123C4×C61#12011yescharacteristic
124C4×C61#12011yescharacteristic
125C4×C61C22×D412yes—
126Dic61—24no—
127Dic61—42no—
128#3021—611nomaximal, Sylow
129C2×C61—21no—
130C2×C61—22no—
131C2×C61—42no—
132C2×C61C2×#12011yescharacteristic
133D61—44no—
134D61—82no—
135#585—611no—
136C2×AGL(1,ℤ/8)—612no—
137#535—611no—
138#454—614no—
139#453—614no—
140#421—612no—
141#413D6111yescharacteristic, complemented
142C61#302111yescharacteristic, complemented, Sylow
1432−1+4—612no—
1442−1+4—1222no—
145H(5,𝔽2)—612no—
146H(5,𝔽2)—1222no—
147H(5,𝔽2)—1222no—
148C2×#41—612no—
149C2×#41—1224no—
150C2×#41—1222no—
151C2×#41C2×D6111yescharacteristic
152C22×D4—611no—
153AGL(1,ℤ/8)—618no—
154AGL(1,ℤ/8)—1224no—
155C2×SD16—1222no—
156C2×D8—1222no—
157C2×M16C2×D6112yescomplemented
158#127—612no—
159#124—612no—
160#121—1222no—
161#120—1222no—
162#117—611no—
163#104—618no—
164#101C2×D6112yescomplemented
165#100C2×D6112yescomplemented
166C24—1221no—
167#41—22no—
168#41—22no—
169#41—614no—
170#41—614no—
171#41—1224no—
172#41—1224no—
173#41—1224no—
174#41—1228no—
175#41—1224no—
176#41—1222no—
177#41—1224no—
178#41—1222no—
179C2×Q8—612no—
180C2×Q8—1222no—
181C2×Q8—1224no—
182C2×Q8C22×D6111yescharacteristic
183C2×D4—612no—
184C2×D4—612no—
185C2×D4—1222no—
186C2×D4—1224no—
187C2×D4—1228no—
188C2×D4—1222no—
189C2×D4—1224no—
190C2×D4—1224no—
191C2×D4—1221no—
192C2×D4—1222no—
193C2×D4—1222no—
194C2×D4D24412yes—
195C2×D4C22×D6111yescharacteristic
196C22×C4—1224no—
197C22×C4—1222no—
198C22×C4D24412yes—
199C22×C4C22×D6111yescharacteristic
200SD16—1228no—
201D8—1228no—
202M16—22no—
203M16C22×D6114yes—
204C2×C8—22no—
205C4⋊C4—1221no—
206C22⋊C4—1221no—
207C22⋊C4—1224no—
208C42—612no—
209C23—1224no—
210C23—1222no—
211C23—1222no—
212C23—4882no—
213C23—2442no—
214C23C2×D24412yes—
215C23C2×D24411yescharacteristic
216Q8—22no—
217Q8—614no—
218Q8—1224no—
219Q8—1222no—
220D4—24no—
221D4—22no—
222D4—614no—
223D4—1224no—
224D4—1228no—
225D4—1224no—
226D4—1224no—
227D4—1224no—
228D4—1222no—
229D4—4884no—
230D4—2441no—
231D4—2441no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—1228no—
235C2×C4—1224no—
236C2×C4—1222no—
237C2×C4—1224no—
238C2×C4—1224no—
239C2×C4—1222no—
240C2×C4C2×D24412yes—
241C2×C4C2×D24411yescharacteristic
242C2×C4D4×D6112yes—
243C2×C4D4×D6112yes—
244C2×C4C23×D6111yescharacteristic
245C8—24no—
246C22—22no—
247C22—41no—
248C22—42no—
249C22—1224no—
250C22—4884no—
251C22—4882no—
252C22—4884no—
253C22—2444no—
254C22—2442no—
255C22#1451974712yes—
256C22C22×D24411yescharacteristic
257C4—22no—
258C4—1224no—
259C4—2442no—
260C4#1451974711yescharacteristic
261C4#1451974711yescharacteristic
262C4C2×D4×D6112yes—
263C2—21no—
264C2—22no—
265C2—42no—
266C2—4882no—
267C2—2444no—
268C2C2×#1451974711yescharacteristic
subgroupG/H
centerC2C2×#14519747
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#413C2
socleC2×C61C2×#120
hypercenter#413D61
hypocenterC61#3021
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
1. #16840598C2semidirect
2. C2×#14519805C2semidirect
3. #16840326C2semidirect
4. #16839937C2semidirect
5. #16839932C2semidirect
6. #16839778C2semidirect
7. C61×#413C2semidirect
8. #14519825C22semidirect
12. #14519822C22semidirect
16. C22×D244C22semidirect
18. #14519805C22semidirect
21. #14519773C22semidirect
22. #14519766C22semidirect
25. #14519736C22semidirect
26. #14519703C22semidirect
28. C2×M16×C61C22semidirect
29. #101×C61C22semidirect
30. #100×C61C22semidirect
53. #11758222D4semidirect
59. C2×D244D4semidirect
64. C2×Dic122D4semidirect
141. #413D61semidirect
142. C61#3021semidirect
157. C2×M16C2×D61semidirect
164. #101C2×D61semidirect
165. #100C2×D61semidirect