Finite Group Databasebeta

← #21456202

Subgroups — #21456202

Order 7808.

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

normal subgroups only

This group has 400 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#16840318C211yesmaximal, characteristic, complemented
2#124×D61C211yesmaximal, characteristic
3#16840123C212yesmaximal, complemented
4#16840120C212yesmaximal, complemented
5#16840119C211yesmaximal, characteristic, complemented
6#16840117C211yesmaximal, characteristic, complemented
7#16840116C211yesmaximal, characteristic, complemented
8#16839769C212yesmaximal, complemented
9#16839765C212yesmaximal
10C4×#11758189C211yesmaximal, characteristic, complemented
11C61×#488C211yesmaximal, characteristic, complemented
12C2×Q8×D61C2211yescharacteristic
13C2×D4×D61C2211yescharacteristic
14C2×#11758189C2212yes—
15#14519776C2212yescomplemented
16#14519769C2211yescharacteristic, complemented
17#14519766C2211yescharacteristic
18#14519765C2211yescharacteristic
19#14519764C2211yescharacteristic
20#14519763—22no—
21#14519755—22no—
22#14519742—22no—
23#14519735C2212yes—
24C22⋊C4×D61—22no—
25C42×D61C2211yescharacteristic
26#14519702C2212yescomplemented
27#14519701C2212yescomplemented
28#14519700C2212yescomplemented
29#14519699C2212yes—
30#14519698C2212yes—
31#14519697C2212yes—
32#14519687C2212yescomplemented
33C4×#92418C2211yescharacteristic, complemented
34#125×C61C2211yescharacteristic, complemented
35#124×C61C2211yescharacteristic
36#103×C61C2212yescomplemented
37#102×C61C2212yes—
38C4×C8×C61C2211yescharacteristic, complemented
39C23×D61—21no—
40C2×Q8×C61C2311yescharacteristic
41C2×D4×C61C2311yescharacteristic
42C2×C22⋊D61—21no—
43Q8×D61—24no—
44D4×D61—24no—
45C2×D244C2311yescharacteristic
46C2×C4×D61—21no—
47C2×C4×D61D412yes—
48C2×C4×D61C2311yescharacteristic
49C2×Dic122—21no—
50C2×Dic122—22no—
51C2×Dic122C2311yescharacteristic
52C2×C8×C61C2312yes—
53C4⋊C4×C61—22no—
54C4⋊C4×C61C2312yes—
55C22⋊C4×C61—22no—
56C42×C61C2311yescharacteristic
57C22⋊Dic61—22no—
58#11758198—22no—
59#11758198—22no—
60#11758198—22no—
61C4⋊Dic61C2312yes—
62#11758196—22no—
63#11758196—22no—
64C4×Dic61—22no—
65C4×Dic61D412yes—
66C4×Dic61C2311yescharacteristic
67C2×#92418C2312yes—
68#11758189—24no—
69C23×C61—21no—
70C22×D61—21no—
71C22×D61—44no—
72C22×D61—42no—
73C22×D61C2×D411yescharacteristic
74Q8×C61—22no—
75D4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—21no—
78C2×C4×C61C2×D412yes—
79C2×C4×C61C2411yescharacteristic
80C22⋊D61—42no—
81C2×Dic61—22no—
82C2×Dic61—21no—
83C2×Dic61C2×D412yes—
84C2×Dic61C2×D411yescharacteristic
85D244—22no—
86C4×D61—42no—
87C4×D61—42no—
88C4×D61#4114yes—
89Dic122—22no—
90Dic122—44no—
91Dic122—42no—
92C8×C61—22no—
93#92418—22no—
94C22×C61—41no—
95C22×C61—42no—
96C22×C61C22×D411yescharacteristic
97C2×D61—22no—
98C2×D61—41no—
99C2×D61—42no—
100C2×D61—84no—
101C2×D61#12412yes—
102C4×C61—22no—
103C4×C61—41no—
104C4×C61—42no—
105C4×C61C2×#4112yes—
106Dic61—22no—
107Dic61—41no—
108Dic61—42no—
109Dic61#12412yes—
110#3140—611nomaximal, Sylow
111C2×C61—81no—
112C2×C61C2×#12411yescharacteristic
113C2×C61#57512yes—
114D61—22no—
115D61—81no—
116#533—611no—
117C2×#124—611no—
118#489—612no—
119#489—612no—
120#488—611no—
121#488—611no—
122#488—611no—
123#488D6111yescharacteristic, complemented
124#419—612no—
125#418—612no—
126C4×M16—611no—
127C61#314011yescharacteristic, complemented, Sylow
128C22×Q8—611no—
129C22×D4—611no—
130C2×M16—612no—
131C4⋊Q8—612no—
132#125—611no—
133#125C2×D6111yescharacteristic, complemented
134#124—611no—
135#124—611no—
136#124—611no—
137#124—1222no—
138#124C2×D6111yescharacteristic
139C22⋊Q8—1222no—
140C4×Q8—1222no—
141#117—612no—
142C2×C22⋊C4—1222no—
143C2×C42—611no—
144#103—612no—
145#103—612no—
146#103—612no—
147#103C2×D6112yescomplemented
148#102—612no—
149#102—612no—
150#102—612no—
151#102C2×D6112yes—
152#97—612no—
153C4×C8—611no—
154C4×C8C2×D6111yescharacteristic, complemented
155C24—1221no—
156C2×Q8—611no—
157C2×Q8—1222no—
158C2×Q8—1221no—
159C2×Q8—1224no—
160C2×Q8C22×D6111yescharacteristic
161C2×D4—611no—
162C2×D4—1224no—
163C2×D4—1221no—
164C2×D4C22×D6111yescharacteristic
165C22×C4—611no—
166C22×C4—612no—
167C22×C4—1221no—
168M16—1224no—
169C2×C8—612no—
170C2×C8C22×D6112yes—
171C4⋊C4—22no—
172C4⋊C4—612no—
173C4⋊C4—1222no—
174C4⋊C4—1222no—
175C4⋊C4C22×D6112yes—
176C22⋊C4—22no—
177C22⋊C4—1222no—
178C22⋊C4—1222no—
179C22⋊C4—1222no—
180C22⋊C4—1222no—
181C42—612no—
182C42—611no—
183C42—1222no—
184C42C22×D6111yescharacteristic
185C23—21no—
186C23—611no—
187C23—1221no—
188C23—2442no—
189C23—2444no—
190Q8—22no—
191Q8—1222no—
192Q8—2442no—
193Q8—2444no—
194D4—22no—
195D4—1222no—
196D4—2442no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—611no—
200C2×C4—614no—
201C2×C4—612no—
202C2×C4—1222no—
203C2×C4—1221no—
204C2×C4—2442no—
205C2×C4—2442no—
206C2×C4D4×D6112yes—
207C2×C4C23×D6111yescharacteristic
208C8—22no—
209C8—1222no—
210C22—41no—
211C22—42no—
212C22—612no—
213C22—1222no—
214C22—4884no—
215C22—2441no—
216C22—2442no—
217C22C2×D4×D6111yescharacteristic
218C4—22no—
219C4—41no—
220C4—42no—
221C4—612no—
222C4—1222no—
223C4—2441no—
224C4—2442no—
225C4#41×D6112yes—
226C2—81no—
227C2—1222no—
228C2—4881no—
229C2#124×D6111yescharacteristic
230C2#1684055912yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#488C2
socleC22×C61C22×D4
hypercenter#488D61
hypocenterC61#3140
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #16840318C2semidirect
3. #16840123C2semidirect
4. #16840120C2semidirect
5. #16840119C2semidirect
6. #16840117C2semidirect
7. #16840116C2semidirect
8. #16839769C2semidirect
10. C4×#11758189C2semidirect
11. C61×#488C2semidirect
15. #14519776C22semidirect
16. #14519769C22semidirect
26. #14519702C22semidirect
27. #14519701C22semidirect
28. #14519700C22semidirect
32. #14519687C22semidirect
33. C4×#92418C22semidirect
34. #125×C61C22semidirect
36. #103×C61C22semidirect
38. C4×C8×C61C22semidirect
123. #488D61semidirect
127. C61#3140semidirect
133. #125C2×D61semidirect
147. #103C2×D61semidirect
154. C4×C8C2×D61semidirect