Finite Group Databasebeta

← #21446851

Subgroups — #21446851

Order 7808.

394 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C2×#14519810C211yesmaximal, characteristic, complemented
2#16840331C211yesmaximal, characteristic
3C2×#14519765C211yesmaximal, characteristic, complemented
4C2×#14519705C211yesmaximal, characteristic, complemented
5#16839770C211yesmaximal, characteristic, complemented
6C2×#14519693C211yesmaximal, characteristic, complemented
7C61×#339C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C22×Dic122C2211yescharacteristic
10C22×D244C2211yescharacteristic
11#14519810—22no—
12#14519810—22no—
13C2×Dic244—21no—
14C2×#11758190—21no—
15C2×#11758194C2211yescharacteristic
16#14519774—21no—
17#14519765—21no—
18#14519765—22no—
19#14519765—22no—
20#14519752—22no—
21#14519747—22no—
22C2×#11758198—22no—
23#14519705—22no—
24#14519700—22no—
25#14519693—22no—
26C2×M16×C61C2211yescharacteristic
27#117×C61C2211yescharacteristic
28C2×C42×C61C2211yescharacteristic
29C23×D61D412yes—
30C22×C4×C61—21no—
31C22×C4×C61C2311yescharacteristic
32C2×C22⋊D61—21no—
33C22×Dic61—21no—
34#11758222—21no—
35#11758222—21no—
36#11758222—21no—
37#11758222—21no—
38C2×D244—21no—
39C2×D244—21no—
40C2×D244—21no—
41C2×D244—21no—
42C2×D244—21no—
43C2×D244—21no—
44C2×D244—24no—
45C2×D244D411yescharacteristic
46C2×C4×D61—21no—
47C2×Dic122—21no—
48C2×Dic122—21no—
49C2×Dic122—21no—
50C2×Dic122—21no—
51C2×Dic122—21no—
52C2×Dic122D411yescharacteristic
53C2×Dic122D412yescomplemented
54M16×C61—21no—
55M16×C61D412yescomplemented
56C2×C8×C61—21no—
57C4⋊C4×C61D412yes—
58C22⋊C4×C61—21no—
59C42×C61—21no—
60C42×C61—21no—
61C42×C61D412yescomplemented
62#11758198—28no—
63#11758198—24no—
64#11758194—21no—
65#11758194—21no—
66C2×#92418—21no—
67Dic244—24no—
68#11758190—24no—
69C23×C61C2×D411yescharacteristic
70C22×D61—22no—
71C22×D61—22no—
72C22×D61—21no—
73C22×D61—22no—
74C22×D61—44no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—42no—
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61#4111yescharacteristic
84C22⋊D61—41no—
85C22⋊D61—41no—
86C2×Dic61—22no—
87C2×Dic61—21no—
88C2×Dic61—41no—
89C2×Dic61—41no—
90D244—21no—
91D244—21no—
92D244—41no—
93D244—41no—
94D244—41no—
95D244—41no—
96D244—84no—
97C4×D61—41no—
98C4×D61—41no—
99Dic122—22no—
100Dic122—21no—
101Dic122—22no—
102Dic122—21no—
103Dic122—41no—
104Dic122—41no—
105C8×C61—22no—
106#92418—41no—
107C22×C61—22no—
108C22×C61#12011yescharacteristic
109C22×C61#12011yescharacteristic
110C22×C61#12111yescharacteristic
111C2×D61—44no—
112C2×D61—41no—
113C2×D61—42no—
114C2×D61—42no—
115C2×D61—44no—
116C2×D61—82no—
117C4×C61—42no—
118C4×C61—42no—
119C4×C61#12011yescharacteristic
120C4×C61#12111yescharacteristic
121C4×C61#12111yescharacteristic
122C4×C61#12711yescharacteristic
123Dic61—42no—
124Dic61—41no—
125#2004—611nomaximal, Sylow
126C2×C61—21no—
127C2×C61—21no—
128C2×C61#39211yescharacteristic
129C2×C61#45512yes—
130D61—81no—
131D61—82no—
132C2×#137—611no—
133#535—611no—
134C2×#124—611no—
135C2×#104—611no—
136#419—611no—
137C2×#100—611no—
138#339D6111yescharacteristic, complemented
139C61#200411yescharacteristic, complemented, Sylow
140C2×#41—611no—
141C22×Q8—611no—
142C22×D4—611no—
143#137—1222no—
144#137—1222no—
145C2×Q16—1221no—
146C2×SD16—1221no—
147C2×M16—611no—
148C2×M16C2×D6111yescharacteristic
149#127—1221no—
150#124—1222no—
151#124—1221no—
152#124—1222no—
153#121—1222no—
154#120—1222no—
155#117C2×D6111yescharacteristic
156C2×C22⋊C4—1222no—
157C2×C42C2×D6111yescharacteristic
158#104—1222no—
159#103—1222no—
160#100—1222no—
161C24—612no—
162#41—1221no—
163#41—1221no—
164#41—1221no—
165#41—1221no—
166C2×Q8—611no—
167C2×Q8—612no—
168C2×Q8—1221no—
169C2×Q8—1221no—
170C2×Q8—1221no—
171C2×Q8—1221no—
172C2×Q8—1221no—
173C2×D4—611no—
174C2×D4—1224no—
175C2×D4—1221no—
176C2×D4—1221no—
177C2×D4—1221no—
178C2×D4—1221no—
179C2×D4—1221no—
180C2×D4—1221no—
181C2×D4—1221no—
182C22×C4—21no—
183C22×C4—1221no—
184C22×C4—1221no—
185C22×C4C22×D6111yescharacteristic
186Q16—1224no—
187SD16—1224no—
188M16—21no—
189M16—1221no—
190M16—1221no—
191M16D24412yescomplemented
192C2×C8—21no—
193C2×C8—1221no—
194C4⋊C4D24412yes—
195C22⋊C4—21no—
196C22⋊C4—1228no—
197C22⋊C4—1224no—
198C42—21no—
199C42—21no—
200C42D24412yescomplemented
201C23—1222no—
202C23—1222no—
203C23—1222no—
204C23—1221no—
205C23—2444no—
206C23D4×D6111yescharacteristic
207Q8—1222no—
208Q8—1221no—
209Q8—1222no—
210Q8—1221no—
211Q8—2441no—
212Q8—2441no—
213D4—1221no—
214D4—1221no—
215D4—4884no—
216D4—2441no—
217D4—2441no—
218D4—2441no—
219D4—2441no—
220D4—2441no—
221D4—2441no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—42no—
225C2×C4—1222no—
226C2×C4—1221no—
227C2×C4—2441no—
228C2×C4—2441no—
229C2×C4—2441no—
230C2×C4—2441no—
231C2×C4C2×D24411yescharacteristic
232C2×C4C2×D24411yescharacteristic
233C2×C4C2×D24411yescharacteristic
234C2×C4D4×D6111yescharacteristic
235C2×C4D4×D6111yescharacteristic
236C2×C4#1175822611yescharacteristic
237C8—22no—
238C8—2441no—
239C22—22no—
240C22—4882no—
241C22—2444no—
242C22—2442no—
243C22—2444no—
244C22—2441no—
245C22—2442no—
246C22#1451974711yescharacteristic
247C22#1451974711yescharacteristic
248C22#1451975211yescharacteristic
249C4—42no—
250C4—42no—
251C4—2441no—
252C4—2442no—
253C4#1451974711yescharacteristic
254C4#1451975211yescharacteristic
255C4#1451975211yescharacteristic
256C4#1451977411yescharacteristic
257C2—21no—
258C2—21no—
259C2—4882no—
260C2—4881no—
261C2#1683967211yescharacteristic
262C2#1683994112yes—
subgroupG/H
centerC22#14519747
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#339C2
socleC22×C61#120
hypercenter#339D61
hypocenterC61#2004
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. C2×#14519810C2semidirect
3. C2×#14519765C2semidirect
4. C2×#14519705C2semidirect
5. #16839770C2semidirect
6. C2×#14519693C2semidirect
7. C61×#339C2semidirect
53. C2×Dic122D4semidirect
55. M16×C61D4semidirect
61. C42×C61D4semidirect
138. #339D61semidirect
139. C61#2004semidirect
191. M16D244semidirect
200. C42D244semidirect