Finite Group Databasebeta

← #21455285

Subgroups — #21455285

Order 7808.

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

normal subgroups only

This group has 548 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
1C2×#14519805C212yesmaximal, complemented
2#16840312C211yesmaximal, characteristic, complemented
3C2×C4×D244C211yesmaximal, characteristic, complemented
4#16839978C214yesmaximal, complemented
5#16839968C212yesmaximal, complemented
6#16839958C212yesmaximal, complemented
7#16839764C212yesmaximal, complemented
8C61×#423C211yesmaximal, characteristic, complemented
9C2×#11758222C2212yes—
10C22×D244C2211yescharacteristic
11C22×C4×D61—21no—
12#14519805—28no—
13C2×#11758190C2214yes—
14C2×D488C2214yes—
15#14519777C2211yescharacteristic, complemented
16#14519774C2211yescharacteristic, complemented
17#14519765C2212yescomplemented
18#14519751—21no—
19#14519751—21no—
20C4×D244—21no—
21C4×D244—21no—
22C4×D244—21no—
23C4×D244—21no—
24C4×D244C2212yes—
25C4×D244C2212yes—
26C2×C4⋊Dic61C2211yescharacteristic
27C2×#11758198—21no—
28#14519702C2214yescomplemented
29#14519699C2214yescomplemented
30C2×M16×C61C2212yes—
31C2×C42×C61C2211yescharacteristic
32C4⋊C8×C61C2212yescomplemented
33C4⋊C8×C61C2212yescomplemented
34C23×D61—21no—
35C22×C4×C61D411yescharacteristic
36C22×C4×C61D411yescharacteristic
37C22×C4×C61C2311yescharacteristic
38C2×C22⋊D61—22no—
39C22×Dic61—21no—
40#11758222—24no—
41#11758222—24no—
42C2×D244—21no—
43C2×D244—22no—
44C2×D244—21no—
45C2×D244—21no—
46C2×D244D414yescomplemented
47C2×D244C2312yes—
48C2×D244C2312yes—
49C2×C4×D61—22no—
50C2×C4×D61—22no—
51C2×C4×D61—22no—
52C2×C4×D61—44no—
53C2×Dic122C2312yes—
54M16×C61—24no—
55C2×C8×C61C2314yes—
56C42×C61D411yescharacteristic
57C42×C61D411yescharacteristic
58C42×C61C2311yescharacteristic
59C42×C61C2311yescharacteristic
60#11758198—22no—
61#11758198—22no—
62#11758198—22no—
63#11758198—22no—
64C4⋊Dic61—21no—
65C4⋊Dic61—21no—
66C4⋊Dic61—21no—
67C4⋊Dic61C2312yes—
68D488—28no—
69#11758190—28no—
70C23×C61C2×D411yescharacteristic
71C22×D61—24no—
72C22×D61—22no—
73C22×D61—22no—
74C22×D61—42no—
75C22×D61—42no—
76C2×C4×C61—22no—
77C2×C4×C61—41no—
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2×D412yes—
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61#4112yes—
85C2×C4×C61C2411yescharacteristic
86C22⋊D61—44no—
87C2×Dic61—22no—
88C2×Dic61—22no—
89C2×Dic61—42no—
90D244—24no—
91D244—22no—
92D244—22no—
93D244—22no—
94D244—42no—
95D244—42no—
96D244C2×D414yes—
97C4×D61—44no—
98C4×D61—44no—
99C4×D61—44no—
100Dic122—22no—
101Dic122—22no—
102C8×C61—24no—
103C22×C61—21no—
104C22×C61—21no—
105C22×C61#12112yes—
106C22×C61C22×D411yescharacteristic
107C2×D61—24no—
108C2×D61—48no—
109C2×D61—42no—
110C2×D61—42no—
111C2×D61—42no—
112C2×D61—42no—
113C2×D61—42no—
114C4×C61—21no—
115C4×C61—21no—
116C4×C61—21no—
117C4×C61#12112yes—
118C4×C61AGL(1,ℤ/8)12yescomplemented
119C4×C61C22×D411yescharacteristic
120C4×C61C2×#4111yescharacteristic
121Dic61—42no—
122Dic61—42no—
123#3036—611nomaximal, Sylow
124C2×C61—22no—
125C2×C61C2×#12111yescharacteristic
126C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
127C2×C61#57511yescharacteristic
128D61—44no—
129D61—82no—
130C2×AGL(1,ℤ/8)—612no—
131#532—611no—
132C2×C4×D4—611no—
133#463—614no—
134#461—612no—
135#459—612no—
136#423D6111yescharacteristic, complemented
137#417—612no—
138C61#303611yescharacteristic, complemented, Sylow
139C2×#41—612no—
140C22×D4—611no—
141C23×C4—1221no—
142AGL(1,ℤ/8)—1228no—
143C2×SD16—614no—
144C2×D8—614no—
145C2×M16C2×D6112yes—
146C4⋊Q8—611no—
147#127—611no—
148#124—612no—
149#121—1221no—
150#121—1221no—
151C4×D4—612no—
152C4×D4—612no—
153C4×D4—1221no—
154C4×D4—1221no—
155C4×D4—1221no—
156C4×D4—1221no—
157C2×C4⋊C4—611no—
158C2×C22⋊C4—1221no—
159C2×C42C2×D6111yescharacteristic
160C4⋊C8C2×D6112yescomplemented
161C4⋊C8C2×D6112yescomplemented
162#103—614no—
163#102—614no—
164C24—1221no—
165#41—1224no—
166#41—1224no—
167C2×Q8—612no—
168C2×D4—614no—
169C2×D4—612no—
170C2×D4—612no—
171C2×D4—1222no—
172C2×D4—1221no—
173C2×D4—1221no—
174C2×D4—1221no—
175C2×D4—1222no—
176C22×C4—1221no—
177C22×C4—1222no—
178C22×C4—1222no—
179C22×C4—1222no—
180C22×C4—2444no—
181C22×C4D24411yescharacteristic
182C22×C4D24411yescharacteristic
183C22×C4C22×D6111yescharacteristic
184SD16—1228no—
185D8—1228no—
186M16—24no—
187C2×C8C22×D6114yes—
188C4⋊C4—612no—
189C4⋊C4—1221no—
190C4⋊C4—1221no—
191C4⋊C4—1221no—
192C22⋊C4—1222no—
193C22⋊C4—1222no—
194C22⋊C4—1222no—
195C22⋊C4—1222no—
196C42D24411yescharacteristic
197C42D24411yescharacteristic
198C42C22×D6111yescharacteristic
199C42C22×D6111yescharacteristic
200C23—1222no—
201C23—1224no—
202C23—1222no—
203C23—2442no—
204C23—2442no—
205C23C2×D24411yescharacteristic
206Q8—1222no—
207Q8—1222no—
208D4—614no—
209D4—1222no—
210D4—1222no—
211D4—1222no—
212D4—1224no—
213D4—2442no—
214D4—2444no—
215D4—2442no—
216C2×C4—22no—
217C2×C4—41no—
218C2×C4—1222no—
219C2×C4—1222no—
220C2×C4—2444no—
221C2×C4—2442no—
222C2×C4—2444no—
223C2×C4—2444no—
224C2×C4C2×D24411yescharacteristic
225C2×C4C2×D24411yescharacteristic
226C2×C4C2×D24411yescharacteristic
227C2×C4C2×D24411yescharacteristic
228C2×C4C2×D24411yescharacteristic
229C2×C4D4×D6112yes—
230C2×C4#1175822612yes—
231C2×C4C23×D6111yescharacteristic
232C8—24no—
233C22—21no—
234C22—21no—
235C22—1224no—
236C22—2448no—
237C22—2442no—
238C22—2442no—
239C22—2442no—
240C22—2442no—
241C22—2442no—
242C22#1451975212yes—
243C22C22×D24411yescharacteristic
244C4—21no—
245C4—21no—
246C4—21no—
247C4—2442no—
248C4—2442no—
249C4#1451975212yes—
250C4#1451980512yescomplemented
251C4C2×D4×D6111yescharacteristic
252C4C2×#1175822611yescharacteristic
253C2—22no—
254C2—4882no—
255C2—2444no—
256C2C2×#1451975211yescharacteristic
257C2C2×#1451980511yescharacteristic
258C2#1684056211yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#423C2
socleC22×C61C22×D4
hypercenter#423D61
hypocenterC61#3036
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
1. C2×#14519805C2semidirect
2. #16840312C2semidirect
3. C2×C4×D244C2semidirect
4. #16839978C2semidirect
5. #16839968C2semidirect
6. #16839958C2semidirect
7. #16839764C2semidirect
8. C61×#423C2semidirect
15. #14519777C22semidirect
16. #14519774C22semidirect
17. #14519765C22semidirect
28. #14519702C22semidirect
29. #14519699C22semidirect
32. C4⋊C8×C61C22semidirect
33. C4⋊C8×C61C22semidirect
46. C2×D244D4semidirect
118. C4×C61AGL(1,ℤ/8)semidirect
136. #423D61semidirect
138. C61#3036semidirect
160. C4⋊C8C2×D61semidirect
161. C4⋊C8C2×D61semidirect
250. C4#14519805semidirect