Finite Group Databasebeta

← #21451550

Subgroups — #21451550

Order 7808.

816 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 816 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C22×#11758222C211yesmaximal, characteristic
2C2×#14519757C212yesmaximal, complemented
3C2×#14519756C211yesmaximal, characteristic, complemented
4#16839683C212yesmaximal, complemented
5#16839680C212yesmaximal, complemented
6#16839678C214yesmaximal, complemented
7#16839619C212yesmaximal, complemented
8C61×#380C211yesmaximal, characteristic, complemented
9C2×#11758222—24no—
10C2×#11758222—28no—
11C22×Dic122C2211yescharacteristic
12C22×Dic122C2211yescharacteristic
13C22×D244C2211yescharacteristic
14C22×C22⋊D61C2212yes—
15C22×C4×D61C2212yes—
16#14519757—28no—
17#14519756—24no—
18C2×C4⋊Dic61C2214yes—
19C2×C4⋊Dic61C2211yescharacteristic
20C2×#11758196C2212yes—
21C2×C22⋊Dic61C2212yes—
22C2×#11758198C2214yes—
23C2×#11758198C2214yes—
24#14519684C2214yes—
25C23×C4×C61C2211yescharacteristic
26C2×C4⋊C4×C61C2212yes—
27C2×C22⋊C4×C61C2212yes—
28#95×C61C2212yes—
29C24×C61C2311yescharacteristic
30C23×D61C2312yes—
31C22×C4×C61—24no—
32C22×C4×C61D414yes—
33C22×C4×C61C2314yes—
34C22×C4×C61C2311yescharacteristic
35C22×C4×C61C2311yescharacteristic
36C2×C22⋊D61—24no—
37C2×C22⋊D61—24no—
38C2×C22⋊D61—24no—
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C22×Dic61C2312yes—
42#11758222—232no—
43C2×D244—24no—
44C2×D244—22no—
45C2×C4×D61—24no—
46C2×C4×D61—24no—
47C2×C4×D61D418yes—
48C2×Dic122—22no—
49C2×Dic122—24no—
50C2×Dic122—22no—
51C2×Dic122—24no—
52C4⋊C4×C61—24no—
53C22⋊C4×C61—42no—
54C22⋊Dic61—24no—
55#11758198—28no—
56#11758198—44no—
57C4⋊Dic61—22no—
58C4⋊Dic61—28no—
59#11758196—24no—
60C23×C61—22no—
61C23×C61—21no—
62C23×C61—22no—
63C23×C61—21no—
64C23×C61C2×D412yes—
65C23×C61C2411yescharacteristic
66C22×D61—22no—
67C22×D61—22no—
68C22×D61—22no—
69C22×D61—22no—
70C22×D61—22no—
71C22×D61—22no—
72C22×D61C2×D414yes—
73C2×C4×C61—22no—
74C2×C4×C61—28no—
75C2×C4×C61—24no—
76C2×C4×C61—24no—
77C2×C4×C61—24no—
78C2×C4×C61C2×D412yes—
79C2×C4×C61C2×D412yes—
80C2×C4×C61C2×D414yes—
81C22⋊D61—216no—
82C2×Dic61—22no—
83C2×Dic61—22no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61—24no—
87C2×Dic61—22no—
88C2×Dic61—22no—
89C2×Dic61C2×D414yes—
90D244—28no—
91C4×D61—216no—
92Dic122—28no—
93Dic122—44no—
94C22×C61—22no—
95C22×C61—22no—
96C22×C61—22no—
97C22×C61—42no—
98C22×C61—42no—
99C22×C61C22×D412yes—
100C22×C61C22×D411yescharacteristic
101C22×C61H(5,𝔽2)11yescharacteristic
102C22×C612−1+412yes—
103C22×C612−1+411yescharacteristic
104C2×D61—24no—
105C2×D61—24no—
106C2×D61—24no—
107C2×D61—42no—
108C2×D61—42no—
109C2×D61—42no—
110C2×D61—42no—
111C4×C61—22no—
112C4×C61—44no—
113C4×C61#12014yes—
114Dic61—24no—
115Dic61—42no—
116Dic61—42no—
117#2616—611nomaximal, Sylow
118C2×C61—42no—
119C2×C61C2×#12011yescharacteristic
120C2×C61#53612yes—
121C2×C61#53611yescharacteristic
122C2×C61#53712yes—
123C2×C61#53711yescharacteristic
124D61—44no—
125C22×#41—611no—
126C2×C22⋊Q8—611no—
127C2×C22⋊Q8—612no—
128#395—612no—
129#394—614no—
130#394—612no—
131#380—612no—
132#380D6111yescharacteristic, complemented
133C61#261611yescharacteristic, complemented, Sylow
134C2×#41—1228no—
135C2×#41—1224no—
136C22×Q8—611no—
137C22×Q8—611no—
138C22×D4—612no—
139C22×D4—611no—
140C23×C4—612no—
141C23×C4C2×D6111yescharacteristic
142C22⋊Q8—1228no—
143C22⋊Q8—1224no—
144C2×C4⋊C4—611no—
145C2×C4⋊C4—612no—
146C2×C4⋊C4—614no—
147C2×C4⋊C4C2×D6112yes—
148C2×C22⋊C4—612no—
149C2×C22⋊C4—614no—
150C2×C22⋊C4—614no—
151C2×C22⋊C4C2×D6112yes—
152#95—614no—
153#95C2×D6112yes—
154C24—612no—
155C24C22×D6111yescharacteristic
156#41—12232no—
157C2×Q8—1224no—
158C2×Q8—1222no—
159C2×Q8—1222no—
160C2×Q8—1224no—
161C2×D4—1224no—
162C2×D4—1224no—
163C2×D4—1224no—
164C2×D4—1224no—
165C2×D4—1222no—
166C22×C4—24no—
167C22×C4—612no—
168C22×C4—618no—
169C22×C4—612no—
170C22×C4—612no—
171C22×C4—1224no—
172C22×C4—1224no—
173C22×C4D24414yes—
174C22×C4C22×D6114yes—
175C22×C4C22×D6111yescharacteristic
176C22×C4C22×D6111yescharacteristic
177C4⋊C4—24no—
178C4⋊C4—1228no—
179C4⋊C4—1224no—
180C4⋊C4—1222no—
181C22⋊C4—42no—
182C22⋊C4—1228no—
183C22⋊C4—1224no—
184C22⋊C4—2444no—
185C23—22no—
186C23—21no—
187C23—22no—
188C23—21no—
189C23—614no—
190C23—1222no—
191C23—1222no—
192C23—1222no—
193C23—1222no—
194C23—1222no—
195C23—1222no—
196C23C2×D24412yes—
197C23C23×D6111yescharacteristic
198Q8—1228no—
199Q8—2444no—
200D4—1228no—
201D4—12216no—
202C2×C4—22no—
203C2×C4—28no—
204C2×C4—24no—
205C2×C4—24no—
206C2×C4—24no—
207C2×C4—614no—
208C2×C4—1222no—
209C2×C4—1222no—
210C2×C4—12216no—
211C2×C4—1224no—
212C2×C4—1222no—
213C2×C4—1222no—
214C2×C4—1222no—
215C2×C4—1222no—
216C2×C4C2×D24412yes—
217C2×C4C2×D24412yes—
218C2×C4D4×D6114yes—
219C22—22no—
220C22—22no—
221C22—22no—
222C22—42no—
223C22—42no—
224C22—1224no—
225C22—1224no—
226C22—1224no—
227C22—2442no—
228C22—2442no—
229C22—2442no—
230C22—2442no—
231C22C2×D4×D6112yes—
232C22C22×D24411yescharacteristic
233C22#1451982211yescharacteristic
234C22#1451982412yes—
235C22#1451982511yescharacteristic
236C4—22no—
237C4—44no—
238C4—1224no—
239C4—2442no—
240C4—2442no—
241C4#1451974714yes—
242C2—42no—
243C2—2444no—
244C2C2×#1451974711yescharacteristic
245C2#1684033512yes—
246C2#1684033811yescharacteristic
247C2#1684034112yes—
248C2#1684034311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#380C2
hypercenter#380D61
hypocenterC61#2616
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C2×#14519757C2semidirect
3. C2×#14519756C2semidirect
4. #16839683C2semidirect
5. #16839680C2semidirect
6. #16839678C2semidirect
7. #16839619C2semidirect
8. C61×#380C2semidirect
132. #380D61semidirect
133. C61#2616semidirect