Finite Group Databasebeta

← #21444325

Subgroups — #21444325

Order 7808.

272 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 63 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#16840307C211yesmaximal, characteristic
2#16839816C211yesmaximal, characteristic, complemented
3#16839607C211yesmaximal, characteristic, complemented
4#16839497C211yesmaximal, characteristic, complemented
5#16839496C211yesmaximal, characteristic, complemented
6#16839495C211yesmaximal, characteristic, complemented
7C61×#327C211yesmaximal, characteristic, complemented
8C2×#11758224—21no—
9#14519776C411yescharacteristic, complemented
10#14519773C411yescharacteristic, complemented
11#14519763—21no—
12#14519751C2211yescharacteristic
13#14519749—21no—
14D4×Dic61C411yescharacteristic, complemented
15#14519739C411yescharacteristic, complemented
16#14519737—21no—
17C2×C4×Dic61—21no—
18C2×C4×Dic61C2211yescharacteristic
19#14519706—21no—
20C22⋊#92418C2211yescharacteristic
21#14519687—21no—
22#14519684—21no—
23#14519684C2211yescharacteristic
24#121×C61C2211yescharacteristic
25C22⋊C8×C61C2211yescharacteristic
26#95×C61C2211yescharacteristic
27C2×D4×C61—21no—
28C2×D4×C61C2×C411yescharacteristic
29C22×C4×C61—21no—
30C22×C4×C61C2311yescharacteristic
31C2×C22⋊D61—21no—
32C2×C22⋊D61—21no—
33C2×C22⋊D61—21no—
34C22×Dic61—21no—
35C22×Dic61—21no—
36C22×Dic61D411yescharacteristic
37C22×Dic61D411yescharacteristic
38#11758224—42no—
39#11758224—42no—
40C2×D244C2×C411yescharacteristic
41C2×C4×D61—21no—
42C2×Dic122—21no—
43C2×C8×C61—21no—
44C4⋊C4×C61C2×C411yescharacteristic
45C22⋊C4×C61—21no—
46C22⋊Dic61—21no—
47#11758198—21no—
48#11758198—21no—
49C4⋊Dic61C2×C411yescharacteristic
50#11758196—21no—
51C4×Dic61—24no—
52C4×Dic61C2×C411yescharacteristic
53C4×Dic61C2×C411yescharacteristic
54C4×Dic61D411yescharacteristic
55C4×Dic61D411yescharacteristic
56C2×#92418—21no—
57C23×C61—21no—
58C23×C61C2×D411yescharacteristic
59C22×D61—21no—
60D4×C61—41no—
61D4×C61—41no—
62D4×C61—41no—
63C2×C4×C61—22no—
64C2×C4×C61—21no—
65C2×C4×C61—41no—
66C2×C4×C61—41no—
67C2×C4×C61—41no—
68C2×C4×C61C22×C411yescharacteristic
69C2×C4×C61C2×D411yescharacteristic
70C22⋊D61—42no—
71C22⋊D61—41no—
72C22⋊D61—41no—
73C22⋊D61—42no—
74C2×Dic61—21no—
75C2×Dic61—21no—
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61—21no—
79C2×Dic61—42no—
80C2×Dic61—41no—
81C2×Dic61—41no—
82C2×Dic61C22⋊C411yescharacteristic
83C2×Dic61C22⋊C411yescharacteristic
84C2×Dic61C22⋊C411yescharacteristic
85C2×Dic61C22⋊C411yescharacteristic
86D244—41no—
87C4×D61—42no—
88Dic122—42no—
89C8×C61—41no—
90#92418—41no—
91C22×C61—21no—
92C22×C61—21no—
93C22×C61—41no—
94C22×C61—41no—
95C22×C61—41no—
96C22×C61C2×C22⋊C411yescharacteristic
97C22×C61AGL(1,ℤ/8)11yescharacteristic
98C22×C61AGL(1,ℤ/8)11yescharacteristic
99C2×D61—41no—
100C2×D61—41no—
101C2×D61—41no—
102C4×C61—21no—
103C4×C61—21no—
104C4×C61—42no—
105C4×C61—41no—
106Dic61—21no—
107Dic61—21no—
108Dic61—21no—
109Dic61—42no—
110Dic61—41no—
111Dic61#10412yes—
112#1505—611nomaximal, Sylow
113C2×C61—21no—
114C2×C61—21no—
115C2×C61—81no—
116C2×C61#41011yescharacteristic
117C2×C61#41811yescharacteristic
118C2×C61C2×#10411yescharacteristic
119D61—81no—
120#532—611no—
121#432—611no—
122#376—611no—
123#327—611no—
124#327—611no—
125#327—611no—
126#327D6111yescharacteristic, complemented
127C61#150511yescharacteristic, complemented, Sylow
128C2×#41—1221no—
129C4⋊Q8—611no—
130#127—611no—
131#124—1221no—
132#121—611no—
133#121—1221no—
134#121C2×D6111yescharacteristic
135C4×D4—611no—
136C4×D4—611no—
137C4×D4—1221no—
138C2×C42—611no—
139C2×C42—1221no—
140C4⋊C8—1221no—
141C22⋊C8—611no—
142C22⋊C8C2×D6111yescharacteristic
143#97—1221no—
144#95—611no—
145#95—1221no—
146#95C2×D6111yescharacteristic
147#41—2442no—
148#41—2442no—
149C2×Q8—1221no—
150C2×D4—21no—
151C2×D4—611no—
152C2×D4—1221no—
153C2×D4—1221no—
154C2×D4—1221no—
155C2×D4C4×D6111yescharacteristic
156C22×C4—21no—
157C22×C4—611no—
158C22×C4—611no—
159C22×C4—1221no—
160C22×C4—1221no—
161C22×C4—1221no—
162C22×C4C22×D6111yescharacteristic
163C2×C8—21no—
164C2×C8—1221no—
165C4⋊C4—611no—
166C4⋊C4—1221no—
167C4⋊C4C4×D6111yescharacteristic
168C22⋊C4—21no—
169C22⋊C4—1221no—
170C22⋊C4—1221no—
171C22⋊C4—1221no—
172C42—611no—
173C42—611no—
174C42—611no—
175C42—611no—
176C42—1224no—
177C23—21no—
178C23—1221no—
179C23D4×D6111yescharacteristic
180Q8—2442no—
181D4—41no—
182D4—41no—
183D4—41no—
184D4—2441no—
185D4—2442no—
186D4—2442no—
187D4—2441no—
188D4—2441no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—611no—
195C2×C4—611no—
196C2×C4—611no—
197C2×C4—611no—
198C2×C4—1222no—
199C2×C4—1221no—
200C2×C4—1221no—
201C2×C4—1222no—
202C2×C4—1221no—
203C2×C4—2442no—
204C2×C4—2442no—
205C2×C4—2441no—
206C2×C4—2441no—
207C2×C4C2×C4×D6111yescharacteristic
208C2×C4D4×D6111yescharacteristic
209C8—41no—
210C8—2441no—
211C22—21no—
212C22—21no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22—2441no—
217C22—2441no—
218C22—2441no—
219C22C22⋊C4×D6111yescharacteristic
220C22#1451980111yescharacteristic
221C22#1451980411yescharacteristic
222C4—21no—
223C4—21no—
224C4—42no—
225C4—41no—
226C4—612no—
227C4—1221no—
228C4—1221no—
229C4—1221no—
230C4—2442no—
231C4—2441no—
232C2—21no—
233C2—21no—
234C2—81no—
235C2—4881no—
236C2#1683973411yescharacteristic
237C2#1683976511yescharacteristic
238C2#104×D6111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#327C2
socleC22×C61C2×C22⋊C4
hypercenter#327D61
hypocenterC61#1505
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #16839816C2semidirect
3. #16839607C2semidirect
4. #16839497C2semidirect
5. #16839496C2semidirect
6. #16839495C2semidirect
7. C61×#327C2semidirect
9. #14519776C4semidirect
10. #14519773C4semidirect
14. D4×Dic61C4semidirect
15. #14519739C4semidirect
126. #327D61semidirect
127. C61#1505semidirect