Finite Group Databasebeta

← #21444144

Subgroups — #21444144

Order 7808.

440 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 71 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×C22⋊C4×D61C211yesmaximal, characteristic
2#16839724C212yesmaximal, complemented
3#16839486C211yesmaximal, characteristic, complemented
4#16839485C212yesmaximal, complemented
5C61×#323C211yesmaximal, characteristic, complemented
6C24×D61C411yescharacteristic
7C22×C4×D61C411yescharacteristic
8C22×C4×D61C2211yescharacteristic
9C2×#11758189—22no—
10C2×C22⋊Dic61C411yescharacteristic
11C2×#11758198C411yescharacteristic
12C2×#11758198C2211yescharacteristic
13C22⋊C4×D61—22no—
14C22⋊C4×D61—22no—
15C22⋊#92418C2212yescomplemented
16#14519689—22no—
17C2×C22⋊C4×C61C2211yescharacteristic
18C22⋊C8×C61C2212yescomplemented
19C24×C61C2×C411yescharacteristic
20C23×D61—22no—
21C23×D61—21no—
22C23×D61—21no—
23C23×D61—22no—
24C23×D61—42no—
25C23×D61—42no—
26C23×D61C2×C411yescharacteristic
27C23×D61C2×C411yescharacteristic
28C22×C4×C61C2×C411yescharacteristic
29C22×C4×C61C2311yescharacteristic
30C22×Dic61C2×C411yescharacteristic
31C22×Dic61C2×C411yescharacteristic
32C2×C4×D61—21no—
33C2×C4×D61—21no—
34C2×C4×D61—42no—
35C2×C4×D61—42no—
36C2×C4×D61D412yes—
37C2×C4×D61D412yes—
38C2×C8×C61—22no—
39C22⋊C4×C61—22no—
40C22⋊Dic61—22no—
41#11758198—22no—
42#11758198—22no—
43C2×#92418—22no—
44#11758189—44no—
45C23×C61—21no—
46C23×C61—21no—
47C23×C61—41no—
48C23×C61—41no—
49C23×C61M1612yescomplemented
50C23×C61C22×C411yescharacteristic
51C22×D61—21no—
52C22×D61—21no—
53C22×D61—22no—
54C22×D61—22no—
55C22×D61—24no—
56C22×D61—24no—
57C22×D61—21no—
58C22×D61—21no—
59C22×D61—48no—
60C22×D61—48no—
61C22×D61—42no—
62C22×D61—42no—
63C22×D61—42no—
64C22×D61—42no—
65C22×D61—41no—
66C22×D61—41no—
67C22×D61C22⋊C411yescharacteristic
68C22×D61C22⋊C411yescharacteristic
69C22×D61M1612yescomplemented
70C2×C4×C61—21no—
71C2×C4×C61—41no—
72C2×C4×C61—41no—
73C2×C4×C61C2×D412yes—
74C2×Dic61—21no—
75C2×Dic61—41no—
76C2×Dic61—41no—
77C2×Dic61C22⋊C412yes—
78C4×D61—24no—
79C4×D61—42no—
80C4×D61—42no—
81C4×D61—42no—
82C8×C61—42no—
83#92418—42no—
84C22×C61—21no—
85C22×C61—21no—
86C22×C61—22no—
87C22×C61—42no—
88C22×C61—42no—
89C22×C61—41no—
90C22×C61—41no—
91C22×C61C2×C22⋊C411yescharacteristic
92C22×C61C2×M1611yescharacteristic
93C22×C61C2×M1611yescharacteristic
94C2×D61—24no—
95C2×D61—24no—
96C2×D61—21no—
97C2×D61—21no—
98C2×D61—21no—
99C2×D61—21no—
100C2×D61—22no—
101C2×D61—48no—
102C2×D61—48no—
103C2×D61—42no—
104C2×D61—41no—
105C2×D61—41no—
106C2×D61—42no—
107C2×D61#9912yes—
108C2×D61#10012yes—
109C4×C61—22no—
110C4×C61—41no—
111Dic61—22no—
112Dic61—41no—
113#1462—611nomaximal, Sylow
114C2×C61—21no—
115C2×C61—21no—
116C2×C61—42no—
117C2×C61#40711yescharacteristic
118C2×C61C2×#9911yescharacteristic
119C2×C61C2×#10011yescharacteristic
120D61—22no—
121D61—22no—
122D61—42no—
123C22×C22⋊C4—611no—
124#407—612no—
125#323—611no—
126#323—612no—
127#323D6111yescharacteristic, complemented
128C61#146211yescharacteristic, complemented, Sylow
129C25—611no—
130C23×C4—611no—
131C23×C4—611no—
132C2×M16—1222no—
133C2×C22⋊C4—611no—
134C2×C22⋊C4—611no—
135C2×C22⋊C4—611no—
136C2×C22⋊C4—1222no—
137C2×C22⋊C4—1222no—
138C2×C22⋊C4C2×D6111yescharacteristic
139C22⋊C8—612no—
140C22⋊C8—1222no—
141C22⋊C8C2×D6112yescomplemented
142C24—611no—
143C24—611no—
144C24—1221no—
145C24—1221no—
146C24—1222no—
147C24—1222no—
148C24—2442no—
149C24—2442no—
150C24C4×D6111yescharacteristic
151C22×C4—611no—
152C22×C4—612no—
153C22×C4—612no—
154C22×C4—611no—
155C22×C4—1221no—
156C22×C4—1221no—
157C22×C4—2442no—
158C22×C4—2442no—
159C22×C4C4×D6111yescharacteristic
160C22×C4C22×D6111yescharacteristic
161M16—2444no—
162C2×C8—22no—
163C2×C8—1222no—
164C22⋊C4—22no—
165C22⋊C4—1222no—
166C22⋊C4—1222no—
167C22⋊C4—1222no—
168C23—21no—
169C23—21no—
170C23—41no—
171C23—41no—
172C23—611no—
173C23—611no—
174C23—612no—
175C23—1222no—
176C23—1222no—
177C23—1224no—
178C23—1224no—
179C23—1221no—
180C23—1221no—
181C23—1221no—
182C23—1221no—
183C23—2441no—
184C23—2441no—
185C23—2442no—
186C23—2442no—
187C23—2448no—
188C23—2448no—
189C23—2442no—
190C23—2442no—
191C23#1175818912yescomplemented
192C23C2×C4×D6111yescharacteristic
193C2×C4—21no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—612no—
197C2×C4—1224no—
198C2×C4—1221no—
199C2×C4—2442no—
200C2×C4—2442no—
201C2×C4—2442no—
202C2×C4—2441no—
203C2×C4—2441no—
204C2×C4D4×D6112yes—
205C8—42no—
206C8—2442no—
207C22—21no—
208C22—21no—
209C22—22no—
210C22—42no—
211C22—42no—
212C22—41no—
213C22—41no—
214C22—612no—
215C22—612no—
216C22—1224no—
217C22—1224no—
218C22—1221no—
219C22—1221no—
220C22—1221no—
221C22—1221no—
222C22—1222no—
223C22—2442no—
224C22—2442no—
225C22—2448no—
226C22—2448no—
227C22—2441no—
228C22—2441no—
229C22C22⋊C4×D6111yescharacteristic
230C22M16×D6111yescharacteristic
231C22C2×#1175818911yescharacteristic
232C4—22no—
233C4—41no—
234C4—1222no—
235C4—2441no—
236C2—21no—
237C2—21no—
238C2—42no—
239C2—1222no—
240C2—1222no—
241C2—2442no—
242C2#1683972411yescharacteristic
243C2#99×D6111yescharacteristic
244C2#100×D6111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D61
commutatorC23×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#323C2
socleC22×C61C2×C22⋊C4
hypercenter#323D61
hypocenterC61#1462
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #16839724C2semidirect
3. #16839486C2semidirect
4. #16839485C2semidirect
5. C61×#323C2semidirect
15. C22⋊#92418C22semidirect
18. C22⋊C8×C61C22semidirect
49. C23×C61M16semidirect
69. C22×D61M16semidirect
127. #323D61semidirect
128. C61#1462semidirect
141. C22⋊C8C2×D61semidirect
191. C23#11758189semidirect