Finite Group Databasebeta

← #21445762

Subgroups — #21445762

Order 7808.

618 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 618 conjugacy classes of subgroups — too many to draw. Only its 105 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×#14519703C214yesmaximal, complemented
3C4×C22⋊Dic61C211yesmaximal, characteristic, complemented
4C61×#407C211yesmaximal, characteristic, complemented
5C2×#11758222—21no—
6C2×#11758222—21no—
7C2×#11758222—28no—
8C2×#11758222C412yescomplemented
9C2×#11758222C2212yes—
10C22×Dic122C411yescharacteristic, complemented
11C22×D244C411yescharacteristic, complemented
12C22×C22⋊D61—21no—
13C22×C4×D61—21no—
14C2×C22⋊Dic61—21no—
15C2×C4×Dic61C2212yescomplemented
16#14519703—28no—
17#14519684—21no—
18C23×C4×C61C2211yescharacteristic
19C2×M16×C61C2212yescomplemented
20C22⋊C8×C61—21no—
21C22⋊C8×C61—21no—
22C24×C61D411yescharacteristic
23C23×D61—21no—
24C22×C4×C61—24no—
25C22×C4×C61C2×C411yescharacteristic
26C22×C4×C61C2×C411yescharacteristic
27C22×C4×C61D411yescharacteristic
28C22×C4×C61D411yescharacteristic
29C22×C4×C61D411yescharacteristic
30C22×C4×C61C2311yescharacteristic
31C2×C22⋊D61—28no—
32C2×C22⋊D61—22no—
33C2×C22⋊D61—22no—
34C22×Dic61—21no—
35C22×Dic61—22no—
36#11758222—28no—
37#11758222—28no—
38#11758222—24no—
39#11758222—24no—
40#11758222—24no—
41#11758222D418yes—
42C2×D244—21no—
43C2×D244—24no—
44C2×D244C2×C412yes—
45C2×C4×D61—28no—
46C2×C4×D61—22no—
47C2×C4×D61—22no—
48C2×Dic122—21no—
49C2×Dic122—24no—
50C2×Dic122C2×C412yes—
51M16×C61—24no—
52C2×C8×C61—22no—
53C22⋊Dic61—24no—
54C4×Dic61—24no—
55C23×C61—22no—
56C23×C61—22no—
57C23×C61—41no—
58C23×C61C22⋊C411yescharacteristic
59C23×C61C22⋊C411yescharacteristic
60C23×C61C2×D411yescharacteristic
61C22×D61—24no—
62C22×D61—22no—
63C22×D61—42no—
64C22×D61—42no—
65C2×C4×C61—22no—
66C2×C4×C61—22no—
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61—22no—
70C2×C4×C61C22⋊C411yescharacteristic
71C2×C4×C61C22⋊C411yescharacteristic
72C2×C4×C61C22×C411yescharacteristic
73C2×C4×C61C2×D414yes—
74C2×C4×C61C2×D411yescharacteristic
75C22⋊D61—28no—
76C22⋊D61—28no—
77C2×Dic61—24no—
78C2×Dic61—22no—
79C2×Dic61—24no—
80C2×Dic61—42no—
81C2×Dic61—42no—
82D244—24no—
83D244—22no—
84D244C22⋊C414yescomplemented
85C4×D61—28no—
86C4×D61—28no—
87Dic122—24no—
88Dic122—22no—
89Dic122C22⋊C414yescomplemented
90C8×C61—42no—
91C22×C61—21no—
92C22×C61—21no—
93C22×C61—21no—
94C22×C61—21no—
95C22×C61—21no—
96C22×C61—21no—
97C22×C61—21no—
98C22×C61—44no—
99C22×C61#10412yescomplemented
100C22×C61C2×C22⋊C411yescharacteristic
101C22×C61#12012yes—
102C2×D61—24no—
103C2×D61—48no—
104C2×D61—42no—
105C2×D61—42no—
106C4×C61—21no—
107C4×C61—21no—
108C4×C61C2×C22⋊C412yes—
109C4×C61#12012yes—
110Dic61—24no—
111Dic61—44no—
112#1789—611nomaximal, Sylow
113C2×C61—22no—
114C2×C61—22no—
115C2×C61—41no—
116C2×C61#37911yescharacteristic
117C2×C61C2×#10411yescharacteristic
118C2×C61#42111yescharacteristic
119D61—44no—
120C22×#41—611no—
121C2×#104—614no—
122#407D6111yescharacteristic, complemented
123C4×C22⋊C4—611no—
124C61#178911yescharacteristic, complemented, Sylow
125C2×#41—612no—
126C2×#41—612no—
127C2×#41—1228no—
128C2×#41—1221no—
129C2×#41—1221no—
130C22×Q8—611no—
131C22×D4—611no—
132C22×D4—1221no—
133C23×C4—1221no—
134C23×C4C2×D6111yescharacteristic
135C2×M16C2×D6112yescomplemented
136C2×C22⋊C4—1221no—
137C2×C42—612no—
138#104—1228no—
139C22⋊C8—21no—
140C22⋊C8—21no—
141#95—1221no—
142C24—1221no—
143C24D24411yescharacteristic
144#41—618no—
145#41—1224no—
146#41—1224no—
147#41—1228no—
148#41—1228no—
149#41—1224no—
150C2×Q8—612no—
151C2×Q8—1224no—
152C2×Q8—1221no—
153C2×D4—612no—
154C2×D4—1224no—
155C2×D4—1228no—
156C2×D4—1222no—
157C2×D4—1222no—
158C2×D4—1221no—
159C22×C4—24no—
160C22×C4—1228no—
161C22×C4—1221no—
162C22×C4—1222no—
163C22×C4—1222no—
164C22×C4—1222no—
165C22×C4C4×D6111yescharacteristic
166C22×C4C4×D6111yescharacteristic
167C22×C4D24411yescharacteristic
168C22×C4C22⋊D6111yescharacteristic
169C22×C4C22⋊D6111yescharacteristic
170C22×C4C22×D6111yescharacteristic
171M16—24no—
172C2×C8—22no—
173C22⋊C4—1224no—
174C42—1224no—
175C23—22no—
176C23—22no—
177C23—41no—
178C23—1224no—
179C23—1222no—
180C23—2442no—
181C23—2442no—
182C23#1175819811yescharacteristic
183C23#1175819811yescharacteristic
184C23C2×D24411yescharacteristic
185Q8—614no—
186Q8—1224no—
187Q8—1222no—
188D4—614no—
189D4—1224no—
190D4—1228no—
191D4—1228no—
192D4—1222no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—1228no—
199C2×C4—1224no—
200C2×C4—1222no—
201C2×C4—1228no—
202C2×C4—1224no—
203C2×C4—2442no—
204C2×C4—2442no—
205C2×C4#1175819811yescharacteristic
206C2×C4#1175819811yescharacteristic
207C2×C4C2×C4×D6111yescharacteristic
208C2×C4D4×D6114yes—
209C2×C4C2×C22⋊D6111yescharacteristic
210C8—42no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—21no—
217C22—21no—
218C22—44no—
219C22—1224no—
220C22—2448no—
221C22—2442no—
222C22—2442no—
223C22#1451970312yescomplemented
224C22C2×#1175819811yescharacteristic
225C22#1451974712yes—
226C4—21no—
227C4—21no—
228C4—1224no—
229C4—2444no—
230C4C22⋊C4×D6112yes—
231C4#1451974512yes—
232C2—22no—
233C2—22no—
234C2—41no—
235C2—2444no—
236C2#1683961711yescharacteristic
237C2C2×#1451970311yescharacteristic
238C2#1683977811yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#407C2
socleC22×C61C2×C22⋊C4
hypercenter#407D61
hypocenterC61#1789
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×#14519703C2semidirect
3. C4×C22⋊Dic61C2semidirect
4. C61×#407C2semidirect
8. C2×#11758222C4semidirect
10. C22×Dic122C4semidirect
11. C22×D244C4semidirect
15. C2×C4×Dic61C22semidirect
19. C2×M16×C61C22semidirect
84. D244C22⋊C4semidirect
89. Dic122C22⋊C4semidirect
99. C22×C61#104semidirect
122. #407D61semidirect
124. C61#1789semidirect
135. C2×M16C2×D61semidirect
223. C22#14519703semidirect