Finite Group Databasebeta

← #21446655

Subgroups — #21446655

Order 7808.

408 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 97 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×#14519751C211yesmaximal, characteristic
2C2×#14519691C214yesmaximal, complemented
3#16839622C211yesmaximal, characteristic, complemented
4C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
5C22×D244C411yescharacteristic, complemented
6C22×C22⋊D61C2212yes—
7#14519751—21no—
8#14519751—21no—
9#14519751—21no—
10#14519751—21no—
11C2×C4⋊Dic61—21no—
12C2×C4⋊Dic61C411yescharacteristic, complemented
13C2×C22⋊Dic61C2212yes—
14C2×#11758198C412yescomplemented
15#14519691—28no—
16#14519684—21no—
17C23×C4×C61C2211yescharacteristic
18C2×C22⋊C4×C61C2212yes—
19C2×C42×C61—21no—
20#95×C61—21no—
21C24×C61C2311yescharacteristic
22C23×D61C2×C412yes—
23C22×C4×C61—22no—
24C22×C4×C61—42no—
25C22×C4×C61C2×C411yescharacteristic
26C22×C4×C61C2×C411yescharacteristic
27C22×C4×C61D411yescharacteristic
28C22×C4×C61D411yescharacteristic
29C22×C4×C61D411yescharacteristic
30C22×C4×C61D411yescharacteristic
31C2×C22⋊D61—24no—
32C2×C22⋊D61—22no—
33C2×C22⋊D61—22no—
34C2×C22⋊D61—24no—
35C22×Dic61—22no—
36C22×Dic61C2×C412yes—
37C2×D244—21no—
38C2×D244—21no—
39C2×D244—42no—
40C22⋊C4×C61—22no—
41C22⋊C4×C61D414yescomplemented
42C42×C61—42no—
43C22⋊Dic61—24no—
44#11758198—22no—
45#11758198—22no—
46C4⋊Dic61—21no—
47C4⋊Dic61—21no—
48C4⋊Dic61—42no—
49C23×C61—41no—
50C23×C61—41no—
51C23×C61C22×C411yescharacteristic
52C23×C61C2×D411yescharacteristic
53C23×C61C2×D411yescharacteristic
54C23×C61C2×D412yes—
55C23×C61#4112yes—
56C22×D61—22no—
57C22×D61—24no—
58C22×D61—42no—
59C22×D61—42no—
60C2×C4×C61—22no—
61C2×C4×C61—22no—
62C2×C4×C61—22no—
63C2×C4×C61—24no—
64C2×C4×C61—41no—
65C2×C4×C61—41no—
66C2×C4×C61—41no—
67C2×C4×C61—42no—
68C2×C4×C61—42no—
69C2×C4×C61C22⋊C411yescharacteristic
70C2×C4×C61C22⋊C411yescharacteristic
71C2×C4×C61C22⋊C411yescharacteristic
72C2×C4×C61C22⋊C411yescharacteristic
73C22⋊D61—44no—
74C22⋊D61—42no—
75C22⋊D61—42no—
76C2×Dic61—22no—
77C2×Dic61—24no—
78C2×Dic61—42no—
79C2×Dic61—42no—
80C2×Dic61—42no—
81D244—42no—
82D244—42no—
83C22×C61—21no—
84C22×C61—21no—
85C22×C61—21no—
86C22×C61—21no—
87C22×C61—21no—
88C22×C61—21no—
89C22×C61—42no—
90C22×C61—42no—
91C22×C61C2×C22⋊C411yescharacteristic
92C22×C61C4×D412yes—
93C22×C61#12112yes—
94C22×C61#12411yescharacteristic
95C22×C61#12711yescharacteristic
96C2×D61—42no—
97C2×D61—42no—
98C2×D61—42no—
99C2×D61—84no—
100C4×C61—21no—
101C4×C61—21no—
102C4×C61—21no—
103C4×C61—44no—
104C4×C61#9912yescomplemented
105Dic61—42no—
106Dic61—82no—
107#1964—611nomaximal, Sylow
108C2×C61—21no—
109C2×C61—22no—
110C2×C61—22no—
111C2×C61—21no—
112C2×C61#39011yescharacteristic
113C2×C61C2×#9911yescharacteristic
114C2×C61#41011yescharacteristic
115D61—82no—
116C2×#121—611no—
117C2×#99—614no—
118#380—611no—
119C4×C22⋊C4D6111yescharacteristic, complemented
120C61#196411yescharacteristic, complemented, Sylow
121C22×D4—612no—
122C22×D4—611no—
123C23×C4C2×D6111yescharacteristic
124#121—1221no—
125#121—1221no—
126#121—1221no—
127#121—1221no—
128C2×C4⋊C4—611no—
129C2×C4⋊C4—1221no—
130C2×C22⋊C4—612no—
131C2×C22⋊C4—612no—
132C2×C22⋊C4C2×D6112yes—
133C2×C42—21no—
134#99—1228no—
135#95—21no—
136#95—1221no—
137C24—612no—
138C24C22×D6111yescharacteristic
139C2×D4—1224no—
140C2×D4—1222no—
141C2×D4—1224no—
142C2×D4—1222no—
143C2×D4—1221no—
144C2×D4—1221no—
145C2×D4—2442no—
146C22×C4—22no—
147C22×C4—42no—
148C22×C4—612no—
149C22×C4—1222no—
150C22×C4C4×D6111yescharacteristic
151C22×C4C4×D6111yescharacteristic
152C22×C4D24411yescharacteristic
153C22×C4D24411yescharacteristic
154C22×C4C22⋊D6111yescharacteristic
155C22×C4C22⋊D6111yescharacteristic
156C4⋊C4—1221no—
157C4⋊C4—1221no—
158C4⋊C4—2442no—
159C22⋊C4—22no—
160C22⋊C4—1222no—
161C22⋊C4—1222no—
162C22⋊C4—1224no—
163C22⋊C4D24414yescomplemented
164C42—42no—
165C23—41no—
166C23—41no—
167C23—1224no—
168C23—1222no—
169C23—2442no—
170C23—2442no—
171C23C2×C4×D6111yescharacteristic
172C23C2×D24411yescharacteristic
173C23C2×D24412yes—
174C23#1175822212yes—
175C23C2×C22⋊D6111yescharacteristic
176D4—2442no—
177D4—2444no—
178D4—2442no—
179D4—2442no—
180D4—2442no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—24no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—1222no—
191C2×C4—1224no—
192C2×C4—2442no—
193C2×C4—2442no—
194C2×C4—2442no—
195C2×C4#1175819811yescharacteristic
196C2×C4#1175819811yescharacteristic
197C2×C4#1175819811yescharacteristic
198C2×C4#1175819811yescharacteristic
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—42no—
206C22—42no—
207C22—4884no—
208C22—2442no—
209C22—2442no—
210C22—2442no—
211C22C2×#1175819811yescharacteristic
212C22C4×D24412yes—
213C22#1451975112yes—
214C22#1451976511yescharacteristic
215C22#1451977411yescharacteristic
216C4—21no—
217C4—21no—
218C4—21no—
219C4—44no—
220C4—4882no—
221C4—2442no—
222C4#1451969112yescomplemented
223C2—22no—
224C2—21no—
225C2—22no—
226C2—21no—
227C2—4882no—
228C2#1683966411yescharacteristic
229C2C2×#1451969111yescharacteristic
230C2#1683973511yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC23×C61C22×C4
FrattiniC24C22×D61
FittingC4×C22⋊C4×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC4×C22⋊C4D61
hypocenterC61#1964
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#14519691C2semidirect
3. #16839622C2semidirect
4. C4×C22⋊C4×C61C2semidirect
5. C22×D244C4semidirect
12. C2×C4⋊Dic61C4semidirect
14. C2×#11758198C4semidirect
41. C22⋊C4×C61D4semidirect
104. C4×C61#99semidirect
119. C4×C22⋊C4D61semidirect
120. C61#1964semidirect
163. C22⋊C4D244semidirect
222. C4#14519691semidirect