Finite Group Databasebeta

← #21450137

Subgroups — #21450137

Order 7808.

584 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 173 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×C4×C22⋊D61C211yesmaximal, characteristic
2C22×C4⋊Dic61C211yesmaximal, characteristic, complemented
3#16839702C212yesmaximal, complemented
4#16839699C212yesmaximal, complemented
5#16839661C212yesmaximal, complemented
6#16839639C212yesmaximal
7#16839637C212yesmaximal, complemented
8#16839619C212yesmaximal, complemented
9C61×#380C211yesmaximal, characteristic, complemented
10C22×C22⋊D61C2211yescharacteristic
11C23×Dic61C2212yes—
12C22×C4×D61C2211yescharacteristic
13C4×C22⋊D61—24no—
14C2×C4⋊Dic61—24no—
15C2×C4⋊Dic61C2212yes—
16C2×C4⋊Dic61C2212yes—
17C2×C4⋊Dic61C2214yes—
18C2×#11758196C2211yescharacteristic
19C2×C22⋊Dic61C2211yescharacteristic
20C2×#11758198C2211yescharacteristic
21C2×#11758198C2214yes—
22C2×C4×Dic61C2211yescharacteristic
23#14519684C2214yes—
24#14519684C2214yes—
25C23×C4×C61C2211yescharacteristic
26C2×C4⋊C4×C61C2212yes—
27C2×C22⋊C4×C61C2212yes—
28#95×C61C2212yes—
29C24×C61C2311yescharacteristic
30C23×D61C2311yescharacteristic
31C22×C4×C61—24no—
32C22×C4×C61D414yes—
33C22×C4×C61C2314yes—
34C22×C4×C61C2311yescharacteristic
35C22×C4×C61C2311yescharacteristic
36C2×C22⋊D61—22no—
37C2×C22⋊D61—22no—
38C2×C22⋊D61Q814yes—
39C22×Dic61—24no—
40C22×Dic61—44no—
41C22×Dic61C2311yescharacteristic
42C22×Dic61C2314yes—
43C22×Dic61C2311yescharacteristic
44C22×Dic61C2311yescharacteristic
45C2×C4×D61—22no—
46C2×C4×D61—24no—
47C4⋊C4×C61—24no—
48C22⋊C4×C61—24no—
49C22⋊Dic61—22no—
50#11758198—22no—
51#11758198—44no—
52C4⋊Dic61—24no—
53C4⋊Dic61—24no—
54C4⋊Dic61—44no—
55#11758196—22no—
56C4×Dic61—22no—
57C23×C61—22no—
58C23×C61—22no—
59C23×C61C2×D412yes—
60C23×C61C2×Q812yes—
61C23×C61#4112yes—
62C23×C61C2411yescharacteristic
63C22×D61—21no—
64C22×D61—22no—
65C22×D61—21no—
66C22×D61—22no—
67C22×D61C2×Q812yes—
68C2×C4×C61—22no—
69C2×C4×C61—28no—
70C2×C4×C61—24no—
71C2×C4×C61—24no—
72C2×C4×C61—24no—
73C2×C4×C61C2×D412yes—
74C2×C4×C61C2×D412yes—
75C2×C4×C61#4114yes—
76C22⋊D61—28no—
77C2×Dic61—21no—
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61—21no—
81C2×Dic61—24no—
82C2×Dic61—22no—
83C2×Dic61—22no—
84C2×Dic61—24no—
85C2×Dic61—24no—
86C2×Dic61—48no—
87C2×Dic61C2×Q812yes—
88C4×D61—44no—
89C22×C61—22no—
90C22×C61—22no—
91C22×C61—24no—
92C22×C61—24no—
93C22×C61C22⋊Q814yes—
94C22×C61C22×D411yescharacteristic
95C22×C61C22×Q811yescharacteristic
96C22×C61C2×#4111yescharacteristic
97C22×C61C2×#4112yes—
98C22×C61H(5,𝔽2)12yes—
99C2×D61—22no—
100C2×D61—24no—
101C2×D61—41no—
102C2×D61—41no—
103C2×D61—42no—
104C4×C61—22no—
105C4×C61—44no—
106C4×C61#12314yes—
107Dic61—22no—
108Dic61—41no—
109Dic61—41no—
110Dic61—44no—
111#2487—611nomaximal, Sylow
112C2×C61—24no—
113C2×C61C2×C22⋊Q811yescharacteristic
114C2×C61C2×#12311yescharacteristic
115C2×C61#53511yescharacteristic
116C2×C61#55312yes—
117C2×C61#55412yes—
118D61—42no—
119C2×C4×D4—611no—
120C22×C4⋊C4—611no—
121#400—612no—
122#399—612no—
123#389—612no—
124#386—612no—
125#385—612no—
126#380—612no—
127#380D6111yescharacteristic, complemented
128C61#248711yescharacteristic, complemented, Sylow
129C22×D4—611no—
130C23×C4—612no—
131C23×C4—611no—
132C23×C4C2×D6111yescharacteristic
133C4×D4—1224no—
134C2×C4⋊C4—612no—
135C2×C4⋊C4—612no—
136C2×C4⋊C4—611no—
137C2×C4⋊C4—614no—
138C2×C4⋊C4—1224no—
139C2×C4⋊C4C2×D6112yes—
140C2×C22⋊C4—611no—
141C2×C22⋊C4—611no—
142C2×C22⋊C4—614no—
143C2×C22⋊C4C2×D6112yes—
144C2×C42—611no—
145#95—614no—
146#95—614no—
147#95C2×D6112yes—
148C24—611no—
149C24C22×D6111yescharacteristic
150C2×D4—614no—
151C2×D4—1222no—
152C2×D4—1222no—
153C22×C4—24no—
154C22×C4—611no—
155C22×C4—611no—
156C22×C4—614no—
157C22×C4—611no—
158C22×C4—1224no—
159C22×C4—1222no—
160C22×C4—1224no—
161C22×C4—2444no—
162C22×C4D24414yes—
163C22×C4C22×D6114yes—
164C22×C4C22×D6111yescharacteristic
165C22×C4C22×D6111yescharacteristic
166C4⋊C4—24no—
167C4⋊C4—1224no—
168C4⋊C4—1224no—
169C4⋊C4—1222no—
170C4⋊C4—2444no—
171C22⋊C4—24no—
172C22⋊C4—1222no—
173C22⋊C4—1222no—
174C22⋊C4—2444no—
175C42—1222no—
176C23—22no—
177C23—22no—
178C23—612no—
179C23—1221no—
180C23—1222no—
181C23—1221no—
182C23—1222no—
183C23C2×D24412yes—
184C23#1175822412yes—
185C23Q8×D6112yes—
186C23C23×D6111yescharacteristic
187D4—1228no—
188C2×C4—22no—
189C2×C4—28no—
190C2×C4—24no—
191C2×C4—24no—
192C2×C4—24no—
193C2×C4—612no—
194C2×C4—1221no—
195C2×C4—1221no—
196C2×C4—1221no—
197C2×C4—1221no—
198C2×C4—1224no—
199C2×C4—1222no—
200C2×C4—1224no—
201C2×C4—1222no—
202C2×C4—1224no—
203C2×C4—2448no—
204C2×C4—2444no—
205C2×C4C2×D24412yes—
206C2×C4C2×D24412yes—
207C2×C4#1175822414yes—
208C22—24no—
209C22—24no—
210C22—22no—
211C22—22no—
212C22—1224no—
213C22—1222no—
214C22—2442no—
215C22—2441no—
216C22—2441no—
217C22#1451975714yes—
218C22C22×D24411yescharacteristic
219C22C2×Q8×D6111yescharacteristic
220C22C2×#1175822411yescharacteristic
221C22C2×#1175822412yes—
222C22#1451982312yes—
223C4—22no—
224C4—44no—
225C4—1222no—
226C4—2441no—
227C4—2441no—
228C4—2444no—
229C4#1451976114yes—
230C2—24no—
231C2—2442no—
232C2C2×#1451975711yescharacteristic
233C2C2×#1451976111yescharacteristic
234C2#1684033111yescharacteristic
235C2#1684046412yes—
236C2#1684047012yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#380C2
hypercenter#380D61
hypocenterC61#2487
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊Dic61C2semidirect
3. #16839702C2semidirect
4. #16839699C2semidirect
5. #16839661C2semidirect
7. #16839637C2semidirect
8. #16839619C2semidirect
9. C61×#380C2semidirect
127. #380D61semidirect
128. C61#2487semidirect