Finite Group Databasebeta

← #21450282

Subgroups — #21450282

Order 7808.

568 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 153 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×#14519736C211yesmaximal, characteristic, complemented
2#16839676C214yesmaximal, complemented
3#16839665C211yesmaximal, characteristic, complemented
4#16839665C211yesmaximal, characteristic, complemented
5#16839650C214yesmaximal, complemented
6#16839631C211yesmaximal, characteristic, complemented
7#16839627C211yesmaximal, characteristic, complemented
8C4×C22⋊Dic61C211yesmaximal, characteristic, complemented
9C2×#121×C61C211yesmaximal, characteristic
10#14519736—24no—
11C2×C4⋊Dic61C2211yescharacteristic
12C2×C4⋊Dic61C2211yescharacteristic
13C2×#11758196C2214yes—
14C2×C22⋊Dic61C2212yes—
15C2×C22⋊Dic61C2212yes—
16C2×C22⋊Dic61C2214yes—
17C2×C22⋊Dic61C2214yes—
18C2×C4×Dic61C2212yes—
19C2×C4×Dic61C2211yescharacteristic
20C2×C4×Dic61C2211yescharacteristic
21#14519684C2212yes—
22#14519684C2214yes—
23C22×D4×C61C2211yescharacteristic
24C22×D4×C61C2212yes—
25C23×C4×C61C2211yescharacteristic
26#121×C61—24no—
27C2×C4⋊C4×C61C2211yescharacteristic
28C2×C22⋊C4×C61C2212yes—
29C24×C61C2312yes—
30C24×C61C2311yescharacteristic
31C2×D4×C61—24no—
32C2×D4×C61—22no—
33C2×D4×C61—22no—
34C2×D4×C61—22no—
35C2×D4×C61—44no—
36C22×C4×C61—22no—
37C22×C4×C61—22no—
38C22×C4×C61D414yes—
39C22×C4×C61C2312yes—
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2311yescharacteristic
42C22×Dic61C2312yes—
43C22×Dic61C2312yes—
44C22×Dic61C2312yes—
45C22×Dic61C2312yes—
46C4⋊C4×C61—22no—
47C22⋊C4×C61—24no—
48C22⋊Dic61—24no—
49C22⋊Dic61—24no—
50C22⋊Dic61—28no—
51C22⋊Dic61—44no—
52C4⋊Dic61—22no—
53C4⋊Dic61—22no—
54#11758196—44no—
55C4×Dic61—24no—
56C4×Dic61—22no—
57C4×Dic61—22no—
58C23×C61—22no—
59C23×C61—21no—
60C23×C61—21no—
61C23×C61—22no—
62C23×C61—22no—
63C23×C61—24no—
64C23×C61—22no—
65C23×C61—22no—
66C23×C61—24no—
67C23×C61C2×D412yes—
68C23×C61C2411yescharacteristic
69D4×C61—48no—
70D4×C61—44no—
71C2×C4×C61—21no—
72C2×C4×C61—21no—
73C2×C4×C61—28no—
74C2×C4×C61—22no—
75C2×C4×C61—24no—
76C2×C4×C61C2×D412yes—
77C2×C4×C61C2×D412yes—
78C2×C4×C61#4112yes—
79C2×C4×C61#4112yes—
80C2×Dic61—22no—
81C2×Dic61—22no—
82C2×Dic61—22no—
83C2×Dic61—22no—
84C2×Dic61—22no—
85C2×Dic61—24no—
86C2×Dic61—22no—
87C2×Dic61—24no—
88C2×Dic61—22no—
89C2×Dic61#4114yes—
90C22×C61—22no—
91C22×C61—22no—
92C22×C61—22no—
93C22×C61—42no—
94C22×C61—42no—
95C22×C61—42no—
96C22×C61—42no—
97C22×C61—42no—
98C22×C61—44no—
99C22×C61—44no—
100C22×C61C22×D411yescharacteristic
101C22×C61C2×#4112yes—
102C22×C61C2×#4111yescharacteristic
103C22×C61C2×#4111yescharacteristic
104C22×C61H(5,𝔽2)12yes—
105C4×C61—22no—
106C4×C61—42no—
107C4×C61#12314yes—
108Dic61—24no—
109Dic61—42no—
110Dic61—42no—
111Dic61—42no—
112#2500—611nomaximal, Sylow
113C2×C61—42no—
114C2×C61—82no—
115C2×C61C2×#12311yescharacteristic
116C2×C61#53211yescharacteristic
117C2×C61#53511yescharacteristic
118C2×C61#55312yes—
119C2×C61#55512yes—
120C2×#121D6111yescharacteristic
121C2×#117—611no—
122#394—614no—
123#390—611no—
124#390—611no—
125#388—614no—
126#384—611no—
127#382—611no—
128C4×C22⋊C4—611no—
129C61#250011yescharacteristic, complemented, Sylow
130C22×D4C2×D6111yescharacteristic
131C22×D4C2×D6112yes—
132C23×C4C2×D6111yescharacteristic
133#121—24no—
134#117—1224no—
135C2×C4⋊C4—611no—
136C2×C4⋊C4—611no—
137C2×C4⋊C4—614no—
138C2×C4⋊C4C2×D6111yescharacteristic
139C2×C22⋊C4—612no—
140C2×C22⋊C4—612no—
141C2×C22⋊C4—614no—
142C2×C22⋊C4—614no—
143C2×C22⋊C4C2×D6112yes—
144C2×C42—612no—
145C2×C42—611no—
146C2×C42—611no—
147#95—612no—
148#95—614no—
149C24C22×D6112yes—
150C24C22×D6111yescharacteristic
151C2×D4—24no—
152C2×D4—22no—
153C2×D4—22no—
154C2×D4—22no—
155C2×D4—44no—
156C22×C4—22no—
157C22×C4—22no—
158C22×C4—612no—
159C22×C4—612no—
160C22×C4—612no—
161C22×C4—612no—
162C22×C4C22⋊D6114yes—
163C22×C4C22×D6112yes—
164C22×C4C22×D6111yescharacteristic
165C22×C4C22×D6111yescharacteristic
166C4⋊C4—22no—
167C4⋊C4—1222no—
168C4⋊C4—1222no—
169C4⋊C4—2444no—
170C22⋊C4—24no—
171C22⋊C4—1224no—
172C22⋊C4—1228no—
173C22⋊C4—1224no—
174C22⋊C4—2444no—
175C42—1222no—
176C42—1222no—
177C42—1224no—
178C23—22no—
179C23—21no—
180C23—21no—
181C23—22no—
182C23—22no—
183C23—24no—
184C23—22no—
185C23—22no—
186C23—24no—
187C23C2×C22⋊D6112yes—
188C23C23×D6111yescharacteristic
189D4—48no—
190D4—44no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—28no—
194C2×C4—22no—
195C2×C4—24no—
196C2×C4—614no—
197C2×C4—1222no—
198C2×C4—1222no—
199C2×C4—1222no—
200C2×C4—1222no—
201C2×C4—1222no—
202C2×C4—1224no—
203C2×C4—1222no—
204C2×C4—1222no—
205C2×C4—1224no—
206C2×C4#1175822412yes—
207C2×C4#1175822412yes—
208C2×C4C2×C22⋊D6112yes—
209C2×C4C2×C22⋊D6112yes—
210C22—22no—
211C22—22no—
212C22—22no—
213C22—42no—
214C22—42no—
215C22—44no—
216C22—44no—
217C22—42no—
218C22—42no—
219C22—42no—
220C22C22×C22⋊D6111yescharacteristic
221C22#41×D6112yes—
222C22C2×#1175822411yescharacteristic
223C22C2×#1175822411yescharacteristic
224C22#1451982212yes—
225C4—22no—
226C4—42no—
227C4—1224no—
228C4—2442no—
229C4—2442no—
230C4—2442no—
231C4#1451975814yes—
232C2—42no—
233C2—82no—
234C2C2×#1451975811yescharacteristic
235C2#1684030811yescharacteristic
236C2#1684032911yescharacteristic
237C2#1684045912yes—
238C2#1684047612yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#121×C61C2
hypercenterC2×#121D61
hypocenterC61#2500
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#14519736C2semidirect
2. #16839676C2semidirect
3. #16839665C2semidirect
4. #16839665C2semidirect
5. #16839650C2semidirect
6. #16839631C2semidirect
7. #16839627C2semidirect
8. C4×C22⋊Dic61C2semidirect
129. C61#2500semidirect