Finite Group Databasebeta

← #21451400

Subgroups — #21451400

Order 7808.

604 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 141 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×D4×Dic61C212yesmaximal, complemented
2#16839687C211yesmaximal, characteristic, complemented
3#16839676C212yesmaximal, complemented
4#16839656C212yesmaximal, complemented
5#16839649C212yesmaximal, complemented
6#16839642C212yesmaximal, complemented
7#16839637C212yesmaximal, complemented
8#16839623C211yesmaximal, characteristic, complemented
9C61×#392C211yesmaximal, characteristic
10C23×Dic61C2212yes—
11C23×Dic61C2211yescharacteristic
12D4×Dic61—28no—
13C2×C4⋊Dic61C2212yes—
14C2×C4⋊Dic61C2211yescharacteristic
15C2×#11758196C2212yes—
16C2×C22⋊Dic61C2212yes—
17C2×C22⋊Dic61C2212yes—
18C2×C22⋊Dic61C2212yes—
19C2×C22⋊Dic61C2211yescharacteristic
20C2×C22⋊Dic61C2212yes—
21C2×C4×Dic61C2212yes—
22#14519684C2212yes—
23#14519684C2211yescharacteristic
24#14519684C2212yes—
25#14519684C2212yes—
26#14519684C2212yes—
27C22×D4×C61C2212yes—
28C22×D4×C61C2211yescharacteristic
29C2×C22⋊C4×C61C2212yes—
30C2×C22⋊C4×C61C2211yescharacteristic
31#95×C61C2211yescharacteristic
32C24×C61C2311yescharacteristic
33C24×C61C2312yes—
34C2×D4×C61—24no—
35C2×D4×C61—24no—
36C2×D4×C61—24no—
37C2×D4×C61—24no—
38C2×D4×C61—41no—
39C22×C4×C61C2311yescharacteristic
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2312yes—
42C22×Dic61—24no—
43C22×Dic61—41no—
44C22×Dic61—41no—
45C22×Dic61—42no—
46C22×Dic61—42no—
47C22×Dic61D414yescomplemented
48C22×Dic61C2312yes—
49C22×Dic61C2312yes—
50C22×Dic61C2312yes—
51C22×Dic61C2312yes—
52C22⋊C4×C61—24no—
53C22⋊C4×C61—41no—
54C22⋊Dic61—24no—
55C22⋊Dic61—24no—
56C22⋊Dic61—24no—
57C22⋊Dic61—41no—
58C22⋊Dic61—42no—
59C4⋊Dic61—24no—
60C4⋊Dic61—41no—
61#11758196—24no—
62C4×Dic61—24no—
63C23×C61—22no—
64C23×C61—22no—
65C23×C61—22no—
66C23×C61—22no—
67C23×C61—22no—
68C23×C61—22no—
69C23×C61—21no—
70C23×C61—22no—
71C23×C61—21no—
72C23×C61—22no—
73C23×C61C2×D412yes—
74C23×C61#4114yes—
75C23×C61C2411yescharacteristic
76D4×C61—216no—
77D4×C61—44no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61#4114yes—
85C2×Dic61—22no—
86C2×Dic61—22no—
87C2×Dic61—22no—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—44no—
97C2×Dic61—48no—
98C2×Dic61C2×D414yes—
99C22×C61—24no—
100C22×C61—24no—
101C22×C61—22no—
102C22×C61—24no—
103C22×C61—24no—
104C22×C61—42no—
105C22×C61—42no—
106C22×C61—41no—
107C22×C61—42no—
108C22×C61—42no—
109C22×C61—42no—
110C22×C61—41no—
111C22×C61C22×D411yescharacteristic
112C22×C61C2×#4112yes—
113C22×C61C2×#4112yes—
114C22×C61H(5,𝔽2)11yescharacteristic
115C22×C61H(5,𝔽2)11yescharacteristic
116C4×C61—24no—
117C4×C61—41no—
118C4×C61—41no—
119Dic61—24no—
120Dic61—42no—
121Dic61—42no—
122Dic61—42no—
123#2600—611nomaximal, Sylow
124C2×C61—42no—
125C2×C61—44no—
126C2×C61#52512yes—
127C2×C61#53411yescharacteristic
128C2×C61#55111yescharacteristic
129C2×C61#55312yes—
130C2×C61#55911yescharacteristic
131C2×C4×D4—612no—
132#397—611no—
133#394—612no—
134#392D6111yescharacteristic
135#388—612no—
136#387—612no—
137#386—612no—
138#385—612no—
139#381—611no—
140C61#260011yescharacteristic, complemented, Sylow
141C22×D4C2×D6112yes—
142C22×D4C2×D6111yescharacteristic
143C23×C4—611no—
144C23×C4—612no—
145C4×D4—1228no—
146C2×C4⋊C4—612no—
147C2×C4⋊C4—612no—
148C2×C4⋊C4—611no—
149C2×C22⋊C4—612no—
150C2×C22⋊C4—612no—
151C2×C22⋊C4—612no—
152C2×C22⋊C4—611no—
153C2×C22⋊C4—612no—
154C2×C22⋊C4C2×D6112yes—
155C2×C22⋊C4C2×D6111yescharacteristic
156C2×C42—612no—
157#95—612no—
158#95—612no—
159#95—612no—
160#95—612no—
161#95—611no—
162#95C2×D6111yescharacteristic
163C24C22×D6111yescharacteristic
164C24C22×D6112yes—
165C2×D4—24no—
166C2×D4—24no—
167C2×D4—24no—
168C2×D4—24no—
169C2×D4—41no—
170C22×C4—612no—
171C22×C4—614no—
172C22×C4—612no—
173C22×C4—612no—
174C22×C4—612no—
175C22×C4—1224no—
176C22×C4—2441no—
177C22×C4—2442no—
178C22×C4—2441no—
179C22×C4—2442no—
180C22×C4C22×D6111yescharacteristic
181C22×C4C22×D6111yescharacteristic
182C22×C4C22×D6112yes—
183C4⋊C4—1224no—
184C4⋊C4—1224no—
185C4⋊C4—2441no—
186C22⋊C4—24no—
187C22⋊C4—41no—
188C22⋊C4—1224no—
189C22⋊C4—1224no—
190C22⋊C4—1224no—
191C22⋊C4—2441no—
192C22⋊C4—2442no—
193C42—1224no—
194C23—22no—
195C23—22no—
196C23—22no—
197C23—22no—
198C23—22no—
199C23—22no—
200C23—21no—
201C23—22no—
202C23—22no—
203C23—21no—
204C23D4×D6112yes—
205C23#1175822414yes—
206C23C23×D6111yescharacteristic
207D4—216no—
208D4—44no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—614no—
216C2×C4—1222no—
217C2×C4—1222no—
218C2×C4—1222no—
219C2×C4—1222no—
220C2×C4—1222no—
221C2×C4—1222no—
222C2×C4—1222no—
223C2×C4—1222no—
224C2×C4—1222no—
225C2×C4—1222no—
226C2×C4—1222no—
227C2×C4—2444no—
228C2×C4—2448no—
229C2×C4#1175822414yes—
230C22—24no—
231C22—24no—
232C22—24no—
233C22—22no—
234C22—24no—
235C22—42no—
236C22—42no—
237C22—42no—
238C22—41no—
239C22—42no—
240C22—42no—
241C22—41no—
242C22C2×D4×D6111yescharacteristic
243C22C2×#1175822412yes—
244C22C2×#1175822412yes—
245C22#1451982211yescharacteristic
246C22#1451982311yescharacteristic
247C4—24no—
248C4—41no—
249C4—41no—
250C4—1224no—
251C4—2442no—
252C4—2442no—
253C4—2442no—
254C2—44no—
255C2—42no—
256C2#1684026812yes—
257C2#1684032011yescharacteristic
258C2#1684044311yescharacteristic
259C2#1684046412yes—
260C2#1684049811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#392C2
hypercenter#392D61
hypocenterC61#2600
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic61C2semidirect
2. #16839687C2semidirect
3. #16839676C2semidirect
4. #16839656C2semidirect
5. #16839649C2semidirect
6. #16839642C2semidirect
7. #16839637C2semidirect
8. #16839623C2semidirect
47. C22×Dic61D4semidirect
140. C61#2600semidirect