Finite Group Databasebeta

← #21449695

Subgroups — #21449695

Order 7808.

660 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14519758C212yesmaximal, complemented
2C2×D4×Dic61C212yesmaximal, complemented
3#16839698C211yesmaximal, characteristic, complemented
4#16839676C212yesmaximal, complemented
5#16839659C212yesmaximal, complemented
6#16839656C212yesmaximal, complemented
7#16839637C212yesmaximal, complemented
8#16839634C211yesmaximal, characteristic, complemented
9C61×#392C211yesmaximal, characteristic
10C23×Dic61C2211yescharacteristic
11C23×Dic61C2212yes—
12#14519758—28no—
13D4×Dic61—28no—
14C2×C4⋊Dic61C2212yes—
15C2×C4⋊Dic61C2211yescharacteristic
16C2×#11758196C2212yes—
17C2×#11758196C2212yes—
18C2×#11758196C2212yes—
19C2×C22⋊Dic61C2212yes—
20C2×C22⋊Dic61C2212yes—
21C2×C22⋊Dic61C2212yes—
22C2×C22⋊Dic61C2211yescharacteristic
23C2×C22⋊Dic61C2212yes—
24C2×C4×Dic61C2212yes—
25#14519684C2211yescharacteristic
26#14519684C2212yes—
27#14519684C2212yes—
28C22×D4×C61C2212yes—
29C22×D4×C61C2211yescharacteristic
30C2×C22⋊C4×C61C2212yes—
31C2×C22⋊C4×C61C2211yescharacteristic
32#95×C61C2211yescharacteristic
33C24×C61C2312yes—
34C24×C61C2311yescharacteristic
35C2×D4×C61—24no—
36C2×D4×C61—24no—
37C2×D4×C61—24no—
38C2×D4×C61—24no—
39C2×D4×C61—41no—
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2312yes—
43C22×Dic61—24no—
44C22×Dic61—24no—
45C22×Dic61—24no—
46C22×Dic61—41no—
47C22×Dic61—42no—
48C22×Dic61C2312yes—
49C22×Dic61C2312yes—
50C22×Dic61C2312yes—
51C22×Dic61C2312yes—
52C22⋊C4×C61—24no—
53C22⋊C4×C61—41no—
54C22⋊Dic61—24no—
55C22⋊Dic61—22no—
56C22⋊Dic61—24no—
57C22⋊Dic61—24no—
58C22⋊Dic61D418yescomplemented
59C4⋊Dic61—24no—
60C4⋊Dic61—41no—
61#11758196—24no—
62#11758196—24no—
63#11758196—24no—
64C4×Dic61—24no—
65C23×C61—22no—
66C23×C61—22no—
67C23×C61—22no—
68C23×C61—22no—
69C23×C61—22no—
70C23×C61—22no—
71C23×C61—21no—
72C23×C61—22no—
73C23×C61—21no—
74C23×C61—22no—
75C23×C61C2×D414yes—
76C23×C61#4112yes—
77C23×C61C2411yescharacteristic
78D4×C61—216no—
79D4×C61—44no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61#4114yes—
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—22no—
97C2×Dic61—44no—
98C2×Dic61—48no—
99C2×Dic61C2×D414yes—
100C2×Dic61C2×D414yes—
101C22×C61—24no—
102C22×C61—24no—
103C22×C61—22no—
104C22×C61—24no—
105C22×C61—24no—
106C22×C61—42no—
107C22×C61—42no—
108C22×C61—41no—
109C22×C61—42no—
110C22×C61—42no—
111C22×C61—42no—
112C22×C61—41no—
113C22×C61C22×D412yes—
114C22×C61C2×#4111yescharacteristic
115C22×C61C2×#4112yes—
116C22×C61H(5,𝔽2)11yescharacteristic
117C22×C612−1+411yescharacteristic
118C4×C61—24no—
119C4×C61—41no—
120C4×C61—41no—
121Dic61—24no—
122Dic61—24no—
123Dic61—42no—
124Dic61—42no—
125#2455—611nomaximal, Sylow
126C2×C61—44no—
127C2×C61—42no—
128C2×C61#52512yes—
129C2×C61#53911yescharacteristic
130C2×C61D4211yescharacteristic
131C2×C61#54712yes—
132C2×C61#55911yescharacteristic
133C2×#123—612no—
134C2×C4×D4—612no—
135#399—611no—
136#394—612no—
137#392D6111yescharacteristic
138#389—612no—
139#388—612no—
140#385—611no—
141#385—612no—
142C61#245511yescharacteristic, complemented, Sylow
143C22×D4C2×D6112yes—
144C22×D4C2×D6111yescharacteristic
145C23×C4—611no—
146C23×C4—612no—
147#123—1228no—
148C4×D4—1228no—
149C2×C4⋊C4—612no—
150C2×C4⋊C4—612no—
151C2×C4⋊C4—612no—
152C2×C4⋊C4—612no—
153C2×C4⋊C4—611no—
154C2×C22⋊C4—612no—
155C2×C22⋊C4—612no—
156C2×C22⋊C4—612no—
157C2×C22⋊C4—612no—
158C2×C22⋊C4—611no—
159C2×C22⋊C4C2×D6112yes—
160C2×C22⋊C4C2×D6111yescharacteristic
161C2×C42—612no—
162#95—612no—
163#95—612no—
164#95—611no—
165#95C2×D6111yescharacteristic
166C24C22×D6112yes—
167C24C22×D6111yescharacteristic
168C2×D4—24no—
169C2×D4—24no—
170C2×D4—24no—
171C2×D4—24no—
172C2×D4—41no—
173C22×C4—612no—
174C22×C4—612no—
175C22×C4—612no—
176C22×C4—612no—
177C22×C4—1224no—
178C22×C4—1224no—
179C22×C4—1224no—
180C22×C4—2441no—
181C22×C4—2442no—
182C22×C4C22×D6111yescharacteristic
183C22×C4C22×D6111yescharacteristic
184C22×C4C22×D6112yes—
185C4⋊C4—1224no—
186C4⋊C4—1224no—
187C4⋊C4—1224no—
188C4⋊C4—1224no—
189C4⋊C4—2441no—
190C22⋊C4—24no—
191C22⋊C4—41no—
192C22⋊C4—618no—
193C22⋊C4—1224no—
194C22⋊C4—1224no—
195C22⋊C4—1224no—
196C22⋊C4—1222no—
197C42—1224no—
198C23—22no—
199C23—22no—
200C23—22no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—21no—
205C23—22no—
206C23—21no—
207C23—22no—
208C23D4×D6114yes—
209C23#1175822412yes—
210C23C23×D6111yescharacteristic
211D4—216no—
212D4—44no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—614no—
220C2×C4—614no—
221C2×C4—1222no—
222C2×C4—1222no—
223C2×C4—1222no—
224C2×C4—1222no—
225C2×C4—1222no—
226C2×C4—1222no—
227C2×C4—1222no—
228C2×C4—1222no—
229C2×C4—1222no—
230C2×C4—1222no—
231C2×C4—2444no—
232C2×C4—2448no—
233C2×C4#1175822414yes—
234C22—24no—
235C22—24no—
236C22—22no—
237C22—24no—
238C22—24no—
239C22—42no—
240C22—41no—
241C22—42no—
242C22—42no—
243C22—41no—
244C22—42no—
245C22—42no—
246C22C2×D4×D6112yes—
247C22C2×#1175822412yes—
248C22C2×#1175822411yescharacteristic
249C22#1451982211yescharacteristic
250C22#1451982411yescharacteristic
251C4—24no—
252C4—41no—
253C4—41no—
254C4—1224no—
255C4—1224no—
256C4—2442no—
257C4—2442no—
258C2—44no—
259C2—42no—
260C2#1684026812yes—
261C2#1684035711yescharacteristic
262C2#1684039411yescharacteristic
263C2#1684041212yes—
264C2#1684049811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#392C2
hypercenter#392D61
hypocenterC61#2455
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#14519758C2semidirect
2. C2×D4×Dic61C2semidirect
3. #16839698C2semidirect
4. #16839676C2semidirect
5. #16839659C2semidirect
6. #16839656C2semidirect
7. #16839637C2semidirect
8. #16839634C2semidirect
58. C22⋊Dic61D4semidirect
142. C61#2455semidirect