Finite Group Databasebeta

← #21450101

Subgroups — #21450101

Order 7808.

512 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 139 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×#14519735C211yesmaximal, characteristic
2C2×C4⋊C4×D61C211yesmaximal, characteristic
3#16839702C211yesmaximal, characteristic, complemented
4#16839701C211yesmaximal, characteristic, complemented
5#16839693C211yesmaximal, characteristic, complemented
6#16839648C212yesmaximal, complemented
7#16839644C212yesmaximal, complemented
8#16839633C212yesmaximal
9#16839624C212yesmaximal
10#16839624C211yesmaximal, characteristic
11C61×#398C211yesmaximal, characteristic, complemented
12C22×C4×D61C2211yescharacteristic
13C22×C4×D61C2211yescharacteristic
14C22×C4×D61C2211yescharacteristic
15#14519735—24no—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×C4⋊Dic61C2211yescharacteristic
18C2×#11758196C2211yescharacteristic
19C2×#11758196C2212yes—
20C2×#11758196C2211yescharacteristic
21C4⋊C4×D61—24no—
22C2×#11758198C2212yes—
23C2×#11758198C2212yes—
24C2×C4×Dic61C2212yes—
25#14519684C2211yescharacteristic
26#14519684C2212yes—
27#14519684C2212yes—
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C2×C4⋊C4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2211yescharacteristic
34C2×C4⋊C4×C61C2212yes—
35#95×C61C2211yescharacteristic
36#95×C61C2212yes—
37C23×D61C2311yescharacteristic
38C22×C4×C61C2311yescharacteristic
39C22×C4×C61C2312yes—
40C22×C4×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2311yescharacteristic
43C22×Dic61C2311yescharacteristic
44C22×Dic61C2312yes—
45C22×Dic61C2312yes—
46C22×Dic61C2311yescharacteristic
47C22×Dic61C2311yescharacteristic
48C2×C4×D61—22no—
49C2×C4×D61—24no—
50C2×C4×D61—22no—
51C2×C4×D61—22no—
52C2×C4×D61—22no—
53C2×C4×D61—24no—
54C2×C4×D61D414yes—
55C4⋊C4×C61—22no—
56C4⋊C4×C61—22no—
57C4⋊C4×C61—24no—
58#11758198—24no—
59#11758198—24no—
60C4⋊Dic61—22no—
61C4⋊Dic61—22no—
62#11758196—22no—
63#11758196—22no—
64#11758196—24no—
65C4×Dic61—24no—
66C23×C61C2411yescharacteristic
67C22×D61—21no—
68C22×D61—21no—
69C22×D61—22no—
70C22×D61C2×D412yes—
71C22×D61#4114yes—
72C2×C4×C61—21no—
73C2×C4×C61—22no—
74C2×C4×C61—21no—
75C2×C4×C61—22no—
76C2×C4×C61—21no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61C2×D412yes—
84C2×C4×C61#4112yes—
85C2×Dic61—21no—
86C2×Dic61—22no—
87C2×Dic61—21no—
88C2×Dic61—22no—
89C2×Dic61—21no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—24no—
94C2×Dic61—22no—
95C2×Dic61C2×D412yes—
96C2×Dic61#4112yes—
97C4×D61—28no—
98C4×D61—28no—
99C4×D61—44no—
100C22×C61C22×D411yescharacteristic
101C22×C61C2×#4112yes—
102C22×C61C2×#4111yescharacteristic
103C22×C61C2×#4111yescharacteristic
104C22×C612−1+412yes—
105C2×D61—22no—
106C2×D61—22no—
107C2×D61—24no—
108C2×D61—24no—
109C2×D61#12314yes—
110C4×C61—22no—
111C4×C61—22no—
112C4×C61—41no—
113C4×C61—42no—
114C4×C61—42no—
115Dic61—22no—
116Dic61—22no—
117Dic61—41no—
118Dic61—42no—
119Dic61—42no—
120#2484—611nomaximal, Sylow
121C2×C61C2×#12311yescharacteristic
122C2×C61#52511yescharacteristic
123C2×C61#53611yescharacteristic
124C2×C61#55212yes—
125C2×C61#55212yes—
126D61—24no—
127C2×#117—611no—
128C22×C4⋊C4—611no—
129#400—611no—
130#400—611no—
131#398—611no—
132#398D6111yescharacteristic, complemented
133#387—612no—
134#387—612no—
135#385—612no—
136#381—611no—
137#381—612no—
138C61#248411yescharacteristic, complemented, Sylow
139C23×C4—611no—
140C23×C4—611no—
141C23×C4—611no—
142#117—1224no—
143C2×C4⋊C4—611no—
144C2×C4⋊C4—611no—
145C2×C4⋊C4—611no—
146C2×C4⋊C4—611no—
147C2×C4⋊C4—612no—
148C2×C4⋊C4—1224no—
149C2×C4⋊C4C2×D6111yescharacteristic
150C2×C4⋊C4C2×D6111yescharacteristic
151C2×C4⋊C4C2×D6112yes—
152C2×C22⋊C4—612no—
153C2×C22⋊C4—612no—
154C2×C42—612no—
155#95—612no—
156#95—612no—
157#95—612no—
158#95—612no—
159#95—611no—
160#95—612no—
161#95—612no—
162#95C2×D6112yes—
163#95C2×D6111yescharacteristic
164C24—611no—
165C22×C4—611no—
166C22×C4—611no—
167C22×C4—614no—
168C22×C4—612no—
169C22×C4—612no—
170C22×C4—611no—
171C22×C4—1222no—
172C22×C4—1222no—
173C22×C4—1224no—
174C22×C4—1222no—
175C22×C4—1224no—
176C22×C4—1222no—
177C22×C4C22×D6112yes—
178C22×C4C22×D6111yescharacteristic
179C22×C4C22×D6112yes—
180C22×C4C22×D6111yescharacteristic
181C22×C4C22×D6111yescharacteristic
182C4⋊C4—22no—
183C4⋊C4—22no—
184C4⋊C4—24no—
185C4⋊C4—1222no—
186C4⋊C4—1222no—
187C4⋊C4—1224no—
188C4⋊C4—1222no—
189C4⋊C4—1222no—
190C22⋊C4—1224no—
191C22⋊C4—1224no—
192C42—1224no—
193C23—612no—
194C23—614no—
195C23—1221no—
196C23—1221no—
197C23—1222no—
198C23C23×D6111yescharacteristic
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—612no—
211C2×C4—612no—
212C2×C4—1228no—
213C2×C4—1228no—
214C2×C4—1221no—
215C2×C4—1222no—
216C2×C4—1221no—
217C2×C4—1222no—
218C2×C4—1221no—
219C2×C4—1222no—
220C2×C4—1222no—
221C2×C4—1222no—
222C2×C4—1224no—
223C2×C4—1222no—
224C2×C4—2444no—
225C2×C4D4×D6112yes—
226C2×C4#1175822412yes—
227C22—614no—
228C22—1222no—
229C22—1222no—
230C22—1224no—
231C22—1224no—
232C22C2×D4×D6111yescharacteristic
233C22#41×D6112yes—
234C22#41×D6111yescharacteristic
235C22C2×#1175822411yescharacteristic
236C22#1451982512yes—
237C4—22no—
238C4—22no—
239C4—41no—
240C4—42no—
241C4—42no—
242C4—1222no—
243C4—1222no—
244C4—2441no—
245C4—2442no—
246C4—2442no—
247C2—1224no—
248C2#123×D6111yescharacteristic
249C2#1684027211yescharacteristic
250C2#1684033711yescharacteristic
251C2#1684044412yes—
252C2#1684044612yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#398C2
hypercenter#398D61
hypocenterC61#2484
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
3. #16839702C2semidirect
4. #16839701C2semidirect
5. #16839693C2semidirect
6. #16839648C2semidirect
7. #16839644C2semidirect
11. C61×#398C2semidirect
132. #398D61semidirect
138. C61#2484semidirect