Finite Group Databasebeta

← #21449701

Subgroups — #21449701

Order 7808.

660 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 145 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×#14519762C212yesmaximal, complemented
2C2×C4×C22⋊D61C212yesmaximal, complemented
3#16839698C211yesmaximal, characteristic, complemented
4#16839677C212yesmaximal, complemented
5#16839671C211yesmaximal, characteristic
6#16839657C212yesmaximal, complemented
7#16839651C212yesmaximal, complemented
8#16839636C212yesmaximal, complemented
9C61×#385C211yesmaximal, characteristic, complemented
10C22×D244C2211yescharacteristic
11C22×C22⋊D61C2212yes—
12C22×C4×D61C2212yes—
13#14519762—28no—
14C4×C22⋊D61—28no—
15C2×C4⋊Dic61C2211yescharacteristic
16C2×#11758196C2212yes—
17C2×#11758196C2212yes—
18C2×#11758196C2212yes—
19C2×C22⋊Dic61C2212yes—
20C2×#11758198C2212yes—
21C2×#11758198C2212yes—
22C2×#11758198C2212yes—
23C2×#11758198C2212yes—
24C2×C4×Dic61C2212yes—
25#14519684C2211yescharacteristic
26#14519684C2212yes—
27#14519684C2211yescharacteristic
28C23×C4×C61C2211yescharacteristic
29C2×C4⋊C4×C61C2212yes—
30C2×C22⋊C4×C61C2211yescharacteristic
31C2×C22⋊C4×C61C2211yescharacteristic
32#95×C61C2212yes—
33C24×C61C2311yescharacteristic
34C23×D61C2312yes—
35C22×C4×C61—24no—
36C22×C4×C61—41no—
37C22×C4×C61C2311yescharacteristic
38C22×C4×C61C2311yescharacteristic
39C22×C4×C61C2312yes—
40C22×C4×C61C2312yes—
41C2×C22⋊D61—24no—
42C2×C22⋊D61—24no—
43C2×C22⋊D61—24no—
44C22×Dic61C2312yes—
45C22×Dic61C2312yes—
46C22×Dic61C2312yes—
47C2×D244—24no—
48C2×D244—41no—
49C2×C4×D61—24no—
50C2×C4×D61—24no—
51C2×C4×D61—42no—
52C4⋊C4×C61—24no—
53C22⋊C4×C61—22no—
54C22⋊C4×C61—41no—
55C22⋊Dic61—24no—
56#11758198—24no—
57#11758198—24no—
58#11758198—24no—
59#11758198D418yescomplemented
60C4⋊Dic61—41no—
61#11758196—24no—
62#11758196—24no—
63#11758196—24no—
64C4×Dic61—24no—
65C23×C61—22no—
66C23×C61—22no—
67C23×C61—21no—
68C23×C61—21no—
69C23×C61#4112yes—
70C23×C61C2411yescharacteristic
71C22×D61—22no—
72C22×D61—22no—
73C22×D61—22no—
74C22×D61—22no—
75C22×D61—22no—
76C22×D61—22no—
77C22×D61C2×D414yes—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—44no—
88C2×C4×C61C2×D414yes—
89C22⋊D61—216no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61C2×D414yes—
98C2×Dic61#4114yes—
99D244—44no—
100C4×D61—48no—
101C22×C61—24no—
102C22×C61—22no—
103C22×C61—41no—
104C22×C61—42no—
105C22×C61—41no—
106C22×C61C22×D412yes—
107C22×C61C2×#4112yes—
108C22×C61C2×#4111yescharacteristic
109C22×C61H(5,𝔽2)11yescharacteristic
110C22×C612−1+411yescharacteristic
111C2×D61—24no—
112C2×D61—24no—
113C2×D61—24no—
114C2×D61—42no—
115C2×D61—42no—
116C2×D61—42no—
117C2×D61—42no—
118C4×C61—24no—
119C4×C61—42no—
120C4×C61—41no—
121C4×C61—41no—
122Dic61—24no—
123Dic61—24no—
124Dic61—42no—
125#2455—611nomaximal, Sylow
126C2×C61—42no—
127C2×C61#52512yes—
128C2×C61#53911yescharacteristic
129C2×C61D4211yescharacteristic
130C2×C61#54712yes—
131C2×C61#55911yescharacteristic
132D61—44no—
133C2×#123—612no—
134C2×C4×D4—612no—
135#399—611no—
136#394—612no—
137#392—611no—
138#389—612no—
139#388—612no—
140#385—612no—
141#385D6111yescharacteristic, complemented
142C61#245511yescharacteristic, complemented, Sylow
143C22×D4—612no—
144C22×D4—611no—
145C23×C4—612no—
146C23×C4C2×D6111yescharacteristic
147#123—1228no—
148C4×D4—1228no—
149C2×C4⋊C4—612no—
150C2×C4⋊C4—612no—
151C2×C4⋊C4—612no—
152C2×C4⋊C4—611no—
153C2×C4⋊C4C2×D6112yes—
154C2×C22⋊C4—612no—
155C2×C22⋊C4—612no—
156C2×C22⋊C4—612no—
157C2×C22⋊C4—612no—
158C2×C22⋊C4—612no—
159C2×C22⋊C4C2×D6111yescharacteristic
160C2×C22⋊C4C2×D6111yescharacteristic
161C2×C42—612no—
162#95—612no—
163#95—611no—
164#95—611no—
165#95C2×D6112yes—
166C24—612no—
167C24C22×D6111yescharacteristic
168C2×D4—1224no—
169C2×D4—1224no—
170C2×D4—1224no—
171C2×D4—1224no—
172C2×D4—2441no—
173C22×C4—24no—
174C22×C4—41no—
175C22×C4—612no—
176C22×C4—612no—
177C22×C4—612no—
178C22×C4—1224no—
179C22×C4—1224no—
180C22×C4—2442no—
181C22×C4C22×D6111yescharacteristic
182C22×C4C22×D6112yes—
183C22×C4C22×D6111yescharacteristic
184C22×C4C22×D6112yes—
185C4⋊C4—24no—
186C4⋊C4—1224no—
187C4⋊C4—1224no—
188C4⋊C4—1224no—
189C4⋊C4—2441no—
190C22⋊C4—22no—
191C22⋊C4—41no—
192C22⋊C4—618no—
193C22⋊C4—1224no—
194C22⋊C4—1224no—
195C22⋊C4—1224no—
196C22⋊C4—1224no—
197C42—1224no—
198C23—22no—
199C23—22no—
200C23—21no—
201C23—21no—
202C23—614no—
203C23—1222no—
204C23—1222no—
205C23—1222no—
206C23—1222no—
207C23—1222no—
208C23—1222no—
209C23#1175822212yes—
210C23C23×D6111yescharacteristic
211D4—12216no—
212D4—2444no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—44no—
223C2×C4—614no—
224C2×C4—614no—
225C2×C4—1222no—
226C2×C4—1222no—
227C2×C4—1222no—
228C2×C4—1222no—
229C2×C4—1222no—
230C2×C4—1222no—
231C2×C4—1222no—
232C2×C4—2448no—
233C2×C4D4×D6114yes—
234C22—24no—
235C22—22no—
236C22—41no—
237C22—41no—
238C22—42no—
239C22—1224no—
240C22—1224no—
241C22—1224no—
242C22—2442no—
243C22—2442no—
244C22—2442no—
245C22—2442no—
246C22C2×D4×D6112yes—
247C22#41×D6112yes—
248C22C2×#1175822211yescharacteristic
249C22#1451982211yescharacteristic
250C22#1451982511yescharacteristic
251C4—24no—
252C4—41no—
253C4—42no—
254C4—41no—
255C4—1224no—
256C4—1224no—
257C4—2442no—
258C2—42no—
259C2—2444no—
260C2#1684027112yes—
261C2#1684035911yescharacteristic
262C2#1684039411yescharacteristic
263C2#1684041412yes—
264C2#1684049611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#385C2
hypercenter#385D61
hypocenterC61#2455
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#14519762C2semidirect
2. C2×C4×C22⋊D61C2semidirect
3. #16839698C2semidirect
4. #16839677C2semidirect
6. #16839657C2semidirect
7. #16839651C2semidirect
8. #16839636C2semidirect
9. C61×#385C2semidirect
59. #11758198D4semidirect
141. #385D61semidirect
142. C61#2455semidirect