Finite Group Databasebeta

← #21448629

Subgroups — #21448629

Order 7808.

540 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 177 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×#14519765C211yesmaximal, characteristic
2#16839666C212yesmaximal, complemented
3#16839654C212yesmaximal, complemented
4#16839651C212yesmaximal, complemented
5#16839640C212yesmaximal
6#16839636C212yesmaximal, complemented
7C4×C4⋊Dic61C211yesmaximal, characteristic, complemented
8#16839609C212yesmaximal, complemented
9C61×#383C211yesmaximal, characteristic, complemented
10C22×Dic122C2211yescharacteristic
11C22×D244C2211yescharacteristic
12C22×C4×D61C2212yes—
13#14519765C418yescomplemented
14C2×C4⋊Dic61C2212yes—
15C2×#11758196C2212yes—
16C2×#11758198C2212yes—
17C2×#11758198C2212yes—
18C2×#11758198C2212yes—
19C2×#11758198C2212yes—
20C2×#11758198C2212yes—
21C2×C4×Dic61C2211yescharacteristic
22C2×C4×Dic61C2212yes—
23C2×C4×Dic61C2211yescharacteristic
24#14519684C2212yes—
25#14519684C2212yes—
26#14519684C2212yes—
27C2×C42×C61C2211yescharacteristic
28#95×C61C2212yes—
29#95×C61C2211yescharacteristic
30#95×C61C2212yes—
31#95×C61C2211yescharacteristic
32C23×D61C2312yes—
33C22×C4×C61C2312yes—
34C22×C4×C61C2312yes—
35C22×C4×C61C2311yescharacteristic
36C22×C4×C61C2311yescharacteristic
37C22×C4×C61C2311yescharacteristic
38C22×Dic61C2312yes—
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C2×D244—42no—
42C2×D244C2×C414yes—
43C2×C4×D61—24no—
44C2×C4×D61—42no—
45C2×C4×D61—42no—
46C2×Dic122—42no—
47C2×Dic122C2×C414yescomplemented
48C42×C61C2×C414yescomplemented
49#11758198—24no—
50#11758198—42no—
51#11758198—42no—
52#11758198C2×C418yescomplemented
53#11758198C2×C418yescomplemented
54C4⋊Dic61—24no—
55#11758196—42no—
56C4×Dic61—42no—
57C4×Dic61—41no—
58C4×Dic61—41no—
59C23×C61C2411yescharacteristic
60C22×D61—22no—
61C22×D61—22no—
62C22×D61—22no—
63C22×D61—22no—
64C22×D61—22no—
65C22×D61—22no—
66C22×D61C22×C414yes—
67C2×C4×C61—22no—
68C2×C4×C61—21no—
69C2×C4×C61—22no—
70C2×C4×C61—21no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61C22×C412yes—
78C2×C4×C61C22×C412yes—
79C2×C4×C61C22×C412yes—
80C2×Dic61—22no—
81C2×Dic61—22no—
82C2×Dic61—22no—
83C2×Dic61—22no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61—22no—
87C2×Dic61C22×C414yes—
88C2×Dic61#4114yes—
89D244—44no—
90C4×D61—48no—
91Dic122—44no—
92C22×C61C23×C411yescharacteristic
93C22×C61C2×#4112yes—
94C22×C61H(5,𝔽2)12yes—
95C22×C61H(5,𝔽2)11yescharacteristic
96C22×C612−1+411yescharacteristic
97C2×D61—24no—
98C2×D61—24no—
99C2×D61—24no—
100C2×D61—42no—
101C2×D61—42no—
102C2×D61—42no—
103C2×D61—42no—
104C4×C61—22no—
105C4×C61—22no—
106C4×C61—22no—
107C4×C61—42no—
108C4×C61—42no—
109Dic61—24no—
110Dic61—24no—
111Dic61—42no—
112#2337—611nomaximal, Sylow
113C2×C61C4×#4111yescharacteristic
114C2×C61#51811yescharacteristic
115C2×C61#52011yescharacteristic
116C2×C61#53812yes—
117C2×C61#54212yes—
118D61—44no—
119C2×#124—611no—
120#391—612no—
121#388—612no—
122#388—612no—
123#386—612no—
124#385—612no—
125#383D6111yescharacteristic, complemented
126C4×C4⋊C4—611no—
127C4×C22⋊C4—612no—
128C61#233711yescharacteristic, complemented, Sylow
129C22×Q8—611no—
130C22×D4—611no—
131C23×C4—612no—
132#124—618no—
133C2×C4⋊C4—612no—
134C2×C4⋊C4—612no—
135C2×C22⋊C4—612no—
136C2×C22⋊C4—612no—
137C2×C22⋊C4—612no—
138C2×C22⋊C4—612no—
139C2×C22⋊C4—612no—
140C2×C42—611no—
141C2×C42—612no—
142C2×C42—611no—
143C2×C42C2×D6111yescharacteristic
144#95—612no—
145#95—612no—
146#95—612no—
147#95C2×D6112yes—
148#95C2×D6111yescharacteristic
149#95C2×D6112yes—
150#95C2×D6111yescharacteristic
151C24—612no—
152C2×Q8—614no—
153C2×Q8—2442no—
154C2×D4—614no—
155C2×D4—2442no—
156C22×C4—612no—
157C22×C4—612no—
158C22×C4—612no—
159C22×C4—1224no—
160C22×C4—2442no—
161C22×C4—2442no—
162C22×C4C22×D6112yes—
163C22×C4C22×D6112yes—
164C22×C4C22×D6111yescharacteristic
165C22×C4C22×D6111yescharacteristic
166C22×C4C22×D6111yescharacteristic
167C4⋊C4—1224no—
168C4⋊C4—2442no—
169C22⋊C4—618no—
170C22⋊C4—618no—
171C22⋊C4—1224no—
172C22⋊C4—2442no—
173C22⋊C4—2442no—
174C42—2441no—
175C42—2441no—
176C42—2442no—
177C42C4×D6114yescomplemented
178C23—614no—
179C23—1222no—
180C23—1222no—
181C23—1222no—
182C23—1222no—
183C23—1222no—
184C23—1222no—
185C23C23×D6111yescharacteristic
186Q8—2444no—
187D4—2444no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—614no—
199C2×C4—614no—
200C2×C4—1222no—
201C2×C4—1222no—
202C2×C4—1222no—
203C2×C4—1222no—
204C2×C4—1222no—
205C2×C4—1222no—
206C2×C4—1222no—
207C2×C4—2448no—
208C2×C4C2×C4×D6112yes—
209C2×C4C2×C4×D6112yes—
210C2×C4C2×C4×D6112yes—
211C22—1224no—
212C22—1224no—
213C22—1224no—
214C22—2442no—
215C22—2442no—
216C22—2442no—
217C22—2442no—
218C22C22×C4×D6111yescharacteristic
219C22#41×D6112yes—
220C22#1451982312yes—
221C22#1451982311yescharacteristic
222C22#1451982411yescharacteristic
223C4—22no—
224C4—22no—
225C4—22no—
226C4—42no—
227C4—42no—
228C4—1224no—
229C4—1224no—
230C4—2442no—
231C2—2444no—
232C2#1684023011yescharacteristic
233C2#1684023611yescharacteristic
234C2#1684024211yescharacteristic
235C2#1684035112yes—
236C2#1684037812yes—
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC61×#383C2
socleC23×C61C24
hypercenter#383D61
hypocenterC61#2337
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #383

Complements

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

NH ≅ G/Ntype
2. #16839666C2semidirect
3. #16839654C2semidirect
4. #16839651C2semidirect
6. #16839636C2semidirect
7. C4×C4⋊Dic61C2semidirect
8. #16839609C2semidirect
9. C61×#383C2semidirect
13. #14519765C4semidirect
47. C2×Dic122C2×C4semidirect
48. C42×C61C2×C4semidirect
52. #11758198C2×C4semidirect
53. #11758198C2×C4semidirect
125. #383D61semidirect
128. C61#2337semidirect
177. C42C4×D61semidirect