Finite Group Databasebeta

← #21455292

Subgroups — #21455292

Order 7808.

484 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 131 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×#14519809C212yesmaximal, complemented
2#16840313C211yesmaximal, characteristic
3C4×Q8×D61C211yesmaximal, characteristic, complemented
4#16839987C212yesmaximal, complemented
5#16839986C212yesmaximal, complemented
6#16839969C211yesmaximal, characteristic, complemented
7#16839963C211yesmaximal, characteristic, complemented
8#16839962C211yesmaximal, characteristic, complemented
9#16839784C211yesmaximal, characteristic, complemented
10#16839762C212yesmaximal, complemented
11C61×#462C211yesmaximal, characteristic, complemented
12C2×#11758226C2212yes—
13C2×Q8×D61C2211yescharacteristic
14#14519809—28no—
15C2×#11758202C2212yes—
16C2×#11758190C2212yes—
17C2×#11758201C2212yes—
18C2×#11758189C2212yes—
19#14519774C2211yescharacteristic
20#14519766C2212yes—
21#14519752—21no—
22#14519752—21no—
23Q8×Dic61C2211yescharacteristic
24C4×Dic122—21no—
25C4×Dic122C2211yescharacteristic
26#14519742—21no—
27#14519742C2211yescharacteristic
28#14519739—21no—
29#14519739—21no—
30C4⋊C4×D61—21no—
31C4⋊C4×D61C2211yescharacteristic
32C42×D61—21no—
33C42×D61C2211yescharacteristic
34C4⋊#92418C2211yescharacteristic
35#14519706C2212yes—
36#14519701C2212yes—
37#14519699C2212yes—
38#14519697C2212yes—
39C2×Q16×C61C2212yes—
40C4⋊Q8×C61C2211yescharacteristic
41C4×Q8×C61C2211yescharacteristic
42C4⋊C8×C61C2211yescharacteristic
43#103×C61C2212yes—
44C2×Q8×C61C2312yes—
45C2×Q8×C61C2311yescharacteristic
46#11758226—24no—
47#11758226—24no—
48Q8×D61—22no—
49Q8×D61D414yescomplemented
50C2×D244—22no—
51C2×D244—21no—
52C2×D244—21no—
53C2×D244C2312yes—
54C2×C4×D61—21no—
55C2×C4×D61—21no—
56C2×C4×D61—22no—
57C2×C4×D61D411yescharacteristic
58C2×C4×D61D411yescharacteristic
59C2×C4×D61C2311yescharacteristic
60C2×Dic122—21no—
61C2×Dic122C2311yescharacteristic
62Q16×C61—24no—
63C2×C8×C61C2312yes—
64C4⋊C4×C61—21no—
65C4⋊C4×C61—21no—
66C4⋊C4×C61—21no—
67C4⋊C4×C61C2311yescharacteristic
68C42×C61—21no—
69C42×C61C2311yescharacteristic
70#11758202—24no—
71#11758201—24no—
72#11758198—22no—
73#11758198—22no—
74C4⋊Dic61—21no—
75C4⋊Dic61C2311yescharacteristic
76#11758196—21no—
77#11758196—21no—
78#11758196—21no—
79C4×Dic61—21no—
80C4×Dic61—21no—
81C4×Dic61—21no—
82C4×Dic61D411yescharacteristic
83C4×Dic61D411yescharacteristic
84C4×Dic61C2311yescharacteristic
85C2×#92418C2312yes—
86#11758190—24no—
87#11758189—24no—
88C22×D61—22no—
89C22×D61C2×D411yescharacteristic
90Q8×C61—21no—
91Q8×C61—22no—
92Q8×C61—22no—
93Q8×C61C2×D412yes—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—22no—
97C2×C4×C61C2×D411yescharacteristic
98C2×C4×C61C2×D411yescharacteristic
99C2×C4×C61C2411yescharacteristic
100C2×Dic61—21no—
101C2×Dic61—21no—
102C2×Dic61C2×D411yescharacteristic
103C2×Dic61C2×D411yescharacteristic
104C2×Dic61C2×D411yescharacteristic
105D244—22no—
106D244—22no—
107D244—42no—
108D244—44no—
109D244—42no—
110C4×D61—24no—
111C4×D61—22no—
112C4×D61—41no—
113C4×D61—42no—
114C4×D61—44no—
115C4×D61C2×D412yes—
116C4×D61#4112yes—
117Dic122—21no—
118Dic122—24no—
119Dic122C2×D412yes—
120C8×C61—22no—
121#92418—22no—
122C22×C61C22×D411yescharacteristic
123C2×D61—21no—
124C2×D61—21no—
125C2×D61—42no—
126C2×D61—42no—
127C2×D61—42no—
128C2×D61#12112yes—
129C4×C61—22no—
130C4×C61—21no—
131C4×C61—42no—
132C4×C61—41no—
133C4×C61#13712yescomplemented
134C4×C61C22×D411yescharacteristic
135C4×C61C2×#4111yescharacteristic
136Dic61—22no—
137Dic61—21no—
138Dic61—21no—
139Dic61—41no—
140Dic61#12112yes—
141#3037—611nomaximal, Sylow
142C2×C61C2×#12111yescharacteristic
143C2×C61C2×#13711yescharacteristic
144C2×C61#57511yescharacteristic
145D61—22no—
146D61—82no—
147C2×#137—612no—
148#532—611no—
149C2×C4×Q8—611no—
150#464—612no—
151#464—612no—
152#462—611no—
153#462D6111yescharacteristic, complemented
154#460—611no—
155#460—611no—
156#423—611no—
157#417—612no—
158C61#303711yescharacteristic, complemented, Sylow
159C2×#41—612no—
160C22×Q8—611no—
161#137—1228no—
162C2×Q16—612no—
163C2×Q16C2×D6112yes—
164C2×SD16—612no—
165C2×SD16—612no—
166C2×M16—612no—
167C4⋊Q8C2×D6111yescharacteristic
168#127—611no—
169#124—612no—
170#121—1221no—
171#121—1221no—
172C4×Q8—611no—
173C4×Q8—611no—
174C4×Q8—611no—
175C4×Q8—1221no—
176C4×Q8—1221no—
177C4×Q8C2×D6111yescharacteristic
178C4×D4—1221no—
179C4×D4—1221no—
180C2×C4⋊C4—611no—
181C2×C4⋊C4—1221no—
182C2×C42—611no—
183C2×C42—1221no—
184C4⋊C8—612no—
185C4⋊C8—611no—
186C4⋊C8C2×D6111yescharacteristic
187#103—612no—
188#103C2×D6112yes—
189#102—612no—
190#102—612no—
191#41—1224no—
192#41—1224no—
193C2×Q8—614no—
194C2×Q8—611no—
195C2×Q8—1221no—
196C2×Q8—1222no—
197C2×Q8C22×D6112yes—
198C2×Q8C22×D6111yescharacteristic
199C2×D4—612no—
200C2×D4—1222no—
201C2×D4—1221no—
202C2×D4—1221no—
203C22×C4—611no—
204C22×C4—611no—
205C22×C4—611no—
206C22×C4—1222no—
207C22×C4—1221no—
208C22×C4—1221no—
209Q16—24no—
210Q16—1224no—
211SD16—1224no—
212SD16—1224no—
213M16—1224no—
214C2×C8—612no—
215C2×C8C22×D6112yes—
216C4⋊C4—21no—
217C4⋊C4—21no—
218C4⋊C4—21no—
219C4⋊C4—611no—
220C4⋊C4—1221no—
221C4⋊C4—1221no—
222C4⋊C4—1221no—
223C4⋊C4—1221no—
224C4⋊C4C22×D6111yescharacteristic
225C22⋊C4—1222no—
226C22⋊C4—1222no—
227C42—21no—
228C42—611no—
229C42—611no—
230C42—611no—
231C42—1221no—
232C42—1221no—
233C42—1221no—
234C42C22×D6111yescharacteristic
235C23—611no—
236C23—1222no—
237Q8—21no—
238Q8—22no—
239Q8—22no—
240Q8—612no—
241Q8—1224no—
242Q8—1221no—
243Q8D4×D6112yes—
244D4—1222no—
245D4—1222no—
246D4—2442no—
247D4—2444no—
248D4—2442no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—611no—
253C2×C4—612no—
254C2×C4—612no—
255C2×C4—611no—
256C2×C4—611no—
257C2×C4—1224no—
258C2×C4—1221no—
259C2×C4—1222no—
260C2×C4—1221no—
261C2×C4—2441no—
262C2×C4—2444no—
263C2×C4—2442no—
264C2×C4D4×D6111yescharacteristic
265C2×C4D4×D6111yescharacteristic
266C2×C4C23×D6111yescharacteristic
267C8—22no—
268C8—1222no—
269C22—612no—
270C22—1221no—
271C22—1221no—
272C22—2442no—
273C22—2442no—
274C22—2442no—
275C22C2×D4×D6111yescharacteristic
276C4—22no—
277C4—21no—
278C4—42no—
279C4—41no—
280C4—612no—
281C4—1222no—
282C4—1221no—
283C4—1221no—
284C4—2441no—
285C4#1451980912yescomplemented
286C4C2×D4×D6111yescharacteristic
287C4#41×D6111yescharacteristic
288C2—1222no—
289C2—4882no—
290C2#121×D6111yescharacteristic
291C2C2×#1451980911yescharacteristic
292C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#462C2
socleC22×C61C22×D4
hypercenter#462D61
hypocenterC61#3037
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
1. C2×#14519809C2semidirect
3. C4×Q8×D61C2semidirect
4. #16839987C2semidirect
5. #16839986C2semidirect
6. #16839969C2semidirect
7. #16839963C2semidirect
8. #16839962C2semidirect
9. #16839784C2semidirect
10. #16839762C2semidirect
11. C61×#462C2semidirect
49. Q8×D61D4semidirect
133. C4×C61#137semidirect
153. #462D61semidirect
158. C61#3037semidirect
285. C4#14519809semidirect