Finite Group Databasebeta

← #21455301

Subgroups — #21455301

Order 7808.

480 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14519806C212yesmaximal
2C4⋊Q8×D61C211yesmaximal, characteristic, complemented
3C4×#11758224C211yesmaximal, characteristic
4#16839973C211yesmaximal, characteristic, complemented
5#16839971C212yesmaximal, complemented
6#16839969C211yesmaximal, characteristic, complemented
7#16839967C211yesmaximal, characteristic, complemented
8#16839965C212yesmaximal, complemented
9#16839784C211yesmaximal, characteristic, complemented
10#16839769C212yesmaximal, complemented
11C61×#461C211yesmaximal, characteristic, complemented
12C2×#11758224C2211yescharacteristic
13C2×Q8×D61C2212yes—
14#14519806—28no—
15C2×Dic244C2212yes—
16C2×#11758202C2212yes—
17C2×#11758200C2212yes—
18C2×#11758189C2212yes—
19#14519777C2211yescharacteristic
20#14519776—21no—
21#14519776—21no—
22#14519775C2212yes—
23C4×Dic122C2211yescharacteristic
24#14519742C2211yescharacteristic
25D4×Dic61C2211yescharacteristic
26C4×C22⋊D61—21no—
27#14519737—21no—
28#14519735C2211yescharacteristic
29#14519733—21no—
30C4⋊C4×D61—21no—
31C4⋊C4×D61—21no—
32C2×C4×Dic61—21no—
33C42×D61C2211yescharacteristic
34C4⋊#92418C2211yescharacteristic
35#14519706C2212yes—
36#14519702C2212yes—
37#14519701C2212yes—
38#14519700C2212yes—
39C2×SD16×C61C2212yes—
40C4⋊Q8×C61C2211yescharacteristic
41C4×D4×C61C2211yescharacteristic
42C4⋊C8×C61C2211yescharacteristic
43#103×C61C2212yes—
44C2×Q8×C61C2312yes—
45C2×D4×C61C2311yescharacteristic
46C22×C4×C61—21no—
47C2×C22⋊D61—21no—
48C22×Dic61—21no—
49C22×Dic61—21no—
50Q8×D61—24no—
51Q8×D61—24no—
52#11758224—22no—
53#11758224D414yes—
54C2×C4×D61—22no—
55C2×C4×D61D411yescharacteristic
56C2×C4×D61D411yescharacteristic
57C2×C4×D61C2311yescharacteristic
58C2×Dic122—22no—
59C2×Dic122C2312yes—
60C2×Dic122C2311yescharacteristic
61SD16×C61—24no—
62C2×C8×C61C2312yes—
63C4⋊C4×C61—21no—
64C4⋊C4×C61—21no—
65C4⋊C4×C61C2311yescharacteristic
66C22⋊C4×C61—21no—
67C42×C61C2311yescharacteristic
68C22⋊Dic61—21no—
69#11758202—24no—
70#11758200—24no—
71#11758198—21no—
72C4⋊Dic61—21no—
73C4⋊Dic61—21no—
74C4⋊Dic61C2311yescharacteristic
75#11758196—21no—
76#11758196—22no—
77#11758196—22no—
78#11758196—21no—
79C4×Dic61—21no—
80C4×Dic61—21no—
81C4×Dic61—21no—
82C4×Dic61D411yescharacteristic
83C4×Dic61D411yescharacteristic
84C4×Dic61C2311yescharacteristic
85C2×#92418C2312yes—
86Dic244—24no—
87#11758189—24no—
88C23×C61—21no—
89C22×D61C2×D411yescharacteristic
90Q8×C61—22no—
91Q8×C61—22no—
92D4×C61—21no—
93D4×C61C2×D412yes—
94C2×C4×C61—21no—
95C2×C4×C61—22no—
96C2×C4×C61—42no—
97C2×C4×C61C2×D411yescharacteristic
98C2×C4×C61C2×D411yescharacteristic
99C2×C4×C61C2411yescharacteristic
100C22⋊D61—24no—
101C2×Dic61—21no—
102C2×Dic61—24no—
103C2×Dic61—21no—
104C2×Dic61—22no—
105C2×Dic61—42no—
106C2×Dic61C2×D411yescharacteristic
107C2×Dic61C2×D411yescharacteristic
108C2×Dic61C2×D411yescharacteristic
109C4×D61—22no—
110C4×D61—22no—
111C4×D61—44no—
112C4×D61C2×D412yes—
113C4×D61#4112yes—
114Dic122—21no—
115Dic122—22no—
116Dic122—22no—
117Dic122—44no—
118Dic122C2×D412yes—
119C8×C61—22no—
120#92418—22no—
121C22×C61—22no—
122C22×C61—41no—
123C22×C61—41no—
124C22×C61C22×D411yescharacteristic
125C2×D61—21no—
126C2×D61—21no—
127C2×D61#12112yes—
128C4×C61—21no—
129C4×C61—42no—
130C4×C61—41no—
131C4×C61#13712yescomplemented
132C4×C61C22×D411yescharacteristic
133C4×C61C2×#4111yescharacteristic
134Dic61—22no—
135Dic61—21no—
136Dic61—42no—
137Dic61—41no—
138Dic61#12112yes—
139Dic61#13712yescomplemented
140#3039—611nomaximal, Sylow
141C2×C61—42no—
142C2×C61C2×#12111yescharacteristic
143C2×C61C2×#13711yescharacteristic
144C2×C61C2×#13711yescharacteristic
145D61—22no—
146C2×#137—612no—
147C2×C4⋊Q8—611no—
148C4×#41—611no—
149#462—611no—
150#462—611no—
151#462—612no—
152#461—612no—
153#461—611no—
154#461D6111yescharacteristic, complemented
155#423—611no—
156#419—612no—
157C61#303911yescharacteristic, complemented, Sylow
158C2×#41—611no—
159C22×Q8—612no—
160#137—1228no—
161C2×Q16—612no—
162C2×Q16—612no—
163C2×SD16—612no—
164C2×SD16C2×D6112yes—
165C2×M16—612no—
166C4⋊Q8—612no—
167C4⋊Q8—611no—
168C4⋊Q8—1221no—
169C4⋊Q8—1221no—
170C4⋊Q8C2×D6111yescharacteristic
171C4×Q8—611no—
172C4×Q8—611no—
173C4×D4—611no—
174C4×D4—1221no—
175C4×D4—1221no—
176C4×D4C2×D6111yescharacteristic
177#117—611no—
178#117—1221no—
179C2×C4⋊C4—1221no—
180C2×C4⋊C4—1221no—
181C2×C42—611no—
182C2×C42—1221no—
183C4⋊C8—612no—
184C4⋊C8—611no—
185C4⋊C8C2×D6111yescharacteristic
186#103—612no—
187#103—612no—
188#103—612no—
189#103C2×D6112yes—
190#41—614no—
191#41—1222no—
192C2×Q8—611no—
193C2×Q8—612no—
194C2×Q8—1222no—
195C2×Q8—1224no—
196C2×Q8—1224no—
197C2×Q8C22×D6112yes—
198C2×D4—1221no—
199C2×D4C22×D6111yescharacteristic
200C22×C4—21no—
201C22×C4—611no—
202C22×C4—611no—
203C22×C4—611no—
204C22×C4—1222no—
205C22×C4—1221no—
206C22×C4—1221no—
207Q16—1224no—
208Q16—1224no—
209SD16—24no—
210SD16—1224no—
211M16—1224no—
212C2×C8—612no—
213C2×C8C22×D6112yes—
214C4⋊C4—21no—
215C4⋊C4—21no—
216C4⋊C4—611no—
217C4⋊C4—1222no—
218C4⋊C4—1222no—
219C4⋊C4—1221no—
220C4⋊C4—1221no—
221C4⋊C4—1221no—
222C4⋊C4—1221no—
223C4⋊C4C22×D6111yescharacteristic
224C22⋊C4—21no—
225C22⋊C4—1221no—
226C22⋊C4—1221no—
227C42—611no—
228C42—611no—
229C42—611no—
230C42—1221no—
231C42—1221no—
232C42—1221no—
233C42C22×D6111yescharacteristic
234C23—21no—
235C23—611no—
236Q8—22no—
237Q8—22no—
238Q8—612no—
239Q8—1221no—
240Q8—1222no—
241Q8—1222no—
242Q8—2444no—
243D4—21no—
244D4—1224no—
245D4D4×D6112yes—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—42no—
249C2×C4—611no—
250C2×C4—611no—
251C2×C4—612no—
252C2×C4—612no—
253C2×C4—611no—
254C2×C4—1222no—
255C2×C4—1224no—
256C2×C4—1221no—
257C2×C4—1222no—
258C2×C4—1221no—
259C2×C4—1222no—
260C2×C4—2444no—
261C2×C4—2442no—
262C2×C4D4×D6111yescharacteristic
263C2×C4D4×D6111yescharacteristic
264C2×C4C23×D6111yescharacteristic
265C8—22no—
266C8—1222no—
267C22—22no—
268C22—41no—
269C22—41no—
270C22—612no—
271C22—1221no—
272C22—1221no—
273C22C2×D4×D6111yescharacteristic
274C4—21no—
275C4—42no—
276C4—41no—
277C4—612no—
278C4—612no—
279C4—1222no—
280C4—1221no—
281C4—2442no—
282C4—2441no—
283C4#1451980612yescomplemented
284C4C2×D4×D6111yescharacteristic
285C4#41×D6111yescharacteristic
286C2—42no—
287C2—1222no—
288C2#121×D6111yescharacteristic
289C2#137×D6111yescharacteristic
290C2C2×#1451980611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#461C2
socleC22×C61C22×D4
hypercenter#461D61
hypocenterC61#3039
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. C4⋊Q8×D61C2semidirect
4. #16839973C2semidirect
5. #16839971C2semidirect
6. #16839969C2semidirect
7. #16839967C2semidirect
8. #16839965C2semidirect
9. #16839784C2semidirect
10. #16839769C2semidirect
11. C61×#461C2semidirect
131. C4×C61#137semidirect
139. Dic61#137semidirect
154. #461D61semidirect
157. C61#3039semidirect
283. C4#14519806semidirect