Finite Group Databasebeta

← #21455303

Subgroups — #21455303

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×#14519809C212yesmaximal
2C4⋊Q8×D61C211yesmaximal, characteristic, complemented
3C4×#11758226C211yesmaximal, characteristic
4#16839972C211yesmaximal, characteristic, complemented
5#16839970C212yesmaximal, complemented
6#16839968C211yesmaximal, characteristic, complemented
7#16839966C212yesmaximal, complemented
8#16839964C211yesmaximal, characteristic, complemented
9#16839784C211yesmaximal, characteristic, complemented
10#16839769C212yesmaximal, complemented
11C61×#462C211yesmaximal, characteristic, complemented
12C2×#11758226C2211yescharacteristic
13C2×Q8×D61C2212yes—
14#14519809—28no—
15C2×#11758202C2212yes—
16C2×#11758190C2212yes—
17C2×#11758201C2212yes—
18C2×#11758189C2212yes—
19#14519777C2211yescharacteristic
20#14519776—21no—
21#14519776—21no—
22#14519775C2212yes—
23Q8×Dic61C2211yescharacteristic
24C4×D244—21no—
25C4×D244C2211yescharacteristic
26#14519739—21no—
27#14519739C2211yescharacteristic
28#14519735—21no—
29#14519735C2211yescharacteristic
30C4⋊C4×D61—21no—
31C4⋊C4×D61—21no—
32C42×D61—21no—
33C42×D61C2211yescharacteristic
34C4⋊#92418C2211yescharacteristic
35#14519706C2212yes—
36#14519702C2212yes—
37#14519701C2212yes—
38#14519700C2212yes—
39C2×Q16×C61C2212yes—
40C4⋊Q8×C61C2211yescharacteristic
41C4×Q8×C61C2211yescharacteristic
42C4⋊C8×C61C2211yescharacteristic
43#103×C61C2212yes—
44C2×Q8×C61C2312yes—
45C2×Q8×C61C2311yescharacteristic
46#11758226—22no—
47#11758226D414yes—
48Q8×D61—24no—
49Q8×D61—24no—
50C2×D244—21no—
51C2×D244C2311yescharacteristic
52C2×C4×D61—21no—
53C2×C4×D61—22no—
54C2×C4×D61—21no—
55C2×C4×D61—21no—
56C2×C4×D61D411yescharacteristic
57C2×C4×D61D411yescharacteristic
58C2×C4×D61C2311yescharacteristic
59C2×Dic122—22no—
60C2×Dic122C2312yes—
61Q16×C61—24no—
62C2×C8×C61C2312yes—
63C4⋊C4×C61—21no—
64C4⋊C4×C61—21no—
65C4⋊C4×C61—21no—
66C4⋊C4×C61C2311yescharacteristic
67C42×C61—21no—
68C42×C61C2311yescharacteristic
69#11758202—24no—
70#11758201—24no—
71#11758198—21no—
72#11758198—21no—
73#11758198—21no—
74C4⋊Dic61—21no—
75C4⋊Dic61—21no—
76C4⋊Dic61—21no—
77C4⋊Dic61C2311yescharacteristic
78#11758196—22no—
79#11758196—22no—
80C4×Dic61—21no—
81C4×Dic61—21no—
82C4×Dic61D411yescharacteristic
83C4×Dic61D411yescharacteristic
84C4×Dic61C2311yescharacteristic
85C2×#92418C2312yes—
86#11758190—24no—
87#11758189—24no—
88C22×D61—21no—
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—22no—
102C2×Dic61C2×D411yescharacteristic
103C2×Dic61C2×D411yescharacteristic
104C2×Dic61C2×D411yescharacteristic
105D244—24no—
106D244—21no—
107D244C2×D412yes—
108C4×D61—22no—
109C4×D61—24no—
110C4×D61—22no—
111C4×D61—44no—
112C4×D61—42no—
113C4×D61—42no—
114C4×D61C2×D412yes—
115C4×D61#4112yes—
116Dic122—22no—
117Dic122—22no—
118Dic122—44no—
119C8×C61—22no—
120#92418—22no—
121C22×C61C22×D411yescharacteristic
122C2×D61—21no—
123C2×D61—21no—
124C2×D61—22no—
125C2×D61—41no—
126C2×D61—41no—
127C2×D61#12112yes—
128C4×C61—22no—
129C4×C61—21no—
130C4×C61—42no—
131C4×C61—41no—
132C4×C61#13712yescomplemented
133C4×C61C22×D411yescharacteristic
134C4×C61C2×#4111yescharacteristic
135Dic61—21no—
136Dic61—42no—
137Dic61—41no—
138Dic61#12112yes—
139Dic61#13712yescomplemented
140#3039—611nomaximal, Sylow
141C2×C61C2×#12111yescharacteristic
142C2×C61C2×#13711yescharacteristic
143C2×C61C2×#13711yescharacteristic
144D61—22no—
145D61—42no—
146C2×#137—612no—
147C2×C4⋊Q8—611no—
148C4×#41—611no—
149#462—612no—
150#462—611no—
151#462D6111yescharacteristic, complemented
152#461—611no—
153#461—611no—
154#461—612no—
155#423—611no—
156#419—612no—
157C61#303911yescharacteristic, complemented, Sylow
158C2×#41—611no—
159C22×Q8—612no—
160#137—1228no—
161C2×Q16—612no—
162C2×Q16C2×D6112yes—
163C2×SD16—612no—
164C2×SD16—612no—
165C2×M16—612no—
166C4⋊Q8—612no—
167C4⋊Q8—611no—
168C4⋊Q8—1221no—
169C4⋊Q8—1221no—
170C4⋊Q8C2×D6111yescharacteristic
171C4×Q8—611no—
172C4×Q8C2×D6111yescharacteristic
173C4×D4—611no—
174C4×D4—611no—
175C4×D4—1221no—
176C4×D4—1221no—
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—612no—
193C2×Q8—1222no—
194C2×Q8—1224no—
195C2×Q8—1224no—
196C2×Q8C22×D6112yes—
197C2×Q8C22×D6111yescharacteristic
198C2×D4—611no—
199C2×D4—1221no—
200C22×C4—611no—
201C22×C4—611no—
202C22×C4—611no—
203C22×C4—1221no—
204C22×C4—1221no—
205C22×C4—1222no—
206C22×C4—1221no—
207Q16—24no—
208Q16—1224no—
209SD16—1224no—
210SD16—1224no—
211M16—1224no—
212C2×C8—612no—
213C2×C8C22×D6112yes—
214C4⋊C4—21no—
215C4⋊C4—21no—
216C4⋊C4—21no—
217C4⋊C4—611no—
218C4⋊C4—1222no—
219C4⋊C4—1222no—
220C4⋊C4—1221no—
221C4⋊C4—1221no—
222C4⋊C4—1221no—
223C4⋊C4C22×D6111yescharacteristic
224C22⋊C4—1221no—
225C22⋊C4—1221no—
226C22⋊C4—1221no—
227C42—21no—
228C42—611no—
229C42—611no—
230C42—611no—
231C42—1221no—
232C42—1221no—
233C42C22×D6111yescharacteristic
234C23—611no—
235C23—1221no—
236Q8—21no—
237Q8—22no—
238Q8—22no—
239Q8—1222no—
240Q8—1222no—
241Q8—2444no—
242Q8D4×D6112yes—
243D4—612no—
244D4—1224no—
245D4—1221no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—611no—
250C2×C4—611no—
251C2×C4—612no—
252C2×C4—612no—
253C2×C4—611no—
254C2×C4—1222no—
255C2×C4—1224no—
256C2×C4—1222no—
257C2×C4—1221no—
258C2×C4—1222no—
259C2×C4—2442no—
260C2×C4—2444no—
261C2×C4—2442no—
262C2×C4D4×D6111yescharacteristic
263C2×C4D4×D6111yescharacteristic
264C2×C4C23×D6111yescharacteristic
265C8—22no—
266C8—1222no—
267C22—612no—
268C22—1221no—
269C22—1221no—
270C22—1222no—
271C22—2441no—
272C22—2441no—
273C22C2×D4×D6111yescharacteristic
274C4—22no—
275C4—21no—
276C4—42no—
277C4—41no—
278C4—612no—
279C4—612no—
280C4—1221no—
281C4—2442no—
282C4—2441no—
283C4#1451980912yescomplemented
284C4C2×D4×D6111yescharacteristic
285C4#41×D6111yescharacteristic
286C2—1222no—
287C2—2442no—
288C2#121×D6111yescharacteristic
289C2#137×D6111yescharacteristic
290C2C2×#1451980911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#462C2
socleC22×C61C22×D4
hypercenter#462D61
hypocenterC61#3039
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
2. C4⋊Q8×D61C2semidirect
4. #16839972C2semidirect
5. #16839970C2semidirect
6. #16839968C2semidirect
7. #16839966C2semidirect
8. #16839964C2semidirect
9. #16839784C2semidirect
10. #16839769C2semidirect
11. C61×#462C2semidirect
132. C4×C61#137semidirect
139. Dic61#137semidirect
151. #462D61semidirect
157. C61#3039semidirect
283. C4#14519809semidirect