Finite Group Databasebeta

← #21456298

Subgroups — #21456298

Order 7808.

564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14519805C211yesmaximal, characteristic, complemented
2C2×#14519797C211yesmaximal, characteristic, complemented
3C22×#11758201C211yesmaximal, characteristic, complemented
4#16840336C211yesmaximal, characteristic, complemented
5#16840326C211yesmaximal, characteristic, complemented
6#16840155C212yesmaximal, complemented
7#16840148C212yesmaximal, complemented
8#16840147C212yesmaximal, complemented
9#16840133C212yesmaximal, complemented
10#16839720C211yesmaximal, characteristic, complemented
11C2×#137×C61C211yesmaximal, characteristic, complemented
12C2×#11758222C2211yescharacteristic
13C22×D244C2211yescharacteristic
14#14519805—24no—
15#14519797—24no—
16C2×#11758202C2211yescharacteristic, complemented
17C2×#11758190C2212yes—
18C2×#11758200C2211yescharacteristic, complemented
19C2×#11758201—24no—
20C2×#11758201C2212yes—
21C2×#11758201C2212yes—
22C2×#11758201C2211yescharacteristic, complemented
23C2×D488C2212yes—
24C2×#11758199C2211yescharacteristic, complemented
25C22×#92418C2211yescharacteristic
26#14519775C2212yescomplemented
27#14519773C2212yes—
28#14519766C2212yes—
29#14519766C2212yescomplemented
30#14519760—22no—
31#14519753—22no—
32#14519751—22no—
33#14519745—22no—
34#14519736C2211yescharacteristic
35#14519687C2212yescomplemented
36C8×Dic61C2212yescomplemented
37C2×#41×C61C2211yescharacteristic
38C22×Q8×C61C2211yescharacteristic
39#137×C61—24no—
40C2×Q16×C61C2212yescomplemented
41C2×SD16×C61C2212yescomplemented
42C2×M16×C61C2211yescharacteristic
43C23×D61—21no—
44#41×C61—22no—
45#41×C61—22no—
46C2×Q8×C61—21no—
47C2×Q8×C61—22no—
48C2×Q8×C61—22no—
49C2×Q8×C61C2312yes—
50C2×Q8×C61C2311yescharacteristic
51C2×D4×C61—21no—
52C2×D4×C61C2311yescharacteristic
53C22×C4×C61—21no—
54C22×C4×C61—21no—
55C22×C4×C61C2311yescharacteristic
56C2×C22⋊D61—21no—
57C2×C22⋊D61—24no—
58#11758222—22no—
59#11758222—22no—
60C2×D244—22no—
61C2×D244—22no—
62C2×D244—21no—
63C2×D244C2312yes—
64C2×D244C2311yescharacteristic
65C2×C4×D61—21no—
66C2×Dic122C2311yescharacteristic
67Q16×C61—24no—
68SD16×C61—24no—
69M16×C61D414yescomplemented
70C2×C8×C61C2312yes—
71C22⋊Dic61D412yes—
72#11758202—22no—
73#11758201—24no—
74#11758201—24no—
75#11758201—22no—
76#11758200—22no—
77#11758199—22no—
78#11758198—24no—
79#11758198—24no—
80C4⋊Dic61D412yes—
81#11758196—24no—
82C4×Dic61C2312yes—
83C2×#92418D414yescomplemented
84C2×#92418C2311yescharacteristic
85C2×#92418C2311yescharacteristic
86D488—24no—
87#11758190—24no—
88C23×C61—21no—
89C23×C61C2×D411yescharacteristic
90C22×D61—21no—
91C22×D61—22no—
92C22×D61—42no—
93C22×D61—82no—
94Q8×C61—22no—
95Q8×C61—21no—
96Q8×C61—22no—
97Q8×C61—21no—
98Q8×C61—42no—
99D4×C61—21no—
100D4×C61—21no—
101D4×C61—42no—
102C2×C4×C61—22no—
103C2×C4×C61—21no—
104C2×C4×C61—42no—
105C2×C4×C61—42no—
106C2×C4×C61C2×D411yescharacteristic
107C2×C4×C61C2×D412yes—
108C2×C4×C61C2×D412yes—
109C2×C4×C61C2411yescharacteristic
110C22⋊D61—42no—
111C22⋊D61—84no—
112C2×Dic61—21no—
113C2×Dic61C2×D414yes—
114D244—22no—
115D244—21no—
116D244—21no—
117D244—22no—
118D244—42no—
119C4×D61—42no—
120Dic122—21no—
121Dic122—21no—
122C8×C61C2×D414yes—
123#92418C2×D412yes—
124#92418C2×D412yes—
125C22×C61—22no—
126C22×C61—41no—
127C22×C61—42no—
128C22×C61#12712yes—
129C22×C61C22×D411yescharacteristic
130C2×D61—41no—
131C2×D61—42no—
132C2×D61—44no—
133C2×D61—42no—
134C2×D61—84no—
135C4×C61—41no—
136C4×C61—42no—
137C4×C61#12712yes—
138C4×C61C22×D411yescharacteristic
139C4×C61C22×D411yescharacteristic
140Dic61—24no—
141Dic61—41no—
142#3154—611nomaximal, Sylow
143C2×C61—22no—
144C2×C61—81no—
145C2×C61C2×#12711yescharacteristic
146C2×C61#57712yes—
147D61—81no—
148D61—82no—
149C2×#137D6111yescharacteristic, complemented
150C2×AGL(1,ℤ/8)—611no—
151C2×#135—611no—
152C22×SD16—611no—
153#536—611no—
154#535—611no—
155#497—612no—
156#496—612no—
157#495—612no—
158#492—612no—
159#405—611no—
160C61#315411yescharacteristic, complemented, Sylow
161C2×#41—611no—
162C2×#41C2×D6111yescharacteristic
163C22×Q8C2×D6111yescharacteristic
164C22×D4—611no—
165#137—24no—
166AGL(1,ℤ/8)—1224no—
167#135—1224no—
168C2×Q16—611no—
169C2×Q16C2×D6112yescomplemented
170C2×SD16—612no—
171C2×SD16—612no—
172C2×SD16—611no—
173C2×SD16—611no—
174C2×SD16—612no—
175C2×SD16—1224no—
176C2×SD16C2×D6112yescomplemented
177C2×D8—611no—
178C2×D8—612no—
179C2×M16C2×D6111yescharacteristic
180C22×C8—611no—
181C4⋊Q8—612no—
182#127—612no—
183#124—612no—
184#124—612no—
185#123—1222no—
186C22⋊Q8—1222no—
187#121—1222no—
188#120—1222no—
189#117—611no—
190#97—612no—
191C4×C8—612no—
192C24—1221no—
193#41—22no—
194#41—22no—
195#41—1222no—
196#41—1222no—
197C2×Q8—21no—
198C2×Q8—22no—
199C2×Q8—22no—
200C2×Q8—611no—
201C2×Q8C22×D6111yescharacteristic
202C2×Q8C22×D6112yes—
203C2×D4—21no—
204C2×D4—611no—
205C2×D4—612no—
206C2×D4—1224no—
207C2×D4—1221no—
208C2×D4—1222no—
209C2×D4—1221no—
210C2×D4—1222no—
211C2×D4C22×D6111yescharacteristic
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—1221no—
215C22×C4C22×D6111yescharacteristic
216Q16—24no—
217Q16—1222no—
218SD16—24no—
219SD16—1222no—
220SD16—1224no—
221SD16—1224no—
222SD16—1222no—
223SD16—1224no—
224D8—1222no—
225D8—1224no—
226M16C22⋊D6114yescomplemented
227C2×C8—614no—
228C2×C8—611no—
229C2×C8—611no—
230C2×C8C22×D6112yes—
231C4⋊C4—612no—
232C4⋊C4—1224no—
233C22⋊C4—612no—
234C22⋊C4—1224no—
235C22⋊C4—1224no—
236C42—612no—
237C23—21no—
238C23—1221no—
239C23—1222no—
240C23—4882no—
241C23—2442no—
242C23D4×D6111yescharacteristic
243Q8—22no—
244Q8—21no—
245Q8—22no—
246Q8—21no—
247Q8—42no—
248Q8—1221no—
249Q8—1221no—
250D4—21no—
251D4—21no—
252D4—42no—
253D4—1221no—
254D4—1222no—
255D4—1221no—
256D4—1222no—
257D4—4884no—
258D4—2442no—
259D4—2442no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—614no—
265C2×C4—1221no—
266C2×C4—2442no—
267C2×C4D4×D6112yes—
268C2×C4D4×D6111yescharacteristic
269C2×C4C2×C22⋊D6112yes—
270C2×C4C23×D6111yescharacteristic
271C8—612no—
272C8—612no—
273C8C2×C22⋊D6114yes—
274C22—22no—
275C22—41no—
276C22—42no—
277C22—4884no—
278C22—2441no—
279C22—2442no—
280C22—2444no—
281C22—2442no—
282C22#1451977312yes—
283C22C2×D4×D6111yescharacteristic
284C4—41no—
285C4—42no—
286C4—1224no—
287C4—2441no—
288C4#1451977312yes—
289C4C2×D4×D6111yescharacteristic
290C4C22×C22⋊D6111yescharacteristic
291C2—22no—
292C2—81no—
293C2—4882no—
294C2—4881no—
295C2C2×#1451977311yescharacteristic
296C2#1684057112yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#137×C61C2
socleC22×C61C22×D4
hypercenterC2×#137D61
hypocenterC61#3154
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#14519805C2semidirect
2. C2×#14519797C2semidirect
3. C22×#11758201C2semidirect
4. #16840336C2semidirect
5. #16840326C2semidirect
6. #16840155C2semidirect
7. #16840148C2semidirect
8. #16840147C2semidirect
9. #16840133C2semidirect
10. #16839720C2semidirect
11. C2×#137×C61C2semidirect
16. C2×#11758202C22semidirect
18. C2×#11758200C22semidirect
22. C2×#11758201C22semidirect
24. C2×#11758199C22semidirect
26. #14519775C22semidirect
29. #14519766C22semidirect
35. #14519687C22semidirect
36. C8×Dic61C22semidirect
40. C2×Q16×C61C22semidirect
41. C2×SD16×C61C22semidirect
69. M16×C61D4semidirect
83. C2×#92418D4semidirect
149. C2×#137D61semidirect
160. C61#3154semidirect
169. C2×Q16C2×D61semidirect
176. C2×SD16C2×D61semidirect
226. M16C22⋊D61semidirect