Finite Group Databasebeta

← #21456286

Subgroups — #21456286

Order 7808.

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

normal subgroups only

This group has 572 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×#14519808C211yesmaximal, characteristic, complemented
2C2×#14519805C211yesmaximal, characteristic, complemented
3C2×#14519802C211yesmaximal, characteristic, complemented
4#16840308C211yesmaximal, characteristic, complemented
5C2×#14519766C211yesmaximal, characteristic, complemented
6#16840155C212yesmaximal, complemented
7#16840148C212yesmaximal, complemented
8#16840147C212yesmaximal, complemented
9#16840143C212yesmaximal, complemented
10M16×Dic61C211yesmaximal, characteristic, complemented
11C2×#137×C61C211yesmaximal, characteristic, complemented
12C2×#11758222C2211yescharacteristic
13C22×D244C2211yescharacteristic
14#14519808—24no—
15#14519805—24no—
16#14519802—24no—
17C2×#11758202C2212yescomplemented
18C2×#11758190C2212yes—
19C2×#11758201C2212yes—
20C2×#11758201C2212yescomplemented
21C2×D488C2212yes—
22C2×#11758199C2212yes—
23C2×#11758194C2211yescharacteristic
24#14519775C2211yescharacteristic, complemented
25#14519773C2211yescharacteristic, complemented
26#14519766—22no—
27#14519766C2212yes—
28#14519766C2212yes—
29#14519766C2211yescharacteristic, complemented
30#14519764C2211yescharacteristic, complemented
31#14519749—22no—
32C4×C22⋊D61—22no—
33C2×#11758198—22no—
34C2×C4×Dic61C2211yescharacteristic
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—22no—
58C22×Dic61D412yes—
59#11758222—22no—
60#11758222—22no—
61C2×D244—22no—
62C2×D244—22no—
63C2×D244—21no—
64C2×D244C2312yes—
65C2×D244C2311yescharacteristic
66C2×C4×D61—21no—
67C2×Dic122C2311yescharacteristic
68Q16×C61—24no—
69SD16×C61—24no—
70M16×C61D414yescomplemented
71C2×C8×C61C2312yes—
72C22⋊Dic61—22no—
73#11758202—24no—
74#11758201—24no—
75#11758201—24no—
76#11758199—24no—
77#11758198—24no—
78#11758198—24no—
79#11758198—22no—
80#11758196—22no—
81C4×Dic61D412yes—
82C4×Dic61C2311yescharacteristic
83C4×Dic61C2311yescharacteristic
84#11758194D414yescomplemented
85C2×#92418C2312yes—
86D488—24no—
87#11758190—24no—
88C23×C61—21no—
89C23×C61C2×D411yescharacteristic
90C22×D61—22no—
91C22×D61—21no—
92C22×D61—44no—
93C22×D61—42no—
94Q8×C61—21no—
95Q8×C61—22no—
96Q8×C61—22no—
97Q8×C61—21no—
98Q8×C61—42no—
99D4×C61—21no—
100D4×C61—21no—
101D4×C61—42no—
102C2×C4×C61—21no—
103C2×C4×C61—22no—
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—44no—
111C22⋊D61—42no—
112C2×Dic61—21no—
113C2×Dic61—42no—
114C2×Dic61C2×D412yes—
115C2×Dic61C2×D412yes—
116D244—22no—
117D244—21no—
118D244—22no—
119D244—21no—
120D244—42no—
121C4×D61—42no—
122Dic122—21no—
123Dic122—21no—
124C8×C61C2×D414yes—
125#92418C2×D414yes—
126C22×C61—22no—
127C22×C61—41no—
128C22×C61—42no—
129C22×C61#12712yes—
130C22×C61C22×D411yescharacteristic
131C2×D61—41no—
132C2×D61—42no—
133C2×D61—42no—
134C2×D61—44no—
135C2×D61—84no—
136C4×C61—41no—
137C4×C61—42no—
138C4×C61#12712yes—
139C4×C61C22×D411yescharacteristic
140C4×C61C22×D411yescharacteristic
141Dic61—22no—
142Dic61—22no—
143Dic61—41no—
144#3153—611nomaximal, Sylow
145C2×C61—22no—
146C2×C61—81no—
147C2×C61C2×#12711yescharacteristic
148C2×C61#57512yes—
149D61—81no—
150D61—82no—
151C2×#137—611no—
152C2×#137D6111yescharacteristic, complemented
153C2×AGL(1,ℤ/8)—611no—
154C2×AGL(1,ℤ/8)—611no—
155#532—611no—
156C2×#124—611no—
157#497—612no—
158#496—612no—
159#495—612no—
160#495—612no—
161C4×M16—611no—
162C61#315311yescharacteristic, complemented, Sylow
163C2×#41—611no—
164C2×#41C2×D6111yescharacteristic
165C22×Q8C2×D6111yescharacteristic
166C22×D4—611no—
167#137—24no—
168#137—1224no—
169AGL(1,ℤ/8)—1224no—
170AGL(1,ℤ/8)—1224no—
171C2×Q16—612no—
172C2×Q16C2×D6112yescomplemented
173C2×SD16—612no—
174C2×SD16—612no—
175C2×SD16—612no—
176C2×SD16C2×D6112yescomplemented
177C2×D8—612no—
178C2×D8—612no—
179C2×M16—611no—
180C2×M16C2×D6111yescharacteristic
181C4⋊Q8—611no—
182#127—611no—
183#124—612no—
184#124—612no—
185#124—611no—
186#124—611no—
187#124—1222no—
188#121—1222no—
189C4×D4—1222no—
190C2×C22⋊C4—1222no—
191C2×C42—611no—
192#97—612no—
193C4×C8—612no—
194C24—1221no—
195#41—22no—
196#41—22no—
197#41—1222no—
198#41—1222no—
199C2×Q8—21no—
200C2×Q8—22no—
201C2×Q8—22no—
202C2×Q8—611no—
203C2×Q8C22×D6112yes—
204C2×Q8C22×D6111yescharacteristic
205C2×D4—21no—
206C2×D4—612no—
207C2×D4—611no—
208C2×D4—1222no—
209C2×D4—1221no—
210C2×D4—1222no—
211C2×D4—1221no—
212C2×D4—1222no—
213C2×D4C22×D6111yescharacteristic
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—612no—
217C22×C4—1221no—
218C22×C4C22×D6111yescharacteristic
219Q16—24no—
220Q16—1224no—
221SD16—24no—
222SD16—1224no—
223SD16—1224no—
224SD16—1224no—
225D8—1224no—
226D8—1224no—
227M16—614no—
228M16C22⋊D6114yescomplemented
229C2×C8—612no—
230C2×C8C22×D6112yes—
231C4⋊C4—1222no—
232C22⋊C4—1224no—
233C22⋊C4—1224no—
234C22⋊C4—1222no—
235C22⋊C4—1222no—
236C42—612no—
237C42—611no—
238C42—611no—
239C23—21no—
240C23—1222no—
241C23—1221no—
242C23—2444no—
243C23—2442no—
244C23D4×D6111yescharacteristic
245Q8—21no—
246Q8—22no—
247Q8—22no—
248Q8—21no—
249Q8—42no—
250Q8—1221no—
251Q8—1221no—
252D4—21no—
253D4—21no—
254D4—42no—
255D4—1222no—
256D4—1221no—
257D4—1221no—
258D4—1222no—
259D4—2444no—
260D4—2442no—
261D4—2442no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—612no—
267C2×C4—612no—
268C2×C4—1221no—
269C2×C4—2442no—
270C2×C4—2442no—
271C2×C4D4×D6112yes—
272C2×C4D4×D6111yescharacteristic
273C2×C4C2×C22⋊D6112yes—
274C2×C4C23×D6111yescharacteristic
275C8—614no—
276C8C2×C22⋊D6114yes—
277C22—22no—
278C22—41no—
279C22—42no—
280C22—4884no—
281C22—2441no—
282C22—2442no—
283C22—2442no—
284C22—2444no—
285C22#1451977312yes—
286C22C2×D4×D6111yescharacteristic
287C4—41no—
288C4—42no—
289C4—1222no—
290C4—1222no—
291C4—2441no—
292C4#1451977312yes—
293C4C2×D4×D6111yescharacteristic
294C4C22×C22⋊D6111yescharacteristic
295C2—22no—
296C2—81no—
297C2—4882no—
298C2—4881no—
299C2C2×#1451977311yescharacteristic
300C2#1684056112yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#137×C61C2
socleC22×C61C22×D4
hypercenterC2×#137D61
hypocenterC61#3153
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×#14519808C2semidirect
2. C2×#14519805C2semidirect
3. C2×#14519802C2semidirect
4. #16840308C2semidirect
5. C2×#14519766C2semidirect
6. #16840155C2semidirect
7. #16840148C2semidirect
8. #16840147C2semidirect
9. #16840143C2semidirect
10. M16×Dic61C2semidirect
11. C2×#137×C61C2semidirect
17. C2×#11758202C22semidirect
20. C2×#11758201C22semidirect
24. #14519775C22semidirect
25. #14519773C22semidirect
29. #14519766C22semidirect
30. #14519764C22semidirect
35. #14519687C22semidirect
36. C8×Dic61C22semidirect
40. C2×Q16×C61C22semidirect
41. C2×SD16×C61C22semidirect
70. M16×C61D4semidirect
84. #11758194D4semidirect
152. C2×#137D61semidirect
162. C61#3153semidirect
172. C2×Q16C2×D61semidirect
176. C2×SD16C2×D61semidirect
228. M16C22⋊D61semidirect