Finite Group Databasebeta

← #21455088

Subgroups — #21455088

Order 7808.

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

normal subgroups only

This group has 784 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×#14519822C211yesmaximal, characteristic, complemented
2C2×#14519805C211yesmaximal, characteristic, complemented
3C22×#11758199C211yesmaximal, characteristic, complemented
4#16840331C211yesmaximal, characteristic, complemented
5#16839908C214yesmaximal, complemented
6#16839897C214yesmaximal, complemented
7#16839756C211yesmaximal, characteristic, complemented
8#16839730C211yesmaximal, characteristic, complemented
9C61×#418C211yesmaximal, characteristic, complemented
10#14519822—24no—
11#14519822—24no—
12C2×#11758222C2211yescharacteristic
13C2×#11758222C2211yescharacteristic
14C2×#11758224—21no—
15C2×#11758224C2212yescomplemented
16C22×D244C2211yescharacteristic, complemented
17C22×C22⋊D61—22no—
18C2×D4×D61—21no—
19C2×D4×D61C2212yescomplemented
20#14519805—24no—
21C2×#11758190C2212yescomplemented
22C2×D488C2212yescomplemented
23C2×#11758199—24no—
24C2×#11758199C2214yescomplemented
25C22×#92418C2211yescharacteristic, complemented
26#14519774—21no—
27#14519765—21no—
28#14519752C2214yescomplemented
29#14519747—22no—
30#14519700C2212yescomplemented
31#14519697C2212yescomplemented
32#14519689C2214yescomplemented
33C22×D4×C61C2211yescharacteristic
34C2×M16×C61C2211yescharacteristic, complemented
35#117×C61C2211yescharacteristic, complemented
36#102×C61C2214yescomplemented
37C24×C61—21no—
38C23×D61—22no—
39C23×D61—21no—
40C2×D4×C61—21no—
41C2×D4×C61—22no—
42C2×D4×C61D414yescomplemented
43C2×D4×C61C2312yes—
44C22×C4×C61C2311yescharacteristic
45C2×C22⋊D61—216no—
46C2×C22⋊D61—21no—
47C2×C22⋊D61—22no—
48C2×C22⋊D61—22no—
49C2×C22⋊D61D412yes—
50C22×Dic61—22no—
51#11758224—28no—
52#11758224—24no—
53#11758224—24no—
54D4×D61—28no—
55D4×D61—24no—
56D4×D61—24no—
57#11758222—22no—
58#11758222—22no—
59#11758222—22no—
60#11758222D414yescomplemented
61C2×D244—22no—
62C2×D244—22no—
63C2×D244—21no—
64C2×D244—24no—
65C2×D244D411yescharacteristic
66C2×D244C2312yes—
67C2×D244C2311yescharacteristic
68C2×C4×D61—21no—
69C2×C4×D61C2312yes—
70C2×Dic122D411yescharacteristic
71C2×Dic122C2311yescharacteristic
72M16×C61—22no—
73C2×C8×C61C2312yes—
74C4⋊C4×C61C2312yes—
75C22⋊C4×C61—21no—
76C42×C61—21no—
77#11758199—28no—
78#11758198—24no—
79C2×#92418—22no—
80C2×#92418C2312yes—
81D488—24no—
82#11758190—24no—
83C23×C61—22no—
84C23×C61—24no—
85C23×C61—82no—
86C23×C61C2×D411yescharacteristic
87C22×D61—21no—
88C22×D61—28no—
89C22×D61—22no—
90C22×D61—42no—
91C22×D61—84no—
92C22×D61—82no—
93C22×D61C2×D412yes—
94D4×C61—24no—
95D4×C61—22no—
96D4×C61C2×D414yes—
97C2×C4×C61—22no—
98C2×C4×C61C2×D411yescharacteristic
99C2×C4×C61C2×D412yes—
100C2×C4×C61C2×D412yes—
101C2×C4×C61C2411yescharacteristic
102C22⋊D61—28no—
103C22⋊D61—28no—
104C22⋊D61—24no—
105C22⋊D61—24no—
106C2×Dic61—28no—
107C2×Dic61—21no—
108C2×Dic61C2×D412yes—
109D244—22no—
110D244—21no—
111D244—22no—
112D244—22no—
113D244—42no—
114D244—84no—
115D244C2×D412yes—
116C4×D61—24no—
117C4×D61—22no—
118C4×D61—22no—
119Dic122—22no—
120Dic122—21no—
121Dic122C2×D412yes—
122C8×C61—22no—
123#92418—22no—
124C22×C61—22no—
125C22×C61—24no—
126C22×C61—44no—
127C22×C61—84no—
128C22×C61#12012yes—
129C22×C61C22×D411yescharacteristic
130C2×D61—22no—
131C2×D61—22no—
132C2×D61—24no—
133C2×D61—42no—
134C2×D61—42no—
135C2×D61—44no—
136C2×D61—88no—
137C2×D61—84no—
138C4×C61—42no—
139C4×C61#12012yes—
140C4×C61C22×D411yescharacteristic
141C4×C61C22×D411yescharacteristic
142Dic61—22no—
143Dic61—22no—
144#3008—611nomaximal, Sylow
145C2×C61—22no—
146C2×C61—44no—
147C2×C61C2×#12011yescharacteristic
148C2×C61#57612yes—
149D61—42no—
150D61—42no—
151D61—82no—
152C2×H(5,𝔽2)—611no—
153C2×AGL(1,ℤ/8)—611no—
154C22×D8—611no—
155#535—611no—
156#449—614no—
157#447—614no—
158#418D6111yescharacteristic, complemented
159#416—611no—
160#408—611no—
161C61#300811yescharacteristic, complemented, Sylow
162H(5,𝔽2)—1224no—
163H(5,𝔽2)—1224no—
164C2×#41—611no—
165C2×#41—612no—
166C2×#41—611no—
167C2×#41—1221no—
168C22×D4—612no—
169C22×D4—611no—
170C22×D4—1221no—
171C22×D4—1222no—
172C22×D4C2×D6111yescharacteristic
173AGL(1,ℤ/8)—1224no—
174C2×SD16—612no—
175C2×D8—614no—
176C2×D8—612no—
177C2×D8—1224no—
178C2×M16C2×D6111yescharacteristic, complemented
179C22×C8—611no—
180#127—1221no—
181#124—1221no—
182#121—614no—
183#120—1222no—
184#117C2×D6111yescharacteristic, complemented
185#103—612no—
186#102—612no—
187#102C2×D6114yescomplemented
188C22⋊C8—614no—
189C24—21no—
190C24—1222no—
191C24—1221no—
192#41—614no—
193#41—1224no—
194#41—1228no—
195#41—1224no—
196#41—1222no—
197#41—1222no—
198#41—1222no—
199C2×Q8—611no—
200C2×Q8—611no—
201C2×D4—21no—
202C2×D4—22no—
203C2×D4—612no—
204C2×D4—611no—
205C2×D4—611no—
206C2×D4—612no—
207C2×D4—1224no—
208C2×D4—1222no—
209C2×D4—1224no—
210C2×D4—1228no—
211C2×D4—1222no—
212C2×D4—12216no—
213C2×D4—1221no—
214C2×D4—1224no—
215C2×D4—1222no—
216C2×D4—1222no—
217C2×D4—1221no—
218C2×D4D24414yescomplemented
219C2×D4C22×D6112yes—
220C22×C4—612no—
221C22×C4—1222no—
222C22×C4—1221no—
223C22×C4C22×D6111yescharacteristic
224SD16—1224no—
225D8—1224no—
226D8—1228no—
227M16—22no—
228C2×C8—612no—
229C2×C8—1222no—
230C2×C8C22×D6112yes—
231C4⋊C4C22×D6112yes—
232C22⋊C4—21no—
233C22⋊C4—1224no—
234C42—21no—
235C23—22no—
236C23—24no—
237C23—82no—
238C23—612no—
239C23—1228no—
240C23—1221no—
241C23—1222no—
242C23—4882no—
243C23—4884no—
244C23—2442no—
245C23D4×D6111yescharacteristic
246Q8—612no—
247Q8—1221no—
248Q8—1222no—
249D4—22no—
250D4—24no—
251D4—612no—
252D4—1228no—
253D4—1228no—
254D4—1224no—
255D4—1224no—
256D4—1222no—
257D4—1221no—
258D4—1222no—
259D4—1222no—
260D4—4884no—
261D4—2442no—
262D4C2×D24414yes—
263C2×C4—22no—
264C2×C4—612no—
265C2×C4—1228no—
266C2×C4—1221no—
267C2×C4—1222no—
268C2×C4—1222no—
269C2×C4—1224no—
270C2×C4C2×D24412yes—
271C2×C4D4×D6112yes—
272C2×C4D4×D6111yescharacteristic
273C2×C4C23×D6111yescharacteristic
274C8—22no—
275C8—1222no—
276C22—22no—
277C22—24no—
278C22—44no—
279C22—84no—
280C22—1222no—
281C22—1222no—
282C22—1224no—
283C22—4884no—
284C22—4888no—
285C22—2442no—
286C22—2444no—
287C22—2442no—
288C22#1451974712yes—
289C22C2×D4×D6111yescharacteristic
290C4—42no—
291C4—1222no—
292C4—1222no—
293C4#1451974712yes—
294C4C2×D4×D6111yescharacteristic
295C4C22×D24411yescharacteristic
296C2—22no—
297C2—44no—
298C2—4882no—
299C2—2442no—
300C2—2442no—
301C2C2×#1451974711yescharacteristic
302C2#1684056612yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#418C2
socleC22×C61C22×D4
hypercenter#418D61
hypocenterC61#3008
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C2×#14519822C2semidirect
2. C2×#14519805C2semidirect
3. C22×#11758199C2semidirect
4. #16840331C2semidirect
5. #16839908C2semidirect
6. #16839897C2semidirect
7. #16839756C2semidirect
8. #16839730C2semidirect
9. C61×#418C2semidirect
15. C2×#11758224C22semidirect
16. C22×D244C22semidirect
19. C2×D4×D61C22semidirect
21. C2×#11758190C22semidirect
22. C2×D488C22semidirect
24. C2×#11758199C22semidirect
25. C22×#92418C22semidirect
28. #14519752C22semidirect
30. #14519700C22semidirect
31. #14519697C22semidirect
32. #14519689C22semidirect
34. C2×M16×C61C22semidirect
35. #117×C61C22semidirect
36. #102×C61C22semidirect
42. C2×D4×C61D4semidirect
60. #11758222D4semidirect
158. #418D61semidirect
161. C61#3008semidirect
178. C2×M16C2×D61semidirect
184. #117C2×D61semidirect
187. #102C2×D61semidirect
218. C2×D4D244semidirect