Finite Group Databasebeta

← #21455090

Subgroups — #21455090

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×#14519823C211yesmaximal, characteristic, complemented
2C2×#14519802C211yesmaximal, characteristic, complemented
3C22×D488C211yesmaximal, characteristic, complemented
4#16840331C211yesmaximal, characteristic, complemented
5#16839910C214yesmaximal, complemented
6#16839897C214yesmaximal, complemented
7#16839766C211yesmaximal, characteristic, complemented
8#16839728C211yesmaximal, characteristic, complemented
9C61×#416C211yesmaximal, characteristic, complemented
10#14519823—24no—
11#14519823—24no—
12C2×#11758226C2212yescomplemented
13C2×#11758222—21no—
14C2×#11758222C2211yescharacteristic
15C22×D244—21no—
16C22×D244C2211yescharacteristic
17C22×D244C2211yescharacteristic, complemented
18C2×D4×D61—22no—
19C2×D4×D61C2212yescomplemented
20#14519802—24no—
21C2×#11758201C2212yescomplemented
22C2×D488—24no—
23C2×D488C2214yescomplemented
24C2×#11758199C2212yescomplemented
25C2×#11758194C2211yescharacteristic, complemented
26#14519774—21no—
27#14519765—21no—
28#14519752C2214yescomplemented
29#14519747—22no—
30#14519697C2214yescomplemented
31#14519689C2214yescomplemented
32C2×#41×C61C2211yescharacteristic
33C22×C8×C61C2211yescharacteristic, complemented
34#117×C61C2211yescharacteristic, complemented
35#103×C61C2212yescomplemented
36#102×C61C2212yescomplemented
37C23×D61—21no—
38C23×D61—22no—
39C23×D61—21no—
40#41×C61—22no—
41#41×C61D414yescomplemented
42C2×Q8×C61C2311yescharacteristic
43C2×D4×C61—21no—
44C2×D4×C61C2311yescharacteristic
45C22×C4×C61—21no—
46C22×C4×C61C2311yescharacteristic
47C2×C22⋊D61—22no—
48C2×C22⋊D61D412yes—
49#11758226—24no—
50#11758226—24no—
51D4×D61—216no—
52D4×D61—24no—
53D4×D61—24no—
54#11758222—28no—
55#11758222—22no—
56#11758222—22no—
57C2×D244—28no—
58C2×D244—22no—
59C2×D244—21no—
60C2×D244—22no—
61C2×D244—22no—
62C2×D244—22no—
63C2×D244—21no—
64C2×D244—24no—
65C2×D244D411yescharacteristic
66C2×D244D414yescomplemented
67C2×D244C2312yes—
68C2×D244C2312yes—
69C2×C4×D61—22no—
70C2×C4×D61C2312yes—
71C2×Dic122D411yescharacteristic
72C2×C8×C61—22no—
73C2×C8×C61C2312yes—
74C4⋊C4×C61C2312yes—
75C22⋊C4×C61—21no—
76C42×C61—21no—
77#11758201—24no—
78#11758199—24no—
79#11758198—24no—
80#11758194—22no—
81C2×#92418C2312yes—
82D488—28no—
83C23×C61—21no—
84C23×C61C2×D411yescharacteristic
85C22×D61—22no—
86C22×D61—28no—
87C22×D61—24no—
88C22×D61—22no—
89C22×D61—42no—
90C22×D61—84no—
91C22×D61—82no—
92C22×D61—82no—
93C22×D61C2×D412yes—
94Q8×C61—21no—
95Q8×C61C2×D412yes—
96D4×C61—24no—
97D4×C61—21no—
98D4×C61C2×D412yes—
99C2×C4×C61—21no—
100C2×C4×C61—24no—
101C2×C4×C61—22no—
102C2×C4×C61C2×D411yescharacteristic
103C2×C4×C61C2×D412yes—
104C2×C4×C61C2×D412yes—
105C2×C4×C61C2411yescharacteristic
106C22⋊D61—28no—
107C22⋊D61—24no—
108C2×Dic61C2×D412yes—
109D244—28no—
110D244—22no—
111D244—24no—
112D244—22no—
113D244—22no—
114D244—22no—
115D244—42no—
116D244—84no—
117D244C2×D414yes—
118C4×D61—28no—
119C4×D61—22no—
120C4×D61—22no—
121Dic122—22no—
122C8×C61—22no—
123#92418—22no—
124C22×C61—22no—
125C22×C61—22no—
126C22×C61—42no—
127C22×C61#12012yes—
128C22×C61C22×D411yescharacteristic
129C2×D61—22no—
130C2×D61—24no—
131C2×D61—24no—
132C2×D61—44no—
133C2×D61—42no—
134C2×D61—44no—
135C2×D61—84no—
136C2×D61—88no—
137C2×D61—84no—
138C4×C61—22no—
139C4×C61—42no—
140C4×C61#12012yes—
141C4×C61C22×D411yescharacteristic
142C4×C61C22×D411yescharacteristic
143Dic61—22no—
144#3008—611nomaximal, Sylow
145C2×C61—22no—
146C2×C61—42no—
147C2×C61C2×#12011yescharacteristic
148C2×C61#57612yes—
149D61—42no—
150D61—44no—
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#418—611no—
159#416D6111yescharacteristic, complemented
160#408—611no—
161C61#300811yescharacteristic, complemented, Sylow
162H(5,𝔽2)—1224no—
163H(5,𝔽2)—1224no—
164C2×#41—611no—
165C2×#41—612no—
166C2×#41—1221no—
167C2×#41C2×D6111yescharacteristic
168C22×D4—612no—
169C22×D4—611no—
170C22×D4—611no—
171C22×D4—1221no—
172C22×D4—1222no—
173AGL(1,ℤ/8)—1224no—
174C2×SD16—612no—
175C2×D8—612no—
176C2×D8—614no—
177C2×D8—1224no—
178C2×M16—611no—
179C22×C8C2×D6111yescharacteristic, complemented
180#127—1221no—
181#124—1221no—
182#121—614no—
183#120—1222no—
184#117C2×D6111yescharacteristic, complemented
185#103C2×D6112yescomplemented
186#102—614no—
187#102C2×D6112yescomplemented
188C22⋊C8—614no—
189C24—1222no—
190C24—1221no—
191C24—1221no—
192#41—22no—
193#41—1228no—
194#41—1224no—
195#41—1224no—
196#41—1222no—
197#41—1222no—
198#41D24414yescomplemented
199C2×Q8—611no—
200C2×Q8C22×D6111yescharacteristic
201C2×D4—21no—
202C2×D4—612no—
203C2×D4—614no—
204C2×D4—611no—
205C2×D4—612no—
206C2×D4—612no—
207C2×D4—1222no—
208C2×D4—1228no—
209C2×D4—1224no—
210C2×D4—1222no—
211C2×D4—1224no—
212C2×D4—12216no—
213C2×D4—1224no—
214C2×D4—1222no—
215C2×D4—1222no—
216C2×D4—1221no—
217C2×D4—1222no—
218C2×D4—1221no—
219C2×D4C22×D6111yescharacteristic
220C22×C4—21no—
221C22×C4—612no—
222C22×C4—1222no—
223C22×C4C22×D6111yescharacteristic
224SD16—1224no—
225D8—1228no—
226D8—1224no—
227M16—1222no—
228C2×C8—22no—
229C2×C8—612no—
230C2×C8C22×D6112yes—
231C4⋊C4C22×D6112yes—
232C22⋊C4—21no—
233C22⋊C4—1224no—
234C42—21no—
235C23—21no—
236C23—612no—
237C23—1228no—
238C23—1224no—
239C23—1222no—
240C23—1222no—
241C23—4882no—
242C23—4882no—
243C23—4884no—
244C23—2442no—
245C23D4×D6111yescharacteristic
246Q8—21no—
247Q8—1222no—
248Q8C2×D24412yes—
249D4—24no—
250D4—21no—
251D4—614no—
252D4—1228no—
253D4—1228no—
254D4—1224no—
255D4—1222no—
256D4—1222no—
257D4—1222no—
258D4—1224no—
259D4—1222no—
260D4—4884no—
261D4—2442no—
262D4C2×D24412yes—
263C2×C4—21no—
264C2×C4—24no—
265C2×C4—22no—
266C2×C4—612no—
267C2×C4—1228no—
268C2×C4—1222no—
269C2×C4—1222no—
270C2×C4C2×D24412yes—
271C2×C4D4×D6112yes—
272C2×C4D4×D6111yescharacteristic
273C2×C4C23×D6111yescharacteristic
274C8—22no—
275C8—1222no—
276C22—22no—
277C22—22no—
278C22—42no—
279C22—1224no—
280C22—1222no—
281C22—1224no—
282C22—4884no—
283C22—4884no—
284C22—4888no—
285C22—2442no—
286C22—2444no—
287C22—2444no—
288C22#1451974712yes—
289C22C2×D4×D6111yescharacteristic
290C4—22no—
291C4—42no—
292C4—1222no—
293C4#1451974712yes—
294C4C2×D4×D6111yescharacteristic
295C4C22×D24411yescharacteristic
296C2—22no—
297C2—42no—
298C2—4882no—
299C2—2442no—
300C2—2444no—
301C2C2×#1451974711yescharacteristic
302C2#1684056412yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#416C2
socleC22×C61C22×D4
hypercenter#416D61
hypocenterC61#3008
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. C2×#14519823C2semidirect
2. C2×#14519802C2semidirect
3. C22×D488C2semidirect
4. #16840331C2semidirect
5. #16839910C2semidirect
6. #16839897C2semidirect
7. #16839766C2semidirect
8. #16839728C2semidirect
9. C61×#416C2semidirect
12. C2×#11758226C22semidirect
17. C22×D244C22semidirect
19. C2×D4×D61C22semidirect
21. C2×#11758201C22semidirect
23. C2×D488C22semidirect
24. C2×#11758199C22semidirect
25. C2×#11758194C22semidirect
28. #14519752C22semidirect
30. #14519697C22semidirect
31. #14519689C22semidirect
33. C22×C8×C61C22semidirect
34. #117×C61C22semidirect
35. #103×C61C22semidirect
36. #102×C61C22semidirect
41. #41×C61D4semidirect
66. C2×D244D4semidirect
159. #416D61semidirect
161. C61#3008semidirect
179. C22×C8C2×D61semidirect
184. #117C2×D61semidirect
185. #103C2×D61semidirect
187. #102C2×D61semidirect
198. #41D244semidirect