Finite Group Databasebeta

← #21457440

Subgroups — #21457440

Order 7808.

556 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 556 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×#14519804C212yesmaximal, complemented
2#16840434C211yesmaximal, characteristic, complemented
3D4×D244C211yesmaximal, characteristic, complemented
4#16840139C211yesmaximal, characteristic, complemented
5#16840016C212yesmaximal, complemented
6#16839962C211yesmaximal, characteristic, complemented
7#16839957C211yesmaximal, characteristic, complemented
8#16839910C212yesmaximal, complemented
9#16839897C212yesmaximal, complemented
10#16839841C211yesmaximal, characteristic, complemented
11C4×SD16×C61C211yesmaximal, characteristic, complemented
12C2×#11758226C2212yescomplemented
13C22×D244—21no—
14C2×D4×D61C2212yes—
15#14519804—28no—
16C2×#11758201C2212yescomplemented
17C2×D488C2212yescomplemented
18C2×D488C2212yescomplemented
19C2×#11758199C2212yes—
20C2×#11758189C2212yescomplemented
21#14519774—21no—
22#14519774C2211yescharacteristic
23#14519774C2211yescharacteristic, complemented
24#14519752—22no—
25#14519752C2212yes—
26#14519752C2212yescomplemented
27#14519751—21no—
28#14519747—22no—
29C4×D244—21no—
30C4×D244C2211yescharacteristic
31C4⋊#92418C2211yescharacteristic, complemented
32#14519697C2212yescomplemented
33#14519697C2212yescomplemented
34#14519689C2212yescomplemented
35C2×SD16×C61C2211yescharacteristic
36C4×Q8×C61C2211yescharacteristic, complemented
37C4×D4×C61C2211yescharacteristic
38#106×C61C2211yescharacteristic, complemented
39#103×C61C2211yescharacteristic, complemented
40#102×C61C2211yescharacteristic
41C4×C8×C61C2211yescharacteristic, complemented
42C23×D61—22no—
43C2×Q8×C61C2311yescharacteristic
44C2×D4×C61C2311yescharacteristic
45C22×C4×C61—21no—
46C2×C22⋊D61—22no—
47#11758226—24no—
48#11758226—42no—
49D4×D61—24no—
50D4×D61—42no—
51C2×D244—22no—
52C2×D244—22no—
53C2×D244—21no—
54C2×D244—21no—
55C2×D244—22no—
56C2×D244—21no—
57C2×D244—21no—
58C2×D244—44no—
59C2×D244D411yescharacteristic
60C2×D244C2312yes—
61C2×D244C2312yes—
62C2×C4×D61—22no—
63C2×C4×D61C2312yes—
64SD16×C61D414yescomplemented
65C2×C8×C61C2311yescharacteristic
66C2×C8×C61C2311yescharacteristic
67C4⋊C4×C61—21no—
68C4⋊C4×C61C2311yescharacteristic
69C4⋊C4×C61C2311yescharacteristic
70C22⋊C4×C61—21no—
71C42×C61—21no—
72C42×C61C2311yescharacteristic
73#11758201—24no—
74#11758199—24no—
75#11758198—22no—
76#11758198—22no—
77#11758198D412yes—
78C4⋊Dic61D411yescharacteristic
79C2×#92418C2312yes—
80D488—24no—
81D488—42no—
82#11758189—24no—
83C23×C61—21no—
84C22×D61—22no—
85C22×D61—22no—
86C22×D61—44no—
87C22×D61—44no—
88C22×D61—82no—
89C22×D61C2×D412yes—
90Q8×C61—21no—
91Q8×C61C2×D412yescomplemented
92D4×C61—21no—
93D4×C61C2×D412yes—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—42no—
98C2×C4×C61C2×D411yescharacteristic
99C2×C4×C61C2×D411yescharacteristic
100C2×C4×C61C2411yescharacteristic
101C22⋊D61—44no—
102C2×Dic61C2×D412yes—
103D244—22no—
104D244—22no—
105D244—22no—
106D244—22no—
107D244—22no—
108D244—44no—
109D244—44no—
110D244—42no—
111D244—42no—
112D244—81no—
113D244—81no—
114D244—82no—
115C4×D61—22no—
116C4×D61—22no—
117C4×D61—44no—
118C8×C61—21no—
119C8×C61C2×D412yescomplemented
120#92418—22no—
121C22×C61—22no—
122C22×C61—41no—
123C22×C61—41no—
124C22×C61C22×D411yescharacteristic
125C2×D61—22no—
126C2×D61—22no—
127C2×D61—22no—
128C2×D61—42no—
129C2×D61—42no—
130C2×D61—42no—
131C2×D61—42no—
132C2×D61—42no—
133C2×D61—42no—
134C2×D61—88no—
135C4×C61—22no—
136C4×C61—21no—
137C4×C61—41no—
138C4×C61—41no—
139C4×C61AGL(1,ℤ/8)12yescomplemented
140C4×C61C22×D411yescharacteristic
141C4×C61H(5,𝔽2)11yescharacteristic
142Dic61—22no—
143#3274—611nomaximal, Sylow
144C2×C61—42no—
145C2×C61D4211yescharacteristic
146C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
147C2×C61#57611yescharacteristic
148D61—42no—
149D61—82no—
150D61—82no—
151C2×AGL(1,ℤ/8)—612no—
152#550—611no—
153D42—611no—
154#493—611no—
155#469—612no—
156#460—611no—
157#459—611no—
158#449—612no—
159#447—612no—
160C4×SD16D6111yescharacteristic, complemented
161#436—611no—
162C61#327411yescharacteristic, complemented, Sylow
163C2×#41—612no—
164C22×D4—612no—
165C22×D4—1221no—
166AGL(1,ℤ/8)—1228no—
167C2×SD16—612no—
168C2×SD16C2×D6111yescharacteristic
169C2×D8—612no—
170C2×D8—612no—
171C2×D8—612no—
172C2×M16—612no—
173#127—611no—
174#127—611no—
175#127—1221no—
176#121—612no—
177#121—612no—
178#121—1222no—
179#121—1221no—
180#120—1222no—
181C4×Q8C2×D6111yescharacteristic, complemented
182C4×D4—611no—
183C4×D4—1221no—
184C4×D4C2×D6111yescharacteristic
185#106C2×D6111yescharacteristic, complemented
186C4⋊C8—611no—
187#103C2×D6111yescharacteristic, complemented
188#102—612no—
189#102—612no—
190#102C2×D6111yescharacteristic
191C22⋊C8—612no—
192C4×C8C2×D6111yescharacteristic, complemented
193C24—1222no—
194#41—1224no—
195#41—2442no—
196C2×Q8C22×D6111yescharacteristic
197C2×D4—611no—
198C2×D4—612no—
199C2×D4—612no—
200C2×D4—1222no—
201C2×D4—1222no—
202C2×D4—1222no—
203C2×D4—1222no—
204C2×D4—1224no—
205C2×D4—1221no—
206C2×D4—1221no—
207C2×D4—1221no—
208C2×D4—1221no—
209C2×D4—2444no—
210C2×D4—2442no—
211C2×D4C22×D6111yescharacteristic
212C22×C4—21no—
213C22×C4—612no—
214C22×C4—1222no—
215SD16—1224no—
216SD16D24414yescomplemented
217D8—1224no—
218D8—1224no—
219D8—2442no—
220M16—1224no—
221C2×C8—612no—
222C2×C8C22×D6111yescharacteristic
223C2×C8C22×D6111yescharacteristic
224C4⋊C4—21no—
225C4⋊C4—611no—
226C4⋊C4C22×D6111yescharacteristic
227C4⋊C4C22×D6111yescharacteristic
228C22⋊C4—21no—
229C22⋊C4—612no—
230C22⋊C4—1222no—
231C22⋊C4—1222no—
232C42—21no—
233C42C22×D6111yescharacteristic
234C23—21no—
235C23—612no—
236C23—1222no—
237C23—1222no—
238C23—4882no—
239C23—2444no—
240C23—2444no—
241Q8—21no—
242Q8C2×D24412yescomplemented
243D4—21no—
244D4—1222no—
245D4—1222no—
246D4—1222no—
247D4—1222no—
248D4—1222no—
249D4—4881no—
250D4—4881no—
251D4—4882no—
252D4—2444no—
253D4—2444no—
254D4—2444no—
255D4—2442no—
256D4—2442no—
257D4C2×D24412yes—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—42no—
262C2×C4—612no—
263C2×C4—1222no—
264C2×C4—1222no—
265C2×C4—2444no—
266C2×C4D4×D6111yescharacteristic
267C2×C4D4×D6111yescharacteristic
268C2×C4C23×D6111yescharacteristic
269C8—21no—
270C8—1222no—
271C8C2×D24412yescomplemented
272C22—22no—
273C22—41no—
274C22—41no—
275C22—1222no—
276C22—1222no—
277C22—1222no—
278C22—4888no—
279C22—2442no—
280C22—2442no—
281C22—2442no—
282C22—2442no—
283C22—2442no—
284C22—2442no—
285C22C2×D4×D6111yescharacteristic
286C4—21no—
287C4—22no—
288C4—41no—
289C4—41no—
290C4—1222no—
291C4#1451980412yescomplemented
292C4C22×D24411yescharacteristic
293C4#1451982311yescharacteristic
294C2—42no—
295C2—4882no—
296C2—4882no—
297C2—2442no—
298C2D4×D24411yescharacteristic
299C2C2×#1451980411yescharacteristic
300C2#1684056411yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC4×SD16×C61C2
socleC22×C61C22×D4
hypercenterC4×SD16D61
hypocenterC61#3274
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#14519804C2semidirect
2. #16840434C2semidirect
3. D4×D244C2semidirect
4. #16840139C2semidirect
5. #16840016C2semidirect
6. #16839962C2semidirect
7. #16839957C2semidirect
8. #16839910C2semidirect
9. #16839897C2semidirect
10. #16839841C2semidirect
11. C4×SD16×C61C2semidirect
12. C2×#11758226C22semidirect
16. C2×#11758201C22semidirect
17. C2×D488C22semidirect
18. C2×D488C22semidirect
20. C2×#11758189C22semidirect
23. #14519774C22semidirect
26. #14519752C22semidirect
31. C4⋊#92418C22semidirect
32. #14519697C22semidirect
33. #14519697C22semidirect
34. #14519689C22semidirect
36. C4×Q8×C61C22semidirect
38. #106×C61C22semidirect
39. #103×C61C22semidirect
41. C4×C8×C61C22semidirect
64. SD16×C61D4semidirect
91. Q8×C61C2×D4semidirect
119. C8×C61C2×D4semidirect
139. C4×C61AGL(1,ℤ/8)semidirect
160. C4×SD16D61semidirect
162. C61#3274semidirect
181. C4×Q8C2×D61semidirect
185. #106C2×D61semidirect
187. #103C2×D61semidirect
192. C4×C8C2×D61semidirect
216. SD16D244semidirect
242. Q8C2×D244semidirect
271. C8C2×D244semidirect
291. C4#14519804semidirect