Finite Group Databasebeta

← #21457435

Subgroups — #21457435

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×#14519803C212yesmaximal, complemented
2#16840433C211yesmaximal, characteristic, complemented
3#16840138C211yesmaximal, characteristic, complemented
4#16840013C212yesmaximal, complemented
5#16839959C211yesmaximal, characteristic, complemented
6#16839957C211yesmaximal, characteristic, complemented
7#16839905C212yesmaximal, complemented
8#16839896C212yesmaximal, complemented
9C4×#11758200C211yesmaximal, characteristic, complemented
10#16839840C211yesmaximal, characteristic, complemented
11D42×C61C211yesmaximal, characteristic, complemented
12C2×#11758222C2212yescomplemented
13#14519803—28no—
14C2×#11758200C2211yescharacteristic
15C2×#11758200C2212yescomplemented
16C2×#11758199C2212yes—
17C2×#11758199C2212yescomplemented
18C2×#11758199C2212yescomplemented
19C2×#11758194C2212yescomplemented
20#14519774C2211yescharacteristic, complemented
21#14519773—21no—
22#14519751C2212yescomplemented
23#14519750—22no—
24C4×Dic122C2211yescharacteristic, complemented
25#14519739—21no—
26#14519708C2211yescharacteristic, complemented
27C4⋊#92418C2211yescharacteristic, complemented
28#14519700C2211yescharacteristic, complemented
29#14519698C2211yescharacteristic
30#14519698C2212yescomplemented
31#14519697C2212yescomplemented
32C22⋊#92418C2212yescomplemented
33C4×#92418C2211yescharacteristic, complemented
34C22×D4×C61—21no—
35C22×D4×C61C2212yes—
36#127×C61C2211yescharacteristic
37#121×C61—21no—
38#121×C61C2212yes—
39#120×C61—22no—
40C4×D4×C61C2211yescharacteristic
41C4×D4×C61C2211yescharacteristic
42C24×C61—22no—
43C2×D4×C61—24no—
44C2×D4×C61—22no—
45C2×D4×C61—22no—
46C2×D4×C61—21no—
47C2×D4×C61—21no—
48C2×D4×C61—42no—
49C2×D4×C61—44no—
50C2×D4×C61D411yescharacteristic
51C2×D4×C61C2312yes—
52C2×D4×C61C2311yescharacteristic
53C22×C4×C61—21no—
54C22×C4×C61C2312yes—
55C2×C22⋊D61—22no—
56C2×C22⋊D61—22no—
57#11758222—24no—
58#11758222—42no—
59C2×D244—21no—
60C2×D244—21no—
61C2×D244C2312yes—
62C2×C4×D61—22no—
63C2×Dic122C2311yescharacteristic
64C4⋊C4×C61D411yescharacteristic
65C4⋊C4×C61C2311yescharacteristic
66C22⋊C4×C61—21no—
67C22⋊C4×C61—22no—
68C22⋊C4×C61D412yes—
69C42×C61C2311yescharacteristic
70#11758200—24no—
71#11758200D414yescomplemented
72#11758199—24no—
73#11758199—24no—
74#11758199—42no—
75#11758198—22no—
76C4⋊Dic61C2311yescharacteristic
77#11758196—21no—
78C4×Dic61—21no—
79#11758194—24no—
80C2×#92418C2311yescharacteristic
81C2×#92418C2312yes—
82C2×#92418C2311yescharacteristic
83C23×C61—21no—
84C23×C61—22no—
85C23×C61—44no—
86C23×C61—44no—
87C23×C61—82no—
88C23×C61C2×D412yes—
89C22×D61—22no—
90D4×C61—22no—
91D4×C61—22no—
92D4×C61—21no—
93D4×C61—22no—
94D4×C61—44no—
95D4×C61—44no—
96D4×C61—42no—
97D4×C61—81no—
98D4×C61C2×D412yes—
99C2×C4×C61—22no—
100C2×C4×C61—22no—
101C2×C4×C61—21no—
102C2×C4×C61—42no—
103C2×C4×C61C2×D411yescharacteristic
104C2×C4×C61C2×D412yes—
105C2×C4×C61C2×D411yescharacteristic
106C2×C4×C61C2411yescharacteristic
107C22⋊D61—44no—
108C22⋊D61—82no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111D244—22no—
112D244—22no—
113D244—42no—
114D244—81no—
115C4×D61—44no—
116Dic122—21no—
117Dic122C2×D412yescomplemented
118#92418—22no—
119#92418—21no—
120#92418C2×D412yescomplemented
121C22×C61—22no—
122C22×C61—22no—
123C22×C61—22no—
124C22×C61—22no—
125C22×C61—41no—
126C22×C61—41no—
127C22×C61—42no—
128C22×C61—42no—
129C22×C61—42no—
130C22×C61—88no—
131C22×C61C22×D411yescharacteristic
132C2×D61—42no—
133C2×D61—42no—
134C2×D61—42no—
135C4×C61—22no—
136C4×C61—21no—
137C4×C61—41no—
138C4×C61AGL(1,ℤ/8)12yescomplemented
139C4×C61C22×D411yescharacteristic
140C4×C61H(5,𝔽2)11yescharacteristic
141Dic61—22no—
142Dic61—41no—
143#3274—611nomaximal, Sylow
144C2×C61—42no—
145C2×C61—42no—
146C2×C61—82no—
147C2×C61D4211yescharacteristic
148C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
149C2×C61#57611yescharacteristic
150D61—82no—
151C2×AGL(1,ℤ/8)—612no—
152#550—611no—
153D42D6111yescharacteristic, complemented
154#493—611no—
155#469—612no—
156#460—611no—
157#459—611no—
158#449—612no—
159#447—612no—
160C4×SD16—611no—
161#436—611no—
162C61#327411yescharacteristic, complemented, Sylow
163C2×#41—612no—
164C22×D4—21no—
165C22×D4C2×D6112yes—
166AGL(1,ℤ/8)—1228no—
167C2×SD16—611no—
168C2×SD16—612no—
169C2×D8—612no—
170C2×D8—612no—
171C2×D8—612no—
172C2×M16—612no—
173#127—611no—
174#127—1221no—
175#127C2×D6111yescharacteristic
176#121—21no—
177#121—612no—
178#121—1222no—
179#121C2×D6112yes—
180#120—22no—
181C4×Q8—611no—
182C4×D4—1221no—
183C4×D4C2×D6111yescharacteristic
184C4×D4C2×D6111yescharacteristic
185#106—611no—
186C4⋊C8—611no—
187#103—611no—
188#102—611no—
189#102—612no—
190#102—612no—
191C22⋊C8—612no—
192C4×C8—611no—
193C24—22no—
194#41—1224no—
195#41—2442no—
196C2×Q8—611no—
197C2×D4—24no—
198C2×D4—22no—
199C2×D4—22no—
200C2×D4—21no—
201C2×D4—21no—
202C2×D4—42no—
203C2×D4—44no—
204C2×D4—612no—
205C2×D4—1222no—
206C2×D4—1222no—
207C2×D4—1221no—
208C2×D4—1221no—
209C2×D4C22⋊D6111yescharacteristic
210C2×D4C22×D6112yes—
211C2×D4C22×D6111yescharacteristic
212C22×C4—21no—
213C22×C4—1222no—
214C22×C4C22×D6112yes—
215SD16—614no—
216SD16—1224no—
217D8—1224no—
218D8—1224no—
219D8—2442no—
220M16—1224no—
221C2×C8—611no—
222C2×C8—611no—
223C2×C8—612no—
224C4⋊C4—611no—
225C4⋊C4—1221no—
226C4⋊C4C22⋊D6111yescharacteristic
227C4⋊C4C22×D6111yescharacteristic
228C22⋊C4—21no—
229C22⋊C4—22no—
230C22⋊C4—1222no—
231C22⋊C4C22⋊D6112yes—
232C42—1221no—
233C42C22×D6111yescharacteristic
234C23—21no—
235C23—22no—
236C23—44no—
237C23—44no—
238C23—82no—
239C23—1222no—
240C23C2×C22⋊D6112yes—
241Q8—612no—
242Q8—1221no—
243D4—22no—
244D4—21no—
245D4—22no—
246D4—22no—
247D4—44no—
248D4—44no—
249D4—42no—
250D4—81no—
251D4—1222no—
252D4—1222no—
253D4—4881no—
254D4—4882no—
255D4—2444no—
256D4—2442no—
257D4D4×D6112yes—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—42no—
262C2×C4—1221no—
263C2×C4—1221no—
264C2×C4—2444no—
265C2×C4C2×C22⋊D6111yescharacteristic
266C2×C4C2×C22⋊D6112yes—
267C2×C4C2×C22⋊D6111yescharacteristic
268C2×C4C23×D6111yescharacteristic
269C8—612no—
270C8—1222no—
271C8—1221no—
272C22—22no—
273C22—22no—
274C22—22no—
275C22—22no—
276C22—41no—
277C22—41no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—88no—
282C22—2442no—
283C22—2442no—
284C22—2442no—
285C22C22×C22⋊D6111yescharacteristic
286C4—21no—
287C4—22no—
288C4—41no—
289C4—1222no—
290C4—2441no—
291C4#1451980312yescomplemented
292C4C2×D4×D6111yescharacteristic
293C4#1451982211yescharacteristic
294C2—42no—
295C2—42no—
296C2—82no—
297C2—4882no—
298C2D4×C22⋊D6111yescharacteristic
299C2C2×#1451980311yescharacteristic
300C2#1684056511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingD42×C61C2
socleC22×C61C22×D4
hypercenterD42D61
hypocenterC61#3274
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C2×#14519803C2semidirect
2. #16840433C2semidirect
3. #16840138C2semidirect
4. #16840013C2semidirect
5. #16839959C2semidirect
6. #16839957C2semidirect
7. #16839905C2semidirect
8. #16839896C2semidirect
9. C4×#11758200C2semidirect
10. #16839840C2semidirect
11. D42×C61C2semidirect
12. C2×#11758222C22semidirect
15. C2×#11758200C22semidirect
17. C2×#11758199C22semidirect
18. C2×#11758199C22semidirect
19. C2×#11758194C22semidirect
20. #14519774C22semidirect
22. #14519751C22semidirect
24. C4×Dic122C22semidirect
26. #14519708C22semidirect
27. C4⋊#92418C22semidirect
28. #14519700C22semidirect
30. #14519698C22semidirect
31. #14519697C22semidirect
32. C22⋊#92418C22semidirect
33. C4×#92418C22semidirect
71. #11758200D4semidirect
117. Dic122C2×D4semidirect
120. #92418C2×D4semidirect
138. C4×C61AGL(1,ℤ/8)semidirect
153. D42D61semidirect
162. C61#3274semidirect
291. C4#14519803semidirect