Finite Group Databasebeta

← #21455294

Subgroups — #21455294

Order 7808.

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

normal subgroups only

This group has 584 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×#14519801C212yesmaximal, complemented
2#127×D61C211yesmaximal, characteristic, complemented
3C4×#11758224C211yesmaximal, characteristic, complemented
4#16839963C211yesmaximal, characteristic, complemented
5#16839961C212yesmaximal, complemented
6#16839959C211yesmaximal, characteristic, complemented
7#16839957C211yesmaximal, characteristic, complemented
8#16839955C212yesmaximal, complemented
9#16839784C211yesmaximal, characteristic, complemented
10#16839765C212yesmaximal, complemented
11C61×#459C211yesmaximal, characteristic, complemented
12C2×#11758224C2211yescharacteristic
13C2×D4×D61—21no—
14C2×D4×D61—21no—
15C2×D4×D61C2212yes—
16#14519801—28no—
17C2×#11758190C2212yescomplemented
18C2×#11758200C2212yescomplemented
19C2×#11758199C2212yescomplemented
20C2×#11758189C2212yes—
21#14519774C2211yescharacteristic
22#14519773—21no—
23#14519773—21no—
24#14519773C2212yes—
25C4×Dic122C2211yescharacteristic, complemented
26#14519742C2211yescharacteristic, complemented
27D4×Dic61C2211yescharacteristic, complemented
28C4×C22⋊D61—21no—
29#14519737—21no—
30#14519735C2211yescharacteristic
31#14519733—21no—
32C2×C4×Dic61—21no—
33C42×D61C2211yescharacteristic
34C4⋊#92418C2211yescharacteristic, complemented
35#14519706C2212yescomplemented
36#14519699C2212yescomplemented
37#14519698C2212yescomplemented
38#14519697C2212yescomplemented
39C2×D8×C61C2212yescomplemented
40#127×C61C2211yescharacteristic
41C4×D4×C61C2211yescharacteristic, complemented
42C4⋊C8×C61C2211yescharacteristic, complemented
43#102×C61C2212yescomplemented
44C23×D61—22no—
45C2×D4×C61—21no—
46C2×D4×C61—21no—
47C2×D4×C61C2312yes—
48C2×D4×C61C2311yescharacteristic
49C22×C4×C61—21no—
50C2×C22⋊D61—21no—
51C2×C22⋊D61—22no—
52C2×C22⋊D61—22no—
53C2×C22⋊D61—22no—
54C22×Dic61—21no—
55C22×Dic61—21no—
56#11758224—22no—
57#11758224D414yescomplemented
58D4×D61—24no—
59D4×D61—24no—
60D4×D61—44no—
61D4×D61—44no—
62C2×D244—21no—
63C2×D244—21no—
64C2×D244C2312yes—
65C2×C4×D61D411yescharacteristic
66C2×C4×D61D411yescharacteristic
67C2×C4×D61C2311yescharacteristic
68C2×Dic122C2311yescharacteristic
69D8×C61—24no—
70C2×C8×C61C2312yes—
71C4⋊C4×C61C2311yescharacteristic
72C22⋊C4×C61—21no—
73C42×C61C2311yescharacteristic
74C22⋊Dic61—21no—
75#11758200—24no—
76#11758199—24no—
77#11758198—21no—
78C4⋊Dic61C2311yescharacteristic
79#11758196—21no—
80#11758196—21no—
81C4×Dic61—21no—
82C4×Dic61—21no—
83C4×Dic61—21no—
84C4×Dic61D411yescharacteristic
85C4×Dic61D411yescharacteristic
86C4×Dic61C2311yescharacteristic
87C2×#92418C2312yes—
88#11758190—24no—
89#11758189—24no—
90C23×C61—21no—
91C23×C61—22no—
92C22×D61—22no—
93C22×D61—44no—
94C22×D61—44no—
95C22×D61—44no—
96C22×D61C2×D411yescharacteristic
97D4×C61—22no—
98D4×C61—21no—
99D4×C61—22no—
100D4×C61—42no—
101D4×C61—42no—
102D4×C61C2×D412yescomplemented
103C2×C4×C61—21no—
104C2×C4×C61—42no—
105C2×C4×C61C2×D411yescharacteristic
106C2×C4×C61C2×D411yescharacteristic
107C2×C4×C61C2411yescharacteristic
108C22⋊D61—24no—
109C22⋊D61—44no—
110C22⋊D61—44no—
111C22⋊D61—44no—
112C2×Dic61—21no—
113C2×Dic61—24no—
114C2×Dic61—21no—
115C2×Dic61—42no—
116C2×Dic61C2×D411yescharacteristic
117C2×Dic61C2×D411yescharacteristic
118C2×Dic61C2×D411yescharacteristic
119D244—22no—
120D244—22no—
121D244—42no—
122D244—42no—
123C4×D61—22no—
124C4×D61—22no—
125C4×D61C2×D412yes—
126C4×D61#4112yes—
127Dic122—21no—
128Dic122C2×D412yescomplemented
129C8×C61—22no—
130#92418—22no—
131C22×C61—22no—
132C22×C61—41no—
133C22×C61—41no—
134C22×C61—42no—
135C22×C61—42no—
136C22×C61—42no—
137C22×C61C22×D411yescharacteristic
138C2×D61—21no—
139C2×D61—21no—
140C2×D61—42no—
141C2×D61—42no—
142C2×D61—42no—
143C2×D61—88no—
144C2×D61#12112yes—
145C4×C61—21no—
146C4×C61—41no—
147C4×C61AGL(1,ℤ/8)12yescomplemented
148C4×C61C22×D411yescharacteristic
149C4×C61C2×#4111yescharacteristic
150Dic61—22no—
151Dic61—21no—
152Dic61—41no—
153Dic61#12112yes—
154Dic61AGL(1,ℤ/8)12yescomplemented
155#3038—611nomaximal, Sylow
156C2×C61—42no—
157C2×C61—82no—
158C2×C61C2×#12111yescharacteristic
159C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
160C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
161D61—22no—
162D61—82no—
163C2×AGL(1,ℤ/8)—612no—
164C2×#127—611no—
165C4×#41—611no—
166#460—611no—
167#460—611no—
168#460—612no—
169#459—612no—
170#459—611no—
171#459D6111yescharacteristic, complemented
172#423—611no—
173#418—612no—
174C61#303811yescharacteristic, complemented, Sylow
175C2×#41—611no—
176C22×D4—612no—
177C22×D4—1221no—
178C22×D4—1221no—
179AGL(1,ℤ/8)—1228no—
180C2×SD16—612no—
181C2×SD16—612no—
182C2×D8—612no—
183C2×D8C2×D6112yescomplemented
184C2×M16—612no—
185#127—612no—
186#127—611no—
187#127—1221no—
188#127—1221no—
189#127C2×D6111yescharacteristic
190C4×Q8—611no—
191C4×Q8—611no—
192C4×D4—611no—
193C4×D4—1221no—
194C4×D4—1221no—
195C4×D4C2×D6111yescharacteristic, complemented
196#117—611no—
197#117—1221no—
198C2×C42—611no—
199C2×C42—1221no—
200C4⋊C8—612no—
201C4⋊C8—611no—
202C4⋊C8C2×D6111yescharacteristic, complemented
203#102—612no—
204#102—612no—
205#102—612no—
206#102C2×D6112yescomplemented
207C24—1222no—
208#41—614no—
209#41—1222no—
210C2×Q8—611no—
211C2×D4—21no—
212C2×D4—21no—
213C2×D4—612no—
214C2×D4—1224no—
215C2×D4—1224no—
216C2×D4—1222no—
217C2×D4—1222no—
218C2×D4—1222no—
219C2×D4—1221no—
220C2×D4—1221no—
221C2×D4—1221no—
222C2×D4—2444no—
223C2×D4—2444no—
224C2×D4C22×D6112yes—
225C2×D4C22×D6111yescharacteristic
226C22×C4—21no—
227C22×C4—611no—
228C22×C4—611no—
229C22×C4—611no—
230C22×C4—1221no—
231C22×C4—1221no—
232SD16—1224no—
233SD16—1224no—
234D8—24no—
235D8—1224no—
236M16—1224no—
237C2×C8—612no—
238C2×C8C22×D6112yes—
239C4⋊C4—611no—
240C4⋊C4—1221no—
241C4⋊C4—1221no—
242C4⋊C4C22×D6111yescharacteristic
243C22⋊C4—21no—
244C22⋊C4—1221no—
245C22⋊C4—1221no—
246C42—611no—
247C42—611no—
248C42—611no—
249C42—1221no—
250C42—1221no—
251C42—1221no—
252C42C22×D6111yescharacteristic
253C23—21no—
254C23—22no—
255C23—611no—
256C23—1222no—
257C23—2444no—
258C23—2444no—
259C23—2444no—
260Q8—612no—
261Q8—1221no—
262D4—22no—
263D4—21no—
264D4—22no—
265D4—42no—
266D4—42no—
267D4—1224no—
268D4—1222no—
269D4—1222no—
270D4—2442no—
271D4—2444no—
272D4—2444no—
273D4—2444no—
274D4—2442no—
275D4D4×D6112yescomplemented
276C2×C4—21no—
277C2×C4—42no—
278C2×C4—611no—
279C2×C4—611no—
280C2×C4—612no—
281C2×C4—612no—
282C2×C4—611no—
283C2×C4—1222no—
284C2×C4—1224no—
285C2×C4—1221no—
286C2×C4—1222no—
287C2×C4—1221no—
288C2×C4—2442no—
289C2×C4D4×D6111yescharacteristic
290C2×C4D4×D6111yescharacteristic
291C2×C4C23×D6111yescharacteristic
292C8—22no—
293C8—1222no—
294C22—22no—
295C22—41no—
296C22—41no—
297C22—42no—
298C22—42no—
299C22—42no—
300C22—612no—
301C22—1221no—
302C22—1221no—
303C22—4888no—
304C22—2442no—
305C22—2442no—
306C22—2442no—
307C22C2×D4×D6111yescharacteristic
308C4—21no—
309C4—41no—
310C4—612no—
311C4—612no—
312C4—1222no—
313C4—1221no—
314C4—2441no—
315C4#1451980112yescomplemented
316C4C2×D4×D6111yescharacteristic
317C4#41×D6111yescharacteristic
318C2—42no—
319C2—82no—
320C2—1222no—
321C2—4882no—
322C2#121×D6111yescharacteristic
323C2AGL(1,ℤ/8)×D6111yescharacteristic
324C2C2×#1451980111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#459C2
socleC22×C61C22×D4
hypercenter#459D61
hypocenterC61#3038
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#14519801C2semidirect
2. #127×D61C2semidirect
3. C4×#11758224C2semidirect
4. #16839963C2semidirect
5. #16839961C2semidirect
6. #16839959C2semidirect
7. #16839957C2semidirect
8. #16839955C2semidirect
9. #16839784C2semidirect
10. #16839765C2semidirect
11. C61×#459C2semidirect
17. C2×#11758190C22semidirect
18. C2×#11758200C22semidirect
19. C2×#11758199C22semidirect
25. C4×Dic122C22semidirect
26. #14519742C22semidirect
27. D4×Dic61C22semidirect
34. C4⋊#92418C22semidirect
35. #14519706C22semidirect
36. #14519699C22semidirect
37. #14519698C22semidirect
38. #14519697C22semidirect
39. C2×D8×C61C22semidirect
41. C4×D4×C61C22semidirect
42. C4⋊C8×C61C22semidirect
43. #102×C61C22semidirect
57. #11758224D4semidirect
102. D4×C61C2×D4semidirect
128. Dic122C2×D4semidirect
147. C4×C61AGL(1,ℤ/8)semidirect
154. Dic61AGL(1,ℤ/8)semidirect
171. #459D61semidirect
174. C61#3038semidirect
183. C2×D8C2×D61semidirect
195. C4×D4C2×D61semidirect
202. C4⋊C8C2×D61semidirect
206. #102C2×D61semidirect
275. D4D4×D61semidirect
315. C4#14519801semidirect