Finite Group Databasebeta

← #21457600

Subgroups — #21457600

Order 7808.

454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 117 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
1#16840579C211yesmaximal, characteristic, complemented
2#16840572C212yesmaximal, complemented
3#16840563C211yesmaximal, characteristic, complemented
4#16840145C211yesmaximal, characteristic, complemented
5#16840038C211yesmaximal, characteristic, complemented
6#16840024C212yesmaximal, complemented
7#16839942C212yesmaximal, complemented
8#16839933C212yesmaximal, complemented
9#16839878C211yesmaximal, characteristic, complemented
10#16839877C211yesmaximal, characteristic, complemented
11C61×#472C211yesmaximal, characteristic, complemented
12#14519824C2212yescomplemented
13#14519822C2212yes—
14#14519810—22no—
15#14519810C2212yes—
16#14519810C2212yescomplemented
17#14519806—22no—
18#14519803C2212yes—
19#14519801—22no—
20#14519801—22no—
21#14519799—21no—
22#14519799C2211yescharacteristic
23#14519797C2211yescharacteristic
24#14519796—22no—
25#14519796—21no—
26C2×Dic244—21no—
27C2×Dic244C2211yescharacteristic, complemented
28C2×#11758200C2212yescomplemented
29SD16×D61—22no—
30D8×D61—21no—
31#14519785C2212yescomplemented
32#14519783C2211yescharacteristic
33#14519764C2212yescomplemented
34#14519712C2211yescharacteristic, complemented
35#14519704C2211yescharacteristic, complemented
36#14519703C2211yescharacteristic
37#14519703C2212yescomplemented
38#14519695C2212yescomplemented
39C8×Dic61C2211yescharacteristic, complemented
40AGL(1,ℤ/8)×C61C2212yescomplemented
41C2×D8×C61C2211yescharacteristic
42#131×C61C2211yescharacteristic, complemented
43#108×C61C2211yescharacteristic, complemented
44#100×C61C2212yescomplemented
45#41×C61C2311yescharacteristic
46C2×D4×C61C2312yes—
47C2×C22⋊D61—42no—
48Q8×D61—22no—
49#11758224—22no—
50#11758224—22no—
51#11758224—22no—
52#11758224—42no—
53D4×D61—22no—
54D4×D61—22no—
55#11758222—22no—
56#11758222C2311yescharacteristic
57#11758222C2312yes—
58C2×Dic122—22no—
59C2×Dic122C2312yes—
60SD16×C61—22no—
61D8×C61—22no—
62D8×C61—21no—
63D8×C61—21no—
64M16×C61—21no—
65M16×C61C2312yes—
66M16×C61C2311yescharacteristic
67C2×C8×C61—21no—
68C2×C8×C61C2311yescharacteristic
69C22⋊Dic61—42no—
70#11758202D411yescharacteristic
71#11758201D411yescharacteristic
72#11758200—22no—
73#11758200—22no—
74#11758200—22no—
75#11758200D411yescharacteristic
76#11758199—22no—
77#11758199D411yescharacteristic
78C4×Dic61C2311yescharacteristic
79#11758194C2311yescharacteristic
80C2×#92418C2311yescharacteristic
81Dic244—22no—
82Dic244—22no—
83Dic244—21no—
84Dic244—21no—
85Dic244D411yescharacteristic
86D488D411yescharacteristic
87#11758190—22no—
88#11758190—22no—
89#11758190D412yes—
90#11758189—21no—
91#11758189—22no—
92C8×D61—21no—
93C8×D61—22no—
94C23×C61—22no—
95C22×D61—42no—
96Q8×C61C2×D411yescharacteristic
97D4×C61—21no—
98D4×C61—22no—
99D4×C61—22no—
100D4×C61C2×D411yescharacteristic
101C2×C4×C61—21no—
102C2×C4×C61C2411yescharacteristic
103C22⋊D61—22no—
104C22⋊D61—21no—
105C22⋊D61—42no—
106C22⋊D61—42no—
107C22⋊D61—42no—
108C2×Dic61—21no—
109C2×Dic61—22no—
110C2×Dic61—42no—
111C2×Dic61—42no—
112D244C2×D411yescharacteristic
113D244C2×D412yes—
114C4×D61—21no—
115C4×D61—22no—
116C4×D61—42no—
117Dic122—22no—
118Dic122—22no—
119Dic122—42no—
120Dic122C2×D412yes—
121Dic122C2×D411yescharacteristic
122C8×C61—22no—
123C8×C61—21no—
124C8×C61C2×D411yescharacteristic
125C8×C61C2×D411yescharacteristic
126#92418—21no—
127#92418C2×D411yescharacteristic
128#92418C2×D411yescharacteristic
129C22×C61—21no—
130C22×C61—42no—
131C22×C61—82no—
132C22×C61H(5,𝔽2)11yescharacteristic
133C2×D61—22no—
134C2×D61—21no—
135C2×D61—162no—
136C4×C61—21no—
137C4×C61C22×D411yescharacteristic
138C4×C61C22×D411yescharacteristic
139Dic61—22no—
140Dic61—21no—
141Dic61—41no—
142Dic61—42no—
143#3290—611nomaximal, Sylow
144C2×C61—21no—
145C2×C61—41no—
146C2×C61—82no—
147C2×C61D4211yescharacteristic
148D61—42no—
149D61—41no—
150#578—611no—
151#577—612no—
152#576—611no—
153#495—611no—
154#473—611no—
155#472D6111yescharacteristic, complemented
156#471—612no—
157#455—612no—
158#454—612no—
159#443—611no—
160#443—611no—
161C61#329011yescharacteristic, complemented, Sylow
1622−1+4—612no—
163H(5,𝔽2)—612no—
164#137—612no—
165#137—612no—
166#137—1222no—
167#137—1222no—
168AGL(1,ℤ/8)—612no—
169AGL(1,ℤ/8)—1222no—
170AGL(1,ℤ/8)—1222no—
171AGL(1,ℤ/8)C2×D6112yescomplemented
172#135—611no—
173#135—611no—
174#135—1221no—
175#135—1222no—
176#135—1221no—
177C2×Q16—611no—
178C2×Q16—1221no—
179C2×SD16—612no—
180C2×SD16—1222no—
181C2×D8—1221no—
182C2×D8C2×D6111yescharacteristic
183#131—612no—
184#131—611no—
185#131C2×D6111yescharacteristic, complemented
186#124—612no—
187#108—611no—
188#108C2×D6111yescharacteristic, complemented
189#104—611no—
190#104—611no—
191#104—612no—
192#101—612no—
193#100C2×D6112yescomplemented
194C4×C8—611no—
195#41—612no—
196#41—611no—
197#41—1222no—
198#41—1222no—
199#41—1222no—
200#41—1222no—
201#41—2442no—
202#41C22×D6111yescharacteristic
203C2×Q8—612no—
204C2×Q8—1222no—
205C2×Q8—1222no—
206C2×D4—1222no—
207C2×D4—1222no—
208C2×D4—2442no—
209C2×D4C22×D6112yes—
210Q16—611no—
211Q16—611no—
212Q16—1222no—
213Q16—1222no—
214Q16—1221no—
215Q16—1221no—
216SD16—22no—
217SD16—611no—
218SD16—611no—
219SD16—612no—
220SD16—1222no—
221SD16—1222no—
222SD16—1222no—
223SD16—1222no—
224SD16—1222no—
225D8—22no—
226D8—21no—
227D8—21no—
228D8—611no—
229D8—611no—
230D8—1222no—
231M16—21no—
232M16—611no—
233M16—1222no—
234M16—1221no—
235M16C22×D6111yescharacteristic
236M16C22×D6112yes—
237C2×C8—21no—
238C2×C8—611no—
239C2×C8—1222no—
240C2×C8—1221no—
241C2×C8C22×D6111yescharacteristic
242C22⋊C4—2442no—
243C42—611no—
244C23—22no—
245C23—2442no—
246Q8—612no—
247Q8—611no—
248Q8—1222no—
249Q8—1222no—
250Q8—2442no—
251Q8D4×D6111yescharacteristic
252D4—21no—
253D4—22no—
254D4—22no—
255D4—612no—
256D4—611no—
257D4—1221no—
258D4—1222no—
259D4—2442no—
260D4—2442no—
261D4—2442no—
262D4D4×D6111yescharacteristic
263C2×C4—21no—
264C2×C4—1221no—
265C2×C4—1222no—
266C2×C4—1221no—
267C2×C4—1222no—
268C2×C4—2442no—
269C2×C4—2442no—
270C2×C4—2442no—
271C2×C4C23×D6111yescharacteristic
272C8—21no—
273C8—22no—
274C8—611no—
275C8—611no—
276C8—1221no—
277C8D4×D6111yescharacteristic
278C8D4×D6111yescharacteristic
279C22—21no—
280C22—42no—
281C22—82no—
282C22—1222no—
283C22—1221no—
284C22—9762no—
285C22#1451982311yescharacteristic
286C4—21no—
287C4—1221no—
288C4—1222no—
289C4—2441no—
290C4—2442no—
291C4C2×D4×D6111yescharacteristic
292C4C2×D4×D6111yescharacteristic
293C2—21no—
294C2—41no—
295C2—82no—
296C2—2441no—
297C2—2442no—
298C2#1684039611yescharacteristic
subgroupG/H
centerC2#16840396
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#472C2
socleC2×C61D42
hypercenter#472D61
hypocenterC61#3290
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #472

Complements

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

NH ≅ G/Ntype
1. #16840579C2semidirect
2. #16840572C2semidirect
3. #16840563C2semidirect
4. #16840145C2semidirect
5. #16840038C2semidirect
6. #16840024C2semidirect
7. #16839942C2semidirect
8. #16839933C2semidirect
9. #16839878C2semidirect
10. #16839877C2semidirect
11. C61×#472C2semidirect
12. #14519824C22semidirect
16. #14519810C22semidirect
27. C2×Dic244C22semidirect
28. C2×#11758200C22semidirect
31. #14519785C22semidirect
33. #14519764C22semidirect
34. #14519712C22semidirect
35. #14519704C22semidirect
37. #14519703C22semidirect
38. #14519695C22semidirect
39. C8×Dic61C22semidirect
40. AGL(1,ℤ/8)×C61C22semidirect
42. #131×C61C22semidirect
43. #108×C61C22semidirect
44. #100×C61C22semidirect
155. #472D61semidirect
161. C61#3290semidirect
171. AGL(1,ℤ/8)C2×D61semidirect
185. #131C2×D61semidirect
188. #108C2×D61semidirect
193. #100C2×D61semidirect