Finite Group Databasebeta

← #21456302

Subgroups — #21456302

Order 7808.

596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 596 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×#14519803C211yesmaximal, characteristic, complemented
2C2×#14519802C211yesmaximal, characteristic, complemented
3C2×#14519797C211yesmaximal, characteristic, complemented
4C22×#11758199C211yesmaximal, characteristic, complemented
5#16840331C211yesmaximal, characteristic, complemented
6#16840152C212yesmaximal, complemented
7#16840149C212yesmaximal, complemented
8#16840144C212yesmaximal, complemented
9#16840138C212yesmaximal, complemented
10#16839718C211yesmaximal, characteristic, complemented
11C61×#535C211yesmaximal, characteristic, complemented
12C2×#11758222C2211yescharacteristic
13C22×D244C2211yescharacteristic
14#14519803—24no—
15#14519802—24no—
16#14519797—24no—
17C2×#11758202C2211yescharacteristic, complemented
18C2×#11758200C2211yescharacteristic, complemented
19C2×#11758200C2212yescomplemented
20C2×#11758201C2211yescharacteristic, complemented
21C2×#11758201C2212yescomplemented
22C2×#11758199—24no—
23C2×#11758199C2212yes—
24C2×#11758199C2212yes—
25C2×#11758199C2211yescharacteristic, complemented
26C2×#11758199C2212yescomplemented
27C2×#11758199C2212yescomplemented
28C2×#11758194C2211yescharacteristic
29C22×#92418C2211yescharacteristic
30#14519774C2212yescomplemented
31#14519765C2212yescomplemented
32#14519752—22no—
33#14519747—22no—
34#14519688C2212yescomplemented
35C4×#92418C2212yescomplemented
36C2×#41×C61C2211yescharacteristic
37C22×D4×C61C2211yescharacteristic
38#127×C61C2212yescomplemented
39#124×C61C2212yescomplemented
40#121×C61—22no—
41#120×C61—22no—
42#117×C61C2211yescharacteristic
43C24×C61—21no—
44C23×D61—21no—
45#41×C61—22no—
46#41×C61—22no—
47C2×Q8×C61C2311yescharacteristic
48C2×D4×C61—21no—
49C2×D4×C61—22no—
50C2×D4×C61—22no—
51C2×D4×C61—21no—
52C2×D4×C61—24no—
53C2×D4×C61C2312yes—
54C2×D4×C61C2311yescharacteristic
55C22×C4×C61—21no—
56C22×C4×C61C2311yescharacteristic
57C2×C22⋊D61—21no—
58#11758222—22no—
59#11758222—22no—
60C2×D244—22no—
61C2×D244—22no—
62C2×D244—21no—
63C2×D244—24no—
64C2×D244C2312yes—
65C2×D244C2311yescharacteristic
66C2×C4×D61—21no—
67C2×Dic122C2311yescharacteristic
68C4⋊C4×C61D412yes—
69C22⋊C4×C61—24no—
70C22⋊C4×C61D412yes—
71C42×C61C2312yes—
72#11758202—22no—
73#11758201—22no—
74#11758201—24no—
75#11758200—22no—
76#11758200—24no—
77#11758199—24no—
78#11758199—24no—
79#11758199—22no—
80#11758199—24no—
81#11758199—24no—
82#11758198—24no—
83#11758194D414yescomplemented
84C2×#92418D414yescomplemented
85C2×#92418C2311yescharacteristic
86C2×#92418C2312yes—
87C2×#92418C2311yescharacteristic
88C23×C61—22no—
89C23×C61—21no—
90C23×C61—42no—
91C23×C61—82no—
92C23×C61C2×D411yescharacteristic
93C22×D61—22no—
94C22×D61—21no—
95C22×D61—42no—
96C22×D61—82no—
97Q8×C61—21no—
98Q8×C61—21no—
99D4×C61—22no—
100D4×C61—21no—
101D4×C61—22no—
102D4×C61—21no—
103D4×C61—42no—
104D4×C61—42no—
105D4×C61—84no—
106C2×C4×C61—21no—
107C2×C4×C61—42no—
108C2×C4×C61C2×D414yes—
109C2×C4×C61C2×D411yescharacteristic
110C2×C4×C61C2×D412yes—
111C2×C4×C61C2×D412yes—
112C2×C4×C61C2411yescharacteristic
113C22⋊D61—42no—
114C2×Dic61—21no—
115D244—22no—
116D244—21no—
117D244—22no—
118D244—21no—
119D244—42no—
120D244—84no—
121C4×D61—42no—
122Dic122—21no—
123Dic122—21no—
124#92418C2×D412yes—
125#92418C2×D412yes—
126#92418C2×D414yes—
127C22×C61—22no—
128C22×C61—41no—
129C22×C61—42no—
130C22×C61—42no—
131C22×C61—44no—
132C22×C61—84no—
133C22×C61#12712yes—
134C22×C61C22×D411yescharacteristic
135C2×D61—41no—
136C2×D61—42no—
137C2×D61—42no—
138C2×D61—44no—
139C2×D61—84no—
140C4×C61—24no—
141C4×C61—41no—
142C4×C61#12712yes—
143C4×C61C22×D411yescharacteristic
144C4×C61C22×D411yescharacteristic
145Dic61—41no—
146#3155—611nomaximal, Sylow
147C2×C61—22no—
148C2×C61—81no—
149C2×C61—82no—
150C2×C61C2×#12711yescharacteristic
151C2×C61#57612yes—
152D61—81no—
153D61—82no—
154C2×AGL(1,ℤ/8)—611no—
155C2×AGL(1,ℤ/8)—611no—
156C2×#135—611no—
157C22×D8—611no—
158#535—611no—
159#535D6111yescharacteristic, complemented
160#496—612no—
161#496—612no—
162#495—612no—
163#493—612no—
164#405—611no—
165C61#315511yescharacteristic, complemented, Sylow
166C2×#41—611no—
167C2×#41C2×D6111yescharacteristic
168C22×D4—611no—
169C22×D4C2×D6111yescharacteristic
170AGL(1,ℤ/8)—1224no—
171AGL(1,ℤ/8)—1224no—
172#135—1224no—
173C2×Q16—611no—
174C2×SD16—611no—
175C2×SD16—612no—
176C2×SD16—611no—
177C2×SD16—612no—
178C2×D8—612no—
179C2×D8—612no—
180C2×D8—611no—
181C2×D8—612no—
182C2×D8—612no—
183C2×D8—1224no—
184C2×M16—611no—
185C22×C8—611no—
186#127—612no—
187#127C2×D6112yescomplemented
188#124—612no—
189#124C2×D6112yescomplemented
190#121—22no—
191#121—1222no—
192#120—22no—
193#120—1222no—
194#117C2×D6111yescharacteristic
195#97—612no—
196C4×C8—612no—
197C24—21no—
198C24—1221no—
199#41—22no—
200#41—22no—
201#41—1222no—
202#41—1222no—
203C2×Q8—611no—
204C2×Q8C22×D6111yescharacteristic
205C2×D4—21no—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—21no—
209C2×D4—24no—
210C2×D4—612no—
211C2×D4—611no—
212C2×D4—1221no—
213C2×D4—1222no—
214C2×D4—1222no—
215C2×D4—1224no—
216C2×D4—1221no—
217C2×D4C22×D6112yes—
218C2×D4C22×D6111yescharacteristic
219C22×C4—21no—
220C22×C4—1221no—
221C22×C4C22×D6111yescharacteristic
222Q16—1222no—
223SD16—1222no—
224SD16—1224no—
225SD16—1222no—
226SD16—1224no—
227D8—1224no—
228D8—1224no—
229D8—1222no—
230D8—1224no—
231D8—1224no—
232M16—614no—
233C2×C8—614no—
234C2×C8—611no—
235C2×C8—612no—
236C2×C8—611no—
237C4⋊C4C22⋊D6112yes—
238C22⋊C4—24no—
239C22⋊C4—1224no—
240C22⋊C4C22⋊D6112yes—
241C42C22×D6112yes—
242C23—22no—
243C23—21no—
244C23—42no—
245C23—82no—
246C23—1222no—
247C23—1221no—
248C23—4882no—
249C23—2442no—
250C23C2×C22⋊D6111yescharacteristic
251Q8—21no—
252Q8—21no—
253Q8—1221no—
254Q8—1221no—
255D4—22no—
256D4—21no—
257D4—22no—
258D4—21no—
259D4—42no—
260D4—42no—
261D4—84no—
262D4—1222no—
263D4—1221no—
264D4—1222no—
265D4—1221no—
266D4—4884no—
267D4—2442no—
268D4—2442no—
269C2×C4—21no—
270C2×C4—42no—
271C2×C4—1221no—
272C2×C4—2442no—
273C2×C4D4×D6112yes—
274C2×C4D4×D6112yes—
275C2×C4C2×C22⋊D6114yes—
276C2×C4C2×C22⋊D6111yescharacteristic
277C2×C4C23×D6111yescharacteristic
278C8—612no—
279C8—612no—
280C8—614no—
281C22—22no—
282C22—41no—
283C22—42no—
284C22—42no—
285C22—44no—
286C22—84no—
287C22—4884no—
288C22—2441no—
289C22—2442no—
290C22—2442no—
291C22—2444no—
292C22#1451977312yes—
293C22C22×C22⋊D6111yescharacteristic
294C4—24no—
295C4—41no—
296C4—2441no—
297C4#1451977312yes—
298C4C2×D4×D6111yescharacteristic
299C4C2×D4×D6111yescharacteristic
300C2—22no—
301C2—82no—
302C2—81no—
303C2—4882no—
304C2—4881no—
305C2C2×#1451977311yescharacteristic
306C2#1684056512yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#535C2
socleC22×C61C22×D4
hypercenter#535D61
hypocenterC61#3155
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#14519803C2semidirect
2. C2×#14519802C2semidirect
3. C2×#14519797C2semidirect
4. C22×#11758199C2semidirect
5. #16840331C2semidirect
6. #16840152C2semidirect
7. #16840149C2semidirect
8. #16840144C2semidirect
9. #16840138C2semidirect
10. #16839718C2semidirect
11. C61×#535C2semidirect
17. C2×#11758202C22semidirect
18. C2×#11758200C22semidirect
19. C2×#11758200C22semidirect
20. C2×#11758201C22semidirect
21. C2×#11758201C22semidirect
25. C2×#11758199C22semidirect
26. C2×#11758199C22semidirect
27. C2×#11758199C22semidirect
30. #14519774C22semidirect
31. #14519765C22semidirect
34. #14519688C22semidirect
35. C4×#92418C22semidirect
38. #127×C61C22semidirect
39. #124×C61C22semidirect
83. #11758194D4semidirect
84. C2×#92418D4semidirect
159. #535D61semidirect
165. C61#3155semidirect
187. #127C2×D61semidirect
189. #124C2×D61semidirect