Finite Group Databasebeta

← #21455048

Subgroups — #21455048

Order 7808.

994 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C22×D4×D61C211yesmaximal, characteristic, complemented
2C2×#14519805C211yesmaximal, characteristic, complemented
3C2×#14519803C211yesmaximal, characteristic, complemented
4#16840274C211yesmaximal, characteristic, complemented
5#16839914C214yesmaximal, complemented
6#16839897C214yesmaximal, complemented
7#16839766C211yesmaximal, characteristic, complemented
8#16839725C211yesmaximal, characteristic, complemented
9C61×#418C211yesmaximal, characteristic, complemented
10C24×D61—21no—
11C2×#11758222C2211yescharacteristic, complemented
12C22×D244C2211yescharacteristic
13C22×C22⋊D61—21no—
14C2×D4×D61—24no—
15C2×D4×D61—24no—
16C2×D4×D61—22no—
17C2×D4×D61C2214yes—
18C22×C4×D61C2211yescharacteristic
19#14519805—24no—
20#14519803—24no—
21C2×#11758190C2212yescomplemented
22C2×#11758200C2212yescomplemented
23C2×D488C2212yescomplemented
24C2×#11758199C2212yescomplemented
25C2×#11758194C2211yescharacteristic, complemented
26#14519761—21no—
27#14519757C2212yescomplemented
28#14519752C2212yescomplemented
29#14519747—21no—
30C4×D244—22no—
31#14519697C2214yescomplemented
32#14519689C2214yescomplemented
33C22×D4×C61C2211yescharacteristic
34C2×M16×C61C2211yescharacteristic, complemented
35#117×C61C2211yescharacteristic, complemented
36#102×C61C2214yescomplemented
37C24×C61—21no—
38C23×D61—28no—
39C23×D61—21no—
40C23×D61—24no—
41C23×D61—48no—
42C23×D61D411yescharacteristic
43C2×D4×C61—21no—
44C2×D4×C61—22no—
45C2×D4×C61D414yescomplemented
46C2×D4×C61C2312yes—
47C22×C4×C61C2311yescharacteristic
48C2×C22⋊D61—28no—
49C2×C22⋊D61—21no—
50C2×C22⋊D61—24no—
51C22×Dic61D411yescharacteristic
52D4×D61—216no—
53D4×D61—28no—
54D4×D61—28no—
55#11758222—22no—
56#11758222—22no—
57C2×D244—21no—
58C2×D244—22no—
59C2×D244—22no—
60C2×D244D414yescomplemented
61C2×D244C2312yes—
62C2×D244C2311yescharacteristic, complemented
63C2×C4×D61—22no—
64C2×C4×D61—22no—
65C2×C4×D61—21no—
66C2×C4×D61D412yes—
67C2×C4×D61C2312yes—
68C2×Dic122C2311yescharacteristic, complemented
69M16×C61—22no—
70C2×C8×C61C2312yescomplemented
71C4⋊C4×C61C2312yescomplemented
72C22⋊C4×C61—21no—
73C42×C61—21no—
74#11758200—24no—
75#11758199—24no—
76#11758198—22no—
77#11758198—22no—
78C4⋊Dic61—22no—
79#11758194—22no—
80C2×#92418C2312yescomplemented
81D488—24no—
82#11758190—24no—
83C23×C61—24no—
84C23×C61—22no—
85C23×C61—44no—
86C23×C61C2×D411yescharacteristic
87C22×D61—22no—
88C22×D61—24no—
89C22×D61—216no—
90C22×D61—24no—
91C22×D61—22no—
92C22×D61—21no—
93C22×D61—432no—
94C22×D61—48no—
95C22×D61—44no—
96C22×D61—48no—
97C22×D61C2×D412yes—
98D4×C61—24no—
99D4×C61—22no—
100D4×C61C2×D414yes—
101C2×C4×C61—22no—
102C2×C4×C61C2×D411yescharacteristic
103C2×C4×C61C2×D412yes—
104C2×C4×C61C2×D412yes—
105C2×C4×C61C2411yescharacteristic
106C22⋊D61—216no—
107C22⋊D61—42no—
108C2×Dic61—22no—
109C2×Dic61—21no—
110C2×Dic61C2×D412yes—
111D244—24no—
112D244—22no—
113D244—21no—
114D244—21no—
115D244—44no—
116D244C2×D414yes—
117C4×D61—24no—
118C4×D61—22no—
119C4×D61—22no—
120C4×D61—42no—
121Dic122—21no—
122Dic122—21no—
123C8×C61—22no—
124#92418—22no—
125C22×C61—22no—
126C22×C61—24no—
127C22×C61—48no—
128C22×C61—44no—
129C22×C61#12012yes—
130C22×C61C22×D411yescharacteristic
131C2×D61—28no—
132C2×D61—22no—
133C2×D61—22no—
134C2×D61—24no—
135C2×D61—432no—
136C2×D61—48no—
137C2×D61—44no—
138C2×D61—41no—
139C2×D61—42no—
140C2×D61AGL(1,ℤ/8)14yescomplemented
141C4×C61—42no—
142C4×C61#12012yes—
143C4×C61C22×D411yescharacteristic
144C4×C61C22×D411yescharacteristic
145Dic61—22no—
146Dic61—41no—
147#3003—611nomaximal, Sylow
148C2×C61—22no—
149C2×C61—44no—
150C2×C61C2×#12011yescharacteristic
151C2×C61C2×AGL(1,ℤ/8)12yes—
152D61—24no—
153D61—44no—
154D61—81no—
155C23×D4—611no—
156C2×AGL(1,ℤ/8)—611no—
157C2×AGL(1,ℤ/8)—611no—
158#525—611no—
159#450—614no—
160#447—614no—
161#418—611no—
162#418D6111yescharacteristic, complemented
163#407—611no—
164C61#300311yescharacteristic, complemented, Sylow
165C25—1221no—
166C2×#41—611no—
167C22×D4—614no—
168C22×D4—611no—
169C22×D4—1222no—
170C22×D4—1221no—
171C22×D4—1224no—
172C22×D4—1224no—
173C22×D4C2×D6111yescharacteristic
174C23×C4—611no—
175AGL(1,ℤ/8)—1224no—
176AGL(1,ℤ/8)—1224no—
177C2×SD16—612no—
178C2×SD16—612no—
179C2×D8—612no—
180C2×D8—612no—
181C2×M16—611no—
182C2×M16C2×D6111yescharacteristic, complemented
183#123—1221no—
184C22⋊Q8—612no—
185#121—612no—
186#120—1221no—
187C4×D4—1222no—
188#117C2×D6111yescharacteristic, complemented
189#102—614no—
190#102C2×D6114yescomplemented
191C22⋊C8—614no—
192C24—21no—
193C24—611no—
194C24—1224no—
195C24—1228no—
196C24—1221no—
197C24—2448no—
198#41—1222no—
199#41—1222no—
200C2×Q8—611no—
201C2×D4—22no—
202C2×D4—21no—
203C2×D4—614no—
204C2×D4—612no—
205C2×D4—611no—
206C2×D4—1222no—
207C2×D4—1224no—
208C2×D4—1228no—
209C2×D4—12216no—
210C2×D4—1228no—
211C2×D4—1228no—
212C2×D4—1221no—
213C2×D4—1222no—
214C2×D4—1221no—
215C2×D4D24414yescomplemented
216C2×D4C22×D6112yes—
217C22×C4—611no—
218C22×C4—612no—
219C22×C4—612no—
220C22×C4—1222no—
221C22×C4—1222no—
222C22×C4—1221no—
223C22×C4C22×D6111yescharacteristic
224SD16—1224no—
225SD16—1224no—
226D8—1224no—
227D8—1224no—
228M16—22no—
229M16—1222no—
230C2×C8—612no—
231C2×C8C22×D6112yescomplemented
232C4⋊C4—1222no—
233C4⋊C4C22×D6112yescomplemented
234C22⋊C4—21no—
235C22⋊C4—1222no—
236C22⋊C4—1222no—
237C42—21no—
238C23—22no—
239C23—24no—
240C23—44no—
241C23—612no—
242C23—1224no—
243C23—12216no—
244C23—1222no—
245C23—1222no—
246C23—1224no—
247C23—1221no—
248C23—2444no—
249C23—2448no—
250C23—24432no—
251C23—2448no—
252C23D4×D6111yescharacteristic
253Q8—1221no—
254Q8—1221no—
255D4—22no—
256D4—24no—
257D4—614no—
258D4—12216no—
259D4—1221no—
260D4—1222no—
261D4—1221no—
262D4—1224no—
263D4—2444no—
264D4—2442no—
265D4C2×D24414yes—
266C2×C4—22no—
267C2×C4—612no—
268C2×C4—1222no—
269C2×C4—1222no—
270C2×C4—1222no—
271C2×C4—1224no—
272C2×C4—1221no—
273C2×C4—2442no—
274C2×C4C2×D24412yes—
275C2×C4D4×D6112yes—
276C2×C4D4×D6111yescharacteristic
277C2×C4C23×D6111yescharacteristic
278C8—22no—
279C8—1222no—
280C22—22no—
281C22—24no—
282C22—48no—
283C22—44no—
284C22—614no—
285C22—1228no—
286C22—1222no—
287C22—1222no—
288C22—1224no—
289C22—2448no—
290C22—24432no—
291C22—2441no—
292C22—2442no—
293C22—2444no—
294C22#1451974712yes—
295C22C2×D4×D6111yescharacteristic
296C4—42no—
297C4—1222no—
298C4—2441no—
299C4#1451974712yes—
300C4C2×D4×D6111yescharacteristic
301C4C22×D24411yescharacteristic
302C2—22no—
303C2—44no—
304C2—1224no—
305C2—4881no—
306C2—2444no—
307C2C2×#1451974711yescharacteristic
308C2AGL(1,ℤ/8)×D6112yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#418C2
socleC22×C61C22×D4
hypercenter#418D61
hypocenterC61#3003
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C22×D4×D61C2semidirect
2. C2×#14519805C2semidirect
3. C2×#14519803C2semidirect
4. #16840274C2semidirect
5. #16839914C2semidirect
6. #16839897C2semidirect
7. #16839766C2semidirect
8. #16839725C2semidirect
9. C61×#418C2semidirect
11. C2×#11758222C22semidirect
21. C2×#11758190C22semidirect
22. C2×#11758200C22semidirect
23. C2×D488C22semidirect
24. C2×#11758199C22semidirect
25. C2×#11758194C22semidirect
27. #14519757C22semidirect
28. #14519752C22semidirect
31. #14519697C22semidirect
32. #14519689C22semidirect
34. C2×M16×C61C22semidirect
35. #117×C61C22semidirect
36. #102×C61C22semidirect
45. C2×D4×C61D4semidirect
60. C2×D244D4semidirect
62. C2×D244C23semidirect
68. C2×Dic122C23semidirect
70. C2×C8×C61C23semidirect
71. C4⋊C4×C61C23semidirect
80. C2×#92418C23semidirect
140. C2×D61AGL(1,ℤ/8)semidirect
162. #418D61semidirect
164. C61#3003semidirect
182. C2×M16C2×D61semidirect
188. #117C2×D61semidirect
190. #102C2×D61semidirect
215. C2×D4D244semidirect
231. C2×C8C22×D61semidirect
233. C4⋊C4C22×D61semidirect