Finite Group Databasebeta

← #21455044

Subgroups — #21455044

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×#14519802C211yesmaximal, characteristic, complemented
3#16840269C211yesmaximal, characteristic, complemented
4#16839911C214yesmaximal, complemented
5#16839894C214yesmaximal, complemented
6#16839768C211yesmaximal, characteristic, complemented
7#16839767C211yesmaximal, characteristic, complemented
8#16839725C211yesmaximal, characteristic, complemented
9C2×AGL(1,ℤ/8)×C61C211yesmaximal, characteristic, complemented
10C24×D61—21no—
11C22×D244C2211yescharacteristic
12C22×C22⋊D61—21no—
13C2×D4×D61—24no—
14C2×D4×D61—24no—
15C2×D4×D61—22no—
16C2×D4×D61C2214yes—
17C22×C4×D61C2211yescharacteristic
18#14519802—24no—
19C2×#11758201C2212yescomplemented
20C2×#11758199C2212yescomplemented
21C2×#11758194C2211yescharacteristic, complemented
22#14519758—21no—
23#14519753C2212yescomplemented
24#14519748C2212yescomplemented
25#14519745—21no—
26C4×C22⋊D61—22no—
27#14519736C2211yescharacteristic, complemented
28#14519699C2214yescomplemented
29#14519698C2214yescomplemented
30#14519689C2214yescomplemented
31C2×#41×C61C2211yescharacteristic, complemented
32C22×D4×C61C2211yescharacteristic
33AGL(1,ℤ/8)×C61—24no—
34C2×SD16×C61C2212yescomplemented
35C2×D8×C61C2212yescomplemented
36C2×M16×C61C2211yescharacteristic, complemented
37C24×C61—21no—
38C23×D61—28no—
39C23×D61—21no—
40C23×D61—24no—
41C23×D61—48no—
42C23×D61D411yescharacteristic
43#41×C61—22no—
44#41×C61—22no—
45C2×Q8×C61C2311yescharacteristic, complemented
46C2×D4×C61—21no—
47C2×D4×C61—21no—
48C2×D4×C61—22no—
49C2×D4×C61D414yescomplemented
50C2×D4×C61C2312yes—
51C2×D4×C61C2311yescharacteristic, complemented
52C22×C4×C61—21no—
53C22×C4×C61C2311yescharacteristic
54C2×C22⋊D61—28no—
55C2×C22⋊D61—22no—
56C2×C22⋊D61—24no—
57C22×Dic61D411yescharacteristic
58D4×D61—216no—
59D4×D61—28no—
60D4×D61—28no—
61C2×D244—21no—
62C2×D244—22no—
63C2×D244D414yescomplemented
64C2×D244C2312yes—
65C2×C4×D61—22no—
66C2×C4×D61—22no—
67C2×C4×D61D412yes—
68C2×C4×D61C2312yes—
69SD16×C61—24no—
70D8×C61—24no—
71M16×C61—22no—
72C2×C8×C61C2312yescomplemented
73C22⋊Dic61—21no—
74C22⋊Dic61—22no—
75#11758201—24no—
76#11758199—24no—
77#11758198—22no—
78C4⋊Dic61C2312yescomplemented
79#11758196—22no—
80C4×Dic61—21no—
81#11758194—22no—
82C2×#92418C2312yescomplemented
83C23×C61—24no—
84C23×C61—22no—
85C23×C61—21no—
86C23×C61—44no—
87C23×C61C2×D411yescharacteristic
88C22×D61—22no—
89C22×D61—24no—
90C22×D61—216no—
91C22×D61—24no—
92C22×D61—22no—
93C22×D61—432no—
94C22×D61—48no—
95C22×D61—44no—
96C22×D61—48no—
97C22×D61C2×D412yes—
98Q8×C61—21no—
99Q8×C61—21no—
100D4×C61—24no—
101D4×C61—22no—
102D4×C61—21no—
103D4×C61—21no—
104D4×C61—42no—
105D4×C61C2×D414yes—
106C2×C4×C61—21no—
107C2×C4×C61—42no—
108C2×C4×C61C2×D411yescharacteristic
109C2×C4×C61C2×D412yes—
110C2×C4×C61C2×D412yes—
111C2×C4×C61C2411yescharacteristic
112C22⋊D61—216no—
113C22⋊D61—44no—
114C2×Dic61—22no—
115C2×Dic61—22no—
116C2×Dic61C2×D412yes—
117D244—24no—
118D244—22no—
119D244C2×D414yes—
120C4×D61—24no—
121C4×D61—22no—
122C4×D61—22no—
123C8×C61—22no—
124#92418—22no—
125C22×C61—22no—
126C22×C61—24no—
127C22×C61—48no—
128C22×C61—44no—
129C22×C61—41no—
130C22×C61—42no—
131C22×C61#12012yes—
132C22×C61C22×D411yescharacteristic
133C2×D61—28no—
134C2×D61—22no—
135C2×D61—22no—
136C2×D61—24no—
137C2×D61—432no—
138C2×D61—48no—
139C2×D61—44no—
140C2×D61AGL(1,ℤ/8)14yescomplemented
141C4×C61—41no—
142C4×C61#12012yes—
143C4×C61C22×D411yescharacteristic
144C4×C61C22×D411yescharacteristic
145Dic61—22no—
146Dic61—42no—
147#3003—611nomaximal, Sylow
148C2×C61—22no—
149C2×C61—44no—
150C2×C61—81no—
151C2×C61C2×#12011yescharacteristic
152C2×C61C2×AGL(1,ℤ/8)12yes—
153D61—24no—
154D61—44no—
155C23×D4—611no—
156C2×AGL(1,ℤ/8)—611no—
157C2×AGL(1,ℤ/8)D6111yescharacteristic, complemented
158#525—611no—
159#450—614no—
160#447—614no—
161#418—611no—
162#418—611no—
163#407—611no—
164C61#300311yescharacteristic, complemented, Sylow
165C25—1221no—
166C2×#41C2×D6111yescharacteristic, complemented
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)—24no—
176AGL(1,ℤ/8)—1224no—
177C2×SD16—612no—
178C2×SD16C2×D6112yescomplemented
179C2×D8—612no—
180C2×D8C2×D6112yescomplemented
181C2×M16—611no—
182C2×M16C2×D6111yescharacteristic, complemented
183#123—1221no—
184C22⋊Q8—612no—
185#121—612no—
186#120—1221no—
187C4×D4—1222no—
188#117—611no—
189#102—614no—
190#102—614no—
191C22⋊C8—614no—
192C24—21no—
193C24—611no—
194C24—1224no—
195C24—1228no—
196C24—1221no—
197C24—2448no—
198#41—22no—
199#41—22no—
200C2×Q8C22×D6111yescharacteristic, complemented
201C2×D4—21no—
202C2×D4—22no—
203C2×D4—21no—
204C2×D4—614no—
205C2×D4—612no—
206C2×D4—1224no—
207C2×D4—1228no—
208C2×D4—12216no—
209C2×D4—1228no—
210C2×D4—1228no—
211C2×D4—1222no—
212C2×D4—1221no—
213C2×D4—1222no—
214C2×D4C22⋊D6114yescomplemented
215C2×D4C22×D6112yes—
216C2×D4C22×D6111yescharacteristic, complemented
217C22×C4—21no—
218C22×C4—611no—
219C22×C4—612no—
220C22×C4—612no—
221C22×C4—1222no—
222C22×C4—1222no—
223C22×C4C22×D6111yescharacteristic
224SD16—24no—
225SD16—1224no—
226D8—24no—
227D8—1224no—
228M16—22no—
229M16—1222no—
230C2×C8—612no—
231C2×C8C22×D6112yescomplemented
232C4⋊C4—612no—
233C4⋊C4—1222no—
234C22⋊C4—1222no—
235C22⋊C4—1222no—
236C22⋊C4—1221no—
237C42—1221no—
238C23—22no—
239C23—24no—
240C23—21no—
241C23—44no—
242C23—612no—
243C23—1224no—
244C23—12216no—
245C23—1222no—
246C23—1222no—
247C23—1224no—
248C23—2444no—
249C23—2448no—
250C23—24432no—
251C23—2448no—
252C23D4×D6111yescharacteristic
253Q8—21no—
254Q8—21no—
255D4—22no—
256D4—21no—
257D4—21no—
258D4—24no—
259D4—42no—
260D4—614no—
261D4—12216no—
262D4—1222no—
263D4—1224no—
264D4—2444no—
265D4C2×C22⋊D6114yes—
266C2×C4—21no—
267C2×C4—42no—
268C2×C4—612no—
269C2×C4—1222no—
270C2×C4—1222no—
271C2×C4—1222no—
272C2×C4—1224no—
273C2×C4—1222no—
274C2×C4D4×D6112yes—
275C2×C4D4×D6111yescharacteristic
276C2×C4C2×C22⋊D6112yes—
277C2×C4C23×D6111yescharacteristic
278C8—22no—
279C8—1222no—
280C22—22no—
281C22—24no—
282C22—48no—
283C22—44no—
284C22—41no—
285C22—42no—
286C22—614no—
287C22—1228no—
288C22—1222no—
289C22—1222no—
290C22—1224no—
291C22—2448no—
292C22—24432no—
293C22—2444no—
294C22#1451974512yes—
295C22C2×D4×D6111yescharacteristic
296C4—41no—
297C4—1222no—
298C4—2442no—
299C4#1451974512yes—
300C4C2×D4×D6111yescharacteristic
301C4C22×C22⋊D6111yescharacteristic
302C2—22no—
303C2—44no—
304C2—81no—
305C2—1224no—
306C2—2444no—
307C2C2×#1451974511yescharacteristic
308C2AGL(1,ℤ/8)×D6112yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×AGL(1,ℤ/8)×C61C2
socleC22×C61C22×D4
hypercenterC2×AGL(1,ℤ/8)D61
hypocenterC61#3003
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C22×D4×D61C2semidirect
2. C2×#14519802C2semidirect
3. #16840269C2semidirect
4. #16839911C2semidirect
5. #16839894C2semidirect
6. #16839768C2semidirect
7. #16839767C2semidirect
8. #16839725C2semidirect
9. C2×AGL(1,ℤ/8)×C61C2semidirect
19. C2×#11758201C22semidirect
20. C2×#11758199C22semidirect
21. C2×#11758194C22semidirect
23. #14519753C22semidirect
24. #14519748C22semidirect
27. #14519736C22semidirect
28. #14519699C22semidirect
29. #14519698C22semidirect
30. #14519689C22semidirect
31. C2×#41×C61C22semidirect
34. C2×SD16×C61C22semidirect
35. C2×D8×C61C22semidirect
36. C2×M16×C61C22semidirect
45. C2×Q8×C61C23semidirect
49. C2×D4×C61D4semidirect
51. C2×D4×C61C23semidirect
63. C2×D244D4semidirect
72. C2×C8×C61C23semidirect
78. C4⋊Dic61C23semidirect
82. C2×#92418C23semidirect
140. C2×D61AGL(1,ℤ/8)semidirect
157. C2×AGL(1,ℤ/8)D61semidirect
164. C61#3003semidirect
166. C2×#41C2×D61semidirect
178. C2×SD16C2×D61semidirect
180. C2×D8C2×D61semidirect
182. C2×M16C2×D61semidirect
200. C2×Q8C22×D61semidirect
214. C2×D4C22⋊D61semidirect
216. C2×D4C22×D61semidirect
231. C2×C8C22×D61semidirect