Finite Group Databasebeta

← #21456268

Subgroups — #21456268

Order 7808.

656 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14519804C212yesmaximal, complemented
2C2×#14519801C212yesmaximal, complemented
3#16840311C211yesmaximal, characteristic, complemented
4#127×D61C211yesmaximal, characteristic, complemented
5#16840152C211yesmaximal, characteristic, complemented
6#16840151C211yesmaximal, characteristic, complemented
7#16840149C211yesmaximal, characteristic, complemented
8#16840137C212yesmaximal, complemented
9#16840133C212yesmaximal, complemented
10#16839714C211yesmaximal, characteristic, complemented
11C61×#496C211yesmaximal, characteristic, complemented
12C2×#11758226C2211yescharacteristic
13C2×#11758224C2211yescharacteristic
14C2×D4×D61—22no—
15C2×D4×D61C2212yes—
16#14519804—28no—
17#14519801—28no—
18C2×#11758190C2212yescomplemented
19C2×#11758200C2212yescomplemented
20C2×#11758201C2212yescomplemented
21C2×D488C2212yescomplemented
22C2×#11758199C2212yescomplemented
23C2×#11758199C2212yescomplemented
24C2×#11758189C2212yes—
25#14519775C2211yescharacteristic, complemented
26#14519774C2211yescharacteristic
27#14519773—22no—
28#14519773C2212yes—
29#14519773C2211yescharacteristic, complemented
30#14519765C2211yescharacteristic, complemented
31#14519750—22no—
32#14519737—22no—
33C42×D61C2211yescharacteristic
34#14519688C2211yescharacteristic, complemented
35C8×Dic61C2212yescomplemented
36C2×SD16×C61C2212yescomplemented
37C2×D8×C61C2212yescomplemented
38#127×C61C2211yescharacteristic
39#124×C61C2211yescharacteristic, complemented
40#97×C61C2211yescharacteristic, complemented
41C23×D61—22no—
42C2×Q8×C61C2311yescharacteristic
43C2×D4×C61—22no—
44C2×D4×C61C2312yes—
45C2×D4×C61C2311yescharacteristic
46C2×C22⋊D61—21no—
47C2×C22⋊D61—24no—
48C2×C22⋊D61—22no—
49C2×C22⋊D61—22no—
50C22×Dic61—21no—
51#11758226—24no—
52#11758224—24no—
53D4×D61—24no—
54D4×D61—24no—
55D4×D61—48no—
56C2×D244—21no—
57C2×D244—22no—
58C2×D244C2312yes—
59C2×D244C2311yescharacteristic
60C2×C4×D61—21no—
61C2×C4×D61D412yes—
62C2×C4×D61C2311yescharacteristic
63C2×Dic122C2311yescharacteristic
64SD16×C61—24no—
65D8×C61—24no—
66C2×C8×C61C2312yes—
67C22⋊C4×C61—22no—
68C42×C61C2311yescharacteristic
69#11758201—24no—
70#11758200—24no—
71#11758199—24no—
72#11758199—24no—
73#11758198—22no—
74#11758196—22no—
75C4×Dic61D412yes—
76C4×Dic61C2311yescharacteristic
77C2×#92418C2312yes—
78D488—24no—
79#11758190—24no—
80#11758189D418yescomplemented
81C23×C61—21no—
82C23×C61—22no—
83C22×D61—21no—
84C22×D61—22no—
85C22×D61—48no—
86C22×D61—44no—
87C22×D61C2×D411yescharacteristic
88Q8×C61—22no—
89D4×C61—22no—
90D4×C61—22no—
91D4×C61—22no—
92D4×C61—44no—
93C2×C4×C61—21no—
94C2×C4×C61C2×D412yes—
95C2×C4×C61C2411yescharacteristic
96C22⋊D61—42no—
97C22⋊D61—44no—
98C22⋊D61—48no—
99C22⋊D61—44no—
100C2×Dic61—21no—
101C2×Dic61—42no—
102C2×Dic61C2×D411yescharacteristic
103C2×Dic61C2×D412yes—
104D244—22no—
105D244—22no—
106D244—22no—
107D244—44no—
108D244—42no—
109C4×D61—24no—
110C4×D61—42no—
111C4×D61C2×D414yes—
112Dic122—22no—
113C8×C61C2×D414yescomplemented
114#92418C2×D414yescomplemented
115C22×C61—41no—
116C22×C61—42no—
117C22×C61—44no—
118C22×C61—42no—
119C22×C61C22×D411yescharacteristic
120C2×D61—22no—
121C2×D61—41no—
122C2×D61—42no—
123C2×D61—44no—
124C2×D61—42no—
125C2×D61—88no—
126C2×D61#12712yes—
127C4×C61—22no—
128C4×C61—41no—
129C4×C61C22×D412yes—
130Dic61—41no—
131Dic61#12712yes—
132Dic61AGL(1,ℤ/8)14yescomplemented
133#3151—611nomaximal, Sylow
134C2×C61—82no—
135C2×C61—81no—
136C2×C61C2×#12711yescharacteristic
137C2×C61C2×AGL(1,ℤ/8)12yes—
138D61—22no—
139D61—81no—
140D61—82no—
141C2×AGL(1,ℤ/8)—612no—
142C2×AGL(1,ℤ/8)—612no—
143#532—611no—
144C2×#127—611no—
145#496—611no—
146#496—611no—
147#496—611no—
148#496D6111yescharacteristic, complemented
149#493—612no—
150#492—612no—
151C4×M16—611no—
152C61#315111yescharacteristic, complemented, Sylow
153C2×#41—611no—
154C2×#41—611no—
155C22×D4—612no—
156C22×D4—1222no—
157AGL(1,ℤ/8)—1228no—
158AGL(1,ℤ/8)—1228no—
159C2×SD16—612no—
160C2×SD16—612no—
161C2×SD16—612no—
162C2×SD16C2×D6112yescomplemented
163C2×D8—612no—
164C2×D8—612no—
165C2×D8—612no—
166C2×D8C2×D6112yescomplemented
167C2×M16—612no—
168C4⋊Q8—611no—
169#127—612no—
170#127—611no—
171#127—611no—
172#127—1222no—
173#127C2×D6111yescharacteristic
174#124—611no—
175#124C2×D6111yescharacteristic, complemented
176#121—1222no—
177C4×D4—1222no—
178C2×C42—611no—
179#97—611no—
180#97C2×D6111yescharacteristic, complemented
181C4×C8—612no—
182C24—1222no—
183#41—1224no—
184#41—1224no—
185C2×Q8—611no—
186C2×Q8C22×D6111yescharacteristic
187C2×D4—22no—
188C2×D4—611no—
189C2×D4—612no—
190C2×D4—1221no—
191C2×D4—1224no—
192C2×D4—1224no—
193C2×D4—1222no—
194C2×D4—1224no—
195C2×D4—1222no—
196C2×D4—1221no—
197C2×D4—1222no—
198C2×D4—2448no—
199C2×D4C22×D6111yescharacteristic
200C2×D4C22×D6112yes—
201C22×C4—611no—
202C22×C4—612no—
203C22×C4—1221no—
204C22×C4—1221no—
205SD16—24no—
206SD16—1224no—
207SD16—1224no—
208SD16—1224no—
209D8—24no—
210D8—1224no—
211D8—1224no—
212D8—1224no—
213M16—618no—
214C2×C8—612no—
215C2×C8C22×D6112yes—
216C4⋊C4—1222no—
217C22⋊C4—22no—
218C22⋊C4—1222no—
219C42—612no—
220C42—611no—
221C42C22×D6111yescharacteristic
222C23—21no—
223C23—22no—
224C23—611no—
225C23—1221no—
226C23—1222no—
227C23—2444no—
228C23—2448no—
229Q8—22no—
230Q8—1222no—
231D4—22no—
232D4—22no—
233D4—22no—
234D4—44no—
235D4—1222no—
236D4—1222no—
237D4—1222no—
238D4—2444no—
239D4—2442no—
240D4—2444no—
241D4—2444no—
242D4—2448no—
243D4—2442no—
244C2×C4—21no—
245C2×C4—612no—
246C2×C4—611no—
247C2×C4—614no—
248C2×C4—1224no—
249C2×C4—1221no—
250C2×C4—2442no—
251C2×C4—2442no—
252C2×C4D4×D6112yes—
253C2×C4C23×D6111yescharacteristic
254C8—614no—
255C8D4×D6114yescomplemented
256C22—44no—
257C22—42no—
258C22—41no—
259C22—42no—
260C22—612no—
261C22—1222no—
262C22—4888no—
263C22—2444no—
264C22—2442no—
265C22—2441no—
266C22—2442no—
267C22C2×D4×D6111yescharacteristic
268C4—22no—
269C4—41no—
270C4—614no—
271C4—612no—
272C4—2441no—
273C4C2×D4×D6112yes—
274C2—82no—
275C2—81no—
276C2—1222no—
277C2—4882no—
278C2—4881no—
279C2#127×D6111yescharacteristic
280C2AGL(1,ℤ/8)×D6112yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#496C2
socleC22×C61C22×D4
hypercenter#496D61
hypocenterC61#3151
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×#14519804C2semidirect
2. C2×#14519801C2semidirect
3. #16840311C2semidirect
4. #127×D61C2semidirect
5. #16840152C2semidirect
6. #16840151C2semidirect
7. #16840149C2semidirect
8. #16840137C2semidirect
9. #16840133C2semidirect
10. #16839714C2semidirect
11. C61×#496C2semidirect
18. C2×#11758190C22semidirect
19. C2×#11758200C22semidirect
20. C2×#11758201C22semidirect
21. C2×D488C22semidirect
22. C2×#11758199C22semidirect
23. C2×#11758199C22semidirect
25. #14519775C22semidirect
29. #14519773C22semidirect
30. #14519765C22semidirect
34. #14519688C22semidirect
35. C8×Dic61C22semidirect
36. C2×SD16×C61C22semidirect
37. C2×D8×C61C22semidirect
39. #124×C61C22semidirect
40. #97×C61C22semidirect
80. #11758189D4semidirect
113. C8×C61C2×D4semidirect
114. #92418C2×D4semidirect
132. Dic61AGL(1,ℤ/8)semidirect
148. #496D61semidirect
152. C61#3151semidirect
162. C2×SD16C2×D61semidirect
166. C2×D8C2×D61semidirect
175. #124C2×D61semidirect
180. #97C2×D61semidirect
255. C8D4×D61semidirect