Finite Group Databasebeta

← #21456284

Subgroups — #21456284

Order 7808.

572 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 137 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×#14519806C212yesmaximal, complemented
2C2×#14519801C212yesmaximal, complemented
3#16840310C211yesmaximal, characteristic, complemented
4#124×D61C211yesmaximal, characteristic, complemented
5#16840157C211yesmaximal, characteristic, complemented
6#16840156C211yesmaximal, characteristic, complemented
7#16840149C211yesmaximal, characteristic, complemented
8#16840145C212yesmaximal, complemented
9#16840143C212yesmaximal, complemented
10#16839714C211yesmaximal, characteristic, complemented
11C61×#496C211yesmaximal, characteristic, complemented
12C2×#11758224C2212yes—
13C2×Q8×D61C2211yescharacteristic
14C2×D4×D61C2211yescharacteristic
15#14519806—28no—
16#14519801—28no—
17C2×Dic244C2212yescomplemented
18C2×#11758202C2212yescomplemented
19C2×#11758190C2212yes—
20C2×#11758200C2212yes—
21C2×#11758200C2212yescomplemented
22C2×#11758199C2212yes—
23C2×#11758189C2212yes—
24#14519777C2211yescharacteristic, complemented
25#14519766C2211yescharacteristic
26#14519765C2211yescharacteristic
27#14519764C2211yescharacteristic
28#14519764C2212yescomplemented
29#14519763—22no—
30#14519748—22no—
31D4×Dic61—22no—
32C22⋊C4×D61—22no—
33C42×D61C2211yescharacteristic
34#14519688C2211yescharacteristic, complemented
35C8×Dic61C2212yescomplemented
36C2×SD16×C61C2212yescomplemented
37C2×D8×C61C2212yes—
38#127×C61C2211yescharacteristic, complemented
39#124×C61C2211yescharacteristic
40#97×C61C2211yescharacteristic, complemented
41C23×D61—21no—
42C2×Q8×C61C2311yescharacteristic
43C2×D4×C61—22no—
44C2×D4×C61C2311yescharacteristic
45C2×D4×C61C2312yes—
46C2×C22⋊D61—22no—
47C2×C22⋊D61—21no—
48C22×Dic61—22no—
49Q8×D61—24no—
50#11758224—24no—
51#11758224—24no—
52D4×D61—24no—
53C2×D244C2311yescharacteristic
54C2×C4×D61—21no—
55C2×C4×D61D412yes—
56C2×C4×D61C2311yescharacteristic
57C2×Dic122—21no—
58C2×Dic122C2311yescharacteristic
59C2×Dic122C2312yes—
60SD16×C61—24no—
61D8×C61—24no—
62C2×C8×C61C2312yes—
63C22⋊C4×C61—22no—
64C42×C61C2311yescharacteristic
65C22⋊Dic61—22no—
66C22⋊Dic61—24no—
67#11758202—24no—
68#11758200—24no—
69#11758200—24no—
70#11758199—24no—
71#11758198—22no—
72#11758198—22no—
73C4⋊Dic61—22no—
74C4×Dic61D412yes—
75C4×Dic61C2311yescharacteristic
76C2×#92418C2312yes—
77Dic244—24no—
78#11758190—24no—
79#11758189D418yescomplemented
80C23×C61—21no—
81C23×C61—22no—
82C22×D61—21no—
83C22×D61—44no—
84C22×D61—42no—
85C22×D61C2×D411yescharacteristic
86Q8×C61—22no—
87D4×C61—22no—
88D4×C61—22no—
89D4×C61—22no—
90D4×C61—44no—
91C2×C4×C61—21no—
92C2×C4×C61C2×D412yes—
93C2×C4×C61C2411yescharacteristic
94C22⋊D61—44no—
95C22⋊D61—42no—
96C2×Dic61—22no—
97C2×Dic61—21no—
98C2×Dic61—44no—
99C2×Dic61C2×D412yes—
100C2×Dic61C2×D411yescharacteristic
101D244—22no—
102C4×D61—42no—
103C4×D61—42no—
104C4×D61C2×D414yes—
105Dic122—22no—
106Dic122—22no—
107Dic122—22no—
108Dic122—42no—
109C8×C61C2×D414yes—
110#92418C2×D414yes—
111C22×C61—42no—
112C22×C61—41no—
113C22×C61—44no—
114C22×C61—42no—
115C22×C61C22×D411yescharacteristic
116C2×D61—22no—
117C2×D61—41no—
118C2×D61—42no—
119C2×D61—84no—
120C2×D61#12712yes—
121C4×C61—22no—
122C4×C61—41no—
123C4×C61C22×D412yes—
124Dic61—22no—
125Dic61—41no—
126Dic61—42no—
127Dic61#12712yes—
128#3153—611nomaximal, Sylow
129C2×C61—81no—
130C2×C61—82no—
131C2×C61C2×#12711yescharacteristic
132C2×C61#57512yes—
133D61—22no—
134D61—81no—
135C2×#137—612no—
136C2×AGL(1,ℤ/8)—612no—
137#532—611no—
138C2×#124—611no—
139#497—611no—
140#497—611no—
141#496—611no—
142#496D6111yescharacteristic, complemented
143#495—612no—
144#495—612no—
145C4×M16—611no—
146C61#315311yescharacteristic, complemented, Sylow
147C2×#41—612no—
148C22×Q8—611no—
149C22×D4—611no—
150#137—1228no—
151AGL(1,ℤ/8)—1228no—
152C2×Q16—612no—
153C2×Q16—612no—
154C2×SD16—612no—
155C2×SD16—612no—
156C2×SD16—612no—
157C2×SD16C2×D6112yescomplemented
158C2×D8—612no—
159C2×D8C2×D6112yes—
160C2×M16—612no—
161C4⋊Q8—611no—
162#127C2×D6111yescharacteristic, complemented
163#124—611no—
164#124—611no—
165#124—612no—
166#124—611no—
167#124—1222no—
168#124C2×D6111yescharacteristic
169#121—1222no—
170C4×D4—1222no—
171C2×C22⋊C4—1222no—
172C2×C42—611no—
173#97—611no—
174#97C2×D6111yescharacteristic, complemented
175C4×C8—612no—
176C24—1221no—
177#41—1224no—
178#41—1224no—
179C2×Q8—611no—
180C2×Q8—612no—
181C2×Q8—1221no—
182C2×Q8—1224no—
183C2×Q8C22×D6111yescharacteristic
184C2×D4—22no—
185C2×D4—611no—
186C2×D4—1224no—
187C2×D4—1221no—
188C2×D4—1222no—
189C2×D4C22×D6111yescharacteristic
190C2×D4C22×D6112yes—
191C22×C4—611no—
192C22×C4—612no—
193C22×C4—1221no—
194C22×C4—1222no—
195Q16—1224no—
196Q16—1224no—
197SD16—24no—
198SD16—1224no—
199SD16—1224no—
200SD16—1224no—
201D8—24no—
202D8—1224no—
203M16—618no—
204C2×C8—612no—
205C2×C8C22×D6112yes—
206C4⋊C4—1222no—
207C22⋊C4—22no—
208C22⋊C4—1222no—
209C22⋊C4—1222no—
210C22⋊C4—1224no—
211C22⋊C4—1222no—
212C42—612no—
213C42—611no—
214C42C22×D6111yescharacteristic
215C23—21no—
216C23—22no—
217C23—611no—
218C23—1221no—
219C23—2442no—
220C23—2444no—
221Q8—22no—
222Q8—1222no—
223Q8—1222no—
224Q8—1222no—
225Q8—2442no—
226D4—22no—
227D4—22no—
228D4—22no—
229D4—44no—
230D4—1222no—
231D4—2442no—
232D4—2444no—
233C2×C4—21no—
234C2×C4—611no—
235C2×C4—614no—
236C2×C4—612no—
237C2×C4—1221no—
238C2×C4—1222no—
239C2×C4—2442no—
240C2×C4—2442no—
241C2×C4—2444no—
242C2×C4D4×D6112yes—
243C2×C4C23×D6111yescharacteristic
244C8—614no—
245C8D4×D6114yes—
246C22—42no—
247C22—41no—
248C22—44no—
249C22—42no—
250C22—612no—
251C22—1222no—
252C22—4884no—
253C22—2441no—
254C22—2442no—
255C22C2×D4×D6111yescharacteristic
256C4—22no—
257C4—41no—
258C4—612no—
259C4—1222no—
260C4—2442no—
261C4—2441no—
262C4C2×D4×D6112yes—
263C2—81no—
264C2—82no—
265C2—1222no—
266C2—4881no—
267C2#127×D6111yescharacteristic
268C2#1684055812yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#496C2
socleC22×C61C22×D4
hypercenter#496D61
hypocenterC61#3153
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×#14519806C2semidirect
2. C2×#14519801C2semidirect
3. #16840310C2semidirect
4. #124×D61C2semidirect
5. #16840157C2semidirect
6. #16840156C2semidirect
7. #16840149C2semidirect
8. #16840145C2semidirect
9. #16840143C2semidirect
10. #16839714C2semidirect
11. C61×#496C2semidirect
17. C2×Dic244C22semidirect
18. C2×#11758202C22semidirect
21. C2×#11758200C22semidirect
24. #14519777C22semidirect
28. #14519764C22semidirect
34. #14519688C22semidirect
35. C8×Dic61C22semidirect
36. C2×SD16×C61C22semidirect
38. #127×C61C22semidirect
40. #97×C61C22semidirect
79. #11758189D4semidirect
142. #496D61semidirect
146. C61#3153semidirect
157. C2×SD16C2×D61semidirect
162. #127C2×D61semidirect
174. #97C2×D61semidirect