Finite Group Databasebeta

← #21454668

Subgroups — #21454668

Order 7808.

528 conjugacy classes of subgroups; only the 175 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 175 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×D8×D61C211yesmaximal, characteristic
2#16840234C212yesmaximal, complemented
3#16839875C211yesmaximal, characteristic, complemented
4#16839874C211yesmaximal, characteristic, complemented
5#16839873C211yesmaximal, characteristic, complemented
6C4×#11758199C212yesmaximal, complemented
7#16839842C212yesmaximal, complemented
8#16839797C211yesmaximal, characteristic, complemented
9#16839765C212yesmaximal, complemented
10#16839719C211yesmaximal, characteristic, complemented
11C61×#442C211yesmaximal, characteristic, complemented
12C2×D4×D61C2212yes—
13C2×D488C2211yescharacteristic
14C2×#11758199C2212yes—
15D8×D61C418yescomplemented
16C2×#11758189C2211yescharacteristic
17C2×C8×D61C2211yescharacteristic
18C4×D244C2212yescomplemented
19D4×Dic61C2212yescomplemented
20#14519739C2212yescomplemented
21C4×C22⋊D61—22no—
22#14519737—22no—
23#14519735C2212yes—
24#14519734C2211yescharacteristic
25C2×#11758198—22no—
26C22⋊C4×D61—22no—
27#14519710C2212yescomplemented
28#14519709C2211yescharacteristic, complemented
29#14519699C2212yescomplemented
30#14519698C2212yescomplemented
31#14519697C2212yescomplemented
32#14519687C2211yescharacteristic, complemented
33C4×#92418C2211yescharacteristic, complemented
34C8×Dic61C2211yescharacteristic, complemented
35C2×D8×C61C2211yescharacteristic
36C4×D4×C61C2212yescomplemented
37#106×C61C2211yescharacteristic, complemented
38#102×C61C2212yescomplemented
39#97×C61C2211yescharacteristic, complemented
40C23×D61—22no—
41C2×D4×C61C2312yes—
42C22×C4×C61—22no—
43C2×C22⋊D61—22no—
44C22×Dic61—22no—
45D4×D61—24no—
46D4×D61C2×C418yescomplemented
47C2×D244C2312yes—
48C2×C4×D61—22no—
49C2×C4×D61—22no—
50C2×C4×D61C2311yescharacteristic
51D8×C61C2×C414yescomplemented
52C2×C8×C61C2311yescharacteristic
53C2×C8×C61C2311yescharacteristic
54C4⋊C4×C61C2312yes—
55C22⋊C4×C61—22no—
56C42×C61C2311yescharacteristic
57C22⋊Dic61—22no—
58#11758199C2×C418yescomplemented
59#11758198—22no—
60#11758198—22no—
61#11758198—22no—
62#11758198D412yes—
63C4⋊Dic61C2312yes—
64#11758196D412yes—
65C4×Dic61—22no—
66C4×Dic61C2311yescharacteristic
67C2×#92418C2311yescharacteristic
68C2×#92418C2311yescharacteristic
69D488C2×C414yescomplemented
70#11758189—22no—
71C8×D61C2×C414yescomplemented
72C23×C61—22no—
73C22×D61—22no—
74C22×D61—28no—
75C22×D61—82no—
76C22×D61—82no—
77C22×D61C2×D411yescharacteristic
78D4×C61—22no—
79D4×C61C22×C414yes—
80C2×C4×C61—22no—
81C2×C4×C61—82no—
82C2×C4×C61C2×D412yes—
83C2×C4×C61C2411yescharacteristic
84C22⋊D61—28no—
85C2×Dic61—22no—
86C2×Dic61—82no—
87C2×Dic61C2×D412yes—
88C2×Dic61C2×D411yescharacteristic
89D244—22no—
90D244C22×C414yes—
91C4×D61—82no—
92C4×D61—82no—
93C4×D61C22×C412yes—
94C4×D61#4112yes—
95C8×C61—21no—
96C8×C61C22×C412yes—
97#92418—21no—
98#92418C22×C412yes—
99C22×C61—24no—
100C22×C61—42no—
101C22×C61—42no—
102C22×C61C22×D411yescharacteristic
103C2×D61—22no—
104C2×D61—24no—
105C2×D61—42no—
106C2×D61—42no—
107C2×D61—88no—
108C2×D61C4×D412yes—
109C4×C61—22no—
110C4×C61—42no—
111C4×C61C23×C411yescharacteristic
112C4×C61C2×#4111yescharacteristic
113Dic61—22no—
114Dic61—42no—
115Dic61C4×D412yes—
116#2948—611nomaximal, Sylow
117C2×C61—44no—
118C2×C61C2×C4×D411yescharacteristic
119C2×C61#57612yes—
120D61—22no—
121D61—44no—
122C22×D8—611no—
123#518—612no—
124#442—611no—
125#442—611no—
126#442—611no—
127#442D6111yescharacteristic, complemented
128C4×D8—612no—
129C4×D8—612no—
130#427—611no—
131#418—612no—
132#405—611no—
133C61#294811yescharacteristic, complemented, Sylow
134C22×D4—612no—
135C2×D8—612no—
136C2×D8—618no—
137C2×D8—611no—
138C2×D8C2×D6111yescharacteristic
139C2×M16—611no—
140C22×C8—611no—
141C4×D4—612no—
142C4×D4—612no—
143C4×D4—612no—
144C4×D4—1222no—
145C4×D4—1222no—
146C4×D4C2×D6112yescomplemented
147#117—611no—
148#117—612no—
149C2×C22⋊C4—1222no—
150C2×C22⋊C4—1222no—
151#107—612no—
152#106—611no—
153#106C2×D6111yescharacteristic, complemented
154#102—612no—
155#102—612no—
156#102—612no—
157#102C2×D6112yescomplemented
158#97—611no—
159#97C2×D6111yescharacteristic, complemented
160C4×C8—611no—
161C4×C8—611no—
162C24—1222no—
163C2×D4—618no—
164C2×D4—612no—
165C2×D4—1224no—
166C2×D4—1222no—
167C2×D4C22×D6112yes—
168C22×C4—22no—
169C22×C4—611no—
170C22×C4—1222no—
171C22×C4—1222no—
172C22×C4—1222no—
173D8—618no—
174D8—614no—
175D8C4×D6114yescomplemented
176M16—1222no—
177C2×C8—611no—
178C2×C8—614no—
179C2×C8—611no—
180C2×C8C22×D6111yescharacteristic
181C2×C8C22×D6111yescharacteristic
182C4⋊C4—612no—
183C4⋊C4—612no—
184C4⋊C4C22×D6112yes—
185C22⋊C4—22no—
186C22⋊C4—612no—
187C22⋊C4—1222no—
188C22⋊C4—1222no—
189C22⋊C4—1222no—
190C22⋊C4—1222no—
191C42—611no—
192C42—1222no—
193C42C22×D6111yescharacteristic
194C23—22no—
195C23—611no—
196C23—1228no—
197C23—1222no—
198C23—4882no—
199C23—4882no—
200D4—22no—
201D4—614no—
202D4—1228no—
203D4—1222no—
204D4C2×C4×D6114yes—
205C2×C4—22no—
206C2×C4—82no—
207C2×C4—611no—
208C2×C4—612no—
209C2×C4—612no—
210C2×C4—612no—
211C2×C4—1222no—
212C2×C4—4882no—
213C2×C4—4882no—
214C2×C4—4882no—
215C2×C4D4×D6112yes—
216C2×C4C23×D6111yescharacteristic
217C8—21no—
218C8—612no—
219C8—1221no—
220C8C2×C4×D6112yes—
221C22—24no—
222C22—42no—
223C22—42no—
224C22—612no—
225C22—1222no—
226C22—1224no—
227C22—4888no—
228C22—2442no—
229C22—2442no—
230C22C2×D4×D6111yescharacteristic
231C4—22no—
232C4—42no—
233C4—612no—
234C4—1222no—
235C4—2442no—
236C4C22×C4×D6111yescharacteristic
237C4#41×D6111yescharacteristic
238C2—44no—
239C2—1222no—
240C2—2444no—
241C2C4×D4×D6111yescharacteristic
242C2#1684056612yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC4×C61C23×C4
FrattiniC2×C4C23×D61
FittingC61×#442C2
socleC22×C61C22×D4
hypercenter#442D61
hypocenterC61#2948
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. #16840234C2semidirect
3. #16839875C2semidirect
4. #16839874C2semidirect
5. #16839873C2semidirect
6. C4×#11758199C2semidirect
7. #16839842C2semidirect
8. #16839797C2semidirect
9. #16839765C2semidirect
10. #16839719C2semidirect
11. C61×#442C2semidirect
15. D8×D61C4semidirect
18. C4×D244C22semidirect
19. D4×Dic61C22semidirect
20. #14519739C22semidirect
27. #14519710C22semidirect
28. #14519709C22semidirect
29. #14519699C22semidirect
30. #14519698C22semidirect
31. #14519697C22semidirect
32. #14519687C22semidirect
33. C4×#92418C22semidirect
34. C8×Dic61C22semidirect
36. C4×D4×C61C22semidirect
37. #106×C61C22semidirect
38. #102×C61C22semidirect
39. #97×C61C22semidirect
46. D4×D61C2×C4semidirect
51. D8×C61C2×C4semidirect
58. #11758199C2×C4semidirect
69. D488C2×C4semidirect
71. C8×D61C2×C4semidirect
127. #442D61semidirect
133. C61#2948semidirect
146. C4×D4C2×D61semidirect
153. #106C2×D61semidirect
157. #102C2×D61semidirect
159. #97C2×D61semidirect
175. D8C4×D61semidirect