Finite Group Databasebeta

← #21456566

Subgroups — #21456566

Order 7808.

520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 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
1#121×D61C212yesmaximal, complemented
2#16840077C212yesmaximal, complemented
3#16840074C212yesmaximal, complemented
4#16839998C211yesmaximal, characteristic, complemented
5#16839996C212yesmaximal, complemented
6#16839897C212yesmaximal, complemented
7#16839894C212yesmaximal, complemented
8C2×#14519689C211yesmaximal, characteristic, complemented
9C61×#466C211yesmaximal, characteristic, complemented
10C2×D4×D61—22no—
11C2×D4×D61C2212yescomplemented
12C22×C4×D61C2211yescharacteristic
13C2×D488C2211yescharacteristic, complemented
14C2×#11758199C2212yescomplemented
15C22×#92418C2211yescharacteristic, complemented
16#14519752C2212yes—
17#14519751C2212yescomplemented
18#14519750—22no—
19#14519749—22no—
20#14519748C2212yes—
21C4⋊C4×D61C2212yescomplemented
22C22⋊C4×D61—22no—
23#14519711C2211yescharacteristic, complemented
24#14519710C2212yescomplemented
25#14519699C2212yescomplemented
26#14519698C2212yescomplemented
27#14519697C2212yescomplemented
28#14519689C2212yescomplemented
29#14519689C2212yescomplemented
30C2×D8×C61C2211yescharacteristic, complemented
31C22×C8×C61C2211yescharacteristic, complemented
32#121×C61C2212yescomplemented
33#107×C61C2211yescharacteristic, complemented
34#102×C61C2212yescomplemented
35C23×D61—22no—
36C23×D61D411yescharacteristic
37C2×D4×C61—22no—
38C2×D4×C61C2312yes—
39C22×C4×C61C2311yescharacteristic
40C2×C22⋊D61—22no—
41C2×C22⋊D61—22no—
42C2×C22⋊D61—22no—
43C22×Dic61D411yescharacteristic
44D4×D61—42no—
45D4×D61—42no—
46D4×D61—48no—
47C2×D244—22no—
48C2×D244C2312yes—
49C2×C4×D61—22no—
50C2×C4×D61—41no—
51C2×C4×D61—41no—
52C2×C4×D61D412yes—
53C2×C4×D61C2312yes—
54D8×C61—41no—
55C2×C8×C61—41no—
56C2×C8×C61C2311yescharacteristic
57C2×C8×C61C2311yescharacteristic
58C4⋊C4×C61C2312yes—
59C22⋊C4×C61—22no—
60C22⋊Dic61—22no—
61#11758199—42no—
62#11758198—22no—
63#11758198—22no—
64C4⋊Dic61C2312yes—
65#11758196—22no—
66C2×#92418—41no—
67C2×#92418C2312yes—
68D488—41no—
69C23×C61—22no—
70C23×C61C2×D411yescharacteristic
71C22×D61—22no—
72C22×D61—41no—
73C22×D61—41no—
74C22×D61—44no—
75C22×D61—44no—
76C22×D61—44no—
77C22×D61D814yescomplemented
78C22×D61C2×D412yes—
79D4×C61—22no—
80D4×C61—22no—
81D4×C61—44no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—22no—
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2411yescharacteristic
87C22⋊D61—44no—
88C22⋊D61—44no—
89C22⋊D61—44no—
90C2×Dic61—22no—
91C2×Dic61—41no—
92C2×Dic61C2×D412yes—
93D244—22no—
94D244—22no—
95D244—44no—
96C4×D61—22no—
97C4×D61—22no—
98C4×D61—42no—
99C4×D61—44no—
100C8×C61—21no—
101C8×C61—21no—
102#92418—22no—
103C22×C61—21no—
104C22×C61—21no—
105C22×C61—42no—
106C22×C61—42no—
107C22×C61—42no—
108C22×C61C2×D812yes—
109C22×C61C22×D411yescharacteristic
110C2×D61—22no—
111C2×D61—22no—
112C2×D61—44no—
113C2×D61—42no—
114C2×D61—42no—
115C2×D61—42no—
116C2×D61—88no—
117C2×D61C2×D814yes—
118C4×C61—21no—
119C4×C61—42no—
120C4×C61H(5,𝔽2)11yescharacteristic
121C4×C61H(5,𝔽2)11yescharacteristic
122Dic61—22no—
123Dic61—42no—
124#3186—611nomaximal, Sylow
125C2×C61—22no—
126C2×C61—82no—
127C2×C61#53411yescharacteristic
128C2×C61C22×D811yescharacteristic
129C2×C61#57511yescharacteristic
130D61—24no—
131D61—82no—
132C2×#121—612no—
133#480—612no—
134#480—612no—
135#466—611no—
136#466—612no—
137#466D6111yescharacteristic, complemented
138#447—612no—
139#447—612no—
140C2×C22⋊C8—611no—
141C61#318611yescharacteristic, complemented, Sylow
142C22×D4—612no—
143C22×D4—1222no—
144C23×C4—611no—
145C2×D8—612no—
146C2×D8—611no—
147C2×D8C2×D6111yescharacteristic, complemented
148C22×C8—611no—
149C22×C8C2×D6111yescharacteristic, complemented
150#121—612no—
151#121—612no—
152#121—612no—
153#121—1222no—
154#121—1222no—
155#121C2×D6112yescomplemented
156C2×C4⋊C4—612no—
157C2×C22⋊C4—1222no—
158#107—611no—
159#107—612no—
160#107C2×D6111yescharacteristic, complemented
161#102—612no—
162#102—612no—
163#102—612no—
164#102C2×D6112yescomplemented
165C22⋊C8—612no—
166C22⋊C8—612no—
167C24—611no—
168C24—1222no—
169C2×D4—22no—
170C2×D4—612no—
171C2×D4—1222no—
172C2×D4—1222no—
173C2×D4—1222no—
174C2×D4—1222no—
175C2×D4—2442no—
176C2×D4—2442no—
177C2×D4—2448no—
178C2×D4C22×D6112yes—
179C22×C4—611no—
180C22×C4—612no—
181C22×C4—612no—
182C22×C4—1222no—
183C22×C4—2441no—
184C22×C4—2441no—
185C22×C4C22×D6111yescharacteristic
186D8—41no—
187D8—2441no—
188D8—2442no—
189C2×C8—41no—
190C2×C8—612no—
191C2×C8—2441no—
192C2×C8C22×D6111yescharacteristic
193C2×C8C22×D6111yescharacteristic
194C4⋊C4—612no—
195C4⋊C4—1222no—
196C4⋊C4C22×D6112yes—
197C22⋊C4—22no—
198C22⋊C4—1222no—
199C22⋊C4—1222no—
200C22⋊C4—1222no—
201C23—22no—
202C23—612no—
203C23—614no—
204C23—1222no—
205C23—2441no—
206C23—2441no—
207C23—2444no—
208C23—2444no—
209C23—2444no—
210C23D4×D6111yescharacteristic
211D4—22no—
212D4—22no—
213D4—44no—
214D4—1222no—
215D4—1222no—
216D4—2444no—
217D4—2444no—
218D4—2444no—
219D4—2444no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—612no—
224C2×C4—1222no—
225C2×C4—1222no—
226C2×C4—1222no—
227C2×C4—2442no—
228C2×C4—2444no—
229C2×C4—2441no—
230C2×C4D4×D6111yescharacteristic
231C2×C4C23×D6111yescharacteristic
232C8—21no—
233C8—21no—
234C8—1222no—
235C22—21no—
236C22—21no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—614no—
241C22—1222no—
242C22—1222no—
243C22—4888no—
244C22—2444no—
245C22—2442no—
246C22—2442no—
247C22—2442no—
248C22D8×D6112yes—
249C22C2×D4×D6111yescharacteristic
250C4—21no—
251C4—42no—
252C4—1222no—
253C4—2442no—
254C4#1451982211yescharacteristic
255C4#1451982311yescharacteristic
256C2—22no—
257C2—82no—
258C2—1224no—
259C2—4882no—
260C2#1684032011yescharacteristic
261C2C2×D8×D6111yescharacteristic
262C2#1684055911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#466C2
socleC22×C61C22×D4
hypercenter#466D61
hypocenterC61#3186
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #121×D61C2semidirect
2. #16840077C2semidirect
3. #16840074C2semidirect
4. #16839998C2semidirect
5. #16839996C2semidirect
6. #16839897C2semidirect
7. #16839894C2semidirect
8. C2×#14519689C2semidirect
9. C61×#466C2semidirect
11. C2×D4×D61C22semidirect
13. C2×D488C22semidirect
14. C2×#11758199C22semidirect
15. C22×#92418C22semidirect
17. #14519751C22semidirect
21. C4⋊C4×D61C22semidirect
23. #14519711C22semidirect
24. #14519710C22semidirect
25. #14519699C22semidirect
26. #14519698C22semidirect
27. #14519697C22semidirect
28. #14519689C22semidirect
29. #14519689C22semidirect
30. C2×D8×C61C22semidirect
31. C22×C8×C61C22semidirect
32. #121×C61C22semidirect
33. #107×C61C22semidirect
34. #102×C61C22semidirect
77. C22×D61D8semidirect
137. #466D61semidirect
141. C61#3186semidirect
147. C2×D8C2×D61semidirect
149. C22×C8C2×D61semidirect
155. #121C2×D61semidirect
160. #107C2×D61semidirect
164. #102C2×D61semidirect