Finite Group Databasebeta

← #21456680

Subgroups — #21456680

Order 7808.

442 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 117 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#16840326C211yesmaximal, characteristic, complemented
2#16840086C212yesmaximal, complemented
3#16840083C212yesmaximal, complemented
4#16840013C212yesmaximal, complemented
5#16839996C212yesmaximal, complemented
6#16839896C212yesmaximal, complemented
7#16839895C212yesmaximal, complemented
8#16839729C211yesmaximal, characteristic, complemented
9C61×#535C211yesmaximal, characteristic, complemented
10C22×D244C2211yescharacteristic, complemented
11C2×#11758199C2212yes—
12C2×#11758199C2212yes—
13C2×#11758194C2211yescharacteristic, complemented
14C22×#92418C2211yescharacteristic, complemented
15#14519773—21no—
16#14519766—21no—
17#14519751C2212yes—
18#14519751C2212yescomplemented
19#14519745—21no—
20#14519745—21no—
21#14519736C2211yescharacteristic, complemented
22#14519710C2212yescomplemented
23#14519708C2212yescomplemented
24#14519698C2212yescomplemented
25#14519698C2212yescomplemented
26#14519697C2212yescomplemented
27#14519697C2212yescomplemented
28C22⋊#92418C2212yescomplemented
29C22⋊#92418C2212yescomplemented
30C2×#41×C61C2211yescharacteristic
31C22×D4×C61C2211yescharacteristic, complemented
32#127×C61—21no—
33#124×C61—21no—
34#121×C61C2212yes—
35#121×C61C2212yescomplemented
36#120×C61—21no—
37#120×C61—21no—
38#117×C61C2211yescharacteristic, complemented
39C24×C61—21no—
40C23×D61—21no—
41#41×C61—41no—
42#41×C61—41no—
43C2×Q8×C61D411yescharacteristic
44C2×D4×C61—22no—
45C2×D4×C61—22no—
46C2×D4×C61—21no—
47C2×D4×C61—41no—
48C2×D4×C61—41no—
49C2×D4×C61D411yescharacteristic
50C2×D4×C61D411yescharacteristic
51C2×D4×C61D411yescharacteristic
52C2×D4×C61C2312yes—
53C22×C4×C61C2311yescharacteristic
54C22×C4×C61C2311yescharacteristic
55C22×C4×C61C2311yescharacteristic
56C2×C22⋊D61—22no—
57C2×C22⋊D61—22no—
58C2×D244—21no—
59C2×D244—41no—
60C2×D244—41no—
61C2×D244C2312yes—
62C4⋊C4×C61C2312yes—
63C22⋊C4×C61—21no—
64C22⋊C4×C61—22no—
65C22⋊C4×C61—22no—
66C42×C61—21no—
67C22⋊Dic61—21no—
68#11758199—42no—
69#11758199—42no—
70#11758198—22no—
71#11758198—22no—
72C4⋊Dic61C2312yes—
73C4×Dic61—21no—
74#11758194—41no—
75C2×#92418—41no—
76C2×#92418C2312yes—
77C2×#92418C2312yes—
78C23×C61—22no—
79C23×C61—42no—
80C23×C61—82no—
81C23×C61C2×D411yescharacteristic
82C23×C61C2×D411yescharacteristic
83C23×C61C2×D411yescharacteristic
84C22×D61—22no—
85C22×D61—42no—
86C22×D61—82no—
87Q8×C61—41no—
88D4×C61—22no—
89D4×C61—22no—
90D4×C61—41no—
91D4×C61—41no—
92D4×C61—41no—
93D4×C61—42no—
94D4×C61—82no—
95D4×C61—82no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—22no—
103C2×C4×C61C2×D411yescharacteristic
104C2×C4×C61C2×D411yescharacteristic
105C2×C4×C61C2×D411yescharacteristic
106C2×C4×C61C2411yescharacteristic
107C22⋊D61—82no—
108C22⋊D61—82no—
109C2×Dic61—22no—
110D244—22no—
111D244—22no—
112D244—42no—
113#92418—22no—
114#92418—22no—
115C22×C61—21no—
116C22×C61—21no—
117C22×C61—21no—
118C22×C61—22no—
119C22×C61—22no—
120C22×C61—22no—
121C22×C61—42no—
122C22×C61—42no—
123C22×C61—42no—
124C22×C61—84no—
125C22×C61C22×D411yescharacteristic
126C2×D61—42no—
127C2×D61—42no—
128C2×D61—42no—
129C2×D61—84no—
130C4×C61—21no—
131C4×C61—21no—
132C4×C61—21no—
133C4×C61—42no—
134C4×C61H(5,𝔽2)11yescharacteristic
135C4×C61H(5,𝔽2)11yescharacteristic
136Dic61—42no—
137#3199—611nomaximal, Sylow
138C2×C61—41no—
139C2×C61—41no—
140C2×C61—41no—
141C2×C61—82no—
142C2×C61#53411yescharacteristic
143C2×C61#57612yes—
144D61—82no—
145#535—611no—
146#535D6111yescharacteristic, complemented
147#482—612no—
148#482—612no—
149#469—612no—
150#466—612no—
151#447—612no—
152#447—612no—
153#408—611no—
154C61#319911yescharacteristic, complemented, Sylow
155C2×#41C2×D6111yescharacteristic
156C22×D4—611no—
157C22×D4C2×D6111yescharacteristic, complemented
158C2×D8—612no—
159C2×D8—612no—
160C2×M16—611no—
161C22×C8—611no—
162#127—21no—
163#127—1221no—
164#124—21no—
165#124—1221no—
166#121—612no—
167#121—612no—
168#121C2×D6112yes—
169#121C2×D6112yescomplemented
170#120—21no—
171#120—21no—
172#120—1221no—
173#120—1221no—
174#117—611no—
175#117C2×D6111yescharacteristic, complemented
176#107—612no—
177#106—612no—
178#102—612no—
179#102—612no—
180#102—612no—
181#102—612no—
182C22⋊C8—612no—
183C22⋊C8—612no—
184C24—21no—
185C24—1221no—
186#41—41no—
187#41—41no—
188C2×Q8C22⋊D6111yescharacteristic
189C2×D4—22no—
190C2×D4—22no—
191C2×D4—21no—
192C2×D4—41no—
193C2×D4—41no—
194C2×D4—612no—
195C2×D4—1222no—
196C2×D4—1222no—
197C2×D4—1221no—
198C2×D4—2441no—
199C2×D4—2441no—
200C2×D4C22⋊D6111yescharacteristic
201C2×D4C22⋊D6111yescharacteristic
202C2×D4C22⋊D6111yescharacteristic
203C2×D4C22×D6112yes—
204C22×C4C22×D6111yescharacteristic
205C22×C4C22×D6111yescharacteristic
206C22×C4C22×D6111yescharacteristic
207D8—2442no—
208D8—2442no—
209M16—2441no—
210C2×C8—612no—
211C2×C8—612no—
212C2×C8—2441no—
213C4⋊C4—612no—
214C4⋊C4C22×D6112yes—
215C22⋊C4—21no—
216C22⋊C4—22no—
217C22⋊C4—22no—
218C22⋊C4—1221no—
219C22⋊C4—1222no—
220C22⋊C4—1222no—
221C42—21no—
222C42—1221no—
223C23—22no—
224C23—42no—
225C23—82no—
226C23—1222no—
227C23—4882no—
228C23—2442no—
229C23C2×C22⋊D6111yescharacteristic
230C23C2×C22⋊D6111yescharacteristic
231C23C2×C22⋊D6111yescharacteristic
232Q8—41no—
233D4—22no—
234D4—22no—
235D4—41no—
236D4—41no—
237D4—41no—
238D4—42no—
239D4—82no—
240D4—82no—
241D4—1222no—
242D4—1222no—
243D4—4882no—
244D4—4882no—
245D4—2442no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—1222no—
254C2×C4C2×C22⋊D6111yescharacteristic
255C2×C4C2×C22⋊D6111yescharacteristic
256C2×C4C2×C22⋊D6111yescharacteristic
257C2×C4C23×D6111yescharacteristic
258C8—1222no—
259C8—1222no—
260C22—22no—
261C22—22no—
262C22—22no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—42no—
267C22—42no—
268C22—42no—
269C22—84no—
270C22—4884no—
271C22—2442no—
272C22—2442no—
273C22—2442no—
274C22C22×C22⋊D6111yescharacteristic
275C4—21no—
276C4—21no—
277C4—21no—
278C4—42no—
279C4—2442no—
280C4#1451982211yescharacteristic
281C4#1451982211yescharacteristic
282C2—41no—
283C2—41no—
284C2—41no—
285C2—82no—
286C2—4882no—
287C2#1684032111yescharacteristic
288C2#1684056512yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#535C2
socleC22×C61C22×D4
hypercenter#535D61
hypocenterC61#3199
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #16840326C2semidirect
2. #16840086C2semidirect
3. #16840083C2semidirect
4. #16840013C2semidirect
5. #16839996C2semidirect
6. #16839896C2semidirect
7. #16839895C2semidirect
8. #16839729C2semidirect
9. C61×#535C2semidirect
10. C22×D244C22semidirect
13. C2×#11758194C22semidirect
14. C22×#92418C22semidirect
18. #14519751C22semidirect
21. #14519736C22semidirect
22. #14519710C22semidirect
23. #14519708C22semidirect
24. #14519698C22semidirect
25. #14519698C22semidirect
26. #14519697C22semidirect
27. #14519697C22semidirect
28. C22⋊#92418C22semidirect
29. C22⋊#92418C22semidirect
31. C22×D4×C61C22semidirect
35. #121×C61C22semidirect
38. #117×C61C22semidirect
146. #535D61semidirect
154. C61#3199semidirect
157. C22×D4C2×D61semidirect
169. #121C2×D61semidirect
175. #117C2×D61semidirect