Finite Group Databasebeta

← #21456801

Subgroups — #21456801

Order 7808.

444 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 111 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#16840310C211yesmaximal, characteristic, complemented
2#124×D61C211yesmaximal, characteristic, complemented
3#16840149C211yesmaximal, characteristic, complemented
4#16840122C211yesmaximal, characteristic, complemented
5#16840121C211yesmaximal, characteristic, complemented
6#16839979C212yesmaximal, complemented
7#16839975C212yesmaximal, complemented
8#16839899C212yesmaximal, complemented
9#16839894C212yesmaximal, complemented
10#16839817C211yesmaximal, characteristic, complemented
11C61×#496C211yesmaximal, characteristic, complemented
12C2×#11758224—21no—
13C2×Q8×D61C2211yescharacteristic
14C2×D4×D61C2211yescharacteristic
15C2×#11758200C2212yescomplemented
16C2×#11758199C2212yes—
17#14519777C2211yescharacteristic, complemented
18#14519766C2211yescharacteristic
19#14519765C2211yescharacteristic
20#14519764—21no—
21#14519764C2211yescharacteristic
22#14519763—21no—
23#14519763—21no—
24#14519748—21no—
25#14519748C2212yes—
26D4×Dic61—21no—
27D4×Dic61C2212yescomplemented
28C22⋊C4×D61—21no—
29C22⋊C4×D61—21no—
30C42×D61C2211yescharacteristic
31#14519706C2212yescomplemented
32#14519702C2212yescomplemented
33#14519701C2212yescomplemented
34#14519699C2212yes—
35#14519698C2212yes—
36#14519689C2212yes—
37#14519688C2211yescharacteristic, complemented
38C2×SD16×C61C2212yescomplemented
39C2×D8×C61C2212yes—
40#127×C61C2211yescharacteristic, complemented
41#124×C61C2211yescharacteristic
42#97×C61C2211yescharacteristic, complemented
43C23×D61—21no—
44C2×Q8×C61C2311yescharacteristic
45C2×D4×C61—21no—
46C2×D4×C61—21no—
47C2×D4×C61C2311yescharacteristic
48C2×D4×C61C2312yes—
49C2×C22⋊D61—22no—
50C2×C22⋊D61—21no—
51C22×Dic61—22no—
52Q8×D61—42no—
53#11758224—44no—
54D4×D61—42no—
55C2×D244C2311yescharacteristic
56C2×C4×D61—21no—
57C2×C4×D61D411yescharacteristic
58C2×C4×D61D411yescharacteristic
59C2×C4×D61C2311yescharacteristic
60C2×Dic122—21no—
61C2×Dic122—21no—
62C2×Dic122C2311yescharacteristic
63SD16×C61—42no—
64D8×C61—42no—
65C2×C8×C61C2312yes—
66C22⋊C4×C61—21no—
67C22⋊C4×C61—21no—
68C42×C61C2311yescharacteristic
69C22⋊Dic61—21no—
70C22⋊Dic61—21no—
71C22⋊Dic61—22no—
72C22⋊Dic61—22no—
73#11758200—42no—
74#11758199—42no—
75#11758198—21no—
76#11758198—21no—
77#11758198—21no—
78#11758198—21no—
79C4⋊Dic61—21no—
80C4⋊Dic61C2312yes—
81C4×Dic61D411yescharacteristic
82C4×Dic61D411yescharacteristic
83C4×Dic61C2311yescharacteristic
84C2×#92418C2312yes—
85C23×C61—21no—
86C23×C61—22no—
87C22×D61—21no—
88C22×D61—42no—
89C22×D61—42no—
90C22×D61—42no—
91C22×D61C2×D411yescharacteristic
92Q8×C61—22no—
93D4×C61—22no—
94D4×C61—22no—
95D4×C61—22no—
96D4×C61—42no—
97D4×C61—42no—
98C2×C4×C61—21no—
99C2×C4×C61C2×D411yescharacteristic
100C2×C4×C61C2×D411yescharacteristic
101C2×C4×C61C2411yescharacteristic
102C22⋊D61—42no—
103C22⋊D61—44no—
104C2×Dic61—22no—
105C2×Dic61—21no—
106C2×Dic61—44no—
107C2×Dic61C2×D411yescharacteristic
108C2×Dic61C2×D411yescharacteristic
109C2×Dic61C2×D411yescharacteristic
110D244—22no—
111C4×D61—22no—
112C4×D61—22no—
113C4×D61—41no—
114C4×D61—42no—
115Dic122—22no—
116Dic122—42no—
117Dic122—42no—
118C8×C61—22no—
119#92418—22no—
120C22×C61—41no—
121C22×C61—42no—
122C22×C61—42no—
123C22×C61—41no—
124C22×C61—42no—
125C22×C61—41no—
126C22×C61C22×D411yescharacteristic
127C2×D61—21no—
128C2×D61—21no—
129C2×D61—41no—
130C2×D61—41no—
131C2×D61—41no—
132C2×D61—84no—
133C2×D61AGL(1,ℤ/8)12yes—
134C4×C61—21no—
135C4×C61—21no—
136C4×C61—41no—
137C4×C61H(5,𝔽2)12yes—
138Dic61—21no—
139Dic61—21no—
140Dic61—21no—
141Dic61—41no—
142Dic61—42no—
143#3213—611nomaximal, Sylow
144C2×C61—81no—
145C2×C61—82no—
146C2×C61#53511yescharacteristic
147C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
148C2×C61#57511yescharacteristic
149D61—22no—
150D61—81no—
151#532—611no—
152C2×#124—611no—
153#496—611no—
154#496D6111yescharacteristic, complemented
155#489—611no—
156#489—611no—
157#463—612no—
158#463—612no—
159#448—612no—
160#447—612no—
161#432—611no—
162C61#321311yescharacteristic, complemented, Sylow
163C2×#41—1221no—
164C22×Q8—611no—
165C22×D4—611no—
166C2×SD16—612no—
167C2×SD16C2×D6112yescomplemented
168C2×D8—612no—
169C2×D8C2×D6112yes—
170C4⋊Q8—611no—
171#127C2×D6111yescharacteristic, complemented
172#124—611no—
173#124—611no—
174#124—611no—
175#124—1221no—
176#124—1221no—
177#124—1221no—
178#124C2×D6111yescharacteristic
179#121—612no—
180#121—1221no—
181C4×D4—612no—
182C4×D4—1221no—
183C2×C22⋊C4—1221no—
184C2×C22⋊C4—1221no—
185C2×C42—611no—
186C4⋊C8—612no—
187#103—612no—
188#103—612no—
189#102—612no—
190#102—612no—
191C22⋊C8—612no—
192#97—611no—
193#97C2×D6111yescharacteristic, complemented
194C24—1221no—
195#41—2444no—
196C2×Q8—611no—
197C2×Q8—1221no—
198C2×Q8—1221no—
199C2×Q8—2442no—
200C2×Q8C22×D6111yescharacteristic
201C2×D4—21no—
202C2×D4—21no—
203C2×D4—611no—
204C2×D4—1221no—
205C2×D4—1222no—
206C2×D4—2442no—
207C2×D4C22×D6111yescharacteristic
208C2×D4C22×D6112yes—
209C22×C4—611no—
210C22×C4—611no—
211C22×C4—611no—
212C22×C4—1221no—
213C22×C4—1222no—
214SD16—42no—
215SD16—2442no—
216D8—42no—
217D8—2442no—
218C2×C8—612no—
219C2×C8C22×D6112yes—
220C4⋊C4—612no—
221C4⋊C4—1221no—
222C22⋊C4—21no—
223C22⋊C4—21no—
224C22⋊C4—1221no—
225C22⋊C4—1221no—
226C22⋊C4—1221no—
227C22⋊C4—1221no—
228C22⋊C4—1222no—
229C22⋊C4—1222no—
230C22⋊C4—1221no—
231C22⋊C4—1221no—
232C42—611no—
233C42—611no—
234C42—611no—
235C42C22×D6111yescharacteristic
236C23—21no—
237C23—22no—
238C23—611no—
239C23—1221no—
240C23—2442no—
241C23—2442no—
242C23—2442no—
243Q8—22no—
244Q8—1222no—
245Q8—2442no—
246Q8—2442no—
247D4—22no—
248D4—22no—
249D4—22no—
250D4—42no—
251D4—42no—
252D4—1222no—
253D4—2442no—
254D4—2444no—
255C2×C4—21no—
256C2×C4—611no—
257C2×C4—611no—
258C2×C4—611no—
259C2×C4—1222no—
260C2×C4—1222no—
261C2×C4—1221no—
262C2×C4—1222no—
263C2×C4—2441no—
264C2×C4—2442no—
265C2×C4—2444no—
266C2×C4D4×D6111yescharacteristic
267C2×C4D4×D6111yescharacteristic
268C2×C4C23×D6111yescharacteristic
269C8—22no—
270C8—1222no—
271C22—42no—
272C22—41no—
273C22—42no—
274C22—41no—
275C22—41no—
276C22—42no—
277C22—612no—
278C22—1221no—
279C22—1221no—
280C22—4884no—
281C22—2441no—
282C22—2441no—
283C22—2441no—
284C22C2×D4×D6111yescharacteristic
285C4—21no—
286C4—21no—
287C4—41no—
288C4—1221no—
289C4—1221no—
290C4—1221no—
291C4—2442no—
292C4—2441no—
293C4#1451982212yes—
294C2—81no—
295C2—82no—
296C2—1222no—
297C2—4881no—
298C2#1684032511yescharacteristic
299C2AGL(1,ℤ/8)×D6111yescharacteristic
300C2#1684055811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#496C2
socleC22×C61C22×D4
hypercenter#496D61
hypocenterC61#3213
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. #16840310C2semidirect
2. #124×D61C2semidirect
3. #16840149C2semidirect
4. #16840122C2semidirect
5. #16840121C2semidirect
6. #16839979C2semidirect
7. #16839975C2semidirect
8. #16839899C2semidirect
9. #16839894C2semidirect
10. #16839817C2semidirect
11. C61×#496C2semidirect
15. C2×#11758200C22semidirect
17. #14519777C22semidirect
27. D4×Dic61C22semidirect
31. #14519706C22semidirect
32. #14519702C22semidirect
33. #14519701C22semidirect
37. #14519688C22semidirect
38. C2×SD16×C61C22semidirect
40. #127×C61C22semidirect
42. #97×C61C22semidirect
154. #496D61semidirect
162. C61#3213semidirect
167. C2×SD16C2×D61semidirect
171. #127C2×D61semidirect
193. #97C2×D61semidirect