Finite Group Databasebeta

← #21456781

Subgroups — #21456781

Order 7808.

410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 113 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#16840293C211yesmaximal, characteristic, complemented
2C2×#14519764C211yesmaximal, characteristic, complemented
3#16840145C212yesmaximal, complemented
4#16840115C212yesmaximal, complemented
5#16839983C212yesmaximal, complemented
6#16839975C212yesmaximal, complemented
7#16839920C211yesmaximal, characteristic, complemented
8#16839913C211yesmaximal, characteristic, complemented
9#16839900C211yesmaximal, characteristic, complemented
10#16839812C211yesmaximal, characteristic, complemented
11C61×#447C211yesmaximal, characteristic
12C22×Dic122C2211yescharacteristic
13C2×Dic244C2212yescomplemented
14C2×#11758200C2212yes—
15C2×#11758200C2212yescomplemented
16#14519770—21no—
17#14519768C2211yescharacteristic, complemented
18#14519764—21no—
19#14519764—21no—
20#14519764C2212yes—
21#14519764C2212yes—
22#14519764C2211yescharacteristic, complemented
23#14519758—21no—
24#14519756C2211yescharacteristic
25#14519742C2211yescharacteristic, complemented
26D4×Dic61—21no—
27D4×Dic61C2211yescharacteristic, complemented
28#14519733—21no—
29C2×C22⋊Dic61—21no—
30C2×C22⋊Dic61—21no—
31C2×C4×Dic61C2211yescharacteristic
32#14519706C2212yescomplemented
33#14519702C2212yescomplemented
34#14519700C2212yescomplemented
35#14519698C2212yes—
36C22⋊#92418C2211yescharacteristic
37C8×Dic61C2212yescomplemented
38C22×D4×C61C2211yescharacteristic
39C2×D8×C61C2212yes—
40#121×C61C2211yescharacteristic
41#102×C61C2212yes—
42C22⋊C8×C61C2211yescharacteristic
43C24×C61—21no—
44C2×D4×C61—21no—
45C2×D4×C61—21no—
46C2×D4×C61—42no—
47C2×D4×C61C2312yes—
48C2×D4×C61C2311yescharacteristic
49C22×C4×C61C2311yescharacteristic
50C22×Dic61—21no—
51C22×Dic61—21no—
52C22×Dic61D411yescharacteristic
53C22×Dic61D411yescharacteristic
54C2×Dic122—21no—
55C2×Dic122—42no—
56C2×Dic122C2312yes—
57C2×Dic122C2311yescharacteristic
58D8×C61—42no—
59C2×C8×C61C2312yes—
60C4⋊C4×C61C2311yescharacteristic
61C22⋊C4×C61—21no—
62C22⋊Dic61—21no—
63C22⋊Dic61—22no—
64C22⋊Dic61—22no—
65C22⋊Dic61—22no—
66C22⋊Dic61—22no—
67C22⋊Dic61—21no—
68C22⋊Dic61—21no—
69C22⋊Dic61—21no—
70#11758200—42no—
71#11758200—42no—
72C4⋊Dic61—21no—
73C4⋊Dic61C2311yescharacteristic
74#11758196—21no—
75#11758196—21no—
76#11758196—21no—
77C4×Dic61—21no—
78C4×Dic61D411yescharacteristic
79C4×Dic61D411yescharacteristic
80C4×Dic61C2311yescharacteristic
81C4×Dic61C2311yescharacteristic
82C2×#92418C2312yes—
83Dic244—42no—
84C23×C61—22no—
85C23×C61—21no—
86C23×C61—42no—
87C23×C61—42no—
88C23×C61—42no—
89C23×C61C2×D411yescharacteristic
90D4×C61—22no—
91D4×C61—22no—
92D4×C61—22no—
93D4×C61—42no—
94D4×C61—42no—
95C2×C4×C61—22no—
96C2×C4×C61—21no—
97C2×C4×C61C2×D411yescharacteristic
98C2×C4×C61C2411yescharacteristic
99C2×Dic61—22no—
100C2×Dic61—21no—
101C2×Dic61—21no—
102C2×Dic61—22no—
103C2×Dic61—41no—
104C2×Dic61—42no—
105C2×Dic61—42no—
106C2×Dic61C2×D411yescharacteristic
107C2×Dic61C2×D411yescharacteristic
108C2×Dic61C2×D411yescharacteristic
109C2×Dic61C2×D411yescharacteristic
110Dic122—22no—
111Dic122—22no—
112Dic122—22no—
113Dic122—42no—
114C8×C61—22no—
115#92418—22no—
116C22×C61—21no—
117C22×C61—21no—
118C22×C61—42no—
119C22×C61—41no—
120C22×C61—41no—
121C22×C61—42no—
122C22×C61—41no—
123C22×C61—42no—
124C22×C61—84no—
125C22×C61#13512yes—
126C22×C61C22×D411yescharacteristic
127C4×C61—21no—
128C4×C61—41no—
129C4×C61H(5,𝔽2)12yes—
130Dic61—21no—
131Dic61—21no—
132Dic61—21no—
133Dic61—21no—
134Dic61—42no—
135Dic61—41no—
136Dic61—41no—
137#3211—611nomaximal, Sylow
138C2×C61—22no—
139C2×C61—81no—
140C2×C61—82no—
141C2×C61#53511yescharacteristic
142C2×C61C2×#13511yescharacteristic
143C2×C61#57511yescharacteristic
144#529—611no—
145C2×#124—611no—
146#495—612no—
147#488—612no—
148#464—612no—
149#463—612no—
150#451—611no—
151#450—611no—
152#448—611no—
153#447D6111yescharacteristic
154#431—611no—
155C61#321111yescharacteristic, complemented, Sylow
156C22×Q8—611no—
157C22×D4C2×D6111yescharacteristic
158C2×Q16—612no—
159C2×SD16—612no—
160C2×SD16—612no—
161C2×D8C2×D6112yes—
162#126—1221no—
163#125—611no—
164#124—612no—
165#124—612no—
166#124—611no—
167#124—1221no—
168#124—1221no—
169#123—1221no—
170C22⋊Q8—611no—
171#121C2×D6111yescharacteristic
172C4×Q8—611no—
173C4×D4—611no—
174C4×D4—1221no—
175#117—1221no—
176C2×C22⋊C4—1221no—
177C2×C22⋊C4—1221no—
178C2×C42—611no—
179C4⋊C8—612no—
180#103—612no—
181#103—612no—
182#102—612no—
183#102C2×D6112yes—
184C22⋊C8—611no—
185C22⋊C8C2×D6111yescharacteristic
186C4×C8—612no—
187C24—21no—
188C2×Q8—612no—
189C2×Q8—611no—
190C2×Q8—1221no—
191C2×Q8—2442no—
192C2×D4—21no—
193C2×D4—21no—
194C2×D4—42no—
195C2×D4C22×D6112yes—
196C2×D4C22×D6111yescharacteristic
197C22×C4—611no—
198C22×C4—611no—
199C22×C4—1221no—
200C22×C4—1221no—
201C22×C4C22×D6111yescharacteristic
202Q16—2442no—
203SD16—2442no—
204SD16—2442no—
205D8—42no—
206C2×C8—612no—
207C2×C8C22×D6112yes—
208C4⋊C4—611no—
209C4⋊C4—1221no—
210C4⋊C4—1221no—
211C4⋊C4—1221no—
212C4⋊C4—1221no—
213C4⋊C4C22×D6111yescharacteristic
214C22⋊C4—21no—
215C22⋊C4—1222no—
216C22⋊C4—1222no—
217C22⋊C4—1222no—
218C22⋊C4—1222no—
219C22⋊C4—1221no—
220C22⋊C4—1221no—
221C22⋊C4—1221no—
222C22⋊C4—1221no—
223C42—611no—
224C42—611no—
225C42—611no—
226C42—611no—
227C42—1221no—
228C23—21no—
229C23—22no—
230C23—42no—
231C23—42no—
232C23—42no—
233C23D4×D6111yescharacteristic
234Q8—1222no—
235Q8—1222no—
236Q8—1222no—
237Q8—2442no—
238D4—22no—
239D4—22no—
240D4—22no—
241D4—42no—
242D4—42no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—611no—
246C2×C4—611no—
247C2×C4—611no—
248C2×C4—611no—
249C2×C4—1222no—
250C2×C4—1221no—
251C2×C4—1222no—
252C2×C4—1221no—
253C2×C4—2441no—
254C2×C4—2442no—
255C2×C4—2442no—
256C2×C4D4×D6111yescharacteristic
257C2×C4C23×D6111yescharacteristic
258C8—22no—
259C8—1222no—
260C22—21no—
261C22—21no—
262C22—41no—
263C22—42no—
264C22—41no—
265C22—42no—
266C22—42no—
267C22—41no—
268C22—84no—
269C22#1451979612yes—
270C22C2×D4×D6111yescharacteristic
271C4—21no—
272C4—41no—
273C4—1221no—
274C4—1221no—
275C4—1221no—
276C4—1221no—
277C4—2441no—
278C4—2442no—
279C4—2441no—
280C4#1451982212yes—
281C2—22no—
282C2—82no—
283C2—81no—
284C2#1684032711yescharacteristic
285C2C2×#1451979611yescharacteristic
286C2#1684055811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#447C2
socleC22×C61C22×D4
hypercenter#447D61
hypocenterC61#3211
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #16840293C2semidirect
2. C2×#14519764C2semidirect
3. #16840145C2semidirect
4. #16840115C2semidirect
5. #16839983C2semidirect
6. #16839975C2semidirect
7. #16839920C2semidirect
8. #16839913C2semidirect
9. #16839900C2semidirect
10. #16839812C2semidirect
13. C2×Dic244C22semidirect
15. C2×#11758200C22semidirect
17. #14519768C22semidirect
22. #14519764C22semidirect
25. #14519742C22semidirect
27. D4×Dic61C22semidirect
32. #14519706C22semidirect
33. #14519702C22semidirect
34. #14519700C22semidirect
37. C8×Dic61C22semidirect
155. C61#3211semidirect