Finite Group Databasebeta

← #21455896

Subgroups — #21455896

Order 7808.

390 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 119 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
2C2×#14519742C211yesmaximal, characteristic, complemented
3#16840092C211yesmaximal, characteristic, complemented
4#16840068C212yesmaximal, complemented
5#16839983C212yesmaximal, complemented
6#16839920C211yesmaximal, characteristic, complemented
7#16839900C211yesmaximal, characteristic
8#16839856C212yesmaximal, complemented
9#16839853C212yesmaximal, complemented
10#16839812C211yesmaximal, characteristic, complemented
11C61×#480C211yesmaximal, characteristic
12C22×Dic122C2211yescharacteristic
13C2×Dic244C2212yes—
14C2×#11758200C2212yes—
15#14519770—21no—
16#14519768C2211yescharacteristic
17#14519764C2211yescharacteristic
18#14519758—21no—
19#14519756C2211yescharacteristic
20#14519742—21no—
21#14519742—21no—
22#14519742C2212yes—
23#14519742C2212yes—
24#14519742C2211yescharacteristic
25D4×Dic61—21no—
26D4×Dic61C2211yescharacteristic
27#14519733—21no—
28C2×#11758196—21no—
29C2×C4×Dic61—21no—
30C2×C4×Dic61C2211yescharacteristic
31#14519708C2212yes—
32#14519706C2212yes—
33#14519702C2212yes—
34#14519700C2212yes—
35#14519700C2212yes—
36C22⋊#92418C2211yescharacteristic
37C8×Dic61C2212yes—
38#121×C61C2211yescharacteristic
39C2×C4⋊C4×C61C2211yescharacteristic
40#107×C61C2212yes—
41#102×C61C2212yes—
42C22⋊C8×C61C2211yescharacteristic
43C2×D4×C61—21no—
44C2×D4×C61C2311yescharacteristic
45C22×C4×C61—21no—
46C22×C4×C61C2311yescharacteristic
47C22×Dic61—21no—
48C22×Dic61—21no—
49C22×Dic61D411yescharacteristic
50C22×Dic61D411yescharacteristic
51C2×Dic122—21no—
52C2×Dic122—24no—
53C2×Dic122C2311yescharacteristic
54C2×Dic122C2312yes—
55C2×C8×C61C2312yes—
56C4⋊C4×C61—21no—
57C4⋊C4×C61C2312yes—
58C4⋊C4×C61C2311yescharacteristic
59C22⋊C4×C61—21no—
60C22⋊Dic61—21no—
61C22⋊Dic61—21no—
62C22⋊Dic61—21no—
63C22⋊Dic61—21no—
64#11758200—24no—
65C4⋊Dic61—21no—
66C4⋊Dic61C2311yescharacteristic
67#11758196—21no—
68#11758196—22no—
69#11758196—22no—
70#11758196—21no—
71#11758196—21no—
72C4×Dic61—22no—
73C4×Dic61—22no—
74C4×Dic61—21no—
75C4×Dic61D411yescharacteristic
76C4×Dic61D411yescharacteristic
77C4×Dic61C2311yescharacteristic
78C4×Dic61C2311yescharacteristic
79C2×#92418C2312yes—
80Dic244—24no—
81C23×C61—21no—
82C23×C61C2×D411yescharacteristic
83D4×C61—22no—
84D4×C61—42no—
85C2×C4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61—21no—
88C2×C4×C61—42no—
89C2×C4×C61C2×D411yescharacteristic
90C2×C4×C61C2411yescharacteristic
91C2×Dic61—24no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—21no—
96C2×Dic61—21no—
97C2×Dic61—42no—
98C2×Dic61C2×D411yescharacteristic
99C2×Dic61C2×D411yescharacteristic
100C2×Dic61C2×D411yescharacteristic
101C2×Dic61C2×D411yescharacteristic
102Dic122—24no—
103Dic122—22no—
104Dic122—22no—
105Dic122#4114yes—
106C8×C61—22no—
107#92418—22no—
108C22×C61—21no—
109C22×C61—21no—
110C22×C61—41no—
111C22×C61—41no—
112C22×C61—41no—
113C22×C61#13512yes—
114C22×C61C22×D411yescharacteristic
115C4×C61—21no—
116C4×C61—42no—
117C4×C61—41no—
118C4×C61C2×#4112yes—
119Dic61—24no—
120Dic61—21no—
121Dic61—21no—
122Dic61—21no—
123Dic61—41no—
124Dic61—41no—
125Dic61#13712yes—
126#3108—611nomaximal, Sylow
127C2×C61—22no—
128C2×C61—81no—
129C2×C61#52511yescharacteristic
130C2×C61C2×#13511yescharacteristic
131C2×C61C2×#13711yescharacteristic
132#529—611no—
133C2×C4×Q8—611no—
134#483—611no—
135#480D6111yescharacteristic
136#479—612no—
137#464—612no—
138#451—611no—
139#448—611no—
140C4×Q16—612no—
141C4×SD16—612no—
142#431—611no—
143C61#310811yescharacteristic, complemented, Sylow
144C22×Q8—611no—
145C2×Q16—612no—
146C2×SD16—612no—
147#126—1221no—
148#125—611no—
149#124—611no—
150#123—1221no—
151C22⋊Q8—611no—
152#121C2×D6111yescharacteristic
153C4×Q8—612no—
154C4×Q8—612no—
155C4×Q8—611no—
156C4×Q8—1221no—
157C4×Q8—1221no—
158C4×D4—611no—
159C4×D4—1221no—
160#117—1221no—
161C2×C4⋊C4—1221no—
162C2×C4⋊C4C2×D6111yescharacteristic
163C2×C42—611no—
164C2×C42—1221no—
165#107C2×D6112yes—
166#106—612no—
167C4⋊C8—612no—
168#103—612no—
169#103—612no—
170#103—612no—
171#102C2×D6112yes—
172C22⋊C8—611no—
173C22⋊C8C2×D6111yescharacteristic
174C4×C8—612no—
175C2×Q8—612no—
176C2×Q8—611no—
177C2×Q8—1224no—
178C2×Q8—1221no—
179C2×D4—21no—
180C2×D4C22×D6111yescharacteristic
181C22×C4—21no—
182C22×C4—611no—
183C22×C4—611no—
184C22×C4—1221no—
185C22×C4—1221no—
186C22×C4C22×D6111yescharacteristic
187Q16—1224no—
188SD16—1224no—
189C2×C8—612no—
190C2×C8C22×D6112yes—
191C4⋊C4—21no—
192C4⋊C4—611no—
193C4⋊C4—1222no—
194C4⋊C4—1222no—
195C4⋊C4—1221no—
196C4⋊C4—1221no—
197C4⋊C4—1221no—
198C4⋊C4—1221no—
199C4⋊C4C22×D6112yes—
200C4⋊C4C22×D6111yescharacteristic
201C22⋊C4—21no—
202C22⋊C4—1221no—
203C22⋊C4—1221no—
204C22⋊C4—1221no—
205C22⋊C4—1221no—
206C42—611no—
207C42—611no—
208C42—611no—
209C42—611no—
210C42—1222no—
211C42—1222no—
212C42—1221no—
213C23—21no—
214C23D4×D6111yescharacteristic
215Q8—614no—
216Q8—1224no—
217Q8—1222no—
218Q8—1222no—
219D4—22no—
220D4—42no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—42no—
225C2×C4—611no—
226C2×C4—611no—
227C2×C4—611no—
228C2×C4—611no—
229C2×C4—1222no—
230C2×C4—1224no—
231C2×C4—1222no—
232C2×C4—1222no—
233C2×C4—1221no—
234C2×C4—1221no—
235C2×C4—2442no—
236C2×C4D4×D6111yescharacteristic
237C2×C4C23×D6111yescharacteristic
238C8—22no—
239C8—1222no—
240C22—21no—
241C22—21no—
242C22—41no—
243C22—41no—
244C22—41no—
245C22#1451979612yes—
246C22C2×D4×D6111yescharacteristic
247C4—21no—
248C4—42no—
249C4—41no—
250C4—612no—
251C4—1224no—
252C4—1221no—
253C4—1221no—
254C4—1221no—
255C4—2441no—
256C4—2441no—
257C4#41×D6112yes—
258C2—22no—
259C2—81no—
260C2#1684027011yescharacteristic
261C2C2×#1451979611yescharacteristic
262C2#137×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#480C2
socleC22×C61C22×D4
hypercenter#480D61
hypocenterC61#3108
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. C2×#14519742C2semidirect
3. #16840092C2semidirect
4. #16840068C2semidirect
5. #16839983C2semidirect
6. #16839920C2semidirect
8. #16839856C2semidirect
9. #16839853C2semidirect
10. #16839812C2semidirect
143. C61#3108semidirect