Finite Group Databasebeta

← #21457768

Subgroups — #21457768

Order 7808.

408 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 115 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#16840478C211yesmaximal, characteristic, complemented
2#16840432C211yesmaximal, characteristic, complemented
3#16840085C212yesmaximal, complemented
4#16840054C211yesmaximal, characteristic, complemented
5#16839997C212yesmaximal, complemented
6#16839954C211yesmaximal, characteristic, complemented
7#16839908C212yesmaximal, complemented
8C4×#11758190C211yesmaximal, characteristic, complemented
9C8×D244C211yesmaximal, characteristic, complemented
10#16839755C212yesmaximal, complemented
11C61×#486C211yesmaximal, characteristic, complemented
12C2×#11758224C2212yes—
13C2×#11758190C2211yescharacteristic
14C2×#11758199C2212yes—
15C2×C8×D61C2212yes—
16#14519773—21no—
17#14519766—22no—
18#14519752—21no—
19#14519752C2212yes—
20#14519749—22no—
21#14519748C2212yes—
22C4×Dic122C2211yescharacteristic
23C4×D244C2211yescharacteristic
24C4×D244C2211yescharacteristic
25D4×Dic61—21no—
26#14519735—21no—
27#14519735C2212yes—
28#14519710C2212yes—
29#14519709C2211yescharacteristic
30C4⋊#92418C2211yescharacteristic
31#14519702C2211yescharacteristic
32#14519700C2212yes—
33#14519699C2211yescharacteristic
34#14519698C2212yes—
35#14519689C2212yes—
36C4⋊Q8×C61C2211yescharacteristic
37#127×C61C2211yescharacteristic
38#102×C61C2212yes—
39#102×C61C2212yes—
40C4×C8×C61C2211yescharacteristic
41C2×Q8×C61—21no—
42C2×D4×C61—21no—
43C2×D4×C61—21no—
44C2×D4×C61C2312yes—
45C2×C22⋊D61—22no—
46C2×C22⋊D61—22no—
47C22×Dic61—22no—
48#11758224—24no—
49#11758224—42no—
50C2×D244—22no—
51C2×D244D411yescharacteristic
52C2×D244C2311yescharacteristic
53C2×C4×D61—21no—
54C2×C4×D61C2312yes—
55C2×Dic122C2311yescharacteristic
56C2×C8×C61C2311yescharacteristic
57C2×C8×C61C2311yescharacteristic
58C4⋊C4×C61—21no—
59C4⋊C4×C61C2312yes—
60C42×C61C2311yescharacteristic
61C22⋊Dic61—22no—
62#11758199—42no—
63#11758198—22no—
64#11758198—21no—
65#11758198—22no—
66#11758198D412yes—
67C4⋊Dic61D411yescharacteristic
68C4⋊Dic61C2311yescharacteristic
69C4⋊Dic61C2311yescharacteristic
70#11758196—21no—
71C4×Dic61—21no—
72C4×Dic61—22no—
73C2×#92418C2312yes—
74#11758190—22no—
75C8×D61—42no—
76C23×C61—22no—
77C22×D61—21no—
78C22×D61C2×D412yes—
79Q8×C61—81no—
80D4×C61—22no—
81D4×C61—22no—
82D4×C61—42no—
83D4×C61—81no—
84C2×C4×C61—22no—
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2×D411yescharacteristic
87C2×C4×C61C2411yescharacteristic
88C22⋊D61—44no—
89C22⋊D61—82no—
90C2×Dic61—21no—
91C2×Dic61—21no—
92C2×Dic61—21no—
93C2×Dic61—44no—
94C2×Dic61C2×D412yes—
95D244—22no—
96D244—21no—
97D244—21no—
98D244—82no—
99C4×D61—22no—
100C4×D61—22no—
101C4×D61—42no—
102Dic122—21no—
103Dic122#4112yes—
104C8×C61—21no—
105C8×C61—21no—
106#92418—22no—
107C22×C61—42no—
108C22×C61—42no—
109C22×C61—42no—
110C22×C61C22×D411yescharacteristic
111C2×D61—22no—
112C2×D61—22no—
113C2×D61—22no—
114C2×D61—41no—
115C2×D61—41no—
116C2×D61—41no—
117C4×C61—21no—
118C4×C61—42no—
119C4×C61#13512yes—
120C4×C61C2×#4111yescharacteristic
121C4×C61H(5,𝔽2)11yescharacteristic
122Dic61—22no—
123Dic61—22no—
124Dic61—41no—
125Dic61—41no—
126#3305—611nomaximal, Sylow
127C2×C61—82no—
128C2×C61#54611yescharacteristic
129C2×C61C2×#13511yescharacteristic
130C2×C61#57611yescharacteristic
131D61—42no—
132D61—81no—
133#555—611no—
134#550—611no—
135#486D6111yescharacteristic, complemented
136#482—612no—
137#477—611no—
138#466—612no—
139#459—611no—
140#449—612no—
141C4×SD16—611no—
142C8×D4—611no—
143#416—612no—
144C61#330511yescharacteristic, complemented, Sylow
145C2×#41—612no—
146C2×SD16—611no—
147C2×D8—612no—
148C22×C8—612no—
149C4⋊Q8C2×D6111yescharacteristic
150#127—1221no—
151#127C2×D6111yescharacteristic
152#124—1222no—
153#121—612no—
154#121—612no—
155#121—1222no—
156#121—1221no—
157C4×Q8—611no—
158C4×D4—611no—
159C4×D4—611no—
160C4×D4—1221no—
161#117—612no—
162#117—1221no—
163#107—612no—
164#106—611no—
165C4⋊C8—611no—
166#103—611no—
167#103—612no—
168#102—612no—
169#102—611no—
170#102C2×D6112yes—
171#102C2×D6112yes—
172C22⋊C8—612no—
173C4×C8C2×D6111yescharacteristic
174#41—1224no—
175#41—2442no—
176C2×Q8—21no—
177C2×Q8—611no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—611no—
181C2×D4—611no—
182C2×D4—1222no—
183C2×D4—1222no—
184C2×D4—1222no—
185C2×D4C22×D6112yes—
186C22×C4—612no—
187C22×C4—1222no—
188C22×C4—1221no—
189SD16—1222no—
190D8—2442no—
191C2×C8—612no—
192C2×C8—2442no—
193C2×C8C22×D6111yescharacteristic
194C2×C8C22×D6111yescharacteristic
195C4⋊C4—21no—
196C4⋊C4—611no—
197C4⋊C4—611no—
198C4⋊C4—611no—
199C4⋊C4—1221no—
200C4⋊C4C22×D6112yes—
201C22⋊C4—612no—
202C22⋊C4—1222no—
203C22⋊C4—1222no—
204C22⋊C4—1222no—
205C22⋊C4—1221no—
206C42—1222no—
207C42—1221no—
208C42C22×D6111yescharacteristic
209C23—22no—
210C23—612no—
211C23—1221no—
212Q8—81no—
213Q8—612no—
214Q8—1221no—
215D4—22no—
216D4—22no—
217D4—42no—
218D4—81no—
219D4—1221no—
220D4—1221no—
221D4—1222no—
222D4—4882no—
223D4—4882no—
224D4—2444no—
225C2×C4—22no—
226C2×C4—612no—
227C2×C4—1221no—
228C2×C4—1222no—
229C2×C4—1222no—
230C2×C4—1221no—
231C2×C4—1221no—
232C2×C4—2444no—
233C2×C4—2442no—
234C2×C4D4×D6111yescharacteristic
235C2×C4D4×D6111yescharacteristic
236C2×C4C23×D6111yescharacteristic
237C8—21no—
238C8—21no—
239C8—1222no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—1222no—
244C22—1222no—
245C22—1222no—
246C22—2441no—
247C22—2441no—
248C22—2441no—
249C22C2×D4×D6111yescharacteristic
250C4—21no—
251C4—42no—
252C4—1222no—
253C4—1222no—
254C4—2441no—
255C4—2441no—
256C4#1451979812yes—
257C4#41×D6111yescharacteristic
258C4#1451982311yescharacteristic
259C2—82no—
260C2—4881no—
261C2—2442no—
262C2#1684040511yescharacteristic
263C2C2×#1451979811yescharacteristic
264C2#1684056311yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#486C2
socleC22×C61C22×D4
hypercenter#486D61
hypocenterC61#3305
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #16840478C2semidirect
2. #16840432C2semidirect
3. #16840085C2semidirect
4. #16840054C2semidirect
5. #16839997C2semidirect
6. #16839954C2semidirect
7. #16839908C2semidirect
8. C4×#11758190C2semidirect
9. C8×D244C2semidirect
10. #16839755C2semidirect
11. C61×#486C2semidirect
135. #486D61semidirect
144. C61#3305semidirect