Finite Group Databasebeta

← #21455959

Subgroups — #21455959

Order 7808.

450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 125 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#16840296C211yesmaximal, characteristic, complemented
2C2×C4×D244C211yesmaximal, characteristic, complemented
3#16840093C211yesmaximal, characteristic, complemented
4#16840076C211yesmaximal, characteristic, complemented
5#16840063C212yesmaximal, complemented
6#16839978C212yesmaximal, complemented
7#16839915C211yesmaximal, characteristic, complemented
8#16839898C211yesmaximal, characteristic
9#16839875C212yesmaximal, complemented
10#16839864C212yesmaximal, complemented
11C61×#432C211yesmaximal, characteristic, complemented
12C22×D244C2211yescharacteristic
13C22×C4×D61—21no—
14C2×#11758190C2212yes—
15C2×D488C2212yes—
16#14519771—21no—
17#14519769C2211yescharacteristic, complemented
18#14519765C2211yescharacteristic, complemented
19#14519760—21no—
20#14519756C2211yescharacteristic
21#14519751C2211yescharacteristic
22C4×Dic122C2211yescharacteristic, complemented
23C4×D244—21no—
24C4×D244—21no—
25C4×D244C2212yes—
26C4×D244C2212yes—
27C4×D244C2211yescharacteristic, complemented
28C4×C22⋊D61—21no—
29#14519734—21no—
30C2×C4⋊Dic61C2211yescharacteristic
31C2×#11758198—21no—
32#14519711C2212yescomplemented
33#14519709C2212yescomplemented
34#14519702C2212yescomplemented
35#14519699C2212yes—
36#14519699C2212yes—
37#14519699C2212yescomplemented
38C2×C42×C61C2211yescharacteristic
39C4⋊C8×C61C2212yescomplemented
40C22⋊C8×C61C2211yescharacteristic
41C22⋊C8×C61C2211yescharacteristic
42#97×C61C2212yescomplemented
43C23×D61—21no—
44C22×C4×C61D411yescharacteristic
45C22×C4×C61D411yescharacteristic
46C22×C4×C61C2311yescharacteristic
47C2×C22⋊D61—21no—
48C22×Dic61—21no—
49C2×D244—21no—
50C2×D244—24no—
51C2×D244C2311yescharacteristic
52C2×D244C2312yes—
53C2×C4×D61—22no—
54C2×C4×D61—22no—
55C2×C4×D61—21no—
56C2×C4×D61—44no—
57C2×Dic122C2311yescharacteristic
58C2×C8×C61C2312yes—
59C2×C8×C61C2312yes—
60C42×C61D411yescharacteristic
61C42×C61D411yescharacteristic
62C42×C61C2311yescharacteristic
63C42×C61C2311yescharacteristic
64C22⋊Dic61—21no—
65#11758198—22no—
66#11758198—22no—
67#11758198—21no—
68#11758198—21no—
69#11758198—21no—
70#11758198—21no—
71C4⋊Dic61—21no—
72C4⋊Dic61C2311yescharacteristic
73C4⋊Dic61C2311yescharacteristic
74C4⋊Dic61C2312yes—
75#11758196—21no—
76#11758196—21no—
77#11758196—21no—
78#11758196—21no—
79C4×Dic61—21no—
80D488—24no—
81#11758190—24no—
82C23×C61C2×D411yescharacteristic
83C22×D61—24no—
84C22×D61—22no—
85C22×D61—21no—
86C22×D61—42no—
87C22×D61—42no—
88C2×C4×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61—41no—
91C2×C4×C61C2×D411yescharacteristic
92C2×C4×C61C2×D411yescharacteristic
93C2×C4×C61C2×D411yescharacteristic
94C2×C4×C61C2×D411yescharacteristic
95C2×C4×C61C2×D411yescharacteristic
96C2×C4×C61C2411yescharacteristic
97C22⋊D61—42no—
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61—21no—
101C2×Dic61—22no—
102C2×Dic61—42no—
103D244—24no—
104D244—22no—
105D244—22no—
106D244#4114yes—
107C4×D61—42no—
108C4×D61—44no—
109C4×D61—44no—
110Dic122—22no—
111C8×C61—22no—
112C8×C61—22no—
113C22×C61—21no—
114C22×C61—21no—
115C22×C61AGL(1,ℤ/8)12yes—
116C22×C61C22×D411yescharacteristic
117C2×D61—24no—
118C2×D61—48no—
119C2×D61—42no—
120C2×D61—42no—
121C2×D61—41no—
122C2×D61—41no—
123C2×D61—41no—
124C4×C61—21no—
125C4×C61—21no—
126C4×C61—21no—
127C4×C61—21no—
128C4×C61—21no—
129C4×C61C2×#4112yes—
130Dic61—41no—
131Dic61—42no—
132Dic61—41no—
133Dic61—41no—
134#3114—611nomaximal, Sylow
135C2×C61—22no—
136C2×C61#52511yescharacteristic
137C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C61#57511yescharacteristic
139D61—44no—
140D61—81no—
141#529—611no—
142C2×C4×D4—611no—
143#483—611no—
144#480—611no—
145#478—612no—
146#463—612no—
147#450—611no—
148#447—611no—
149#442—612no—
150#440—612no—
151#432D6111yescharacteristic, complemented
152C61#311411yescharacteristic, complemented, Sylow
153C22×D4—611no—
154C23×C4—1221no—
155C2×SD16—612no—
156C2×D8—612no—
157#126—1221no—
158#125—611no—
159#124—611no—
160#123—1221no—
161C22⋊Q8—611no—
162#121—611no—
163C4×Q8—611no—
164C4×D4—612no—
165C4×D4—612no—
166C4×D4—611no—
167C4×D4—1221no—
168C4×D4—1221no—
169C4×D4—1221no—
170#117—1221no—
171C2×C4⋊C4—611no—
172C2×C22⋊C4—1221no—
173C2×C42C2×D6111yescharacteristic
174#107—612no—
175#106—612no—
176C4⋊C8C2×D6112yescomplemented
177#103—612no—
178#102—612no—
179#102—612no—
180#102—612no—
181C22⋊C8C2×D6111yescharacteristic
182C22⋊C8C2×D6111yescharacteristic
183#97C2×D6112yescomplemented
184C24—1221no—
185C2×Q8—611no—
186C2×D4—612no—
187C2×D4—611no—
188C2×D4—1224no—
189C2×D4—1221no—
190C2×D4—1221no—
191C22×C4—1221no—
192C22×C4—1221no—
193C22×C4—1222no—
194C22×C4—1222no—
195C22×C4—2444no—
196C22×C4D24411yescharacteristic
197C22×C4D24411yescharacteristic
198C22×C4C22×D6111yescharacteristic
199SD16—1224no—
200D8—1224no—
201C2×C8C22×D6112yes—
202C2×C8C22×D6112yes—
203C4⋊C4—611no—
204C4⋊C4—611no—
205C4⋊C4—612no—
206C4⋊C4—1221no—
207C4⋊C4—1221no—
208C4⋊C4—1221no—
209C4⋊C4—1221no—
210C4⋊C4—1221no—
211C22⋊C4—1221no—
212C22⋊C4—1222no—
213C22⋊C4—1222no—
214C22⋊C4—1221no—
215C22⋊C4—1221no—
216C22⋊C4—1221no—
217C22⋊C4—1221no—
218C42—1221no—
219C42D24411yescharacteristic
220C42D24411yescharacteristic
221C42C22×D6111yescharacteristic
222C42C22×D6111yescharacteristic
223C23—1224no—
224C23—1222no—
225C23—1221no—
226C23—2442no—
227C23—2442no—
228C23C2×D24411yescharacteristic
229Q8—1222no—
230D4—614no—
231D4—1224no—
232D4—1222no—
233D4—1222no—
234D4—2442no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—41no—
238C2×C4—1221no—
239C2×C4—1221no—
240C2×C4—1221no—
241C2×C4—1222no—
242C2×C4—2442no—
243C2×C4—2444no—
244C2×C4—2444no—
245C2×C4—2442no—
246C2×C4C2×D24411yescharacteristic
247C2×C4C2×D24411yescharacteristic
248C2×C4C2×D24411yescharacteristic
249C2×C4C2×D24411yescharacteristic
250C2×C4C2×D24411yescharacteristic
251C2×C4C23×D6111yescharacteristic
252C8—22no—
253C8—22no—
254C22—21no—
255C22—21no—
256C22—1224no—
257C22—2448no—
258C22—2441no—
259C22—2441no—
260C22—2441no—
261C22—2442no—
262C22—2442no—
263C22#1451980512yes—
264C22C22×D24411yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—2441no—
271C4—2442no—
272C4—2441no—
273C4—2441no—
274C4#41×D6112yes—
275C2—22no—
276C2—4881no—
277C2—2444no—
278C2#1684027411yescharacteristic
279C2C2×#1451980511yescharacteristic
280C2#1684056211yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#432C2
socleC22×C61C22×D4
hypercenter#432D61
hypocenterC61#3114
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #16840296C2semidirect
2. C2×C4×D244C2semidirect
3. #16840093C2semidirect
4. #16840076C2semidirect
5. #16840063C2semidirect
6. #16839978C2semidirect
7. #16839915C2semidirect
9. #16839875C2semidirect
10. #16839864C2semidirect
11. C61×#432C2semidirect
17. #14519769C22semidirect
18. #14519765C22semidirect
22. C4×Dic122C22semidirect
27. C4×D244C22semidirect
32. #14519711C22semidirect
33. #14519709C22semidirect
34. #14519702C22semidirect
37. #14519699C22semidirect
39. C4⋊C8×C61C22semidirect
42. #97×C61C22semidirect
151. #432D61semidirect
152. C61#3114semidirect
176. C4⋊C8C2×D61semidirect
183. #97C2×D61semidirect