Finite Group Databasebeta

← #21455866

Subgroups — #21455866

Order 7808.

454 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 133 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
2#16840097C211yesmaximal, characteristic, complemented
3#16840080C211yesmaximal, characteristic, complemented
4#16840062C212yesmaximal, complemented
5#16839977C212yesmaximal, complemented
6#16839913C211yesmaximal, characteristic, complemented
7#16839896C211yesmaximal, characteristic
8C4×#11758200C212yesmaximal, complemented
9C4×#11758199C212yesmaximal, complemented
10#16839815C211yesmaximal, characteristic, complemented
11C2×C4×D4×C61C211yesmaximal, characteristic, complemented
12C2×#11758200C2212yes—
13C2×#11758199C2212yes—
14#14519771—21no—
15#14519769C2211yescharacteristic, complemented
16#14519765C2211yescharacteristic, complemented
17#14519760—21no—
18#14519756C2211yescharacteristic
19#14519751C2211yescharacteristic
20C4×Dic122C2211yescharacteristic, complemented
21C4×D244C2211yescharacteristic, complemented
22C4×C22⋊D61—21no—
23#14519734—21no—
24#14519710C2212yescomplemented
25#14519708C2212yescomplemented
26C4⋊#92418C2212yescomplemented
27#14519700C2212yescomplemented
28#14519698C2212yes—
29#14519698C2212yes—
30#14519697C2212yescomplemented
31C22⋊#92418C2211yescharacteristic
32C22⋊#92418C2211yescharacteristic
33C4×#92418C2212yescomplemented
34C22×D4×C61C2211yescharacteristic
35C23×C4×C61—21no—
36C4×D4×C61—21no—
37C4×D4×C61—21no—
38C4×D4×C61C2212yes—
39C4×D4×C61C2212yes—
40C2×C4⋊C4×C61C2211yescharacteristic
41C2×C22⋊C4×C61—21no—
42C2×C42×C61C2211yescharacteristic
43C24×C61—21no—
44C2×D4×C61—24no—
45C2×D4×C61—21no—
46C2×D4×C61C2312yes—
47C22×C4×C61—21no—
48C22×C4×C61—22no—
49C22×C4×C61—22no—
50C22×C4×C61—44no—
51C22×C4×C61D411yescharacteristic
52C22×C4×C61D411yescharacteristic
53C22×C4×C61C2311yescharacteristic
54C2×C22⋊D61—21no—
55C2×D244C2311yescharacteristic
56C2×C4×D61—21no—
57C2×Dic122C2311yescharacteristic
58C4⋊C4×C61—21no—
59C4⋊C4×C61C2312yes—
60C22⋊C4×C61—22no—
61C22⋊C4×C61—22no—
62C42×C61D411yescharacteristic
63C42×C61D411yescharacteristic
64C42×C61C2311yescharacteristic
65C42×C61C2311yescharacteristic
66C22⋊Dic61—21no—
67#11758200—24no—
68#11758199—24no—
69#11758198—21no—
70#11758198—21no—
71#11758198—21no—
72#11758198—21no—
73C4⋊Dic61C2311yescharacteristic
74C4⋊Dic61C2311yescharacteristic
75#11758196—21no—
76#11758196—21no—
77#11758196—21no—
78#11758196—21no—
79C4×Dic61—21no—
80C2×#92418C2312yes—
81C2×#92418C2312yes—
82C23×C61—24no—
83C23×C61—22no—
84C23×C61—42no—
85C23×C61—42no—
86C23×C61C2×D411yescharacteristic
87C22×D61—21no—
88D4×C61—24no—
89D4×C61—22no—
90D4×C61#4114yes—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—22no—
94C2×C4×C61—22no—
95C2×C4×C61—44no—
96C2×C4×C61—42no—
97C2×C4×C61—44no—
98C2×C4×C61C2×D411yescharacteristic
99C2×C4×C61C2×D411yescharacteristic
100C2×C4×C61C2×D411yescharacteristic
101C2×C4×C61C2×D411yescharacteristic
102C2×C4×C61C2×D411yescharacteristic
103C2×C4×C61C2411yescharacteristic
104C22⋊D61—42no—
105C2×Dic61—21no—
106C2×Dic61—21no—
107C2×Dic61—21no—
108D244—22no—
109C4×D61—42no—
110Dic122—22no—
111#92418—22no—
112#92418—22no—
113C22×C61—21no—
114C22×C61—21no—
115C22×C61—24no—
116C22×C61—48no—
117C22×C61—42no—
118C22×C61—42no—
119C22×C61#13512yes—
120C22×C61C22×D411yescharacteristic
121C2×D61—41no—
122C2×D61—41no—
123C2×D61—41no—
124C4×C61—21no—
125C4×C61—21no—
126C4×C61—21no—
127C4×C61—21no—
128C4×C61—42no—
129C4×C61AGL(1,ℤ/8)12yes—
130C4×C61C2×#4112yes—
131Dic61—41no—
132Dic61—41no—
133Dic61—41no—
134#3105—611nomaximal, Sylow
135C2×C61—22no—
136C2×C61—44no—
137C2×C61#52511yescharacteristic
138C2×C61C2×#13511yescharacteristic
139C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
140D61—81no—
141#529—611no—
142C2×C4×D4D6111yescharacteristic, complemented
143#484—611no—
144#481—611no—
145#478—612no—
146#463—612no—
147#450—611no—
148#447—611no—
149C4×SD16—612no—
150C4×D8—612no—
151#431—611no—
152C61#310511yescharacteristic, complemented, Sylow
153C22×D4C2×D6111yescharacteristic
154C23×C4—21no—
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—21no—
165C4×D4—21no—
166C4×D4—611no—
167C4×D4—1221no—
168C4×D4C2×D6112yes—
169C4×D4C2×D6112yes—
170#117—1221no—
171C2×C4⋊C4C2×D6111yescharacteristic
172C2×C22⋊C4—21no—
173C2×C42C2×D6111yescharacteristic
174#107—612no—
175#106—612no—
176C4⋊C8—612no—
177#103—612no—
178#102—612no—
179#102—612no—
180#102—612no—
181C22⋊C8—611no—
182C22⋊C8—611no—
183C4×C8—612no—
184C24—21no—
185C2×Q8—611no—
186C2×D4—24no—
187C2×D4—21no—
188C2×D4—611no—
189C2×D4—1221no—
190C2×D4C22×D6112yes—
191C22×C4—21no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—44no—
195C22×C4—1221no—
196C22×C4C22⋊D6111yescharacteristic
197C22×C4C22⋊D6111yescharacteristic
198C22×C4C22×D6111yescharacteristic
199SD16—1224no—
200D8—1224no—
201C2×C8—612no—
202C2×C8—612no—
203C4⋊C4—21no—
204C4⋊C4—611no—
205C4⋊C4—611no—
206C4⋊C4—1221no—
207C4⋊C4—1221no—
208C4⋊C4—1221no—
209C4⋊C4—1221no—
210C4⋊C4C22×D6112yes—
211C22⋊C4—22no—
212C22⋊C4—22no—
213C22⋊C4—1221no—
214C22⋊C4—1221no—
215C22⋊C4—1221no—
216C22⋊C4—1221no—
217C22⋊C4—1221no—
218C42—1221no—
219C42C22⋊D6111yescharacteristic
220C42C22⋊D6111yescharacteristic
221C42C22×D6111yescharacteristic
222C42C22×D6111yescharacteristic
223C23—24no—
224C23—22no—
225C23—42no—
226C23—42no—
227C23—1221no—
228C23C2×C22⋊D6111yescharacteristic
229Q8—1222no—
230D4—24no—
231D4—22no—
232D4—1222no—
233D4—2442no—
234D4#1175822214yes—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—44no—
240C2×C4—42no—
241C2×C4—44no—
242C2×C4—1221no—
243C2×C4—1221no—
244C2×C4—1221no—
245C2×C4—2442no—
246C2×C4C2×C22⋊D6111yescharacteristic
247C2×C4C2×C22⋊D6111yescharacteristic
248C2×C4C2×C22⋊D6111yescharacteristic
249C2×C4C2×C22⋊D6111yescharacteristic
250C2×C4C2×C22⋊D6111yescharacteristic
251C2×C4C23×D6111yescharacteristic
252C8—1222no—
253C8—1222no—
254C22—21no—
255C22—21no—
256C22—24no—
257C22—48no—
258C22—42no—
259C22—42no—
260C22—2441no—
261C22—2441no—
262C22—2441no—
263C22#1451979712yes—
264C22C22×C22⋊D6111yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—42no—
270C4—2441no—
271C4—2441no—
272C4—2441no—
273C4#1451980312yes—
274C4C2×#1175822212yes—
275C2—22no—
276C2—44no—
277C2—4881no—
278C2#1684027311yescharacteristic
279C2C2×#1451979711yescharacteristic
280C2C2×#1451980311yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×C4×D4×C61C2
socleC22×C61C22×D4
hypercenterC2×C4×D4D61
hypocenterC61#3105
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #16840296C2semidirect
2. #16840097C2semidirect
3. #16840080C2semidirect
4. #16840062C2semidirect
5. #16839977C2semidirect
6. #16839913C2semidirect
8. C4×#11758200C2semidirect
9. C4×#11758199C2semidirect
10. #16839815C2semidirect
11. C2×C4×D4×C61C2semidirect
15. #14519769C22semidirect
16. #14519765C22semidirect
20. C4×Dic122C22semidirect
21. C4×D244C22semidirect
24. #14519710C22semidirect
25. #14519708C22semidirect
26. C4⋊#92418C22semidirect
27. #14519700C22semidirect
30. #14519697C22semidirect
33. C4×#92418C22semidirect
142. C2×C4×D4D61semidirect
152. C61#3105semidirect