Finite Group Databasebeta

← #21455060

Subgroups — #21455060

Order 7808.

758 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 758 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C22×#11758226C211yesmaximal, characteristic, complemented
2C2×#14519802C211yesmaximal, characteristic, complemented
3#16840269C211yesmaximal, characteristic, complemented
4#16839923C214yesmaximal, complemented
5#16839906C214yesmaximal, complemented
6#16839771C211yesmaximal, characteristic, complemented
7#16839768C211yesmaximal, characteristic, complemented
8#16839725C211yesmaximal, characteristic, complemented
9C2×#137×C61C211yesmaximal, characteristic, complemented
10C2×#11758226—24no—
11C2×#11758226—24no—
12C2×#11758226—22no—
13C2×#11758226C2214yes—
14C22×D244—21no—
15C22×D244C2211yescharacteristic
16C22×C4×D61—21no—
17C22×C4×D61C2211yescharacteristic
18#14519802—24no—
19C2×#11758201C2212yescomplemented
20C2×#11758199C2212yescomplemented
21C2×#11758194C2211yescharacteristic
22#14519758—21no—
23#14519753C2212yescomplemented
24#14519748C2212yescomplemented
25#14519745—21no—
26C4×C22⋊D61—22no—
27#14519736C2211yescharacteristic
28#14519701C2214yescomplemented
29#14519699C2214yescomplemented
30#14519689C2214yescomplemented
31C2×#41×C61C2211yescharacteristic
32C22×Q8×C61C2211yescharacteristic
33#137×C61—24no—
34C2×Q16×C61C2212yescomplemented
35C2×SD16×C61C2212yescomplemented
36C2×M16×C61C2211yescharacteristic
37C23×D61—21no—
38C23×D61D411yescharacteristic
39#41×C61—22no—
40#41×C61—22no—
41C2×Q8×C61—22no—
42C2×Q8×C61—21no—
43C2×Q8×C61D414yescomplemented
44C2×Q8×C61C2311yescharacteristic
45C2×Q8×C61C2312yes—
46C2×D4×C61—21no—
47C2×D4×C61C2311yescharacteristic
48C22×C4×C61—21no—
49C22×C4×C61—21no—
50C22×C4×C61C2311yescharacteristic
51C2×C22⋊D61—22no—
52C22×Dic61D411yescharacteristic
53#11758226—216no—
54#11758226—28no—
55#11758226—28no—
56C2×D244—28no—
57C2×D244—24no—
58C2×D244—21no—
59C2×D244—22no—
60C2×D244D414yescomplemented
61C2×D244C2312yes—
62C2×C4×D61—28no—
63C2×C4×D61—22no—
64C2×C4×D61—22no—
65C2×C4×D61—24no—
66C2×C4×D61D412yes—
67C2×C4×D61C2312yes—
68Q16×C61—24no—
69SD16×C61—24no—
70M16×C61—22no—
71C2×C8×C61C2312yes—
72C22⋊Dic61—21no—
73C22⋊Dic61—22no—
74#11758201—24no—
75#11758199—24no—
76#11758198—22no—
77C4⋊Dic61C2312yes—
78#11758196—22no—
79C4×Dic61—21no—
80#11758194—22no—
81C2×#92418C2312yes—
82C23×C61—21no—
83C23×C61C2×D411yescharacteristic
84C22×D61—22no—
85C22×D61—24no—
86C22×D61—22no—
87C22×D61—42no—
88C22×D61—44no—
89C22×D61C2×D412yes—
90Q8×C61—24no—
91Q8×C61—22no—
92Q8×C61—21no—
93Q8×C61—21no—
94Q8×C61C2×D414yes—
95D4×C61—21no—
96D4×C61—21no—
97D4×C61—42no—
98C2×C4×C61—24no—
99C2×C4×C61—22no—
100C2×C4×C61—21no—
101C2×C4×C61—42no—
102C2×C4×C61C2×D411yescharacteristic
103C2×C4×C61C2×D412yes—
104C2×C4×C61C2×D412yes—
105C2×C4×C61C2411yescharacteristic
106C22⋊D61—44no—
107C2×Dic61—22no—
108C2×Dic61—22no—
109C2×Dic61C2×D412yes—
110D244—216no—
111D244—24no—
112D244—22no—
113D244C2×D414yes—
114C4×D61—216no—
115C4×D61—24no—
116C4×D61—22no—
117C4×D61—22no—
118C8×C61—22no—
119#92418—22no—
120C22×C61—22no—
121C22×C61—41no—
122C22×C61—42no—
123C22×C61#12012yes—
124C22×C61C22×D411yescharacteristic
125C2×D61—22no—
126C2×D61—24no—
127C2×D61—22no—
128C2×D61—22no—
129C2×D61—44no—
130C2×D61—48no—
131C2×D61—44no—
132C4×C61—24no—
133C4×C61—41no—
134C4×C61#12012yes—
135C4×C61C22×D411yescharacteristic
136C4×C61C22×D411yescharacteristic
137Dic61—22no—
138Dic61—42no—
139#3005—611nomaximal, Sylow
140C2×C61—22no—
141C2×C61—81no—
142C2×C61C2×#12011yescharacteristic
143C2×C61#57512yes—
144D61—42no—
145D61—44no—
146C22×#41—611no—
147C2×#137D6111yescharacteristic, complemented
148C2×AGL(1,ℤ/8)—611no—
149#525—611no—
150#452—614no—
151#449—614no—
152#419—611no—
153#418—611no—
154#407—611no—
155C61#300511yescharacteristic, complemented, Sylow
156C2×#41—614no—
157C2×#41—1222no—
158C2×#41—1224no—
159C2×#41—1224no—
160C2×#41C2×D6111yescharacteristic
161C22×Q8C2×D6111yescharacteristic
162C22×D4—611no—
163C22×D4—1221no—
164C23×C4—611no—
165C23×C4—1221no—
166#137—24no—
167AGL(1,ℤ/8)—1224no—
168C2×Q16C2×D6112yescomplemented
169C2×SD16—612no—
170C2×SD16C2×D6112yescomplemented
171C2×D8—612no—
172C2×M16—611no—
173C2×M16C2×D6111yescharacteristic
174#123—1221no—
175C22⋊Q8—612no—
176#121—612no—
177#120—1221no—
178C4×D4—1222no—
179#117—611no—
180#103—614no—
181#102—614no—
182C22⋊C8—614no—
183C24—611no—
184C24—1221no—
185#41—22no—
186#41—22no—
187#41—1228no—
188#41—12216no—
189#41—1228no—
190C2×Q8—21no—
191C2×Q8—22no—
192C2×Q8C22⋊D6114yescomplemented
193C2×Q8C22×D6111yescharacteristic
194C2×Q8C22×D6112yes—
195C2×D4—21no—
196C2×D4—614no—
197C2×D4—612no—
198C2×D4—1224no—
199C2×D4—1228no—
200C2×D4—1222no—
201C2×D4—1221no—
202C2×D4—1222no—
203C2×D4C22×D6111yescharacteristic
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—611no—
207C22×C4—612no—
208C22×C4—612no—
209C22×C4—1224no—
210C22×C4—1228no—
211C22×C4—1222no—
212C22×C4—1222no—
213C22×C4C22×D6111yescharacteristic
214Q16—24no—
215SD16—24no—
216SD16—1224no—
217D8—1224no—
218M16—22no—
219M16—1222no—
220C2×C8—612no—
221C2×C8C22×D6112yes—
222C4⋊C4—612no—
223C4⋊C4—1222no—
224C22⋊C4—1222no—
225C22⋊C4—1222no—
226C22⋊C4—1221no—
227C42—1221no—
228C23—21no—
229C23—612no—
230C23—1222no—
231C23—1224no—
232C23—1222no—
233C23—2442no—
234C23—2444no—
235C23D4×D6111yescharacteristic
236Q8—22no—
237Q8—24no—
238Q8—21no—
239Q8—21no—
240Q8C2×C22⋊D6114yes—
241D4—21no—
242D4—21no—
243D4—42no—
244D4—614no—
245D4—12216no—
246D4—1222no—
247D4—1224no—
248D4—2444no—
249C2×C4—22no—
250C2×C4—24no—
251C2×C4—21no—
252C2×C4—42no—
253C2×C4—612no—
254C2×C4—12216no—
255C2×C4—1222no—
256C2×C4—1222no—
257C2×C4—1222no—
258C2×C4—1224no—
259C2×C4—1222no—
260C2×C4D4×D6112yes—
261C2×C4D4×D6111yescharacteristic
262C2×C4C2×C22⋊D6112yes—
263C2×C4C23×D6111yescharacteristic
264C8—22no—
265C8—1222no—
266C22—22no—
267C22—41no—
268C22—42no—
269C22—1224no—
270C22—1222no—
271C22—1222no—
272C22—1222no—
273C22—2444no—
274C22—2448no—
275C22—2444no—
276C22#1451974512yes—
277C22C2×D4×D6111yescharacteristic
278C4—24no—
279C4—41no—
280C4—1222no—
281C4—2442no—
282C4#1451974512yes—
283C4C2×D4×D6111yescharacteristic
284C4C22×C22⋊D6111yescharacteristic
285C2—22no—
286C2—81no—
287C2—2442no—
288C2—2444no—
289C2C2×#1451974511yescharacteristic
290C2#1684056112yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#137×C61C2
socleC22×C61C22×D4
hypercenterC2×#137D61
hypocenterC61#3005
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C22×#11758226C2semidirect
2. C2×#14519802C2semidirect
3. #16840269C2semidirect
4. #16839923C2semidirect
5. #16839906C2semidirect
6. #16839771C2semidirect
7. #16839768C2semidirect
8. #16839725C2semidirect
9. C2×#137×C61C2semidirect
19. C2×#11758201C22semidirect
20. C2×#11758199C22semidirect
23. #14519753C22semidirect
24. #14519748C22semidirect
28. #14519701C22semidirect
29. #14519699C22semidirect
30. #14519689C22semidirect
34. C2×Q16×C61C22semidirect
35. C2×SD16×C61C22semidirect
43. C2×Q8×C61D4semidirect
60. C2×D244D4semidirect
147. C2×#137D61semidirect
155. C61#3005semidirect
168. C2×Q16C2×D61semidirect
170. C2×SD16C2×D61semidirect
192. C2×Q8C22⋊D61semidirect