Finite Group Databasebeta

← #21455061

Subgroups — #21455061

Order 7808.

758 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 758 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C2×#14519808C211yesmaximal, characteristic, complemented
2C2×#14519803C211yesmaximal, characteristic, complemented
3#16840273C211yesmaximal, characteristic, complemented
4#16839924C214yesmaximal, complemented
5#16839907C214yesmaximal, complemented
6#16839771C211yesmaximal, characteristic, complemented
7#16839767C211yesmaximal, characteristic, complemented
8#16839726C211yesmaximal, characteristic, complemented
9C22×#41×C61C211yesmaximal, characteristic, complemented
10C2×#11758222C2211yescharacteristic
11#14519808—24no—
12#14519803—24no—
13C2×#11758202C2212yescomplemented
14C2×#11758200C2212yescomplemented
15C2×#11758201C2212yescomplemented
16C2×#11758199C2212yescomplemented
17C2×#11758194C2211yescharacteristic
18C2×#11758194C2211yescharacteristic
19#14519760—21no—
20#14519756C2212yescomplemented
21#14519751C2212yescomplemented
22#14519746—21no—
23C4×C22⋊D61—22no—
24#14519736C2211yescharacteristic
25#14519701C2214yescomplemented
26#14519698C2214yescomplemented
27C22⋊#92418C2214yescomplemented
28C2×#41×C61—24no—
29C2×#41×C61—24no—
30C2×#41×C61—22no—
31C2×#41×C61C2214yes—
32C22×Q8×C61C2211yescharacteristic
33C22×D4×C61—21no—
34C22×D4×C61C2211yescharacteristic
35C23×C4×C61—21no—
36C23×C4×C61C2211yescharacteristic
37C24×C61—21no—
38C24×C61D411yescharacteristic
39#41×C61—216no—
40#41×C61—28no—
41#41×C61—28no—
42C2×Q8×C61—22no—
43C2×Q8×C61—21no—
44C2×Q8×C61D414yescomplemented
45C2×Q8×C61C2312yes—
46C2×D4×C61—28no—
47C2×D4×C61—24no—
48C2×D4×C61—21no—
49C2×D4×C61—22no—
50C2×D4×C61D414yescomplemented
51C2×D4×C61C2312yes—
52C22×C4×C61—28no—
53C22×C4×C61—21no—
54C22×C4×C61—24no—
55C22×C4×C61—22no—
56C22×C4×C61—22no—
57C22×C4×C61D411yescharacteristic
58C22×C4×C61D412yes—
59C22×C4×C61C2312yes—
60C22×C4×C61C2311yescharacteristic
61C2×C22⋊D61—21no—
62C2×C22⋊D61—22no—
63#11758222—22no—
64#11758222—22no—
65C2×D244C2311yescharacteristic
66C2×C4×D61—21no—
67C2×Dic122C2311yescharacteristic
68C22⋊Dic61—21no—
69C22⋊Dic61—22no—
70#11758202—24no—
71#11758201—24no—
72#11758200—24no—
73#11758199—24no—
74#11758198—22no—
75C4⋊Dic61C2312yes—
76#11758196—22no—
77C4×Dic61—21no—
78#11758194—22no—
79#11758194—22no—
80C2×#92418C2312yes—
81C2×#92418C2312yes—
82C23×C61—22no—
83C23×C61—24no—
84C23×C61—22no—
85C23×C61—42no—
86C23×C61—44no—
87C23×C61C2×D412yes—
88C23×C61C2×D411yescharacteristic
89C22×D61—21no—
90Q8×C61—24no—
91Q8×C61—22no—
92Q8×C61C2×D414yes—
93D4×C61—216no—
94D4×C61—24no—
95D4×C61—22no—
96D4×C61C2×D414yes—
97C2×C4×C61—216no—
98C2×C4×C61—22no—
99C2×C4×C61—24no—
100C2×C4×C61—22no—
101C2×C4×C61—24no—
102C2×C4×C61—22no—
103C2×C4×C61—22no—
104C2×C4×C61C2×D412yes—
105C2×C4×C61C2×D411yescharacteristic
106C2×C4×C61C2×D412yes—
107C2×C4×C61C2×D412yes—
108C2×C4×C61C2411yescharacteristic
109C22⋊D61—44no—
110C22⋊D61—42no—
111C2×Dic61—22no—
112C2×Dic61—21no—
113D244—21no—
114D244—21no—
115C4×D61—42no—
116Dic122—21no—
117Dic122—21no—
118#92418—22no—
119#92418—22no—
120C22×C61—22no—
121C22×C61—22no—
122C22×C61—24no—
123C22×C61—22no—
124C22×C61—22no—
125C22×C61—44no—
126C22×C61—48no—
127C22×C61—44no—
128C22×C61#12012yes—
129C22×C61C22×D411yescharacteristic
130C2×D61—41no—
131C2×D61—42no—
132C4×C61—22no—
133C4×C61—24no—
134C4×C61#12012yes—
135C4×C61C22×D411yescharacteristic
136C4×C61C22×D411yescharacteristic
137Dic61—41no—
138Dic61—42no—
139#3005—611nomaximal, Sylow
140C2×C61—22no—
141C2×C61—42no—
142C2×C61—44no—
143C2×C61C2×#12011yescharacteristic
144C2×C61#57512yes—
145D61—81no—
146C22×#41D6111yescharacteristic, complemented
147C2×#137—611no—
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—24no—
157C2×#41—24no—
158C2×#41—22no—
159C2×#41—611no—
160C2×#41C2×D6114yes—
161C22×Q8C2×D6111yescharacteristic
162C22×D4—21no—
163C22×D4C2×D6111yescharacteristic
164C23×C4—21no—
165C23×C4C2×D6111yescharacteristic
166#137—1224no—
167AGL(1,ℤ/8)—1224no—
168C2×Q16—612no—
169C2×SD16—612no—
170C2×SD16—612no—
171C2×D8—612no—
172C2×M16—611no—
173C2×M16—611no—
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—21no—
184C24C22⋊D6111yescharacteristic
185#41—216no—
186#41—28no—
187#41—28no—
188#41—1222no—
189#41—1222no—
190C2×Q8—21no—
191C2×Q8—22no—
192C2×Q8—611no—
193C2×Q8C22⋊D6114yescomplemented
194C2×Q8C22×D6112yes—
195C2×D4—28no—
196C2×D4—24no—
197C2×D4—22no—
198C2×D4—21no—
199C2×D4—611no—
200C2×D4—1222no—
201C2×D4—1221no—
202C2×D4C22⋊D6114yescomplemented
203C2×D4C22×D6112yes—
204C22×C4—28no—
205C22×C4—21no—
206C22×C4—24no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—1221no—
210C22×C4C22⋊D6112yes—
211C22×C4C22⋊D6111yescharacteristic
212C22×C4C22×D6112yes—
213C22×C4C22×D6111yescharacteristic
214Q16—1224no—
215SD16—1224no—
216SD16—1224no—
217D8—1224no—
218M16—1222no—
219M16—1222no—
220C2×C8—612no—
221C2×C8—612no—
222C4⋊C4—612no—
223C4⋊C4—1222no—
224C22⋊C4—1221no—
225C22⋊C4—1222no—
226C22⋊C4—1222no—
227C42—1221no—
228C23—22no—
229C23—22no—
230C23—24no—
231C23—42no—
232C23—44no—
233C23—1221no—
234C23C2×C22⋊D6112yes—
235C23C2×C22⋊D6111yescharacteristic
236Q8—22no—
237Q8—24no—
238Q8—1221no—
239Q8—1221no—
240Q8C2×C22⋊D6114yes—
241D4—216no—
242D4—22no—
243D4—24no—
244D4—1221no—
245D4—1221no—
246D4—2444no—
247D4—2442no—
248D4C2×C22⋊D6114yes—
249C2×C4—216no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—24no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—24no—
256C2×C4—1222no—
257C2×C4—1221no—
258C2×C4—2442no—
259C2×C4C2×C22⋊D6112yes—
260C2×C4C2×C22⋊D6112yes—
261C2×C4C2×C22⋊D6112yes—
262C2×C4C2×C22⋊D6111yescharacteristic
263C2×C4C23×D6111yescharacteristic
264C8—1222no—
265C8—1222no—
266C22—22no—
267C22—22no—
268C22—24no—
269C22—22no—
270C22—22no—
271C22—44no—
272C22—48no—
273C22—44no—
274C22—2441no—
275C22—2442no—
276C22#1451974612yes—
277C22C22×C22⋊D6111yescharacteristic
278C4—22no—
279C4—24no—
280C4—2441no—
281C4—2442no—
282C4#1451974612yes—
283C4C22×C22⋊D6111yescharacteristic
284C4C22×C22⋊D6111yescharacteristic
285C2—22no—
286C2—42no—
287C2—44no—
288C2—4881no—
289C2C2×#1451974611yescharacteristic
290C2#1684056012yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC22×#41×C61C2
socleC22×C61C22×D4
hypercenterC22×#41D61
hypocenterC61#3005
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#14519808C2semidirect
2. C2×#14519803C2semidirect
3. #16840273C2semidirect
4. #16839924C2semidirect
5. #16839907C2semidirect
6. #16839771C2semidirect
7. #16839767C2semidirect
8. #16839726C2semidirect
9. C22×#41×C61C2semidirect
13. C2×#11758202C22semidirect
14. C2×#11758200C22semidirect
15. C2×#11758201C22semidirect
16. C2×#11758199C22semidirect
20. #14519756C22semidirect
21. #14519751C22semidirect
25. #14519701C22semidirect
26. #14519698C22semidirect
27. C22⋊#92418C22semidirect
44. C2×Q8×C61D4semidirect
50. C2×D4×C61D4semidirect
146. C22×#41D61semidirect
155. C61#3005semidirect
193. C2×Q8C22⋊D61semidirect
202. C2×D4C22⋊D61semidirect