Finite Group Databasebeta

← #21455210

Subgroups — #21455210

Order 7808.

766 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 766 conjugacy classes of subgroups — too many to draw. Only its 145 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#16840598C211yesmaximal, characteristic, complemented
2#16840273C212yesmaximal, complemented
3#16839951C214yesmaximal, complemented
4#16839948C214yesmaximal, complemented
5#16839736C211yesmaximal, characteristic, complemented
6#16839735C212yesmaximal, complemented
7C61×#525C211yesmaximal, characteristic, complemented
8#14519825—21no—
9#14519824—22no—
10#14519823—22no—
11#14519822—21no—
12#14519822C2214yes—
13C2×#11758222—22no—
14C2×#11758222C2212yes—
15#41×D61—24no—
16#14519760C2214yescomplemented
17#14519756—22no—
18#14519751—22no—
19#14519746C2214yescomplemented
20C4×C22⋊D61—24no—
21#14519736C2212yescomplemented
22#14519692C2214yescomplemented
23#14519691C2218yescomplemented
24C2×#41×C61C2211yescharacteristic
25C23×C4×C61C2211yescharacteristic, complemented
26#123×C61C2212yescomplemented
27C22⋊Q8×C61—21no—
28#121×C61—21no—
29#120×C61C2212yescomplemented
30C4×D4×C61—22no—
31#117×C61C2211yescharacteristic, complemented
32C24×C61C2311yescharacteristic
33#41×C61—22no—
34#41×C61—22no—
35C2×Q8×C61D411yescharacteristic, complemented
36C2×D4×C61—22no—
37C2×D4×C61D411yescharacteristic, complemented
38C2×D4×C61C2312yes—
39C22×C4×C61—21no—
40C22×C4×C61—21no—
41C22×C4×C61—22no—
42C22×C4×C61—22no—
43C22×C4×C61D412yescomplemented
44C22×C4×C61C2311yescharacteristic
45C22×C4×C61C2311yescharacteristic
46C2×C22⋊D61—24no—
47C2×C22⋊D61—24no—
48C2×C22⋊D61C2314yes—
49#11758226—24no—
50Q8×D61—24no—
51#11758224—24no—
52#11758224—28no—
53D4×D61—24no—
54D4×D61—28no—
55#11758222—24no—
56#11758222—24no—
57#11758222—22no—
58#11758222—22no—
59#11758222—24no—
60#11758222—22no—
61#11758222—22no—
62C2×D244—22no—
63C2×D244D412yescomplemented
64C2×C4×D61—24no—
65C2×C4×D61D414yescomplemented
66C2×Dic122—22no—
67C2×Dic122D412yescomplemented
68C4⋊C4×C61—21no—
69C4⋊C4×C61—22no—
70C22⋊C4×C61—22no—
71C22⋊C4×C61—22no—
72C22⋊C4×C61C2312yes—
73C42×C61—21no—
74C22⋊Dic61—24no—
75C22⋊Dic61C2314yes—
76#11758198—24no—
77C4⋊Dic61—22no—
78#11758196—24no—
79C4×Dic61—22no—
80C23×C61—22no—
81C23×C61—21no—
82C23×C61—42no—
83C23×C61C2×D412yes—
84C23×C61C2411yescharacteristic
85C22×D61—24no—
86C22×D61C2×D414yes—
87Q8×C61—22no—
88D4×C61—24no—
89D4×C61—22no—
90D4×C61—44no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—22no—
94C2×C4×C61—22no—
95C2×C4×C61—21no—
96C2×C4×C61—41no—
97C2×C4×C61—42no—
98C2×C4×C61—41no—
99C2×C4×C61C2×D412yes—
100C2×C4×C61C2×D412yes—
101C2×C4×C61C2×D412yes—
102C2×C4×C61C2×D411yescharacteristic
103C2×C4×C61C2×D411yescharacteristic
104C22⋊D61—28no—
105C22⋊D61—24no—
106C22⋊D61—24no—
107C22⋊D61—48no—
108C2×Dic61—24no—
109C2×Dic61—24no—
110C2×Dic61C2×D414yes—
111D244—24no—
112D244—22no—
113D244—22no—
114C4×D61—28no—
115C4×D61—24no—
116C4×D61—24no—
117Dic122—24no—
118Dic122—22no—
119Dic122—22no—
120C22×C61—24no—
121C22×C61—22no—
122C22×C61—22no—
123C22×C61—41no—
124C22×C61—42no—
125C22×C61—42no—
126C22×C61—41no—
127C22×C61—41no—
128C22×C61C22×D412yes—
129C22×C61C22×D411yescharacteristic
130C2×D61—24no—
131C2×D61—44no—
132C2×D61—84no—
133C4×C61—22no—
134C4×C61—42no—
135C4×C61—41no—
136C4×C61#12011yescharacteristic
137C4×C61#12012yes—
138C4×C61#12011yescharacteristic
139Dic61—24no—
140Dic61—44no—
141#3025—611nomaximal, Sylow
142C2×C61—22no—
143C2×C61—21no—
144C2×C61—42no—
145C2×C61—42no—
146C2×C61C2×#12011yescharacteristic
147D61—44no—
148#585—611no—
149#525—612no—
150#525D6111yescharacteristic, complemented
151#458—614no—
152B(4,𝔽2)—614no—
153#410—611no—
154#410—612no—
155C61#302511yescharacteristic, complemented, Sylow
1562−1+4—1222no—
1572−1+4—1221no—
158H(5,𝔽2)—614no—
159H(5,𝔽2)—1222no—
160H(5,𝔽2)—1221no—
161C2×#41—612no—
162C2×#41—1224no—
163C2×#41—1222no—
164C2×#41C2×D6111yescharacteristic
165C23×C4C2×D6111yescharacteristic, complemented
166#123—614no—
167#123C2×D6112yescomplemented
168C22⋊Q8—21no—
169C22⋊Q8—1222no—
170#121—21no—
171#121—1222no—
172#120—614no—
173#120C2×D6112yescomplemented
174C4×D4—22no—
175C4×D4—1224no—
176#117—612no—
177#117C2×D6111yescharacteristic, complemented
178#99—614no—
179#99—618no—
180C24C22×D6111yescharacteristic
181#41—22no—
182#41—22no—
183#41—1224no—
184#41—1224no—
185#41—1228no—
186#41—1224no—
187#41—1224no—
188#41—1222no—
189#41—1222no—
190#41—1222no—
191#41—1222no—
192#41—1224no—
193C2×Q8—612no—
194C2×Q8—1222no—
195C2×Q8—1224no—
196C2×Q8C22⋊D6111yescharacteristic, complemented
197C2×D4—22no—
198C2×D4—614no—
199C2×D4—612no—
200C2×D4—1222no—
201C2×D4—1228no—
202C2×D4—1224no—
203C2×D4—1224no—
204C2×D4—1224no—
205C2×D4C22⋊D6111yescharacteristic, complemented
206C2×D4C22×D6112yes—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—614no—
212C22×C4—1224no—
213C22×C4C22⋊D6112yescomplemented
214C22×C4C22×D6111yescharacteristic
215C22×C4C22×D6111yescharacteristic
216C4⋊C4—21no—
217C4⋊C4—22no—
218C4⋊C4—1224no—
219C4⋊C4—1222no—
220C22⋊C4—22no—
221C22⋊C4—22no—
222C22⋊C4—614no—
223C22⋊C4—1224no—
224C22⋊C4—1224no—
225C22⋊C4C22×D6112yes—
226C42—21no—
227C42—1222no—
228C23—22no—
229C23—21no—
230C23—42no—
231C23—614no—
232C23—1224no—
233C23C2×C22⋊D6112yes—
234C23C23×D6111yescharacteristic
235Q8—22no—
236Q8—1224no—
237Q8—1222no—
238Q8—1222no—
239D4—24no—
240D4—22no—
241D4—44no—
242D4—1224no—
243D4—1228no—
244D4—1224no—
245D4—1224no—
246D4—1222no—
247D4—1222no—
248D4—2448no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—41no—
255C2×C4—42no—
256C2×C4—41no—
257C2×C4—614no—
258C2×C4—1228no—
259C2×C4—1224no—
260C2×C4—1224no—
261C2×C4—1224no—
262C2×C4—1224no—
263C2×C4D4×D6112yes—
264C2×C4D4×D6112yes—
265C2×C4C2×C22⋊D6112yes—
266C2×C4C2×C22⋊D6111yescharacteristic
267C2×C4C2×C22⋊D6111yescharacteristic
268C22—22no—
269C22—24no—
270C22—22no—
271C22—41no—
272C22—42no—
273C22—41no—
274C22—42no—
275C22—41no—
276C22—1224no—
277C22—4884no—
278C22—2444no—
279C22C2×D4×D6112yes—
280C22C22×C22⋊D6111yescharacteristic
281C4—22no—
282C4—42no—
283C4—41no—
284C4—1224no—
285C4—2444no—
286C4#1451974511yescharacteristic
287C4#1451974512yes—
288C4#1451974511yescharacteristic
289C2—21no—
290C2—22no—
291C2—42no—
292C2—42no—
293C2—2444no—
294C2C2×#1451974511yescharacteristic
subgroupG/H
centerC4#14519745
commutatorC23×C61C24
FrattiniC23C23×D61
FittingC61×#525C2
socleC2×C61C2×#120
hypercenter#525D61
hypocenterC61#3025
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #16840598C2semidirect
2. #16840273C2semidirect
3. #16839951C2semidirect
4. #16839948C2semidirect
5. #16839736C2semidirect
6. #16839735C2semidirect
7. C61×#525C2semidirect
16. #14519760C22semidirect
19. #14519746C22semidirect
21. #14519736C22semidirect
22. #14519692C22semidirect
23. #14519691C22semidirect
25. C23×C4×C61C22semidirect
26. #123×C61C22semidirect
29. #120×C61C22semidirect
31. #117×C61C22semidirect
35. C2×Q8×C61D4semidirect
37. C2×D4×C61D4semidirect
43. C22×C4×C61D4semidirect
63. C2×D244D4semidirect
65. C2×C4×D61D4semidirect
67. C2×Dic122D4semidirect
150. #525D61semidirect
155. C61#3025semidirect
165. C23×C4C2×D61semidirect
167. #123C2×D61semidirect
173. #120C2×D61semidirect
177. #117C2×D61semidirect
196. C2×Q8C22⋊D61semidirect
205. C2×D4C22⋊D61semidirect
213. C22×C4C22⋊D61semidirect