Finite Group Databasebeta

← #21455213

Subgroups — #21455213

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#16840274C212yesmaximal, complemented
3#16840269C211yesmaximal, characteristic, complemented
4#16839953C214yesmaximal, complemented
5#16839950C214yesmaximal, complemented
6#16839735C212yesmaximal, complemented
7C61×#410C211yesmaximal, 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—
16C22×C4×D61C2211yescharacteristic, complemented
17#14519761C2214yescomplemented
18#14519758C2212yescomplemented
19#14519757—22no—
20#14519753—21no—
21#14519752—22no—
22#14519748—21no—
23#14519747C2214yescomplemented
24#14519745C2212yescomplemented
25C4×D244—24no—
26C4×C22⋊D61—22no—
27#14519736C2211yescharacteristic, complemented
28#14519691C2218yescomplemented
29C2×#41×C61C2211yescharacteristic
30#117×C61C2212yescomplemented
31#99×C61C2214yescomplemented
32C23×D61C2311yescharacteristic
33#41×C61—22no—
34#41×C61—22no—
35C2×Q8×C61D411yescharacteristic, complemented
36C2×D4×C61D411yescharacteristic, complemented
37C2×D4×C61C2312yes—
38C22×C4×C61D412yescomplemented
39C22×C4×C61C2311yescharacteristic
40C2×C22⋊D61—24no—
41C2×C22⋊D61—22no—
42C2×C22⋊D61C2314yes—
43C22×Dic61C2311yescharacteristic
44#11758226—24no—
45Q8×D61—24no—
46#11758224—24no—
47#11758224—28no—
48D4×D61—24no—
49D4×D61—28no—
50#11758222—24no—
51#11758222—24no—
52#11758222—22no—
53#11758222—22no—
54#11758222—24no—
55#11758222—22no—
56#11758222—22no—
57C2×D244—22no—
58C2×D244—24no—
59C2×D244D412yescomplemented
60C2×C4×D61—24no—
61C2×C4×D61—21no—
62C2×C4×D61—22no—
63C2×C4×D61—21no—
64C2×C4×D61—22no—
65C2×C4×D61D414yescomplemented
66C2×Dic122—22no—
67C2×Dic122D412yescomplemented
68C4⋊C4×C61—22no—
69C22⋊C4×C61C2314yes—
70C42×C61—22no—
71C22⋊Dic61—22no—
72C22⋊Dic61C2312yes—
73#11758198—24no—
74#11758198—22no—
75#11758198—24no—
76C4⋊Dic61—21no—
77C4⋊Dic61—24no—
78#11758196—22no—
79C4×Dic61—21no—
80C23×C61C2×D412yes—
81C23×C61C2411yescharacteristic
82C22×D61—22no—
83C22×D61—21no—
84C22×D61—24no—
85C22×D61—42no—
86C22×D61C2×D414yes—
87Q8×C61—22no—
88D4×C61—24no—
89D4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—24no—
93C2×C4×C61C2×D412yes—
94C2×C4×C61C2×D411yescharacteristic
95C2×C4×C61C2×D411yescharacteristic
96C2×C4×C61C2×D412yes—
97C2×C4×C61C2×D412yes—
98C22⋊D61—28no—
99C22⋊D61—24no—
100C22⋊D61—24no—
101C22⋊D61—44no—
102C2×Dic61—24no—
103C2×Dic61—22no—
104C2×Dic61—21no—
105C2×Dic61—22no—
106C2×Dic61C2×D414yes—
107D244—24no—
108D244—22no—
109D244—22no—
110D244—48no—
111C4×D61—28no—
112C4×D61—24no—
113C4×D61—24no—
114C4×D61—41no—
115C4×D61—42no—
116C4×D61—41no—
117Dic122—24no—
118Dic122—22no—
119Dic122—22no—
120C22×C61—22no—
121C22×C61—41no—
122C22×C61—42no—
123C22×C61C22×D412yes—
124C22×C61C22×D411yescharacteristic
125C2×D61—24no—
126C2×D61—22no—
127C2×D61—24no—
128C2×D61—41no—
129C2×D61—42no—
130C2×D61—41no—
131C2×D61—44no—
132C2×D61—84no—
133C4×C61—22no—
134C4×C61—44no—
135C4×C61#12011yescharacteristic
136C4×C61#12012yes—
137C4×C61#12011yescharacteristic
138Dic61—24no—
139Dic61—42no—
140Dic61—41no—
141#3025—611nomaximal, Sylow
142C2×C61—21no—
143C2×C61—22no—
144C2×C61—42no—
145C2×C61C2×#12011yescharacteristic
146D61—42no—
147D61—44no—
148#585—611no—
149#525—611no—
150#525—612no—
151#458—614no—
152B(4,𝔽2)—614no—
153#410—612no—
154#410D6111yescharacteristic, complemented
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×C4—611no—
166#123—612no—
167#123—614no—
168C22⋊Q8—1222no—
169C22⋊Q8—1221no—
170#121—1222no—
171#121—1221no—
172#120—612no—
173#120—614no—
174C4×D4—1224no—
175C4×D4—1222no—
176#117—611no—
177#117C2×D6112yescomplemented
178#99—618no—
179#99C2×D6114yescomplemented
180C24—611no—
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—1224no—
191#41—1222no—
192#41—1222no—
193C2×Q8—612no—
194C2×Q8—1222no—
195C2×Q8—1224no—
196C2×Q8D24411yescharacteristic, complemented
197C2×D4—614no—
198C2×D4—612no—
199C2×D4—1222no—
200C2×D4—1224no—
201C2×D4—1228no—
202C2×D4—1224no—
203C2×D4—1224no—
204C2×D4—1222no—
205C2×D4D24411yescharacteristic, complemented
206C2×D4C22×D6112yes—
207C22×C4—614no—
208C22×C4—611no—
209C22×C4—1224no—
210C22×C4—1221no—
211C22×C4—1221no—
212C22×C4—1222no—
213C22×C4—1222no—
214C22×C4D24412yescomplemented
215C22×C4C22×D6111yescharacteristic
216C4⋊C4—22no—
217C4⋊C4—1224no—
218C4⋊C4—1222no—
219C4⋊C4—1221no—
220C22⋊C4—612no—
221C22⋊C4—1224no—
222C22⋊C4—1224no—
223C22⋊C4—1222no—
224C22⋊C4—1222no—
225C22⋊C4C22×D6114yes—
226C42—22no—
227C42—1221no—
228C23—614no—
229C23—1224no—
230C23—1222no—
231C23—1221no—
232C23—2442no—
233C23C2×D24412yes—
234C23C23×D6111yescharacteristic
235Q8—22no—
236Q8—1224no—
237Q8—1222no—
238Q8—1222no—
239D4—24no—
240D4—22no—
241D4—1224no—
242D4—1228no—
243D4—1224no—
244D4—1224no—
245D4—1222no—
246D4—1222no—
247D4—2448no—
248D4—2444no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—24no—
252C2×C4—614no—
253C2×C4—1228no—
254C2×C4—1224no—
255C2×C4—1224no—
256C2×C4—1224no—
257C2×C4—1222no—
258C2×C4—1222no—
259C2×C4—1221no—
260C2×C4—2441no—
261C2×C4—2442no—
262C2×C4—2441no—
263C2×C4C2×D24412yes—
264C2×C4C2×D24411yescharacteristic
265C2×C4C2×D24411yescharacteristic
266C2×C4D4×D6112yes—
267C2×C4D4×D6112yes—
268C22—22no—
269C22—41no—
270C22—42no—
271C22—1224no—
272C22—1222no—
273C22—1224no—
274C22—4884no—
275C22—2444no—
276C22—2442no—
277C22—2441no—
278C22—2441no—
279C22C2×D4×D6112yes—
280C22C22×D24411yescharacteristic
281C4—22no—
282C4—44no—
283C4—1224no—
284C4—2442no—
285C4—2441no—
286C4#1451974711yescharacteristic
287C4#1451974712yes—
288C4#1451974711yescharacteristic
289C2—22no—
290C2—21no—
291C2—42no—
292C2—2442no—
293C2—2444no—
294C2C2×#1451974711yescharacteristic
subgroupG/H
centerC4#14519747
commutatorC23×C61C24
FrattiniC23C23×D61
FittingC61×#410C2
socleC2×C61C2×#120
hypercenter#410D61
hypocenterC61#3025
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #16840598C2semidirect
2. #16840274C2semidirect
3. #16840269C2semidirect
4. #16839953C2semidirect
5. #16839950C2semidirect
6. #16839735C2semidirect
7. C61×#410C2semidirect
16. C22×C4×D61C22semidirect
17. #14519761C22semidirect
18. #14519758C22semidirect
23. #14519747C22semidirect
24. #14519745C22semidirect
27. #14519736C22semidirect
28. #14519691C22semidirect
30. #117×C61C22semidirect
31. #99×C61C22semidirect
35. C2×Q8×C61D4semidirect
36. C2×D4×C61D4semidirect
38. C22×C4×C61D4semidirect
59. C2×D244D4semidirect
65. C2×C4×D61D4semidirect
67. C2×Dic122D4semidirect
154. #410D61semidirect
155. C61#3025semidirect
177. #117C2×D61semidirect
179. #99C2×D61semidirect
196. C2×Q8D244semidirect
205. C2×D4D244semidirect
214. C22×C4D244semidirect