Finite Group Databasebeta

← #21455222

Subgroups — #21455222

Order 7808.

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

normal subgroups only

This group has 772 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#16840331C212yesmaximal, complemented
3#16840326C211yesmaximal, characteristic, complemented
4#16839950C218yesmaximal, complemented
5#16839735C212yesmaximal, complemented
6C61×#410C211yesmaximal, characteristic, complemented
7#14519825—21no—
8#14519824—22no—
9#14519823—22no—
10#14519822—21no—
11#14519822C2214yes—
12C2×#11758222—22no—
13C2×#11758222C2212yes—
14#41×D61—24no—
15C22×D244C2211yescharacteristic, complemented
16#14519774—22no—
17#14519773—21no—
18#14519766—21no—
19#14519765—22no—
20#14519752—24no—
21#14519751—22no—
22#14519747C2218yescomplemented
23#14519745C2214yescomplemented
24#14519736C2211yescharacteristic, complemented
25#14519691C2218yescomplemented
26C2×#41×C61C2211yescharacteristic
27#117×C61C2212yescomplemented
28#99×C61C2214yescomplemented
29C23×D61C2312yes—
30#41×C61—22no—
31#41×C61—22no—
32C2×Q8×C61D411yescharacteristic, complemented
33C2×D4×C61D411yescharacteristic, complemented
34C2×D4×C61C2312yes—
35C22×C4×C61D412yescomplemented
36C22×C4×C61C2311yescharacteristic
37C2×C22⋊D61—24no—
38C2×C22⋊D61—24no—
39C2×C22⋊D61C2314yes—
40#11758226—24no—
41Q8×D61—24no—
42#11758224—24no—
43#11758224—28no—
44D4×D61—24no—
45D4×D61—28no—
46#11758222—24no—
47#11758222—24no—
48#11758222—22no—
49#11758222—22no—
50#11758222—24no—
51#11758222—22no—
52#11758222—22no—
53C2×D244—22no—
54C2×D244—21no—
55C2×D244—22no—
56C2×D244—22no—
57C2×D244—21no—
58C2×D244—28no—
59C2×D244D412yescomplemented
60C2×C4×D61—24no—
61C2×C4×D61D414yescomplemented
62C2×Dic122—22no—
63C2×Dic122D412yescomplemented
64C4⋊C4×C61—22no—
65C22⋊C4×C61C2314yes—
66C42×C61—22no—
67C22⋊Dic61C2312yes—
68#11758198—24no—
69#11758198—28no—
70C4⋊Dic61—21no—
71C4×Dic61—21no—
72C23×C61C2×D412yes—
73C23×C61C2411yescharacteristic
74C22×D61—24no—
75C22×D61—24no—
76C22×D61—22no—
77C22×D61—82no—
78C22×D61C2×D414yes—
79Q8×C61—22no—
80D4×C61—24no—
81D4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61—24no—
85C2×C4×C61C2×D412yes—
86C2×C4×C61C2×D411yescharacteristic
87C2×C4×C61C2×D411yescharacteristic
88C2×C4×C61C2×D412yes—
89C2×C4×C61C2×D412yes—
90C22⋊D61—28no—
91C22⋊D61—24no—
92C22⋊D61—24no—
93C22⋊D61—84no—
94C2×Dic61—24no—
95C2×Dic61—22no—
96C2×Dic61C2×D414yes—
97D244—24no—
98D244—22no—
99D244—22no—
100D244—41no—
101D244—42no—
102D244—41no—
103D244—88no—
104C4×D61—28no—
105C4×D61—24no—
106C4×D61—24no—
107Dic122—24no—
108Dic122—22no—
109Dic122—22no—
110C22×C61—22no—
111C22×C61—41no—
112C22×C61—42no—
113C22×C61C22×D412yes—
114C22×C61C22×D411yescharacteristic
115C2×D61—24no—
116C2×D61—44no—
117C2×D61—48no—
118C2×D61—44no—
119C2×D61—42no—
120C2×D61—84no—
121C4×C61—22no—
122C4×C61—44no—
123C4×C61#12011yescharacteristic
124C4×C61#12012yes—
125C4×C61#12011yescharacteristic
126Dic61—24no—
127Dic61—42no—
128#3027—611nomaximal, Sylow
129C2×C61—21no—
130C2×C61—22no—
131C2×C61—42no—
132C2×C61C2×#12011yescharacteristic
133D61—44no—
134D61—82no—
135#585—611no—
136#535—611no—
137#535—612no—
138B(4,𝔽2)—618no—
139#410—612no—
140#410D6111yescharacteristic, complemented
141C61#302711yescharacteristic, complemented, Sylow
1422−1+4—1222no—
1432−1+4—1221no—
144H(5,𝔽2)—614no—
145H(5,𝔽2)—1222no—
146H(5,𝔽2)—1221no—
147C2×#41—612no—
148C2×#41—1224no—
149C2×#41—1222no—
150C2×#41C2×D6111yescharacteristic
151C22×D4—611no—
152#127—1222no—
153#127—1221no—
154#124—1222no—
155#124—1221no—
156#121—1224no—
157#121—1222no—
158#120—614no—
159#120—618no—
160#117—611no—
161#117C2×D6112yescomplemented
162#99—618no—
163#99C2×D6114yescomplemented
164C24—612no—
165#41—22no—
166#41—22no—
167#41—1224no—
168#41—1224no—
169#41—1228no—
170#41—1224no—
171#41—1224no—
172#41—1222no—
173#41—1222no—
174#41—1224no—
175#41—1222no—
176#41—1222no—
177C2×Q8—612no—
178C2×Q8—1222no—
179C2×Q8—1224no—
180C2×Q8D24411yescharacteristic, complemented
181C2×D4—614no—
182C2×D4—612no—
183C2×D4—1222no—
184C2×D4—1228no—
185C2×D4—1228no—
186C2×D4—1224no—
187C2×D4—1224no—
188C2×D4—1224no—
189C2×D4—1221no—
190C2×D4—1221no—
191C2×D4—1222no—
192C2×D4—1222no—
193C2×D4D24411yescharacteristic, complemented
194C2×D4C22×D6112yes—
195C22×C4—614no—
196C22×C4—1224no—
197C22×C4D24412yescomplemented
198C22×C4C22×D6111yescharacteristic
199C4⋊C4—22no—
200C4⋊C4—1221no—
201C22⋊C4—612no—
202C22⋊C4—1228no—
203C22⋊C4—1224no—
204C22⋊C4C22×D6114yes—
205C42—22no—
206C42—1221no—
207C23—614no—
208C23—1224no—
209C23—1224no—
210C23—1222no—
211C23—4882no—
212C23C2×D24412yes—
213C23C23×D6111yescharacteristic
214Q8—22no—
215Q8—1224no—
216Q8—1222no—
217Q8—1222no—
218D4—24no—
219D4—22no—
220D4—1224no—
221D4—1228no—
222D4—1224no—
223D4—1224no—
224D4—1222no—
225D4—1222no—
226D4—4888no—
227D4—4884no—
228D4—2441no—
229D4—2441no—
230D4—2442no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—24no—
234C2×C4—614no—
235C2×C4—1228no—
236C2×C4—1224no—
237C2×C4—1224no—
238C2×C4—1224no—
239C2×C4—1222no—
240C2×C4C2×D24412yes—
241C2×C4C2×D24411yescharacteristic
242C2×C4C2×D24411yescharacteristic
243C2×C4D4×D6112yes—
244C2×C4D4×D6112yes—
245C22—22no—
246C22—41no—
247C22—42no—
248C22—1224no—
249C22—4884no—
250C22—2448no—
251C22—2444no—
252C22—2444no—
253C22—2442no—
254C22C2×D4×D6112yes—
255C22C22×D24411yescharacteristic
256C4—22no—
257C4—44no—
258C4—1224no—
259C4—2442no—
260C4#1451974711yescharacteristic
261C4#1451974711yescharacteristic
262C4#1451974712yes—
263C2—22no—
264C2—21no—
265C2—42no—
266C2—4882no—
267C2—2444no—
268C2C2×#1451974711yescharacteristic
subgroupG/H
centerC2C2×#14519747
commutatorC23×C61C24
FrattiniC23C23×D61
FittingC61×#410C2
socleC2×C61C2×#120
hypercenter#410D61
hypocenterC61#3027
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #16840598C2semidirect
2. #16840331C2semidirect
3. #16840326C2semidirect
4. #16839950C2semidirect
5. #16839735C2semidirect
6. C61×#410C2semidirect
15. C22×D244C22semidirect
22. #14519747C22semidirect
23. #14519745C22semidirect
24. #14519736C22semidirect
25. #14519691C22semidirect
27. #117×C61C22semidirect
28. #99×C61C22semidirect
32. C2×Q8×C61D4semidirect
33. C2×D4×C61D4semidirect
35. C22×C4×C61D4semidirect
59. C2×D244D4semidirect
61. C2×C4×D61D4semidirect
63. C2×Dic122D4semidirect
140. #410D61semidirect
141. C61#3027semidirect
161. #117C2×D61semidirect
163. #99C2×D61semidirect
180. C2×Q8D244semidirect
193. C2×D4D244semidirect
197. C22×C4D244semidirect