Finite Group Databasebeta

← #21455190

Subgroups — #21455190

Order 7808.

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

normal subgroups only

This group has 736 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
2C2×#14519803C212yesmaximal, complemented
3#16839934C214yesmaximal, complemented
4#16839929C214yesmaximal, complemented
5#16839780C212yesmaximal, complemented
6#16839746C211yesmaximal, characteristic, complemented
7C61×#535C211yesmaximal, characteristic, complemented
8#14519825C2212yescomplemented
9#14519824—22no—
10#14519823—22no—
11#14519822—22no—
12#14519822C2212yescomplemented
13C2×#11758222—22no—
14C2×#11758222C2212yes—
15#41×D61—24no—
16#14519803—24no—
17#14519803C2218yescomplemented
18C2×#11758200—22no—
19C2×#11758199—22no—
20C2×#11758194C2212yescomplemented
21#14519705C2218yescomplemented
22#14519696C2212yescomplemented
23#14519694C2212yescomplemented
24C2×#41×C61C2211yescharacteristic
25C22×D4×C61C2211yescharacteristic, complemented
26#127×C61C2212yescomplemented
27#124×C61C2212yescomplemented
28#121×C61—22no—
29#120×C61—22no—
30#117×C61C2211yescharacteristic, complemented
31C24×C61—21no—
32#41×C61—22no—
33#41×C61—22no—
34C2×Q8×C61C2311yescharacteristic
35C2×D4×C61—24no—
36C2×D4×C61—22no—
37C2×D4×C61—22no—
38C2×D4×C61—21no—
39C2×D4×C61D412yes—
40C2×D4×C61C2312yes—
41C2×D4×C61C2311yescharacteristic
42C22×C4×C61D412yes—
43C22×C4×C61C2311yescharacteristic
44C2×C22⋊D61—24no—
45C2×C22⋊D61—22no—
46#11758226—24no—
47Q8×D61—24no—
48#11758224—28no—
49#11758224—24no—
50D4×D61—28no—
51D4×D61—24no—
52#11758222—24no—
53#11758222—24no—
54#11758222—22no—
55#11758222—24no—
56#11758222—22no—
57#11758222D414yescomplemented
58#11758222C2314yes—
59C2×D244—22no—
60C2×D244D412yescomplemented
61C2×C4×D61—24no—
62C2×C4×D61—22no—
63C2×Dic122—22no—
64C2×Dic122D412yescomplemented
65C4⋊C4×C61—21no—
66C22⋊C4×C61—21no—
67C22⋊C4×C61—24no—
68C42×C61C2312yes—
69#11758200—28no—
70#11758199—28no—
71#11758194—22no—
72#11758194C2314yes—
73C2×#92418—22no—
74C23×C61—22no—
75C23×C61—42no—
76C23×C61—82no—
77C23×C61C2×D412yes—
78C23×C61C2×D411yescharacteristic
79C22×D61—24no—
80C22×D61—22no—
81Q8×C61—22no—
82D4×C61—24no—
83D4×C61—22no—
84D4×C61—24no—
85D4×C61—41no—
86D4×C61—41no—
87D4×C61—84no—
88C2×C4×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61C2×D412yes—
92C2×C4×C61C2×D411yescharacteristic
93C2×C4×C61C2×D412yes—
94C2×C4×C61C2×D412yes—
95C2×C4×C61C2411yescharacteristic
96C22⋊D61—28no—
97C22⋊D61—24no—
98C22⋊D61—24no—
99C2×Dic61—24no—
100C2×Dic61—22no—
101D244—24no—
102D244—22no—
103D244C2×D414yes—
104C4×D61—28no—
105C4×D61—24no—
106C4×D61—24no—
107Dic122—24no—
108Dic122—22no—
109Dic122C2×D414yes—
110#92418—24no—
111C22×C61—22no—
112C22×C61—41no—
113C22×C61—42no—
114C22×C61—44no—
115C22×C61—42no—
116C22×C61—84no—
117C22×C61#12012yes—
118C22×C61C22×D411yescharacteristic
119C2×D61—24no—
120C2×D61—82no—
121C2×D61—84no—
122C4×C61—22no—
123C4×C61—42no—
124C4×C61#12011yescharacteristic
125C4×C61#12011yescharacteristic
126C4×C61C22×D412yes—
127Dic61—24no—
128#3021—611nomaximal, Sylow
129C2×C61—21no—
130C2×C61—22no—
131C2×C61—42no—
132C2×C61—82no—
133C2×C61C2×#12011yescharacteristic
134D61—44no—
135#585—611no—
136C2×AGL(1,ℤ/8)—612no—
137#535D6111yescharacteristic, complemented
138#454—614no—
139#453—614no—
140#421—612no—
141#413—611no—
142C61#302111yescharacteristic, complemented, Sylow
1432−1+4—612no—
1442−1+4—1222no—
145H(5,𝔽2)—612no—
146H(5,𝔽2)—1222no—
147H(5,𝔽2)—1222no—
148C2×#41—612no—
149C2×#41—1224no—
150C2×#41—1222no—
151C2×#41C2×D6111yescharacteristic
152C22×D4C2×D6111yescharacteristic, complemented
153AGL(1,ℤ/8)—618no—
154AGL(1,ℤ/8)—1224no—
155C2×SD16—1222no—
156C2×D8—1222no—
157C2×M16—612no—
158#127C2×D6112yescomplemented
159#124C2×D6112yescomplemented
160#121—22no—
161#120—22no—
162#117C2×D6111yescharacteristic, complemented
163#104—618no—
164#101—612no—
165#100—612no—
166C24—21no—
167#41—22no—
168#41—22no—
169#41—614no—
170#41—614no—
171#41—1224no—
172#41—1224no—
173#41—1224no—
174#41—1228no—
175#41—1224no—
176#41—1222no—
177#41—1222no—
178#41—1224no—
179C2×Q8—612no—
180C2×Q8—1222no—
181C2×Q8—1224no—
182C2×Q8C22×D6111yescharacteristic
183C2×D4—24no—
184C2×D4—22no—
185C2×D4—22no—
186C2×D4—21no—
187C2×D4—612no—
188C2×D4—1222no—
189C2×D4—1224no—
190C2×D4—1228no—
191C2×D4—1222no—
192C2×D4—1224no—
193C2×D4C22⋊D6112yes—
194C2×D4C22×D6112yes—
195C2×D4C22×D6111yescharacteristic
196C22×C4—1224no—
197C22×C4—1222no—
198C22×C4C22⋊D6112yes—
199C22×C4C22×D6111yescharacteristic
200SD16—1228no—
201D8—1228no—
202M16—614no—
203M16—1222no—
204C2×C8—1222no—
205C4⋊C4—21no—
206C22⋊C4—21no—
207C22⋊C4—24no—
208C42C22×D6112yes—
209C23—22no—
210C23—42no—
211C23—82no—
212C23—1224no—
213C23—1222no—
214C23C2×C22⋊D6112yes—
215C23C2×C22⋊D6111yescharacteristic
216Q8—22no—
217Q8—614no—
218Q8—1224no—
219Q8—1222no—
220D4—24no—
221D4—22no—
222D4—24no—
223D4—41no—
224D4—41no—
225D4—84no—
226D4—614no—
227D4—1224no—
228D4—1228no—
229D4—1224no—
230D4—1224no—
231D4—1222no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—1228no—
236C2×C4—1224no—
237C2×C4—1222no—
238C2×C4—1224no—
239C2×C4—1224no—
240C2×C4D4×D6112yes—
241C2×C4D4×D6112yes—
242C2×C4C2×C22⋊D6112yes—
243C2×C4C2×C22⋊D6111yescharacteristic
244C2×C4C23×D6111yescharacteristic
245C8—1224no—
246C22—22no—
247C22—41no—
248C22—42no—
249C22—44no—
250C22—42no—
251C22—84no—
252C22—1224no—
253C22—4882no—
254C22—4884no—
255C22#1451974512yes—
256C22C22×C22⋊D6111yescharacteristic
257C4—22no—
258C4—42no—
259C4—1224no—
260C4#1451974511yescharacteristic
261C4#1451974511yescharacteristic
262C4C2×D4×D6112yes—
263C2—21no—
264C2—22no—
265C2—42no—
266C2—82no—
267C2—2444no—
268C2C2×#1451974511yescharacteristic
subgroupG/H
centerC2C2×#14519745
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#535C2
socleC2×C61C2×#120
hypercenter#535D61
hypocenterC61#3021
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #16840598C2semidirect
2. C2×#14519803C2semidirect
3. #16839934C2semidirect
4. #16839929C2semidirect
5. #16839780C2semidirect
6. #16839746C2semidirect
7. C61×#535C2semidirect
8. #14519825C22semidirect
12. #14519822C22semidirect
17. #14519803C22semidirect
20. C2×#11758194C22semidirect
21. #14519705C22semidirect
22. #14519696C22semidirect
23. #14519694C22semidirect
25. C22×D4×C61C22semidirect
26. #127×C61C22semidirect
27. #124×C61C22semidirect
30. #117×C61C22semidirect
57. #11758222D4semidirect
60. C2×D244D4semidirect
64. C2×Dic122D4semidirect
137. #535D61semidirect
142. C61#3021semidirect
152. C22×D4C2×D61semidirect
158. #127C2×D61semidirect
159. #124C2×D61semidirect
162. #117C2×D61semidirect