Finite Group Databasebeta

← #21455197

Subgroups — #21455197

Order 7808.

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

normal subgroups only

This group has 704 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
2C2×#14519808C212yesmaximal, complemented
3#16839944C214yesmaximal, complemented
4#16839939C214yesmaximal, complemented
5#16839780C212yesmaximal, complemented
6#16839746C211yesmaximal, characteristic, complemented
7C61×#536C211yesmaximal, characteristic, complemented
8#14519825C2212yes—
9#14519824—22no—
10#14519823—22no—
11#14519822—22no—
12#14519822C2212yes—
13C2×#11758222—22no—
14C2×#11758222C2212yes—
15#41×D61—24no—
16#14519808—24no—
17#14519808C2218yescomplemented
18C2×#11758202—22no—
19C2×#11758201—22no—
20C2×#11758194C2212yescomplemented
21#14519705C2218yescomplemented
22#14519696C2212yescomplemented
23#14519694C2212yescomplemented
24C2×#41×C61C2211yescharacteristic
25C22×Q8×C61C2211yescharacteristic, complemented
26C4⋊Q8×C61C2212yescomplemented
27#124×C61C2212yescomplemented
28#123×C61—22no—
29C22⋊Q8×C61—22no—
30#117×C61C2211yescharacteristic, complemented
31#41×C61—22no—
32#41×C61—22no—
33C2×Q8×C61—21no—
34C2×Q8×C61—22no—
35C2×Q8×C61—22no—
36C2×Q8×C61C2312yes—
37C2×Q8×C61C2311yescharacteristic
38C2×D4×C61D412yes—
39C2×D4×C61C2311yescharacteristic
40C22×C4×C61—21no—
41C22×C4×C61D412yes—
42C22×C4×C61C2311yescharacteristic
43C2×C22⋊D61—24no—
44C2×C22⋊D61—22no—
45#11758226—24no—
46Q8×D61—24no—
47#11758224—28no—
48#11758224—24no—
49D4×D61—28no—
50D4×D61—24no—
51#11758222—24no—
52#11758222—24no—
53#11758222—22no—
54#11758222—24no—
55#11758222—22no—
56#11758222D414yes—
57#11758222C2314yes—
58C2×D244—22no—
59C2×D244D412yes—
60C2×C4×D61—24no—
61C2×C4×D61—22no—
62C2×Dic122—22no—
63C2×Dic122D412yes—
64C4⋊C4×C61—21no—
65C4⋊C4×C61—24no—
66C22⋊C4×C61—21no—
67C22⋊C4×C61—24no—
68C42×C61C2312yes—
69#11758202—28no—
70#11758201—28no—
71#11758194—22no—
72#11758194C2314yes—
73C2×#92418—22no—
74C23×C61C2×D412yes—
75C23×C61C2×D411yescharacteristic
76C22×D61—24no—
77C22×D61—22no—
78Q8×C61—22no—
79Q8×C61—24no—
80Q8×C61—41no—
81Q8×C61—41no—
82D4×C61—24no—
83D4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—42no—
89C2×C4×C61C2×D412yes—
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61C2×D412yes—
92C2×C4×C61C2×D412yes—
93C2×C4×C61C2411yescharacteristic
94C22⋊D61—28no—
95C22⋊D61—24no—
96C22⋊D61—24no—
97C2×Dic61—24no—
98C2×Dic61—22no—
99D244—24no—
100D244—22no—
101D244C2×D414yes—
102C4×D61—28no—
103C4×D61—24no—
104C4×D61—24no—
105Dic122—24no—
106Dic122—22no—
107Dic122C2×D414yes—
108#92418—24no—
109C22×C61—22no—
110C22×C61—41no—
111C22×C61—42no—
112C22×C61#12012yes—
113C22×C61C22×D411yescharacteristic
114C2×D61—24no—
115C2×D61—82no—
116C2×D61—84no—
117C4×C61—22no—
118C4×C61—42no—
119C4×C61—42no—
120C4×C61#12011yescharacteristic
121C4×C61#12011yescharacteristic
122C4×C61C22×D412yes—
123Dic61—24no—
124#3022—611nomaximal, Sylow
125C2×C61—21no—
126C2×C61—22no—
127C2×C61—42no—
128C2×C61C2×#12011yescharacteristic
129D61—44no—
130#585—611no—
131C2×#137—612no—
132#536D6111yescharacteristic, complemented
133#456—614no—
134#455—614no—
135#421—612no—
136#413—611no—
137C61#302211yescharacteristic, complemented, Sylow
1382−1+4—612no—
1392−1+4—1222no—
140H(5,𝔽2)—612no—
141H(5,𝔽2)—1222no—
142H(5,𝔽2)—1222no—
143C2×#41—612no—
144C2×#41—1224no—
145C2×#41—1222no—
146C2×#41C2×D6111yescharacteristic
147C22×Q8C2×D6111yescharacteristic, complemented
148#137—618no—
149#137—1224no—
150C2×Q16—1222no—
151C2×SD16—1222no—
152C2×M16—612no—
153C4⋊Q8C2×D6112yescomplemented
154#124C2×D6112yescomplemented
155#123—22no—
156C22⋊Q8—22no—
157#117C2×D6111yescharacteristic, complemented
158#104—618no—
159#101—612no—
160#100—612no—
161#41—22no—
162#41—22no—
163#41—614no—
164#41—614no—
165#41—1224no—
166#41—1224no—
167#41—1224no—
168#41—1228no—
169#41—1224no—
170#41—1222no—
171#41—1222no—
172#41—1224no—
173C2×Q8—21no—
174C2×Q8—22no—
175C2×Q8—22no—
176C2×Q8—612no—
177C2×Q8—1222no—
178C2×Q8—1224no—
179C2×Q8C22×D6112yes—
180C2×Q8C22×D6111yescharacteristic
181C2×D4—612no—
182C2×D4—1222no—
183C2×D4—1224no—
184C2×D4—1228no—
185C2×D4—1222no—
186C2×D4—1224no—
187C2×D4C22⋊D6112yes—
188C2×D4C22×D6111yescharacteristic
189C22×C4—21no—
190C22×C4—1224no—
191C22×C4—1222no—
192C22×C4C22⋊D6112yes—
193C22×C4C22×D6111yescharacteristic
194Q16—1228no—
195SD16—1228no—
196M16—614no—
197M16—1222no—
198C2×C8—1222no—
199C4⋊C4—21no—
200C4⋊C4—24no—
201C22⋊C4—21no—
202C22⋊C4—24no—
203C42C22×D6112yes—
204C23—1224no—
205C23—1222no—
206C23C2×C22⋊D6112yes—
207C23C2×C22⋊D6111yescharacteristic
208Q8—22no—
209Q8—24no—
210Q8—41no—
211Q8—41no—
212Q8—614no—
213Q8—1224no—
214Q8—1222no—
215D4—24no—
216D4—22no—
217D4—614no—
218D4—1224no—
219D4—1228no—
220D4—1224no—
221D4—1224no—
222D4—1222no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—42no—
228C2×C4—1228no—
229C2×C4—1224no—
230C2×C4—1222no—
231C2×C4—1224no—
232C2×C4—1224no—
233C2×C4D4×D6112yes—
234C2×C4D4×D6112yes—
235C2×C4C2×C22⋊D6112yes—
236C2×C4C2×C22⋊D6111yescharacteristic
237C2×C4C23×D6111yescharacteristic
238C8—1224no—
239C22—22no—
240C22—41no—
241C22—42no—
242C22—1224no—
243C22—4882no—
244C22—4884no—
245C22#1451974512yes—
246C22C22×C22⋊D6111yescharacteristic
247C4—22no—
248C4—42no—
249C4—42no—
250C4—1224no—
251C4#1451974511yescharacteristic
252C4#1451974511yescharacteristic
253C4C2×D4×D6112yes—
254C2—21no—
255C2—22no—
256C2—42no—
257C2—2444no—
258C2C2×#1451974511yescharacteristic
subgroupG/H
centerC2C2×#14519745
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#536C2
socleC2×C61C2×#120
hypercenter#536D61
hypocenterC61#3022
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
2. C2×#14519808C2semidirect
3. #16839944C2semidirect
4. #16839939C2semidirect
5. #16839780C2semidirect
6. #16839746C2semidirect
7. C61×#536C2semidirect
17. #14519808C22semidirect
20. C2×#11758194C22semidirect
21. #14519705C22semidirect
22. #14519696C22semidirect
23. #14519694C22semidirect
25. C22×Q8×C61C22semidirect
26. C4⋊Q8×C61C22semidirect
27. #124×C61C22semidirect
30. #117×C61C22semidirect
132. #536D61semidirect
137. C61#3022semidirect
147. C22×Q8C2×D61semidirect
153. C4⋊Q8C2×D61semidirect
154. #124C2×D61semidirect
157. #117C2×D61semidirect