Finite Group Databasebeta

← #21455099

Subgroups — #21455099

Order 7808.

752 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 752 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×#14519823C211yesmaximal, characteristic
2C2×#14519807C211yesmaximal, characteristic, complemented
3C22×#11758190C211yesmaximal, characteristic, complemented
4#16840338C211yesmaximal, characteristic, complemented
5#16839927C214yesmaximal, complemented
6#16839914C214yesmaximal, complemented
7#16839766C211yesmaximal, characteristic, complemented
8#16839728C211yesmaximal, characteristic, complemented
9C61×#416C211yesmaximal, characteristic, complemented
10#14519823—24no—
11#14519823—24no—
12C2×#11758226C2212yes—
13C2×#11758222—21no—
14C2×#11758222C2211yescharacteristic
15C22×Dic122C2211yescharacteristic, complemented
16C22×D244—21no—
17C22×D244C2211yescharacteristic
18C2×D4×D61—22no—
19C2×D4×D61C2212yes—
20#14519807—24no—
21C2×#11758202C2212yescomplemented
22C2×#11758190—24no—
23C2×#11758190C2214yescomplemented
24C2×#11758200C2212yescomplemented
25C2×#11758194C2211yescharacteristic, complemented
26#14519777—21no—
27#14519765—21no—
28#14519761—22no—
29#14519757C2214yescomplemented
30#14519697C2214yescomplemented
31#14519689C2214yescomplemented
32C2×#41×C61C2211yescharacteristic
33C22×C8×C61C2211yescharacteristic, complemented
34#117×C61C2211yescharacteristic, complemented
35#103×C61C2212yescomplemented
36#102×C61C2212yescomplemented
37C23×D61—21no—
38C23×D61—22no—
39#41×C61—22no—
40#41×C61D414yes—
41C2×Q8×C61C2311yescharacteristic
42C2×D4×C61—21no—
43C2×D4×C61C2311yescharacteristic
44C22×C4×C61—21no—
45C22×C4×C61C2311yescharacteristic
46C2×C22⋊D61—22no—
47C2×C22⋊D61D412yes—
48C22×Dic61—21no—
49#11758226—24no—
50#11758226—24no—
51D4×D61—216no—
52D4×D61—24no—
53D4×D61—24no—
54#11758222—28no—
55#11758222—22no—
56#11758222—22no—
57C2×D244—28no—
58C2×D244—22no—
59C2×D244—21no—
60C2×D244—22no—
61C2×D244D411yescharacteristic
62C2×D244D414yes—
63C2×D244C2312yes—
64C2×C4×D61—22no—
65C2×C4×D61C2312yes—
66C2×Dic122—22no—
67C2×Dic122—22no—
68C2×Dic122—21no—
69C2×Dic122D411yescharacteristic
70C2×Dic122C2312yes—
71C2×C8×C61—22no—
72C2×C8×C61C2312yes—
73C4⋊C4×C61C2312yes—
74C22⋊C4×C61—21no—
75C42×C61—21no—
76#11758202—24no—
77#11758200—24no—
78#11758198—24no—
79C4⋊Dic61—24no—
80#11758194—22no—
81C2×#92418C2312yes—
82#11758190—28no—
83C23×C61—21no—
84C23×C61C2×D411yescharacteristic
85C22×D61—22no—
86C22×D61—28no—
87C22×D61—24no—
88C22×D61—84no—
89C22×D61—82no—
90C22×D61C2×D412yes—
91Q8×C61—21no—
92Q8×C61C2×D412yes—
93D4×C61—24no—
94D4×C61—21no—
95D4×C61C2×D412yes—
96C2×C4×C61—21no—
97C2×C4×C61—24no—
98C2×C4×C61—22no—
99C2×C4×C61C2×D411yescharacteristic
100C2×C4×C61C2×D412yes—
101C2×C4×C61C2×D412yes—
102C2×C4×C61C2411yescharacteristic
103C22⋊D61—28no—
104C22⋊D61—24no—
105C2×Dic61—22no—
106C2×Dic61—42no—
107C2×Dic61C2×D412yes—
108D244—28no—
109D244—22no—
110D244—24no—
111D244—22no—
112D244C2×D414yes—
113C4×D61—28no—
114C4×D61—22no—
115C4×D61—22no—
116Dic122—22no—
117Dic122—22no—
118Dic122—22no—
119Dic122—42no—
120C8×C61—22no—
121#92418—22no—
122C22×C61—22no—
123C22×C61—22no—
124C22×C61—42no—
125C22×C61#12012yes—
126C22×C61C22×D411yescharacteristic
127C2×D61—22no—
128C2×D61—24no—
129C2×D61—24no—
130C2×D61—44no—
131C2×D61—84no—
132C2×D61—88no—
133C4×C61—22no—
134C4×C61—42no—
135C4×C61#12012yes—
136C4×C61C22×D411yescharacteristic
137C4×C61C22×D411yescharacteristic
138Dic61—22no—
139Dic61—42no—
140#3009—611nomaximal, Sylow
141C2×C61—22no—
142C2×C61—42no—
143C2×C61C2×#12011yescharacteristic
144C2×C61#57712yes—
145D61—42no—
146D61—44no—
147C2×H(5,𝔽2)—611no—
148C2×#137—611no—
149C22×SD16—611no—
150#536—611no—
151#452—614no—
152#450—614no—
153#418—611no—
154#416D6111yescharacteristic, complemented
155#408—611no—
156C61#300911yescharacteristic, complemented, Sylow
157H(5,𝔽2)—1224no—
158H(5,𝔽2)—1224no—
159C2×#41—611no—
160C2×#41—612no—
161C2×#41—1221no—
162C2×#41C2×D6111yescharacteristic
163C22×Q8—611no—
164C22×D4—612no—
165C22×D4—611no—
166C22×D4—1221no—
167C22×D4—1222no—
168#137—1224no—
169C2×Q16—612no—
170C2×SD16—612no—
171C2×SD16—614no—
172C2×SD16—1224no—
173C2×M16—611no—
174C22×C8C2×D6111yescharacteristic, complemented
175C4⋊Q8—1221no—
176#124—1221no—
177#123—1222no—
178C22⋊Q8—614no—
179#117C2×D6111yescharacteristic, complemented
180#103C2×D6112yescomplemented
181#102—614no—
182#102C2×D6112yescomplemented
183C22⋊C8—614no—
184C24—1222no—
185C24—1221no—
186#41—22no—
187#41—1228no—
188#41—1224no—
189#41—1224no—
190#41—1222no—
191#41—1222no—
192#41D24414yes—
193C2×Q8—611no—
194C2×Q8—612no—
195C2×Q8—1221no—
196C2×Q8—1222no—
197C2×Q8—1222no—
198C2×Q8C22×D6111yescharacteristic
199C2×D4—21no—
200C2×D4—612no—
201C2×D4—614no—
202C2×D4—611no—
203C2×D4—612no—
204C2×D4—1222no—
205C2×D4—1228no—
206C2×D4—1222no—
207C2×D4—1224no—
208C2×D4—12216no—
209C2×D4—1224no—
210C2×D4—1222no—
211C2×D4—1221no—
212C2×D4C22×D6111yescharacteristic
213C22×C4—21no—
214C22×C4—612no—
215C22×C4—1222no—
216C22×C4—1221no—
217C22×C4C22×D6111yescharacteristic
218Q16—1224no—
219SD16—1228no—
220SD16—1224no—
221M16—1222no—
222C2×C8—22no—
223C2×C8—612no—
224C2×C8C22×D6112yes—
225C4⋊C4—1224no—
226C4⋊C4C22×D6112yes—
227C22⋊C4—21no—
228C22⋊C4—1224no—
229C42—21no—
230C23—21no—
231C23—612no—
232C23—1228no—
233C23—1224no—
234C23—1222no—
235C23—4882no—
236C23—4884no—
237C23D4×D6111yescharacteristic
238Q8—21no—
239Q8—1222no—
240Q8—1222no—
241Q8—1222no—
242Q8—2442no—
243Q8C2×D24412yes—
244D4—24no—
245D4—21no—
246D4—614no—
247D4—1228no—
248D4—1228no—
249D4—1224no—
250D4—1222no—
251D4—1224no—
252D4—1222no—
253D4C2×D24412yes—
254C2×C4—21no—
255C2×C4—24no—
256C2×C4—22no—
257C2×C4—612no—
258C2×C4—1228no—
259C2×C4—1222no—
260C2×C4—1222no—
261C2×C4—1222no—
262C2×C4—2442no—
263C2×C4C2×D24412yes—
264C2×C4D4×D6112yes—
265C2×C4D4×D6111yescharacteristic
266C2×C4C23×D6111yescharacteristic
267C8—22no—
268C8—1222no—
269C22—22no—
270C22—22no—
271C22—42no—
272C22—1224no—
273C22—1222no—
274C22—1224no—
275C22—4884no—
276C22—4888no—
277C22—2444no—
278C22#1451974712yes—
279C22C2×D4×D6111yescharacteristic
280C4—22no—
281C4—42no—
282C4—1222no—
283C4—2442no—
284C4#1451974712yes—
285C4C2×D4×D6111yescharacteristic
286C4C22×D24411yescharacteristic
287C2—22no—
288C2—42no—
289C2—2442no—
290C2—2444no—
291C2C2×#1451974711yescharacteristic
292C2#1684056912yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#416C2
socleC22×C61C22×D4
hypercenter#416D61
hypocenterC61#3009
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. C2×#14519807C2semidirect
3. C22×#11758190C2semidirect
4. #16840338C2semidirect
5. #16839927C2semidirect
6. #16839914C2semidirect
7. #16839766C2semidirect
8. #16839728C2semidirect
9. C61×#416C2semidirect
15. C22×Dic122C22semidirect
21. C2×#11758202C22semidirect
23. C2×#11758190C22semidirect
24. C2×#11758200C22semidirect
25. C2×#11758194C22semidirect
29. #14519757C22semidirect
30. #14519697C22semidirect
31. #14519689C22semidirect
33. C22×C8×C61C22semidirect
34. #117×C61C22semidirect
35. #103×C61C22semidirect
36. #102×C61C22semidirect
154. #416D61semidirect
156. C61#3009semidirect
174. C22×C8C2×D61semidirect
179. #117C2×D61semidirect
180. #103C2×D61semidirect
182. #102C2×D61semidirect