Finite Group Databasebeta

← #21455125

Subgroups — #21455125

Order 7808.

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

normal subgroups only

This group has 764 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, complemented
2C2×#14519805C211yesmaximal, characteristic, complemented
3C2×#14519797C211yesmaximal, characteristic, complemented
4#16840343C211yesmaximal, characteristic, complemented
5#16839927C212yesmaximal, complemented
6#16839914C212yesmaximal, complemented
7#16839910C212yesmaximal, complemented
8#16839897C212yesmaximal, complemented
9C2×#14519697C211yesmaximal, characteristic, complemented
10#16839730C211yesmaximal, characteristic, complemented
11C61×#417C211yesmaximal, characteristic, complemented
12#14519823—24no—
13#14519823—24no—
14C2×#11758226C2212yes—
15C2×#11758222—21no—
16C2×#11758222C2211yescharacteristic
17C2×#11758222C2211yescharacteristic, complemented
18C22×D244—21no—
19C22×D244C2211yescharacteristic
20C2×D4×D61—22no—
21C2×D4×D61C2212yes—
22#14519805—24no—
23#14519797—24no—
24C2×#11758202C2211yescharacteristic, complemented
25C2×#11758190C2212yescomplemented
26C2×#11758200C2211yescharacteristic, complemented
27C2×#11758201C2211yescharacteristic, complemented
28C2×D488C2212yescomplemented
29C2×#11758199C2211yescharacteristic, complemented
30C22×#92418C2211yescharacteristic, complemented
31#14519757—21no—
32#14519757C2212yescomplemented
33#14519752—21no—
34#14519752C2212yescomplemented
35#14519751—22no—
36#14519697C2212yescomplemented
37#14519697C2212yescomplemented
38#14519689C2212yescomplemented
39#14519689C2212yescomplemented
40C2×#41×C61C2211yescharacteristic
41C2×M16×C61C2211yescharacteristic, complemented
42C2×C4⋊C4×C61C2211yescharacteristic, complemented
43#103×C61C2212yescomplemented
44#102×C61C2212yescomplemented
45C23×D61—21no—
46C23×D61—22no—
47#41×C61—22no—
48#41×C61D414yescomplemented
49C2×Q8×C61C2311yescharacteristic
50C2×D4×C61—21no—
51C2×D4×C61C2311yescharacteristic
52C22×C4×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61C2311yescharacteristic
55C2×C22⋊D61—21no—
56C2×C22⋊D61—22no—
57C2×C22⋊D61D412yes—
58#11758226—24no—
59#11758226—24no—
60D4×D61—216no—
61D4×D61—24no—
62D4×D61—24no—
63#11758222—28no—
64#11758222—22no—
65#11758222—22no—
66#11758222—22no—
67#11758222—22no—
68C2×D244—28no—
69C2×D244—22no—
70C2×D244—21no—
71C2×D244—22no—
72C2×D244—22no—
73C2×D244D411yescharacteristic
74C2×D244D414yescomplemented
75C2×D244C2311yescharacteristic
76C2×D244C2312yes—
77C2×C4×D61—22no—
78C2×C4×D61—21no—
79C2×C4×D61C2312yes—
80C2×Dic122D411yescharacteristic
81C2×Dic122C2311yescharacteristic
82M16×C61—22no—
83C2×C8×C61C2312yes—
84C4⋊C4×C61—21no—
85C4⋊C4×C61C2312yes—
86#11758202—22no—
87#11758201—22no—
88#11758200—22no—
89#11758199—22no—
90#11758198—22no—
91#11758198—22no—
92C4⋊Dic61—22no—
93C2×#92418—22no—
94C2×#92418C2311yescharacteristic
95C2×#92418C2311yescharacteristic
96D488—24no—
97#11758190—24no—
98C23×C61—21no—
99C23×C61C2×D411yescharacteristic
100C22×D61—22no—
101C22×D61—28no—
102C22×D61—24no—
103C22×D61—21no—
104C22×D61—82no—
105C22×D61—82no—
106C22×D61—81no—
107C22×D61—81no—
108C22×D61C2×D412yes—
109Q8×C61—21no—
110Q8×C61C2×D412yes—
111D4×C61—24no—
112D4×C61—21no—
113D4×C61C2×D412yes—
114C2×C4×C61—21no—
115C2×C4×C61—24no—
116C2×C4×C61—22no—
117C2×C4×C61—81no—
118C2×C4×C61C2×D411yescharacteristic
119C2×C4×C61C2×D412yes—
120C2×C4×C61C2×D412yes—
121C2×C4×C61C2411yescharacteristic
122C22⋊D61—28no—
123C22⋊D61—24no—
124C22⋊D61—42no—
125C2×Dic61—21no—
126C2×Dic61C2×D412yes—
127D244—28no—
128D244—22no—
129D244—24no—
130D244—22no—
131D244—21no—
132D244—21no—
133D244—82no—
134D244C2×D414yes—
135C4×D61—28no—
136C4×D61—22no—
137C4×D61—22no—
138C4×D61—42no—
139Dic122—22no—
140Dic122—21no—
141Dic122—21no—
142C8×C61—22no—
143#92418—21no—
144#92418—21no—
145C22×C61—21no—
146C22×C61—21no—
147C22×C61—22no—
148C22×C61—41no—
149C22×C61—41no—
150C22×C61#12012yes—
151C22×C61C22×D411yescharacteristic
152C2×D61—22no—
153C2×D61—24no—
154C2×D61—22no—
155C2×D61—22no—
156C2×D61—42no—
157C2×D61—42no—
158C2×D61—41no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—84no—
162C2×D61—88no—
163C4×C61—22no—
164C4×C61—42no—
165C4×C61#12012yes—
166C4×C61C22×D411yescharacteristic
167C4×C61C22×D411yescharacteristic
168Dic61—22no—
169Dic61—41no—
170#3012—611nomaximal, Sylow
171C2×C61—22no—
172C2×C61—42no—
173C2×C61C2×#12011yescharacteristic
174C2×C61#57611yescharacteristic
175C2×C61#57711yescharacteristic
176D61—42no—
177D61—44no—
178D61—81no—
179C2×H(5,𝔽2)—611no—
180C2×AGL(1,ℤ/8)—611no—
181C2×#135—611no—
182#537—611no—
183#452—612no—
184#450—612no—
185#449—612no—
186#447—612no—
187#417D6111yescharacteristic, complemented
188C2×#102—611no—
189#408—611no—
190C61#301211yescharacteristic, complemented, Sylow
191H(5,𝔽2)—1224no—
192H(5,𝔽2)—1224no—
193C2×#41—611no—
194C2×#41—612no—
195C2×#41—611no—
196C2×#41—1221no—
197C2×#41C2×D6111yescharacteristic
198C22×D4—612no—
199C22×D4—611no—
200C22×D4—1221no—
201C22×D4—1222no—
202AGL(1,ℤ/8)—1224no—
203#135—1224no—
204C2×Q16—611no—
205C2×SD16—611no—
206C2×SD16—611no—
207C2×SD16—612no—
208C2×D8—611no—
209C2×D8—612no—
210C2×M16C2×D6111yescharacteristic, complemented
211C22×C8—611no—
212C22⋊Q8—612no—
213C22⋊Q8—1221no—
214#121—612no—
215#121—1221no—
216#121—1222no—
217C2×C4⋊C4C2×D6111yescharacteristic, complemented
218#103C2×D6112yescomplemented
219#102—612no—
220#102—612no—
221#102C2×D6112yescomplemented
222C22⋊C8—612no—
223C22⋊C8—612no—
224C24—1222no—
225C24—1221no—
226#41—22no—
227#41—1228no—
228#41—1224no—
229#41—1224no—
230#41—1222no—
231#41—1222no—
232#41—1222no—
233#41—1222no—
234#41D24414yescomplemented
235C2×Q8—611no—
236C2×Q8—611no—
237C2×Q8C22×D6111yescharacteristic
238C2×D4—21no—
239C2×D4—612no—
240C2×D4—614no—
241C2×D4—611no—
242C2×D4—612no—
243C2×D4—611no—
244C2×D4—1222no—
245C2×D4—1228no—
246C2×D4—1222no—
247C2×D4—1222no—
248C2×D4—1224no—
249C2×D4—12216no—
250C2×D4—1224no—
251C2×D4—1221no—
252C2×D4—1222no—
253C2×D4—1221no—
254C2×D4C22×D6111yescharacteristic
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—612no—
258C22×C4—1222no—
259C22×C4—1221no—
260C22×C4C22×D6111yescharacteristic
261Q16—1222no—
262SD16—1224no—
263SD16—1222no—
264SD16—1222no—
265D8—1224no—
266D8—1222no—
267M16—22no—
268C2×C8—611no—
269C2×C8—611no—
270C2×C8—1222no—
271C2×C8C22×D6112yes—
272C4⋊C4—21no—
273C4⋊C4—1222no—
274C4⋊C4C22×D6112yes—
275C22⋊C4—1222no—
276C22⋊C4—1222no—
277C23—21no—
278C23—612no—
279C23—1228no—
280C23—1224no—
281C23—1222no—
282C23—1221no—
283C23—4881no—
284C23—4881no—
285C23—4882no—
286C23—4882no—
287C23D4×D6111yescharacteristic
288Q8—21no—
289Q8—1222no—
290Q8—1221no—
291Q8—1221no—
292Q8C2×D24412yes—
293D4—24no—
294D4—21no—
295D4—614no—
296D4—1228no—
297D4—1228no—
298D4—1224no—
299D4—1221no—
300D4—1222no—
301D4—1221no—
302D4—1224no—
303D4—1222no—
304D4—4882no—
305D4—2442no—
306D4C2×D24412yes—
307C2×C4—21no—
308C2×C4—24no—
309C2×C4—22no—
310C2×C4—81no—
311C2×C4—612no—
312C2×C4—1228no—
313C2×C4—1222no—
314C2×C4—1222no—
315C2×C4—1221no—
316C2×C4—2442no—
317C2×C4C2×D24412yes—
318C2×C4D4×D6112yes—
319C2×C4D4×D6111yescharacteristic
320C2×C4C23×D6111yescharacteristic
321C8—22no—
322C8—1221no—
323C8—1221no—
324C22—21no—
325C22—21no—
326C22—22no—
327C22—41no—
328C22—41no—
329C22—1224no—
330C22—1222no—
331C22—1222no—
332C22—1222no—
333C22—4884no—
334C22—4888no—
335C22—2441no—
336C22—2441no—
337C22—2441no—
338C22—2442no—
339C22—2442no—
340C22#1451974712yes—
341C22C2×D4×D6111yescharacteristic
342C4—22no—
343C4—42no—
344C4—1222no—
345C4—2441no—
346C4#1451974712yes—
347C4C2×D4×D6111yescharacteristic
348C4C22×D24411yescharacteristic
349C2—22no—
350C2—42no—
351C2—4881no—
352C2—2442no—
353C2—2444no—
354C2C2×#1451974711yescharacteristic
355C2#1684056611yescharacteristic
356C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#417C2
socleC22×C61C22×D4
hypercenter#417D61
hypocenterC61#3012
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. C2×#14519823C2semidirect
2. C2×#14519805C2semidirect
3. C2×#14519797C2semidirect
4. #16840343C2semidirect
5. #16839927C2semidirect
6. #16839914C2semidirect
7. #16839910C2semidirect
8. #16839897C2semidirect
9. C2×#14519697C2semidirect
10. #16839730C2semidirect
11. C61×#417C2semidirect
17. C2×#11758222C22semidirect
24. C2×#11758202C22semidirect
25. C2×#11758190C22semidirect
26. C2×#11758200C22semidirect
27. C2×#11758201C22semidirect
28. C2×D488C22semidirect
29. C2×#11758199C22semidirect
30. C22×#92418C22semidirect
32. #14519757C22semidirect
34. #14519752C22semidirect
36. #14519697C22semidirect
37. #14519697C22semidirect
38. #14519689C22semidirect
39. #14519689C22semidirect
41. C2×M16×C61C22semidirect
42. C2×C4⋊C4×C61C22semidirect
43. #103×C61C22semidirect
44. #102×C61C22semidirect
48. #41×C61D4semidirect
74. C2×D244D4semidirect
187. #417D61semidirect
190. C61#3012semidirect
210. C2×M16C2×D61semidirect
217. C2×C4⋊C4C2×D61semidirect
218. #103C2×D61semidirect
221. #102C2×D61semidirect
234. #41D244semidirect