Finite Group Databasebeta

← #21455047

Subgroups — #21455047

Order 7808.

994 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C22×D4×D61C211yesmaximal, characteristic, complemented
2C2×#14519804C212yesmaximal, complemented
3#16840275C211yesmaximal, characteristic, complemented
4#16839912C211yesmaximal, characteristic, complemented
5#16839911C212yesmaximal, complemented
6#16839898C211yesmaximal, characteristic, complemented
7#16839897C212yesmaximal, complemented
8#16839896C211yesmaximal, characteristic, complemented
9#16839765C212yesmaximal, complemented
10#16839724C211yesmaximal, characteristic, complemented
11C61×#450C211yesmaximal, characteristic, complemented
12C24×D61—21no—
13C2×#11758226C2211yescharacteristic, complemented
14C22×D244C2211yescharacteristic
15C22×C22⋊D61—21no—
16C2×D4×D61—28no—
17C2×D4×D61—21no—
18C2×D4×D61—21no—
19C2×D4×D61C2212yes—
20C2×D4×D61C2212yes—
21C22×C4×D61C2211yescharacteristic
22#14519804—28no—
23C2×#11758201C2212yescomplemented
24C2×D488C2212yescomplemented
25C2×#11758199C2212yescomplemented
26C2×#11758189C2212yescomplemented
27#14519762—21no—
28#14519753C2211yescharacteristic, complemented
29#14519752C2211yescharacteristic, complemented
30#14519751C2211yescharacteristic, complemented
31#14519747—21no—
32#14519739—21no—
33#14519737—21no—
34#14519735C2211yescharacteristic, complemented
35#14519699C2212yescomplemented
36#14519698C2212yescomplemented
37#14519697C2212yescomplemented
38C22⋊#92418C2211yescharacteristic, complemented
39#14519689C2212yescomplemented
40C22×D4×C61C2211yescharacteristic
41C2×SD16×C61C2212yescomplemented
42C22⋊Q8×C61C2211yescharacteristic, complemented
43#102×C61C2212yescomplemented
44C22⋊C8×C61C2211yescharacteristic, complemented
45C24×C61—21no—
46C23×D61—28no—
47C23×D61—21no—
48C23×D61—22no—
49C23×D61—22no—
50C23×D61—44no—
51C23×D61—44no—
52C23×D61D411yescharacteristic
53C2×Q8×C61C2311yescharacteristic, complemented
54C2×D4×C61—24no—
55C2×D4×C61—21no—
56C2×D4×C61C2312yes—
57C22×C4×C61C2311yescharacteristic
58C2×C22⋊D61—28no—
59C2×C22⋊D61—21no—
60C2×C22⋊D61—22no—
61C2×C22⋊D61—22no—
62C22×Dic61D411yescharacteristic
63#11758226—24no—
64D4×D61—28no—
65D4×D61—28no—
66D4×D61—24no—
67D4×D61—24no—
68D4×D61—24no—
69D4×D61D418yescomplemented
70C2×D244—21no—
71C2×D244—24no—
72C2×D244—21no—
73C2×D244—21no—
74C2×D244C2312yes—
75C2×D244C2311yescharacteristic, complemented
76C2×C4×D61—24no—
77C2×C4×D61—21no—
78C2×C4×D61D411yescharacteristic
79C2×C4×D61D411yescharacteristic
80C2×C4×D61C2311yescharacteristic
81C2×C4×D61C2311yescharacteristic
82SD16×C61—24no—
83C2×C8×C61C2312yescomplemented
84C4⋊C4×C61—21no—
85C4⋊C4×C61C2311yescharacteristic, complemented
86C22⋊C4×C61—21no—
87#11758201—24no—
88#11758199—24no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93C4⋊Dic61C2311yescharacteristic, complemented
94#11758196—21no—
95C4×Dic61—21no—
96C2×#92418C2312yescomplemented
97D488—24no—
98#11758189—24no—
99C23×C61—24no—
100C23×C61—22no—
101C23×C61—42no—
102C23×C61—42no—
103C23×C61C2×D411yescharacteristic
104C22×D61—22no—
105C22×D61—22no—
106C22×D61—22no—
107C22×D61—24no—
108C22×D61—28no—
109C22×D61—22no—
110C22×D61—28no—
111C22×D61—21no—
112C22×D61—432no—
113C22×D61—44no—
114C22×D61—44no—
115C22×D61—44no—
116C22×D61—42no—
117C22×D61—42no—
118C22×D61—44no—
119C22×D61C2×D411yescharacteristic
120C22×D61C2×D411yescharacteristic
121Q8×C61—22no—
122D4×C61—24no—
123D4×C61—22no—
124D4×C61C2×D414yes—
125C2×C4×C61—22no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2411yescharacteristic
130C22⋊D61—28no—
131C22⋊D61—28no—
132C22⋊D61—42no—
133C2×Dic61—22no—
134C2×Dic61—21no—
135C2×Dic61C2×D411yescharacteristic
136C2×Dic61C2×D411yescharacteristic
137D244—24no—
138D244—22no—
139D244—22no—
140D244—42no—
141D244—42no—
142D244C2×D414yes—
143C4×D61—22no—
144C4×D61—22no—
145C4×D61—22no—
146C4×D61—42no—
147C4×D61C2×D414yes—
148C8×C61—22no—
149#92418—22no—
150C22×C61—21no—
151C22×C61—21no—
152C22×C61—24no—
153C22×C61—48no—
154C22×C61—42no—
155C22×C61—42no—
156C22×C61AGL(1,ℤ/8)12yescomplemented
157C22×C61C22×D411yescharacteristic
158C2×D61—28no—
159C2×D61—21no—
160C2×D61—21no—
161C2×D61—21no—
162C2×D61—21no—
163C2×D61—24no—
164C2×D61—416no—
165C2×D61—416no—
166C2×D61—48no—
167C2×D61—42no—
168C2×D61—42no—
169C2×D61—41no—
170C2×D61—41no—
171C2×D61—41no—
172C2×D61#12012yes—
173C2×D61AGL(1,ℤ/8)12yescomplemented
174C4×C61—21no—
175C4×C61—41no—
176C4×C61—41no—
177C4×C61C22×D412yes—
178Dic61—21no—
179Dic61—41no—
180Dic61#12012yes—
181#3003—611nomaximal, Sylow
182C2×C61—22no—
183C2×C61—44no—
184C2×C61C2×#12011yescharacteristic
185C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
186C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
187D61—22no—
188D61—22no—
189D61—44no—
190D61—81no—
191C23×D4—611no—
192C2×AGL(1,ℤ/8)—612no—
193#525—611no—
194#450—612no—
195#450—611no—
196#450D6111yescharacteristic, complemented
197#447—611no—
198#447—612no—
199#447—611no—
200#418—612no—
201#407—611no—
202C61#300311yescharacteristic, complemented, Sylow
203C25—1221no—
204C2×#41—611no—
205C22×D4—612no—
206C22×D4—612no—
207C22×D4—611no—
208C22×D4—1221no—
209C22×D4—1221no—
210C22×D4—1221no—
211C22×D4—1228no—
212C22×D4C2×D6111yescharacteristic
213C23×C4—611no—
214AGL(1,ℤ/8)—1228no—
215C2×SD16—612no—
216C2×SD16C2×D6112yescomplemented
217C2×D8—612no—
218C2×D8—612no—
219C2×M16—612no—
220#123—1221no—
221C22⋊Q8—611no—
222C22⋊Q8C2×D6111yescharacteristic, complemented
223#121—611no—
224#121—611no—
225#120—1221no—
226C4×D4—1221no—
227C4×D4—1221no—
228#117—611no—
229#102—612no—
230#102—612no—
231#102—612no—
232#102C2×D6112yescomplemented
233C22⋊C8—611no—
234C22⋊C8—612no—
235C22⋊C8C2×D6111yescharacteristic, complemented
236C24—21no—
237C24—611no—
238C24—1222no—
239C24—1222no—
240C24—1228no—
241C24—1221no—
242C24—2444no—
243C24—2444no—
244#41—1224no—
245C2×Q8C22×D6111yescharacteristic, complemented
246C2×D4—24no—
247C2×D4—21no—
248C2×D4—618no—
249C2×D4—612no—
250C2×D4—611no—
251C2×D4—1224no—
252C2×D4—1221no—
253C2×D4—1221no—
254C2×D4—1224no—
255C2×D4—1222no—
256C2×D4—1222no—
257C2×D4—1224no—
258C2×D4—1228no—
259C2×D4—1228no—
260C2×D4—1228no—
261C2×D4—1224no—
262C2×D4—1221no—
263C2×D4—1221no—
264C2×D4C22×D6112yes—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—611no—
268C22×C4—611no—
269C22×C4—611no—
270C22×C4—1224no—
271C22×C4—1221no—
272C22×C4C22×D6111yescharacteristic
273SD16—24no—
274SD16—1224no—
275D8—1224no—
276D8—1224no—
277M16—1224no—
278C2×C8—612no—
279C2×C8C22×D6112yescomplemented
280C4⋊C4—21no—
281C4⋊C4—611no—
282C4⋊C4—1221no—
283C4⋊C4C22×D6111yescharacteristic, complemented
284C22⋊C4—21no—
285C22⋊C4—1221no—
286C22⋊C4—1221no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C42—1221no—
290C23—24no—
291C23—22no—
292C23—42no—
293C23—42no—
294C23—611no—
295C23—611no—
296C23—1222no—
297C23—1222no—
298C23—1228no—
299C23—1224no—
300C23—1228no—
301C23—1222no—
302C23—1222no—
303C23—1221no—
304C23—2442no—
305C23—2444no—
306C23—24432no—
307C23—2444no—
308C23—2444no—
309C23—2444no—
310C23—2442no—
311C23D4×D6111yescharacteristic
312Q8—22no—
313D4—24no—
314D4—22no—
315D4—614no—
316D4—1224no—
317D4—1228no—
318D4—1228no—
319D4—1222no—
320D4—1222no—
321D4—2442no—
322D4—2442no—
323D4—2442no—
324D4D4×D6114yes—
325C2×C4—22no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—611no—
329C2×C4—614no—
330C2×C4—611no—
331C2×C4—1222no—
332C2×C4—1222no—
333C2×C4—1222no—
334C2×C4—1222no—
335C2×C4—1221no—
336C2×C4—2442no—
337C2×C4D4×D6111yescharacteristic
338C2×C4C23×D6111yescharacteristic
339C8—22no—
340C8—1222no—
341C22—21no—
342C22—21no—
343C22—24no—
344C22—48no—
345C22—42no—
346C22—42no—
347C22—612no—
348C22—612no—
349C22—1228no—
350C22—1221no—
351C22—1221no—
352C22—1221no—
353C22—1221no—
354C22—1224no—
355C22—2448no—
356C22—24416no—
357C22—24416no—
358C22—2441no—
359C22—2441no—
360C22—2441no—
361C22—2442no—
362C22—2442no—
363C22#1451980412yescomplemented
364C22C2×D4×D6111yescharacteristic
365C4—21no—
366C4—41no—
367C4—41no—
368C4—612no—
369C4—1221no—
370C4—2441no—
371C4C2×D4×D6112yes—
372C2—22no—
373C2—44no—
374C2—1222no—
375C2—1222no—
376C2—4881no—
377C2—2444no—
378C2#120×D6111yescharacteristic
379C2AGL(1,ℤ/8)×D6111yescharacteristic
380C2C2×#1451980411yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#450C2
socleC22×C61C22×D4
hypercenter#450D61
hypocenterC61#3003
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C22×D4×D61C2semidirect
2. C2×#14519804C2semidirect
3. #16840275C2semidirect
4. #16839912C2semidirect
5. #16839911C2semidirect
6. #16839898C2semidirect
7. #16839897C2semidirect
8. #16839896C2semidirect
9. #16839765C2semidirect
10. #16839724C2semidirect
11. C61×#450C2semidirect
13. C2×#11758226C22semidirect
23. C2×#11758201C22semidirect
24. C2×D488C22semidirect
25. C2×#11758199C22semidirect
26. C2×#11758189C22semidirect
28. #14519753C22semidirect
29. #14519752C22semidirect
30. #14519751C22semidirect
34. #14519735C22semidirect
35. #14519699C22semidirect
36. #14519698C22semidirect
37. #14519697C22semidirect
38. C22⋊#92418C22semidirect
39. #14519689C22semidirect
41. C2×SD16×C61C22semidirect
42. C22⋊Q8×C61C22semidirect
43. #102×C61C22semidirect
44. C22⋊C8×C61C22semidirect
53. C2×Q8×C61C23semidirect
69. D4×D61D4semidirect
75. C2×D244C23semidirect
83. C2×C8×C61C23semidirect
85. C4⋊C4×C61C23semidirect
93. C4⋊Dic61C23semidirect
96. C2×#92418C23semidirect
156. C22×C61AGL(1,ℤ/8)semidirect
173. C2×D61AGL(1,ℤ/8)semidirect
196. #450D61semidirect
202. C61#3003semidirect
216. C2×SD16C2×D61semidirect
222. C22⋊Q8C2×D61semidirect
232. #102C2×D61semidirect
235. C22⋊C8C2×D61semidirect
245. C2×Q8C22×D61semidirect
279. C2×C8C22×D61semidirect
283. C4⋊C4C22×D61semidirect
363. C22#14519804semidirect