Finite Group Databasebeta

← #21455066

Subgroups — #21455066

Order 7808.

806 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 806 conjugacy classes of subgroups — too many to draw. Only its 141 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×#11758224C211yesmaximal, characteristic, complemented
2C2×#14519801C212yesmaximal, complemented
3#121×D61C211yesmaximal, characteristic, complemented
4#16839908C212yesmaximal, complemented
5#16839904C212yesmaximal, complemented
6#16839903C211yesmaximal, characteristic, complemented
7#16839900C211yesmaximal, characteristic, complemented
8#16839896C211yesmaximal, characteristic, complemented
9#16839760C212yesmaximal, complemented
10#16839724C211yesmaximal, characteristic, complemented
11C61×#447C211yesmaximal, characteristic, complemented
12C2×#11758224—28no—
13C2×#11758224—21no—
14C2×#11758224—21no—
15C2×#11758224C2212yes—
16C2×#11758224C2212yescomplemented
17C22×Dic122C2211yescharacteristic, complemented
18C22×C22⋊D61—21no—
19C2×D4×D61—21no—
20C2×D4×D61C2211yescharacteristic, complemented
21C23×Dic61—21no—
22C22×C4×D61C2211yescharacteristic
23#14519801—28no—
24C2×#11758190C2212yescomplemented
25C2×#11758200C2212yescomplemented
26C2×#11758199C2212yescomplemented
27C2×#11758189C2212yescomplemented
28#14519752C2211yescharacteristic, complemented
29#14519751C2211yescharacteristic
30#14519750—21no—
31#14519749—21no—
32#14519748C2211yescharacteristic, complemented
33C4⋊C4×D61C2211yescharacteristic, complemented
34C22⋊C4×D61—21no—
35#14519702C2212yescomplemented
36#14519700C2212yescomplemented
37#14519698C2212yescomplemented
38C22⋊#92418C2211yescharacteristic, complemented
39#14519689C2212yescomplemented
40C22×D4×C61C2211yescharacteristic, complemented
41C2×D8×C61C2212yescomplemented
42#121×C61C2211yescharacteristic
43#102×C61C2212yescomplemented
44C22⋊C8×C61C2211yescharacteristic, complemented
45C24×C61—21no—
46C23×D61—21no—
47C23×D61D411yescharacteristic
48C2×D4×C61—24no—
49C2×D4×C61—21no—
50C2×D4×C61—21no—
51C2×D4×C61C2311yescharacteristic
52C2×D4×C61C2312yes—
53C22×C4×C61C2311yescharacteristic
54C2×C22⋊D61—28no—
55C2×C22⋊D61—22no—
56C2×C22⋊D61—22no—
57C2×C22⋊D61—21no—
58C2×C22⋊D61—21no—
59C2×C22⋊D61—21no—
60C22×Dic61—28no—
61C22×Dic61—21no—
62C22×Dic61—22no—
63C22×Dic61—22no—
64C22×Dic61D411yescharacteristic
65#11758224—28no—
66#11758224—28no—
67#11758224—24no—
68#11758224—24no—
69#11758224—24no—
70#11758224D418yescomplemented
71D4×D61—24no—
72D4×D61—44no—
73C2×D244—21no—
74C2×D244C2311yescharacteristic
75C2×C4×D61—24no—
76C2×C4×D61—21no—
77C2×C4×D61D411yescharacteristic
78C2×C4×D61D411yescharacteristic
79C2×C4×D61C2311yescharacteristic
80C2×C4×D61C2311yescharacteristic
81C2×Dic122—21no—
82C2×Dic122—24no—
83C2×Dic122C2312yes—
84D8×C61—24no—
85C2×C8×C61C2312yes—
86C4⋊C4×C61C2311yescharacteristic
87C22⋊C4×C61—21no—
88C22⋊Dic61—21no—
89#11758200—24no—
90#11758199—24no—
91#11758198—21no—
92#11758198—21no—
93C4⋊Dic61C2311yescharacteristic
94#11758196—21no—
95C2×#92418C2312yes—
96#11758190—24no—
97#11758189—24no—
98C23×C61—24no—
99C23×C61—22no—
100C23×C61—21no—
101C23×C61—42no—
102C23×C61—42no—
103C23×C61C2×D411yescharacteristic
104C22×D61—22no—
105C22×D61—22no—
106C22×D61—21no—
107C22×D61—41no—
108C22×D61—42no—
109C22×D61—42no—
110C22×D61—42no—
111C22×D61C2×D411yescharacteristic
112C22×D61C2×D411yescharacteristic
113D4×C61—24no—
114D4×C61—22no—
115D4×C61—22no—
116D4×C61—42no—
117D4×C61C2×D414yescomplemented
118C2×C4×C61—22no—
119C2×C4×C61—21no—
120C2×C4×C61C2×D411yescharacteristic
121C2×C4×C61C2411yescharacteristic
122C22⋊D61—28no—
123C22⋊D61—28no—
124C22⋊D61—42no—
125C22⋊D61—42no—
126C22⋊D61—42no—
127C2×Dic61—24no—
128C2×Dic61—28no—
129C2×Dic61—22no—
130C2×Dic61—22no—
131C2×Dic61—28no—
132C2×Dic61—21no—
133C2×Dic61C2×D411yescharacteristic
134C2×Dic61C2×D411yescharacteristic
135D244—22no—
136D244—42no—
137C4×D61—22no—
138C4×D61—22no—
139C4×D61—22no—
140C4×D61—42no—
141C4×D61C2×D414yes—
142Dic122—24no—
143Dic122—22no—
144Dic122C2×D414yescomplemented
145C8×C61—22no—
146#92418—22no—
147C22×C61—21no—
148C22×C61—21no—
149C22×C61—24no—
150C22×C61—48no—
151C22×C61—42no—
152C22×C61—42no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61AGL(1,ℤ/8)12yescomplemented
157C22×C61C22×D411yescharacteristic
158C2×D61—21no—
159C2×D61—21no—
160C2×D61—21no—
161C2×D61—21no—
162C2×D61—21no—
163C2×D61—44no—
164C2×D61—41no—
165C2×D61—41no—
166C2×D61—41no—
167C2×D61—84no—
168C2×D61#12012yes—
169C4×C61—21no—
170C4×C61—41no—
171C4×C61C22×D412yes—
172Dic61—24no—
173Dic61—21no—
174Dic61—41no—
175Dic61#12012yes—
176#3006—611nomaximal, Sylow
177C2×C61—22no—
178C2×C61—44no—
179C2×C61—81no—
180C2×C61C2×#12011yescharacteristic
181C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
182C2×C61#57511yescharacteristic
183D61—22no—
184D61—41no—
185D61—81no—
186C22×#41—611no—
187C2×AGL(1,ℤ/8)—612no—
188C2×#121—611no—
189#449—612no—
190#449—612no—
191#448—611no—
192#448—611no—
193#447—611no—
194#447D6111yescharacteristic, complemented
195#417—612no—
196#407—611no—
197C61#300611yescharacteristic, complemented, Sylow
198C2×#41—612no—
199C2×#41—612no—
200C2×#41—1221no—
201C2×#41—1221no—
202C2×#41—1228no—
203C22×Q8—611no—
204C22×D4—611no—
205C22×D4—1221no—
206C22×D4—1221no—
207C22×D4C2×D6111yescharacteristic, complemented
208C23×C4—611no—
209C23×C4—1221no—
210AGL(1,ℤ/8)—1228no—
211C2×SD16—612no—
212C2×SD16—612no—
213C2×D8—612no—
214C2×D8C2×D6112yescomplemented
215C2×M16—612no—
216#121—611no—
217#121—611no—
218#121—611no—
219#121—1221no—
220#121—1221no—
221#121C2×D6111yescharacteristic
222C2×C4⋊C4—611no—
223C2×C22⋊C4—1221no—
224#103—612no—
225#103—612no—
226#102—612no—
227#102C2×D6112yescomplemented
228C22⋊C8—611no—
229C22⋊C8—612no—
230C22⋊C8C2×D6111yescharacteristic, complemented
231C24—21no—
232C24—611no—
233C24—1221no—
234#41—618no—
235#41—1224no—
236#41—1224no—
237#41—1228no—
238#41—1228no—
239#41—1224no—
240C2×Q8—612no—
241C2×Q8—1224no—
242C2×Q8—1221no—
243C2×D4—24no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—611no—
247C2×D4—1221no—
248C2×D4—1224no—
249C2×D4—1221no—
250C2×D4—1222no—
251C2×D4—1222no—
252C2×D4—1228no—
253C2×D4—1221no—
254C2×D4—1221no—
255C2×D4—2444no—
256C2×D4C22×D6111yescharacteristic
257C2×D4C22×D6112yes—
258C22×C4—611no—
259C22×C4—611no—
260C22×C4—611no—
261C22×C4—611no—
262C22×C4—611no—
263C22×C4—1224no—
264C22×C4—1221no—
265C22×C4—1222no—
266C22×C4—1222no—
267C22×C4—1228no—
268C22×C4—1221no—
269C22×C4C22×D6111yescharacteristic
270SD16—1224no—
271SD16—1224no—
272D8—24no—
273D8—1224no—
274M16—1224no—
275C2×C8—612no—
276C2×C8C22×D6112yes—
277C4⋊C4—611no—
278C4⋊C4—1221no—
279C4⋊C4C22×D6111yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C23—24no—
285C23—22no—
286C23—21no—
287C23—42no—
288C23—42no—
289C23—611no—
290C23—611no—
291C23—1222no—
292C23—1222no—
293C23—1221no—
294C23—2441no—
295C23—2442no—
296C23—2442no—
297C23—2442no—
298C23D4×D6111yescharacteristic
299Q8—614no—
300Q8—1224no—
301Q8—1222no—
302D4—24no—
303D4—22no—
304D4—22no—
305D4—42no—
306D4—1228no—
307D4—1228no—
308D4—1222no—
309D4—2442no—
310D4—2442no—
311D4—2442no—
312D4—2442no—
313D4D4×D6114yescomplemented
314C2×C4—22no—
315C2×C4—21no—
316C2×C4—611no—
317C2×C4—614no—
318C2×C4—611no—
319C2×C4—1222no—
320C2×C4—1222no—
321C2×C4—1222no—
322C2×C4—1228no—
323C2×C4—1224no—
324C2×C4—1228no—
325C2×C4—1222no—
326C2×C4—1222no—
327C2×C4—1221no—
328C2×C4—2442no—
329C2×C4D4×D6111yescharacteristic
330C2×C4C23×D6111yescharacteristic
331C8—22no—
332C8—1222no—
333C22—21no—
334C22—21no—
335C22—24no—
336C22—48no—
337C22—42no—
338C22—42no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—612no—
343C22—1221no—
344C22—1221no—
345C22—1221no—
346C22—1221no—
347C22—1221no—
348C22—4884no—
349C22—2444no—
350C22—2441no—
351C22—2441no—
352C22—2441no—
353C22#1451980112yescomplemented
354C22C2×D4×D6111yescharacteristic
355C4—21no—
356C4—41no—
357C4—612no—
358C4—1221no—
359C4—1224no—
360C4—2441no—
361C4C2×D4×D6112yes—
362C2—22no—
363C2—44no—
364C2—81no—
365C2—1222no—
366C2—4881no—
367C2—2441no—
368C2#120×D6111yescharacteristic
369C2C2×#1451980111yescharacteristic
370C2#1684055811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#447C2
socleC22×C61C22×D4
hypercenter#447D61
hypocenterC61#3006
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C22×#11758224C2semidirect
2. C2×#14519801C2semidirect
3. #121×D61C2semidirect
4. #16839908C2semidirect
5. #16839904C2semidirect
6. #16839903C2semidirect
7. #16839900C2semidirect
8. #16839896C2semidirect
9. #16839760C2semidirect
10. #16839724C2semidirect
11. C61×#447C2semidirect
16. C2×#11758224C22semidirect
17. C22×Dic122C22semidirect
20. C2×D4×D61C22semidirect
24. C2×#11758190C22semidirect
25. C2×#11758200C22semidirect
26. C2×#11758199C22semidirect
27. C2×#11758189C22semidirect
28. #14519752C22semidirect
32. #14519748C22semidirect
33. C4⋊C4×D61C22semidirect
35. #14519702C22semidirect
36. #14519700C22semidirect
37. #14519698C22semidirect
38. C22⋊#92418C22semidirect
39. #14519689C22semidirect
40. C22×D4×C61C22semidirect
41. C2×D8×C61C22semidirect
43. #102×C61C22semidirect
44. C22⋊C8×C61C22semidirect
70. #11758224D4semidirect
117. D4×C61C2×D4semidirect
144. Dic122C2×D4semidirect
156. C22×C61AGL(1,ℤ/8)semidirect
194. #447D61semidirect
197. C61#3006semidirect
207. C22×D4C2×D61semidirect
214. C2×D8C2×D61semidirect
227. #102C2×D61semidirect
230. C22⋊C8C2×D61semidirect
313. D4D4×D61semidirect
353. C22#14519801semidirect