Finite Group Databasebeta

← #20252764

Subgroups — #20252764

Order 6016.

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#15689959C211yesmaximal, characteristic
2C2×#13094055C211yesmaximal, characteristic, complemented
3#15689697C211yesmaximal, characteristic, complemented
4#15689304C214yesmaximal, complemented
5#15689299C214yesmaximal, complemented
6#15689140C211yesmaximal, characteristic, complemented
7#15689139C211yesmaximal, characteristic, complemented
8#15689105C211yesmaximal, characteristic, complemented
9C2×#137×C47C211yesmaximal, characteristic, complemented
10#13094072—21no—
11#13094071—21no—
12#13094071C2212yes—
13#13094070—21no—
14#13094070C2212yes—
15#13094069—21no—
16#13094069—22no—
17C2×#10625350—22no—
18C2×#10625350C2211yescharacteristic
19C2×#10625350C2211yescharacteristic
20#41×D47—22no—
21#41×D47—22no—
22#13094055—22no—
23#13094055C2214yescomplemented
24C2×#10625337—21no—
25C2×#10625336—21no—
26C2×#10625329C2211yescharacteristic, complemented
27#13094022C2212yescomplemented
28#13094013C2212yescomplemented
29#13094007—22no—
30#13094000—22no—
31#13093983C2211yescharacteristic, complemented
32#13093951C2214yescomplemented
33#13093950C2214yescomplemented
34#13093942C2212yescomplemented
35#13093940C2212yescomplemented
36C2×#41×C47C2211yescharacteristic
37C22×Q8×C47C2211yescharacteristic, complemented
38#137×C47—22no—
39#137×C47C2214yescomplemented
40C2×Q16×C47—21no—
41C2×SD16×C47—21no—
42C2×M16×C47C2211yescharacteristic, complemented
43#41×C47—21no—
44#41×C47—21no—
45#41×C47D412yes—
46#41×C47C2312yes—
47C2×Q8×C47—21no—
48C2×Q8×C47—21no—
49C2×Q8×C47—21no—
50C2×Q8×C47—21no—
51C2×Q8×C47—21no—
52C2×Q8×C47D411yescharacteristic
53C2×Q8×C47C2312yes—
54C2×D4×C47—21no—
55C2×D4×C47D411yescharacteristic
56C22×C4×C47—21no—
57C22×C4×C47—21no—
58C22×C4×C47C2311yescharacteristic
59C2×C22⋊D47—24no—
60C2×C22⋊D47—21no—
61C2×C22⋊D47D412yes—
62#10625354—22no—
63#10625354—22no—
64Q8×D47—22no—
65Q8×D47—22no—
66#10625352—24no—
67#10625352—22no—
68#10625352—22no—
69#10625352—24no—
70D4×D47—24no—
71D4×D47—22no—
72D4×D47—24no—
73D4×D47—22no—
74#10625350—24no—
75#10625350—24no—
76#10625350—21no—
77#10625350—21no—
78#10625350—21no—
79#10625350—21no—
80#10625350—21no—
81#10625350—21no—
82#10625350—22no—
83#10625350—22no—
84#10625350D412yes—
85#10625350C2312yes—
86C2×D188—22no—
87C2×D188D411yescharacteristic
88C2×D188C2311yescharacteristic
89C2×C4×D47—24no—
90C2×C4×D47—21no—
91C2×C4×D47D412yes—
92C2×Dic94—22no—
93C2×Dic94D411yescharacteristic
94C2×Dic94C2311yescharacteristic
95Q16×C47—24no—
96SD16×C47—24no—
97M16×C47—21no—
98M16×C47C2312yes—
99C2×C8×C47—21no—
100C22⋊Dic47—21no—
101#10625337—24no—
102#10625336—24no—
103(C2×D47)⋊C4—24no—
104C4⋊Dic47—21no—
105Dic47⋊C4—24no—
106C4×Dic47C2312yes—
107#10625329—21no—
108#10625329C2312yes—
109C2×C47⋊C8—21no—
110C23×C47—21no—
111C23×C47C2×D411yescharacteristic
112C22×D47—24no—
113C22×D47—21no—
114C22×D47C2×D412yes—
115Q8×C47—21no—
116Q8×C47—22no—
117Q8×C47—22no—
118Q8×C47—41no—
119Q8×C47—41no—
120Q8×C47C2×D412yes—
121D4×C47—22no—
122D4×C47—22no—
123D4×C47—21no—
124D4×C47C2×D412yes—
125C2×C4×C47—21no—
126C2×C4×C47—22no—
127C2×C4×C47—22no—
128C2×C4×C47—22no—
129C2×C4×C47—41no—
130C2×C4×C47—41no—
131C2×C4×C47C2×D411yescharacteristic
132C2×C4×C47C2×D411yescharacteristic
133C2×C4×C47C2×D411yescharacteristic
134C2×C4×C47C2×D411yescharacteristic
135C2×C4×C47C2×D411yescharacteristic
136C2×C4×C47C2411yescharacteristic
137C22⋊D47—24no—
138C22⋊D47—24no—
139C22⋊D47—22no—
140C22⋊D47—22no—
141C22⋊D47—22no—
142C22⋊D47—22no—
143C2×Dic47—24no—
144C2×Dic47—21no—
145C2×Dic47—22no—
146C2×Dic47C2×D412yes—
147D188—24no—
148D188—21no—
149D188—21no—
150D188—21no—
151D188C2×D412yes—
152C4×D47—24no—
153C4×D47—24no—
154C4×D47—22no—
155C4×D47—22no—
156C4×D47—22no—
157C4×D47—22no—
158Dic94—24no—
159Dic94—21no—
160Dic94—21no—
161Dic94—21no—
162Dic94C2×D412yes—
163C8×C47—22no—
164C47⋊C8—22no—
165C22×C47—22no—
166C22×C47—41no—
167C22×C47—81no—
168C22×C47#12011yescharacteristic
169C22×C47#12011yescharacteristic
170C22×C47C22×D411yescharacteristic
171C2×D47—22no—
172C2×D47—22no—
173C2×D47—42no—
174C2×D47—81no—
175C2×D47—84no—
176C4×C47—22no—
177C4×C47—42no—
178C4×C47#12011yescharacteristic
179C4×C47#12011yescharacteristic
180C4×C47C22×D411yescharacteristic
181C4×C47C22×D411yescharacteristic
182Dic47—22no—
183Dic47—22no—
184Dic47—42no—
185#3022—471nomaximal, Sylow
186C2×C47—21no—
187C2×C47—21no—
188C2×C47—21no—
189C2×C47—42no—
190C2×C47C2×#12011yescharacteristic
191D47—42no—
192D47—42no—
193#585—471no—
194C2×#137—471no—
195C2×#137D4711yescharacteristic, complemented
196#536—471no—
197#456—474no—
198#455—474no—
199#421—471no—
200#421—471no—
201#413—471no—
202C47#302211yescharacteristic, complemented, Sylow
2032−1+4—472no—
2042−1+4—941no—
2052−1+4—941no—
206H(5,𝔽2)—472no—
207H(5,𝔽2)—942no—
208H(5,𝔽2)—941no—
209H(5,𝔽2)—941no—
210C2×#41—471no—
211C2×#41—471no—
212C2×#41—942no—
213C2×#41—942no—
214C2×#41—942no—
215C2×#41C2×D4711yescharacteristic
216C22×Q8C2×D4711yescharacteristic, complemented
217#137—22no—
218#137—474no—
219#137—942no—
220#137C2×D4714yescomplemented
221C2×Q16—21no—
222C2×Q16—941no—
223C2×SD16—21no—
224C2×SD16—941no—
225C2×M16—471no—
226C2×M16C2×D4711yescharacteristic, complemented
227C4⋊Q8—472no—
228#124—472no—
229#123—942no—
230C22⋊Q8—942no—
231#117—471no—
232#104—474no—
233#104—474no—
234#101—472no—
235#100—472no—
236#41—21no—
237#41—21no—
238#41—472no—
239#41—472no—
240#41—942no—
241#41—942no—
242#41—944no—
243#41—944no—
244#41—944no—
245#41—944no—
246#41—942no—
247#41—942no—
248#41—942no—
249#41—942no—
250#41—941no—
251#41—941no—
252#41—941no—
253#41—941no—
254#41—941no—
255#41—941no—
256#41C22⋊D4712yes—
257#41C22×D4712yes—
258C2×Q8—21no—
259C2×Q8—21no—
260C2×Q8—21no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—471no—
264C2×Q8—471no—
265C2×Q8—942no—
266C2×Q8—942no—
267C2×Q8—942no—
268C2×Q8C22⋊D4711yescharacteristic
269C2×Q8C22×D4712yes—
270C2×D4—21no—
271C2×D4—472no—
272C2×D4—471no—
273C2×D4—471no—
274C2×D4—942no—
275C2×D4—944no—
276C2×D4—944no—
277C2×D4—942no—
278C2×D4—944no—
279C2×D4—941no—
280C2×D4—942no—
281C2×D4C22⋊D4711yescharacteristic
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—472no—
285C22×C4—944no—
286C22×C4—941no—
287C22×C4C22×D4711yescharacteristic
288Q16—24no—
289Q16—944no—
290SD16—24no—
291SD16—944no—
292M16—21no—
293M16—472no—
294M16—941no—
295M16C22×D4712yes—
296C2×C8—21no—
297C2×C8—941no—
298C4⋊C4—944no—
299C4⋊C4—941no—
300C22⋊C4—944no—
301C22⋊C4—941no—
302C42—472no—
303C23—21no—
304C23—472no—
305C23—944no—
306C23—941no—
307C23D4×D4711yescharacteristic
308Q8—21no—
309Q8—22no—
310Q8—22no—
311Q8—41no—
312Q8—41no—
313Q8—472no—
314Q8—944no—
315Q8—941no—
316Q8—941no—
317Q8—941no—
318Q8C2×C22⋊D4712yes—
319D4—22no—
320D4—22no—
321D4—21no—
322D4—472no—
323D4—944no—
324D4—944no—
325D4—944no—
326D4—942no—
327D4—942no—
328D4—942no—
329D4—942no—
330D4—941no—
331D4—941no—
332D4—941no—
333D4C2×C22⋊D4712yes—
334C2×C4—21no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—472no—
341C2×C4—944no—
342C2×C4—944no—
343C2×C4—944no—
344C2×C4—941no—
345C2×C4—942no—
346C2×C4—942no—
347C2×C4—942no—
348C2×C4—942no—
349C2×C4—942no—
350C2×C4D4×D4711yescharacteristic
351C2×C4D4×D4711yescharacteristic
352C2×C4D4×D4711yescharacteristic
353C2×C4C2×C22⋊D4711yescharacteristic
354C2×C4C2×C22⋊D4711yescharacteristic
355C2×C4C23×D4711yescharacteristic
356C8—22no—
357C8—942no—
358C22—22no—
359C22—41no—
360C22—81no—
361C22—942no—
362C22—942no—
363C22—3761no—
364C22—3764no—
365C22—1882no—
366C22#1309399211yescharacteristic
367C22#1309399211yescharacteristic
368C22C2×D4×D4711yescharacteristic
369C4—22no—
370C4—42no—
371C4—942no—
372C4—942no—
373C4—1882no—
374C4#1309399211yescharacteristic
375C4#1309399211yescharacteristic
376C4C2×D4×D4711yescharacteristic
377C4C22×C22⋊D4711yescharacteristic
378C2—21no—
379C2—21no—
380C2—21no—
381C2—42no—
382C2—1882no—
383C2—1882no—
384C2C2×#1309399211yescharacteristic
subgroupG/H
centerC2C2×#13093992
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#137×C47C2
socleC2×C47C2×#120
hypercenterC2×#137D47
hypocenterC47#3022
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
2. C2×#13094055C2semidirect
3. #15689697C2semidirect
4. #15689304C2semidirect
5. #15689299C2semidirect
6. #15689140C2semidirect
7. #15689139C2semidirect
8. #15689105C2semidirect
9. C2×#137×C47C2semidirect
23. #13094055C22semidirect
26. C2×#10625329C22semidirect
27. #13094022C22semidirect
28. #13094013C22semidirect
31. #13093983C22semidirect
32. #13093951C22semidirect
33. #13093950C22semidirect
34. #13093942C22semidirect
35. #13093940C22semidirect
37. C22×Q8×C47C22semidirect
39. #137×C47C22semidirect
42. C2×M16×C47C22semidirect
195. C2×#137D47semidirect
202. C47#3022semidirect
216. C22×Q8C2×D47semidirect
220. #137C2×D47semidirect
226. C2×M16C2×D47semidirect