Finite Group Databasebeta

← #20247020

Subgroups — #20247020

Order 6016.

1348 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 1348 conjugacy classes of subgroups — too many to draw. Only its 181 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×D47C211yesmaximal, characteristic, complemented
2C2×#13094020C212yesmaximal, complemented
3C2×#13093997C211yesmaximal, characteristic, complemented
4C2×#13093994C212yesmaximal, complemented
5C2×#13093992C212yesmaximal, complemented
6#15689033C211yesmaximal, characteristic, complemented
7#15689032C211yesmaximal, characteristic, complemented
8#15689031C211yesmaximal, characteristic, complemented
9#15689023C212yesmaximal, complemented
10#15688970C211yesmaximal, characteristic, complemented
11C47×#392C211yesmaximal, characteristic, complemented
12C24×D47C2212yes—
13C22×D188C2211yescharacteristic
14C22×D188C2211yescharacteristic
15C22×D188C2212yescomplemented
16C22×C22⋊D47C2211yescharacteristic
17C22×C22⋊D47C2212yes—
18C22×C22⋊D47C2211yescharacteristic, complemented
19C22×C22⋊D47C2212yescomplemented
20C22×C22⋊D47C2212yescomplemented
21C2×D4×D47—28no—
22C2×D4×D47—24no—
23C22×C4×D47C2211yescharacteristic
24#13094020—28no—
25#13093997—24no—
26#13093994—28no—
27#13093992—28no—
28C2×Dic47⋊C4C2211yescharacteristic, complemented
29C2×C22⋊Dic47C2212yescomplemented
30C2×(C2×D47)⋊C4C2212yes—
31C2×(C2×D47)⋊C4C2212yescomplemented
32C2×(C2×D47)⋊C4C2212yescomplemented
33C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
34C2×C4×Dic47C2212yescomplemented
35C47⋊#95C2211yescharacteristic, complemented
36C22×D4×C47C2211yescharacteristic
37C22×D4×C47C2212yescomplemented
38C2×C22⋊C4×C47C2212yescomplemented
39C2×C22⋊C4×C47C2211yescharacteristic, complemented
40#95×C47C2211yescharacteristic, complemented
41C24×C47C2311yescharacteristic
42C24×C47C2312yes—
43C23×D47—24no—
44C23×D47—24no—
45C23×D47—24no—
46C23×D47—24no—
47C23×D47—24no—
48C23×D47—42no—
49C23×D47—42no—
50C23×D47C2311yescharacteristic
51C23×D47C2312yes—
52C23×D47C2311yescharacteristic
53C2×D4×C47—24no—
54C2×D4×C47—24no—
55C2×D4×C47—22no—
56C2×D4×C47—24no—
57C2×D4×C47—42no—
58C22×C4×C47C2311yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C22×C4×C47C2312yes—
61C2×C22⋊D47—24no—
62C2×C22⋊D47—24no—
63C2×C22⋊D47—22no—
64C2×C22⋊D47—24no—
65C2×C22⋊D47—24no—
66C2×C22⋊D47—24no—
67C2×C22⋊D47—22no—
68C2×C22⋊D47—24no—
69C2×C22⋊D47—24no—
70C2×C22⋊D47—24no—
71C2×C22⋊D47—42no—
72C2×C22⋊D47—42no—
73C2×C22⋊D47D418yescomplemented
74C22×Dic47C2311yescharacteristic
75C22×Dic47C2312yes—
76C22×Dic47C2311yescharacteristic
77D4×D47—232no—
78C2×D188—24no—
79C2×D188—22no—
80C2×D188—24no—
81C2×D188—22no—
82C2×D188—24no—
83C2×D188—24no—
84C2×D188—42no—
85C2×C4×D47—24no—
86C2×C4×D47D414yescomplemented
87C22⋊C4×C47—22no—
88C22⋊C4×C47—24no—
89C22⋊Dic47—24no—
90(C2×D47)⋊C4—22no—
91(C2×D47)⋊C4—24no—
92(C2×D47)⋊C4—24no—
93(C2×D47)⋊C4D418yescomplemented
94Dic47⋊C4—22no—
95C4×Dic47—24no—
96C23×C47—22no—
97C23×C47—22no—
98C23×C47—22no—
99C23×C47—22no—
100C23×C47—22no—
101C23×C47—22no—
102C23×C47—21no—
103C23×C47—22no—
104C23×C47—22no—
105C23×C47—21no—
106C23×C47—21no—
107C23×C47C2×D414yes—
108C23×C47C2411yescharacteristic
109C22×D47—22no—
110C22×D47—21no—
111C22×D47—21no—
112C22×D47—216no—
113C22×D47—22no—
114C22×D47—22no—
115C22×D47—22no—
116C22×D47—22no—
117C22×D47—22no—
118C22×D47—22no—
119C22×D47—21no—
120C22×D47—22no—
121C22×D47—22no—
122C22×D47—21no—
123C22×D47—21no—
124C22×D47—48no—
125C22×D47—48no—
126C22×D47—48no—
127C22×D47—48no—
128C22×D47—48no—
129C22×D47—48no—
130C22×D47C2×D414yes—
131C22×D47C2×D414yes—
132C22×D47C2×D412yes—
133D4×C47—28no—
134D4×C47—48no—
135C2×C4×C47—22no—
136C2×C4×C47—22no—
137C2×C4×C47—22no—
138C2×C4×C47—21no—
139C2×C4×C47—22no—
140C2×C4×C47C2×D412yes—
141C2×C4×C47C2×D414yescomplemented
142C22⋊D47—216no—
143C22⋊D47—48no—
144C22⋊D47—48no—
145C22⋊D47—44no—
146C22⋊D47—44no—
147C2×Dic47—22no—
148C2×Dic47—22no—
149C2×Dic47—21no—
150C2×Dic47—22no—
151C2×Dic47C2×D414yes—
152C2×Dic47C2×D412yes—
153C2×Dic47C2×D414yescomplemented
154D188—28no—
155D188—48no—
156D188—44no—
157C4×D47—28no—
158C22×C47—24no—
159C22×C47—24no—
160C22×C47—24no—
161C22×C47—42no—
162C22×C47—42no—
163C22×C47—42no—
164C22×C47—42no—
165C22×C47—41no—
166C22×C47—41no—
167C22×C47—41no—
168C22×C47—42no—
169C22×C47—42no—
170C22×C47C22×D411yescharacteristic
171C22×C47C22×D412yes—
172C22×C47C22×D412yes—
173C22×C47H(5,𝔽2)11yescharacteristic
174C22×C47H(5,𝔽2)11yescharacteristic
175C2×D47—22no—
176C2×D47—22no—
177C2×D47—24no—
178C2×D47—24no—
179C2×D47—24no—
180C2×D47—24no—
181C2×D47—24no—
182C2×D47—432no—
183C2×D47—42no—
184C2×D47—42no—
185C2×D47—42no—
186C2×D47—42no—
187C2×D47—41no—
188C2×D47—41no—
189C2×D47—41no—
190C2×D47—42no—
191C2×D47—42no—
192C2×D47#12714yescomplemented
193C4×C47—22no—
194C4×C47—24no—
195C4×C47—41no—
196Dic47—24no—
197Dic47—41no—
198Dic47#12014yescomplemented
199#2433—471nomaximal, Sylow
200C2×C47—44no—
201C2×C47—81no—
202C2×C47C2×#12011yescharacteristic
203C2×C47C2×#12711yescharacteristic
204C2×C47#53511yescharacteristic
205C2×C47D4212yes—
206C2×C47D4212yes—
207D47—24no—
208D47—44no—
209D47—81no—
210C23×D4—471no—
211C2×#127—472no—
212C2×#121—471no—
213C2×#120—472no—
214C2×#120—472no—
215#392—471no—
216#392—471no—
217#392—471no—
218#392D4711yescharacteristic, complemented
219#390—472no—
220C4×C22⋊C4—471no—
221C47#243311yescharacteristic, complemented, Sylow
222C25—472no—
223C22×D4—472no—
224C22×D4—471no—
225C22×D4—471no—
226C22×D4—472no—
227C22×D4—472no—
228C22×D4—471no—
229C22×D4—471no—
230C22×D4—472no—
231C22×D4—944no—
232C22×D4—948no—
233C22×D4C2×D4711yescharacteristic
234C22×D4C2×D4712yescomplemented
235C23×C4—471no—
236#127—948no—
237#121—944no—
238#120—948no—
239#120—948no—
240C2×C4⋊C4—471no—
241C2×C22⋊C4—472no—
242C2×C22⋊C4—472no—
243C2×C22⋊C4—472no—
244C2×C22⋊C4—472no—
245C2×C22⋊C4—471no—
246C2×C22⋊C4C2×D4712yescomplemented
247C2×C22⋊C4C2×D4711yescharacteristic, complemented
248C2×C42—472no—
249#95—471no—
250#95C2×D4711yescharacteristic, complemented
251C24—471no—
252C24—472no—
253C24—471no—
254C24—944no—
255C24—944no—
256C24—944no—
257C24—944no—
258C24—944no—
259C24—1882no—
260C24—1882no—
261C24C22×D4711yescharacteristic
262C24C22×D4712yes—
263C2×D4—24no—
264C2×D4—24no—
265C2×D4—22no—
266C2×D4—24no—
267C2×D4—42no—
268C2×D4—478no—
269C2×D4—944no—
270C2×D4—944no—
271C2×D4—942no—
272C2×D4—944no—
273C2×D4—944no—
274C2×D4—944no—
275C2×D4—944no—
276C2×D4—944no—
277C2×D4—942no—
278C2×D4—944no—
279C2×D4—9432no—
280C2×D4—944no—
281C2×D4—942no—
282C2×D4—944no—
283C2×D4—944no—
284C2×D4—942no—
285C2×D4—944no—
286C2×D4—1882no—
287C2×D4—1882no—
288C2×D4—1882no—
289C22×C4—471no—
290C22×C4—472no—
291C22×C4—474no—
292C22×C4—471no—
293C22×C4—944no—
294C22×C4C22×D4711yescharacteristic
295C22×C4C22×D4711yescharacteristic
296C22×C4C22×D4712yes—
297C4⋊C4—942no—
298C22⋊C4—22no—
299C22⋊C4—24no—
300C22⋊C4—478no—
301C22⋊C4—944no—
302C22⋊C4—944no—
303C22⋊C4—942no—
304C22⋊C4—944no—
305C42—944no—
306C23—22no—
307C23—22no—
308C23—22no—
309C23—22no—
310C23—22no—
311C23—22no—
312C23—21no—
313C23—22no—
314C23—22no—
315C23—21no—
316C23—21no—
317C23—474no—
318C23—472no—
319C23—474no—
320C23—9416no—
321C23—942no—
322C23—941no—
323C23—941no—
324C23—942no—
325C23—942no—
326C23—942no—
327C23—942no—
328C23—942no—
329C23—942no—
330C23—941no—
331C23—942no—
332C23—942no—
333C23—941no—
334C23—941no—
335C23—1888no—
336C23—1888no—
337C23—1888no—
338C23—1888no—
339C23—1888no—
340C23—1888no—
341C23D4×D4714yes—
342C23C23×D4711yescharacteristic
343D4—28no—
344D4—48no—
345D4—948no—
346D4—9416no—
347D4—1888no—
348D4—1884no—
349D4—1884no—
350D4—1888no—
351D4—1888no—
352D4—1884no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—21no—
358C2×C4—474no—
359C2×C4—472no—
360C2×C4—474no—
361C2×C4—948no—
362C2×C4—942no—
363C2×C4—942no—
364C2×C4—942no—
365C2×C4—941no—
366C2×C4D4×D4712yes—
367C2×C4D4×D4714yescomplemented
368C22—24no—
369C22—24no—
370C22—24no—
371C22—42no—
372C22—42no—
373C22—42no—
374C22—42no—
375C22—42no—
376C22—42no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—474no—
381C22—944no—
382C22—944no—
383C22—942no—
384C22—942no—
385C22—944no—
386C22—944no—
387C22—944no—
388C22—18832no—
389C22—1882no—
390C22—1882no—
391C22—1881no—
392C22—1881no—
393C22—1881no—
394C22—1882no—
395C22—1882no—
396C22—1882no—
397C22—1882no—
398C22C2×D4×D4712yes—
399C22C2×D4×D4712yes—
400C22C2×D4×D4711yescharacteristic
401C22#1309406911yescharacteristic
402C22#1309407011yescharacteristic
403C4—24no—
404C4—22no—
405C4—41no—
406C4—474no—
407C4—944no—
408C4—1881no—
409C2—44no—
410C2—81no—
411C2—944no—
412C2—3761no—
413C2—1884no—
414C2#120×D4711yescharacteristic
415C2#127×D4711yescharacteristic
416C2#1568968911yescharacteristic
417C2#1568975512yes—
418C2#1568975712yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#392C2
hypercenter#392D47
hypocenterC47#2433
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×D4×D47C2semidirect
2. C2×#13094020C2semidirect
3. C2×#13093997C2semidirect
4. C2×#13093994C2semidirect
5. C2×#13093992C2semidirect
6. #15689033C2semidirect
7. #15689032C2semidirect
8. #15689031C2semidirect
9. #15689023C2semidirect
10. #15688970C2semidirect
11. C47×#392C2semidirect
15. C22×D188C22semidirect
18. C22×C22⋊D47C22semidirect
19. C22×C22⋊D47C22semidirect
20. C22×C22⋊D47C22semidirect
28. C2×Dic47⋊C4C22semidirect
29. C2×C22⋊Dic47C22semidirect
31. C2×(C2×D47)⋊C4C22semidirect
32. C2×(C2×D47)⋊C4C22semidirect
33. C2×(C2×D47)⋊C4C22semidirect
34. C2×C4×Dic47C22semidirect
35. C47⋊#95C22semidirect
37. C22×D4×C47C22semidirect
38. C2×C22⋊C4×C47C22semidirect
39. C2×C22⋊C4×C47C22semidirect
40. #95×C47C22semidirect
73. C2×C22⋊D47D4semidirect
86. C2×C4×D47D4semidirect
93. (C2×D47)⋊C4D4semidirect
141. C2×C4×C47C2×D4semidirect
153. C2×Dic47C2×D4semidirect
192. C2×D47#127semidirect
198. Dic47#120semidirect
218. #392D47semidirect
221. C47#2433semidirect
234. C22×D4C2×D47semidirect
246. C2×C22⋊C4C2×D47semidirect
247. C2×C22⋊C4C2×D47semidirect
250. #95C2×D47semidirect
367. C2×C4D4×D47semidirect