Finite Group Databasebeta

← #20246739

Subgroups — #20246739

Order 6016.

1232 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 171 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×#13093997C212yesmaximal, complemented
3C2×#13093994C212yesmaximal, complemented
4C2×#13093986C211yesmaximal, characteristic, complemented
5#15689040C211yesmaximal, characteristic, complemented
6#15689033C211yesmaximal, characteristic, complemented
7#15689031C211yesmaximal, characteristic, complemented
8#15689023C212yesmaximal, complemented
9#15688982C211yesmaximal, characteristic, complemented
10#15688978C212yesmaximal, complemented
11C47×#394C211yesmaximal, characteristic, complemented
12C24×D47C2212yes—
13C22×D188C2211yescharacteristic
14C22×D188C2211yescharacteristic
15C22×D188C2212yescomplemented
16C22×C22⋊D47C2212yes—
17C22×C22⋊D47C2212yescomplemented
18C2×D4×D47—28no—
19C2×D4×D47—24no—
20C22×C4×D47C2211yescharacteristic
21C22×C4×D47C2211yescharacteristic, complemented
22#13093997—28no—
23#13093994—28no—
24#13093986—24no—
25C2×Dic47⋊C4C2212yescomplemented
26C2×C22⋊Dic47C2212yescomplemented
27C2×(C2×D47)⋊C4C2211yescharacteristic
28C2×(C2×D47)⋊C4C2212yes—
29C2×(C2×D47)⋊C4C2212yescomplemented
30C2×(C2×D47)⋊C4C2212yescomplemented
31C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
32C2×(C2×D47)⋊C4C2212yescomplemented
33C2×C4×Dic47C2211yescharacteristic, complemented
34C47⋊#95C2211yescharacteristic, complemented
35C22×D4×C47C2211yescharacteristic
36C2×C4⋊C4×C47C2211yescharacteristic, complemented
37C2×C22⋊C4×C47C2212yescomplemented
38C2×C22⋊C4×C47C2212yescomplemented
39#95×C47C2211yescharacteristic, complemented
40C24×C47C2312yes—
41C23×D47—24no—
42C23×D47—24no—
43C23×D47—24no—
44C23×D47—24no—
45C23×D47—24no—
46C23×D47—42no—
47C23×D47—42no—
48C23×D47C2312yes—
49C23×D47C2311yescharacteristic
50C23×D47C2311yescharacteristic
51C2×D4×C47—24no—
52C2×D4×C47—22no—
53C22×C4×C47C2311yescharacteristic
54C22×C4×C47C2312yes—
55C22×C4×C47C2311yescharacteristic
56C22×C4×C47C2311yescharacteristic
57C2×C22⋊D47—24no—
58C2×C22⋊D47—24no—
59C2×C22⋊D47—24no—
60C2×C22⋊D47—24no—
61C2×C22⋊D47—42no—
62C2×C22⋊D47D418yescomplemented
63C22×Dic47C2312yes—
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66D4×D47—232no—
67C2×D188—22no—
68C2×D188—24no—
69C2×D188—22no—
70C2×D188—22no—
71C2×D188—24no—
72C2×D188—24no—
73C2×D188—42no—
74C2×D188D414yescomplemented
75C2×C4×D47—24no—
76C2×C4×D47—22no—
77C2×C4×D47—24no—
78C2×C4×D47D414yescomplemented
79C4⋊C4×C47—22no—
80C22⋊C4×C47—24no—
81C22⋊C4×C47—24no—
82C22⋊Dic47—42no—
83(C2×D47)⋊C4—22no—
84(C2×D47)⋊C4—24no—
85(C2×D47)⋊C4—24no—
86(C2×D47)⋊C4—22no—
87(C2×D47)⋊C4—24no—
88(C2×D47)⋊C4—42no—
89Dic47⋊C4—24no—
90C4×Dic47—22no—
91C23×C47—22no—
92C23×C47—22no—
93C23×C47—22no—
94C23×C47—22no—
95C23×C47—22no—
96C23×C47—22no—
97C23×C47C2×D414yes—
98C23×C47C2411yescharacteristic
99C22×D47—22no—
100C22×D47—22no—
101C22×D47—216no—
102C22×D47—21no—
103C22×D47—22no—
104C22×D47—22no—
105C22×D47—22no—
106C22×D47—22no—
107C22×D47—21no—
108C22×D47—22no—
109C22×D47—22no—
110C22×D47—22no—
111C22×D47—22no—
112C22×D47—48no—
113C22×D47—48no—
114C22×D47—48no—
115C22×D47—48no—
116C22×D47—48no—
117C22×D47—48no—
118C22×D47C2×D414yes—
119C22×D47C2×D412yes—
120C22×D47C2×D412yes—
121C22×D47C2×D412yescomplemented
122C22×D47#4112yes—
123D4×C47—28no—
124C2×C4×C47—21no—
125C2×C4×C47—22no—
126C2×C4×C47—21no—
127C2×C4×C47—22no—
128C2×C4×C47—22no—
129C2×C4×C47—22no—
130C2×C4×C47—21no—
131C2×C4×C47—22no—
132C2×C4×C47C2×D412yes—
133C2×C4×C47C2×D412yescomplemented
134C22⋊D47—216no—
135C22⋊D47—48no—
136C2×Dic47—21no—
137C2×Dic47—22no—
138C2×Dic47—22no—
139C2×Dic47—22no—
140C2×Dic47—22no—
141C2×Dic47C2×D412yes—
142C2×Dic47C2×D414yes—
143D188—28no—
144D188—28no—
145D188—48no—
146C4×D47—28no—
147C4×D47—44no—
148C22×C47—24no—
149C22×C47—24no—
150C22×C47—24no—
151C22×C47—42no—
152C22×C47—42no—
153C22×C47—42no—
154C22×C47—42no—
155C22×C47C22×D411yescharacteristic
156C22×C47C22×D412yes—
157C22×C47C22×D411yescharacteristic
158C22×C47C2×#4111yescharacteristic
159C22×C47H(5,𝔽2)12yes—
160C2×D47—22no—
161C2×D47—22no—
162C2×D47—24no—
163C2×D47—24no—
164C2×D47—24no—
165C2×D47—22no—
166C2×D47—24no—
167C2×D47—24no—
168C2×D47—24no—
169C2×D47—432no—
170C2×D47—41no—
171C2×D47—42no—
172C2×D47—41no—
173C2×D47—42no—
174C2×D47—42no—
175C2×D47—42no—
176C2×D47—42no—
177C2×D47#12114yescomplemented
178C4×C47—22no—
179C4×C47—22no—
180C4×C47—41no—
181C4×C47—42no—
182Dic47—41no—
183Dic47—42no—
184Dic47#12014yescomplemented
185#2408—471nomaximal, Sylow
186C2×C47—44no—
187C2×C47C2×#12011yescharacteristic
188C2×C47C2×#12111yescharacteristic
189C2×C47#53511yescharacteristic
190C2×C47D4212yes—
191C2×C47#54612yes—
192D47—24no—
193D47—42no—
194D47—44no—
195C23×D4—471no—
196C2×#121—472no—
197C2×#120—472no—
198C2×C4×D4—471no—
199#394—471no—
200#394D4711yescharacteristic, complemented
201#392—471no—
202#392—471no—
203#390—472no—
204#380—471no—
205#379—472no—
206C47#240811yescharacteristic, complemented, Sylow
207C25—472no—
208C22×D4—472no—
209C22×D4—472no—
210C22×D4—471no—
211C22×D4—471no—
212C22×D4—472no—
213C22×D4—944no—
214C22×D4—948no—
215C22×D4C2×D4711yescharacteristic
216C23×C4—471no—
217C23×C4—471no—
218#121—948no—
219#120—948no—
220C4×D4—944no—
221C2×C4⋊C4—472no—
222C2×C4⋊C4C2×D4711yescharacteristic, complemented
223C2×C22⋊C4—471no—
224C2×C22⋊C4—471no—
225C2×C22⋊C4—472no—
226C2×C22⋊C4—472no—
227C2×C22⋊C4—472no—
228C2×C22⋊C4—472no—
229C2×C22⋊C4—472no—
230C2×C22⋊C4C2×D4712yescomplemented
231C2×C22⋊C4C2×D4712yescomplemented
232C2×C42—471no—
233#95—471no—
234#95C2×D4711yescharacteristic, complemented
235C24—471no—
236C24—472no—
237C24—471no—
238C24—944no—
239C24—944no—
240C24—944no—
241C24—944no—
242C24—944no—
243C24—1882no—
244C24—1882no—
245C24C22×D4712yes—
246C2×D4—24no—
247C2×D4—22no—
248C2×D4—478no—
249C2×D4—474no—
250C2×D4—942no—
251C2×D4—942no—
252C2×D4—944no—
253C2×D4—944no—
254C2×D4—944no—
255C2×D4—944no—
256C2×D4—944no—
257C2×D4—9432no—
258C2×D4—944no—
259C2×D4—944no—
260C2×D4—942no—
261C2×D4—1882no—
262C2×D4—1882no—
263C22×C4—471no—
264C22×C4—474no—
265C22×C4—472no—
266C22×C4—471no—
267C22×C4—944no—
268C22×C4—942no—
269C22×C4—944no—
270C22×C4C22×D4712yes—
271C22×C4C22×D4711yescharacteristic
272C22×C4C22×D4711yescharacteristic
273C22×C4C22×D4711yescharacteristic
274C4⋊C4—22no—
275C4⋊C4—944no—
276C22⋊C4—24no—
277C22⋊C4—24no—
278C22⋊C4—942no—
279C22⋊C4—944no—
280C22⋊C4—944no—
281C22⋊C4—942no—
282C22⋊C4—944no—
283C22⋊C4—1882no—
284C22⋊C4—1882no—
285C42—942no—
286C23—22no—
287C23—22no—
288C23—22no—
289C23—22no—
290C23—22no—
291C23—22no—
292C23—472no—
293C23—472no—
294C23—472no—
295C23—474no—
296C23—472no—
297C23—9416no—
298C23—942no—
299C23—942no—
300C23—941no—
301C23—942no—
302C23—942no—
303C23—942no—
304C23—942no—
305C23—941no—
306C23—942no—
307C23—942no—
308C23—942no—
309C23—942no—
310C23—1888no—
311C23—1888no—
312C23—1888no—
313C23—1888no—
314C23—1888no—
315C23—1888no—
316C23D4×D4714yes—
317C23C23×D4711yescharacteristic
318D4—28no—
319D4—948no—
320D4—948no—
321D4—9416no—
322D4—1888no—
323D4—1888no—
324C2×C4—21no—
325C2×C4—22no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—472no—
333C2×C4—474no—
334C2×C4—948no—
335C2×C4—941no—
336C2×C4—942no—
337C2×C4—942no—
338C2×C4—942no—
339C2×C4—942no—
340C2×C4—1884no—
341C2×C4D4×D4712yes—
342C2×C4D4×D4712yescomplemented
343C22—24no—
344C22—24no—
345C22—24no—
346C22—42no—
347C22—42no—
348C22—42no—
349C22—42no—
350C22—474no—
351C22—944no—
352C22—944no—
353C22—942no—
354C22—942no—
355C22—944no—
356C22—944no—
357C22—944no—
358C22—944no—
359C22—942no—
360C22—18832no—
361C22—1882no—
362C22—1882no—
363C22—1882no—
364C22—1881no—
365C22—1882no—
366C22—1882no—
367C22—1881no—
368C22C2×D4×D4711yescharacteristic
369C22C2×D4×D4712yes—
370C22C2×D4×D4711yescharacteristic
371C22#41×D4711yescharacteristic
372C22#1309407012yes—
373C4—22no—
374C4—22no—
375C4—42no—
376C4—41no—
377C4—474no—
378C4—1882no—
379C4—1881no—
380C2—44no—
381C2—944no—
382C2—1884no—
383C2—1882no—
384C2#120×D4711yescharacteristic
385C2#121×D4711yescharacteristic
386C2#1568969111yescharacteristic
387C2#1568975712yes—
388C2#1568976512yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#394C2
hypercenter#394D47
hypocenterC47#2408
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C22×D4×D47C2semidirect
2. C2×#13093997C2semidirect
3. C2×#13093994C2semidirect
4. C2×#13093986C2semidirect
5. #15689040C2semidirect
6. #15689033C2semidirect
7. #15689031C2semidirect
8. #15689023C2semidirect
9. #15688982C2semidirect
10. #15688978C2semidirect
11. C47×#394C2semidirect
15. C22×D188C22semidirect
17. C22×C22⋊D47C22semidirect
21. C22×C4×D47C22semidirect
25. C2×Dic47⋊C4C22semidirect
26. C2×C22⋊Dic47C22semidirect
29. C2×(C2×D47)⋊C4C22semidirect
30. C2×(C2×D47)⋊C4C22semidirect
31. C2×(C2×D47)⋊C4C22semidirect
32. C2×(C2×D47)⋊C4C22semidirect
33. C2×C4×Dic47C22semidirect
34. C47⋊#95C22semidirect
36. C2×C4⋊C4×C47C22semidirect
37. C2×C22⋊C4×C47C22semidirect
38. C2×C22⋊C4×C47C22semidirect
39. #95×C47C22semidirect
62. C2×C22⋊D47D4semidirect
74. C2×D188D4semidirect
78. C2×C4×D47D4semidirect
121. C22×D47C2×D4semidirect
133. C2×C4×C47C2×D4semidirect
177. C2×D47#121semidirect
184. Dic47#120semidirect
200. #394D47semidirect
206. C47#2408semidirect
222. C2×C4⋊C4C2×D47semidirect
230. C2×C22⋊C4C2×D47semidirect
231. C2×C22⋊C4C2×D47semidirect
234. #95C2×D47semidirect
342. C2×C4D4×D47semidirect