Finite Group Databasebeta

← #20249605

Subgroups — #20249605

Order 6016.

932 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 932 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C2×#13094020C211yesmaximal, characteristic, complemented
2C2×#13093996C212yesmaximal, complemented
3C2×#13093993C212yesmaximal, complemented
4#15689038C212yesmaximal, complemented
5#15689032C212yesmaximal, complemented
6#15689031C212yesmaximal, complemented
7#15689011C212yesmaximal, complemented
8#15689003C211yesmaximal, characteristic, complemented
9C2×#120×C47C211yesmaximal, characteristic, complemented
10C22×D188C2211yescharacteristic, complemented
11C22×C22⋊D47C2212yes—
12C22×C22⋊D47C2212yes—
13C22×C22⋊D47C2212yes—
14C22×C22⋊D47C2212yescomplemented
15C23×Dic47C2211yescharacteristic, complemented
16#13094020—24no—
17#13093996—28no—
18#13093993—28no—
19C2×Dic47⋊C4C2212yescomplemented
20C2×C22⋊Dic47C2212yes—
21C2×C22⋊Dic47C2212yes—
22C2×C22⋊Dic47C2212yes—
23C2×C22⋊Dic47C2211yescharacteristic, complemented
24C2×(C2×D47)⋊C4C2212yescomplemented
25C2×(C2×D47)⋊C4C2212yescomplemented
26C2×C4×Dic47C2211yescharacteristic, complemented
27C47⋊#95C2212yescomplemented
28C47⋊#95C2212yescomplemented
29C25×C47C2211yescharacteristic
30C22×D4×C47C2212yes—
31C22×D4×C47C2211yescharacteristic
32#120×C47—24no—
33C2×C22⋊C4×C47C2212yes—
34C2×C22⋊C4×C47C2211yescharacteristic
35C24×C47—22no—
36C24×C47—24no—
37C24×C47—42no—
38C24×C47—41no—
39C24×C47—41no—
40C24×C47C2311yescharacteristic
41C24×C47C2312yes—
42C24×C47C2311yescharacteristic
43C23×D47C2312yes—
44C2×D4×C47—24no—
45C2×D4×C47—24no—
46C2×D4×C47—41no—
47C2×D4×C47—41no—
48C2×D4×C47—42no—
49C2×D4×C47D414yescomplemented
50C22×C4×C47C2312yes—
51C22×C4×C47C2311yescharacteristic
52C2×C22⋊D47—24no—
53C2×C22⋊D47—24no—
54C2×C22⋊D47—24no—
55C2×C22⋊D47—24no—
56C2×C22⋊D47—24no—
57C2×C22⋊D47—24no—
58C2×C22⋊D47—24no—
59C2×C22⋊D47—42no—
60C2×C22⋊D47—42no—
61C2×C22⋊D47—42no—
62C2×C22⋊D47—42no—
63C2×C22⋊D47—42no—
64C22×Dic47—24no—
65C22×Dic47—41no—
66C22×Dic47C2312yes—
67C22×Dic47C2312yes—
68C22×Dic47C2312yes—
69C2×D188—22no—
70C2×D188—41no—
71C2×D188—41no—
72C22⋊C4×C47—22no—
73C22⋊C4×C47—24no—
74C22⋊Dic47—24no—
75C22⋊Dic47—24no—
76C22⋊Dic47—41no—
77C22⋊Dic47D418yescomplemented
78(C2×D47)⋊C4—24no—
79(C2×D47)⋊C4—42no—
80Dic47⋊C4—24no—
81C4×Dic47—22no—
82C23×C47—22no—
83C23×C47—22no—
84C23×C47—22no—
85C23×C47—22no—
86C23×C47—21no—
87C23×C47—21no—
88C23×C47—22no—
89C23×C47—22no—
90C23×C47—22no—
91C23×C47—22no—
92C23×C47—22no—
93C23×C47—21no—
94C23×C47—21no—
95C23×C47—22no—
96C23×C47—44no—
97C23×C47—48no—
98C23×C47—44no—
99C23×C47—48no—
100C23×C47—44no—
101C23×C47C2×D414yes—
102C23×C47C2×D412yes—
103C23×C47C2×D412yes—
104C23×C47C2411yescharacteristic
105C22×D47—22no—
106C22×D47—22no—
107C22×D47—22no—
108C22×D47—22no—
109C22×D47—22no—
110C22×D47—22no—
111C22×D47—22no—
112D4×C47—44no—
113D4×C47—48no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—22no—
117C2×C4×C47—22no—
118C2×C4×C47—22no—
119C2×C4×C47C2×D412yes—
120C22⋊D47—48no—
121C22⋊D47—48no—
122C22⋊D47—48no—
123C22⋊D47—48no—
124C2×Dic47—22no—
125C2×Dic47—22no—
126C2×Dic47—22no—
127C2×Dic47—22no—
128C2×Dic47—22no—
129C2×Dic47—22no—
130C2×Dic47—22no—
131C2×Dic47—44no—
132C2×Dic47C2×D414yes—
133C2×Dic47C2×D414yes—
134D188—44no—
135C22×C47—22no—
136C22×C47—22no—
137C22×C47—24no—
138C22×C47—24no—
139C22×C47—24no—
140C22×C47—24no—
141C22×C47—24no—
142C22×C47—416no—
143C22×C47—42no—
144C22×C47—42no—
145C22×C47—42no—
146C22×C47—42no—
147C22×C47—41no—
148C22×C47—41no—
149C22×C47—42no—
150C22×C47—41no—
151C22×C47—41no—
152C22×C47—42no—
153C22×C47C22×D412yes—
154C22×C47C22×D411yescharacteristic
155C22×C47H(5,𝔽2)11yescharacteristic
156C22×C47H(5,𝔽2)11yescharacteristic
157C22×C47H(5,𝔽2)12yes—
158C2×D47—42no—
159C2×D47—42no—
160C2×D47—42no—
161C2×D47—42no—
162C2×D47—42no—
163C2×D47—42no—
164C2×D47—42no—
165C4×C47—22no—
166C4×C47—42no—
167Dic47—24no—
168Dic47—24no—
169Dic47—42no—
170#2669—471nomaximal, Sylow
171C2×C47—42no—
172C2×C47—42no—
173C2×C47—44no—
174C2×C47#53411yescharacteristic
175C2×C47#53512yes—
176C2×C47D4211yescharacteristic
177C2×C47D4212yes—
178C2×C47#56011yescharacteristic
179D47—82no—
180C2×#127—471no—
181C2×#121—472no—
182C2×#120—472no—
183C2×#120D4711yescharacteristic, complemented
184#394—472no—
185#392—472no—
186#392—472no—
187#388—472no—
188#386—471no—
189C47#266911yescharacteristic, complemented, Sylow
190C25C2×D4711yescharacteristic
191C22×D4—472no—
192C22×D4—472no—
193C22×D4—472no—
194C22×D4—472no—
195C22×D4—471no—
196C22×D4C2×D4712yes—
197C22×D4C2×D4711yescharacteristic
198C23×C4—471no—
199#127—944no—
200#121—948no—
201#120—24no—
202#120—948no—
203C2×C4⋊C4—472no—
204C2×C22⋊C4—472no—
205C2×C22⋊C4—472no—
206C2×C22⋊C4—472no—
207C2×C22⋊C4—472no—
208C2×C22⋊C4—471no—
209C2×C22⋊C4—472no—
210C2×C22⋊C4C2×D4712yes—
211C2×C22⋊C4C2×D4711yescharacteristic
212C2×C42—471no—
213#95—472no—
214#95—472no—
215C24—24no—
216C24—22no—
217C24—42no—
218C24—41no—
219C24—41no—
220C24—472no—
221C24C22×D4712yes—
222C24C22×D4711yescharacteristic
223C24C22×D4711yescharacteristic
224C2×D4—24no—
225C2×D4—24no—
226C2×D4—41no—
227C2×D4—41no—
228C2×D4—42no—
229C2×D4—944no—
230C2×D4—944no—
231C2×D4—944no—
232C2×D4—944no—
233C2×D4—944no—
234C2×D4—944no—
235C2×D4—944no—
236C2×D4—942no—
237C2×D4—1881no—
238C2×D4—1881no—
239C2×D4—1882no—
240C2×D4—1882no—
241C2×D4—1882no—
242C2×D4—1882no—
243C2×D4—1882no—
244C2×D4C22⋊D4714yescomplemented
245C22×C4—472no—
246C22×C4—472no—
247C22×C4—472no—
248C22×C4—944no—
249C22×C4—1881no—
250C22×C4C22×D4712yes—
251C22×C4C22×D4711yescharacteristic
252C4⋊C4—944no—
253C22⋊C4—22no—
254C22⋊C4—24no—
255C22⋊C4—478no—
256C22⋊C4—944no—
257C22⋊C4—944no—
258C22⋊C4—944no—
259C22⋊C4—1882no—
260C22⋊C4—1881no—
261C42—942no—
262C23—22no—
263C23—22no—
264C23—22no—
265C23—22no—
266C23—21no—
267C23—21no—
268C23—22no—
269C23—22no—
270C23—21no—
271C23—21no—
272C23—22no—
273C23—22no—
274C23—22no—
275C23—22no—
276C23—44no—
277C23—48no—
278C23—44no—
279C23—48no—
280C23—44no—
281C23—942no—
282C23—942no—
283C23—942no—
284C23—942no—
285C23—942no—
286C23—942no—
287C23—942no—
288C23D4×D4714yes—
289C23C2×C22⋊D4712yes—
290C23C2×C22⋊D4712yes—
291C23C23×D4711yescharacteristic
292D4—44no—
293D4—48no—
294D4—1884no—
295D4—1888no—
296D4—1888no—
297D4—1888no—
298D4—1888no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—474no—
305C2×C4—474no—
306C2×C4—942no—
307C2×C4—942no—
308C2×C4—942no—
309C2×C4—942no—
310C2×C4—942no—
311C2×C4—942no—
312C2×C4—942no—
313C2×C4—1884no—
314C2×C4C2×C22⋊D4712yes—
315C22—24no—
316C22—24no—
317C22—24no—
318C22—24no—
319C22—22no—
320C22—22no—
321C22—24no—
322C22—416no—
323C22—41no—
324C22—41no—
325C22—42no—
326C22—42no—
327C22—41no—
328C22—41no—
329C22—42no—
330C22—42no—
331C22—42no—
332C22—42no—
333C22—1882no—
334C22—1882no—
335C22—1882no—
336C22—1882no—
337C22—1882no—
338C22—1882no—
339C22—1882no—
340C22C2×D4×D4712yes—
341C22C22×C22⋊D4711yescharacteristic
342C22#1309406911yescharacteristic
343C22#1309406912yes—
344C22#1309406911yescharacteristic
345C4—22no—
346C4—42no—
347C4—944no—
348C4—944no—
349C4—1882no—
350C2—44no—
351C2—42no—
352C2—42no—
353C2—3762no—
354C2#1568968211yescharacteristic
355C2#1568968812yes—
356C2#1568975511yescharacteristic
357C2D4×C22⋊D4712yes—
358C2#1568986211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#120×C47C2
hypercenterC2×#120D47
hypocenterC47#2669
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×#13094020C2semidirect
2. C2×#13093996C2semidirect
3. C2×#13093993C2semidirect
4. #15689038C2semidirect
5. #15689032C2semidirect
6. #15689031C2semidirect
7. #15689011C2semidirect
8. #15689003C2semidirect
9. C2×#120×C47C2semidirect
10. C22×D188C22semidirect
14. C22×C22⋊D47C22semidirect
15. C23×Dic47C22semidirect
19. C2×Dic47⋊C4C22semidirect
23. C2×C22⋊Dic47C22semidirect
24. C2×(C2×D47)⋊C4C22semidirect
25. C2×(C2×D47)⋊C4C22semidirect
26. C2×C4×Dic47C22semidirect
27. C47⋊#95C22semidirect
28. C47⋊#95C22semidirect
49. C2×D4×C47D4semidirect
77. C22⋊Dic47D4semidirect
183. C2×#120D47semidirect
189. C47#2669semidirect
244. C2×D4C22⋊D47semidirect