Finite Group Databasebeta

← #20249121

Subgroups — #20249121

Order 6016.

824 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 824 conjugacy classes of subgroups — too many to draw. Only its 143 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×#13093995C211yesmaximal, characteristic, complemented
2C2×#13093992C212yesmaximal, complemented
3C2×C22⋊C4×D47C211yesmaximal, characteristic, complemented
4#15689050C211yesmaximal, characteristic, complemented
5#15689048C211yesmaximal, characteristic, complemented
6#15689038C212yesmaximal, complemented
7#15689037C212yesmaximal, complemented
8#15689031C211yesmaximal, characteristic, complemented
9#15688999C212yesmaximal, complemented
10#15688982C211yesmaximal, characteristic, complemented
11C47×#392C211yesmaximal, characteristic, complemented
12C24×D47C2211yescharacteristic
13C22×C22⋊D47C2212yes—
14C22×C22⋊D47C2212yes—
15C22×C4×D47C2211yescharacteristic
16C22×C4×D47C2211yescharacteristic
17#13093995—24no—
18#13093992—28no—
19C2×C4⋊Dic47C2211yescharacteristic, complemented
20C2×Dic47⋊C4C2212yescomplemented
21C2×C22⋊Dic47C2211yescharacteristic
22C2×C22⋊Dic47C2212yes—
23C2×C22⋊Dic47C2212yescomplemented
24C2×C22⋊Dic47C2212yescomplemented
25C2×(C2×D47)⋊C4C2212yes—
26C2×(C2×D47)⋊C4C2211yescharacteristic
27C2×(C2×D47)⋊C4C2211yescharacteristic
28C2×(C2×D47)⋊C4C2212yes—
29C22⋊C4×D47—24no—
30C47⋊#95C2211yescharacteristic, complemented
31C47⋊#95C2212yescomplemented
32C47⋊#95C2212yescomplemented
33C22×D4×C47C2212yes—
34C22×D4×C47C2211yescharacteristic, complemented
35C2×C22⋊C4×C47C2211yescharacteristic
36C2×C22⋊C4×C47C2212yescomplemented
37#95×C47C2211yescharacteristic, complemented
38C24×C47C2312yes—
39C24×C47C2311yescharacteristic
40C23×D47—22no—
41C23×D47—22no—
42C23×D47—42no—
43C23×D47—42no—
44C23×D47D414yescomplemented
45C23×D47C2311yescharacteristic
46C23×D47C2311yescharacteristic
47C2×D4×C47—24no—
48C2×D4×C47—22no—
49C2×D4×C47—42no—
50C2×D4×C47—42no—
51C2×D4×C47—42no—
52C22×C4×C47C2311yescharacteristic
53C22×C4×C47C2312yes—
54C22×C4×C47C2311yescharacteristic
55C2×C22⋊D47—24no—
56C2×C22⋊D47—24no—
57C2×C22⋊D47—24no—
58C2×C22⋊D47—24no—
59C2×C22⋊D47—42no—
60C2×C22⋊D47—42no—
61C22×Dic47C2311yescharacteristic
62C22×Dic47C2312yes—
63C22×Dic47C2312yes—
64C22×Dic47C2311yescharacteristic
65C2×C4×D47—22no—
66C2×C4×D47—42no—
67C2×C4×D47—42no—
68C2×C4×D47D414yescomplemented
69C22⋊C4×C47—22no—
70C22⋊C4×C47—42no—
71C22⋊Dic47—24no—
72C22⋊Dic47—22no—
73C22⋊Dic47—24no—
74C22⋊Dic47—42no—
75(C2×D47)⋊C4—24no—
76(C2×D47)⋊C4—24no—
77(C2×D47)⋊C4—22no—
78(C2×D47)⋊C4—22no—
79C4⋊Dic47—22no—
80Dic47⋊C4—42no—
81C23×C47—21no—
82C23×C47—21no—
83C23×C47—22no—
84C23×C47—22no—
85C23×C47—22no—
86C23×C47—22no—
87C23×C47—22no—
88C23×C47—22no—
89C23×C47—22no—
90C23×C47—22no—
91C23×C47—22no—
92C23×C47C2×D412yes—
93C23×C47C2411yescharacteristic
94C22×D47—22no—
95C22×D47—22no—
96C22×D47—21no—
97C22×D47—21no—
98C22×D47—22no—
99C22×D47—22no—
100C22×D47—28no—
101C22×D47—48no—
102C22×D47—44no—
103C22×D47—44no—
104C22×D47—48no—
105C22×D47C2×D412yes—
106C22×D47C2×D412yes—
107C22×D47C2×D412yes—
108C22×D47#4112yes—
109D4×C47—44no—
110D4×C47—48no—
111C2×C4×C47—22no—
112C2×C4×C47—22no—
113C2×C4×C47—21no—
114C2×C4×C47—22no—
115C2×C4×C47—22no—
116C2×C4×C47—22no—
117C2×C4×C47C2×D412yes—
118C22⋊D47—48no—
119C22⋊D47—48no—
120C2×Dic47—22no—
121C2×Dic47—22no—
122C2×Dic47—21no—
123C2×Dic47—22no—
124C2×Dic47—22no—
125C2×Dic47—22no—
126C2×Dic47—22no—
127C2×Dic47—22no—
128C2×Dic47—22no—
129C2×Dic47C2×D412yes—
130C4×D47—44no—
131C4×D47—44no—
132C22×C47—22no—
133C22×C47—24no—
134C22×C47—41no—
135C22×C47—41no—
136C22×C47—42no—
137C22×C47—42no—
138C22×C47—42no—
139C22×C47—42no—
140C22×C47—42no—
141C22×C47—42no—
142C22×C47—42no—
143C22×C47—42no—
144C22×C47C22×D411yescharacteristic
145C22×C47C22×D411yescharacteristic
146C22×C47C2×#4111yescharacteristic
147C22×C47H(5,𝔽2)12yes—
148C22×C47H(5,𝔽2)12yes—
149C2×D47—22no—
150C2×D47—24no—
151C2×D47—22no—
152C2×D47—24no—
153C2×D47—22no—
154C2×D47—24no—
155C2×D47—416no—
156C2×D47—41no—
157C2×D47—41no—
158C2×D47—42no—
159C2×D47#12114yes—
160C4×C47—22no—
161C4×C47—42no—
162C4×C47—41no—
163Dic47—22no—
164Dic47—42no—
165Dic47—42no—
166Dic47—41no—
167#2617—471nomaximal, Sylow
168C2×C47—42no—
169C2×C47—82no—
170C2×C47C2×#12111yescharacteristic
171C2×C47#53411yescharacteristic
172C2×C47#53412yes—
173C2×C47#53511yescharacteristic
174C2×C47#53812yes—
175D47—24no—
176D47—42no—
177C2×#121—471no—
178C2×#120—472no—
179C22×C22⋊C4—471no—
180#397—471no—
181#397—471no—
182#394—472no—
183#394—472no—
184#392—471no—
185#392D4711yescharacteristic, complemented
186#386—472no—
187#380—471no—
188C47#261711yescharacteristic, complemented, Sylow
189C25—471no—
190C22×D4—472no—
191C22×D4—472no—
192C22×D4C2×D4712yes—
193C22×D4C2×D4711yescharacteristic, complemented
194C23×C4—471no—
195C23×C4—471no—
196#121—944no—
197#120—948no—
198C2×C4⋊C4—471no—
199C2×C4⋊C4—472no—
200C2×C22⋊C4—471no—
201C2×C22⋊C4—472no—
202C2×C22⋊C4—472no—
203C2×C22⋊C4—471no—
204C2×C22⋊C4—471no—
205C2×C22⋊C4—472no—
206C2×C22⋊C4—472no—
207C2×C22⋊C4—472no—
208C2×C22⋊C4—944no—
209C2×C22⋊C4C2×D4711yescharacteristic
210C2×C22⋊C4C2×D4712yescomplemented
211#95—471no—
212#95—472no—
213#95—472no—
214#95C2×D4711yescharacteristic, complemented
215C24—471no—
216C24—471no—
217C24—474no—
218C24—942no—
219C24—942no—
220C24—1882no—
221C24—1882no—
222C24C22×D4712yes—
223C24C22×D4711yescharacteristic
224C2×D4—24no—
225C2×D4—22no—
226C2×D4—42no—
227C2×D4—42no—
228C2×D4—42no—
229C2×D4—944no—
230C2×D4—944no—
231C2×D4—944no—
232C2×D4—944no—
233C2×D4—1882no—
234C2×D4—1882no—
235C22×C4—471no—
236C22×C4—474no—
237C22×C4—471no—
238C22×C4—472no—
239C22×C4—472no—
240C22×C4—942no—
241C22×C4—1882no—
242C22×C4—1882no—
243C22×C4C22×D4711yescharacteristic
244C22×C4C22×D4712yes—
245C22×C4C22×D4711yescharacteristic
246C4⋊C4—942no—
247C4⋊C4—1882no—
248C22⋊C4—22no—
249C22⋊C4—42no—
250C22⋊C4—942no—
251C22⋊C4—944no—
252C22⋊C4—944no—
253C22⋊C4—942no—
254C22⋊C4—944no—
255C22⋊C4—944no—
256C22⋊C4—942no—
257C22⋊C4—1882no—
258C23—21no—
259C23—21no—
260C23—22no—
261C23—22no—
262C23—22no—
263C23—22no—
264C23—22no—
265C23—22no—
266C23—22no—
267C23—22no—
268C23—22no—
269C23—472no—
270C23—472no—
271C23—472no—
272C23—472no—
273C23—948no—
274C23—942no—
275C23—942no—
276C23—941no—
277C23—941no—
278C23—942no—
279C23—942no—
280C23—1888no—
281C23—1884no—
282C23—1884no—
283C23—1888no—
284C23D4×D4712yes—
285C23C23×D4711yescharacteristic
286D4—44no—
287D4—48no—
288D4—1888no—
289D4—1888no—
290C2×C4—22no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—472no—
297C2×C4—942no—
298C2×C4—941no—
299C2×C4—942no—
300C2×C4—942no—
301C2×C4—942no—
302C2×C4—942no—
303C2×C4—942no—
304C2×C4—942no—
305C2×C4—942no—
306C2×C4—1884no—
307C2×C4—1884no—
308C2×C4D4×D4712yes—
309C22—22no—
310C22—24no—
311C22—41no—
312C22—41no—
313C22—42no—
314C22—42no—
315C22—42no—
316C22—42no—
317C22—42no—
318C22—42no—
319C22—42no—
320C22—42no—
321C22—474no—
322C22—942no—
323C22—944no—
324C22—942no—
325C22—944no—
326C22—942no—
327C22—944no—
328C22—18816no—
329C22—1881no—
330C22—1881no—
331C22—1882no—
332C22C2×D4×D4711yescharacteristic
333C22C2×D4×D4711yescharacteristic
334C22#41×D4711yescharacteristic
335C22#1309406912yes—
336C22#1309406912yes—
337C4—22no—
338C4—42no—
339C4—41no—
340C4—942no—
341C4—1882no—
342C4—1882no—
343C4—1881no—
344C2—42no—
345C2—82no—
346C2—944no—
347C2—1882no—
348C2#121×D4711yescharacteristic
349C2#1568968311yescharacteristic
350C2#1568968312yes—
351C2#1568968611yescharacteristic
352C2#1568970512yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#392C2
hypercenter#392D47
hypocenterC47#2617
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#13093995C2semidirect
2. C2×#13093992C2semidirect
3. C2×C22⋊C4×D47C2semidirect
4. #15689050C2semidirect
5. #15689048C2semidirect
6. #15689038C2semidirect
7. #15689037C2semidirect
8. #15689031C2semidirect
9. #15688999C2semidirect
10. #15688982C2semidirect
11. C47×#392C2semidirect
19. C2×C4⋊Dic47C22semidirect
20. C2×Dic47⋊C4C22semidirect
23. C2×C22⋊Dic47C22semidirect
24. C2×C22⋊Dic47C22semidirect
30. C47⋊#95C22semidirect
31. C47⋊#95C22semidirect
32. C47⋊#95C22semidirect
34. C22×D4×C47C22semidirect
36. C2×C22⋊C4×C47C22semidirect
37. #95×C47C22semidirect
44. C23×D47D4semidirect
68. C2×C4×D47D4semidirect
185. #392D47semidirect
188. C47#2617semidirect
193. C22×D4C2×D47semidirect
210. C2×C22⋊C4C2×D47semidirect
214. #95C2×D47semidirect