Finite Group Databasebeta

← #20249126

Subgroups — #20249126

Order 6016.

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

normal subgroups only

This group has 824 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×#13093996C211yesmaximal, characteristic, complemented
2C2×#13093993C211yesmaximal, characteristic, complemented
3C22×C22⋊Dic47C211yesmaximal, characteristic, complemented
4#15689051C212yesmaximal, complemented
5#15689038C212yesmaximal, complemented
6#15689037C212yesmaximal, complemented
7#15689031C212yesmaximal, complemented
8#15689003C211yesmaximal, characteristic, complemented
9#15689000C211yesmaximal, characteristic, complemented
10#15688981C211yesmaximal, characteristic, complemented
11C2×#120×C47C211yesmaximal, characteristic, complemented
12C22×C22⋊D47C2211yescharacteristic
13C22×C22⋊D47C2212yes—
14C22×C22⋊D47C2211yescharacteristic, complemented
15C23×Dic47C2211yescharacteristic
16C23×Dic47C2211yescharacteristic
17#13093996—24no—
18#13093993—24no—
19C2×Dic47⋊C4C2211yescharacteristic, complemented
20C2×Dic47⋊C4C2212yescomplemented
21C2×C22⋊Dic47—24no—
22C2×C22⋊Dic47C2211yescharacteristic
23C2×C22⋊Dic47C2212yes—
24C2×C22⋊Dic47C2212yes—
25C2×C22⋊Dic47C2212yes—
26C2×C22⋊Dic47C2211yescharacteristic, complemented
27C2×C22⋊Dic47C2212yescomplemented
28C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
29C2×(C2×D47)⋊C4C2212yescomplemented
30C47⋊#95C2212yescomplemented
31C47⋊#95C2212yescomplemented
32C47⋊#95C2212yescomplemented
33C25×C47C2211yescharacteristic
34C22×D4×C47C2211yescharacteristic
35C22×D4×C47C2212yes—
36#120×C47—24no—
37C2×C22⋊C4×C47C2211yescharacteristic
38C2×C22⋊C4×C47C2212yes—
39C24×C47—22no—
40C24×C47—22no—
41C24×C47—42no—
42C24×C47—42no—
43C24×C47D414yescomplemented
44C24×C47C2311yescharacteristic
45C24×C47C2312yes—
46C24×C47C2311yescharacteristic
47C23×D47C2311yescharacteristic
48C2×D4×C47—24no—
49C2×D4×C47—22no—
50C2×D4×C47—22no—
51C2×D4×C47—22no—
52C2×D4×C47—42no—
53C2×D4×C47—42no—
54C22×C4×C47C2311yescharacteristic
55C22×C4×C47C2312yes—
56C2×C22⋊D47—24no—
57C2×C22⋊D47—22no—
58C2×C22⋊D47—22no—
59C2×C22⋊D47—22no—
60C2×C22⋊D47—22no—
61C2×C22⋊D47—42no—
62C2×C22⋊D47—42no—
63C2×C22⋊D47—42no—
64C22×Dic47—22no—
65C22×Dic47—42no—
66C22×Dic47—42no—
67C22×Dic47D414yescomplemented
68C22×Dic47C2312yes—
69C22×Dic47C2311yescharacteristic
70C22×Dic47C2312yes—
71C22×Dic47C2311yescharacteristic
72C22×Dic47C2311yescharacteristic
73C22⋊C4×C47—24no—
74C22⋊C4×C47—22no—
75C22⋊Dic47—24no—
76C22⋊Dic47—22no—
77C22⋊Dic47—24no—
78C22⋊Dic47—24no—
79C22⋊Dic47—22no—
80C22⋊Dic47—42no—
81(C2×D47)⋊C4—22no—
82(C2×D47)⋊C4—42no—
83Dic47⋊C4—22no—
84Dic47⋊C4—42no—
85C23×C47—22no—
86C23×C47—22no—
87C23×C47—28no—
88C23×C47—22no—
89C23×C47—22no—
90C23×C47—22no—
91C23×C47—22no—
92C23×C47—22no—
93C23×C47—22no—
94C23×C47—21no—
95C23×C47—21no—
96C23×C47—21no—
97C23×C47—22no—
98C23×C47—22no—
99C23×C47—48no—
100C23×C47—44no—
101C23×C47—44no—
102C23×C47—48no—
103C23×C47C2×D412yes—
104C23×C47C2×D414yes—
105C23×C47C2×D412yes—
106C23×C47#4112yes—
107C23×C47C2411yescharacteristic
108C22×D47—21no—
109C22×D47—21no—
110C22×D47—21no—
111C22×D47—22no—
112C22×D47—22no—
113D4×C47—48no—
114D4×C47—44no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—22no—
118C2×C4×C47—21no—
119C2×C4×C47—22no—
120C2×C4×C47—22no—
121C22⋊D47—44no—
122C22⋊D47—48no—
123C22⋊D47—44no—
124C2×Dic47—22no—
125C2×Dic47—22no—
126C2×Dic47—21no—
127C2×Dic47—22no—
128C2×Dic47—21no—
129C2×Dic47—22no—
130C2×Dic47—21no—
131C2×Dic47—22no—
132C2×Dic47—22no—
133C2×Dic47—22no—
134C2×Dic47—22no—
135C2×Dic47—44no—
136C2×Dic47—44no—
137C2×Dic47C2×D412yes—
138C2×Dic47C2×D412yes—
139C22×C47—22no—
140C22×C47—24no—
141C22×C47—22no—
142C22×C47—24no—
143C22×C47—24no—
144C22×C47—24no—
145C22×C47—24no—
146C22×C47—416no—
147C22×C47—42no—
148C22×C47—42no—
149C22×C47—42no—
150C22×C47—42no—
151C22×C47—41no—
152C22×C47—41no—
153C22×C47—42no—
154C22×C47—41no—
155C22×C47—42no—
156C22×C47#12114yes—
157C22×C47C22×D411yescharacteristic
158C22×C47C22×D411yescharacteristic
159C22×C47C2×#4111yescharacteristic
160C22×C47H(5,𝔽2)12yes—
161C22×C47H(5,𝔽2)12yes—
162C2×D47—41no—
163C2×D47—42no—
164C2×D47—41no—
165C2×D47—41no—
166C2×D47—42no—
167C4×C47—41no—
168C4×C47—42no—
169Dic47—22no—
170Dic47—22no—
171Dic47—41no—
172Dic47—42no—
173Dic47—42no—
174#2617—471nomaximal, Sylow
175C2×C47—24no—
176C2×C47—44no—
177C2×C47—81no—
178C2×C47C2×#12111yescharacteristic
179C2×C47#53412yes—
180C2×C47#53411yescharacteristic
181C2×C47#53511yescharacteristic
182C2×C47#53812yes—
183D47—81no—
184C2×#121—471no—
185C2×#120—471no—
186C2×#120D4711yescharacteristic, complemented
187C22×C22⋊C4—471no—
188#397—472no—
189#394—472no—
190#394—472no—
191#392—472no—
192#386—471no—
193#386—471no—
194#380—471no—
195C47#261711yescharacteristic, complemented, Sylow
196C25C2×D4711yescharacteristic
197C22×D4—471no—
198C22×D4—472no—
199C22×D4—471no—
200C22×D4C2×D4711yescharacteristic
201C22×D4C2×D4712yes—
202C23×C4—471no—
203C23×C4—471no—
204#121—944no—
205#120—24no—
206#120—944no—
207C2×C4⋊C4—471no—
208C2×C4⋊C4—472no—
209C2×C22⋊C4—472no—
210C2×C22⋊C4—472no—
211C2×C22⋊C4—471no—
212C2×C22⋊C4—472no—
213C2×C22⋊C4—471no—
214C2×C22⋊C4—471no—
215C2×C22⋊C4—472no—
216C2×C22⋊C4—472no—
217C2×C22⋊C4—944no—
218C2×C22⋊C4C2×D4711yescharacteristic
219C2×C22⋊C4C2×D4712yes—
220#95—472no—
221#95—472no—
222#95—472no—
223C24—22no—
224C24—22no—
225C24—42no—
226C24—42no—
227C24—471no—
228C24C22⋊D4714yescomplemented
229C24C22×D4711yescharacteristic
230C24C22×D4712yes—
231C24C22×D4711yescharacteristic
232C2×D4—22no—
233C2×D4—22no—
234C2×D4—24no—
235C2×D4—22no—
236C2×D4—42no—
237C2×D4—42no—
238C2×D4—942no—
239C2×D4—942no—
240C2×D4—942no—
241C2×D4—944no—
242C2×D4—942no—
243C2×D4—1882no—
244C2×D4—1882no—
245C2×D4—1882no—
246C22×C4—471no—
247C22×C4—471no—
248C22×C4—474no—
249C22×C4—472no—
250C22×C4—471no—
251C22×C4—472no—
252C22×C4—942no—
253C22×C4—1882no—
254C22×C4—1882no—
255C22×C4C22×D4711yescharacteristic
256C22×C4C22×D4712yes—
257C4⋊C4—942no—
258C4⋊C4—1882no—
259C22⋊C4—24no—
260C22⋊C4—22no—
261C22⋊C4—942no—
262C22⋊C4—944no—
263C22⋊C4—944no—
264C22⋊C4—942no—
265C22⋊C4—944no—
266C22⋊C4—942no—
267C22⋊C4—1882no—
268C22⋊C4—1882no—
269C23—22no—
270C23—22no—
271C23—28no—
272C23—22no—
273C23—22no—
274C23—22no—
275C23—22no—
276C23—22no—
277C23—22no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—22no—
282C23—22no—
283C23—48no—
284C23—44no—
285C23—44no—
286C23—48no—
287C23—941no—
288C23—941no—
289C23—941no—
290C23—942no—
291C23—942no—
292C23D4×D4712yes—
293C23#1062535212yes—
294C23C2×C22⋊D4714yes—
295C23C2×C22⋊D4712yes—
296C23C23×D4711yescharacteristic
297D4—48no—
298D4—44no—
299D4—1884no—
300D4—1888no—
301D4—1884no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—472no—
309C2×C4—472no—
310C2×C4—942no—
311C2×C4—942no—
312C2×C4—942no—
313C2×C4—941no—
314C2×C4—941no—
315C2×C4—942no—
316C2×C4—941no—
317C2×C4—942no—
318C2×C4—942no—
319C2×C4—942no—
320C2×C4—942no—
321C2×C4—1884no—
322C2×C4—1884no—
323C22—24no—
324C22—22no—
325C22—22no—
326C22—24no—
327C22—24no—
328C22—24no—
329C22—24no—
330C22—416no—
331C22—42no—
332C22—42no—
333C22—42no—
334C22—42no—
335C22—41no—
336C22—42no—
337C22—41no—
338C22—41no—
339C22—42no—
340C22—1881no—
341C22—1882no—
342C22—1881no—
343C22—1881no—
344C22—1882no—
345C22#1309399614yes—
346C22C2×D4×D4711yescharacteristic
347C22C22×C22⋊D4711yescharacteristic
348C22C2×#1062535211yescharacteristic
349C22#1309406912yes—
350C22#1309406912yes—
351C4—41no—
352C4—42no—
353C4—942no—
354C4—942no—
355C4—1881no—
356C4—1882no—
357C4—1882no—
358C2—24no—
359C2—44no—
360C2—81no—
361C2—3761no—
362C2C2×#1309399611yescharacteristic
363C2#1568968212yes—
364C2#1568968311yescharacteristic
365C2#1568968811yescharacteristic
366C2#1568970812yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#120×C47C2
hypercenterC2×#120D47
hypocenterC47#2617
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×#13093996C2semidirect
2. C2×#13093993C2semidirect
3. C22×C22⋊Dic47C2semidirect
4. #15689051C2semidirect
5. #15689038C2semidirect
6. #15689037C2semidirect
7. #15689031C2semidirect
8. #15689003C2semidirect
9. #15689000C2semidirect
10. #15688981C2semidirect
11. C2×#120×C47C2semidirect
14. C22×C22⋊D47C22semidirect
19. C2×Dic47⋊C4C22semidirect
20. C2×Dic47⋊C4C22semidirect
26. C2×C22⋊Dic47C22semidirect
27. C2×C22⋊Dic47C22semidirect
28. C2×(C2×D47)⋊C4C22semidirect
29. C2×(C2×D47)⋊C4C22semidirect
30. C47⋊#95C22semidirect
31. C47⋊#95C22semidirect
32. C47⋊#95C22semidirect
43. C24×C47D4semidirect
67. C22×Dic47D4semidirect
186. C2×#120D47semidirect
195. C47#2617semidirect
228. C24C22⋊D47semidirect