Finite Group Databasebeta

← #20246782

Subgroups — #20246782

Order 6016.

814 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 814 conjugacy classes of subgroups — too many to draw. Only its 165 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×#13094008C211yesmaximal, characteristic, complemented
2C2×#13093994C211yesmaximal, characteristic
3C22×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D47C211yesmaximal, characteristic, complemented
5#15689050C212yesmaximal, complemented
6#15689040C212yesmaximal, complemented
7#15689002C211yesmaximal, characteristic, complemented
8#15689001C212yesmaximal, complemented
9#15688984C211yesmaximal, characteristic, complemented
10#15688980C212yesmaximal, complemented
11C47×#385C211yesmaximal, characteristic, complemented
12C24×D47C2211yescharacteristic
13C22×D188C2211yescharacteristic
14C22×D188C2211yescharacteristic
15C22×C22⋊D47C2211yescharacteristic
16C23×Dic47C2211yescharacteristic
17C22×C4×D47C2212yes—
18#13094008—24no—
19#13093994—24no—
20C2×C4⋊Dic47C2212yescomplemented
21C2×C22⋊Dic47C2211yescharacteristic
22C2×(C2×D47)⋊C4—24no—
23C2×(C2×D47)⋊C4C2211yescharacteristic
24C2×(C2×D47)⋊C4C2212yes—
25C2×(C2×D47)⋊C4C2212yes—
26C2×(C2×D47)⋊C4C2212yes—
27C2×(C2×D47)⋊C4C2211yescharacteristic
28C2×(C2×D47)⋊C4C2212yescomplemented
29C2×(C2×D47)⋊C4C2212yescomplemented
30C22⋊C4×D47—24no—
31C47⋊#95C2212yescomplemented
32C47⋊#95C2212yescomplemented
33C47⋊#95C2212yescomplemented
34C23×C4×C47C2211yescharacteristic
35C2×C4⋊C4×C47C2212yescomplemented
36C2×C22⋊C4×C47C2211yescharacteristic
37C2×C22⋊C4×C47C2211yescharacteristic
38#95×C47C2212yescomplemented
39C24×C47C2311yescharacteristic
40C23×D47—22no—
41C23×D47—22no—
42C23×D47—24no—
43C23×D47—42no—
44C23×D47D414yes—
45C23×D47C2311yescharacteristic
46C23×D47C2311yescharacteristic
47C23×D47C2311yescharacteristic
48C22×C4×C47—22no—
49C22×C4×C47—42no—
50C22×C4×C47C2311yescharacteristic
51C22×C4×C47C2311yescharacteristic
52C22×C4×C47C2312yes—
53C22×C4×C47C2312yes—
54C2×C22⋊D47—22no—
55C2×C22⋊D47—22no—
56C2×C22⋊D47—22no—
57C22×Dic47—22no—
58C22×Dic47—22no—
59C22×Dic47—22no—
60C22×Dic47C2312yes—
61C22×Dic47C2312yes—
62C22×Dic47C2311yescharacteristic
63C2×D188—22no—
64C2×D188—22no—
65C2×D188—24no—
66C2×D188—42no—
67C2×C4×D47—24no—
68C2×C4×D47—24no—
69C2×C4×D47—42no—
70C4⋊C4×C47—42no—
71C22⋊C4×C47—22no—
72C22⋊C4×C47D414yescomplemented
73C22⋊Dic47—22no—
74(C2×D47)⋊C4—24no—
75(C2×D47)⋊C4—24no—
76(C2×D47)⋊C4—22no—
77(C2×D47)⋊C4—22no—
78(C2×D47)⋊C4—24no—
79(C2×D47)⋊C4—24no—
80(C2×D47)⋊C4—42no—
81C4⋊Dic47—24no—
82C23×C47—22no—
83C23×C47—22no—
84C23×C47C2×D412yes—
85C23×C47C2×D412yes—
86C23×C47#4112yes—
87C23×C47C2411yescharacteristic
88C22×D47—21no—
89C22×D47—21no—
90C22×D47—22no—
91C22×D47—28no—
92C22×D47—21no—
93C22×D47—22no—
94C22×D47—21no—
95C22×D47—22no—
96C22×D47—28no—
97C22×D47—21no—
98C22×D47—21no—
99C22×D47—22no—
100C22×D47—21no—
101C22×D47—22no—
102C22×D47—44no—
103C22×D47—48no—
104C22×D47—48no—
105C22×D47C2×D412yes—
106C22×D47C2×D412yes—
107C22×D47#4114yes—
108C2×C4×C47—22no—
109C2×C4×C47—22no—
110C2×C4×C47—22no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—22no—
114C2×C4×C47—22no—
115C2×C4×C47—22no—
116C2×C4×C47—22no—
117C2×C4×C47—44no—
118C2×C4×C47C2×D414yes—
119C22⋊D47—44no—
120C2×Dic47—21no—
121C2×Dic47—22no—
122C2×Dic47—22no—
123C2×Dic47—21no—
124C2×Dic47—22no—
125C2×Dic47—22no—
126C2×Dic47—22no—
127C2×Dic47—21no—
128C2×Dic47—22no—
129C2×Dic47—44no—
130D188—44no—
131D188—44no—
132C4×D47—48no—
133C22×C47—22no—
134C22×C47—22no—
135C22×C47—24no—
136C22×C47—24no—
137C22×C47#12114yes—
138C22×C47C22×D411yescharacteristic
139C22×C47C22×D411yescharacteristic
140C22×C47C2×#4112yes—
141C22×C47C2×#4111yescharacteristic
142C22×C47H(5,𝔽2)12yes—
143C2×D47—22no—
144C2×D47—22no—
145C2×D47—24no—
146C2×D47—24no—
147C2×D47—22no—
148C2×D47—22no—
149C2×D47—22no—
150C2×D47—416no—
151C2×D47—42no—
152C2×D47—42no—
153C2×D47—41no—
154C2×D47—41no—
155C2×D47—41no—
156C2×D47—42no—
157C2×D47—42no—
158C2×D47#12314yescomplemented
159C4×C47—24no—
160C4×C47—41no—
161C4×C47—41no—
162C4×C47—42no—
163Dic47—42no—
164Dic47—41no—
165Dic47—42no—
166#2412—471nomaximal, Sylow
167C2×C47—24no—
168C2×C47C2×#12111yescharacteristic
169C2×C47C2×#12311yescharacteristic
170C2×C47#53411yescharacteristic
171C2×C47#54612yes—
172C2×C47#55112yes—
173D47—24no—
174D47—42no—
175D47—81no—
176C2×#123—471no—
177C2×#120—471no—
178C22×C22⋊C4—471no—
179C22×C22⋊C4—471no—
180#397—472no—
181#394—472no—
182#386—471no—
183#386—472no—
184#385D4711yescharacteristic, complemented
185#381—471no—
186#380—472no—
187C47#241211yescharacteristic, complemented, Sylow
188C25—471no—
189C22×D4—471no—
190C22×D4—471no—
191C22×D4—471no—
192C23×C4—471no—
193C23×C4—472no—
194C23×C4C2×D4711yescharacteristic
195#123—944no—
196#120—944no—
197C2×C4⋊C4—472no—
198C2×C4⋊C4C2×D4712yescomplemented
199C2×C22⋊C4—471no—
200C2×C22⋊C4—472no—
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—944no—
208C2×C22⋊C4—944no—
209C2×C22⋊C4C2×D4711yescharacteristic
210C2×C22⋊C4C2×D4711yescharacteristic
211#95—472no—
212#95—472no—
213#95—472no—
214#95C2×D4712yescomplemented
215C24—471no—
216C24—471no—
217C24—474no—
218C24—471no—
219C24—944no—
220C24—942no—
221C24—942no—
222C24—1882no—
223C24C22×D4711yescharacteristic
224C2×D4—942no—
225C2×D4—942no—
226C2×D4—944no—
227C2×D4—942no—
228C2×D4—942no—
229C2×D4—942no—
230C2×D4—1882no—
231C22×C4—22no—
232C22×C4—42no—
233C22×C4—472no—
234C22×C4—472no—
235C22×C4—471no—
236C22×C4—944no—
237C22×C4—942no—
238C22×C4—942no—
239C22×C4—942no—
240C22×C4—944no—
241C22×C4—1882no—
242C22×C4C22×D4711yescharacteristic
243C22×C4C22×D4711yescharacteristic
244C22×C4C22×D4712yes—
245C22×C4C22×D4712yes—
246C4⋊C4—42no—
247C4⋊C4—944no—
248C22⋊C4—22no—
249C22⋊C4—944no—
250C22⋊C4—944no—
251C22⋊C4—942no—
252C22⋊C4—942no—
253C22⋊C4—942no—
254C22⋊C4—944no—
255C22⋊C4—944no—
256C22⋊C4—1882no—
257C22⋊C4D18814yescomplemented
258C23—22no—
259C23—22no—
260C23—472no—
261C23—474no—
262C23—472no—
263C23—948no—
264C23—941no—
265C23—941no—
266C23—942no—
267C23—948no—
268C23—941no—
269C23—942no—
270C23—941no—
271C23—942no—
272C23—941no—
273C23—941no—
274C23—942no—
275C23—941no—
276C23—942no—
277C23—1884no—
278C23—1888no—
279C23—1888no—
280C23C2×D18812yes—
281C23D4×D4712yes—
282C23#1062535412yes—
283C23C23×D4711yescharacteristic
284D4—1884no—
285D4—1884no—
286D4—1884no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—44no—
297C2×C4—942no—
298C2×C4—941no—
299C2×C4—942no—
300C2×C4—942no—
301C2×C4—941no—
302C2×C4—942no—
303C2×C4—942no—
304C2×C4—941no—
305C2×C4—942no—
306C2×C4—1888no—
307C2×C4—1884no—
308C2×C4C2×D18814yes—
309C22—24no—
310C22—24no—
311C22—22no—
312C22—22no—
313C22—474no—
314C22—944no—
315C22—944no—
316C22—942no—
317C22—942no—
318C22—942no—
319C22—942no—
320C22—942no—
321C22—18816no—
322C22—1882no—
323C22—1882no—
324C22—1881no—
325C22—1881no—
326C22—1881no—
327C22—1882no—
328C22—1882no—
329C22#1309399914yes—
330C22C2×D4×D4711yescharacteristic
331C22C22×D18811yescharacteristic
332C22#41×D4712yes—
333C22C2×#1062535411yescharacteristic
334C22#1309406912yes—
335C4—24no—
336C4—41no—
337C4—42no—
338C4—41no—
339C4—1882no—
340C4—1882no—
341C4—1881no—
342C2—24no—
343C2—944no—
344C2—3761no—
345C2—1882no—
346C2C2×#1309399911yescharacteristic
347C2#123×D4711yescharacteristic
348C2#1568968311yescharacteristic
349C2#1568976812yes—
350C2#1568980012yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#385C2
hypercenter#385D47
hypocenterC47#2412
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#13094008C2semidirect
3. C22×(C2×D47)⋊C4C2semidirect
4. C2×C22⋊C4×D47C2semidirect
5. #15689050C2semidirect
6. #15689040C2semidirect
7. #15689002C2semidirect
8. #15689001C2semidirect
9. #15688984C2semidirect
10. #15688980C2semidirect
11. C47×#385C2semidirect
20. C2×C4⋊Dic47C22semidirect
28. C2×(C2×D47)⋊C4C22semidirect
29. C2×(C2×D47)⋊C4C22semidirect
31. C47⋊#95C22semidirect
32. C47⋊#95C22semidirect
33. C47⋊#95C22semidirect
35. C2×C4⋊C4×C47C22semidirect
38. #95×C47C22semidirect
72. C22⋊C4×C47D4semidirect
158. C2×D47#123semidirect
184. #385D47semidirect
187. C47#2412semidirect
198. C2×C4⋊C4C2×D47semidirect
214. #95C2×D47semidirect
257. C22⋊C4D188semidirect