Finite Group Databasebeta

← #20249111

Subgroups — #20249111

Order 6016.

932 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 932 conjugacy classes of subgroups — too many to draw. Only its 153 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×#10625352C211yesmaximal, characteristic, complemented
2C2×#13093997C211yesmaximal, characteristic, complemented
3C2×#13093996C212yesmaximal, complemented
4#15689036C211yesmaximal, characteristic, complemented
5#15689035C211yesmaximal, characteristic, complemented
6#15689032C212yesmaximal, complemented
7#15689031C211yesmaximal, characteristic, complemented
8#15689031C212yesmaximal, complemented
9#15688982C211yesmaximal, characteristic, complemented
10#15688981C212yesmaximal, complemented
11C47×#392C211yesmaximal, characteristic, complemented
12C2×#10625352—28no—
13C2×#10625352—24no—
14C22×Dic94C2211yescharacteristic
15C22×D188C2211yescharacteristic
16C22×C22⋊D47C2212yes—
17C22×C22⋊D47C2211yescharacteristic
18C22×C22⋊D47C2211yescharacteristic
19C22×C22⋊D47C2212yes—
20C23×Dic47C2212yes—
21C22×C4×D47C2211yescharacteristic
22#13093997—24no—
23#13093996—28no—
24C2×Dic47⋊C4C2211yescharacteristic
25C2×Dic47⋊C4C2212yes—
26C2×C22⋊Dic47C2212yes—
27C2×C22⋊Dic47C2212yes—
28C2×(C2×D47)⋊C4C2211yescharacteristic
29C2×(C2×D47)⋊C4C2212yes—
30C2×(C2×D47)⋊C4C2212yes—
31C47⋊#95C2212yes—
32C47⋊#95C2212yes—
33C47⋊#95C2211yescharacteristic
34C22×D4×C47C2211yescharacteristic
35C22×D4×C47C2212yes—
36C2×C22⋊C4×C47C2211yescharacteristic
37C2×C22⋊C4×C47C2212yes—
38#95×C47C2211yescharacteristic
39C24×C47C2311yescharacteristic
40C24×C47C2312yes—
41C23×D47C2311yescharacteristic
42C23×D47C2311yescharacteristic
43C2×D4×C47—24no—
44C2×D4×C47—24no—
45C2×D4×C47—22no—
46C2×D4×C47—42no—
47C2×D4×C47—42no—
48C22×C4×C47C2311yescharacteristic
49C22×C4×C47C2312yes—
50C22×C4×C47C2311yescharacteristic
51C2×C22⋊D47—24no—
52C2×C22⋊D47—24no—
53C2×C22⋊D47—24no—
54C2×C22⋊D47—22no—
55C2×C22⋊D47—24no—
56C2×C22⋊D47—24no—
57C2×C22⋊D47—22no—
58C2×C22⋊D47—42no—
59C2×C22⋊D47—42no—
60C2×C22⋊D47—42no—
61C22×Dic47—24no—
62C22×Dic47—24no—
63C22×Dic47D418yescomplemented
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2312yes—
66C22×Dic47C2312yes—
67C22×Dic47C2311yescharacteristic
68#10625352—232no—
69C2×D188—22no—
70C2×D188—42no—
71C2×C4×D47—24no—
72C2×C4×D47D414yescomplemented
73C2×Dic94—22no—
74C2×Dic94—24no—
75C22⋊C4×C47—22no—
76C22⋊C4×C47—42no—
77C22⋊Dic47—24no—
78C22⋊Dic47—42no—
79(C2×D47)⋊C4—22no—
80(C2×D47)⋊C4—24no—
81(C2×D47)⋊C4—42no—
82Dic47⋊C4—24no—
83Dic47⋊C4—22no—
84C23×C47—22no—
85C23×C47—22no—
86C23×C47—22no—
87C23×C47—22no—
88C23×C47—22no—
89C23×C47—22no—
90C23×C47—22no—
91C23×C47—21no—
92C23×C47—22no—
93C23×C47—21no—
94C23×C47—21no—
95C23×C47C2×D414yes—
96C23×C47C2411yescharacteristic
97C22×D47—22no—
98C22×D47—21no—
99C22×D47—22no—
100C22×D47—21no—
101C22×D47—21no—
102C22×D47—22no—
103C22×D47—22no—
104C22×D47—21no—
105C22×D47—21no—
106C22×D47C2×D412yes—
107D4×C47—28no—
108D4×C47—48no—
109C2×C4×C47—22no—
110C2×C4×C47—22no—
111C2×C4×C47—21no—
112C2×C4×C47—22no—
113C2×C4×C47—22no—
114C2×C4×C47—22no—
115C2×C4×C47C2×D412yes—
116C22⋊D47—216no—
117C22⋊D47—44no—
118C22⋊D47—48no—
119C22⋊D47—44no—
120C2×Dic47—22no—
121C2×Dic47—22no—
122C2×Dic47—216no—
123C2×Dic47—21no—
124C2×Dic47—22no—
125C2×Dic47—22no—
126C2×Dic47—22no—
127C2×Dic47—22no—
128C2×Dic47C2×D414yes—
129C2×Dic47C2×D414yes—
130C2×Dic47C2×D412yes—
131D188—44no—
132C4×D47—28no—
133Dic94—28no—
134C22×C47—24no—
135C22×C47—24no—
136C22×C47—24no—
137C22×C47—42no—
138C22×C47—42no—
139C22×C47—42no—
140C22×C47—42no—
141C22×C47—41no—
142C22×C47—41no—
143C22×C47—42no—
144C22×C47—42no—
145C22×C47—41no—
146C22×C47C22×D411yescharacteristic
147C22×C47C22×D412yes—
148C22×C47H(5,𝔽2)12yes—
149C22×C47H(5,𝔽2)11yescharacteristic
150C22×C472−1+411yescharacteristic
151C2×D47—22no—
152C2×D47—22no—
153C2×D47—22no—
154C2×D47—42no—
155C2×D47—42no—
156C2×D47—41no—
157C2×D47—41no—
158C2×D47—42no—
159C2×D47—42no—
160C2×D47—41no—
161C4×C47—22no—
162C4×C47—41no—
163C4×C47—42no—
164Dic47—24no—
165Dic47—41no—
166Dic47—42no—
167Dic47#12014yes—
168#2615—471nomaximal, Sylow
169C2×C47—44no—
170C2×C47—81no—
171C2×C47C2×#12011yescharacteristic
172C2×C47#53511yescharacteristic
173C2×C47#53512yes—
174C2×C47#53712yes—
175C2×C47#53711yescharacteristic
176D47—42no—
177D47—81no—
178C22×#41—471no—
179C2×#121—472no—
180C2×#121—471no—
181#393—471no—
182#393—471no—
183#392—472no—
184#392—471no—
185#392—472no—
186#392D4711yescharacteristic, complemented
187#380—472no—
188#380—471no—
189C47#261511yescharacteristic, complemented, Sylow
190C2×#41—948no—
191C2×#41—944no—
192C22×Q8—471no—
193C22×D4—471no—
194C22×D4—472no—
195C22×D4—471no—
196C22×D4—472no—
197C22×D4—471no—
198C22×D4C2×D4711yescharacteristic
199C22×D4C2×D4712yes—
200C23×C4—472no—
201C23×C4—471no—
202#121—944no—
203#121—948no—
204C2×C4⋊C4—471no—
205C2×C4⋊C4—472no—
206C2×C22⋊C4—472no—
207C2×C22⋊C4—472no—
208C2×C22⋊C4—471no—
209C2×C22⋊C4—472no—
210C2×C22⋊C4—472no—
211C2×C22⋊C4C2×D4711yescharacteristic
212C2×C22⋊C4C2×D4712yes—
213#95—472no—
214#95—472no—
215#95—471no—
216#95C2×D4711yescharacteristic
217C24—471no—
218C24—471no—
219C24C22×D4711yescharacteristic
220C24C22×D4712yes—
221#41—9432no—
222C2×Q8—944no—
223C2×Q8—942no—
224C2×D4—24no—
225C2×D4—24no—
226C2×D4—22no—
227C2×D4—42no—
228C2×D4—42no—
229C2×D4—942no—
230C2×D4—944no—
231C2×D4—942no—
232C2×D4—944no—
233C2×D4—944no—
234C2×D4—944no—
235C2×D4—942no—
236C2×D4—944no—
237C2×D4—1882no—
238C2×D4—1882no—
239C2×D4—1882no—
240C2×D4—1882no—
241C22×C4—471no—
242C22×C4—478no—
243C22×C4—472no—
244C22×C4—474no—
245C22×C4—472no—
246C22×C4—471no—
247C22×C4—944no—
248C22×C4—944no—
249C22×C4—944no—
250C22×C4C22×D4711yescharacteristic
251C22×C4C22×D4712yes—
252C22×C4C22×D4711yescharacteristic
253C4⋊C4—942no—
254C4⋊C4—944no—
255C22⋊C4—22no—
256C22⋊C4—42no—
257C22⋊C4—944no—
258C22⋊C4—944no—
259C22⋊C4—942no—
260C22⋊C4—1882no—
261C22⋊C4—1882no—
262C23—22no—
263C23—22no—
264C23—22no—
265C23—22no—
266C23—22no—
267C23—22no—
268C23—21no—
269C23—22no—
270C23—21no—
271C23—22no—
272C23—21no—
273C23—472no—
274C23—942no—
275C23—941no—
276C23—942no—
277C23—941no—
278C23—941no—
279C23—942no—
280C23—942no—
281C23—941no—
282C23—941no—
283C23D4×D4714yes—
284C23C23×D4711yescharacteristic
285Q8—948no—
286D4—28no—
287D4—48no—
288D4—9416no—
289D4—1884no—
290D4—1884no—
291D4—1888no—
292D4—1884no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—472no—
300C2×C4—474no—
301C2×C4—474no—
302C2×C4—948no—
303C2×C4—9416no—
304C2×C4—942no—
305C2×C4—942no—
306C2×C4—941no—
307C2×C4—942no—
308C2×C4—942no—
309C2×C4—942no—
310C2×C4—942no—
311C2×C4D4×D4712yes—
312C22—24no—
313C22—24no—
314C22—24no—
315C22—42no—
316C22—42no—
317C22—42no—
318C22—42no—
319C22—41no—
320C22—41no—
321C22—42no—
322C22—42no—
323C22—41no—
324C22—942no—
325C22—942no—
326C22—942no—
327C22—1881no—
328C22—1881no—
329C22—1882no—
330C22—1882no—
331C22—1881no—
332C22—1882no—
333C22—1882no—
334C22C2×D4×D4711yescharacteristic
335C22C2×D4×D4712yes—
336C22#1309406912yes—
337C22#1309406911yescharacteristic
338C22#1309407111yescharacteristic
339C4—22no—
340C4—41no—
341C4—42no—
342C4—474no—
343C4—944no—
344C4—1881no—
345C4—1882no—
346C2—44no—
347C2—81no—
348C2—3761no—
349C2—1882no—
350C2#120×D4711yescharacteristic
351C2#1568968611yescharacteristic
352C2#1568968812yes—
353C2#1568970012yes—
354C2#1568970211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#392C2
hypercenter#392D47
hypocenterC47#2615
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×#10625352C2semidirect
2. C2×#13093997C2semidirect
3. C2×#13093996C2semidirect
4. #15689036C2semidirect
5. #15689035C2semidirect
6. #15689032C2semidirect
7. #15689031C2semidirect
8. #15689031C2semidirect
9. #15688982C2semidirect
10. #15688981C2semidirect
11. C47×#392C2semidirect
63. C22×Dic47D4semidirect
72. C2×C4×D47D4semidirect
186. #392D47semidirect
189. C47#2615semidirect