Finite Group Databasebeta

← #20247003

Subgroups — #20247003

Order 6016.

952 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 952 conjugacy classes of subgroups — too many to draw. Only its 185 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×#13094013C211yesmaximal, characteristic, complemented
3C2×#13093998C211yesmaximal, characteristic, complemented
4#15689031C214yesmaximal, complemented
5#15689030C211yesmaximal, characteristic, complemented
6#15689026C211yesmaximal, characteristic, complemented
7#15689002C214yesmaximal, complemented
8C4×C22⋊Dic47C211yesmaximal, characteristic, complemented
9C22×#41×C47C211yesmaximal, characteristic, complemented
10C22×D188C2211yescharacteristic
11C22×C22⋊D47C2214yes—
12C22×C22⋊D47C2212yes—
13#13094020—24no—
14#13094013—24no—
15#13093998—24no—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×C22⋊Dic47C2212yes—
18C2×C22⋊Dic47C2214yes—
19C2×(C2×D47)⋊C4C2212yes—
20C2×(C2×D47)⋊C4C2214yes—
21C2×C4×Dic47C2211yescharacteristic
22C2×C4×Dic47C2211yescharacteristic
23C47⋊#95C2212yes—
24C47⋊#95C2214yes—
25C2×#41×C47—24no—
26C2×#41×C47—24no—
27C2×#41×C47—24no—
28C22×Q8×C47C2211yescharacteristic
29C22×D4×C47C2212yes—
30C22×D4×C47C2211yescharacteristic
31C23×C4×C47C2212yes—
32C23×C4×C47C2211yescharacteristic
33C24×C47C2311yescharacteristic
34C24×C47C2312yes—
35C23×D47C2312yes—
36#41×C47—232no—
37C2×Q8×C47—22no—
38C2×Q8×C47—22no—
39C2×Q8×C47D414yescomplemented
40C2×D4×C47—24no—
41C2×D4×C47—24no—
42C2×D4×C47—24no—
43C2×D4×C47—22no—
44C2×D4×C47—22no—
45C2×D4×C47D414yescomplemented
46C22×C4×C47—24no—
47C22×C4×C47—24no—
48C22×C4×C47—24no—
49C22×C4×C47—22no—
50C22×C4×C47—22no—
51C22×C4×C47D414yescomplemented
52C22×C4×C47C2311yescharacteristic
53C22×C4×C47C2312yes—
54C22×C4×C47C2311yescharacteristic
55C2×C22⋊D47—24no—
56C2×C22⋊D47—28no—
57C2×C22⋊D47—28no—
58C2×C22⋊D47—44no—
59C2×C22⋊D47—44no—
60C22×Dic47C2312yes—
61C22×Dic47C2312yes—
62C22×Dic47C2312yes—
63C2×D188—22no—
64C2×D188—22no—
65C2×D188—22no—
66C22⋊Dic47—24no—
67C22⋊Dic47—44no—
68(C2×D47)⋊C4—24no—
69(C2×D47)⋊C4—28no—
70C4⋊Dic47—22no—
71C4×Dic47—22no—
72C4×Dic47—22no—
73C23×C47—22no—
74C23×C47—21no—
75C23×C47—22no—
76C23×C47—21no—
77C23×C47—22no—
78C23×C47—24no—
79C23×C47—24no—
80C23×C47—22no—
81C23×C47C2×D414yes—
82C23×C47C2×D412yes—
83C23×C47C2411yescharacteristic
84C22×D47—22no—
85C22×D47—22no—
86C22×D47—22no—
87C22×D47—24no—
88C22×D47—24no—
89Q8×C47—28no—
90D4×C47—216no—
91D4×C47—28no—
92C2×C4×C47—216no—
93C2×C4×C47—21no—
94C2×C4×C47—21no—
95C2×C4×C47—22no—
96C2×C4×C47—22no—
97C2×C4×C47—28no—
98C2×C4×C47C2×D412yes—
99C2×C4×C47C2×D414yes—
100C2×C4×C47C2×D412yes—
101C2×C4×C47C2×D412yes—
102C2×C4×C47C2×D412yes—
103C22⋊D47—416no—
104C22⋊D47—48no—
105C2×Dic47—22no—
106C2×Dic47—22no—
107C2×Dic47—22no—
108C2×Dic47—22no—
109C2×Dic47—22no—
110C2×Dic47—22no—
111C2×Dic47—24no—
112C2×Dic47#4114yescomplemented
113D188—44no—
114C22×C47—24no—
115C22×C47—22no—
116C22×C47—22no—
117C22×C47—22no—
118C22×C47—28no—
119C22×C47—42no—
120C22×C47—42no—
121C22×C47—42no—
122C22×C47—42no—
123C22×C47—44no—
124C22×C47C22×D411yescharacteristic
125C22×C47C22×D411yescharacteristic
126C22×C47C22×D411yescharacteristic
127C22×C47C2×#4112yes—
128C22×C47H(5,𝔽2)12yes—
129C2×D47—42no—
130C2×D47—42no—
131C2×D47—42no—
132C2×D47—44no—
133C2×D47—44no—
134C4×C47—22no—
135C4×C47—24no—
136C4×C47#12014yes—
137Dic47—24no—
138Dic47—42no—
139Dic47—42no—
140#2431—471nomaximal, Sylow
141C2×C47—42no—
142C2×C47—44no—
143C2×C47C2×#12011yescharacteristic
144C2×C47#53211yescharacteristic
145C2×C47#53511yescharacteristic
146C2×C47#54612yes—
147C2×C47#55012yes—
148D47—82no—
149C22×#41D4711yescharacteristic, complemented
150C2×#127—471no—
151C2×#124—471no—
152C2×#121—471no—
153#392—474no—
154#391—471no—
155#390—471no—
156#386—474no—
157C4×C22⋊C4—471no—
158C47#243111yescharacteristic, complemented, Sylow
159C2×#41—24no—
160C2×#41—24no—
161C2×#41—24no—
162C22×Q8C2×D4711yescharacteristic
163C22×D4—474no—
164C22×D4—472no—
165C22×D4—471no—
166C22×D4C2×D4712yes—
167C22×D4C2×D4711yescharacteristic
168C23×C4C2×D4712yes—
169C23×C4C2×D4711yescharacteristic
170#127—944no—
171#124—944no—
172#121—944no—
173C2×C4⋊C4—471no—
174C2×C22⋊C4—472no—
175C2×C22⋊C4—472no—
176C2×C22⋊C4—474no—
177C2×C22⋊C4—474no—
178C2×C42—471no—
179C2×C42—471no—
180#95—472no—
181#95—474no—
182C24—472no—
183C24C22×D4711yescharacteristic
184C24C22×D4712yes—
185#41—232no—
186C2×Q8—22no—
187C2×Q8—22no—
188C2×Q8C22⋊D4714yescomplemented
189C2×D4—24no—
190C2×D4—24no—
191C2×D4—24no—
192C2×D4—22no—
193C2×D4—22no—
194C2×D4—948no—
195C2×D4—944no—
196C2×D4—948no—
197C2×D4—942no—
198C2×D4—942no—
199C2×D4—942no—
200C2×D4—1884no—
201C2×D4—1884no—
202C2×D4C22⋊D4714yescomplemented
203C22×C4—24no—
204C22×C4—24no—
205C22×C4—24no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—472no—
209C22×C4—472no—
210C22×C4—472no—
211C22×C4C22⋊D4714yescomplemented
212C22×C4C22×D4711yescharacteristic
213C22×C4C22×D4712yes—
214C22×C4C22×D4711yescharacteristic
215C4⋊C4—942no—
216C22⋊C4—944no—
217C22⋊C4—944no—
218C22⋊C4—948no—
219C22⋊C4—1884no—
220C42—942no—
221C42—942no—
222C23—21no—
223C23—22no—
224C23—21no—
225C23—22no—
226C23—22no—
227C23—24no—
228C23—24no—
229C23—22no—
230C23—942no—
231C23—942no—
232C23—942no—
233C23—944no—
234C23—944no—
235C23C2×C22⋊D4714yes—
236C23C2×C22⋊D4712yes—
237C23C23×D4711yescharacteristic
238Q8—28no—
239D4—216no—
240D4—28no—
241D4—18816no—
242D4—1888no—
243D4—1884no—
244C2×C4—216no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—28no—
250C2×C4—474no—
251C2×C4—942no—
252C2×C4—942no—
253C2×C4—942no—
254C2×C4—942no—
255C2×C4—942no—
256C2×C4—942no—
257C2×C4—944no—
258C2×C4C2×C22⋊D4712yes—
259C2×C4C2×C22⋊D4714yes—
260C2×C4C2×C22⋊D4712yes—
261C2×C4C2×C22⋊D4712yes—
262C2×C4C2×C22⋊D4712yes—
263C22—28no—
264C22—24no—
265C22—22no—
266C22—22no—
267C22—22no—
268C22—42no—
269C22—42no—
270C22—44no—
271C22—42no—
272C22—42no—
273C22—1884no—
274C22—1884no—
275C22—1882no—
276C22—1882no—
277C22—1882no—
278C22C22×C22⋊D4711yescharacteristic
279C22C22×C22⋊D4711yescharacteristic
280C22C22×C22⋊D4711yescharacteristic
281C22#41×D4712yes—
282C22#1309407012yes—
283C4—22no—
284C4—24no—
285C4—944no—
286C4—1882no—
287C4—1882no—
288C4#1309399314yes—
289C2—44no—
290C2—42no—
291C2—3762no—
292C2C2×#1309399311yescharacteristic
293C2#1568966911yescharacteristic
294C2#1568968711yescharacteristic
295C2#1568976112yes—
296C2#1568979212yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC22×#41×C47C2
hypercenterC22×#41D47
hypocenterC47#2431
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#13094020C2semidirect
2. C2×#13094013C2semidirect
3. C2×#13093998C2semidirect
4. #15689031C2semidirect
5. #15689030C2semidirect
6. #15689026C2semidirect
7. #15689002C2semidirect
8. C4×C22⋊Dic47C2semidirect
9. C22×#41×C47C2semidirect
39. C2×Q8×C47D4semidirect
45. C2×D4×C47D4semidirect
51. C22×C4×C47D4semidirect
112. C2×Dic47#41semidirect
149. C22×#41D47semidirect
158. C47#2431semidirect
188. C2×Q8C22⋊D47semidirect
202. C2×D4C22⋊D47semidirect
211. C22×C4C22⋊D47semidirect