Finite Group Databasebeta

← #20248351

Subgroups — #20248351

Order 6016.

724 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 724 conjugacy classes of subgroups — too many to draw. Only its 147 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×#13093997C212yesmaximal, complemented
2C2×#13093995C211yesmaximal, characteristic, complemented
3C2×#13093986C211yesmaximal, characteristic, complemented
4#15689053C211yesmaximal, characteristic, complemented
5#15689050C211yesmaximal, characteristic, complemented
6#15689031C211yesmaximal, characteristic, complemented
7#15689017C212yesmaximal, complemented
8#15688999C212yesmaximal, complemented
9#15688999C212yesmaximal, complemented
10#95×D47C211yesmaximal, characteristic, complemented
11C47×#394C211yesmaximal, characteristic, complemented
12C22×D188C2211yescharacteristic
13C22×C22⋊D47C2212yes—
14C22×C22⋊D47C2212yes—
15C22×C4×D47C2212yes—
16C22×C4×D47C2211yescharacteristic
17C22×C4×D47C2211yescharacteristic
18#13093997—28no—
19#13093995—24no—
20#13093986—24no—
21C2×C4⋊Dic47C2211yescharacteristic
22C2×Dic47⋊C4C2212yes—
23C2×C22⋊Dic47C2212yes—
24C2×C22⋊Dic47C2212yes—
25C2×(C2×D47)⋊C4C2211yescharacteristic
26C2×(C2×D47)⋊C4C2212yes—
27C2×(C2×D47)⋊C4C2211yescharacteristic
28C2×C4×Dic47C2211yescharacteristic
29C47⋊#95C2212yes—
30C47⋊#95C2211yescharacteristic
31C47⋊#95C2212yes—
32C47⋊#95C2212yes—
33C22×D4×C47C2211yescharacteristic
34C2×C4⋊C4×C47C2211yescharacteristic
35C2×C22⋊C4×C47C2212yes—
36C2×C22⋊C4×C47C2212yes—
37#95×C47C2211yescharacteristic
38C24×C47C2312yes—
39C23×D47C2311yescharacteristic
40C23×D47C2311yescharacteristic
41C2×D4×C47—22no—
42C2×D4×C47—42no—
43C22×C4×C47C2311yescharacteristic
44C22×C4×C47C2312yes—
45C22×C4×C47C2311yescharacteristic
46C22×C4×C47C2311yescharacteristic
47C2×C22⋊D47—24no—
48C2×C22⋊D47—24no—
49C2×C22⋊D47—24no—
50C2×C22⋊D47—24no—
51C2×C22⋊D47—24no—
52C2×C22⋊D47—42no—
53C22×Dic47C2311yescharacteristic
54C22×Dic47C2312yes—
55C22×Dic47C2311yescharacteristic
56C22×Dic47C2312yes—
57C2×D188—22no—
58C2×D188—22no—
59C2×D188D414yescomplemented
60C2×C4×D47—24no—
61C2×C4×D47—22no—
62C2×C4×D47—24no—
63C2×C4×D47—42no—
64C2×C4×D47—42no—
65C2×C4×D47—42no—
66C2×C4×D47D414yescomplemented
67C4⋊C4×C47—22no—
68C22⋊C4×C47—24no—
69C22⋊C4×C47—42no—
70C22⋊Dic47—24no—
71C22⋊Dic47—24no—
72(C2×D47)⋊C4—22no—
73(C2×D47)⋊C4—24no—
74(C2×D47)⋊C4—22no—
75C4⋊Dic47—22no—
76Dic47⋊C4—24no—
77C4×Dic47—22no—
78C23×C47—22no—
79C23×C47—22no—
80C23×C47—22no—
81C23×C47—22no—
82C23×C47—22no—
83C23×C47—22no—
84C23×C47—22no—
85C23×C47C2411yescharacteristic
86C22×D47—22no—
87C22×D47—22no—
88C22×D47—21no—
89C22×D47—21no—
90C22×D47—22no—
91C22×D47—22no—
92C22×D47C2×D412yes—
93C22×D47C2×D412yes—
94C22×D47C2×D412yes—
95C22×D47#4112yes—
96D4×C47—44no—
97C2×C4×C47—21no—
98C2×C4×C47—21no—
99C2×C4×C47—22no—
100C2×C4×C47—22no—
101C2×C4×C47—21no—
102C2×C4×C47—22no—
103C2×C4×C47—22no—
104C2×C4×C47—22no—
105C2×C4×C47C2×D412yes—
106C2×C4×C47C2×D412yes—
107C22⋊D47—48no—
108C22⋊D47—48no—
109C2×Dic47—22no—
110C2×Dic47—22no—
111C2×Dic47—22no—
112C2×Dic47—21no—
113C2×Dic47—22no—
114C2×Dic47—22no—
115C2×Dic47—22no—
116C2×Dic47—22no—
117C2×Dic47C2×D412yes—
118C2×Dic47#4114yes—
119D188—28no—
120C4×D47—44no—
121C4×D47—48no—
122C4×D47—44no—
123C22×C47—42no—
124C22×C47—42no—
125C22×C47—42no—
126C22×C47—42no—
127C22×C47—42no—
128C22×C47—42no—
129C22×C47—42no—
130C22×C47C22×D411yescharacteristic
131C22×C47C22×D411yescharacteristic
132C22×C47C2×#4111yescharacteristic
133C22×C47C2×#4112yes—
134C22×C47H(5,𝔽2)12yes—
135C2×D47—22no—
136C2×D47—22no—
137C2×D47—24no—
138C2×D47—24no—
139C2×D47—22no—
140C2×D47—24no—
141C2×D47—41no—
142C2×D47—41no—
143C2×D47—42no—
144C2×D47#12114yes—
145C4×C47—22no—
146C4×C47—22no—
147C4×C47—41no—
148C4×C47—42no—
149Dic47—22no—
150Dic47—24no—
151Dic47—42no—
152Dic47—41no—
153#2543—471nomaximal, Sylow
154C2×C47—82no—
155C2×C47C2×#12111yescharacteristic
156C2×C47#53211yescharacteristic
157C2×C47#53411yescharacteristic
158C2×C47#54612yes—
159C2×C47#55312yes—
160D47—24no—
161D47—42no—
162C2×#121—471no—
163C2×#121—472no—
164C2×C4×D4—471no—
165#398—471no—
166#397—471no—
167#394D4711yescharacteristic, complemented
168#392—471no—
169#388—472no—
170#386—472no—
171#386—472no—
172C2×#95—471no—
173C47#254311yescharacteristic, complemented, Sylow
174C22×D4—472no—
175C22×D4—472no—
176C22×D4—471no—
177C22×D4C2×D4711yescharacteristic
178C23×C4—471no—
179C23×C4—472no—
180C23×C4—471no—
181#121—948no—
182#121—944no—
183C4×D4—944no—
184C2×C4⋊C4—472no—
185C2×C4⋊C4—471no—
186C2×C4⋊C4C2×D4711yescharacteristic
187C2×C22⋊C4—472no—
188C2×C22⋊C4—472no—
189C2×C22⋊C4—471no—
190C2×C22⋊C4—471no—
191C2×C22⋊C4—472no—
192C2×C22⋊C4C2×D4712yes—
193C2×C22⋊C4C2×D4712yes—
194C2×C42—471no—
195#95—472no—
196#95—471no—
197#95—472no—
198#95—472no—
199#95C2×D4711yescharacteristic
200C24—471no—
201C24—471no—
202C24C22×D4712yes—
203C2×D4—22no—
204C2×D4—42no—
205C2×D4—474no—
206C2×D4—942no—
207C2×D4—942no—
208C2×D4—944no—
209C2×D4—944no—
210C2×D4—944no—
211C2×D4—944no—
212C2×D4—944no—
213C2×D4—1882no—
214C22×C4—472no—
215C22×C4—471no—
216C22×C4—474no—
217C22×C4—471no—
218C22×C4—472no—
219C22×C4—942no—
220C22×C4—944no—
221C22×C4—944no—
222C22×C4—1882no—
223C22×C4—1882no—
224C22×C4—1882no—
225C22×C4C22×D4712yes—
226C22×C4C22×D4711yescharacteristic
227C22×C4C22×D4711yescharacteristic
228C22×C4C22×D4711yescharacteristic
229C4⋊C4—22no—
230C4⋊C4—944no—
231C4⋊C4—942no—
232C22⋊C4—24no—
233C22⋊C4—42no—
234C22⋊C4—942no—
235C22⋊C4—944no—
236C22⋊C4—944no—
237C22⋊C4—944no—
238C22⋊C4—942no—
239C42—942no—
240C23—22no—
241C23—22no—
242C23—22no—
243C23—22no—
244C23—22no—
245C23—22no—
246C23—22no—
247C23—472no—
248C23—472no—
249C23—472no—
250C23—472no—
251C23—942no—
252C23—942no—
253C23—941no—
254C23—942no—
255C23—941no—
256C23—942no—
257C23C23×D4711yescharacteristic
258D4—44no—
259D4—948no—
260D4—1888no—
261D4—1888no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—472no—
271C2×C4—474no—
272C2×C4—942no—
273C2×C4—942no—
274C2×C4—942no—
275C2×C4—941no—
276C2×C4—942no—
277C2×C4—942no—
278C2×C4—942no—
279C2×C4—942no—
280C2×C4—1884no—
281C2×C4—1888no—
282C2×C4—1884no—
283C2×C4D4×D4712yes—
284C2×C4D4×D4712yes—
285C22—42no—
286C22—42no—
287C22—42no—
288C22—42no—
289C22—42no—
290C22—42no—
291C22—42no—
292C22—474no—
293C22—944no—
294C22—944no—
295C22—942no—
296C22—942no—
297C22—944no—
298C22—942no—
299C22—1882no—
300C22—1881no—
301C22—1881no—
302C22C2×D4×D4711yescharacteristic
303C22C2×D4×D4711yescharacteristic
304C22#41×D4712yes—
305C22#41×D4711yescharacteristic
306C22#1309406912yes—
307C4—22no—
308C4—22no—
309C4—42no—
310C4—41no—
311C4—944no—
312C4—942no—
313C4—1882no—
314C4—1881no—
315C2—82no—
316C2—944no—
317C2—1882no—
318C2#121×D4711yescharacteristic
319C2#1568967211yescharacteristic
320C2#1568968311yescharacteristic
321C2#1568977012yes—
322C2#1568981812yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#394C2
hypercenter#394D47
hypocenterC47#2543
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#13093997C2semidirect
2. C2×#13093995C2semidirect
3. C2×#13093986C2semidirect
4. #15689053C2semidirect
5. #15689050C2semidirect
6. #15689031C2semidirect
7. #15689017C2semidirect
8. #15688999C2semidirect
9. #15688999C2semidirect
10. #95×D47C2semidirect
11. C47×#394C2semidirect
59. C2×D188D4semidirect
66. C2×C4×D47D4semidirect
167. #394D47semidirect
173. C47#2543semidirect