Finite Group Databasebeta

← #20246720

Subgroups — #20246720

Order 6016.

864 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10625352C211yesmaximal, characteristic
2C2×#13094007C211yesmaximal, characteristic, complemented
3C22×Dic47⋊C4C211yesmaximal, characteristic, complemented
4#15689043C212yesmaximal, complemented
5#15689038C212yesmaximal, complemented
6#15689003C211yesmaximal, characteristic, complemented
7#15689000C211yesmaximal, characteristic, complemented
8#15688995C212yesmaximal, complemented
9#15688994C212yesmaximal, complemented
10#15688984C211yesmaximal, characteristic, complemented
11C2×#123×C47C211yesmaximal, characteristic, complemented
12C2×#10625352—24no—
13C2×#10625352—24no—
14C2×#10625352—24no—
15C22×Dic94C2211yescharacteristic
16C22×C22⋊D47C2211yescharacteristic
17C22×C22⋊D47C2211yescharacteristic
18C23×Dic47C2211yescharacteristic
19C23×Dic47C2211yescharacteristic
20C23×Dic47C2211yescharacteristic
21C22×C4×D47C2211yescharacteristic
22#13094007—24no—
23C2×Dic47⋊C4—24no—
24C2×Dic47⋊C4C2212yes—
25C2×Dic47⋊C4C2212yes—
26C2×Dic47⋊C4C2212yes—
27C2×C22⋊Dic47C2211yescharacteristic
28C2×C22⋊Dic47C2212yes—
29C2×(C2×D47)⋊C4C2212yes—
30C2×(C2×D47)⋊C4C2212yes—
31C47⋊#95C2212yes—
32C47⋊#95C2212yes—
33C47⋊#95C2212yes—
34C47⋊#95C2212yes—
35C22×D4×C47C2211yescharacteristic
36C23×C4×C47C2211yescharacteristic
37#123×C47—24no—
38C2×C4⋊C4×C47C2212yes—
39C2×C22⋊C4×C47C2211yescharacteristic
40C2×C22⋊C4×C47C2212yes—
41C24×C47C2311yescharacteristic
42C24×C47C2311yescharacteristic
43C23×D47C2311yescharacteristic
44C2×D4×C47—22no—
45C2×D4×C47—22no—
46C2×D4×C47D414yes—
47C22×C4×C47—22no—
48C22×C4×C47—22no—
49C22×C4×C47—22no—
50C22×C4×C47C2312yes—
51C22×C4×C47C2312yes—
52C22×C4×C47C2311yescharacteristic
53C2×C22⋊D47—22no—
54C2×C22⋊D47—22no—
55C2×C22⋊D47—22no—
56C2×C22⋊D47—22no—
57C2×C22⋊D47—22no—
58C2×C22⋊D47D414yes—
59C22×Dic47—22no—
60C22×Dic47—22no—
61C22×Dic47—22no—
62C22×Dic47—22no—
63C22×Dic47—22no—
64C22×Dic47—22no—
65C22×Dic47—24no—
66C22×Dic47D414yes—
67C22×Dic47C2312yes—
68C22×Dic47C2311yescharacteristic
69C22×Dic47C2311yescharacteristic
70C22×Dic47C2311yescharacteristic
71C22×Dic47C2312yes—
72#10625352—232no—
73C2×C4×D47—22no—
74C2×C4×D47—22no—
75C2×C4×D47—22no—
76C2×Dic94—22no—
77C2×Dic94—22no—
78C2×Dic94—22no—
79C4⋊C4×C47—24no—
80C22⋊C4×C47—22no—
81C22⋊C4×C47—24no—
82C22⋊Dic47—22no—
83C22⋊Dic47—24no—
84(C2×D47)⋊C4—24no—
85(C2×D47)⋊C4—24no—
86Dic47⋊C4—24no—
87Dic47⋊C4—24no—
88Dic47⋊C4—24no—
89C23×C47—22no—
90C23×C47—22no—
91C23×C47—21no—
92C23×C47—21no—
93C23×C47—22no—
94C23×C47—22no—
95C23×C47C2×D412yes—
96C23×C47C2×D412yes—
97C23×C47C2×D412yes—
98C23×C47C2×D412yes—
99C23×C47C2411yescharacteristic
100C22×D47—21no—
101C22×D47—21no—
102C22×D47—22no—
103C22×D47—22no—
104C22×D47C2×D412yes—
105D4×C47—28no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—22no—
109C2×C4×C47—22no—
110C2×C4×C47—22no—
111C2×C4×C47—22no—
112C2×C4×C47—22no—
113C2×C4×C47—22no—
114C2×C4×C47—44no—
115C2×C4×C47C2×D412yes—
116C22⋊D47—28no—
117C22⋊D47—28no—
118C2×Dic47—28no—
119C2×Dic47—28no—
120C2×Dic47—28no—
121C2×Dic47—22no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—22no—
129C2×Dic47—22no—
130C2×Dic47—22no—
131C2×Dic47—22no—
132C2×Dic47C2×D412yes—
133C2×Dic47C2×D412yes—
134C2×Dic47C2×D412yes—
135C2×Dic47#4114yescomplemented
136C4×D47—28no—
137Dic94—28no—
138C22×C47—22no—
139C22×C47—22no—
140C22×C47—24no—
141C22×C47—24no—
142C22×C47—22no—
143C22×C47—24no—
144C22×C47—41no—
145C22×C47—41no—
146C22×C47—42no—
147C22×C47#12014yes—
148C22×C47C22×D411yescharacteristic
149C22×C47C22×D411yescharacteristic
150C22×C47C22×D411yescharacteristic
151C22×C47C2×#4112yes—
152C22×C472−1+412yes—
153C2×D47—22no—
154C2×D47—24no—
155C2×D47—41no—
156C2×D47—41no—
157C2×D47—42no—
158C4×C47—22no—
159C4×C47—42no—
160C4×C47—42no—
161Dic47—22no—
162Dic47—22no—
163Dic47—22no—
164Dic47—24no—
165Dic47—42no—
166#2406—471nomaximal, Sylow
167C2×C47—24no—
168C2×C47—42no—
169C2×C47C2×#12011yescharacteristic
170C2×C47#52511yescharacteristic
171C2×C47#53611yescharacteristic
172C2×C47#54712yes—
173C2×C47#54712yes—
174D47—42no—
175C22×#41—471no—
176C2×#123—471no—
177C2×#123D4711yescharacteristic, complemented
178C22×C4⋊C4—471no—
179#395—472no—
180#394—472no—
181#386—471no—
182#386—471no—
183#385—472no—
184#385—472no—
185#381—471no—
186C47#240611yescharacteristic, complemented, Sylow
187C2×#41—944no—
188C2×#41—944no—
189C2×#41—944no—
190C22×Q8—471no—
191C22×D4—471no—
192C22×D4—471no—
193C22×D4C2×D4711yescharacteristic
194C23×C4—471no—
195C23×C4—471no—
196C23×C4—471no—
197C23×C4—471no—
198C23×C4C2×D4711yescharacteristic
199#123—24no—
200#123—944no—
201C2×C4⋊C4—472no—
202C2×C4⋊C4—472no—
203C2×C4⋊C4—472no—
204C2×C4⋊C4—944no—
205C2×C4⋊C4C2×D4712yes—
206C2×C22⋊C4—471no—
207C2×C22⋊C4—472no—
208C2×C22⋊C4—472no—
209C2×C22⋊C4—472no—
210C2×C22⋊C4C2×D4711yescharacteristic
211C2×C22⋊C4C2×D4712yes—
212#95—472no—
213#95—472no—
214#95—472no—
215#95—472no—
216C24—471no—
217C24C22×D4711yescharacteristic
218C24C22×D4711yescharacteristic
219#41—9432no—
220C2×Q8—942no—
221C2×Q8—942no—
222C2×Q8—942no—
223C2×D4—22no—
224C2×D4—22no—
225C2×D4—474no—
226C2×D4—942no—
227C2×D4—942no—
228C2×D4—942no—
229C2×D4—942no—
230C2×D4—942no—
231C2×D4C22⋊D4714yes—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—474no—
236C22×C4—472no—
237C22×C4—471no—
238C22×C4—471no—
239C22×C4—471no—
240C22×C4—472no—
241C22×C4—942no—
242C22×C4—942no—
243C22×C4—944no—
244C22×C4—942no—
245C22×C4—942no—
246C22×C4—942no—
247C22×C4—942no—
248C22×C4—942no—
249C22×C4—942no—
250C22×C4—942no—
251C22×C4C22×D4712yes—
252C22×C4C22×D4712yes—
253C22×C4C22×D4711yescharacteristic
254C4⋊C4—24no—
255C4⋊C4—944no—
256C4⋊C4—944no—
257C4⋊C4—944no—
258C22⋊C4—22no—
259C22⋊C4—24no—
260C22⋊C4—944no—
261C22⋊C4—944no—
262C22⋊C4—944no—
263C22⋊C4—942no—
264C23—22no—
265C23—22no—
266C23—21no—
267C23—21no—
268C23—22no—
269C23—22no—
270C23—472no—
271C23—941no—
272C23—941no—
273C23—942no—
274C23—942no—
275C23D4×D4712yes—
276C23D4×D4712yes—
277C23C2×C22⋊D4712yes—
278C23C2×C22⋊D4712yes—
279C23C23×D4711yescharacteristic
280Q8—948no—
281D4—28no—
282D4—948no—
283D4—948no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—44no—
293C2×C4—472no—
294C2×C4—472no—
295C2×C4—472no—
296C2×C4—474no—
297C2×C4—948no—
298C2×C4—948no—
299C2×C4—948no—
300C2×C4—948no—
301C2×C4—942no—
302C2×C4—941no—
303C2×C4—941no—
304C2×C4—941no—
305C2×C4—941no—
306C2×C4—941no—
307C2×C4—941no—
308C2×C4—942no—
309C2×C4—942no—
310C2×C4—942no—
311C2×C4—942no—
312C2×C4C2×C22⋊D4712yes—
313C22—24no—
314C22—24no—
315C22—22no—
316C22—22no—
317C22—24no—
318C22—22no—
319C22—42no—
320C22—41no—
321C22—41no—
322C22—944no—
323C22—942no—
324C22—1882no—
325C22—1881no—
326C22—1881no—
327C22#1309399214yes—
328C22C2×D4×D4711yescharacteristic
329C22C2×D4×D4711yescharacteristic
330C22C22×C22⋊D4711yescharacteristic
331C22#41×D4712yes—
332C22#1309407112yes—
333C4—22no—
334C4—42no—
335C4—42no—
336C4—942no—
337C4—942no—
338C4—942no—
339C4—944no—
340C4—1882no—
341C2—24no—
342C2—42no—
343C2—1882no—
344C2C2×#1309399211yescharacteristic
345C2#1568963111yescharacteristic
346C2#1568969511yescharacteristic
347C2#1568977112yes—
348C2#1568977212yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#123×C47C2
hypercenterC2×#123D47
hypocenterC47#2406
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
2. C2×#13094007C2semidirect
3. C22×Dic47⋊C4C2semidirect
4. #15689043C2semidirect
5. #15689038C2semidirect
6. #15689003C2semidirect
7. #15689000C2semidirect
8. #15688995C2semidirect
9. #15688994C2semidirect
10. #15688984C2semidirect
11. C2×#123×C47C2semidirect
135. C2×Dic47#41semidirect
177. C2×#123D47semidirect
186. C47#2406semidirect