Finite Group Databasebeta

← C4⋊C4×C22⋊D47 #20246287

Subgroups — C4⋊C4×C22⋊D47 #20246287

Order 6016.

776 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊D47C212yesmaximal
2C2×C4×C22⋊D47C211yesmaximal, characteristic
3C2×C4⋊C4×D47C211yesmaximal, characteristic, complemented
4#15689018C212yesmaximal, complemented
5#15688996C212yesmaximal, complemented
6#15688994C212yesmaximal, complemented
7#15688992C211yesmaximal, characteristic, complemented
8#15688983C211yesmaximal, characteristic, complemented
9#15688980C211yesmaximal, characteristic, complemented
10C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
11C22×C4⋊C4×C47C211yesmaximal, characteristic, complemented
12C22×C22⋊D47C2211yescharacteristic
13C22×C4×D47C2212yes—
14C22×C4×D47C2211yescharacteristic
15C4×C22⋊D47—28no—
16C4×C22⋊D47C418yescomplemented
17C2×C4⋊Dic47C2211yescharacteristic
18C2×C4⋊Dic47C2211yescharacteristic
19C2×Dic47⋊C4C2212yes—
20C2×Dic47⋊C4C2212yes—
21C2×Dic47⋊C4C2212yes—
22C2×Dic47⋊C4C2211yescharacteristic
23C4⋊C4×D47—24no—
24C2×C22⋊Dic47C2212yes—
25C2×C22⋊Dic47C2211yescharacteristic
26C2×(C2×D47)⋊C4C2212yes—
27C2×(C2×D47)⋊C4C2211yescharacteristic
28C2×C4×Dic47C2212yes—
29C2×C4×Dic47C2211yescharacteristic
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C47⋊#95C2212yes—
33C23×C4×C47C2212yes—
34C23×C4×C47C2211yescharacteristic
35C2×C4⋊C4×C47—24no—
36C2×C4⋊C4×C47C2211yescharacteristic
37C2×C4⋊C4×C47C2212yes—
38C2×C4⋊C4×C47C2211yescharacteristic
39C24×C47C2311yescharacteristic
40C23×D47C2311yescharacteristic
41C22×C4×C47—22no—
42C22×C4×C47—22no—
43C22×C4×C47—24no—
44C22×C4×C47—24no—
45C22×C4×C47—42no—
46C22×C4×C47C2×C414yescomplemented
47C22×C4×C47C2312yes—
48C22×C4×C47C2311yescharacteristic
49C22×C4×C47C2312yes—
50C22×C4×C47C2311yescharacteristic
51C2×C22⋊D47C2×C414yes—
52C2×C22⋊D47D414yes—
53C2×C22⋊D47Q814yes—
54C22×Dic47C2312yes—
55C22×Dic47C2312yes—
56C22×Dic47C2311yescharacteristic
57C22×Dic47C2311yescharacteristic
58C22×Dic47C2311yescharacteristic
59C2×C4×D47—22no—
60C2×C4×D47—22no—
61C2×C4×D47—24no—
62C2×C4×D47—24no—
63C2×C4×D47—42no—
64C2×C4×D47C2×C414yescomplemented
65C4⋊C4×C47—24no—
66C4⋊C4×C47—22no—
67C4⋊C4×C47D414yescomplemented
68C22⋊Dic47—24no—
69C22⋊Dic47C2×C414yescomplemented
70(C2×D47)⋊C4—24no—
71(C2×D47)⋊C4C2×C414yescomplemented
72C4⋊Dic47—22no—
73C4⋊Dic47—22no—
74Dic47⋊C4—24no—
75Dic47⋊C4—24no—
76Dic47⋊C4—42no—
77Dic47⋊C4C2×C414yescomplemented
78C4×Dic47—24no—
79C4×Dic47C2×C414yescomplemented
80C23×C47—21no—
81C23×C47—21no—
82C23×C47—21no—
83C23×C47—21no—
84C23×C47C22×C412yes—
85C23×C47C2×D412yes—
86C23×C47C2×Q812yes—
87C23×C47C2411yescharacteristic
88C22×D47—21no—
89C22×D47—21no—
90C22×D47—21no—
91C22×D47—21no—
92C22×D47C22×C412yes—
93C22×D47C2×D412yes—
94C22×D47C2×Q812yes—
95C2×C4×C47—22no—
96C2×C4×C47—21no—
97C2×C4×C47—21no—
98C2×C4×C47—22no—
99C2×C4×C47—28no—
100C2×C4×C47—22no—
101C2×C4×C47—22no—
102C2×C4×C47—22no—
103C2×C4×C47—48no—
104C2×C4×C47C22×C412yes—
105C2×C4×C47C22×C412yes—
106C2×C4×C47C2×D414yes—
107C2×C4×C47C2×D412yes—
108C2×C4×C47#4112yes—
109C22⋊D47C4⋊C4116yesdirect product factor
110C2×Dic47—21no—
111C2×Dic47—21no—
112C2×Dic47—21no—
113C2×Dic47—21no—
114C2×Dic47—22no—
115C2×Dic47—22no—
116C2×Dic47—22no—
117C2×Dic47—22no—
118C2×Dic47—22no—
119C2×Dic47—22no—
120C2×Dic47C22×C412yes—
121C2×Dic47C22×C412yes—
122C2×Dic47C22×C412yes—
123C2×Dic47C2×D412yes—
124C2×Dic47C2×Q812yes—
125C4×D47—28no—
126C4×D47—48no—
127C22×C47—22no—
128C22×C47—22no—
129C22×C47—22no—
130C22×C47—22no—
131C22×C47—22no—
132C22×C47—22no—
133C22×C47C2×C4⋊C414yescomplemented
134C22×C47C23×C411yescharacteristic
135C22×C47C22×D411yescharacteristic
136C22×C47C22×D411yescharacteristic
137C22×C47C22×Q811yescharacteristic
138C22×C47C2×#4111yescharacteristic
139C22×C47H(5,𝔽2)11yescharacteristic
140C22×C472−1+411yescharacteristic
141C2×D47—22no—
142C2×D47—22no—
143C2×D47—22no—
144C2×D47—22no—
145C2×D47—22no—
146C2×D47—22no—
147C2×D47C2×C4⋊C414yescomplemented
148C4×C47—22no—
149C4×C47—24no—
150C4×C47—42no—
151C4×C47C4×D414yescomplemented
152Dic47—22no—
153Dic47—22no—
154Dic47—42no—
155Dic47—42no—
156Dic47C2×C4⋊C414yescomplemented
157D4×C4⋊C4—471nomaximal, Sylow
158C2×C47—24no—
159C2×C47C22×C4⋊C411yescharacteristic
160C2×C47C2×C4×D411yescharacteristic
161C2×C47#52011yescharacteristic
162C2×C47D4211yescharacteristic
163C2×C47#54711yescharacteristic
164C2×C47D4×Q811yescharacteristic
165C2×C47#55411yescharacteristic
166D47—24no—
167C2×C4×D4—471no—
168C2×C4×D4—472no—
169C22×C4⋊C4—471no—
170C22×C4⋊C4D4711yescharacteristic, complemented
171#389—472no—
172#385—472no—
173#385—472no—
174#384—471no—
175#380—471no—
176#380—471no—
177C4×C4⋊C4—471no—
178C47D4×C4⋊C411yescharacteristic, complemented, Sylow
179C22×D4—471no—
180C23×C4—471no—
181C23×C4—472no—
182C23×C4C2×D4712yes—
183C23×C4C2×D4711yescharacteristic
184C4×D4—478no—
185C4×D4—948no—
186C2×C4⋊C4—24no—
187C2×C4⋊C4—471no—
188C2×C4⋊C4—472no—
189C2×C4⋊C4—471no—
190C2×C4⋊C4—472no—
191C2×C4⋊C4—471no—
192C2×C4⋊C4—472no—
193C2×C4⋊C4—944no—
194C2×C4⋊C4C2×D4711yescharacteristic
195C2×C4⋊C4C2×D4712yes—
196C2×C4⋊C4C2×D4711yescharacteristic
197C2×C22⋊C4—471no—
198C2×C22⋊C4—471no—
199C2×C22⋊C4—472no—
200C2×C22⋊C4—472no—
201C2×C42—471no—
202C2×C42—472no—
203#95—472no—
204#95—472no—
205#95—472no—
206C24—471no—
207C24C22×D4711yescharacteristic
208C2×D4—474no—
209C2×D4—474no—
210C2×D4—474no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—24no—
214C22×C4—24no—
215C22×C4—42no—
216C22×C4—471no—
217C22×C4—471no—
218C22×C4—471no—
219C22×C4—474no—
220C22×C4—472no—
221C22×C4—472no—
222C22×C4—944no—
223C22×C4—942no—
224C22×C4—942no—
225C22×C4—944no—
226C22×C4—1882no—
227C22×C4C4×D4714yescomplemented
228C22×C4C22×D4712yes—
229C22×C4C22×D4711yescharacteristic
230C22×C4C22×D4712yes—
231C22×C4C22×D4711yescharacteristic
232C4⋊C4—24no—
233C4⋊C4—22no—
234C4⋊C4—474no—
235C4⋊C4—944no—
236C4⋊C4—942no—
237C4⋊C4—944no—
238C4⋊C4—942no—
239C4⋊C4—1882no—
240C4⋊C4C22⋊D4714yesdirect product factor
241C22⋊C4—474no—
242C22⋊C4—474no—
243C22⋊C4—944no—
244C22⋊C4—944no—
245C42—474no—
246C42—944no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23—21no—
251C23—472no—
252C23—472no—
253C23—472no—
254C23—941no—
255C23—941no—
256C23—941no—
257C23—941no—
258C23C2×C4×D4712yes—
259C23D4×D4712yes—
260C23Q8×D4712yes—
261C23C23×D4711yescharacteristic
262D4—4716no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—28no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—48no—
272C2×C4—472no—
273C2×C4—472no—
274C2×C4—472no—
275C2×C4—472no—
276C2×C4—472no—
277C2×C4—941no—
278C2×C4—941no—
279C2×C4—941no—
280C2×C4—941no—
281C2×C4—948no—
282C2×C4—942no—
283C2×C4—942no—
284C2×C4—942no—
285C2×C4—942no—
286C2×C4—942no—
287C2×C4—942no—
288C2×C4—1888no—
289C2×C4C2×C4×D4712yes—
290C2×C4C2×C4×D4712yes—
291C2×C4#1062535012yes—
292C2×C4C2×C22⋊D4714yes—
293C2×C4C2×C22⋊D4712yes—
294C22—22no—
295C22—22no—
296C22—22no—
297C22—22no—
298C22—22no—
299C22—22no—
300C22—474no—
301C22—942no—
302C22—942no—
303C22—942no—
304C22—942no—
305C22—942no—
306C22—942no—
307C22C4⋊C4×D4714yescomplemented
308C22C22×C4×D4711yescharacteristic
309C22C2×D4×D4711yescharacteristic
310C22C22×C22⋊D4711yescharacteristic
311C22C2×Q8×D4711yescharacteristic
312C22C2×#1062535011yescharacteristic
313C22#1309406911yescharacteristic
314C22#1309407211yescharacteristic
315C4—24no—
316C4—22no—
317C4—42no—
318C4—474no—
319C4—942no—
320C4—942no—
321C4—1882no—
322C4—1882no—
323C4C4×C22⋊D4714yescomplemented
324C2—24no—
325C2—944no—
326C2C2×C4⋊C4×D4711yescharacteristic
327C2C2×C4×C22⋊D4711yescharacteristic
328C2#1568960411yescharacteristic
329C2D4×C22⋊D4711yescharacteristic
330C2#1568977411yescharacteristic
331C2Q8×C22⋊D4711yescharacteristic
332C2#1568982811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC22×C4⋊C4×C47C2
socleC23×C47C24
hypercenterC22×C4⋊C4D47
hypocenterC47D4×C4⋊C4
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×D47C2semidirect
4. #15689018C2semidirect
5. #15688996C2semidirect
6. #15688994C2semidirect
7. #15688992C2semidirect
8. #15688983C2semidirect
9. #15688980C2semidirect
10. C4⋊C4×Dic47C2semidirect
11. C22×C4⋊C4×C47C2semidirect
16. C4×C22⋊D47C4semidirect
46. C22×C4×C47C2×C4semidirect
64. C2×C4×D47C2×C4semidirect
67. C4⋊C4×C47D4semidirect
69. C22⋊Dic47C2×C4semidirect
71. (C2×D47)⋊C4C2×C4semidirect
77. Dic47⋊C4C2×C4semidirect
79. C4×Dic47C2×C4semidirect
109. C22⋊D47C4⋊C4direct (N × H)
133. C22×C47C2×C4⋊C4semidirect
147. C2×D47C2×C4⋊C4semidirect
151. C4×C47C4×D4semidirect
156. Dic47C2×C4⋊C4semidirect
170. C22×C4⋊C4D47semidirect
178. C47D4×C4⋊C4semidirect
227. C22×C4C4×D47semidirect
240. C4⋊C4C22⋊D47direct (N × H)
307. C22C4⋊C4×D47semidirect
323. C4C4×C22⋊D47semidirect