Finite Group Databasebeta

← C4×#13094056 #20252208

Subgroups — C4×#13094056 #20252208

Order 6016.

484 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094056C211yesmaximal, characteristic
2C4×#10625354C211yesmaximal, characteristic
3C4×Q8×D47C211yesmaximal, characteristic, complemented
4#15689230C211yesmaximal, characteristic, complemented
5#15689227C211yesmaximal, characteristic, complemented
6#15689226C211yesmaximal, characteristic, complemented
7#15689222C211yesmaximal, characteristic, complemented
8C4×#10625337C211yesmaximal, characteristic, complemented
9C4×#10625325C211yesmaximal, characteristic, complemented
10C4×#10625336C211yesmaximal, characteristic, complemented
11#15689164C211yesmaximal, characteristic, complemented
12#15689130C211yesmaximal, characteristic, complemented
13#15689123C211yesmaximal, characteristic
14C4×#10625324C211yesmaximal, characteristic, complemented
15C4×Q16×C47C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×Q8×D47C2211yescharacteristic
18#13094056C418yesdirect product factor
19C2×#10625337C2211yescharacteristic
20C2×#10625325C2211yescharacteristic
21C2×#10625336C2211yescharacteristic
22C2×#10625324C2211yescharacteristic
23C2×#10625324C2211yescharacteristic
24Q8×Dic47C2211yescharacteristic
25Q8×Dic47C2211yescharacteristic
26C4×Dic94—21no—
27C4×Dic94C2211yescharacteristic
28#13093989—21no—
29#13093989C2211yescharacteristic
30C4×D188—21no—
31C4×D188C2211yescharacteristic
32#13093986—21no—
33#13093986C2211yescharacteristic
34#13093982—21no—
35#13093982C2211yescharacteristic
36C4⋊C4×D47—21no—
37C4⋊C4×D47C2211yescharacteristic
38C42×D47—21no—
39C42×D47—21no—
40C42×D47C2211yescharacteristic
41#13093957C2211yescharacteristic
42#13093956C2211yescharacteristic
43#13093955C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093947C2211yescharacteristic
48#13093946C2211yescharacteristic
49#13093944C2211yescharacteristic
50#13093934C2211yescharacteristic
51#13093934C2211yescharacteristic
52C4×C47⋊C8C2211yescharacteristic
53C2×Q16×C47C2211yescharacteristic
54C4×Q8×C47C2211yescharacteristic
55C4×Q8×C47C2211yescharacteristic
56#107×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#103×C47C2211yescharacteristic
59C4×C8×C47C2211yescharacteristic
60C2×Q8×C47C2311yescharacteristic
61C2×Q8×C47C2311yescharacteristic
62#10625354—22no—
63#10625354C2×C414yes—
64Q8×D47—22no—
65Q8×D47C2×C414yescomplemented
66C2×D188—21no—
67C2×D188C2311yescharacteristic
68C2×C4×D47—21no—
69C2×C4×D47—21no—
70C2×C4×D47—21no—
71C2×C4×D47—21no—
72C2×C4×D47—21no—
73C2×C4×D47D411yescharacteristic
74C2×C4×D47D411yescharacteristic
75C2×C4×D47C2311yescharacteristic
76C2×Dic94—21no—
77C2×Dic94C2311yescharacteristic
78Q16×C47C2×C414yescomplemented
79C2×C8×C47C2311yescharacteristic
80C2×C8×C47C2311yescharacteristic
81C4⋊C4×C47—21no—
82C4⋊C4×C47—21no—
83C4⋊C4×C47C2311yescharacteristic
84C4⋊C4×C47C2311yescharacteristic
85C42×C47—21no—
86C42×C47—21no—
87C42×C47C2311yescharacteristic
88#10625337C2×C414yescomplemented
89#10625336C2×C414yescomplemented
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93C4⋊Dic47—21no—
94C4⋊Dic47—21no—
95C4⋊Dic47C2311yescharacteristic
96C4⋊Dic47C2311yescharacteristic
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100C4×Dic47—21no—
101C4×Dic47—21no—
102C4×Dic47—21no—
103C4×Dic47—21no—
104C4×Dic47—21no—
105C4×Dic47D411yescharacteristic
106C4×Dic47D411yescharacteristic
107C4×Dic47C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110#10625325C2×C414yescomplemented
111#10625324—22no—
112#10625324C2×C414yescomplemented
113C22×D47—21no—
114C22×D47C2×D411yescharacteristic
115Q8×C47—21no—
116Q8×C47—21no—
117Q8×C47C22×C412yes—
118Q8×C47C22×C412yes—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2411yescharacteristic
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47C2×D411yescharacteristic
130C2×Dic47C2×D411yescharacteristic
131C2×Dic47C2×D411yescharacteristic
132D188—24no—
133D188—21no—
134D188C22×C412yes—
135C4×D47—24no—
136C4×D47—22no—
137C4×D47—24no—
138C4×D47—41no—
139C4×D47—42no—
140C4×D47—42no—
141C4×D47—42no—
142C4×D47C22×C412yes—
143C4×D47#4112yes—
144Dic94—21no—
145Dic94—24no—
146Dic94C22×C412yes—
147C8×C47—21no—
148C8×C47C22×C412yes—
149C47⋊C8—21no—
150C47⋊C8C22×C412yes—
151C22×C47C22×D411yescharacteristic
152C2×D47—21no—
153C2×D47—21no—
154C2×D47—22no—
155C2×D47—41no—
156C2×D47—41no—
157C2×D47C4×D412yes—
158C4×C47—22no—
159C4×C47—22no—
160C4×C47—21no—
161C4×C47—41no—
162C4×C47—41no—
163C4×C47#13712yescomplemented
164C4×C47C23×C411yescharacteristic
165C4×C47C2×#4111yescharacteristic
166Dic47—22no—
167Dic47—21no—
168Dic47—21no—
169Dic47—41no—
170Dic47—41no—
171Dic47C4×D412yes—
172C4×#137—471nomaximal, Sylow
173C2×C47C2×C4×D411yescharacteristic
174C2×C47C2×#13711yescharacteristic
175C2×C47#57511yescharacteristic
176D47—22no—
177D47—42no—
178C2×#137—471no—
179C4×#41—471no—
180C2×C4×Q8—471no—
181#441—471no—
182#441—471no—
183#440—471no—
184#440—471no—
185C4×Q16—471no—
186C4×Q16D4711yescharacteristic, complemented
187C4×SD16—471no—
188C4×SD16—471no—
189#428—471no—
190#419—471no—
191#417—471no—
192C4×M16—471no—
193C47C4×#13711yescharacteristic, complemented, Sylow
194C2×#41—471no—
195C22×Q8—471no—
196#137—478no—
197C2×Q16—471no—
198C2×Q16C2×D4711yescharacteristic
199C2×SD16—471no—
200C2×SD16—471no—
201C2×M16—471no—
202C2×M16—471no—
203C4×Q8—471no—
204C4×Q8—471no—
205C4×Q8—471no—
206C4×Q8—471no—
207C4×Q8—941no—
208C4×Q8—941no—
209C4×Q8C2×D4711yescharacteristic
210C4×Q8C2×D4711yescharacteristic
211C4×D4—471no—
212C4×D4—471no—
213C4×D4—941no—
214C4×D4—941no—
215#117—471no—
216#117—941no—
217C2×C4⋊C4—471no—
218C2×C4⋊C4—941no—
219C2×C42—471no—
220C2×C42—941no—
221C2×C42—941no—
222#107—471no—
223#107C2×D4711yescharacteristic
224#106—471no—
225#106—471no—
226#103—471no—
227#103—471no—
228#103—471no—
229#103—471no—
230#103C2×D4711yescharacteristic
231#103C2×D4711yescharacteristic
232#102—471no—
233#102—471no—
234#97—471no—
235#97—471no—
236C4×C8—471no—
237C4×C8C2×D4711yescharacteristic
238#41—474no—
239#41—942no—
240C2×Q8—474no—
241C2×Q8—471no—
242C2×Q8—941no—
243C2×Q8—942no—
244C2×Q8C22×D4711yescharacteristic
245C2×Q8C22×D4711yescharacteristic
246C2×D4—471no—
247C2×D4—941no—
248C22×C4—471no—
249C22×C4—471no—
250C22×C4—471no—
251C22×C4—941no—
252C22×C4—941no—
253C22×C4—941no—
254C22×C4—941no—
255C22×C4—941no—
256Q16—474no—
257Q16C4×D4714yescomplemented
258SD16—474no—
259SD16—474no—
260M16—474no—
261M16—942no—
262C2×C8—471no—
263C2×C8—471no—
264C2×C8C22×D4711yescharacteristic
265C2×C8C22×D4711yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—471no—
269C4⋊C4—471no—
270C4⋊C4—941no—
271C4⋊C4—941no—
272C4⋊C4—941no—
273C4⋊C4—941no—
274C4⋊C4—941no—
275C4⋊C4C22×D4711yescharacteristic
276C4⋊C4C22×D4711yescharacteristic
277C22⋊C4—941no—
278C22⋊C4—941no—
279C22⋊C4—941no—
280C42—21no—
281C42—21no—
282C42—471no—
283C42—471no—
284C42—471no—
285C42—941no—
286C42—941no—
287C42—941no—
288C42—941no—
289C42—941no—
290C42C22×D4711yescharacteristic
291C23—471no—
292C23—941no—
293Q8—21no—
294Q8—21no—
295Q8—472no—
296Q8—944no—
297Q8—941no—
298Q8C2×C4×D4712yes—
299Q8C2×C4×D4712yes—
300D4—472no—
301D4—944no—
302D4—941no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—471no—
308C2×C4—472no—
309C2×C4—472no—
310C2×C4—471no—
311C2×C4—471no—
312C2×C4—944no—
313C2×C4—944no—
314C2×C4—941no—
315C2×C4—942no—
316C2×C4—941no—
317C2×C4—941no—
318C2×C4—1881no—
319C2×C4—1882no—
320C2×C4—1882no—
321C2×C4—1882no—
322C2×C4D4×D4711yescharacteristic
323C2×C4D4×D4711yescharacteristic
324C2×C4C23×D4711yescharacteristic
325C8—21no—
326C8—472no—
327C8—941no—
328C8C2×C4×D4712yes—
329C22—472no—
330C22—941no—
331C22—941no—
332C22—942no—
333C22—1881no—
334C22—1881no—
335C22C2×D4×D4711yescharacteristic
336C4—22no—
337C4—22no—
338C4—21no—
339C4—41no—
340C4—41no—
341C4—472no—
342C4—942no—
343C4—941no—
344C4—941no—
345C4—1881no—
346C4—1881no—
347C4#1309405612yesdirect product factor
348C4C22×C4×D4711yescharacteristic
349C4#41×D4711yescharacteristic
350C2—942no—
351C2—1882no—
352C2C4×D4×D4711yescharacteristic
353C2C2×#1309405611yescharacteristic
354C2#1568992011yescharacteristic
subgroupG/H
centerC2×C4D4×D47
commutatorC4×C47C23×C4
FrattiniC2×C4C23×D47
FittingC4×Q16×C47C2
socleC22×C47C22×D4
hypercenterC4×Q16D47
hypocenterC47C4×#137
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
3. C4×Q8×D47C2semidirect
4. #15689230C2semidirect
5. #15689227C2semidirect
6. #15689226C2semidirect
7. #15689222C2semidirect
8. C4×#10625337C2semidirect
9. C4×#10625325C2semidirect
10. C4×#10625336C2semidirect
11. #15689164C2semidirect
12. #15689130C2semidirect
14. C4×#10625324C2semidirect
15. C4×Q16×C47C2semidirect
18. #13094056C4direct (N × H)
65. Q8×D47C2×C4semidirect
78. Q16×C47C2×C4semidirect
88. #10625337C2×C4semidirect
89. #10625336C2×C4semidirect
110. #10625325C2×C4semidirect
112. #10625324C2×C4semidirect
163. C4×C47#137semidirect
186. C4×Q16D47semidirect
193. C47C4×#137semidirect
257. Q16C4×D47semidirect
347. C4#13094056direct (N × H)