Finite Group Databasebeta

← C4×#15688913 #26131415

Subgroups — C4×#15688913 #26131415

Order 12032.

576 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15688913C212yesmaximal
2C4×#13093941C211yesmaximal, characteristic
3C4×#13093939C211yesmaximal, characteristic
4#20241506C212yesmaximal
5C4×#123×C47C211yesmaximal, characteristic
6C2×#13093941C2212yes—
7C2×#13093939C2212yes—
8C4×#10625329—21no—
9C4×C22⋊Dic47—21no—
10#15688913C418yesdirect product factor
11#15688892—21no—
12#15688890—21no—
13C2×#123×C47C2211yescharacteristic
14C2×C4×D4×C47C2211yescharacteristic
15C22×C42×C47C411yescharacteristic, complemented
16C47×#388—21no—
17C47×#387—21no—
18C47×#386C2211yescharacteristic
19C47×#385C411yescharacteristic, complemented
20C47×#381C411yescharacteristic, complemented
21C4×C4⋊C4×C47—21no—
22C4×C22⋊C4×C47—21no—
23C4×C22⋊C4×C47C411yescharacteristic, complemented
24C2×#10625329—22no—
25C2×C22⋊Dic47—22no—
26C2×C4×Dic47—41no—
27#13093941—22no—
28#13093941C2×C414yes—
29#13093939—22no—
30#13093939C2×C414yes—
31#13093935—41no—
32C4×C47⋊C8—41no—
33C47⋊#95—41no—
34C22×D4×C47C2311yescharacteristic
35C23×C4×C47C2×C411yescharacteristic
36C23×C4×C47C2×C411yescharacteristic
37C23×C4×C47C2×C411yescharacteristic
38C23×C4×C47D411yescharacteristic
39#123×C47—22no—
40#123×C47C2×C414yes—
41C4×D4×C47—41no—
42C4×D4×C47—41no—
43C2×C4⋊C4×C47—21no—
44C2×C4⋊C4×C47—21no—
45C2×C4⋊C4×C47D411yescharacteristic
46C2×C22⋊C4×C47—21no—
47C2×C22⋊C4×C47—21no—
48C2×C22⋊C4×C47C2×C411yescharacteristic
49C2×C22⋊C4×C47C2×C411yescharacteristic
50C2×C22⋊C4×C47C2×C411yescharacteristic
51C2×C22⋊C4×C47D411yescharacteristic
52C2×C42×C47—21no—
53C2×C42×C47—21no—
54C2×C42×C47—21no—
55C2×C42×C47—41no—
56C2×C42×C47—41no—
57C2×C42×C47D411yescharacteristic
58#95×C47—21no—
59#95×C47—21no—
60#95×C47—21no—
61#95×C47—21no—
62#95×C47—21no—
63C24×C47C22×C411yescharacteristic
64C24×C47C2×D411yescharacteristic
65C2×D4×C47—41no—
66C2×D4×C47—41no—
67C2×D4×C47C22×C412yes—
68C2×D4×C47#4112yes—
69C22×C4×C47—21no—
70C22×C4×C47—21no—
71C22×C4×C47—21no—
72C22×C4×C47—21no—
73C22×C4×C47—21no—
74C22×C4×C47—21no—
75C22×C4×C47—21no—
76C22×C4×C47—21no—
77C22×C4×C47—21no—
78C22×C4×C47—42no—
79C22×C4×C47—42no—
80C22×C4×C47—42no—
81C22×C4×C47—41no—
82C22×C4×C47—41no—
83C22×C4×C47—41no—
84C22×C4×C47C4212yescomplemented
85C22×C4×C47C22⋊C411yescharacteristic
86C22×C4×C47C22⋊C411yescharacteristic
87C22×C4×C47C22⋊C411yescharacteristic
88C22×C4×C47C22⋊C411yescharacteristic
89C22×C4×C47C2×D411yescharacteristic
90C22×Dic47—42no—
91C4⋊C4×C47—24no—
92C4⋊C4×C47—41no—
93C4⋊C4×C47—42no—
94C22⋊C4×C47—21no—
95C22⋊C4×C47—24no—
96C22⋊C4×C47—41no—
97C22⋊C4×C47—41no—
98C22⋊C4×C47—42no—
99C22⋊C4×C47—41no—
100C22⋊C4×C47C4212yescomplemented
101C42×C47—21no—
102C42×C47—21no—
103C42×C47—42no—
104C42×C47—42no—
105C42×C47—41no—
106C42×C47—41no—
107C22⋊Dic47—24no—
108C22⋊Dic47—42no—
109C4×Dic47—82no—
110#10625329—24no—
111#10625329—42no—
112C2×C47⋊C8—42no—
113C23×C47—21no—
114C23×C47—21no—
115C23×C47—21no—
116C23×C47—21no—
117C23×C47—41no—
118C23×C47—41no—
119C23×C47—41no—
120C23×C47—41no—
121C23×C47C2×C4211yescharacteristic
122C23×C47C2×C22⋊C411yescharacteristic
123C23×C47#11711yescharacteristic
124C23×C47C4×D412yes—
125D4×C47—42no—
126D4×C47—42no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—22no—
130C2×C4×C47—22no—
131C2×C4×C47—22no—
132C2×C4×C47—22no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47—42no—
137C2×C4×C47—41no—
138C2×C4×C47—41no—
139C2×C4×C47—41no—
140C2×C4×C47—42no—
141C2×C4×C47—42no—
142C2×C4×C47—41no—
143C2×C4×C47—41no—
144C2×C4×C47—41no—
145C2×C4×C47—42no—
146C2×C4×C47—42no—
147C2×C4×C47—41no—
148C2×C4×C47—42no—
149C2×C4×C47—41no—
150C2×C4×C47—41no—
151C2×C4×C47—42no—
152C2×C4×C47—41no—
153C2×C4×C47—41no—
154C2×C4×C47—41no—
155C2×C4×C47—81no—
156C2×C4×C47#9911yescharacteristic
157C2×C4×C47#9911yescharacteristic
158C2×C4×C47C4×D412yes—
159C2×Dic47—44no—
160C2×Dic47—82no—
161C2×Dic47—82no—
162C47⋊C8—44no—
163C4×#352—471nomaximal, Sylow
164C22×C47—21no—
165C22×C47—21no—
166C22×C47—22no—
167C22×C47—21no—
168C22×C47—21no—
169C22×C47—41no—
170C22×C47—41no—
171C22×C47—42no—
172C22×C47—42no—
173C22×C47—41no—
174C22×C47—41no—
175C22×C47—41no—
176C22×C47—41no—
177C22×C47—81no—
178C22×C47C4×C22⋊C411yescharacteristic
179C22×C47C2×#9911yescharacteristic
180C22×C47#41011yescharacteristic
181C4×C47—21no—
182C4×C47—22no—
183C4×C47—42no—
184C4×C47—41no—
185C4×C47—41no—
186C4×C47—41no—
187C4×C47—42no—
188C4×C47—42no—
189C4×C47—81no—
190C4×C47#35212yescomplemented
191Dic47—84no—
192C4×#123D4711yescharacteristic
193C2×#352—472no—
194C4×#100—471no—
195C4×#99—471no—
196#1390—472no—
197C2×C47—21no—
198C2×C47—21no—
199C2×C47—42no—
200C2×C47—41no—
201C2×C47—41no—
202C2×C47C4×#9911yescharacteristic
203C2×C47C2×#35211yescharacteristic
204C2×C47#212011yescharacteristic
205C2×#123C2×D4711yescharacteristic
206C2×C4×D4C2×D4711yescharacteristic
207C22×C42Dic4711yescharacteristic, complemented
208C2×#100—472no—
209C2×#99—472no—
210C4×M16—941no—
211#388—21no—
212#387—21no—
213#386C2×D4711yescharacteristic
214#385Dic4711yescharacteristic, complemented
215#381Dic4711yescharacteristic, complemented
216C4×C4⋊C4—21no—
217C4×C22⋊C4—21no—
218C4×C22⋊C4—941no—
219C4×C22⋊C4Dic4711yescharacteristic, complemented
220#352—478no—
221#343—941no—
222#342—941no—
223C47C4×#35211yescharacteristic, complemented, Sylow
224C22×D4C22×D4711yescharacteristic
225C23×C4C2×Dic4711yescharacteristic
226C23×C4C2×Dic4711yescharacteristic
227C23×C4C2×Dic4711yescharacteristic
228C23×C4C22⋊D4711yescharacteristic
229C2×M16—942no—
230#123—22no—
231#123C4×D4714yes—
232C4×D4—41no—
233C4×D4—41no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4C22⋊D4711yescharacteristic
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—942no—
240C2×C22⋊C4C2×Dic4711yescharacteristic
241C2×C22⋊C4C2×Dic4711yescharacteristic
242C2×C22⋊C4C2×Dic4711yescharacteristic
243C2×C22⋊C4C22⋊D4711yescharacteristic
244C2×C42—21no—
245C2×C42—21no—
246C2×C42—21no—
247C2×C42—41no—
248C2×C42—41no—
249C2×C42—1881no—
250C2×C42C22⋊D4711yescharacteristic
251#100—474no—
252#100—942no—
253#99—474no—
254#99—942no—
255#97—1881no—
256C4×C8—1881no—
257#95—21no—
258#95—21no—
259#95—21no—
260#95—21no—
261#95—21no—
262#95—1881no—
263C24C22×Dic4711yescharacteristic
264C24C2×C22⋊D4711yescharacteristic
265C2×D4—41no—
266C2×D4—41no—
267C2×D4C2×C4×D4712yes—
268C2×D4#1062535012yes—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—1882no—
285C22×C4C4×Dic4712yescomplemented
286C22×C4C22⋊Dic4711yescharacteristic
287C22×C4C22⋊Dic4711yescharacteristic
288C22×C4C22⋊Dic4711yescharacteristic
289C22×C4C22⋊Dic4711yescharacteristic
290C22×C4C2×C22⋊D4711yescharacteristic
291M16—944no—
292M16—1882no—
293C2×C8—1882no—
294C4⋊C4—24no—
295C4⋊C4—41no—
296C4⋊C4—42no—
297C22⋊C4—21no—
298C22⋊C4—24no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—42no—
302C22⋊C4—41no—
303C22⋊C4—944no—
304C22⋊C4—1882no—
305C22⋊C4C4×Dic4712yescomplemented
306C42—21no—
307C42—21no—
308C42—42no—
309C42—42no—
310C42—41no—
311C42—41no—
312C42—3762no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23C2×C4×Dic4711yescharacteristic
322C23C2×C22⋊Dic4711yescharacteristic
323C23#1309398311yescharacteristic
324C23C4×C22⋊D4712yes—
325D4—42no—
326D4—42no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—81no—
356C2×C4—3762no—
357C2×C4—3762no—
358C2×C4—1884no—
359C2×C4#1309393911yescharacteristic
360C2×C4#1309393911yescharacteristic
361C2×C4C4×C22⋊D4712yes—
362C8—1884no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—22no—
368C22—41no—
369C22—41no—
370C22—42no—
371C22—42no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—81no—
377C22C4×C22⋊Dic4711yescharacteristic
378C22C2×#1309393911yescharacteristic
379C22#1568909711yescharacteristic
380C4—21no—
381C4—22no—
382C4—42no—
383C4—41no—
384C4—41no—
385C4—42no—
386C4—41no—
387C4—42no—
388C4—81no—
389C4—3764no—
390C4#1568891312yesdirect product factor
391C2—21no—
392C2—21no—
393C2—42no—
394C2—41no—
395C2—41no—
396C2C4×#1309393911yescharacteristic
397C2C2×#1568891311yescharacteristic
398C2#2024502911yescharacteristic
subgroupG/H
centerC2×C4#13093939
commutatorC23×C47C2×C42
FrattiniC22×D4C22×D47
FittingC4×#123×C47C2
socleC22×C47C2×#99
prime radical, cosocleC22×D4×C47C23
hypercenterC4×#123D47
hypocenterC47C4×#352
LCSG ▷ C23×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#123

Complements

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

NH ≅ G/Ntype
10. #15688913C4direct (N × H)
15. C22×C42×C47C4semidirect
19. C47×#385C4semidirect
20. C47×#381C4semidirect
23. C4×C22⋊C4×C47C4semidirect
84. C22×C4×C47C42semidirect
100. C22⋊C4×C47C42semidirect
190. C4×C47#352semidirect
207. C22×C42Dic47semidirect
214. #385Dic47semidirect
215. #381Dic47semidirect
219. C4×C22⋊C4Dic47semidirect
223. C47C4×#352semidirect
285. C22×C4C4×Dic47semidirect
305. C22⋊C4C4×Dic47semidirect
390. C4#15688913direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#156889132
C4×#130939412
C4×#130939392
#202415062
C4×#123×C472
C4×#35247