Finite Group Databasebeta

← C4×#15689060 #26138108

Subgroups — C4×#15689060 #26138108

Order 12032.

1966 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689060C211yesmaximal, characteristic
2C2×C4×C4⋊Dic47C213yesmaximal, complemented
3C2×C4×(C2×D47)⋊C4C213yesmaximal
4#20241655C213yesmaximal, complemented
5#20241653C211yesmaximal, characteristic, complemented
6#20241634C213yesmaximal
7C4×#95×C47C211yesmaximal, characteristic, complemented
8C23×C4×D47C2211yescharacteristic
9C22×C4⋊Dic47C2213yes—
10C22×C4⋊Dic47C2213yes—
11C22×(C2×D47)⋊C4C2213yes—
12C22×(C2×D47)⋊C4C2213yes—
13C22×C4×Dic47C2213yes—
14#15689060C418yesdirect product factor
15C4×C4⋊Dic47—212no—
16C4×(C2×D47)⋊C4—212no—
17C2×C47⋊#95C2213yes—
18C2×C47⋊#95C2213yes—
19C2×C47⋊#95C2216yes—
20C22×C42×C47C2213yes—
21C2×#95×C47C2213yes—
22C2×#95×C47C2211yescharacteristic
23C24×D47C2311yescharacteristic
24C23×Dic47C2313yes—
25C23×Dic47C2311yescharacteristic
26C23×Dic47C2313yes—
27C22×C4×D47—26no—
28C22×C4×D47—26no—
29C22×C4×D47Q814yes—
30C2×C4⋊Dic47—26no—
31C2×C4⋊Dic47—26no—
32C2×C4⋊Dic47—26no—
33C2×C4⋊Dic47—212no—
34C2×C4⋊Dic47C2×C4112yescomplemented
35C2×(C2×D47)⋊C4—26no—
36C2×(C2×D47)⋊C4—26no—
37C2×(C2×D47)⋊C4—26no—
38C2×(C2×D47)⋊C4—26no—
39C2×(C2×D47)⋊C4—26no—
40C2×(C2×D47)⋊C4C2×C4112yes—
41C2×C4×Dic47—26no—
42C2×C4×Dic47—212no—
43C47⋊#95—26no—
44C47⋊#95—26no—
45C47⋊#95—212no—
46C23×C4×C47C2313yes—
47C23×C4×C47C2313yes—
48C23×C4×C47C2311yescharacteristic
49C2×C42×C47—212no—
50C2×C42×C47D4112yes—
51#95×C47—26no—
52#95×C47C2×C414yescomplemented
53C24×C47C2411yescharacteristic
54C23×D47—23no—
55C23×D47—23no—
56C23×D47—23no—
57C23×D47—23no—
58C23×D47C22×C412yes—
59C23×D47C2×Q812yes—
60C23×D47#4112yes—
61C22×C4×C47—26no—
62C22×C4×C47—26no—
63C22×C4×C47—26no—
64C22×C4×C47—23no—
65C22×C4×C47—23no—
66C22×C4×C47—26no—
67C22×C4×C47C22×C416yes—
68C22×C4×C47C2×D416yes—
69C22×C4×C47C2×D416yes—
70C22×C4×C47C2×D416yes—
71C22×C4×C47C2×Q812yes—
72C22×C4×C47#4116yes—
73C22×C4×C47#4116yes—
74C22×Dic47—23no—
75C22×Dic47—23no—
76C22×Dic47—23no—
77C22×Dic47—26no—
78C22×Dic47—26no—
79C22×Dic47—23no—
80C22×Dic47—23no—
81C22×Dic47—26no—
82C22×Dic47—26no—
83C22×Dic47—23no—
84C22×Dic47C22×C416yes—
85C22×Dic47C2×Q812yes—
86C22×Dic47#4116yes—
87C2×C4×D47—224no—
88C2×C4×D47—412no—
89C2×C4×D47—44no—
90C42×C47—224no—
91(C2×D47)⋊C4—224no—
92(C2×D47)⋊C4—224no—
93C4⋊Dic47—224no—
94C4⋊Dic47—224no—
95C4×Dic47—412no—
96C23×C47C23×C411yescharacteristic
97C23×C47C22×D413yes—
98C23×C47C22×Q811yescharacteristic
99C23×C47C2×#4111yescharacteristic
100C23×C47C2×#4113yes—
101C23×C47C2×#4113yes—
102C23×C47C2×#4113yes—
103C22×D47—26no—
104C22×D47—26no—
105C22×D47—26no—
106C22×D47—26no—
107C22×D47—26no—
108C22×D47—26no—
109C22×D47—43no—
110C22×D47—43no—
111C22×D47—46no—
112C22×D47—41no—
113C22×D47—43no—
114C22×D47C4×Q814yes—
115C2×C4×C47—212no—
116C2×C4×C47—26no—
117C2×C4×C47—26no—
118C2×C4×C47—212no—
119C2×C4×C47—26no—
120C2×C4×C47—26no—
121C2×C4×C47—26no—
122C2×C4×C47—46no—
123C2×C4×C47—46no—
124C2×C4×C47C4×D4112yes—
125C2×C4×C47C22⋊Q8112yes—
126C2×C4×C47#123112yes—
127C2×C4×C47#12714yes—
128C2×Dic47—212no—
129C2×Dic47—26no—
130C2×Dic47—26no—
131C2×Dic47—212no—
132C2×Dic47—26no—
133C2×Dic47—43no—
134C2×Dic47—46no—
135C2×Dic47—43no—
136C2×Dic47—43no—
137C2×Dic47—43no—
138C2×Dic47—41no—
139C2×Dic47—43no—
140C2×Dic47—46no—
141C4×D47—416no—
142C4×#399—471nomaximal, Sylow
143C22×C47C2×C4×D413yes—
144C22×C47C2×C4×Q811yescharacteristic
145C22×C47C4×#4113yes—
146C22×C47C2×C22⋊Q813yes—
147C22×C47C2×#12313yes—
148C22×C47#52513yes—
149C22×C47#52513yes—
150C22×C47#52916yes—
151C22×C47#52913yes—
152C22×C47C2×#12711yescharacteristic
153C22×C47#53213yes—
154C22×C47#53313yes—
155C2×D47—212no—
156C2×D47—42no—
157C2×D47—42no—
158C2×D47—46no—
159C2×D47—46no—
160C2×D47—42no—
161C2×D47—46no—
162C4×C47—212no—
163C4×C47—46no—
164C4×C47#39918yescomplemented
165Dic47—46no—
166Dic47—42no—
167Dic47—46no—
168C2×#399—471no—
169C2×C4×C4⋊C4—473no—
170C2×C4×C22⋊C4—473no—
171#1445—473no—
172#1444—471no—
173#1439—473no—
174C4×#95D4711yescharacteristic, complemented
175C2×C47C4×#12313yes—
176C2×C47C4×C22⋊Q813yes—
177C2×C47C4×#12711yescharacteristic
178C2×C47C2×#39911yescharacteristic
179C2×C47#239513yes—
180C2×C47#239613yes—
181C2×C47#239711yescharacteristic
182D47—44no—
183C24×C4—471no—
184C22×C4⋊C4—473no—
185C22×C4⋊C4—473no—
186C22×C22⋊C4—473no—
187C22×C22⋊C4—473no—
188C22×C42—473no—
189C22×C42C2×D4713yes—
190#399—478no—
191C4×C4⋊C4—9412no—
192C4×C22⋊C4—9412no—
193C2×#95—476no—
194C2×#95—473no—
195C2×#95—473no—
196C2×#95C2×D4713yes—
197C2×#95C2×D4711yescharacteristic
198C47C4×#39911yescharacteristic, complemented, Sylow
199C25—471no—
200C23×C4—473no—
201C23×C4—473no—
202C23×C4—471no—
203C23×C4—474no—
204C23×C4—946no—
205C23×C4—946no—
206C23×C4C22×D4713yes—
207C23×C4C22×D4713yes—
208C23×C4C22×D4711yescharacteristic
209C2×C4⋊C4—4712no—
210C2×C4⋊C4—9412no—
211C2×C4⋊C4—946no—
212C2×C4⋊C4—946no—
213C2×C4⋊C4—946no—
214C2×C22⋊C4—4712no—
215C2×C22⋊C4—946no—
216C2×C22⋊C4—946no—
217C2×C22⋊C4—946no—
218C2×C22⋊C4—946no—
219C2×C22⋊C4—946no—
220C2×C42—212no—
221C2×C42—946no—
222C2×C42—9412no—
223C2×C42D188112yes—
224#95—26no—
225#95—946no—
226#95—946no—
227#95—9412no—
228#95C4×D4714yescomplemented
229C24—472no—
230C24—472no—
231C24—472no—
232C24—943no—
233C24—943no—
234C24—943no—
235C24—943no—
236C24C23×D4711yescharacteristic
237C22×C4—26no—
238C22×C4—26no—
239C22×C4—23no—
240C22×C4—23no—
241C22×C4—26no—
242C22×C4—26no—
243C22×C4—476no—
244C22×C4—472no—
245C22×C4—476no—
246C22×C4—943no—
247C22×C4—943no—
248C22×C4—943no—
249C22×C4—946no—
250C22×C4—946no—
251C22×C4—943no—
252C22×C4—946no—
253C22×C4—943no—
254C22×C4—943no—
255C22×C4—946no—
256C22×C4—9424no—
257C22×C4—18812no—
258C22×C4—1884no—
259C22×C4C2×C4×D4716yes—
260C22×C4C2×D18816yes—
261C22×C4C2×D18816yes—
262C22×C4C2×D18816yes—
263C22×C4#1062535016yes—
264C22×C4#1062535216yes—
265C22×C4Q8×D4712yes—
266C4⋊C4—9424no—
267C4⋊C4—9424no—
268C22⋊C4—9424no—
269C22⋊C4—9424no—
270C42—224no—
271C42—18812no—
272C23—474no—
273C23—946no—
274C23—946no—
275C23—946no—
276C23—946no—
277C23—946no—
278C23—946no—
279C23—1883no—
280C23—1883no—
281C23—1886no—
282C23—1881no—
283C23—1883no—
284C23C22×C4×D4711yescharacteristic
285C23C22×D18813yes—
286C23C2×Q8×D4711yescharacteristic
287C23#41×D4711yescharacteristic
288C23#41×D4713yes—
289C23C2×#1062535213yes—
290C23C2×#1062535013yes—
291C2×C4—212no—
292C2×C4—26no—
293C2×C4—26no—
294C2×C4—212no—
295C2×C4—26no—
296C2×C4—26no—
297C2×C4—26no—
298C2×C4—46no—
299C2×C4—46no—
300C2×C4—946no—
301C2×C4—9412no—
302C2×C4—946no—
303C2×C4—946no—
304C2×C4—9412no—
305C2×C4—1883no—
306C2×C4—1886no—
307C2×C4—1883no—
308C2×C4—1883no—
309C2×C4—1883no—
310C2×C4—1881no—
311C2×C4—1883no—
312C2×C4—1886no—
313C2×C4—18816no—
314C2×C4C4×D188112yes—
315C2×C4#13094004112yes—
316C2×C4#13094008112yes—
317C2×C4#1309402114yes—
318C22—9412no—
319C22—1882no—
320C22—1886no—
321C22—1886no—
322C22—1882no—
323C22—1886no—
324C22—1882no—
325C22C2×C4×D18813yes—
326C22C4×Q8×D4711yescharacteristic
327C22C4×#1062535213yes—
328C22C2×#1309400413yes—
329C22C2×#1309400813yes—
330C22#1568963513yes—
331C22#1568963513yes—
332C22#1568965316yes—
333C22#1568965513yes—
334C22C2×#1309402111yescharacteristic
335C22#1568967313yes—
336C22#1568967713yes—
337C4—212no—
338C4—46no—
339C4—1882no—
340C4—1886no—
341C4—1886no—
342C4#1568906018yesdirect product factor
343C2—1884no—
344C2C4×#1309400813yes—
345C2C4×#1309400413yes—
346C2C4×#1309402111yescharacteristic
347C2C2×#1568906011yescharacteristic
348C2#2024664813yes—
349C2#2024666013yes—
350C2#2024666911yescharacteristic
subgroupG/H
centerC23×C4C22×D47
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC4×#95×C47C2
socle, cosocleC24×C47C24
prime radicalC24×D47C23
hypercenterC4×#95D47
hypocenterC47C4×#399
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. C2×C4×C4⋊Dic47C2semidirect
4. #20241655C2semidirect
5. #20241653C2semidirect
7. C4×#95×C47C2semidirect
14. #15689060C4direct (N × H)
34. C2×C4⋊Dic47C2×C4semidirect
52. #95×C47C2×C4semidirect
164. C4×C47#399semidirect
174. C4×#95D47semidirect
198. C47C4×#399semidirect
228. #95C4×D47semidirect
342. C4#15689060direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156890602
C2×C4×C4⋊Dic472
C2×C4×(C2×D47)⋊C42
#202416552
#202416532
#202416342
C4×#95×C472
C4×#39947