Finite Group Databasebeta

← C2×C8×#10625354 #27080711

Subgroups — C2×C8×#10625354 #27080711

Order 12032.

2566 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10625354C211yesmaximal, characteristic
2C8×#10625354C2116yesmaximal, direct product factor
3C2×Q8×C47⋊C8C211yesmaximal, characteristic, complemented
4C2×C8×D188C213yesmaximal, complemented
5C2×#15689188C213yesmaximal, complemented
6C2×#15689175C213yesmaximal, complemented
7C2×C4×C8×D47C213yesmaximal, complemented
8C2×C8×Q8×C47C211yesmaximal, characteristic, complemented
9C22×#10625354C411yescharacteristic
10C22×C8×D47C2213yes—
11C22×C8×D47C2213yes—
12C4×#10625354C418yes—
13C4×#10625354C2218yes—
14C2×Q8×Dic47C411yescharacteristic
15C2×C4×D188C2213yes—
16C2×#13093986C413yes—
17C2×#13093982C413yes—
18C2×C42×D47C2213yes—
19Q8×C47⋊C8C2218yescomplemented
20C8×D188C22124yescomplemented
21#15689188C22124yescomplemented
22#15689175C22124yescomplemented
23C2×C4⋊(C47⋊C8)C2213yes—
24C2×(C2×D47)⋊C8C2216yes—
25C2×C4×C47⋊C8C2213yes—
26C2×C8×Dic47C2213yes—
27C2×C8×Dic47C2211yescharacteristic
28C4×C8×D47C22124yescomplemented
29C2×C4×Q8×C47C2211yescharacteristic
30C8×Q8×C47C2218yescomplemented
31C2×C4⋊C8×C47C2213yes—
32C2×C4×C8×C47C2213yes—
33C2×#10625354C8116yesdirect product factor
34C2×#10625354C2×C418yes—
35C22×D188C2×C413yes—
36C22×C4×D47C2×C413yes—
37C22×C4×D47C2×C413yes—
38C22×C4×D47C2313yes—
39C22×C47⋊C8C2313yes—
40C22×C47⋊C8C2311yescharacteristic
41C2×C8×D47—212no—
42C2×C8×D47—212no—
43C2×C8×D47C23112yes—
44C2×C8×D47C23112yes—
45Q8×Dic47C2×C418yes—
46C4×D188C2×C4112yes—
47C4×D188C23112yes—
48#13093986C2×C4124yes—
49#13093982C2×C4124yes—
50C2×C4⋊Dic47C2×C413yes—
51C2×(C2×D47)⋊C4C2×C416yes—
52C2×C4×Dic47C2×C413yes—
53C2×C4×Dic47C2×C413yes—
54C2×C4×Dic47C2311yescharacteristic
55C42×D47C2×C4112yes—
56C42×D47C23112yes—
57C4⋊(C47⋊C8)C23112yes—
58(C2×D47)⋊C8C23124yes—
59C4×C47⋊C8C23112yes—
60C8×Dic47C2314yes—
61C8×Dic47C23112yes—
62C22×Q8×C47C2×C411yescharacteristic
63C22×C8×C47C2313yes—
64C22×C8×C47C2311yescharacteristic
65C4×Q8×C47C2×C414yes—
66C4×Q8×C47C2314yes—
67C2×C4⋊C4×C47C2×C413yes—
68C2×C42×C47C2313yes—
69C4⋊C8×C47C23112yes—
70C4×C8×C47C23112yes—
71C23×D47C22×C413yes—
72C2×Q8×C47C2×C818yescomplemented
73C2×Q8×C47C22×C414yes—
74C22×C4×C47C22×C413yes—
75C22×C4×C47C22×C413yes—
76C22×C4×C47C2411yescharacteristic
77C22×Dic47C22×C413yes—
78C22×Dic47C22×C411yescharacteristic
79C22×Dic47C22×C411yescharacteristic
80#10625354C2×C8164yesdirect product factor
81C2×D188C2×C8124yescomplemented
82C2×D188C22×C4112yes—
83C2×C4×D47—26no—
84C2×C4×D47—26no—
85C2×C4×D47—212no—
86C2×C4×D47C2×C8124yescomplemented
87C2×C4×D47C22×C416yes—
88C2×C4×D47C22×C4112yes—
89C2×C4×D47C22×C4112yes—
90C2×C4×D47C2416yes—
91C2×C8×C47—26no—
92C2×C8×C47#4114yescomplemented
93C2×C8×C47C2416yes—
94C2×C8×C47C2412yes—
95C4⋊C4×C47C22×C4112yes—
96C42×C47C22×C416yes—
97C42×C47C2416yes—
98(C2×D47)⋊C4C22×C4124yes—
99C4⋊Dic47C22×C4112yes—
100C4×Dic47C22×C412yes—
101C4×Dic47C22×C4112yes—
102C4×Dic47C22×C4112yes—
103C4×Dic47C2412yes—
104C2×C47⋊C8—26no—
105C2×C47⋊C8#4114yescomplemented
106C2×C47⋊C8C2416yes—
107C2×C47⋊C8C2412yes—
108C8×D47—224no—
109C8×D47—224no—
110C23×C47C23×C411yescharacteristic
111C22×D47—26no—
112C22×D47—26no—
113C22×D47C22×C8112yes—
114C22×D47C23×C416yes—
115Q8×C47C22×C8116yescomplemented
116C2×C4×C47—26no—
117C2×C4×C47C22×C8112yes—
118C2×C4×C47C23×C416yes—
119C2×C4×C47C23×C411yescharacteristic
120C2×C4×C47C23×C416yes—
121C2×C4×C47C2×#4112yes—
122C2×C4×C47C2×#4112yes—
123C2×C4×C47C2511yescharacteristic
124C2×Dic47—26no—
125C2×Dic47C22×C814yes—
126C2×Dic47#13114yes—
127C2×Dic47C23×C416yes—
128C2×Dic47C23×C412yes—
129C2×Dic47C23×C412yes—
130D188C22×C8148yescomplemented
131C4×D47—212no—
132C4×D47—26no—
133C4×D47—26no—
134C4×D47—224no—
135C4×D47C22×C8148yescomplemented
136C8×C47—26no—
137C8×C47C2×#4114yescomplemented
138C47⋊C8—26no—
139C47⋊C8C2×#4114yescomplemented
140C2×C8×#41—471nomaximal, Sylow
141C22×C47C4×#4112yes—
142C22×C47C23×C812yes—
143C22×C47C2×#13112yes—
144C22×C47C24×C411yescharacteristic
145C2×D47—26no—
146C2×D47—224no—
147C2×D47—26no—
148C2×D47C23×C8112yes—
149C4×C47—26no—
150C4×C47C4×#4112yes—
151C4×C47C23×C8112yes—
152C4×C47C22×#4111yescharacteristic
153C4×C47C22×#4111yescharacteristic
154Dic47—26no—
155Dic47C23×C814yes—
156Dic47C2×#13114yes—
157C2×C4×#41—471no—
158C8×#41—4716no—
159C2×C8×Q8—471no—
160C2×C8×Q8D4711yescharacteristic, complemented
161C2×C8×D4—473no—
162C2×C8×D4—473no—
163C2×#431—473no—
164C22×C4×C8—473no—
165C2×C47C8×#4114yescomplemented
166C2×C47C2×C4×#4111yescharacteristic
167C2×C47C24×C811yescharacteristic
168C2×C47C22×#13111yescharacteristic
169D47—212no—
170C22×#41—471no—
171C23×C8—473no—
172C23×C8—473no—
173C4×#41—478no—
174C4×#41—478no—
175C2×C4×Q8—471no—
176C2×C4×Q8C2×D4711yescharacteristic
177C2×C4×D4—473no—
178C2×C4×D4—473no—
179C2×#117—473no—
180C22×C42—473no—
181C8×Q8—478no—
182C8×Q8C2×D4718yescomplemented
183C8×D4—4724no—
184C8×D4—4724no—
185#431—4724no—
186C2×C4⋊C8—473no—
187C2×C4⋊C8C2×D4713yes—
188C2×C22⋊C8—476no—
189C2×C4×C8—473no—
190C2×C4×C8—471no—
191C2×C4×C8—473no—
192C2×C4×C8—4724no—
193C2×C4×C8C2×D4713yes—
194C47C2×C8×#4111yescharacteristic, complemented, Sylow
195C2×#41—4716no—
196C2×#41—478no—
197C22×Q8C4×D4711yescharacteristic
198C22×D4—473no—
199C23×C4—473no—
200C23×C4—473no—
201C23×C4—473no—
202C22×C8—471no—
203C22×C8—473no—
204C22×C8—4712no—
205C22×C8—4712no—
206C22×C8—9412no—
207C22×C8—9412no—
208C22×C8C22×D4713yes—
209C22×C8C22×D4711yescharacteristic
210C4×Q8—478no—
211C4×Q8C4×D4714yes—
212C4×Q8C22×D4714yes—
213C4×D4—4724no—
214C4×D4—4712no—
215C4×D4—4712no—
216#117—4724no—
217C2×C4⋊C4—473no—
218C2×C4⋊C4C4×D4713yes—
219C2×C22⋊C4—476no—
220C2×C42—473no—
221C2×C42—473no—
222C2×C42—471no—
223C2×C42—4712no—
224C2×C42—4712no—
225C2×C42C22×D4713yes—
226C4⋊C8—4712no—
227C4⋊C8C22×D47112yes—
228C22⋊C8—4724no—
229C4×C8—474no—
230C4×C8—4712no—
231C4×C8—4712no—
232C4×C8C22×D47112yes—
233C24—473no—
234#41—4764no—
235C2×Q8C8×D4718yescomplemented
236C2×Q8C2×C4×D4714yes—
237C2×D4—4724no—
238C2×D4—4712no—
239C22×C4—471no—
240C22×C4—471no—
241C22×C4—4724no—
242C22×C4—4712no—
243C22×C4—473no—
244C22×C4—4712no—
245C22×C4—476no—
246C22×C4—476no—
247C22×C4—9412no—
248C22×C4—946no—
249C22×C4—946no—
250C22×C4C2×C4×D4713yes—
251C22×C4C2×C4×D4713yes—
252C22×C4C23×D4711yescharacteristic
253C2×C8—26no—
254C2×C8—474no—
255C2×C8—472no—
256C2×C8—476no—
257C2×C8—9424no—
258C2×C8—946no—
259C2×C8—9424no—
260C2×C8#1062535414yesdirect product factor
261C2×C8C23×D4716yes—
262C2×C8C23×D4712yes—
263C4⋊C4—4712no—
264C4⋊C4C2×C4×D47112yes—
265C22⋊C4—4724no—
266C42—472no—
267C42—4712no—
268C42—4712no—
269C42—472no—
270C42C2×C4×D4716yes—
271C42C23×D4716yes—
272C23—4712no—
273C23—476no—
274C23—946no—
275C23—946no—
276C23C22×C4×D4711yescharacteristic
277Q8C2×C8×D47116yescomplemented
278D4—4748no—
279C2×C4—26no—
280C2×C4—474no—
281C2×C4—474no—
282C2×C4—472no—
283C2×C4—472no—
284C2×C4—4748no—
285C2×C4—476no—
286C2×C4—9424no—
287C2×C4—946no—
288C2×C4—9412no—
289C2×C4—946no—
290C2×C4—946no—
291C2×C4C2×C8×D47112yes—
292C2×C4C22×C4×D4716yes—
293C2×C4C22×C4×D4711yescharacteristic
294C2×C4C22×C4×D4716yes—
295C2×C4#41×D4712yes—
296C2×C4C2×#1062535412yes—
297C2×C4C24×D4711yescharacteristic
298C8—26no—
299C8—474no—
300C8—946no—
301C8C2×#1062535414yesdirect product factor
302C22—4712no—
303C22—946no—
304C22—946no—
305C22—9424no—
306C22C4×#1062535412yes—
307C22C22×C8×D4712yes—
308C22#131×D4712yes—
309C22C23×C4×D4711yescharacteristic
310C4—26no—
311C4—474no—
312C4—474no—
313C4—946no—
314C4C4×#1062535412yes—
315C4C22×C8×D47112yes—
316C4C2×#41×D4711yescharacteristic
317C4C22×#1062535411yescharacteristic
318C2—9412no—
319C2C8×#1062535414yesdirect product factor
320C2C2×C4×#1062535411yescharacteristic
321C2C23×C8×D4711yescharacteristic
322C2C2×#131×D4711yescharacteristic
subgroupG/H
centerC22×C8C22×D47
commutatorC2×C47C24×C8
FrattiniC2×C4C24×D47
FittingC2×C8×Q8×C47C2
socleC23×C47C23×C4
prime radicalC22×#10625354C4
cosocleC2×C4×C47C25
hypercenterC2×C8×Q8D47
hypocenterC47C2×C8×#41
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C8 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
2. C8×#10625354C2direct (N × H)
3. C2×Q8×C47⋊C8C2semidirect
4. C2×C8×D188C2semidirect
5. C2×#15689188C2semidirect
6. C2×#15689175C2semidirect
7. C2×C4×C8×D47C2semidirect
8. C2×C8×Q8×C47C2semidirect
19. Q8×C47⋊C8C22semidirect
20. C8×D188C22semidirect
21. #15689188C22semidirect
22. #15689175C22semidirect
28. C4×C8×D47C22semidirect
30. C8×Q8×C47C22semidirect
33. C2×#10625354C8direct (N × H)
72. C2×Q8×C47C2×C8semidirect
80. #10625354C2×C8direct (N × H)
81. C2×D188C2×C8semidirect
86. C2×C4×D47C2×C8semidirect
92. C2×C8×C47#41semidirect
105. C2×C47⋊C8#41semidirect
115. Q8×C47C22×C8semidirect
130. D188C22×C8semidirect
135. C4×D47C22×C8semidirect
137. C8×C47C2×#41semidirect
139. C47⋊C8C2×#41semidirect
160. C2×C8×Q8D47semidirect
165. C2×C47C8×#41semidirect
182. C8×Q8C2×D47semidirect
194. C47C2×C8×#41semidirect
235. C2×Q8C8×D47semidirect
260. C2×C8#10625354direct (N × H)
277. Q8C2×C8×D47semidirect
301. C8C2×#10625354direct (N × H)
319. C2C8×#10625354direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#106253542
C8×#106253542
C2×Q8×C47⋊C82
C2×C8×D1882
C2×#156891882
C2×#156891752
C2×C4×C8×D472
C2×C8×Q8×C472
C2×C8×#4147