Finite Group Databasebeta

← C2×#20245173 #26369309

Subgroups — C2×#20245173 #26369309

Order 12032.

718 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093963C211yesmaximal, characteristic
2C2×#15689160C211yesmaximal, characteristic
3C2×#107×D47C211yesmaximal, characteristic
4#20245173C218yesmaximal, direct product factor
5C2×#15688951C211yesmaximal, characteristic, complemented
6C2×#15688950C211yesmaximal, characteristic, complemented
7C2×#15688948C211yesmaximal, characteristic, complemented
8C2×C47×#366C211yesmaximal, characteristic, complemented
9C22×C8×D47C2211yescharacteristic
10C2×#13093982—21no—
11C2×C4⋊C4×D47—21no—
12C2×#13093963C418yescomplemented
13C2×#13093963C2214yes—
14C22×C47⋊C16C2211yescharacteristic
15#15689160—22no—
16#15689160C2214yes—
17C2×#13093958C2211yescharacteristic
18C2×#13093958C2211yescharacteristic
19C2×#13093957—21no—
20#107×D47—22no—
21#107×D47C2214yes—
22C2×#13093955—21no—
23#15688951C2214yescomplemented
24#15688950C2214yescomplemented
25#15688948C2214yescomplemented
26C22×C16×C47C2211yescharacteristic
27C2×#107×C47C2211yescharacteristic
28C2×#107×C47C2211yescharacteristic
29C47×#366C2214yescomplemented
30C22×C4×D47—41no—
31C22×C4×D47D411yescharacteristic
32C22×C47⋊C8D411yescharacteristic
33C2×C8×D47C2×C414yes—
34C2×C8×D47D412yes—
35C2×C8×D47Q814yes—
36C2×C8×D47C2312yes—
37#13093982—24no—
38#13093982—42no—
39C2×C4⋊Dic47—21no—
40C2×C4⋊Dic47—21no—
41C2×Dic47⋊C4—41no—
42C4⋊C4×D47—24no—
43C4⋊C4×D47—42no—
44C2×(C2×D47)⋊C4—41no—
45C2×C4×Dic47—41no—
46#13093963C2×C4116yescomplemented
47C2×C47⋊C16C2×C414yescomplemented
48C2×C47⋊C16C2312yes—
49#13093958—21no—
50#13093958—21no—
51#13093958C2312yes—
52#13093958C2312yes—
53#13093957—24no—
54#13093955—24no—
55C22×C8×C47C2311yescharacteristic
56C2×C4⋊C4×C47—21no—
57C2×C4⋊C4×C47—21no—
58C2×C16×C47C2×C414yescomplemented
59C2×C16×C47C2312yes—
60#107×C47—21no—
61#107×C47—21no—
62#107×C47C2312yes—
63#107×C47C2312yes—
64C23×D47D811yescharacteristic
65C22×C4×C47—41no—
66C22×C4×C47—41no—
67C22×C4×C47C2×D411yescharacteristic
68C22×Dic47—41no—
69C22×Dic47—41no—
70C22×Dic47D811yescharacteristic
71C2×C4×D47—44no—
72C2×C4×D47—84no—
73C2×C4×D47C4⋊C414yes—
74C2×C4×D47D812yes—
75C2×C4×D47Q1614yes—
76C2×C4×D47C2×D412yes—
77C2×C8×C47C22×C412yes—
78C2×C8×C47C2×D411yescharacteristic
79C2×C8×C47C2×Q812yes—
80C2×C8×C47C2411yescharacteristic
81C4⋊C4×C47—22no—
82C4⋊C4×C47—22no—
83C4⋊C4×C47—41no—
84C4⋊C4×C47—41no—
85(C2×D47)⋊C4—44no—
86C4⋊Dic47—22no—
87C4⋊Dic47—22no—
88C4⋊Dic47—41no—
89C4⋊Dic47—41no—
90Dic47⋊C4—44no—
91C4×Dic47—44no—
92C2×C47⋊C8C4⋊C414yes—
93C2×C47⋊C8C2×D412yes—
94C8×D47C4⋊C418yes—
95C8×D47C22×C414yes—
96C8×D47C2×Q814yes—
97C16×C47C22×C414yescomplemented
98C47⋊C16C22×C414yescomplemented
99C23×C47C2×D811yescharacteristic
100C22×D47—22no—
101C22×D47—22no—
102C22×D47#10714yes—
103C22×D47C2×D812yes—
104C2×C4×C47—42no—
105C2×C4×C47—42no—
106C2×C4×C47—82no—
107C2×C4×C47—82no—
108C2×C4×C47C2×C4⋊C412yes—
109C2×C4×C47C2×D811yescharacteristic
110C2×C4×C47C2×Q1612yes—
111C2×C4×C47C22×D411yescharacteristic
112C2×Dic47—42no—
113C2×Dic47—42no—
114C2×Dic47—82no—
115C2×Dic47—82no—
116C2×Dic47#10714yes—
117C2×Dic47C2×D812yes—
118C4×D47—88no—
119C4×D47#10718yes—
120C4×D47C2×C4⋊C414yes—
121C4×D47C2×Q1614yes—
122C8×C47C2×C4⋊C412yes—
123C8×C47C23×C411yescharacteristic
124C8×C47C22×Q811yescharacteristic
125C47⋊C8C2×C4⋊C414yes—
126C2×#2159—471nomaximal, Sylow
127C22×C47C2×#10712yes—
128C22×C47#50912yes—
129C22×C47#51012yes—
130C22×C47C22×D811yescharacteristic
131C2×D47—22no—
132C2×D47—22no—
133C2×D47—28no—
134C2×D47C2×#10714yes—
135C4×C47—82no—
136C4×C47—82no—
137C4×C47C2×#10712yes—
138C4×C47C22×C4⋊C411yescharacteristic
139C4×C47C22×Q1611yescharacteristic
140Dic47—82no—
141Dic47—82no—
142Dic47C2×#10714yes—
143C22×M32—471no—
144C2×#427—471no—
145C22×#107—471no—
146#2159—478no—
147C2×#367—471no—
148C2×#367—471no—
149C2×#366—471no—
150C2×#366D4711yescharacteristic, complemented
151C2×C47#215914yescomplemented
152C2×C47C22×#10711yescharacteristic
153C2×C47C2×#50911yescharacteristic
154C2×C47C2×#51011yescharacteristic
155D47—24no—
156C23×C8—471no—
157C2×#117—941no—
158C22×C4⋊C4—941no—
159C2×M32—478no—
160C2×M32—474no—
161C22×C16—471no—
162C22×C16C2×D4711yescharacteristic
163#427—474no—
164#427—942no—
165C2×#107—471no—
166C2×#107—471no—
167C2×#107—474no—
168C2×#107—942no—
169C2×#107—941no—
170C2×#107C2×D4711yescharacteristic
171C2×#107C2×D4711yescharacteristic
172C2×#106—941no—
173#367—474no—
174#367—474no—
175#366—474no—
176#366C2×D4714yescomplemented
177C47C2×#215911yescharacteristic, complemented, Sylow
178C23×C4—471no—
179C23×C4—1881no—
180C22×C8—471no—
181C22×C8—474no—
182C22×C8—472no—
183C22×C8—474no—
184C22×C8—472no—
185C22×C8C22×D4711yescharacteristic
186#117—944no—
187#117—1882no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—944no—
191C2×C4⋊C4—941no—
192C2×C4⋊C4—941no—
193C2×C4⋊C4—1882no—
194C2×C4⋊C4—1881no—
195C2×C22⋊C4—1881no—
196C2×C42—1881no—
197M32—4716no—
198C2×C16—474no—
199C2×C16—472no—
200C2×C16C4×D4714yescomplemented
201C2×C16C22×D4712yes—
202#107—21no—
203#107—21no—
204#107—472no—
205#107—472no—
206#107—944no—
207#107—941no—
208#107—941no—
209#107C22×D4712yes—
210#107C22×D4712yes—
211#106—944no—
212C24—471no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—471no—
216C22×C4—474no—
217C22×C4—472no—
218C22×C4—474no—
219C22×C4—472no—
220C22×C4—3764no—
221C22×C4—1884no—
222C22×C4—1881no—
223C22×C4—1881no—
224C22×C4D4×D4711yescharacteristic
225C2×C8—474no—
226C2×C8—472no—
227C2×C8—478no—
228C2×C8—474no—
229C2×C8—474no—
230C2×C8C2×C4×D4712yes—
231C2×C8D4×D4711yescharacteristic
232C2×C8Q8×D4712yes—
233C2×C8C23×D4711yescharacteristic
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—942no—
239C4⋊C4—942no—
240C4⋊C4—1884no—
241C4⋊C4—1881no—
242C4⋊C4—1881no—
243C22⋊C4—1884no—
244C42—1884no—
245C16—474no—
246C16C2×C4×D4714yescomplemented
247C23—472no—
248C23—474no—
249C23—942no—
250C23—942no—
251C23D8×D4711yescharacteristic
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—82no—
255C2×C4—82no—
256C2×C4—472no—
257C2×C4—474no—
258C2×C4—474no—
259C2×C4—474no—
260C2×C4—478no—
261C2×C4—3768no—
262C2×C4—3762no—
263C2×C4—3762no—
264C2×C4—1882no—
265C2×C4—1882no—
266C2×C4C4⋊C4×D4712yes—
267C2×C4D8×D4711yescharacteristic
268C2×C4Q16×D4712yes—
269C2×C4C2×D4×D4711yescharacteristic
270C8—474no—
271C8C4⋊C4×D4712yes—
272C8C22×C4×D4711yescharacteristic
273C8C2×Q8×D4711yescharacteristic
274C22—474no—
275C22—942no—
276C22—948no—
277C22—942no—
278C22#107×D4712yes—
279C22#1568955712yes—
280C22#1568956512yes—
281C22C2×D8×D4711yescharacteristic
282C4—82no—
283C4—82no—
284C4—474no—
285C4—3762no—
286C4—3762no—
287C4#107×D4712yes—
288C4C2×C4⋊C4×D4711yescharacteristic
289C4C2×Q16×D4711yescharacteristic
290C2—944no—
291C2#2024517314yesdirect product factor
292C2C2×#107×D4711yescharacteristic
293C2C2×#1568955711yescharacteristic
294C2C2×#1568956511yescharacteristic
subgroupG/H
centerC23D8×D47
commutatorC8×C47C23×C4
FrattiniC2×C8C23×D47
FittingC2×C47×#366C2
socleC23×C47C2×D8
prime radicalC23×D47D8
cosocleC2×C8×C47C24
hypercenterC2×#366D47
hypocenterC47C2×#2159
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#366

Complements

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

NH ≅ G/Ntype
4. #20245173C2direct (N × H)
5. C2×#15688951C2semidirect
6. C2×#15688950C2semidirect
7. C2×#15688948C2semidirect
8. C2×C47×#366C2semidirect
12. C2×#13093963C4semidirect
23. #15688951C22semidirect
24. #15688950C22semidirect
25. #15688948C22semidirect
29. C47×#366C22semidirect
46. #13093963C2×C4semidirect
47. C2×C47⋊C16C2×C4semidirect
58. C2×C16×C47C2×C4semidirect
97. C16×C47C22×C4semidirect
98. C47⋊C16C22×C4semidirect
150. C2×#366D47semidirect
151. C2×C47#2159semidirect
176. #366C2×D47semidirect
177. C47C2×#2159semidirect
200. C2×C16C4×D47semidirect
246. C16C2×C4×D47semidirect
291. C2#20245173direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130939632
C2×#156891602
C2×#107×D472
#202451732
C2×#156889512
C2×#156889502
C2×#156889482
C2×C47×#3662
C2×#215947