Finite Group Databasebeta

← C2×#20244265 #26220115

Subgroups — C2×#20244265 #26220115

Order 12032.

2006 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093956C211yesmaximal, characteristic, complemented
2C22×#13093945C212yesmaximal, complemented
3C22×#13093934C211yesmaximal, characteristic, complemented
4C2×#15689026C212yesmaximal, complemented
5#20244265C218yesmaximal, direct product factor
6C23×D8×C47C211yesmaximal, characteristic
7C23×C47⋊C8C2211yescharacteristic
8C22×C4⋊Dic47C2212yes—
9C22×C22⋊Dic47—24no—
10C22×C4×Dic47C2211yescharacteristic
11C2×#13093956—24no—
12C2×#13093956C2214yescomplemented
13C2×#13093945—28no—
14C2×#13093945C2218yescomplemented
15C2×#13093934—24no—
16C2×#13093934C2214yescomplemented
17#15689026—24no—
18#15689026C2218yescomplemented
19C23×D4×C47C2212yes—
20C22×D8×C47—24no—
21C22×D8×C47—24no—
22C22×D8×C47C418yescomplemented
23C22×D8×C47C2214yes—
24C23×C8×C47C2211yescharacteristic
25C23×Dic47—22no—
26C23×Dic47D412yes—
27C22×C47⋊C8—22no—
28C22×C47⋊C8—22no—
29C22×C47⋊C8D414yes—
30C22×C47⋊C8C2312yes—
31C2×C4⋊Dic47—24no—
32C2×C4⋊Dic47—24no—
33C2×C4⋊Dic47—22no—
34C2×C4⋊Dic47C2314yes—
35C2×C22⋊Dic47—216no—
36C2×C22⋊Dic47—416no—
37C2×C4×Dic47—22no—
38C2×C4×Dic47—22no—
39C2×C4×Dic47D412yes—
40C2×C4×Dic47C2312yes—
41#13093956—28no—
42#13093945—216no—
43#13093934—28no—
44C25×C47—22no—
45C22×D4×C47—24no—
46C22×D4×C47—24no—
47C22×D4×C47—24no—
48C22×D4×C47—22no—
49C22×D4×C47—24no—
50C22×D4×C47—24no—
51C22×D4×C47C2×C418yes—
52C22×D4×C47C2314yes—
53C23×C4×C47C2311yescharacteristic
54C2×D8×C47—232no—
55C2×D8×C47—28no—
56C2×D8×C47—28no—
57C2×D8×C47C2×C4116yescomplemented
58C22×C8×C47C2×C414yes—
59C22×C8×C47D414yes—
60C22×C8×C47D414yes—
61C22×C8×C47C2312yes—
62C24×C47—28no—
63C24×C47—24no—
64C24×C47—44no—
65C24×C47—44no—
66C24×C47—48no—
67C24×C47—48no—
68C24×C47C2×D411yescharacteristic
69C2×D4×C47—216no—
70C2×D4×C47—216no—
71C2×D4×C47—28no—
72C2×D4×C47—24no—
73C2×D4×C47—24no—
74C2×D4×C47—24no—
75C2×D4×C47—24no—
76C2×D4×C47—24no—
77C2×D4×C47—48no—
78C2×D4×C47—44no—
79C2×D4×C47—48no—
80C2×D4×C47—44no—
81C2×D4×C47C22×C418yes—
82C22×C4×C47C22×C412yes—
83C22×C4×C47C2×D412yes—
84C22×C4×C47C2×D412yes—
85C22×C4×C47C2×D411yescharacteristic
86C22×C4×C47C2×D412yes—
87C22×C4×C47#4112yes—
88C22×C4×C47#4112yes—
89C22×C4×C47C2411yescharacteristic
90C22×Dic47—24no—
91C22×Dic47—28no—
92C22×Dic47—24no—
93C22×Dic47—44no—
94C22×Dic47—48no—
95C22×Dic47C2×D414yes—
96D8×C47—232no—
97C2×C8×C47C22⋊C4116yescomplemented
98C2×C8×C47C22×C414yes—
99C2×C8×C47C2×D414yes—
100C2×C8×C47C2×D414yes—
101C22⋊Dic47—432no—
102C4⋊Dic47—24no—
103C4⋊Dic47—24no—
104C4⋊Dic47—44no—
105C4×Dic47—24no—
106C4×Dic47—22no—
107C4×Dic47—22no—
108C2×C47⋊C8—28no—
109C2×C47⋊C8—22no—
110C2×C47⋊C8—22no—
111C2×C47⋊C8C2×D414yes—
112C23×C47—28no—
113C23×C47—44no—
114C23×C47—44no—
115C23×C47—48no—
116C23×C47—48no—
117C23×C47—416no—
118C23×C47—432no—
119C23×C47—816no—
120C23×C47—88no—
121C23×C47—88no—
122C23×C47C4×D412yes—
123C23×C47#12112yes—
124C23×C47#12712yes—
125C23×C47AGL(1,ℤ/8)18yes—
126C23×C47C22×D411yescharacteristic
127D4×C47—28no—
128D4×C47—28no—
129D4×C47—44no—
130D4×C47—44no—
131D4×C47—416no—
132C2×C4×C47C2×C22⋊C414yes—
133C2×C4×C47C4×D414yes—
134C2×C4×C47C4×D412yes—
135C2×C4×C47#12114yes—
136C2×C4×C47#12112yes—
137C2×C4×C47#12414yes—
138C2×C4×C47#12712yes—
139C2×C4×C47C23×C411yescharacteristic
140C2×C4×C47C22×D411yescharacteristic
141C2×C4×C47C22×D411yescharacteristic
142C2×C4×C47C22×D411yescharacteristic
143C2×C4×C47C2×#4111yescharacteristic
144C2×C4×C47C2×#4111yescharacteristic
145C2×Dic47—24no—
146C2×Dic47—28no—
147C2×Dic47—48no—
148C2×Dic47—44no—
149C2×Dic47—48no—
150C2×Dic47—88no—
151C8×C47C2×C22⋊C418yescomplemented
152C47⋊C8—24no—
153C2×#1972—471nomaximal, Sylow
154C22×C47—416no—
155C22×C47—48no—
156C22×C47—84no—
157C22×C47—84no—
158C22×C47—832no—
159C22×C47—88no—
160C22×C47#39014yes—
161C22×C47#44218yes—
162C22×C47#46918yes—
163C22×C47#49618yes—
164C22×C47C2×C4×D411yescharacteristic
165C22×C47C2×#12111yescharacteristic
166C22×C47C2×#12711yescharacteristic
167C22×C47C2×AGL(1,ℤ/8)14yes—
168C4×C47#39014yes—
169C4×C47C22×C22⋊C411yescharacteristic
170C4×C47C2×C4×D411yescharacteristic
171C4×C47C2×#12111yescharacteristic
172C4×C47C2×#12411yescharacteristic
173Dic47—44no—
174Dic47—84no—
175C23×D8D4711yescharacteristic
176C22×#106—471no—
177C22×#102—472no—
178C22×#97—471no—
179C2×#390—472no—
180#1972—478no—
181C2×C47—88no—
182C2×C47#197218yescomplemented
183C2×C47C2×#39011yescharacteristic
184C2×C47C2×#44212yes—
185C2×C47C2×#46912yes—
186C2×C47C2×#49612yes—
187C23×D4C2×D4712yes—
188C22×D8—24no—
189C22×D8—24no—
190C22×D8Dic4718yescomplemented
191C22×D8C2×D4714yes—
192C23×C8—471no—
193C23×C8C2×D4711yescharacteristic
194C22×C4⋊C4—472no—
195C22×C22⋊C4—944no—
196C22×C42—471no—
197C2×#106—474no—
198C2×#106—944no—
199C2×#102—478no—
200C2×#102—948no—
201C2×#97—474no—
202C2×#97—944no—
203#390—478no—
204#390—944no—
205C47C2×#197211yescharacteristic, complemented, Sylow
206C25—22no—
207C22×D4—24no—
208C22×D4—22no—
209C22×D4—24no—
210C22×D4—24no—
211C22×D4—24no—
212C22×D4—24no—
213C22×D4C2×Dic4718yes—
214C22×D4C22×D4714yes—
215C23×C4—472no—
216C23×C4—942no—
217C23×C4C22×D4711yescharacteristic
218C2×D8—232no—
219C2×D8—28no—
220C2×D8—28no—
221C2×D8C2×Dic47116yescomplemented
222C22×C8—474no—
223C22×C8—472no—
224C22×C8—942no—
225C22×C8—942no—
226C22×C8C2×Dic4714yes—
227C22×C8C22⋊D4714yes—
228C22×C8C22⋊D4714yes—
229C22×C8C22×D4712yes—
230C2×C4⋊C4—474no—
231C2×C4⋊C4—944no—
232C2×C4⋊C4—944no—
233C2×C4⋊C4—942no—
234C2×C22⋊C4—9416no—
235C2×C22⋊C4—18816no—
236C2×C42—472no—
237C2×C42—472no—
238C2×C42—942no—
239C2×C42—942no—
240#106—948no—
241#102—9416no—
242#97—948no—
243C24—28no—
244C24—24no—
245C24—44no—
246C24—44no—
247C24—48no—
248C24—48no—
249C24D4×D4711yescharacteristic
250C2×D4—216no—
251C2×D4—216no—
252C2×D4—28no—
253C2×D4—24no—
254C2×D4—24no—
255C2×D4—24no—
256C2×D4—24no—
257C2×D4—24no—
258C2×D4—44no—
259C2×D4—48no—
260C2×D4—48no—
261C2×D4—44no—
262C2×D4C22×Dic4718yes—
263C22×C4—474no—
264C22×C4—944no—
265C22×C4—948no—
266C22×C4—944no—
267C22×C4—1884no—
268C22×C4—1888no—
269C22×C4D4×D4711yescharacteristic
270C22×C4D4×D4712yes—
271C22×C4#1062535212yes—
272C22×C4#1062535212yes—
273C22×C4C22×Dic4712yes—
274C22×C4C2×C22⋊D4712yes—
275C22×C4C2×C22⋊D4712yes—
276C22×C4C23×D4711yescharacteristic
277D8—232no—
278C2×C8—474no—
279C2×C8—948no—
280C2×C8—942no—
281C2×C8—942no—
282C2×C8C22⋊Dic47116yescomplemented
283C2×C8C22×Dic4714yes—
284C2×C8C2×C22⋊D4714yes—
285C2×C8C2×C22⋊D4714yes—
286C4⋊C4—944no—
287C4⋊C4—944no—
288C4⋊C4—1884no—
289C22⋊C4—18832no—
290C42—944no—
291C42—942no—
292C42—942no—
293C23—28no—
294C23—432no—
295C23—416no—
296C23—44no—
297C23—48no—
298C23—48no—
299C23—44no—
300C23—88no—
301C23—88no—
302C23—816no—
303C23D4×Dic4712yes—
304C23#1309399512yes—
305C23#1309402012yes—
306C23#1309404818yes—
307C23C2×D4×D4711yescharacteristic
308D4—28no—
309D4—28no—
310D4—416no—
311D4—44no—
312D4—44no—
313C2×C4—944no—
314C2×C4—948no—
315C2×C4—3768no—
316C2×C4—1888no—
317C2×C4—1884no—
318C2×C4—1888no—
319C2×C4C2×C22⋊Dic4714yes—
320C2×C4D4×Dic4712yes—
321C2×C4D4×Dic4714yes—
322C2×C4#1309399512yes—
323C2×C4#1309399514yes—
324C2×C4#1309401114yes—
325C2×C4#1309402012yes—
326C2×C4C23×Dic4711yescharacteristic
327C2×C4C2×D4×D4711yescharacteristic
328C2×C4C22×C22⋊D4711yescharacteristic
329C2×C4C22×C22⋊D4711yescharacteristic
330C2×C4C2×#1062535211yescharacteristic
331C2×C4C2×#1062535211yescharacteristic
332C8—944no—
333C8C2×C22⋊Dic4718yescomplemented
334C22—416no—
335C22—48no—
336C22—832no—
337C22—88no—
338C22—84no—
339C22—84no—
340C22#1568902614yes—
341C22#1568923518yes—
342C22#1568937318yes—
343C22#1568951118yes—
344C22C2×D4×Dic4711yescharacteristic
345C22C2×#1309399511yescharacteristic
346C22C2×#1309402011yescharacteristic
347C22C2×#1309404814yes—
348C4—3764no—
349C4—1884no—
350C4#1568902614yes—
351C4C22×C22⋊Dic4711yescharacteristic
352C4C2×D4×Dic4711yescharacteristic
353C4C2×#1309399511yescharacteristic
354C4C2×#1309401111yescharacteristic
355C2—88no—
356C2#2024426518yesdirect product factor
357C2C2×#1568902611yescharacteristic
358C2C2×#1568923512yes—
359C2C2×#1568937312yes—
360C2C2×#1568951112yes—
subgroupG/H
centerC24D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
Fitting, prime radicalC23×D8×C47C2
socleC24×C47C2×D4
cosocleC22×C4×C47C24
hypercenterC23×D8D47
hypocenterC47C2×#1972
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×D8

Complements

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

NH ≅ G/Ntype
1. C22×#13093956C2semidirect
2. C22×#13093945C2semidirect
3. C22×#13093934C2semidirect
4. C2×#15689026C2semidirect
5. #20244265C2direct (N × H)
12. C2×#13093956C22semidirect
14. C2×#13093945C22semidirect
16. C2×#13093934C22semidirect
18. #15689026C22semidirect
22. C22×D8×C47C4semidirect
57. C2×D8×C47C2×C4semidirect
97. C2×C8×C47C22⋊C4semidirect
151. C8×C47C2×C22⋊C4semidirect
182. C2×C47#1972semidirect
190. C22×D8Dic47semidirect
205. C47C2×#1972semidirect
221. C2×D8C2×Dic47semidirect
282. C2×C8C22⋊Dic47semidirect
333. C8C2×C22⋊Dic47semidirect
356. C2#20244265direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130939562
C22×#130939452
C22×#130939342
C2×#156890262
#202442652
C23×D8×C472
C2×#197247