Finite Group Databasebeta

← C2×#20244952 #26246187

Subgroups — C2×#20244952 #26246187

Order 12032.

998 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689021C211yesmaximal, characteristic
2C2×#15688993C211yesmaximal, characteristic
3#20244952C218yesmaximal, direct product factor
4C2×#15688886C212yesmaximal
5C2×#15688886C212yesmaximal
6C2×C47×#336C211yesmaximal, characteristic
7C22×C4⋊Dic47—21no—
8C22×C4⋊Dic47—21no—
9C22×C4⋊Dic47C2212yes—
10C22×C4⋊Dic47C2211yescharacteristic
11C22×C4⋊Dic47C2211yescharacteristic
12C22×Dic47⋊C4—21no—
13#15689021—22no—
14#15689021C2214yes—
15#15688993—22no—
16#15688993C2214yes—
17C2×C47⋊#95—21no—
18#15688886C2218yes—
19#15688886C2218yes—
20C23×C8×C47C2212yes—
21C22×C42×C47C2211yescharacteristic
22C47×#336C2214yes—
23C23×Dic47—21no—
24C23×Dic47—21no—
25C23×Dic47—22no—
26C2×C4⋊Dic47—21no—
27C2×C4⋊Dic47—22no—
28C2×C4⋊Dic47—24no—
29C2×C4⋊Dic47—28no—
30C2×C4⋊Dic47—22no—
31C2×C4⋊Dic47—24no—
32C2×C4⋊Dic47—24no—
33C2×C4⋊Dic47—21no—
34C2×C4⋊Dic47—44no—
35C2×C4⋊Dic47—44no—
36C2×C4⋊Dic47Q814yes—
37C2×C4⋊Dic47C2314yes—
38C2×C4⋊Dic47C2312yes—
39C2×C4⋊Dic47C2312yes—
40C2×Dic47⋊C4—24no—
41C2×Dic47⋊C4—44no—
42C47⋊#95—24no—
43C23×C4×C47D411yescharacteristic
44C23×C4×C47D411yescharacteristic
45C23×C4×C47C2311yescharacteristic
46C22×C8×C47—24no—
47C22×C8×C47—24no—
48C22×C8×C47—24no—
49C22×C8×C47C2314yes—
50C2×C42×C47—24no—
51C2×C42×C47D412yes—
52C2×C42×C47C2312yes—
53C24×C47C2×D411yescharacteristic
54C22×C4×C47—22no—
55C22×C4×C47—22no—
56C22×C4×C47—22no—
57C22×C4×C47—22no—
58C22×C4×C47SD1614yes—
59C22×C4×C47Q1614yes—
60C22×C4×C47C2×D412yes—
61C22×C4×C47C2×D412yes—
62C22×C4×C47C2×D411yescharacteristic
63C22×C4×C47C2×Q812yes—
64C22×C4×C47#4112yes—
65C22×C4×C47#4114yes—
66C22×C4×C47#4114yes—
67C22×C4×C47C2411yescharacteristic
68C22×Dic47—24no—
69C22×Dic47—22no—
70C22×Dic47—22no—
71C22×Dic47—24no—
72C22×Dic47—42no—
73C22×Dic47—42no—
74C22×Dic47—42no—
75C22×Dic47—44no—
76C22×Dic47—42no—
77C22×Dic47—44no—
78C22×Dic47—44no—
79C22×Dic47—42no—
80C2×C8×C47—24no—
81C2×C8×C47—24no—
82C2×C8×C47—24no—
83C2×C8×C47—48no—
84C42×C47—24no—
85C42×C47—24no—
86C4⋊Dic47—24no—
87C4⋊Dic47—22no—
88C4⋊Dic47—24no—
89C4⋊Dic47—28no—
90C4⋊Dic47—48no—
91C4⋊Dic47—48no—
92C4⋊Dic47—42no—
93C4⋊Dic47—44no—
94C4⋊Dic47C2×Q814yes—
95Dic47⋊C4—48no—
96C23×C47C22⋊Q812yes—
97C23×C47#12312yes—
98C23×C47#12412yes—
99C23×C47C2×SD1612yes—
100C23×C47C2×Q1612yes—
101C23×C47AGL(1,ℤ/8)12yes—
102C23×C47AGL(1,ℤ/8)12yes—
103C23×C47C22×D411yescharacteristic
104C2×C4×C47—22no—
105C2×C4×C47—22no—
106C2×C4×C47—22no—
107C2×C4×C47—22no—
108C2×C4×C47—28no—
109C2×C4×C47—28no—
110C2×C4×C47C22⋊Q812yes—
111C2×C4×C47#12312yes—
112C2×C4×C47#12412yes—
113C2×C4×C47#12518yes—
114C2×C4×C47#12618yes—
115C2×C4×C47C2×SD1614yes—
116C2×C4×C47C2×Q1614yes—
117C2×C4×C47C22×Q811yescharacteristic
118C2×C4×C47C2×#4112yes—
119C2×C4×C47C2×#4111yescharacteristic
120C2×C4×C47C2×#4112yes—
121C2×Dic47—24no—
122C2×Dic47—42no—
123C2×Dic47—42no—
124C2×Dic47—48no—
125C2×Dic47—42no—
126C2×Dic47—44no—
127C2×Dic47—42no—
128C2×Dic47—44no—
129C2×Dic47—44no—
130C2×Dic47—42no—
131C2×Dic47—84no—
132C2×Dic47—88no—
133C8×C47—44no—
134C2×#2100—471nomaximal, Sylow
135C22×C47#40014yes—
136C22×C47#47614yes—
137C22×C47#47714yes—
138C22×C47#48114yes—
139C22×C47#48414yes—
140C22×C47#48714yes—
141C22×C47#49014yes—
142C22×C47C2×C22⋊Q811yescharacteristic
143C22×C47C2×#12311yescharacteristic
144C22×C47C2×#12411yescharacteristic
145C22×C47C22×SD1611yescharacteristic
146C22×C47C22×Q1611yescharacteristic
147C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
148C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
149C4×C47—24no—
150C4×C47—24no—
151C4×C47#40014yes—
152C4×C47C2×#12512yes—
153C4×C47C2×#12612yes—
154Dic47—44no—
155Dic47—82no—
156Dic47—84no—
157C2×#389—471no—
158C2×#384—471no—
159#2100—478no—
160C2×#340—472no—
161C2×#340—472no—
162C2×#336D4711yescharacteristic
163C2×C47#210018yescomplemented
164C2×C47C2×#40011yescharacteristic
165C2×C47C2×#47611yescharacteristic
166C2×C47C2×#47711yescharacteristic
167C2×C47C2×#48111yescharacteristic
168C2×C47C2×#48411yescharacteristic
169C2×C47C2×#48711yescharacteristic
170C2×C47C2×#49011yescharacteristic
171C23×C8C2×D4712yes—
172C22×C4⋊C4—471no—
173C22×C4⋊C4—472no—
174C22×C4⋊C4—471no—
175C22×C4⋊C4—941no—
176C22×C4⋊C4—941no—
177C22×C4⋊C4—941no—
178C22×C42C2×D4711yescharacteristic
179#389—474no—
180#389—942no—
181#384—474no—
182#384—942no—
183C2×#95—941no—
184#340—478no—
185#340—478no—
186#336C2×D4714yes—
187C47C2×#210011yescharacteristic, complemented, Sylow
188C23×C4—941no—
189C23×C4—942no—
190C23×C4—941no—
191C23×C4D18811yescharacteristic
192C23×C4D18811yescharacteristic
193C23×C4C22×D4711yescharacteristic
194C22×C8—24no—
195C22×C8—24no—
196C22×C8—24no—
197C22×C8C22×D4714yes—
198C2×C4⋊C4—474no—
199C2×C4⋊C4—472no—
200C2×C4⋊C4—474no—
201C2×C4⋊C4—472no—
202C2×C4⋊C4—941no—
203C2×C4⋊C4—942no—
204C2×C4⋊C4—948no—
205C2×C4⋊C4—944no—
206C2×C4⋊C4—942no—
207C2×C4⋊C4—941no—
208C2×C4⋊C4—944no—
209C2×C4⋊C4—944no—
210C2×C4⋊C4—944no—
211C2×C4⋊C4—1884no—
212C2×C4⋊C4—1884no—
213C2×C4⋊C4—1884no—
214C2×C42—24no—
215C2×C42D18812yes—
216C2×C42C22×D4712yes—
217#95—944no—
218C24C2×D18811yescharacteristic
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—944no—
224C22×C4—942no—
225C22×C4—942no—
226C22×C4—944no—
227C22×C4—1882no—
228C22×C4—1884no—
229C22×C4—1882no—
230C22×C4—1884no—
231C22×C4—1884no—
232C22×C4—1882no—
233C22×C4—1882no—
234C22×C4—1882no—
235C22×C4#1062532514yes—
236C22×C4Dic18814yes—
237C22×C4C2×D18812yes—
238C22×C4C2×D18812yes—
239C22×C4C2×D18811yescharacteristic
240C22×C4#1062535014yes—
241C22×C4#1062535212yes—
242C22×C4#1062535214yes—
243C22×C4Q8×D4712yes—
244C22×C4C23×D4711yescharacteristic
245C2×C8—24no—
246C2×C8—24no—
247C2×C8—24no—
248C2×C8—48no—
249C4⋊C4—474no—
250C4⋊C4—944no—
251C4⋊C4—942no—
252C4⋊C4—944no—
253C4⋊C4—948no—
254C4⋊C4—1888no—
255C4⋊C4—1888no—
256C4⋊C4—1882no—
257C4⋊C4—1884no—
258C4⋊C4—1888no—
259C42—24no—
260C42—24no—
261C23#1309400412yes—
262C23#1309400812yes—
263C23#1309401212yes—
264C23C2×#1062532512yes—
265C23C2×Dic18812yes—
266C23#1309405212yes—
267C23#1309405212yes—
268C23C22×D18811yescharacteristic
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—28no—
274C2×C4—28no—
275C2×C4—944no—
276C2×C4—3768no—
277C2×C4—3764no—
278C2×C4—1882no—
279C2×C4—1884no—
280C2×C4—1882no—
281C2×C4—1884no—
282C2×C4—1884no—
283C2×C4—1882no—
284C2×C4—1882no—
285C2×C4—1882no—
286C2×C4—1888no—
287C2×C4#1309400412yes—
288C2×C4#1309400812yes—
289C2×C4#1309401212yes—
290C2×C4#1309401418yes—
291C2×C4#1309401718yes—
292C2×C4C2×#1062532514yes—
293C2×C4C2×Dic18814yes—
294C2×C4C2×Q8×D4711yescharacteristic
295C2×C4C2×#1062535212yes—
296C2×C4C2×#1062535211yescharacteristic
297C2×C4C2×#1062535012yes—
298C8—44no—
299C22#1568906314yes—
300C22#1568941414yes—
301C22#1568941914yes—
302C22#1568944214yes—
303C22#1568945914yes—
304C22#1568947414yes—
305C22#1568948814yes—
306C22C2×#1309400411yescharacteristic
307C22C2×#1309400811yescharacteristic
308C22C2×#1309401211yescharacteristic
309C22C22×#1062532511yescharacteristic
310C22C22×Dic18811yescharacteristic
311C22C2×#1309405211yescharacteristic
312C22C2×#1309405211yescharacteristic
313C4—24no—
314C4—24no—
315C4—3764no—
316C4—3762no—
317C4—1884no—
318C4#1568906314yes—
319C4C2×#1309401412yes—
320C4C2×#1309401712yes—
321C2#2024495218yesdirect product factor
322C2C2×#1568906311yescharacteristic
323C2C2×#1568941411yescharacteristic
324C2C2×#1568941911yescharacteristic
325C2C2×#1568944211yescharacteristic
326C2C2×#1568945911yescharacteristic
327C2C2×#1568947411yescharacteristic
328C2C2×#1568948811yescharacteristic
subgroupG/H
centerC24C2×D188
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC2×C47×#336C2
socle, prime radicalC24×C47C2×D4
hypercenterC2×#336D47
hypocenterC47C2×#2100
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
3. #20244952C2direct (N × H)
163. C2×C47#2100semidirect
187. C47C2×#2100semidirect
321. C2#20244952direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156890212
C2×#156889932
#202449522
C2×#156888862
C2×C47×#3362
C2×#210047