Finite Group Databasebeta

← C2×#20243479 #26216065

Subgroups — C2×#20243479 #26216065

Order 12032.

1878 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
1C23×C4⋊Dic47C211yesmaximal, characteristic
2C2×#15688983C211yesmaximal, characteristic
3#20243479C218yesmaximal, direct product factor
4C2×#15688886C214yesmaximal, complemented
5C22×C22⋊C8×C47C211yesmaximal, characteristic
6C24×Dic47—21no—
7C22×C4⋊Dic47—21no—
8C22×C4⋊Dic47—22no—
9C22×C4⋊Dic47—24no—
10C22×C4⋊Dic47C418yescomplemented
11C22×C4⋊Dic47C2212yes—
12C22×C4⋊Dic47C2212yes—
13C22×C4⋊Dic47C2214yes—
14C22×C22⋊Dic47—21no—
15#15688983—22no—
16#15688983C2214yes—
17C2×C47⋊#95—21no—
18#15688886C22116yescomplemented
19C24×C4×C47C2211yescharacteristic
20C23×C8×C47C2212yes—
21C2×C22⋊C8×C47—24no—
22C2×C22⋊C8×C47C2214yes—
23C23×Dic47—28no—
24C23×Dic47—22no—
25C23×Dic47—24no—
26C23×Dic47—22no—
27C23×Dic47—48no—
28C2×C4⋊Dic47—216no—
29C2×C4⋊Dic47—28no—
30C2×C4⋊Dic47—22no—
31C2×C4⋊Dic47—24no—
32C2×C4⋊Dic47—24no—
33C2×C4⋊Dic47—28no—
34C2×C4⋊Dic47—28no—
35C2×C4⋊Dic47—22no—
36C2×C4⋊Dic47C2×C418yes—
37C2×C4⋊Dic47C2×C4116yescomplemented
38C2×C4⋊Dic47C2314yes—
39C2×C4⋊Dic47C2314yes—
40C2×C22⋊Dic47—24no—
41C2×C22⋊Dic47—44no—
42C47⋊#95—24no—
43C25×C47D411yescharacteristic
44C23×C4×C47—28no—
45C23×C4×C47C2×C414yes—
46C23×C4×C47D411yescharacteristic
47C23×C4×C47D412yes—
48C23×C4×C47D414yes—
49C23×C4×C47C2312yes—
50C23×C4×C47C2311yescharacteristic
51C22×C8×C47—24no—
52C22×C8×C47—28no—
53C22×C8×C47C2314yes—
54C22⋊C8×C47—28no—
55C24×C47—24no—
56C24×C47—24no—
57C24×C47C22⋊C414yes—
58C24×C47SD1614yes—
59C24×C47Q1614yes—
60C24×C47C2×D412yes—
61C24×C47C2×D411yescharacteristic
62C22×C4×C47—24no—
63C22×C4×C47—216no—
64C22×C4×C47—28no—
65C22×C4×C47—216no—
66C22×C4×C47—28no—
67C22×C4×C47C22⋊C414yes—
68C22×C4×C47C22⋊C418yes—
69C22×C4×C47C22×C414yes—
70C22×C4×C47C22×C412yes—
71C22×C4×C47C2×D412yes—
72C22×C4×C47C2×D414yes—
73C22×C4×C47C2×D411yescharacteristic
74C22×C4×C47C2×D412yes—
75C22×C4×C47#4118yes—
76C22×C4×C47C2411yescharacteristic
77C22×Dic47—28no—
78C22×Dic47—216no—
79C22×Dic47—24no—
80C22×Dic47—24no—
81C22×Dic47—416no—
82C22×Dic47—432no—
83C22×Dic47—48no—
84C22×Dic47—44no—
85C22×Dic47—44no—
86C22×Dic47—44no—
87C2×C8×C47—24no—
88C2×C8×C47—28no—
89C2×C8×C47—48no—
90C22⋊Dic47—48no—
91C4⋊Dic47—28no—
92C4⋊Dic47—216no—
93C4⋊Dic47—24no—
94C4⋊Dic47—28no—
95C4⋊Dic47—44no—
96C4⋊Dic47C22×C418yes—
97C23×C47—24no—
98C23×C47—24no—
99C23×C47—28no—
100C23×C47—28no—
101C23×C47—216no—
102C23×C47—216no—
103C23×C47#103116yes—
104C23×C47C2×C22⋊C414yes—
105C23×C47C2×C22⋊C412yes—
106C23×C47#12314yes—
107C23×C47C2×SD1614yes—
108C23×C47C2×SD1612yes—
109C23×C47C2×Q1614yes—
110C23×C47C2×Q1612yes—
111C23×C47AGL(1,ℤ/8)14yes—
112C23×C47C22×D411yescharacteristic
113C2×C4×C47—24no—
114C2×C4×C47—28no—
115C2×C4×C47—28no—
116C2×C4×C47—28no—
117C2×C4×C47—216no—
118C2×C4×C47C2×C22⋊C414yes—
119C2×C4×C47C2×C22⋊C412yes—
120C2×C4×C47#11718yes—
121C2×C4×C47#12318yes—
122C2×C4×C47#12314yes—
123C2×C4×C47C23×C411yescharacteristic
124C2×C4×C47C22×D411yescharacteristic
125C2×C4×C47C2×#4114yes—
126C2×Dic47—28no—
127C2×Dic47—432no—
128C2×Dic47—48no—
129C2×Dic47—416no—
130C2×Dic47—44no—
131C2×Dic47—44no—
132C2×Dic47—44no—
133C2×Dic47—88no—
134C8×C47—44no—
135C2×#1824—471nomaximal, Sylow
136C22×C47—28no—
137C22×C47—28no—
138C22×C47—232no—
139C22×C47—24no—
140C22×C47—24no—
141C22×C47#38114yes—
142C22×C47C2×#10318yes—
143C22×C47C2×#10314yes—
144C22×C47#41814yes—
145C22×C47#48118yes—
146C22×C47#48418yes—
147C22×C47C22×C22⋊C411yescharacteristic
148C22×C47C2×#12312yes—
149C22×C47C22×SD1611yescharacteristic
150C22×C47C22×Q1611yescharacteristic
151C22×C47C2×AGL(1,ℤ/8)12yes—
152C4×C47—24no—
153C4×C47#38114yes—
154C4×C47C2×#11712yes—
155C4×C47C2×#12312yes—
156Dic47—48no—
157Dic47—84no—
158C23×C4⋊C4—471no—
159C22×C22⋊C8D4711yescharacteristic
160C2×#380—471no—
161#1824—478no—
162C2×#340—474no—
163C2×C47—28no—
164C2×C47#182418yescomplemented
165C2×C47C2×#38111yescharacteristic
166C2×C47C22×#10311yescharacteristic
167C2×C47C2×#41811yescharacteristic
168C2×C47C2×#48112yes—
169C2×C47C2×#48412yes—
170C24×C4—941no—
171C24×C4C2×D4711yescharacteristic
172C23×C8C2×D4712yes—
173C22×C4⋊C4—478no—
174C22×C4⋊C4—474no—
175C22×C4⋊C4—472no—
176C22×C4⋊C4—472no—
177C22×C4⋊C4—942no—
178C22×C4⋊C4—941no—
179C22×C4⋊C4—944no—
180C22×C22⋊C4—941no—
181C2×C22⋊C8—24no—
182C2×C22⋊C8C2×D4714yes—
183#380—474no—
184#380—942no—
185C2×#95—941no—
186#340—4716no—
187C47C2×#182411yescharacteristic, complemented, Sylow
188C25D18811yescharacteristic
189C23×C4—28no—
190C23×C4—948no—
191C23×C4—944no—
192C23×C4—942no—
193C23×C4—942no—
194C23×C4—1888no—
195C23×C4C4×D4714yes—
196C23×C4D18812yes—
197C23×C4D18811yescharacteristic
198C23×C4C22⋊D4714yes—
199C23×C4C22×D4712yes—
200C23×C4C22×D4711yescharacteristic
201C22×C8—28no—
202C22×C8—24no—
203C22×C8C22×D4714yes—
204C2×C4⋊C4—478no—
205C2×C4⋊C4—4716no—
206C2×C4⋊C4—474no—
207C2×C4⋊C4—474no—
208C2×C4⋊C4—948no—
209C2×C4⋊C4—9416no—
210C2×C4⋊C4—944no—
211C2×C4⋊C4—942no—
212C2×C4⋊C4—948no—
213C2×C4⋊C4—944no—
214C2×C4⋊C4—948no—
215C2×C4⋊C4—942no—
216C2×C22⋊C4—944no—
217C2×C22⋊C4—1884no—
218C22⋊C8—28no—
219#95—944no—
220C24—24no—
221C24—24no—
222C24#1062532514yes—
223C24Dic18814yes—
224C24(C2×D47)⋊C414yes—
225C24C2×D18812yes—
226C24C2×D18811yescharacteristic
227C22×C4—24no—
228C22×C4—216no—
229C22×C4—216no—
230C22×C4—28no—
231C22×C4—28no—
232C22×C4—9416no—
233C22×C4—948no—
234C22×C4—944no—
235C22×C4—944no—
236C22×C4—1884no—
237C22×C4—1884no—
238C22×C4—1884no—
239C22×C4—18832no—
240C22×C4—18816no—
241C22×C4—1888no—
242C22×C4(C2×D47)⋊C414yes—
243C22×C4(C2×D47)⋊C418yes—
244C22×C4C2×C4×D4714yes—
245C22×C4C2×C4×D4712yes—
246C22×C4C2×D18812yes—
247C22×C4C2×D18811yescharacteristic
248C22×C4#1062535218yes—
249C22×C4C2×C22⋊D4714yes—
250C22×C4C2×C22⋊D4712yes—
251C22×C4C23×D4711yescharacteristic
252C2×C8—24no—
253C2×C8—28no—
254C2×C8—48no—
255C4⋊C4—478no—
256C4⋊C4—9416no—
257C4⋊C4—948no—
258C4⋊C4—944no—
259C4⋊C4—948no—
260C4⋊C4—1884no—
261C22⋊C4—1888no—
262C23—28no—
263C23—24no—
264C23—28no—
265C23—24no—
266C23—216no—
267C23—216no—
268C23#13093949116yes—
269C23C2×(C2×D47)⋊C414yes—
270C23C2×(C2×D47)⋊C412yes—
271C23#1309400814yes—
272C23C2×#1062532514yes—
273C23C2×#1062532512yes—
274C23C2×Dic18814yes—
275C23C2×Dic18812yes—
276C23#1309405214yes—
277C23C22×D18811yescharacteristic
278C2×C4—28no—
279C2×C4—24no—
280C2×C4—216no—
281C2×C4—28no—
282C2×C4—28no—
283C2×C4—948no—
284C2×C4—3768no—
285C2×C4—1884no—
286C2×C4—1884no—
287C2×C4—1884no—
288C2×C4—18832no—
289C2×C4—18816no—
290C2×C4—1888no—
291C2×C4C2×(C2×D47)⋊C414yes—
292C2×C4C2×(C2×D47)⋊C412yes—
293C2×C4#1309398018yes—
294C2×C4#1309400518yes—
295C2×C4#1309400814yes—
296C2×C4C22×C4×D4711yescharacteristic
297C2×C4C22×C22⋊D4711yescharacteristic
298C2×C4C2×#1062535214yes—
299C8—44no—
300C22—24no—
301C22—232no—
302C22—28no—
303C22—28no—
304C22—24no—
305C22#1568898414yes—
306C22C2×#1309394918yes—
307C22C2×#1309394914yes—
308C22#1568912914yes—
309C22#1568944218yes—
310C22#1568945918yes—
311C22C22×(C2×D47)⋊C411yescharacteristic
312C22C2×#1309400812yes—
313C22C22×#1062532511yescharacteristic
314C22C22×Dic18811yescharacteristic
315C22C2×#1309405212yes—
316C4—24no—
317C4—3764no—
318C4—1888no—
319C4#1568898414yes—
320C4C2×#1309398012yes—
321C4C2×#1309400512yes—
322C2—28no—
323C2#2024347918yesdirect product factor
324C2C2×#1568898411yescharacteristic
325C2C22×#1309394911yescharacteristic
326C2C2×#1568912911yescharacteristic
327C2C2×#1568944212yes—
328C2C2×#1568945912yes—
subgroupG/H
centerC24C2×D188
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC22×C22⋊C8×C47C2
socleC24×C47C2×D4
prime radicalC25×C47D4
cosocleC22×C4×C47C24
hypercenterC22×C22⋊C8D47
hypocenterC47C2×#1824
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. #20243479C2direct (N × H)
4. C2×#15688886C2semidirect
10. C22×C4⋊Dic47C4semidirect
18. #15688886C22semidirect
37. C2×C4⋊Dic47C2×C4semidirect
164. C2×C47#1824semidirect
187. C47C2×#1824semidirect
323. C2#20243479direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4⋊Dic472
C2×#156889832
#202434792
C2×#156888862
C22×C22⋊C8×C472
C2×#182447