Finite Group Databasebeta

← #26122082

Subgroups — #26122082

Order 12032.

842 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10625329C211yesmaximal, characteristic
2#20245795C211yesmaximal, characteristic
3C2×#15688879C214yesmaximal
4C47×#2285C211yesmaximal, characteristic
5C22×#10625329C2212yes—
6C2×#13093983C2212yes—
7C4×#10625329—21no—
8C4×#10625329—21no—
9C4×#10625329—21no—
10C4×#10625329—21no—
11C2×#13093935C412yescomplemented
12C2×C4×C47⋊C8C412yescomplemented
13#15688993—21no—
14#15688989—21no—
15#15688983—22no—
16C4×C4⋊Dic47C414yescomplemented
17#15688879—28no—
18C2×#117×C47C2212yes—
19C22×C42×C47C2211yescharacteristic
20C47×#384—21no—
21C47×#382—21no—
22C47×#380—22no—
23C4×C4⋊C4×C47C414yescomplemented
24C2×#10625329—22no—
25C2×#10625329—22no—
26C2×#10625329—22no—
27C2×#10625329—22no—
28C2×#10625329D414yes—
29C2×#10625329Q814yes—
30C22×C47⋊C8C2×C414yes—
31#13093983—24no—
32#13093983—24no—
33C2×C4⋊Dic47—24no—
34C2×C4⋊Dic47—22no—
35C2×C22⋊Dic47—22no—
36C2×C4×Dic47C2×C414yes—
37#13093935—22no—
38#13093935—22no—
39C4×C47⋊C8—22no—
40C4×C47⋊C8—22no—
41C47⋊#95—24no—
42C23×C4×C47D412yes—
43C23×C4×C47C2311yescharacteristic
44#117×C47—24no—
45#117×C47—24no—
46C2×C4⋊C4×C47—24no—
47C2×C4⋊C4×C47—22no—
48C2×C22⋊C4×C47—22no—
49C2×C42×C47C2×C414yes—
50C2×C42×C47C2×C411yescharacteristic
51C2×C42×C47C2×C411yescharacteristic
52C2×C42×C47C2×C412yes—
53C2×C42×C47C2×C412yes—
54C2×C42×C47D411yescharacteristic
55C2×C42×C47D411yescharacteristic
56C2×C42×C47D411yescharacteristic
57C2×C42×C47D411yescharacteristic
58C2×C42×C47Q812yes—
59#95×C47—24no—
60C24×C47C2×D411yescharacteristic
61C22×C4×C47—24no—
62C22×C4×C47—44no—
63C22×C4×C47C22⋊C412yes—
64C22×C4×C47C22⋊C412yes—
65C22×C4×C47C22⋊C412yes—
66C22×C4×C47C22⋊C412yes—
67C22×C4×C47C4⋊C412yes—
68C22×C4×C47C4⋊C412yes—
69C22×C4×C47C22×C411yescharacteristic
70C22×C4×C47C22×C411yescharacteristic
71C22×C4×C47C22×C411yescharacteristic
72C22×C4×C47C2×D411yescharacteristic
73C22×C4×C47C2×D411yescharacteristic
74C22×C4×C47C2×D412yes—
75C22×C4×C47C2×Q811yescharacteristic
76C22×C4×C47C2×Q812yes—
77C22×C4×C47#4112yes—
78C22×C4×C47#4112yes—
79C22×Dic47—24no—
80C4⋊C4×C47—48no—
81C4⋊C4×C47—44no—
82C22⋊C4×C47—42no—
83C22⋊C4×C47—42no—
84C42×C47—28no—
85C42×C47C4212yes—
86C42×C47C4212yes—
87C42×C47C22⋊C411yescharacteristic
88C42×C47C22⋊C411yescharacteristic
89C42×C47C22⋊C411yescharacteristic
90C42×C47C22⋊C411yescharacteristic
91C42×C47C4⋊C412yes—
92C42×C47C4⋊C412yes—
93C42×C47C4⋊C412yes—
94C42×C47C4⋊C412yes—
95C22⋊Dic47—42no—
96C22⋊Dic47—42no—
97C4⋊Dic47—48no—
98C4⋊Dic47—44no—
99C4×Dic47—28no—
100#10625329—24no—
101#10625329—24no—
102#10625329—24no—
103#10625329—24no—
104C2×C47⋊C8—24no—
105C2×C47⋊C8—24no—
106C2×C47⋊C8C4⋊C418yescomplemented
107C23×C47—42no—
108C23×C47C2×C22⋊C411yescharacteristic
109C23×C47C2×C22⋊C411yescharacteristic
110C23×C47C2×C4⋊C411yescharacteristic
111C23×C47#12411yescharacteristic
112C23×C47#12411yescharacteristic
113C23×C47#12711yescharacteristic
114C23×C47C4⋊Q811yescharacteristic
115C2×C4×C47—24no—
116C2×C4×C47—24no—
117C2×C4×C47—24no—
118C2×C4×C47—42no—
119C2×C4×C47—42no—
120C2×C4×C47—42no—
121C2×C4×C47—48no—
122C2×C4×C47—44no—
123C2×C4×C47#9512yes—
124C2×C4×C47#9512yes—
125C2×C4×C47#9512yes—
126C2×C4×C47#9512yes—
127C2×C4×C47C2×C4211yescharacteristic
128C2×C4×C47C2×C22⋊C411yescharacteristic
129C2×C4×C47C2×C4⋊C412yes—
130C2×C4×C47C2×C4⋊C411yescharacteristic
131C2×C4×C47C2×C4⋊C411yescharacteristic
132C2×C4×C47#11712yes—
133C2×C4×C47C4×D412yes—
134C2×C4×C47C4×D412yes—
135C2×C4×C47C4×Q812yes—
136C2×C4×C47C4×Q812yes—
137C2×C4×C47#12112yes—
138C2×C4×C47#12112yes—
139C2×C4×C47C22⋊Q812yes—
140C2×C4×C47C22⋊Q812yes—
141C2×C4×C47#12512yes—
142C2×C4×C47C4⋊Q812yes—
143C2×Dic47—48no—
144C2×Dic47—44no—
145C47⋊C8—28no—
146#10837—471nomaximal, Sylow
147C22×C47—22no—
148C22×C47—22no—
149C22×C47—22no—
150C22×C47—41no—
151C22×C47—41no—
152C22×C47—41no—
153C22×C47—41no—
154C22×C47C2×#9511yescharacteristic
155C22×C47#38211yescharacteristic
156C22×C47#38411yescharacteristic
157C22×C47#39011yescharacteristic
158C22×C47#39011yescharacteristic
159C22×C47#39111yescharacteristic
160C22×C47#39111yescharacteristic
161C4×C47—22no—
162C4×C47—22no—
163C4×C47—22no—
164C4×C47—84no—
165C4×C47H(3,ℤ/4)14yescomplemented
166C4×C47C4×C4⋊C412yes—
167C4×C47#38012yes—
168C4×C47#38912yes—
169C4×C47#38912yes—
170Dic47—84no—
171C2×C4×M16—471no—
172#2285—471no—
173#2285D4711yescharacteristic
174C2×H(3,ℤ/4)—474no—
175C2×C47—21no—
176C2×C47—21no—
177C2×C47—21no—
178C2×C47—21no—
179C2×C47—21no—
180C2×C47—21no—
181C2×C47C4⋊#9511yescharacteristic
182C2×C47C2×H(3,ℤ/4)12yes—
183C22×M16—472no—
184C2×#117—472no—
185C2×#117C2×D4712yes—
186C22×C42C2×D4711yescharacteristic
187C4×M16—941no—
188C4×M16—941no—
189C4×M16—941no—
190C4×M16—941no—
191C2×#97—472no—
192C2×C4×C8—472no—
193#384—21no—
194#384—941no—
195#382—21no—
196#382—941no—
197#380—22no—
198#380—942no—
199C4×C4⋊C4—474no—
200C4×C4⋊C4Dic4714yescomplemented
201H(3,ℤ/4)—948no—
202C47#1083711yescharacteristic, complemented, Sylow
203C23×C4C22⋊D4712yes—
204C23×C4C22×D4711yescharacteristic
205C2×M16—474no—
206C2×M16—474no—
207C2×M16—942no—
208C2×M16—942no—
209C2×M16—942no—
210C2×M16—942no—
211C22×C8—474no—
212#117—24no—
213#117—24no—
214#117—944no—
215#117—944no—
216C2×C4⋊C4—24no—
217C2×C4⋊C4—22no—
218C2×C4⋊C4—944no—
219C2×C4⋊C4—942no—
220C2×C22⋊C4—22no—
221C2×C22⋊C4—942no—
222C2×C42—474no—
223C2×C42Dic9412yes—
224C2×C42C4×D4712yes—
225C2×C42C4×D4711yescharacteristic
226C2×C42C4×D4711yescharacteristic
227C2×C42D18811yescharacteristic
228C2×C42D18811yescharacteristic
229C2×C42C2×Dic4714yes—
230C2×C42C2×Dic4712yes—
231C2×C42C22⋊D4711yescharacteristic
232C2×C42C22⋊D4711yescharacteristic
233#97—942no—
234#97—942no—
235C4×C8—942no—
236C4×C8—942no—
237#95—24no—
238#95—944no—
239C24C2×C22⋊D4711yescharacteristic
240C22×C4—24no—
241C22×C4—44no—
242C22×C4—944no—
243C22×C4Dic47⋊C412yes—
244C22×C4Dic47⋊C412yes—
245C22×C4(C2×D47)⋊C412yes—
246C22×C4(C2×D47)⋊C412yes—
247C22×C4C22⋊Dic4712yes—
248C22×C4C22⋊Dic4712yes—
249C22×C4C2×Dic9411yescharacteristic
250C22×C4C2×C4×D4711yescharacteristic
251C22×C4C2×C4×D4711yescharacteristic
252C22×C4C2×D18811yescharacteristic
253C22×C4D4×D4712yes—
254C22×C4#1062535212yes—
255C22×C4Q8×D4712yes—
256C22×C4#1062535412yes—
257C22×C4C22×Dic4711yescharacteristic
258C22×C4C2×C22⋊D4711yescharacteristic
259M16—944no—
260M16—944no—
261M16—944no—
262M16—944no—
263C2×C8—478no—
264C2×C8—944no—
265C2×C8—944no—
266C4⋊C4—48no—
267C4⋊C4—44no—
268C4⋊C4—1888no—
269C4⋊C4—1884no—
270C22⋊C4—42no—
271C22⋊C4—42no—
272C22⋊C4—1882no—
273C22⋊C4—1882no—
274C42—28no—
275C42—948no—
276C42C4×Dic4712yes—
277C42C4×Dic4712yes—
278C42Dic47⋊C412yes—
279C42Dic47⋊C412yes—
280C42C4⋊Dic4712yes—
281C42C4⋊Dic4712yes—
282C42(C2×D47)⋊C411yescharacteristic
283C42(C2×D47)⋊C411yescharacteristic
284C42(C2×D47)⋊C411yescharacteristic
285C42(C2×D47)⋊C411yescharacteristic
286C23—42no—
287C23C2×(C2×D47)⋊C411yescharacteristic
288C23C2×C22⋊Dic4711yescharacteristic
289C23C2×Dic47⋊C411yescharacteristic
290C23#1309401111yescharacteristic
291C23#1309401311yescharacteristic
292C23#1309402011yescharacteristic
293C23#1309402211yescharacteristic
294C2×C4—24no—
295C2×C4—24no—
296C2×C4—24no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—48no—
301C2×C4—44no—
302C2×C4—1888no—
303C2×C4—1884no—
304C2×C4C47⋊#9512yes—
305C2×C4C47⋊#9512yes—
306C2×C4C47⋊#9512yes—
307C2×C4C47⋊#9512yes—
308C2×C4C2×C4×Dic4711yescharacteristic
309C2×C4C2×(C2×D47)⋊C411yescharacteristic
310C2×C4C4⋊C4×D4712yes—
311C2×C4C2×Dic47⋊C411yescharacteristic
312C2×C4C2×C4⋊Dic4711yescharacteristic
313C2×C4#1309398212yes—
314C2×C4#1309398612yes—
315C2×C4D4×Dic4712yes—
316C2×C4#1309398912yes—
317C2×C4Q8×Dic4712yes—
318C2×C4#1309399512yes—
319C2×C4#1309399912yes—
320C2×C4#1309400012yes—
321C2×C4#1309400412yes—
322C2×C4#1309401512yes—
323C2×C4#1309402312yes—
324C8—948no—
325C22—22no—
326C22—22no—
327C22—22no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22C2×C47⋊#9511yescharacteristic
333C22#1568898811yescharacteristic
334C22#1568899211yescharacteristic
335C22#1568902411yescharacteristic
336C22#1568902611yescharacteristic
337C22#1568902811yescharacteristic
338C22#1568903011yescharacteristic
339C4—22no—
340C4—22no—
341C4—22no—
342C4—84no—
343C4—3764no—
344C4#1568887914yescomplemented
345C4C4⋊C4×Dic4712yes—
346C4#1568898012yes—
347C4#1568901912yes—
348C4#1568902212yes—
349C2—21no—
350C2—21no—
351C2—21no—
352C2—21no—
353C2—21no—
354C2—21no—
355C2#2024161711yescharacteristic
356C2C2×#1568887912yes—
subgroupG/H
centerC2×C4C2×C4×Dic47
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC47×#2285C2
socleC22×C47C2×#95
prime radicalC24×C47C2×D4
cosocleC23×C4×C47C23
hypercenter#2285D47
hypocenterC47#10837
LCSG ▷ C2×C4×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #2285

Complements

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

NH ≅ G/Ntype
11. C2×#13093935C4semidirect
12. C2×C4×C47⋊C8C4semidirect
16. C4×C4⋊Dic47C4semidirect
23. C4×C4⋊C4×C47C4semidirect
106. C2×C47⋊C8C4⋊C4semidirect
165. C4×C47H(3,ℤ/4)semidirect
200. C4×C4⋊C4Dic47semidirect
202. C47#10837semidirect
344. C4#15688879semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106253292
#202457952
C2×#156888792
C47×#22852
#1083747