Finite Group Databasebeta

← #26132317

Subgroups — #26132317

Order 12032.

510 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×Dic47C211yesmaximal, characteristic
2C2×Dic47⋊C16C211yesmaximal, characteristic, complemented
3C2×#15688924C211yesmaximal, characteristic
4#20243546C211yesmaximal, characteristic, complemented
5#20241480C211yesmaximal, characteristic, complemented
6#20241479C211yesmaximal, characteristic, complemented
7C2×C47×#357C211yesmaximal, characteristic
8C2×D4×Dic47—21no—
9C22×C47⋊C16C2211yescharacteristic
10D8×Dic47—22no—
11D8×Dic47C414yescomplemented
12C2×#13093958C2211yescharacteristic
13C2×#13093958C2211yescharacteristic
14C2×#13093957—21no—
15C2×#13093945—21no—
16C2×C8×Dic47C2211yescharacteristic
17#15688992—21no—
18Dic47⋊C16—22no—
19#15688924—22no—
20C22×D8×C47C2211yescharacteristic
21C22×C16×C47C2211yescharacteristic
22C2×#107×C47C2211yescharacteristic
23C47×#357—22no—
24C23×Dic47—41no—
25C22×C47⋊C8D411yescharacteristic
26D4×Dic47—24no—
27D4×Dic47—42no—
28C2×C4⋊Dic47—21no—
29C2×C4⋊Dic47—21no—
30C2×Dic47⋊C4—41no—
31C2×Dic47⋊C4—41no—
32C2×C22⋊Dic47—41no—
33C2×C4×Dic47D411yescharacteristic
34C2×C47⋊C16—21no—
35C2×C47⋊C16—21no—
36C2×C47⋊C16—21no—
37#13093958—21no—
38#13093958—21no—
39#13093958—21no—
40#13093958C2×C412yes—
41#13093957—42no—
42#13093945—24no—
43C8×Dic47C2×C412yes—
44C8×Dic47D412yes—
45C22×D4×C47—21no—
46C2×D8×C47—21no—
47C2×D8×C47—21no—
48C2×D8×C47—21no—
49C2×D8×C47C2×C412yes—
50C2×D8×C47D412yes—
51C2×D8×C47Q812yes—
52C22×C8×C47C2311yescharacteristic
53C2×C4⋊C4×C47—21no—
54C2×C16×C47—21no—
55C2×C16×C47—21no—
56C2×C16×C47—21no—
57#107×C47—21no—
58#107×C47—21no—
59C24×C47—41no—
60C2×D4×C47—22no—
61C2×D4×C47—22no—
62C2×D4×C47—22no—
63C2×D4×C47—41no—
64C2×D4×C47—41no—
65C2×D4×C47—41no—
66C22×C4×C47—41no—
67C22×C4×C47C2×D411yescharacteristic
68C22×Dic47—41no—
69C22×Dic47—44no—
70C22×Dic47—41no—
71C22×Dic47—82no—
72C22×Dic47—82no—
73C22×Dic47D811yescharacteristic
74C22×Dic47D811yescharacteristic
75D8×C47—22no—
76D8×C47—22no—
77D8×C47—22no—
78D8×C47C4⋊C414yescomplemented
79C2×C8×C47C22×C411yescharacteristic
80C2×C8×C47C2×D411yescharacteristic
81C2×C8×C47C2×D411yescharacteristic
82C2×C8×C47C2×Q811yescharacteristic
83C2×C8×C47#4111yescharacteristic
84C2×C8×C47#4111yescharacteristic
85C4⋊C4×C47—41no—
86C4⋊C4×C47—41no—
87C22⋊Dic47—44no—
88C4⋊Dic47—22no—
89C4⋊Dic47—41no—
90C4⋊Dic47—41no—
91C4⋊Dic47—41no—
92Dic47⋊C4—82no—
93Dic47⋊C4—82no—
94C4×Dic47C22⋊C412yes—
95C4×Dic47SD1612yes—
96C2×C47⋊C8—21no—
97C2×C47⋊C8—21no—
98C2×C47⋊C8C22⋊C412yes—
99C16×C47—41no—
100C47⋊C16—41no—
101C23×C47—42no—
102C23×C47—42no—
103C23×C47—42no—
104C23×C47—81no—
105C23×C47—81no—
106C23×C47—81no—
107C23×C47—81no—
108C23×C47C2×D811yescharacteristic
109D4×C47—24no—
110D4×C47—42no—
111D4×C47—42no—
112D4×C47—42no—
113C2×C4×C47—81no—
114C2×C4×C47—81no—
115C2×C4×C47—81no—
116C2×C4×C47C2×C22⋊C411yescharacteristic
117C2×C4×C47#12111yescharacteristic
118C2×C4×C47C22⋊Q811yescharacteristic
119C2×C4×C47C2×SD1611yescharacteristic
120C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C47#13711yescharacteristic
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—42no—
125C2×Dic47—81no—
126C2×Dic47—81no—
127C2×Dic47—88no—
128C2×Dic47—81no—
129C2×Dic47—81no—
130C2×Dic47—81no—
131C2×Dic47#10212yes—
132C2×Dic47#10212yes—
133C2×Dic47D1612yes—
134C2×Dic47SD3212yes—
135C8×C47C2×C4⋊C411yescharacteristic
136C8×C47#11711yescharacteristic
137C8×C47#12111yescharacteristic
138C8×C47C22⋊Q811yescharacteristic
139C47⋊C8—22no—
140#12811—471nomaximal, Sylow
141C22×C47—44no—
142C22×C47—82no—
143C22×C47—82no—
144C22×C47—82no—
145C22×C47—82no—
146C22×C47—82no—
147C22×C47—82no—
148C22×C47C2×#10211yescharacteristic
149C22×C47#45911yescharacteristic
150C22×C47#47411yescharacteristic
151C22×C47C2×D1611yescharacteristic
152C22×C47C2×SD3211yescharacteristic
153C22×C47#50911yescharacteristic
154C22×C47#51011yescharacteristic
155C4×C47—161no—
156C4×C47#38011yescharacteristic
157C4×C47#41711yescharacteristic
158C4×C47#46111yescharacteristic
159C4×C47#47611yescharacteristic
160Dic47—22no—
161Dic47—82no—
162Dic47—161no—
163Dic47#35714yescomplemented
164C2×C4×D8—471no—
165C2×C4⋊C16—471no—
166C2×#357—471no—
167C2×#357D4711yescharacteristic
168#1845—471no—
169#1380—471no—
170#1380—471no—
171C2×C47—84no—
172C2×C47#180211yescharacteristic
173C2×C47C2×#35711yescharacteristic
174C2×C47#213911yescharacteristic
175C2×C47#220611yescharacteristic
176C2×C47#220811yescharacteristic
177C2×C47#222411yescharacteristic
178C2×C47#222611yescharacteristic
179C22×D8C2×D4711yescharacteristic
180C2×C4×D4—941no—
181C22×C16—471no—
182C22×C16C2×D4711yescharacteristic
183C4×D8—474no—
184C4×D8—942no—
185C2×#107—471no—
186C2×#107—471no—
187C2×#107—941no—
188C2×#107C2×D4711yescharacteristic
189C2×#102—941no—
190C2×C4×C8—471no—
191#384—941no—
192C4⋊C16—942no—
193#357—22no—
194#357—942no—
195C47#1281111yescharacteristic, complemented, Sylow
196C22×D4—21no—
197C23×C4—1881no—
198C2×D8—21no—
199C2×D8—21no—
200C2×D8—21no—
201C2×D8Dic9412yes—
202C2×D8C4×D4712yes—
203C2×D8C22⋊D4712yes—
204C22×C8—471no—
205C22×C8C22×D4711yescharacteristic
206C4×D4—944no—
207C4×D4—1882no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—941no—
210C2×C4⋊C4—941no—
211C2×C4⋊C4—1881no—
212C2×C4⋊C4—1881no—
213C2×C22⋊C4—1881no—
214C2×C42—471no—
215C2×C16—21no—
216C2×C16—21no—
217C2×C16—21no—
218C2×C16—941no—
219C2×C16—941no—
220C2×C16—941no—
221#107—21no—
222#107—21no—
223#107—472no—
224#107—941no—
225#107—941no—
226#107—941no—
227#107—1882no—
228#102—944no—
229C4×C8—472no—
230C4×C8—472no—
231C24—41no—
232C2×D4—22no—
233C2×D4—22no—
234C2×D4—22no—
235C2×D4—41no—
236C2×D4—41no—
237C2×D4—41no—
238C22×C4—41no—
239C22×C4—471no—
240C22×C4—471no—
241C22×C4—3762no—
242C22×C4—3762no—
243C22×C4—1884no—
244C22×C4—1881no—
245C22×C4—1881no—
246C22×C4D4×D4711yescharacteristic
247D8—22no—
248D8—22no—
249D8—22no—
250D8Dic47⋊C414yescomplemented
251C2×C8—472no—
252C2×C8—941no—
253C2×C8—941no—
254C2×C8C2×Dic9411yescharacteristic
255C2×C8C2×C4×D4711yescharacteristic
256C2×C8D4×D4711yescharacteristic
257C2×C8#1062535211yescharacteristic
258C2×C8#1062535211yescharacteristic
259C2×C8C2×C22⋊D4711yescharacteristic
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—942no—
263C4⋊C4—3762no—
264C4⋊C4—3762no—
265C4⋊C4—1881no—
266C4⋊C4—1881no—
267C4⋊C4—1881no—
268C22⋊C4—1884no—
269C42—472no—
270C42—472no—
271C16—41no—
272C16—1881no—
273C23—42no—
274C23—42no—
275C23—42no—
276C23—81no—
277C23—81no—
278C23—81no—
279C23—81no—
280C23D8×D4711yescharacteristic
281D4—24no—
282D4—42no—
283D4—42no—
284D4—42no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—472no—
289C2×C4—472no—
290C2×C4—472no—
291C2×C4—472no—
292C2×C4—941no—
293C2×C4—941no—
294C2×C4—3768no—
295C2×C4—3761no—
296C2×C4—3761no—
297C2×C4—3761no—
298C2×C4—3761no—
299C2×C4—3761no—
300C2×C4—1882no—
301C2×C4C22⋊C4×D4711yescharacteristic
302C2×C4#1309399611yescharacteristic
303C2×C4#1309400111yescharacteristic
304C2×C4SD16×D4711yescharacteristic
305C2×C4#1309404811yescharacteristic
306C2×C4#1309405311yescharacteristic
307C8—942no—
308C8C2×Dic47⋊C411yescharacteristic
309C8#1309398011yescharacteristic
310C8#1309399611yescharacteristic
311C8#1309400111yescharacteristic
312C22—44no—
313C22—82no—
314C22—82no—
315C22—82no—
316C22—82no—
317C22—82no—
318C22—82no—
319C22#102×D4711yescharacteristic
320C22#1568931611yescharacteristic
321C22#1568940111yescharacteristic
322C22D16×D4711yescharacteristic
323C22SD32×D4711yescharacteristic
324C22#1568955711yescharacteristic
325C22#1568956211yescharacteristic
326C4—161no—
327C4—474no—
328C4—942no—
329C4—3762no—
330C4—7521no—
331C4#1568898111yescharacteristic
332C4#1568912111yescharacteristic
333C4#1568932611yescharacteristic
334C4#1568941111yescharacteristic
335C2—84no—
336C2#2024338611yescharacteristic
337C2#357×D4711yescharacteristic
338C2#2024509711yescharacteristic
339C2#2024542111yescharacteristic
340C2#2024543111yescharacteristic
341C2#2024552311yescharacteristic
342C2#2024553311yescharacteristic
subgroupG/H
centerC23D8×D47
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC2×C47×#357C2
socleC23×C47C2×D8
prime radicalC22×D8×C47C22
cosocleC22×C8×C47C23
hypercenterC2×#357D47
hypocenterC47#12811
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
2. C2×Dic47⋊C16C2semidirect
4. #20243546C2semidirect
5. #20241480C2semidirect
6. #20241479C2semidirect
11. D8×Dic47C4semidirect
78. D8×C47C4⋊C4semidirect
163. Dic47#357semidirect
195. C47#12811semidirect
250. D8Dic47⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×D8×Dic472
C2×Dic47⋊C162
C2×#156889242
#202435462
#202414802
#202414792
C2×C47×#3572
#1281147