Finite Group Databasebeta

← #361×Dic47 #26131533

Subgroups — #361×Dic47 #26131533

Order 12032.

498 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×Dic47C211yesmaximal, characteristic
2C2×#15688936C211yesmaximal, characteristic
3M32×Dic47C211yesmaximal, characteristic, complemented
4#108×Dic47C211yesmaximal, characteristic, complemented
5#20241498C211yesmaximal, characteristic, complemented
6#20241497C211yesmaximal, characteristic, complemented
7C2×C47×#361C211yesmaximal, characteristic
8C2×D4×Dic47—21no—
9C2×#13093964C2211yescharacteristic
10D8×Dic47—21no—
11D8×Dic47—21no—
12D8×Dic47C412yes—
13D8×Dic47C412yes—
14C2×#13093960C2211yescharacteristic
15C2×#13093958C2211yescharacteristic
16C2×#13093945—21no—
17M16×Dic47—21no—
18C2×C8×Dic47C2211yescharacteristic
19#15688936C414yescomplemented
20#15688898—21no—
21C16×Dic47—21no—
22#15688887—21no—
23C22×D8×C47C2211yescharacteristic
24C2×M32×C47C2211yescharacteristic
25C2×#108×C47C2211yescharacteristic
26C47×#361C414yescomplemented
27C23×Dic47—41no—
28C2×#10625329—21no—
29C22×C47⋊C8D411yescharacteristic
30D4×Dic47—22no—
31D4×Dic47—22no—
32D4×Dic47—41no—
33D4×Dic47—41no—
34C2×C4⋊Dic47—21no—
35C2×C22⋊Dic47—41no—
36C2×C4×Dic47D411yescharacteristic
37#13093964—21no—
38#13093964C2×C412yescomplemented
39C2×C47⋊C16—21no—
40#13093960—21no—
41#13093960C2×C412yescomplemented
42#13093958—21no—
43#13093958C2×C412yes—
44#13093945—22no—
45#13093945—22no—
46#13093934—41no—
47C8×Dic47—41no—
48C8×Dic47C2×C411yescharacteristic
49C8×Dic47C2×C411yescharacteristic
50C8×Dic47D411yescharacteristic
51C8×Dic47D411yescharacteristic
52C22×D4×C47—21no—
53C2×D8×C47—21no—
54C2×D8×C47—21no—
55C2×D8×C47—21no—
56C2×D8×C47C2×C412yes—
57C2×D8×C47C2×C412yes—
58C2×D8×C47C2×C412yes—
59C2×M16×C47—21no—
60C22×C8×C47C2311yescharacteristic
61M32×C47—21no—
62M32×C47C2×C412yescomplemented
63C2×C16×C47—21no—
64#108×C47—21no—
65#108×C47C2×C412yescomplemented
66C24×C47—41no—
67C2×D4×C47—22no—
68C2×D4×C47—22no—
69C2×D4×C47—22no—
70C2×D4×C47—41no—
71C2×D4×C47—41no—
72C2×D4×C47—41no—
73C22×C4×C47C2×D411yescharacteristic
74C22×Dic47—41no—
75C22×Dic47—42no—
76C22×Dic47—42no—
77C22×Dic47—84no—
78C22×Dic47SD1611yescharacteristic
79C22×Dic47SD1611yescharacteristic
80D8×C47—22no—
81D8×C47—22no—
82D8×C47—22no—
83D8×C47C4214yes—
84M16×C47—22no—
85M16×C47—41no—
86C2×C8×C47—41no—
87C2×C8×C47C22×C411yescharacteristic
88C2×C8×C47C22×C411yescharacteristic
89C2×C8×C47C22×C411yescharacteristic
90C2×C8×C47C2×D411yescharacteristic
91C2×C8×C47#4111yescharacteristic
92C2×C8×C47#4111yescharacteristic
93C22⋊Dic47—42no—
94C22⋊Dic47—42no—
95C4⋊Dic47—22no—
96C4⋊Dic47—41no—
97C4×Dic47C22⋊C411yescharacteristic
98C4×Dic47C22⋊C411yescharacteristic
99C4×Dic47D811yescharacteristic
100C4×Dic47D811yescharacteristic
101#10625329—22no—
102#10625329—41no—
103C2×C47⋊C8—21no—
104C2×C47⋊C8—21no—
105C2×C47⋊C8—41no—
106C2×C47⋊C8C22⋊C411yescharacteristic
107C2×C47⋊C8C22⋊C411yescharacteristic
108C16×C47—22no—
109C47⋊C16—22no—
110C23×C47—42no—
111C23×C47—42no—
112C23×C47—42no—
113C23×C47—82no—
114C23×C47—82no—
115C23×C47C2×SD1611yescharacteristic
116D4×C47—24no—
117D4×C47—42no—
118D4×C47—42no—
119D4×C47—42no—
120C2×C4×C47C2×C22⋊C411yescharacteristic
121C2×C4×C47C4×D411yescharacteristic
122C2×C4×C47C4×D411yescharacteristic
123C2×C4×C47C2×D811yescharacteristic
124C2×C4×C47#13511yescharacteristic
125C2×C4×C47#13511yescharacteristic
126C2×Dic47—22no—
127C2×Dic47—41no—
128C2×Dic47—42no—
129C2×Dic47—84no—
130C2×Dic47—82no—
131C2×Dic47—84no—
132C2×Dic47#10211yescharacteristic
133C2×Dic47#10211yescharacteristic
134C2×Dic47#10211yescharacteristic
135C2×Dic47#10211yescharacteristic
136C8×C47—42no—
137C8×C47C2×C4211yescharacteristic
138C8×C47#11711yescharacteristic
139C8×C47C4×D411yescharacteristic
140C8×C47C4×D411yescharacteristic
141C47⋊C8—21no—
142C47⋊C8—21no—
143C47⋊C8—42no—
144C4×#361—471nomaximal, Sylow
145C22×C47—21no—
146C22×C47—21no—
147C22×C47—44no—
148C22×C47—84no—
149C22×C47—84no—
150C22×C47—82no—
151C22×C47—82no—
152C22×C47C2×#10211yescharacteristic
153C22×C47C4×SD1611yescharacteristic
154C22×C47C4×SD1611yescharacteristic
155C4×C47C4×C22⋊C411yescharacteristic
156C4×C47#41611yescharacteristic
157C4×C47C4×D811yescharacteristic
158C4×C47C4×D811yescharacteristic
159Dic47—21no—
160Dic47—21no—
161Dic47—21no—
162Dic47—82no—
163Dic47#36112yesdirect product factor
164C2×C4×D8—471no—
165C2×#361—471no—
166C2×#361D4711yescharacteristic
167C4×M32—471no—
168C4×#108—471no—
169#1387—471no—
170#1387—471no—
171C2×C47—21no—
172C2×C47—21no—
173C2×C47—84no—
174C2×C47C4×#10211yescharacteristic
175C2×C47C2×#36111yescharacteristic
176C2×C47#214811yescharacteristic
177C22×D8C2×D4711yescharacteristic
178C2×C4×D4—941no—
179C2×M32—471no—
180C2×M32C2×D4711yescharacteristic
181C4×D8—472no—
182C4×D8—472no—
183C4×D8—941no—
184C4×D8—941no—
185C2×#108—471no—
186C2×#108C2×D4711yescharacteristic
187C2×#107—471no—
188C2×#102—941no—
189C4×M16—941no—
190C2×C4×C8—471no—
191#361—474no—
192#361Dic4714yesdirect product factor
193#346—941no—
194C4×C16—941no—
195#341—941no—
196C47C4×#36111yescharacteristic, complemented, Sylow
197C22×D4—21no—
198C23×C4—1881no—
199C2×D8—21no—
200C2×D8—21no—
201C2×D8—21no—
202C2×D8C4×D4712yes—
203C2×D8C4×D4712yes—
204C2×D8C2×Dic4712yes—
205C2×M16—21no—
206C2×M16—941no—
207C22×C8—471no—
208C22×C8C22×D4711yescharacteristic
209C4×D4—942no—
210C4×D4—942no—
211C4×D4—1881no—
212C4×D4—1881no—
213C2×C4⋊C4—941no—
214C2×C22⋊C4—1881no—
215C2×C42—471no—
216M32—21no—
217M32—472no—
218M32—941no—
219M32C2×Dic4712yescomplemented
220C2×C16—21no—
221C2×C16—941no—
222#108—21no—
223#108—472no—
224#108—941no—
225#108C2×Dic4712yescomplemented
226#107—472no—
227#107—941no—
228#102—942no—
229#102—942no—
230#97—1881no—
231C4×C8—471no—
232C4×C8—471no—
233C4×C8—471no—
234C4×C8—471no—
235C4×C8—1881no—
236C24—41no—
237C2×D4—22no—
238C2×D4—22no—
239C2×D4—22no—
240C2×D4—41no—
241C2×D4—41no—
242C2×D4—41no—
243C22×C4—471no—
244C22×C4—471no—
245C22×C4—3764no—
246C22×C4—1882no—
247C22×C4—1882no—
248C22×C4—1881no—
249C22×C4D4×D4711yescharacteristic
250D8—22no—
251D8—22no—
252D8—22no—
253D8C4×Dic4714yes—
254M16—22no—
255M16—41no—
256M16—942no—
257M16—1881no—
258C2×C8—41no—
259C2×C8—471no—
260C2×C8—471no—
261C2×C8—941no—
262C2×C8—941no—
263C2×C8—1881no—
264C2×C8C2×C4×D4711yescharacteristic
265C2×C8C2×C4×D4711yescharacteristic
266C2×C8D4×D4711yescharacteristic
267C2×C8#1062535211yescharacteristic
268C2×C8#1062535211yescharacteristic
269C2×C8C22×Dic4711yescharacteristic
270C4⋊C4—942no—
271C4⋊C4—1881no—
272C22⋊C4—1882no—
273C22⋊C4—1882no—
274C42—471no—
275C42—471no—
276C42—471no—
277C42—471no—
278C16—22no—
279C16—942no—
280C23—42no—
281C23—42no—
282C23—42no—
283C23—82no—
284C23—82no—
285C23SD16×D4711yescharacteristic
286D4—24no—
287D4—42no—
288D4—42no—
289D4—42no—
290C2×C4—471no—
291C2×C4—471no—
292C2×C4—471no—
293C2×C4—471no—
294C2×C4—942no—
295C2×C4—3764no—
296C2×C4—3764no—
297C2×C4—3762no—
298C2×C4—1881no—
299C2×C4—1882no—
300C2×C4C22⋊C4×D4711yescharacteristic
301C2×C4(C22⋊D47)⋊C411yescharacteristic
302C2×C4D4×Dic4711yescharacteristic
303C2×C4D8×D4711yescharacteristic
304C2×C4#1309404311yescharacteristic
305C2×C4#1309404511yescharacteristic
306C8—42no—
307C8—941no—
308C8—941no—
309C8—1882no—
310C8C2×C4×Dic4711yescharacteristic
311C8#1309398011yescharacteristic
312C8(C22⋊D47)⋊C411yescharacteristic
313C8D4×Dic4711yescharacteristic
314C22—21no—
315C22—21no—
316C22—44no—
317C22—84no—
318C22—84no—
319C22—82no—
320C22—82no—
321C22#102×D4711yescharacteristic
322C22SD16×Dic4711yescharacteristic
323C22#1568921411yescharacteristic
324C4—472no—
325C4—941no—
326C4—941no—
327C4—941no—
328C4—3762no—
329C4C22⋊C4×Dic4711yescharacteristic
330C4#1568911611yescharacteristic
331C4#1568920311yescharacteristic
332C4D8×Dic4711yescharacteristic
333C2—21no—
334C2—21no—
335C2—84no—
336C2#102×Dic4711yescharacteristic
337C2#361×D4711yescharacteristic
338C2#2024513411yescharacteristic
subgroupG/H
centerC22#102×D47
commutatorC8×C47C2×C42
FrattiniC22×C8C22×D47
FittingC2×C47×#361C2
socleC22×C47C2×#102
prime radicalC22×D8×C47C22
cosocleC22×C8×C47C23
hypercenterC2×#361D47
hypocenterC47C4×#361
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#361

Complements

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

NH ≅ G/Ntype
3. M32×Dic47C2semidirect
4. #108×Dic47C2semidirect
5. #20241498C2semidirect
6. #20241497C2semidirect
19. #15688936C4semidirect
26. C47×#361C4semidirect
38. #13093964C2×C4semidirect
41. #13093960C2×C4semidirect
62. M32×C47C2×C4semidirect
65. #108×C47C2×C4semidirect
163. Dic47#361direct (N × H)
192. #361Dic47direct (N × H)
196. C47C4×#361semidirect
219. M32C2×Dic47semidirect
225. #108C2×Dic47semidirect

Maximal subgroups

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

subgroupindex
C2×D8×Dic472
C2×#156889362
M32×Dic472
#108×Dic472
#202414982
#202414972
C2×C47×#3612
C4×#36147