Finite Group Databasebeta

← #26131530

Subgroups — #26131530

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×#15689205C211yesmaximal, characteristic
2C2×#15688937C211yesmaximal, characteristic
3C2×#15688935C211yesmaximal, characteristic
4M32×Dic47C211yesmaximal, characteristic, complemented
5#108×Dic47C211yesmaximal, characteristic, complemented
6#20241496C211yesmaximal, characteristic, complemented
7C47×#1387C211yesmaximal, characteristic, complemented
8C22×D376C2211yescharacteristic
9C2×#13093986—21no—
10C2×#13093964C2211yescharacteristic
11#15689205—21no—
12#15689205—21no—
13#15689205C412yes—
14#15689205C412yes—
15C2×#13093960C2211yescharacteristic
16C2×#13093944—21no—
17M16×Dic47—21no—
18C2×C8×Dic47C2211yescharacteristic
19#15688937C414yescomplemented
20#15688935C414yescomplemented
21#15688898—21no—
22C16×Dic47—21no—
23#15688887—21no—
24C2×M32×C47C2211yescharacteristic
25C2×#108×C47C2211yescharacteristic
26C2×#107×C47C2211yescharacteristic
27C22×D188—21no—
28C22×C4×D47—41no—
29C2×D376—21no—
30C2×D376—21no—
31C2×D376—21no—
32C2×D376C2×C412yes—
33C2×D376C2×C412yes—
34C2×D376C2×C412yes—
35C2×#10625329—21no—
36C22×C47⋊C8D411yescharacteristic
37#13093986—22no—
38#13093986—22no—
39#13093986—41no—
40#13093986—41no—
41C2×(C2×D47)⋊C4—41no—
42C2×C4×Dic47D411yescharacteristic
43#13093964—21no—
44#13093964C2×C412yescomplemented
45C2×C47⋊C16—21no—
46#13093960—21no—
47#13093960C2×C412yescomplemented
48#13093944—22no—
49#13093944—22no—
50#13093934—41no—
51C8×Dic47—41no—
52C8×Dic47C2×C411yescharacteristic
53C8×Dic47C2×C411yescharacteristic
54C8×Dic47D411yescharacteristic
55C8×Dic47D411yescharacteristic
56C2×M16×C47—21no—
57C22×C8×C47C2311yescharacteristic
58C2×C4⋊C4×C47—21no—
59M32×C47—21no—
60M32×C47C2×C412yescomplemented
61C2×C16×C47—21no—
62#108×C47—21no—
63#108×C47C2×C412yescomplemented
64#107×C47—21no—
65#107×C47C2×C412yes—
66C23×D47—41no—
67C22×C4×C47—41no—
68C22×C4×C47C2×D411yescharacteristic
69C22×Dic47SD1611yescharacteristic
70C22×Dic47SD1611yescharacteristic
71C2×D188—22no—
72C2×D188—22no—
73C2×D188—22no—
74C2×D188—41no—
75C2×D188—41no—
76C2×D188—41no—
77C2×C4×D47—42no—
78C2×C4×D47—42no—
79C2×C4×D47—84no—
80M16×C47—22no—
81M16×C47—41no—
82C2×C8×C47—41no—
83C2×C8×C47C22×C411yescharacteristic
84C2×C8×C47C22×C411yescharacteristic
85C2×C8×C47C22×C411yescharacteristic
86C2×C8×C47C2×D411yescharacteristic
87C2×C8×C47#4111yescharacteristic
88C2×C8×C47#4111yescharacteristic
89C4⋊C4×C47—22no—
90C4⋊C4×C47—41no—
91(C2×D47)⋊C4—42no—
92(C2×D47)⋊C4—42no—
93C4×Dic47C22⋊C411yescharacteristic
94C4×Dic47C22⋊C411yescharacteristic
95C4×Dic47D811yescharacteristic
96C4×Dic47D811yescharacteristic
97#10625329—22no—
98#10625329—41no—
99C2×C47⋊C8—21no—
100C2×C47⋊C8—21no—
101C2×C47⋊C8—41no—
102C2×C47⋊C8C22⋊C411yescharacteristic
103C2×C47⋊C8C22⋊C411yescharacteristic
104D376—22no—
105D376—22no—
106D376—22no—
107D376C4214yes—
108C16×C47—22no—
109C47⋊C16—22no—
110C23×C47C2×SD1611yescharacteristic
111C22×D47—42no—
112C22×D47—42no—
113C22×D47—42no—
114C22×D47—82no—
115C22×D47—82no—
116C2×C4×C47—42no—
117C2×C4×C47—82no—
118C2×C4×C47C2×C22⋊C411yescharacteristic
119C2×C4×C47C4×D411yescharacteristic
120C2×C4×C47C4×D411yescharacteristic
121C2×C4×C47C2×D811yescharacteristic
122C2×C4×C47#13511yescharacteristic
123C2×C4×C47#13511yescharacteristic
124C2×Dic47—22no—
125C2×Dic47—41no—
126C2×Dic47#10211yescharacteristic
127C2×Dic47#10211yescharacteristic
128C2×Dic47#10211yescharacteristic
129C2×Dic47#10211yescharacteristic
130D188—24no—
131D188—42no—
132D188—42no—
133D188—42no—
134C4×D47—84no—
135C4×D47—84no—
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×C47C2×#10211yescharacteristic
148C22×C47C4×SD1611yescharacteristic
149C22×C47C4×SD1611yescharacteristic
150C2×D47—44no—
151C2×D47—84no—
152C2×D47—84no—
153C2×D47—82no—
154C2×D47—82no—
155C4×C47—82no—
156C4×C47C4×C22⋊C411yescharacteristic
157C4×C47#41611yescharacteristic
158C4×C47C4×D811yescharacteristic
159C4×C47C4×D811yescharacteristic
160Dic47—21no—
161Dic47—21no—
162Dic47—21no—
163Dic47#36112yescomplemented
164C2×C4×D8—471no—
165C2×#361—471no—
166C2×#361—471no—
167C4×M32—471no—
168C4×#108—471no—
169#1387—471no—
170#1387D4711yescharacteristic, complemented
171C2×C47—21no—
172C2×C47—21no—
173C2×C47C4×#10211yescharacteristic
174C2×C47C2×#36111yescharacteristic
175C2×C47#214811yescharacteristic
176D47—84no—
177C22×D8—471no—
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×#107C2×D4711yescharacteristic
188C2×#102—941no—
189C4×M16—941no—
190C2×C4×C8—471no—
191#361—474no—
192#361—474no—
193#346—941no—
194C4×C16—941no—
195#341—941no—
196C47C4×#36111yescharacteristic, complemented, Sylow
197C22×D4—941no—
198C23×C4—1881no—
199C2×D8—472no—
200C2×D8—472no—
201C2×D8—472no—
202C2×D8—941no—
203C2×D8—941no—
204C2×D8—941no—
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—21no—
214C2×C22⋊C4—1881no—
215C2×C42—471no—
216M32—21no—
217M32—472no—
218M32—941no—
219M32C4×D4712yescomplemented
220C2×C16—21no—
221C2×C16—941no—
222#108—21no—
223#108—472no—
224#108—941no—
225#108C4×D4712yescomplemented
226#107—21no—
227#107C4×D4712yes—
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—1881no—
237C2×D4—942no—
238C2×D4—942no—
239C2×D4—942no—
240C2×D4—1881no—
241C2×D4—1881no—
242C2×D4—1881no—
243C22×C4—41no—
244C22×C4—471no—
245C22×C4—471no—
246C22×C4—3764no—
247C22×C4—1882no—
248C22×C4—1882no—
249C22×C4D4×D4711yescharacteristic
250D8—474no—
251D8—942no—
252D8—942no—
253D8—942no—
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×C8C2×C4×D4711yescharacteristic
267C2×C8D4×D4711yescharacteristic
268C2×C8#1062535211yescharacteristic
269C2×C8#1062535411yescharacteristic
270C4⋊C4—22no—
271C4⋊C4—41no—
272C22⋊C4—1882no—
273C22⋊C4—1882no—
274C42—471no—
275C42—471no—
276C42—471no—
277C42—471no—
278C16—22no—
279C16—942no—
280C23—3762no—
281C23—3762no—
282C23—1882no—
283C23—1882no—
284C23—1882no—
285C23SD16×D4711yescharacteristic
286D4—944no—
287D4—1882no—
288D4—1882no—
289D4—1882no—
290C2×C4—42no—
291C2×C4—82no—
292C2×C4—471no—
293C2×C4—471no—
294C2×C4—471no—
295C2×C4—471no—
296C2×C4—942no—
297C2×C4—3764no—
298C2×C4—3764no—
299C2×C4—1881no—
300C2×C4C22⋊C4×D4711yescharacteristic
301C2×C4(C22⋊D47)⋊C411yescharacteristic
302C2×C4#1309398611yescharacteristic
303C2×C4D8×D4711yescharacteristic
304C2×C4#1309404511yescharacteristic
305C2×C4#1309404711yescharacteristic
306C8—42no—
307C8—941no—
308C8—941no—
309C8—1882no—
310C8C42×D4711yescharacteristic
311C8#1309398211yescharacteristic
312C8(C22⋊D47)⋊C411yescharacteristic
313C8#1309398611yescharacteristic
314C22—21no—
315C22—21no—
316C22—3764no—
317C22—3764no—
318C22—3762no—
319C22—3762no—
320C22—1884no—
321C22#102×D4711yescharacteristic
322C22#1568920811yescharacteristic
323C22#1568921011yescharacteristic
324C4—82no—
325C4—472no—
326C4—941no—
327C4—941no—
328C4—941no—
329C4#1568897011yescharacteristic
330C4#1568911811yescharacteristic
331C4#1568920311yescharacteristic
332C4#1568920511yescharacteristic
333C2—21no—
334C2—21no—
335C2—3764no—
336C2#2024320211yescharacteristic
337C2#361×D4711yescharacteristic
338C2#2024513611yescharacteristic
subgroupG/H
centerC22#102×D47
commutatorC8×C47C2×C42
FrattiniC22×C8C22×D47
FittingC47×#1387C2
socleC22×C47C2×#102
prime radicalC22×D376C22
cosocleC22×C8×C47C23
hypercenter#1387D47
hypocenterC47C4×#361
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1387

Complements

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

NH ≅ G/Ntype
4. M32×Dic47C2semidirect
5. #108×Dic47C2semidirect
6. #20241496C2semidirect
7. C47×#1387C2semidirect
19. #15688937C4semidirect
20. #15688935C4semidirect
44. #13093964C2×C4semidirect
47. #13093960C2×C4semidirect
60. M32×C47C2×C4semidirect
63. #108×C47C2×C4semidirect
163. Dic47#361semidirect
170. #1387D47semidirect
196. C47C4×#361semidirect
219. M32C4×D47semidirect
225. #108C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156892052
C2×#156889372
C2×#156889352
M32×Dic472
#108×Dic472
#202414962
C47×#13872
C4×#36147