Finite Group Databasebeta

← #26132586

Subgroups — #26132586

Order 12032.

442 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#107×D47C211yesmaximal, characteristic
2#20244998C211yesmaximal, characteristic
3#20243423C211yesmaximal, characteristic
4#20241498C211yesmaximal, characteristic, complemented
5#20241497C211yesmaximal, characteristic, complemented
6#20241496C211yesmaximal, characteristic, complemented
7C47×#1387C211yesmaximal, characteristic, complemented
8C22×C8×D47C2211yescharacteristic
9C2×C4⋊C4×D47—21no—
10C2×#13093964C2211yescharacteristic
11C2×#13093960C2211yescharacteristic
12C2×#13093958C2211yescharacteristic
13C2×#13093957—21no—
14#107×D47—21no—
15#107×D47—21no—
16#107×D47C412yes—
17#107×D47C412yes—
18#15689086—21no—
19(C2×D47)⋊C16—21no—
20(C2×D47)⋊C16—21no—
21#15688887—21no—
22C2×M32×C47C2211yescharacteristic
23C2×#108×C47C2211yescharacteristic
24C2×#107×C47C2211yescharacteristic
25C22×C4×D47—41no—
26C22×C4×D47D411yescharacteristic
27C2×#10625329—21no—
28C22×C47⋊C8D411yescharacteristic
29C2×C8×D47—21no—
30C2×C8×D47—21no—
31C2×C8×D47—21no—
32C2×C8×D47—21no—
33C2×C8×D47C2×C411yescharacteristic
34C2×C8×D47C2×C411yescharacteristic
35C2×C8×D47D411yescharacteristic
36C2×C8×D47D411yescharacteristic
37C2×C4⋊Dic47—21no—
38C2×Dic47⋊C4—41no—
39C4⋊C4×D47—22no—
40C4⋊C4×D47—22no—
41C4⋊C4×D47—41no—
42C4⋊C4×D47—41no—
43#13093964—21no—
44#13093964—21no—
45C2×C47⋊C16—21no—
46#13093960—21no—
47#13093960—21no—
48#13093958—21no—
49#13093958C2×C412yes—
50#13093957—22no—
51#13093957—22no—
52(C2×D47)⋊C8—41no—
53(C2×D47)⋊C8—41no—
54C2×M16×C47—21no—
55C22×C8×C47C2311yescharacteristic
56C2×C4⋊C4×C47—21no—
57M32×C47—21no—
58M32×C47—21no—
59C2×C16×C47—21no—
60#108×C47—21no—
61#108×C47—21no—
62#107×C47—21no—
63#107×C47C2×C412yes—
64C23×D47SD1611yescharacteristic
65C22×C4×C47—41no—
66C22×C4×C47C2×D411yescharacteristic
67C22×Dic47—41no—
68C22×Dic47SD1611yescharacteristic
69C2×C4×D47—21no—
70C2×C4×D47—21no—
71C2×C4×D47—21no—
72C2×C4×D47—21no—
73C2×C4×D47—42no—
74C2×C4×D47—42no—
75C2×C4×D47—84no—
76C2×C4×D47C22⋊C411yescharacteristic
77C2×C4×D47C22⋊C411yescharacteristic
78C2×C4×D47D811yescharacteristic
79C2×C4×D47D811yescharacteristic
80M16×C47—41no—
81M16×C47—41no—
82C2×C8×C47—41no—
83C2×C8×C47C22×C411yescharacteristic
84C2×C8×C47C2×D411yescharacteristic
85C2×C8×C47#4111yescharacteristic
86C2×C8×C47#4111yescharacteristic
87C2×C8×C47#4111yescharacteristic
88C2×C8×C47#4111yescharacteristic
89C4⋊C4×C47—22no—
90C4⋊C4×C47—41no—
91C4⋊Dic47—22no—
92C4⋊Dic47—41no—
93Dic47⋊C4—42no—
94Dic47⋊C4—42no—
95#10625329—41no—
96#10625329—41no—
97C2×C47⋊C8—21no—
98C2×C47⋊C8—21no—
99C2×C47⋊C8—41no—
100C2×C47⋊C8C22⋊C411yescharacteristic
101C2×C47⋊C8C22⋊C411yescharacteristic
102C8×D47—21no—
103C8×D47—21no—
104C8×D47—21no—
105C8×D47—21no—
106C8×D47—21no—
107C8×D47—21no—
108C8×D47—21no—
109C8×D47—21no—
110C16×C47—41no—
111C47⋊C16—41no—
112C23×C47C2×SD1611yescharacteristic
113C22×D47—21no—
114C22×D47—21no—
115C22×D47—22no—
116C22×D47—22no—
117C22×D47#10211yescharacteristic
118C22×D47#10211yescharacteristic
119C2×C4×C47—42no—
120C2×C4×C47—82no—
121C2×C4×C47C2×C22⋊C411yescharacteristic
122C2×C4×C47#12311yescharacteristic
123C2×C4×C47#12311yescharacteristic
124C2×C4×C47C2×D811yescharacteristic
125C2×C4×C47#13711yescharacteristic
126C2×C4×C47#13711yescharacteristic
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—42no—
130C2×Dic47—82no—
131C2×Dic47#10211yescharacteristic
132C2×Dic47#10211yescharacteristic
133C4×D47—21no—
134C4×D47—21no—
135C4×D47—21no—
136C4×D47—21no—
137C4×D47—21no—
138C4×D47—21no—
139C4×D47—21no—
140C4×D47—21no—
141C4×D47—84no—
142C4×D47—84no—
143C8×C47—81no—
144C8×C47#11711yescharacteristic
145C8×C47#11711yescharacteristic
146C8×C47#12311yescharacteristic
147C8×C47#12311yescharacteristic
148C47⋊C8—21no—
149C47⋊C8—21no—
150C47⋊C8—81no—
151#12871—471nomaximal, Sylow
152C22×C47—21no—
153C22×C47—21no—
154C22×C47C2×#10211yescharacteristic
155C22×C47#48311yescharacteristic
156C22×C47#48311yescharacteristic
157C2×D47—24no—
158C2×D47—24no—
159C2×D47—21no—
160C2×D47—21no—
161C2×D47—21no—
162C2×D47—21no—
163C2×D47#36112yes—
164C2×D47#36212yes—
165C4×C47—82no—
166C4×C47#38111yescharacteristic
167C4×C47#41911yescharacteristic
168C4×C47#48011yescharacteristic
169C4×C47#48011yescharacteristic
170Dic47—21no—
171Dic47—21no—
172Dic47—82no—
173C22×#107—471no—
174#2112—471no—
175#1810—471no—
176#1387—471no—
177#1387—471no—
178#1387—471no—
179#1387D4711yescharacteristic, complemented
180C2×C47—21no—
181C2×C47—21no—
182C2×C47#182311yescharacteristic
183C2×C47C2×#36111yescharacteristic
184C2×C47C2×#36211yescharacteristic
185D47—22no—
186D47—22no—
187C23×C8—471no—
188C22×C4⋊C4—941no—
189C2×M32—471no—
190C2×M32C2×D4711yescharacteristic
191C2×#108—471no—
192C2×#108C2×D4711yescharacteristic
193C2×#107—471no—
194C2×#107—472no—
195C2×#107—472no—
196C2×#107—941no—
197C2×#107—941no—
198C2×#107—941no—
199C2×#107C2×D4711yescharacteristic
200#407—941no—
201C22⋊C16—941no—
202C22⋊C16—941no—
203#341—941no—
204C47#1287111yescharacteristic, complemented, Sylow
205C23×C4—471no—
206C23×C4—1881no—
207C2×M16—21no—
208C2×M16—941no—
209C22×C8—471no—
210C22×C8—471no—
211C22×C8—471no—
212C22×C8—471no—
213C22×C8—471no—
214C22×C8—941no—
215C22×C8—941no—
216C22×C8—941no—
217C22×C8—941no—
218C22×C8C22×D4711yescharacteristic
219C2×C4⋊C4—21no—
220C2×C4⋊C4—942no—
221C2×C4⋊C4—942no—
222C2×C4⋊C4—941no—
223C2×C4⋊C4—1881no—
224C2×C4⋊C4—1881no—
225C2×C4⋊C4—1881no—
226M32—21no—
227M32—21no—
228M32—941no—
229M32—941no—
230C2×C16—21no—
231C2×C16—941no—
232#108—21no—
233#108—21no—
234#108—941no—
235#108—941no—
236#107—21no—
237#107—472no—
238#107—942no—
239#107—942no—
240#107—941no—
241#107C4×D4712yes—
242C22⋊C8—1881no—
243C22⋊C8—1881no—
244C24—471no—
245C22×C4—41no—
246C22×C4—471no—
247C22×C4—471no—
248C22×C4—471no—
249C22×C4—471no—
250C22×C4—471no—
251C22×C4—941no—
252C22×C4—941no—
253C22×C4—941no—
254C22×C4—941no—
255C22×C4—3764no—
256C22×C4—1882no—
257C22×C4—1882no—
258C22×C4—1881no—
259C22×C4D4×D4711yescharacteristic
260M16—41no—
261M16—41no—
262M16—1881no—
263M16—1881no—
264C2×C8—41no—
265C2×C8—471no—
266C2×C8—471no—
267C2×C8—941no—
268C2×C8—941no—
269C2×C8—941no—
270C2×C8—941no—
271C2×C8—941no—
272C2×C8—941no—
273C2×C8—941no—
274C2×C8—941no—
275C2×C8—941no—
276C2×C8—941no—
277C2×C8—1881no—
278C2×C8C2×C4×D4711yescharacteristic
279C2×C8#1062535011yescharacteristic
280C2×C8#1062535011yescharacteristic
281C2×C8D4×D4711yescharacteristic
282C2×C8#1062535211yescharacteristic
283C2×C8#1062535411yescharacteristic
284C4⋊C4—22no—
285C4⋊C4—41no—
286C4⋊C4—942no—
287C4⋊C4—1882no—
288C4⋊C4—1882no—
289C4⋊C4—1881no—
290C16—41no—
291C16—1881no—
292C23—471no—
293C23—471no—
294C23—942no—
295C23—942no—
296C23—941no—
297C23—941no—
298C23SD16×D4711yescharacteristic
299C2×C4—42no—
300C2×C4—82no—
301C2×C4—471no—
302C2×C4—471no—
303C2×C4—941no—
304C2×C4—941no—
305C2×C4—941no—
306C2×C4—941no—
307C2×C4—941no—
308C2×C4—941no—
309C2×C4—941no—
310C2×C4—941no—
311C2×C4—941no—
312C2×C4—941no—
313C2×C4—3764no—
314C2×C4—3764no—
315C2×C4—3762no—
316C2×C4—1882no—
317C2×C4C22⋊C4×D4711yescharacteristic
318C2×C4#1309400611yescharacteristic
319C2×C4#1309400911yescharacteristic
320C2×C4D8×D4711yescharacteristic
321C2×C4#1309405311yescharacteristic
322C2×C4#1309405611yescharacteristic
323C8—81no—
324C8—941no—
325C8—941no—
326C8—3761no—
327C8#1309398111yescharacteristic
328C8#1309398211yescharacteristic
329C8#1309400611yescharacteristic
330C8#1309400911yescharacteristic
331C22—21no—
332C22—21no—
333C22—472no—
334C22—472no—
335C22—944no—
336C22—944no—
337C22—941no—
338C22—941no—
339C22—941no—
340C22—941no—
341C22#102×D4711yescharacteristic
342C22#1568945211yescharacteristic
343C22#1568945511yescharacteristic
344C4—82no—
345C4—941no—
346C4—941no—
347C4—3762no—
348C4#1568898511yescharacteristic
349C4#1568913011yescharacteristic
350C4#1568943511yescharacteristic
351C4#1568943811yescharacteristic
352C2—21no—
353C2—21no—
354C2—942no—
355C2—942no—
356C2#2024347311yescharacteristic
357C2#361×D4711yescharacteristic
358C2#362×D4711yescharacteristic
subgroupG/H
centerC22#102×D47
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC47×#1387C2
socleC22×C47C2×#102
prime radicalC23×D47SD16
cosocleC22×C8×C47C23
hypercenter#1387D47
hypocenterC47#12871
LCSG ▷ C2×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. #20241498C2semidirect
5. #20241497C2semidirect
6. #20241496C2semidirect
7. C47×#1387C2semidirect
179. #1387D47semidirect
204. C47#12871semidirect

Maximal subgroups

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

subgroupindex
C2×#107×D472
#202449982
#202434232
#202414982
#202414972
#202414962
C47×#13872
#1287147