Finite Group Databasebeta

← #26133230

Subgroups — #26133230

Order 12032.

530 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689365C211yesmaximal, characteristic
2C2×#15689160C211yesmaximal, characteristic
3C2×#15688928C211yesmaximal, characteristic, complemented
4C2×#15688926C211yesmaximal, characteristic, complemented
5C2×(C2×D47)⋊C16C211yesmaximal, characteristic
6#20241479C211yesmaximal, characteristic, complemented
7C47×#1380C211yesmaximal, characteristic, complemented
8C22×Dic188C2211yescharacteristic
9C22×C8×D47C2211yescharacteristic
10C2×#13094004—21no—
11C2×#13093982—21no—
12C22×C47⋊C16C2211yescharacteristic
13#15689365—22no—
14#15689365C414yescomplemented
15#15689160—22no—
16#15689160—22no—
17C2×#13093958C2211yescharacteristic
18C2×#13093955—21no—
19C2×#13093947—21no—
20#15688928—22no—
21#15688926—22no—
22(C2×D47)⋊C16—22no—
23C22×C16×C47C2211yescharacteristic
24C2×#107×C47C2211yescharacteristic
25C2×#107×C47C2211yescharacteristic
26C22×Dic94—21no—
27C22×C4×D47D411yescharacteristic
28C2×Dic188—21no—
29C2×Dic188—21no—
30C2×Dic188—21no—
31C2×Dic188—21no—
32C2×Dic188—21no—
33C2×Dic188C2×C412yes—
34C22×C47⋊C8D411yescharacteristic
35C2×C8×D47—21no—
36C2×C8×D47—21no—
37C2×C8×D47—21no—
38C2×C8×D47—21no—
39C2×C8×D47C2×C412yes—
40C2×C8×D47D412yes—
41#13094004—24no—
42#13094004—42no—
43#13093982—24no—
44#13093982—42no—
45C2×C4⋊Dic47—21no—
46C2×C4⋊Dic47—41no—
47C2×(C2×D47)⋊C4—41no—
48C2×(C2×D47)⋊C4—41no—
49C2×C4×Dic47—41no—
50C2×C47⋊C16—21no—
51C2×C47⋊C16—21no—
52C2×C47⋊C16—21no—
53#13093958—21no—
54#13093958D412yes—
55#13093955—24no—
56#13093947—24no—
57C22×C8×C47C2311yescharacteristic
58C2×C4⋊C4×C47—21no—
59C2×C4⋊C4×C47—21no—
60C2×C16×C47—21no—
61C2×C16×C47—21no—
62C2×C16×C47—21no—
63#107×C47—21no—
64#107×C47—21no—
65#107×C47C2×C412yes—
66#107×C47D412yes—
67C23×D47D811yescharacteristic
68C22×C4×C47—41no—
69C22×C4×C47—41no—
70C22×C4×C47C2×D411yescharacteristic
71C22×Dic47—41no—
72C22×Dic47—41no—
73C22×Dic47D811yescharacteristic
74C2×C4×D47—21no—
75C2×C4×D47—21no—
76C2×C4×D47—21no—
77C2×C4×D47—21no—
78C2×C4×D47C22⋊C412yes—
79C2×C4×D47SD1612yes—
80C2×Dic94—22no—
81C2×Dic94—41no—
82C2×Dic94—41no—
83C2×Dic94—41no—
84C2×Dic94—41no—
85C2×Dic94—41no—
86C2×C8×C47C22×C411yescharacteristic
87C2×C8×C47C2×D411yescharacteristic
88C2×C8×C47C2×D411yescharacteristic
89C2×C8×C47C2×D411yescharacteristic
90C2×C8×C47#4111yescharacteristic
91C2×C8×C47#4111yescharacteristic
92C4⋊C4×C47—22no—
93C4⋊C4×C47—22no—
94C4⋊C4×C47—41no—
95C4⋊C4×C47—41no—
96(C2×D47)⋊C4—44no—
97(C2×D47)⋊C4—44no—
98C4⋊Dic47—22no—
99C4⋊Dic47—41no—
100C4⋊Dic47—44no—
101C4×Dic47—44no—
102C2×C47⋊C8—21no—
103C2×C47⋊C8—21no—
104C2×C47⋊C8C22⋊C412yes—
105Dic188—22no—
106Dic188—22no—
107Dic188—41no—
108Dic188—41no—
109C8×D47—22no—
110C8×D47—22no—
111C8×D47—22no—
112C8×D47—22no—
113C16×C47—41no—
114C47⋊C16—41no—
115C23×C47C2×D811yescharacteristic
116C22×D47—21no—
117C22×D47—21no—
118C22×D47—21no—
119C22×D47—21no—
120C22×D47—21no—
121C22×D47—21no—
122C22×D47#10212yes—
123C2×C4×C47—42no—
124C2×C4×C47—42no—
125C2×C4×C47—81no—
126C2×C4×C47—81no—
127C2×C4×C47—81no—
128C2×C4×C47—81no—
129C2×C4×C47C2×C22⋊C411yescharacteristic
130C2×C4×C47#12011yescharacteristic
131C2×C4×C47#12311yescharacteristic
132C2×C4×C47C2×SD1611yescharacteristic
133C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C47#13711yescharacteristic
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—42no—
138C2×Dic47—42no—
139C2×Dic47—81no—
140C2×Dic47—81no—
141C2×Dic47—81no—
142C2×Dic47—81no—
143C2×Dic47#10212yes—
144C4×D47—22no—
145C4×D47—22no—
146C4×D47—22no—
147C4×D47—22no—
148Dic94—42no—
149Dic94—42no—
150Dic94—81no—
151Dic94—81no—
152C8×C47C4×D411yescharacteristic
153C8×C47C4×D411yescharacteristic
154C8×C47#12111yescharacteristic
155C8×C47#12111yescharacteristic
156C47⋊C8—22no—
157#12994—471nomaximal, Sylow
158C22×C47C2×#10211yescharacteristic
159C22×C47#44711yescharacteristic
160C22×C47#48011yescharacteristic
161C22×C47#50811yescharacteristic
162C22×C47#50811yescharacteristic
163C22×C47#51011yescharacteristic
164C22×C47#51011yescharacteristic
165C2×D47—22no—
166C2×D47—22no—
167C2×D47—22no—
168C2×D47—41no—
169C2×D47—41no—
170C2×D47—41no—
171C2×D47—41no—
172C4×C47—82no—
173C4×C47—82no—
174C4×C47#38611yescharacteristic
175C4×C47#41711yescharacteristic
176C4×C47#44811yescharacteristic
177C4×C47#48111yescharacteristic
178Dic47—22no—
179Dic47—82no—
180Dic47—82no—
181C2×#467—471no—
182C2×#427—471no—
183C2×#358—471no—
184C2×#358—471no—
185C2×C22⋊C16—471no—
186#1380—471no—
187#1380D4711yescharacteristic, complemented
188C2×C47#187411yescharacteristic
189C2×C47#213811yescharacteristic
190C2×C47#214111yescharacteristic
191C2×C47#218911yescharacteristic
192C2×C47#218911yescharacteristic
193C2×C47#223711yescharacteristic
194C2×C47#223711yescharacteristic
195D47—42no—
196C22×Q16—471no—
197C23×C8—471no—
198C2×C22⋊Q8—941no—
199C2×#117—941no—
200C22×C16—471no—
201C22×C16C2×D4711yescharacteristic
202#467—474no—
203#467—942no—
204#427—942no—
205#427—942no—
206C2×#107—471no—
207C2×#107C2×D4711yescharacteristic
208C2×#107C2×D4711yescharacteristic
209C2×#106—941no—
210C2×#103—941no—
211#358—942no—
212#358—942no—
213C22⋊C16—942no—
214C47#1299411yescharacteristic, complemented, Sylow
215C22×Q8—941no—
216C23×C4—471no—
217C2×Q16—472no—
218C2×Q16—941no—
219C2×Q16—941no—
220C2×Q16—941no—
221C2×Q16—941no—
222C2×Q16—941no—
223C22×C8—471no—
224C22×C8—472no—
225C22×C8—472no—
226C22×C8—941no—
227C22×C8—941no—
228C22×C8—941no—
229C22×C8—941no—
230C22×C8C22×D4711yescharacteristic
231C22⋊Q8—944no—
232C22⋊Q8—1882no—
233#117—944no—
234#117—1882no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—941no—
238C2×C4⋊C4—1881no—
239C2×C22⋊C4—1881no—
240C2×C22⋊C4—1881no—
241C2×C42—1881no—
242C2×C16—21no—
243C2×C16—21no—
244C2×C16—21no—
245C2×C16—941no—
246C2×C16—941no—
247C2×C16—941no—
248#107—21no—
249#107—21no—
250#107—472no—
251#107—941no—
252#107C4×D4712yes—
253#107D18812yes—
254#106—944no—
255#103—944no—
256C24—471no—
257C2×Q8—942no—
258C2×Q8—1881no—
259C2×Q8—1881no—
260C2×Q8—1881no—
261C2×Q8—1881no—
262C2×Q8—1881no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—471no—
266C22×C4—472no—
267C22×C4—472no—
268C22×C4—941no—
269C22×C4—941no—
270C22×C4—941no—
271C22×C4—941no—
272C22×C4—1881no—
273C22×C4—1881no—
274C22×C4D4×D4711yescharacteristic
275Q16—942no—
276Q16—942no—
277Q16—1881no—
278Q16—1881no—
279C2×C8—472no—
280C2×C8—941no—
281C2×C8—941no—
282C2×C8—942no—
283C2×C8—942no—
284C2×C8—942no—
285C2×C8—942no—
286C2×C8C2×C4×D4711yescharacteristic
287C2×C8C2×D18811yescharacteristic
288C2×C8#1062535011yescharacteristic
289C2×C8D4×D4711yescharacteristic
290C2×C8D4×D4711yescharacteristic
291C2×C8#1062535411yescharacteristic
292C4⋊C4—22no—
293C4⋊C4—22no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—942no—
297C4⋊C4—1884no—
298C4⋊C4—1881no—
299C22⋊C4—1884no—
300C22⋊C4—1884no—
301C42—1884no—
302C16—41no—
303C16—1881no—
304C23—472no—
305C23—941no—
306C23—941no—
307C23—941no—
308C23—941no—
309C23—941no—
310C23—941no—
311C23D8×D4711yescharacteristic
312Q8—3761no—
313Q8—3761no—
314Q8—1882no—
315Q8—1882no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—472no—
323C2×C4—941no—
324C2×C4—941no—
325C2×C4—942no—
326C2×C4—942no—
327C2×C4—942no—
328C2×C4—942no—
329C2×C4—3761no—
330C2×C4—3761no—
331C2×C4—3761no—
332C2×C4—3761no—
333C2×C4—1882no—
334C2×C4—1882no—
335C2×C4C22⋊C4×D4711yescharacteristic
336C2×C4#1309399411yescharacteristic
337C2×C4#1309400911yescharacteristic
338C2×C4SD16×D4711yescharacteristic
339C2×C4#1309405111yescharacteristic
340C2×C4#1309405611yescharacteristic
341C8—942no—
342C8#1309398611yescharacteristic
343C8C4×D18811yescharacteristic
344C8#1309399711yescharacteristic
345C8#1309399911yescharacteristic
346C22—942no—
347C22—942no—
348C22—942no—
349C22—1881no—
350C22—1881no—
351C22—1881no—
352C22—1881no—
353C22#102×D4711yescharacteristic
354C22#1568925811yescharacteristic
355C22#1568943811yescharacteristic
356C22#1568955211yescharacteristic
357C22#1568955411yescharacteristic
358C22#1568956211yescharacteristic
359C22#1568956511yescharacteristic
360C4—82no—
361C4—82no—
362C4—942no—
363C4—3762no—
364C4—3762no—
365C4#1568900111yescharacteristic
366C4#1568912311yescharacteristic
367C4#1568926311yescharacteristic
368C4#1568944311yescharacteristic
369C2—1882no—
370C2#2024370411yescharacteristic
371C2#2024509211yescharacteristic
372C2#2024510611yescharacteristic
373C2#2024532911yescharacteristic
374C2#2024533111yescharacteristic
375C2#2024559811yescharacteristic
376C2#2024559911yescharacteristic
subgroupG/H
centerC23D8×D47
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC47×#1380C2
socleC23×C47C2×D8
prime radicalC23×D47D8
cosocleC22×C8×C47C23
hypercenter#1380D47
hypocenterC47#12994
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
3. C2×#15688928C2semidirect
4. C2×#15688926C2semidirect
6. #20241479C2semidirect
7. C47×#1380C2semidirect
14. #15689365C4semidirect
187. #1380D47semidirect
214. C47#12994semidirect

Maximal subgroups

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

subgroupindex
C2×#156893652
C2×#156891602
C2×#156889282
C2×#156889262
C2×(C2×D47)⋊C162
#202414792
C47×#13802
#1299447