Finite Group Databasebeta

← #26133223

Subgroups — #26133223

Order 12032.

574 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689361C211yesmaximal, characteristic
2C2×#107×D47C211yesmaximal, characteristic
3C2×#15688927C211yesmaximal, characteristic, complemented
4C2×(C2×D47)⋊C16C211yesmaximal, characteristic
5#20241480C211yesmaximal, characteristic, complemented
6#20241479C211yesmaximal, characteristic, complemented
7C2×C47×#358C211yesmaximal, characteristic, complemented
8C22×C8×D47C2211yescharacteristic
9C2×#13094000—21no—
10C2×C4⋊C4×D47—21no—
11C22×C47⋊C16C2211yescharacteristic
12#15689361—22no—
13#15689361C414yescomplemented
14C2×#13093958C2211yescharacteristic
15C2×#13093958C2211yescharacteristic
16C2×#13093957—21no—
17#107×D47—22no—
18#107×D47—22no—
19C2×#13093948—21no—
20#15688927—22no—
21(C2×D47)⋊C16—22no—
22C22×Q16×C47C2211yescharacteristic
23C22×C16×C47C2211yescharacteristic
24C2×#107×C47C2211yescharacteristic
25C47×#358—22no—
26C22×C4×D47—41no—
27C22×C4×D47D411yescharacteristic
28C22×C47⋊C8D411yescharacteristic
29C2×C8×D47—21no—
30C2×C8×D47—21no—
31C2×C8×D47—21no—
32C2×C8×D47—21no—
33C2×C8×D47C2×C412yes—
34C2×C8×D47D412yes—
35#13094000—24no—
36#13094000—42no—
37C2×C4⋊Dic47—21no—
38C2×C4⋊Dic47—21no—
39C2×Dic47⋊C4—41no—
40C2×Dic47⋊C4—41no—
41C4⋊C4×D47—24no—
42C4⋊C4×D47—42no—
43C2×(C2×D47)⋊C4—41no—
44C2×C47⋊C16—21no—
45C2×C47⋊C16—21no—
46C2×C47⋊C16—21no—
47#13093958—21no—
48#13093958—21no—
49#13093958C2×C412yescomplemented
50#13093958D412yes—
51#13093957—24no—
52#13093948—24no—
53C22×Q8×C47—21no—
54C2×Q16×C47—21no—
55C2×Q16×C47—21no—
56C2×Q16×C47—21no—
57C2×Q16×C47—21no—
58C2×Q16×C47—21no—
59C2×Q16×C47C2×C412yescomplemented
60C22×C8×C47C2311yescharacteristic
61C2×C4⋊C4×C47—21no—
62C2×C16×C47—21no—
63C2×C16×C47—21no—
64C2×C16×C47—21no—
65#107×C47—21no—
66#107×C47D412yes—
67C23×D47D811yescharacteristic
68C2×Q8×C47—22no—
69C2×Q8×C47—41no—
70C2×Q8×C47—41no—
71C2×Q8×C47—41no—
72C2×Q8×C47—41no—
73C2×Q8×C47—41no—
74C22×C4×C47—41no—
75C22×C4×C47—41no—
76C22×C4×C47C2×D411yescharacteristic
77C22×Dic47—41no—
78C22×Dic47—41no—
79C22×Dic47D811yescharacteristic
80C2×C4×D47—21no—
81C2×C4×D47—21no—
82C2×C4×D47—21no—
83C2×C4×D47—21no—
84C2×C4×D47—44no—
85C2×C4×D47—82no—
86C2×C4×D47—82no—
87C2×C4×D47C22⋊C412yes—
88C2×C4×D47SD1612yes—
89Q16×C47—22no—
90Q16×C47—22no—
91Q16×C47—41no—
92Q16×C47—41no—
93C2×C8×C47C22×C411yescharacteristic
94C2×C8×C47C2×D411yescharacteristic
95C2×C8×C47C2×D411yescharacteristic
96C2×C8×C47C2×D411yescharacteristic
97C2×C8×C47#4111yescharacteristic
98C2×C8×C47#4111yescharacteristic
99C4⋊C4×C47—22no—
100C4⋊C4×C47—41no—
101(C2×D47)⋊C4—44no—
102C4⋊Dic47—22no—
103C4⋊Dic47—22no—
104C4⋊Dic47—41no—
105C4⋊Dic47—41no—
106Dic47⋊C4—44no—
107Dic47⋊C4—44no—
108C2×C47⋊C8—21no—
109C2×C47⋊C8—21no—
110C2×C47⋊C8C22⋊C412yes—
111C8×D47—22no—
112C8×D47—22no—
113C8×D47—22no—
114C8×D47—22no—
115C16×C47—41no—
116C47⋊C16—41no—
117C23×C47C2×D811yescharacteristic
118C22×D47—21no—
119C22×D47—21no—
120C22×D47—21no—
121C22×D47—21no—
122C22×D47#10212yes—
123C22×D47SD3212yes—
124C22×D47Q3212yes—
125Q8×C47—42no—
126Q8×C47—42no—
127Q8×C47—81no—
128Q8×C47—81no—
129C2×C4×C47—42no—
130C2×C4×C47—42no—
131C2×C4×C47—81no—
132C2×C4×C47—81no—
133C2×C4×C47—81no—
134C2×C4×C47—81no—
135C2×C4×C47C2×C22⋊C411yescharacteristic
136C2×C4×C47#12011yescharacteristic
137C2×C4×C47#12311yescharacteristic
138C2×C4×C47C2×SD1611yescharacteristic
139C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C47#13711yescharacteristic
141C2×Dic47—21no—
142C2×Dic47—21no—
143C2×Dic47—42no—
144C2×Dic47—42no—
145C2×Dic47—81no—
146C2×Dic47—81no—
147C2×Dic47—81no—
148C2×Dic47—81no—
149C2×Dic47#10212yes—
150C4×D47—22no—
151C4×D47—22no—
152C4×D47—22no—
153C4×D47—22no—
154C4×D47—88no—
155C8×C47C4×D411yescharacteristic
156C8×C47C4×D411yescharacteristic
157C8×C47#12111yescharacteristic
158C8×C47#12111yescharacteristic
159C47⋊C8—22no—
160#12993—471nomaximal, Sylow
161C22×C47C2×#10211yescharacteristic
162C22×C47#44711yescharacteristic
163C22×C47#48011yescharacteristic
164C22×C47C2×SD3211yescharacteristic
165C22×C47C2×Q3211yescharacteristic
166C22×C47#50911yescharacteristic
167C22×C47#51011yescharacteristic
168C2×D47—22no—
169C2×D47—22no—
170C2×D47—22no—
171C2×D47—22no—
172C2×D47—22no—
173C2×D47—22no—
174C2×D47#35814yescomplemented
175C4×C47—82no—
176C4×C47—82no—
177C4×C47#38611yescharacteristic
178C4×C47#41711yescharacteristic
179C4×C47#44811yescharacteristic
180C4×C47#48111yescharacteristic
181Dic47—22no—
182Dic47—82no—
183Dic47—82no—
184C2×#467—471no—
185C22×#107—471no—
186C2×#358—471no—
187C2×#358D4711yescharacteristic, complemented
188C2×C22⋊C16—471no—
189#1380—471no—
190#1380—471no—
191C2×C47#187411yescharacteristic
192C2×C47C2×#35811yescharacteristic
193C2×C47#213911yescharacteristic
194C2×C47#218711yescharacteristic
195C2×C47#218811yescharacteristic
196C2×C47#223511yescharacteristic
197C2×C47#223611yescharacteristic
198D47—24no—
199C22×Q16C2×D4711yescharacteristic
200C23×C8—471no—
201C2×C22⋊Q8—941no—
202C22×C4⋊C4—941no—
203C22×C16—471no—
204C22×C16C2×D4711yescharacteristic
205#467—474no—
206#467—942no—
207C2×#107—471no—
208C2×#107—471no—
209C2×#107—942no—
210C2×#107—941no—
211C2×#107—942no—
212C2×#107C2×D4711yescharacteristic
213C2×#103—941no—
214#358—22no—
215#358—942no—
216C22⋊C16—942no—
217C47#1299311yescharacteristic, complemented, Sylow
218C22×Q8—21no—
219C23×C4—471no—
220C23×C4—1881no—
221C2×Q16—21no—
222C2×Q16—21no—
223C2×Q16—21no—
224C2×Q16—21no—
225C2×Q16—21no—
226C2×Q16C4×D4712yescomplemented
227C22×C8—471no—
228C22×C8—472no—
229C22×C8—472no—
230C22×C8—941no—
231C22×C8—941no—
232C22×C8—941no—
233C22×C8—941no—
234C22×C8C22×D4711yescharacteristic
235C22⋊Q8—944no—
236C22⋊Q8—1882no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—944no—
239C2×C4⋊C4—941no—
240C2×C4⋊C4—941no—
241C2×C4⋊C4—1882no—
242C2×C4⋊C4—1881no—
243C2×C4⋊C4—1881no—
244C2×C22⋊C4—1881no—
245C2×C16—21no—
246C2×C16—21no—
247C2×C16—21no—
248C2×C16—941no—
249C2×C16—941no—
250C2×C16—941no—
251#107—21no—
252#107—472no—
253#107—472no—
254#107—944no—
255#107—941no—
256#107—941no—
257#107C22⋊D4712yes—
258#103—944no—
259C24—471no—
260C2×Q8—22no—
261C2×Q8—41no—
262C2×Q8—41no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×Q8—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—471no—
269C22×C4—472no—
270C22×C4—472no—
271C22×C4—941no—
272C22×C4—941no—
273C22×C4—941no—
274C22×C4—941no—
275C22×C4—3762no—
276C22×C4—3762no—
277C22×C4—1884no—
278C22×C4—1881no—
279C22×C4—1881no—
280C22×C4D4×D4711yescharacteristic
281Q16—22no—
282Q16—22no—
283Q16—41no—
284Q16—41no—
285C2×C8—472no—
286C2×C8—941no—
287C2×C8—941no—
288C2×C8—942no—
289C2×C8—942no—
290C2×C8—942no—
291C2×C8—942no—
292C2×C8C2×C4×D4711yescharacteristic
293C2×C8#1062535011yescharacteristic
294C2×C8D4×D4711yescharacteristic
295C2×C8D4×D4711yescharacteristic
296C2×C8#1062535211yescharacteristic
297C2×C8C2×C22⋊D4711yescharacteristic
298C4⋊C4—22no—
299C4⋊C4—41no—
300C4⋊C4—942no—
301C4⋊C4—942no—
302C4⋊C4—1884no—
303C4⋊C4—1884no—
304C4⋊C4—1881no—
305C4⋊C4—1881no—
306C22⋊C4—1884no—
307C16—41no—
308C16—1881no—
309C23—472no—
310C23—472no—
311C23—472no—
312C23—941no—
313C23—941no—
314C23—941no—
315C23—941no—
316C23D8×D4711yescharacteristic
317Q8—42no—
318Q8—42no—
319Q8—81no—
320Q8—81no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—472no—
328C2×C4—941no—
329C2×C4—941no—
330C2×C4—942no—
331C2×C4—942no—
332C2×C4—942no—
333C2×C4—942no—
334C2×C4—3768no—
335C2×C4—3761no—
336C2×C4—3761no—
337C2×C4—3761no—
338C2×C4—3761no—
339C2×C4—1882no—
340C2×C4—1882no—
341C2×C4C22⋊C4×D4711yescharacteristic
342C2×C4#1309399211yescharacteristic
343C2×C4#1309400611yescharacteristic
344C2×C4SD16×D4711yescharacteristic
345C2×C4#1309404811yescharacteristic
346C2×C4#1309405311yescharacteristic
347C8—942no—
348C8(C22⋊D47)⋊C411yescharacteristic
349C8C4×C22⋊D4711yescharacteristic
350C8#1309399511yescharacteristic
351C8#1309399711yescharacteristic
352C22—474no—
353C22—942no—
354C22—942no—
355C22—942no—
356C22—942no—
357C22—942no—
358C22—942no—
359C22#102×D4711yescharacteristic
360C22#1568925511yescharacteristic
361C22#1568943511yescharacteristic
362C22SD32×D4711yescharacteristic
363C22Q32×D4711yescharacteristic
364C22#1568956011yescharacteristic
365C22#1568956511yescharacteristic
366C4—82no—
367C4—82no—
368C4—942no—
369C4—3762no—
370C4—3762no—
371C4#1568899911yescharacteristic
372C4#1568912111yescharacteristic
373C4#1568926011yescharacteristic
374C4#1568944011yescharacteristic
375C2—944no—
376C2#2024370211yescharacteristic
377C2#358×D4711yescharacteristic
378C2#2024509911yescharacteristic
379C2#2024531511yescharacteristic
380C2#2024532011yescharacteristic
381C2#2024558411yescharacteristic
382C2#2024558911yescharacteristic
subgroupG/H
centerC23D8×D47
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC2×C47×#358C2
socleC23×C47C2×D8
prime radicalC23×D47D8
cosocleC22×C8×C47C23
hypercenterC2×#358D47
hypocenterC47#12993
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
3. C2×#15688927C2semidirect
5. #20241480C2semidirect
6. #20241479C2semidirect
7. C2×C47×#358C2semidirect
13. #15689361C4semidirect
49. #13093958C2×C4semidirect
59. C2×Q16×C47C2×C4semidirect
174. C2×D47#358semidirect
187. C2×#358D47semidirect
217. C47#12993semidirect
226. C2×Q16C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156893612
C2×#107×D472
C2×#156889272
C2×(C2×D47)⋊C162
#202414802
#202414792
C2×C47×#3582
#1299347