Finite Group Databasebeta

← #26112578

Subgroups — #26112578

Order 12032.

512 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253419C211yesmaximal, characteristic
2#20244216C211yesmaximal, characteristic
3#20241882C211yesmaximal, characteristic
4#20241817C211yesmaximal, characteristic, complemented
5#20241291C211yesmaximal, characteristic, complemented
6#20241221C211yesmaximal, characteristic, complemented
7C47×#2295C211yesmaximal, characteristic, complemented
8#15689673C2211yescharacteristic
9#15689441—21no—
10#15689408C412yescomplemented
11#15689323C412yescomplemented
12#15689262—21no—
13C4×#10625336—22no—
14#15689176C2211yescharacteristic
15#15689176C2211yescharacteristic
16#15689147C2211yescharacteristic
17C2×#13093952—21no—
18C2×#13093952—21no—
19#15688856—22no—
20Q8⋊(C47⋊C8)—22no—
21C2×C4×Q8×C47C2211yescharacteristic
22C47×#391—21no—
23C47×#389—21no—
24C47×#387—22no—
25C4×C4⋊C4×C47—21no—
26C4×C4⋊C4×C47C2211yescharacteristic
27C47×#376—21no—
28C43×C47C2211yescharacteristic
29C2×#10625350—21no—
30C2×#10625336—22no—
31C2×#10625329—21no—
32#13094024C2×C411yescharacteristic
33#13094021C2×C411yescharacteristic
34#13094012—21no—
35#13093998—21no—
36#13093998—21no—
37C4×D188—21no—
38C4×D188—21no—
39#13093955—22no—
40C4⋊(C47⋊C8)—21no—
41C4⋊(C47⋊C8)—21no—
42C4⋊(C47⋊C8)—21no—
43C4⋊(C47⋊C8)C2×C412yes—
44#13093952—42no—
45#13093952—42no—
46#13093948—22no—
47#13093944—22no—
48C22⋊(C47⋊C8)—21no—
49C22⋊(C47⋊C8)—21no—
50C4×C47⋊C8—21no—
51C4×C47⋊C8—21no—
52C22×Q8×C47D411yescharacteristic
53C4×Q8×C47—21no—
54C4×Q8×C47—21no—
55C4×Q8×C47C2×C412yes—
56C4×Q8×C47D412yes—
57C2×C4⋊C4×C47—21no—
58C2×C4⋊C4×C47—22no—
59C2×C4⋊C4×C47—21no—
60C2×C4⋊C4×C47D411yescharacteristic
61C2×C42×C47—21no—
62C2×C42×C47—21no—
63C2×C42×C47—21no—
64C2×C42×C47—21no—
65C2×C42×C47D411yescharacteristic
66C2×C42×C47D411yescharacteristic
67C2×C42×C47C2311yescharacteristic
68#95×C47—22no—
69#95×C47—22no—
70#95×C47—22no—
71#95×C47D412yes—
72C2×Q8×C47—21no—
73C2×Q8×C47—42no—
74C2×Q8×C47C22⋊C412yes—
75C22×C4×C47—21no—
76C22×C4×C47—21no—
77C22×C4×C47—21no—
78C22×C4×C47—21no—
79C22×C4×C47—22no—
80C22×C4×C47C2×D411yescharacteristic
81C22×C4×C47C2×D411yescharacteristic
82C22×C4×C47C2×D411yescharacteristic
83C2×C22⋊D47—41no—
84#10625350—41no—
85#10625350—41no—
86#10625350—41no—
87#10625350—41no—
88C2×D188—21no—
89C2×D188—21no—
90C2×D188—21no—
91C2×C4×D47—41no—
92C2×Dic94—21no—
93C4⋊C4×C47—22no—
94C4⋊C4×C47—22no—
95C4⋊C4×C47—21no—
96C4⋊C4×C47—42no—
97C4⋊C4×C47—44no—
98C4⋊C4×C47C22⋊C412yes—
99C42×C47—22no—
100C42×C47—22no—
101C42×C47—21no—
102C42×C47—21no—
103C42×C47—21no—
104C42×C47—42no—
105C42×C47—42no—
106C42×C47—41no—
107C42×C47—41no—
108C42×C47SD1612yescomplemented
109C42×C47C22×C411yescharacteristic
110C42×C47C2×D411yescharacteristic
111C42×C47#4111yescharacteristic
112C42×C47#4111yescharacteristic
113#10625336—44no—
114(C2×D47)⋊C4—41no—
115(C2×D47)⋊C4—41no—
116C4⋊Dic47—21no—
117C4⋊Dic47—21no—
118#10625329—41no—
119#10625329—41no—
120C2×C47⋊C8—22no—
121C2×C47⋊C8—41no—
122C2×C47⋊C8—41no—
123C23×C47#12011yescharacteristic
124C22×D47—41no—
125Q8×C47—22no—
126Q8×C47—22no—
127Q8×C47—42no—
128C2×C4×C47—22no—
129C2×C4×C47—22no—
130C2×C4×C47—22no—
131C2×C4×C47—22no—
132C2×C4×C47—22no—
133C2×C4×C47—41no—
134C2×C4×C47—41no—
135C2×C4×C47—41no—
136C2×C4×C47—41no—
137C2×C4×C47—42no—
138C2×C4×C47—42no—
139C2×C4×C47—41no—
140C2×C4×C47—42no—
141C2×C4×C47—42no—
142C2×C4×C47—42no—
143C2×C4×C47C2×C22⋊C411yescharacteristic
144C2×C4×C47C4×D411yescharacteristic
145C2×C4×C47C4×D411yescharacteristic
146C2×C4×C47#12111yescharacteristic
147C2×C4×C47#12111yescharacteristic
148C2×C4×C47#12311yescharacteristic
149C2×C4×C47C2×SD1611yescharacteristic
150C2×C4×C47#13511yescharacteristic
151C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C47#13711yescharacteristic
153C22⋊D47—81no—
154C22⋊D47—81no—
155C2×Dic47—41no—
156D188—42no—
157D188—41no—
158D188—41no—
159D188—81no—
160C4×D47—81no—
161C4×D47—81no—
162Dic94—41no—
163Dic94—41no—
164C47⋊C8—42no—
165C47⋊C8—81no—
166C47⋊C8—81no—
167#9238—471nomaximal, Sylow
168C22×C47—21no—
169C22×C47—21no—
170C22×C47#38611yescharacteristic
171C22×C47#44811yescharacteristic
172C22×C47#44911yescharacteristic
173C2×D47—81no—
174C2×D47—81no—
175C2×D47—81no—
176C4×C47—21no—
177C4×C47—21no—
178C4×C47—21no—
179C4×C47—42no—
180C4×C47—42no—
181C4×C47—42no—
182C4×C47—42no—
183C4×C47—82no—
184C4×C47#42112yes—
185C4×C47C4×SD1611yescharacteristic
186C4×C47#44011yescharacteristic
187C4×C47#46011yescharacteristic
188C4×C47#46411yescharacteristic
189Dic47—81no—
190#3103—471no—
191#2295D4711yescharacteristic, complemented
192#1962—471no—
193#1502—471no—
194#1487—471no—
195#1303—471no—
196#1276—471no—
197C2×C47—21no—
198C2×C47—21no—
199C2×C47#188011yescharacteristic
200C2×C47#189711yescharacteristic
201C2×C47#190611yescharacteristic
202D47—161no—
203#532—471no—
204C2×C4×Q8C2×D4711yescharacteristic
205#481—941no—
206#475—472no—
207#460—472no—
208#448—941no—
209C4×SD16—942no—
210#431—471no—
211#431—471no—
212#423—471no—
213C2×#104—941no—
214C2×#104—941no—
215#391—21no—
216#389—21no—
217#387—22no—
218C4×C4⋊C4—21no—
219C4×C4⋊C4C2×D4711yescharacteristic
220#376—21no—
221C43C2×D4711yescharacteristic
222#327—942no—
223Q8⋊C8—942no—
224C47#923811yescharacteristic, complemented, Sylow
225C2×#41—941no—
226C22×Q8C22⋊D4711yescharacteristic
227C2×SD16—942no—
228C2×M16—941no—
229C4⋊Q8—471no—
230#127—471no—
231#124—941no—
232#121—941no—
233#121—941no—
234C4×Q8—21no—
235C4×Q8—21no—
236C4×Q8C4×D4712yes—
237C4×Q8D18812yes—
238C4×D4—941no—
239C4×D4—941no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4C22⋊D4711yescharacteristic
244C2×C42—21no—
245C2×C42—21no—
246C2×C42—21no—
247C2×C42—21no—
248C2×C42C22⋊D4711yescharacteristic
249C2×C42C22⋊D4711yescharacteristic
250C2×C42C22×D4711yescharacteristic
251#106—942no—
252C4⋊C8—472no—
253C4⋊C8—941no—
254C4⋊C8—941no—
255C4⋊C8—941no—
256#104—1882no—
257#104—1882no—
258#103—942no—
259#102—942no—
260C22⋊C8—941no—
261C22⋊C8—941no—
262C4×C8—941no—
263C4×C8—941no—
264#95—22no—
265#95—22no—
266#95—22no—
267#95C22⋊D4712yes—
268#41—1881no—
269#41—1881no—
270#41—1881no—
271#41—1881no—
272C2×Q8—21no—
273C2×Q8—42no—
274C2×Q8—941no—
275C2×Q8(C2×D47)⋊C412yes—
276C2×D4—941no—
277C2×D4—941no—
278C2×D4—941no—
279C2×D4—1881no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—22no—
285C22×C4—1881no—
286C22×C4C2×C22⋊D4711yescharacteristic
287C22×C4C2×C22⋊D4711yescharacteristic
288C22×C4C2×C22⋊D4711yescharacteristic
289SD16—1884no—
290M16—1881no—
291M16—1881no—
292C2×C8—942no—
293C2×C8—1881no—
294C2×C8—1881no—
295C4⋊C4—22no—
296C4⋊C4—22no—
297C4⋊C4—21no—
298C4⋊C4—42no—
299C4⋊C4—44no—
300C4⋊C4—941no—
301C4⋊C4—941no—
302C4⋊C4(C2×D47)⋊C412yes—
303C22⋊C4—1881no—
304C22⋊C4—1881no—
305C42—22no—
306C42—22no—
307C42—21no—
308C42—21no—
309C42—21no—
310C42—42no—
311C42—42no—
312C42—41no—
313C42—41no—
314C42#1062533612yescomplemented
315C42C2×C4×D4711yescharacteristic
316C42C2×D18811yescharacteristic
317C42#1062535011yescharacteristic
318C42#1062535011yescharacteristic
319C23—1881no—
320C23#1309399311yescharacteristic
321Q8—22no—
322Q8—22no—
323Q8—42no—
324Q8—1881no—
325Q8—1881no—
326D4—3761no—
327D4—3761no—
328D4—3761no—
329D4—1881no—
330D4—1882no—
331D4—1881no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—3761no—
348C2×C4—3761no—
349C2×C4—1881no—
350C2×C4C2×(C2×D47)⋊C411yescharacteristic
351C2×C4C4×C22⋊D4711yescharacteristic
352C2×C4C4×C22⋊D4711yescharacteristic
353C2×C4#1309399811yescharacteristic
354C2×C4#1309399811yescharacteristic
355C2×C4#1309400711yescharacteristic
356C2×C4C2×#1062533611yescharacteristic
357C2×C4#1309404411yescharacteristic
358C2×C4#1309404911yescharacteristic
359C2×C4#1309405511yescharacteristic
360C8—3761no—
361C8—3761no—
362C8—1882no—
363C22—21no—
364C22—21no—
365C22—3761no—
366C22—3761no—
367C22—3761no—
368C22#1568900211yescharacteristic
369C22#1568926211yescharacteristic
370C22#1568926811yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—42no—
375C4—42no—
376C4—42no—
377C4—42no—
378C4—82no—
379C4—3761no—
380C4#1568914112yes—
381C4C4×#1062533611yescharacteristic
382C4#1568922111yescharacteristic
383C4#1568932311yescharacteristic
384C4#1568934511yescharacteristic
385C2—21no—
386C2—21no—
387C2—7521no—
388C2#2024374311yescharacteristic
389C2#2024383611yescharacteristic
390C2#2024388911yescharacteristic
subgroupG/H
centerC2×C4#13093998
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#2295C2
socleC22×C47#386
prime radical#15689673C22
cosocleC2×C42×C47C23
hypercenter#2295D47
hypocenterC47#9238
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2295

Complements

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

NH ≅ G/Ntype
4. #20241817C2semidirect
5. #20241291C2semidirect
6. #20241221C2semidirect
7. C47×#2295C2semidirect
10. #15689408C4semidirect
11. #15689323C4semidirect
108. C42×C47SD16semidirect
191. #2295D47semidirect
224. C47#9238semidirect
314. C42#10625336semidirect

Maximal subgroups

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

subgroupindex
#202534192
#202442162
#202418822
#202418172
#202412912
#202412212
C47×#22952
#923847