Finite Group Databasebeta

← #26371220

Subgroups — #26371220

Order 12032.

558 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253958C211yesmaximal, characteristic, complemented
2#20245596C211yesmaximal, characteristic, complemented
3#20245579C211yesmaximal, characteristic, complemented
4#20245552C211yesmaximal, characteristic, complemented
5#20245545C211yesmaximal, characteristic, complemented
6#20245450C211yesmaximal, characteristic, complemented
7#20245443C211yesmaximal, characteristic, complemented
8#20245328C211yesmaximal, characteristic, complemented
9#20245311C211yesmaximal, characteristic
10C4×#13093970C211yesmaximal, characteristic, complemented
11C4×#13093967C211yesmaximal, characteristic, complemented
12C4×#13093968C211yesmaximal, characteristic, complemented
13C4×#13093965C211yesmaximal, characteristic, complemented
14#20245187C211yesmaximal, characteristic, complemented
15C4×#135×C47C211yesmaximal, characteristic, complemented
16#15689657—21no—
17C2×#13093970C2211yescharacteristic
18C2×#13093968C2211yescharacteristic
19C2×#13093967C2211yescharacteristic
20C2×#13093965C2211yescharacteristic
21#15689525C2211yescharacteristic
22#15689507C2211yescharacteristic
23#15689478—21no—
24#15689364C2211yescharacteristic
25#15689359C2211yescharacteristic
26#15689352—21no—
27C4×Dic188C2211yescharacteristic
28C4×#10625325—21no—
29C4×D376C2211yescharacteristic
30#15688950C2211yescharacteristic
31#15688950C2211yescharacteristic
32#15688948C2211yescharacteristic
33#15688948C2211yescharacteristic
34C4⋊(C47⋊C16)C2211yescharacteristic
35C4⋊(C47⋊C16)C2211yescharacteristic
36#15688927C2211yescharacteristic
37#15688927C2211yescharacteristic
38#15688926C2211yescharacteristic
39#15688926C2211yescharacteristic
40#15688924C2211yescharacteristic
41#15688924C2211yescharacteristic
42#15688923C2211yescharacteristic
43#15688923C2211yescharacteristic
44C22⋊(C47⋊C16)C2211yescharacteristic
45C22⋊(C47⋊C16)C2211yescharacteristic
46C4×C47⋊C16C2211yescharacteristic
47C4×C47⋊C16C2211yescharacteristic
48C2×#135×C47C2211yescharacteristic
49C4×#41×C47—21no—
50C4×Q16×C47C2211yescharacteristic
51C4×Q16×C47C2211yescharacteristic
52C4×SD16×C47—21no—
53C4×SD16×C47—21no—
54C4×D8×C47C2211yescharacteristic
55C4×D8×C47C2211yescharacteristic
56C47×#427C2211yescharacteristic
57C47×#416—21no—
58C2×C4×C8×C47C2211yescharacteristic
59C2×Dic188C2311yescharacteristic
60C2×#10625325—21no—
61C2×D376C2311yescharacteristic
62#13094018—41no—
63#13094016—21no—
64#13094012—21no—
65#13094007—41no—
66#13094003—21no—
67#13093998—21no—
68C4×Dic94—21no—
69C4×D188—21no—
70C4×C22⋊D47—41no—
71#13093981—41no—
72#13093970—22no—
73#13093968—22no—
74#13093967—22no—
75#13093965—22no—
76C2×C47⋊C16C2311yescharacteristic
77C2×C47⋊C16C2311yescharacteristic
78C2×C47⋊C16C2311yescharacteristic
79C2×C47⋊C16C2311yescharacteristic
80#13093958C2311yescharacteristic
81#13093958C2311yescharacteristic
82#13093956—21no—
83#13093949—21no—
84#13093949—21no—
85#13093946—21no—
86#13093946—21no—
87C2×#41×C47—21no—
88#135×C47—22no—
89#135×C47—22no—
90C2×Q16×C47C2311yescharacteristic
91C2×SD16×C47—21no—
92C2×D8×C47C2311yescharacteristic
93C22×C8×C47D411yescharacteristic
94C22×C8×C47C2311yescharacteristic
95C4×Q8×C47—21no—
96C4×Q8×C47—21no—
97C4×D4×C47—21no—
98C4×D4×C47—21no—
99C4×D4×C47—41no—
100C4×D4×C47—41no—
101#117×C47—21no—
102#117×C47—41no—
103C2×C42×C47—41no—
104C2×C42×C47D411yescharacteristic
105#107×C47C2311yescharacteristic
106#107×C47C2311yescharacteristic
107#106×C47—21no—
108#103×C47—21no—
109#103×C47—21no—
110#102×C47—21no—
111#102×C47—21no—
112C4×C8×C47D411yescharacteristic
113C4×C8×C47D411yescharacteristic
114C4×C8×C47C2311yescharacteristic
115C4×C8×C47C2311yescharacteristic
116#41×C47—24no—
117#41×C47—42no—
118C2×Q8×C47—21no—
119C2×D4×C47—21no—
120C2×D4×C47—41no—
121C22×C4×C47—41no—
122C22×C4×C47—41no—
123C22×C4×C47—41no—
124C22×C4×C47D811yescharacteristic
125C22×C4×C47D811yescharacteristic
126C22×C4×C47C2×D411yescharacteristic
127C2×C22⋊D47—41no—
128C2×D188—21no—
129C2×C4×D47—41no—
130C2×Dic94—21no—
131Q16×C47—21no—
132Q16×C47#4112yes—
133SD16×C47—24no—
134D8×C47—21no—
135D8×C47#4112yes—
136C2×C8×C47—21no—
137C2×C8×C47—21no—
138C2×C8×C47—41no—
139C2×C8×C47C2×D411yescharacteristic
140C2×C8×C47C2×D411yescharacteristic
141C2×C8×C47C2×D411yescharacteristic
142C2×C8×C47C2411yescharacteristic
143C4⋊C4×C47—21no—
144C4⋊C4×C47—21no—
145C4⋊C4×C47—41no—
146C4⋊C4×C47—41no—
147C22⋊C4×C47—41no—
148C22⋊C4×C47—41no—
149C22⋊C4×C47—41no—
150C42×C47—41no—
151C42×C47—41no—
152C42×C47—41no—
153C42×C47D811yescharacteristic
154C42×C47D811yescharacteristic
155C42×C47C2×D411yescharacteristic
156C42×C47C2×D411yescharacteristic
157C22⋊Dic47—41no—
158(C2×D47)⋊C4—41no—
159(C2×D47)⋊C4—41no—
160(C2×D47)⋊C4—41no—
161(C2×D47)⋊C4—41no—
162C4⋊Dic47—21no—
163C4⋊Dic47—21no—
164Dic47⋊C4—41no—
165Dic47⋊C4—41no—
166Dic47⋊C4—41no—
167Dic47⋊C4—41no—
168C4×Dic47—41no—
169Dic188—21no—
170Dic188—21no—
171D376—21no—
172D376—21no—
173#10625325—42no—
174C47⋊C16—21no—
175C47⋊C16—21no—
176C47⋊C16—21no—
177C47⋊C16—21no—
178C23×C47—41no—
179C23×C47C2×D811yescharacteristic
180C22×D47—41no—
181Q8×C47—22no—
182Q8×C47—41no—
183D4×C47—22no—
184D4×C47—44no—
185D4×C47—41no—
186C2×C4×C47—21no—
187C2×C4×C47—21no—
188C2×C4×C47—22no—
189C2×C4×C47—41no—
190C2×C4×C47—44no—
191C2×C4×C47—41no—
192C2×C4×C47—41no—
193C2×C4×C47—41no—
194C2×C4×C47—82no—
195C2×C4×C47—82no—
196C2×C4×C47C2×D811yescharacteristic
197C2×C4×C47C2×D811yescharacteristic
198C2×C4×C47C2×D811yescharacteristic
199C2×C4×C47C2×D811yescharacteristic
200C2×C4×C47C2×D811yescharacteristic
201C2×C4×C47C22×D411yescharacteristic
202C22⋊D47—82no—
203C2×Dic47—41no—
204C2×Dic47—41no—
205C2×Dic47—41no—
206D188—41no—
207D188—41no—
208C4×D47—82no—
209Dic94—41no—
210Dic94—41no—
211C8×C47—21no—
212C8×C47—21no—
213C8×C47—21no—
214C8×C47C2×#4111yescharacteristic
215C8×C47C2×#4111yescharacteristic
216#33662—471nomaximal, Sylow
217C22×C47—21no—
218C22×C47—21no—
219C22×C47—21no—
220C22×C47—42no—
221C22×C47—81no—
222C22×C47—81no—
223C22×C47C22×D811yescharacteristic
224C2×D47—81no—
225C2×D47—81no—
226C2×D47—81no—
227C4×C47—21no—
228C4×C47—21no—
229C4×C47—21no—
230C4×C47—21no—
231C4×C47—42no—
232C4×C47—81no—
233C4×C47—81no—
234C4×C47#50812yes—
235C4×C47#52511yescharacteristic
236C4×C47#57511yescharacteristic
237Dic47—81no—
238Dic47—81no—
239Dic47—81no—
240#3168—471no—
241C4×#135D4711yescharacteristic, complemented
242#2237—471no—
243#2234—471no—
244#2229—471no—
245#2228—471no—
246#2211—471no—
247#2210—471no—
248#2189—471no—
249#2186—471no—
250C4×Q32—471no—
251C4×SD32—471no—
252C4×SD32—471no—
253C4×D16—471no—
254#2162—471no—
255C2×C47—41no—
256C2×C47—82no—
257C2×C47#310011yescharacteristic
258C2×C47C2×#50811yescharacteristic
259C2×C47#341411yescharacteristic
260D47—161no—
261C2×#135C2×D4711yescharacteristic
262#529—941no—
263C4×#41—21no—
264C2×Q32—471no—
265C2×SD32—471no—
266C2×SD32—471no—
267C2×D16—471no—
268#499—471no—
269#495—471no—
270#488—941no—
271#467—471no—
272#466—471no—
273#465—941no—
274C4×Q16—471no—
275C4×Q16C2×D4711yescharacteristic
276C4×Q16C2×D4711yescharacteristic
277C4×SD16—21no—
278C4×SD16—21no—
279C4×SD16—941no—
280C4×D8—471no—
281C4×D8C2×D4711yescharacteristic
282C4×D8C2×D4711yescharacteristic
283#427C2×D4711yescharacteristic
284#416—21no—
285C2×C4×C8C2×D4711yescharacteristic
286#367—471no—
287#367—471no—
288#366—471no—
289#366—471no—
290C4⋊C16—471no—
291C4⋊C16—471no—
292#358—471no—
293#358—471no—
294#358—471no—
295#358—471no—
296#357—471no—
297#357—471no—
298#357—471no—
299#357—471no—
300C22⋊C16—471no—
301C22⋊C16—471no—
302C4×C16—471no—
303C4×C16—471no—
304C47#3366211yescharacteristic, complemented, Sylow
305C2×#41—21no—
306#135—22no—
307#135—22no—
308C2×Q16—471no—
309C2×Q16C22×D4711yescharacteristic
310C2×SD16—21no—
311C2×SD16—941no—
312C2×D8—471no—
313C2×D8C22×D4711yescharacteristic
314C22×C8C22⋊D4711yescharacteristic
315C22×C8C22×D4711yescharacteristic
316#126—1881no—
317#125—941no—
318#124—941no—
319#123—1881no—
320C22⋊Q8—941no—
321#121—941no—
322C4×Q8—21no—
323C4×Q8—21no—
324C4×Q8—941no—
325C4×D4—21no—
326C4×D4—21no—
327C4×D4—41no—
328C4×D4—41no—
329C4×D4—941no—
330C4×D4—1881no—
331#117—21no—
332#117—41no—
333#117—1881no—
334C2×C42—41no—
335C2×C42C22⋊D4711yescharacteristic
336Q32—942no—
337SD32—942no—
338SD32—942no—
339D16—942no—
340C2×C16—471no—
341C2×C16—471no—
342C2×C16—471no—
343C2×C16—471no—
344#107—471no—
345#107—471no—
346#107C22×D4711yescharacteristic
347#107C22×D4711yescharacteristic
348#106—21no—
349#106—941no—
350#103—21no—
351#103—21no—
352#103—941no—
353#103—941no—
354#102—21no—
355#102—21no—
356#102—941no—
357#102—941no—
358C4×C8C22⋊D4711yescharacteristic
359C4×C8C22⋊D4711yescharacteristic
360C4×C8C22×D4711yescharacteristic
361C4×C8C22×D4711yescharacteristic
362#41—24no—
363#41—42no—
364C2×Q8—21no—
365C2×Q8—941no—
366C2×D4—21no—
367C2×D4—41no—
368C2×D4—941no—
369C2×D4—1881no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—1881no—
374C22×C4#1062533411yescharacteristic
375C22×C4#1062533411yescharacteristic
376C22×C4C2×C22⋊D4711yescharacteristic
377Q16—21no—
378Q16—941no—
379Q16—941no—
380Q16#1062535012yes—
381SD16—24no—
382SD16—1882no—
383D8—21no—
384D8—941no—
385D8—941no—
386D8#1062535012yes—
387C2×C8—21no—
388C2×C8—21no—
389C2×C8—41no—
390C2×C8C2×C22⋊D4711yescharacteristic
391C2×C8C2×C22⋊D4711yescharacteristic
392C2×C8C2×C22⋊D4711yescharacteristic
393C2×C8C23×D4711yescharacteristic
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—41no—
397C4⋊C4—41no—
398C4⋊C4—941no—
399C4⋊C4—941no—
400C4⋊C4—1881no—
401C4⋊C4—1881no—
402C4⋊C4—1881no—
403C4⋊C4—1881no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C22⋊C4—41no—
407C22⋊C4—1881no—
408C22⋊C4—1881no—
409C22⋊C4—1881no—
410C22⋊C4—1881no—
411C22⋊C4—1881no—
412C42—41no—
413C42—41no—
414C42—41no—
415C42—1881no—
416C42#1062533411yescharacteristic
417C42#1062533411yescharacteristic
418C42C2×C22⋊D4711yescharacteristic
419C42C2×C22⋊D4711yescharacteristic
420C16—941no—
421C16—941no—
422C16—941no—
423C16—941no—
424C23—41no—
425C23—1881no—
426C23C2×#1062533411yescharacteristic
427Q8—22no—
428Q8—41no—
429Q8—1881no—
430Q8—1881no—
431D4—22no—
432D4—44no—
433D4—41no—
434D4—3762no—
435D4—1881no—
436D4—1881no—
437C2×C4—22no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—41no—
441C2×C4—44no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—82no—
446C2×C4—82no—
447C2×C4—3762no—
448C2×C4—1881no—
449C2×C4—1881no—
450C2×C4—1881no—
451C2×C4C2×#1062533411yescharacteristic
452C2×C4C2×#1062533411yescharacteristic
453C2×C4C2×#1062533411yescharacteristic
454C2×C4C2×#1062533411yescharacteristic
455C2×C4C2×#1062533411yescharacteristic
456C2×C4C22×C22⋊D4711yescharacteristic
457C8—21no—
458C8—21no—
459C8—21no—
460C8C2×#1062535011yescharacteristic
461C8C2×#1062535011yescharacteristic
462C22—21no—
463C22—21no—
464C22—21no—
465C22—42no—
466C22—81no—
467C22—81no—
468C22—3761no—
469C22—3761no—
470C22—3761no—
471C22C22×#1062533411yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—42no—
477C4—81no—
478C4—81no—
479C4—3761no—
480C4—3761no—
481C4—3761no—
482C4#1568955312yes—
483C4#1568963411yescharacteristic
484C4#1568992111yescharacteristic
485C2—41no—
486C2—82no—
487C2—7521no—
488C2#2025338811yescharacteristic
489C2C2×#1568955311yescharacteristic
490C2#2025652211yescharacteristic
subgroupG/H
centerC2×C4C2×#10625334
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC4×#135×C47C2
socleC22×C47C22×D8
prime radical#20245311C2
hypercenterC4×#135D47
hypocenterC47#33662
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×#135

Complements

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

NH ≅ G/Ntype
1. #20253958C2semidirect
2. #20245596C2semidirect
3. #20245579C2semidirect
4. #20245552C2semidirect
5. #20245545C2semidirect
6. #20245450C2semidirect
7. #20245443C2semidirect
8. #20245328C2semidirect
10. C4×#13093970C2semidirect
11. C4×#13093967C2semidirect
12. C4×#13093968C2semidirect
13. C4×#13093965C2semidirect
14. #20245187C2semidirect
15. C4×#135×C47C2semidirect
241. C4×#135D47semidirect
304. C47#33662semidirect

Maximal subgroups

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

subgroupindex
#202539582
#202455962
#202455792
#202455522
#202455452
#202454502
#202454432
#202453282
#202453112
C4×#130939702
C4×#130939672
C4×#130939682
C4×#130939652
#202451872
C4×#135×C472
#3366247