Finite Group Databasebeta

← C4×#15689395 #26223163

Subgroups — C4×#15689395 #26223163

Order 12032.

882 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689395C211yesmaximal, characteristic
2C4×#13094055C212yesmaximal
3C4×#13094030C211yesmaximal, characteristic
4#20244304C211yesmaximal, characteristic, complemented
5#20244171C211yesmaximal, characteristic, complemented
6#20244040C212yesmaximal, complemented
7#20243906C212yesmaximal
8#20243453C211yesmaximal, characteristic
9C4×#13093960C211yesmaximal, characteristic, complemented
10C4×#13093943C212yesmaximal, complemented
11C2×C4×Q16×C47C211yesmaximal, characteristic, complemented
12C2×#13094055C2212yes—
13C2×#13094030C2211yescharacteristic
14C2×#13094030C2211yescharacteristic
15C4×#10625350C2211yescharacteristic
16#15689395C418yesdirect product factor
17#15689228—22no—
18#15689221—22no—
19C4×#10625337—22no—
20C4×#10625336—22no—
21C2×#13093960C2211yescharacteristic
22C2×#13093960C2211yescharacteristic
23#15689163C2212yes—
24#15689132C2212yes—
25#15689122C2212yes—
26C2×#13093943C2212yes—
27C2×#13093943C2212yes—
28#15689078C2211yescharacteristic
29#15689078C2211yescharacteristic
30#15689077—21no—
31#15689077—21no—
32C4×#10625329C2212yes—
33C4×#10625329C2211yescharacteristic
34C4×#10625324—21no—
35C4×C8×D47—21no—
36#15688892C2212yes—
37#15688892C2212yes—
38#15688888C2212yes—
39C22×Q16×C47C2211yescharacteristic
40C2×C4×Q8×C47C2212yes—
41C4×Q16×C47—21no—
42C4×Q16×C47—21no—
43C4×Q16×C47—21no—
44C4×Q16×C47—21no—
45C2×#107×C47C2211yescharacteristic
46C2×#103×C47C2212yes—
47C2×C4×C8×C47C2211yescharacteristic
48C2×#10625350C2311yescharacteristic
49#13094055—24no—
50#13094055C2×C418yes—
51C2×#10625337—22no—
52C2×#10625336—22no—
53#13094030—22no—
54#13094030—22no—
55#13094030—22no—
56#13094030C2×C414yes—
57C2×#10625329C2312yes—
58C2×#10625329C2311yescharacteristic
59C2×#10625329C2312yes—
60C2×#10625329C2311yescharacteristic
61C2×#10625324—21no—
62C2×#10625324—21no—
63C2×C8×D47—21no—
64C2×C8×D47—21no—
65C4×Dic94D411yescharacteristic
66C4×Dic94D411yescharacteristic
67C4×D188D411yescharacteristic
68C4×D188D411yescharacteristic
69C4×C22⋊D47—21no—
70C4×C22⋊D47—21no—
71#13093983C2311yescharacteristic
72#13093981—21no—
73C42×D47—21no—
74#13093960—22no—
75#13093960C2×C414yescomplemented
76#13093957—22no—
77#13093955—22no—
78#13093948—22no—
79#13093948—22no—
80#13093947—22no—
81#13093944—22no—
82#13093943—24no—
83#13093943C2×C418yescomplemented
84#13093935—22no—
85#13093935—21no—
86#13093934—21no—
87#13093934—21no—
88C4×C47⋊C8—22no—
89C4×C47⋊C8—21no—
90C8×Dic47—21no—
91C8×Dic47—21no—
92C22×Q8×C47C2312yes—
93C2×Q16×C47—21no—
94C2×Q16×C47—21no—
95C2×Q16×C47—22no—
96C2×Q16×C47C2×C414yescomplemented
97C22×C8×C47C2311yescharacteristic
98C22×C8×C47C2311yescharacteristic
99C4×Q8×C47—22no—
100C4×Q8×C47—22no—
101C4×Q8×C47—22no—
102C4×Q8×C47—22no—
103C2×C4⋊C4×C47—22no—
104C2×C4⋊C4×C47C2312yes—
105C2×C42×C47—22no—
106C2×C42×C47C2311yescharacteristic
107#107×C47—21no—
108#107×C47—21no—
109#103×C47—22no—
110#103×C47—22no—
111C4×C8×C47D411yescharacteristic
112C4×C8×C47D411yescharacteristic
113C4×C8×C47D411yescharacteristic
114C4×C8×C47D411yescharacteristic
115C2×Q8×C47—22no—
116C2×Q8×C47—22no—
117C2×Q8×C47—22no—
118C2×Q8×C47—22no—
119C2×Q8×C47—22no—
120C2×Q8×C47C22×C414yes—
121C22×C4×C47—22no—
122C22×C4×C47—22no—
123C22×C4×C47#4111yescharacteristic
124C22×C4×C47#4111yescharacteristic
125C22×C4×C47C2411yescharacteristic
126C2×C22⋊D47—21no—
127#10625350—21no—
128#10625350—21no—
129#10625350C22×C412yes—
130#10625350#4112yes—
131C2×D188C2×D411yescharacteristic
132C2×C4×D47—21no—
133C2×C4×D47—21no—
134C2×C4×D47—21no—
135C2×Dic94C2×D411yescharacteristic
136Q16×C47—24no—
137Q16×C47—24no—
138C2×C8×C47—21no—
139C2×C8×C47—21no—
140C2×C8×C47C22×C412yes—
141C2×C8×C47C2×D411yescharacteristic
142C2×C8×C47C2×D411yescharacteristic
143C2×C8×C47C2×D411yescharacteristic
144C2×C8×C47C2×D411yescharacteristic
145C2×C8×C47#4112yes—
146C4⋊C4×C47—22no—
147C4⋊C4×C47—22no—
148C4⋊C4×C47—42no—
149C4⋊C4×C47—42no—
150C42×C47—42no—
151C42×C47—42no—
152C42×C47C2×D411yescharacteristic
153C42×C47C2×D411yescharacteristic
154C42×C47C2×D411yescharacteristic
155C42×C47C2×D411yescharacteristic
156C22⋊Dic47—21no—
157#10625337—28no—
158#10625336—28no—
159(C2×D47)⋊C4—21no—
160(C2×D47)⋊C4—21no—
161C4⋊Dic47C2×D411yescharacteristic
162C4⋊Dic47C2×D411yescharacteristic
163Dic47⋊C4—21no—
164Dic47⋊C4—21no—
165C4×Dic47—21no—
166C4×Dic47—21no—
167C4×Dic47—21no—
168#10625329—21no—
169#10625329—21no—
170#10625329—22no—
171#10625329—22no—
172#10625329—22no—
173#10625329C22×C412yes—
174#10625329C22×C414yes—
175#10625329#4112yes—
176C2×C47⋊C8—21no—
177C2×C47⋊C8—21no—
178C2×C47⋊C8—22no—
179C2×C47⋊C8—22no—
180#10625324—24no—
181#10625324—24no—
182C8×D47—24no—
183C8×D47—24no—
184C23×C47C2×#4111yescharacteristic
185C22×D47—21no—
186Q8×C47—24no—
187Q8×C47—24no—
188Q8×C47—42no—
189Q8×C47—42no—
190C2×C4×C47—22no—
191C2×C4×C47—24no—
192C2×C4×C47—41no—
193C2×C4×C47—42no—
194C2×C4×C47—42no—
195C2×C4×C47—42no—
196C2×C4×C47—82no—
197C2×C4×C47#12111yescharacteristic
198C2×C4×C47#12111yescharacteristic
199C2×C4×C47#12111yescharacteristic
200C2×C4×C47#12111yescharacteristic
201C2×C4×C47C23×C411yescharacteristic
202C2×C4×C47C22×D411yescharacteristic
203C2×C4×C47C22×D411yescharacteristic
204C2×C4×C47C2×#4111yescharacteristic
205C2×C4×C47C2×#4111yescharacteristic
206C2×C4×C47C2×#4111yescharacteristic
207C22⋊D47—22no—
208C22⋊D47—22no—
209C2×Dic47—21no—
210C2×Dic47—21no—
211C2×Dic47—21no—
212D188—21no—
213D188C4×D412yes—
214C4×D47—22no—
215C4×D47—22no—
216C4×D47—42no—
217C4×D47—42no—
218Dic94—21no—
219Dic94C4×D412yes—
220C8×C47—21no—
221C8×C47—21no—
222C8×C47C4×D412yes—
223C8×C47C4×D412yes—
224C47⋊C8—22no—
225C47⋊C8—24no—
226C47⋊C8—22no—
227C47⋊C8—42no—
228C4×#473—471nomaximal, Sylow
229C22×C47—21no—
230C22×C47—21no—
231C22×C47C4×#4111yescharacteristic
232C22×C47C2×#12111yescharacteristic
233C22×C47#52911yescharacteristic
234C2×D47—22no—
235C2×D47—41no—
236C2×D47—41no—
237C4×C47—21no—
238C4×C47—21no—
239C4×C47—21no—
240C4×C47—44no—
241C4×C47—82no—
242C4×C47#47312yescomplemented
243C4×C47C2×C4×D411yescharacteristic
244C4×C47C2×C4×D411yescharacteristic
245C4×C47#52511yescharacteristic
246C4×C47#53211yescharacteristic
247Dic47—22no—
248Dic47—41no—
249Dic47—41no—
250C2×#473—471no—
251C4×#137—472no—
252C2×C4×Q16D4711yescharacteristic, complemented
253C4×#131—471no—
254#1979—471no—
255#1952—471no—
256#1930—472no—
257#1908—472no—
258#1816—471no—
259C4×#108—471no—
260C4×#101—472no—
261C2×C47—21no—
262C2×C47—21no—
263C2×C47C4×#12111yescharacteristic
264C2×C47C2×#47311yescharacteristic
265C2×C47#306711yescharacteristic
266D47—42no—
267C2×#137—472no—
268C22×Q16C2×D4711yescharacteristic
269C2×#131—471no—
270C2×#131—471no—
271C4×#41—471no—
272C2×C4×Q8C2×D4712yes—
273#473—478no—
274#441—942no—
275#440—942no—
276C4×Q16—21no—
277C4×Q16—21no—
278C4×Q16—21no—
279C4×Q16—21no—
280C4×Q16—942no—
281C4×SD16—942no—
282C2×#108—471no—
283C2×#108—471no—
284#428—472no—
285C2×#107C2×D4711yescharacteristic
286#419—472no—
287#417—472no—
288C2×#103C2×D4712yes—
289C2×#101—472no—
290C2×#101—472no—
291#405—471no—
292#405—471no—
293#405—941no—
294#405—941no—
295C4×M16—471no—
296C4×M16—472no—
297C4×M16—941no—
298C2×C4×C8—941no—
299C2×C4×C8C2×D4711yescharacteristic
300#343—472no—
301#343—472no—
302#341—472no—
303C47C4×#47311yescharacteristic, complemented, Sylow
304C2×#41—471no—
305C22×Q8C22×D4712yes—
306#137—478no—
307#137—944no—
308C2×Q16—22no—
309C2×Q16—21no—
310C2×Q16—21no—
311C2×Q16—942no—
312C2×Q16C4×D4714yescomplemented
313C2×SD16—942no—
314#131—474no—
315#131—942no—
316#131—942no—
317#131—942no—
318C2×M16—471no—
319C2×M16—471no—
320C2×M16—472no—
321C2×M16—472no—
322C2×M16—941no—
323C2×M16—941no—
324C22×C8—941no—
325C22×C8—941no—
326C22×C8C22×D4711yescharacteristic
327C22×C8C22×D4711yescharacteristic
328C4×Q8—22no—
329C4×Q8—22no—
330C4×Q8—22no—
331C4×Q8—22no—
332C4×Q8—471no—
333C4×Q8—471no—
334C4×D4—471no—
335C4×D4—471no—
336C4×D4—941no—
337C4×D4—941no—
338#117—471no—
339#117—941no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4C22×D4712yes—
342C2×C42—22no—
343C2×C42—941no—
344C2×C42C22×D4711yescharacteristic
345#108—474no—
346#108—942no—
347#107—21no—
348#107—21no—
349#107—942no—
350#106—942no—
351#103—22no—
352#103—22no—
353#103—942no—
354#103—942no—
355#103—942no—
356#102—942no—
357#101—478no—
358#101—944no—
359#97—941no—
360#97—941no—
361#97—942no—
362#97—941no—
363C4×C8—941no—
364C4×C8—941no—
365C4×C8—942no—
366C4×C8—941no—
367C4×C8C22⋊D4711yescharacteristic
368C4×C8C22⋊D4711yescharacteristic
369C4×C8C22⋊D4711yescharacteristic
370C4×C8C22⋊D4711yescharacteristic
371#41—472no—
372#41—472no—
373#41—941no—
374#41—941no—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—471no—
381C2×Q8C2×C4×D4714yes—
382C2×D4—471no—
383C2×D4—941no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—941no—
387C22×C4—941no—
388C22×C4—941no—
389C22×C4#1062535211yescharacteristic
390C22×C4#1062535211yescharacteristic
391C22×C4C23×D4711yescharacteristic
392Q16—24no—
393Q16—24no—
394Q16—948no—
395SD16—948no—
396M16—472no—
397M16—474no—
398M16—472no—
399M16—944no—
400M16—941no—
401M16—942no—
402M16—941no—
403M16—944no—
404M16—942no—
405M16—942no—
406C2×C8—21no—
407C2×C8—21no—
408C2×C8—944no—
409C2×C8—942no—
410C2×C8—941no—
411C2×C8—941no—
412C2×C8—944no—
413C2×C8—942no—
414C2×C8C2×C4×D4712yes—
415C2×C8#1062535012yes—
416C2×C8C2×C22⋊D4711yescharacteristic
417C2×C8C2×C22⋊D4711yescharacteristic
418C2×C8C2×C22⋊D4711yescharacteristic
419C2×C8C2×C22⋊D4711yescharacteristic
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—42no—
423C4⋊C4—42no—
424C4⋊C4—471no—
425C4⋊C4—471no—
426C4⋊C4—941no—
427C4⋊C4—941no—
428C22⋊C4—941no—
429C22⋊C4—941no—
430C22⋊C4—941no—
431C42—42no—
432C42—42no—
433C42—941no—
434C42—941no—
435C42—941no—
436C42D4×D4711yescharacteristic
437C42D4×D4711yescharacteristic
438C42C2×C22⋊D4711yescharacteristic
439C42C2×C22⋊D4711yescharacteristic
440C23—941no—
441C23C2×#1062535211yescharacteristic
442Q8—24no—
443Q8—24no—
444Q8—42no—
445Q8—42no—
446Q8—472no—
447Q8—941no—
448D4—472no—
449D4—942no—
450D4—942no—
451D4—941no—
452C2×C4—22no—
453C2×C4—24no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—82no—
459C2×C4—941no—
460C2×C4—942no—
461C2×C4—942no—
462C2×C4—941no—
463C2×C4—941no—
464C2×C4—1882no—
465C2×C4—1882no—
466C2×C4#1309399511yescharacteristic
467C2×C4#1309399511yescharacteristic
468C2×C4#1309399511yescharacteristic
469C2×C4#1309399511yescharacteristic
470C2×C4C22×C4×D4711yescharacteristic
471C2×C4C2×D4×D4711yescharacteristic
472C2×C4C22×C22⋊D4711yescharacteristic
473C2×C4#41×D4711yescharacteristic
474C2×C4#41×D4711yescharacteristic
475C2×C4C2×#1062535011yescharacteristic
476C8—21no—
477C8—21no—
478C8—944no—
479C8—942no—
480C8—942no—
481C8—1882no—
482C8C4×C22⋊D4712yes—
483C8C4×C22⋊D4712yes—
484C22—21no—
485C22—21no—
486C22—942no—
487C22—1881no—
488C22—1881no—
489C22C4×#1062535211yescharacteristic
490C22C2×#1309399511yescharacteristic
491C22#1568965511yescharacteristic
492C4—21no—
493C4—21no—
494C4—21no—
495C4—44no—
496C4—82no—
497C4—942no—
498C4—1881no—
499C4—1881no—
500C4#1568939512yesdirect product factor
501C4C4×D4×D4711yescharacteristic
502C4C2×C4×C22⋊D4711yescharacteristic
503C4#1568963011yescharacteristic
504C4#1568967011yescharacteristic
505C2—21no—
506C2—21no—
507C2—1882no—
508C2C4×#1309399511yescharacteristic
509C2C2×#1568939511yescharacteristic
510C2#2025310411yescharacteristic
subgroupG/H
centerC2×C4#13093995
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C4×Q16×C47C2
socleC22×C47C2×#121
prime radicalC2×#10625350C23
cosocleC22×C4×C47C24
hypercenterC2×C4×Q16D47
hypocenterC47C4×#473
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
4. #20244304C2semidirect
5. #20244171C2semidirect
6. #20244040C2semidirect
9. C4×#13093960C2semidirect
10. C4×#13093943C2semidirect
11. C2×C4×Q16×C47C2semidirect
16. #15689395C4direct (N × H)
75. #13093960C2×C4semidirect
83. #13093943C2×C4semidirect
96. C2×Q16×C47C2×C4semidirect
242. C4×C47#473semidirect
252. C2×C4×Q16D47semidirect
303. C47C4×#473semidirect
312. C2×Q16C4×D47semidirect
500. C4#15689395direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156893952
C4×#130940552
C4×#130940302
#202443042
#202441712
#202440402
#202439062
#202434532
C4×#130939602
C4×#130939432
C2×C4×Q16×C472
C4×#47347